Handbook on ice slurries : fundamentals and engineering

Handbook on Ice Slurries – Fundamentals and Engineering – Editors: Michael Kauffeld, Masahiro Kawaji, Peter W. Egolf ...

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Handbook on

Ice Slurries

– Fundamentals and Engineering – Editors: Michael Kauffeld, Masahiro Kawaji, Peter W. Egolf

Extensively reviewed by Åke Melinder, Tom W. Davies

Published by INTERNATIONAL INSTITUTE OF REFRIGERATION 177 boulevard Malesherbes – 75017 Paris, France Tel.: +33 1 4227 3235 – Fax: +33 1 4763 1798 E-mail: [email protected] – Web site : www.iifiir.org

ISBN n° 2-913149-42-1 Copyright and Disclaimer “The information provided in this document is based on the current state of art and is designed to assist engineers, scientists, companies and other organizations. It is a preliminary source of information that will need to be complemented prior to any detailed application or project. Whilst all possible care has been taken in the production of this document, the IIR, its employees, officers and experts cannot accept any liability for the accuracy or correctness of the information provided nor for the consequences of its use or misuse. For full or partial reproduction of anything published in this document, proper acknowledgement should be made to the original source and its author(s). No parts of the book may be commercially reproduced, recorded and stored in a retrieval system or transmitted in any form or by any means (mechanical, electrostatic, magnetic, optic photographic, multimedia, Internet-based or otherwise) without permission in writing from the IIR.

© Copyright 2005 International Institute of Refrigeration

IIF-IIR – Handbook on Ice Slurries – 2005

— Table of contents — Foreword ............................................................................................................................... 9 Preface .................................................................................................................................. 10 1. Summary of Ice Slurry Technology .................................................................... 11 1.1 Introduction ............................................................................................................. 1.2 Existing technologies .............................................................................................. 1.2.1 Heterogeneous nucleation ............................................................................. 1.2.2 Homogeneous or spontaneous nucleation ..................................................... 1.3 Modern ice slurry applications ................................................................................ 1.4 International Institute of Refrigeration (IIR) Working Party on Ice Slurries ...... 1.4.1 Scientific challenges...................................................................................... 1.4.2 Technical challenges ..................................................................................... 1.4.3 Objectives of the working party .................................................................... 1.5 Research institutes.................................................................................................... 1.6 Conclusions and outlook on the use of ice slurry ................................................... 1.7 Other Phase Change Slurries (PCSs)...................................................................... 1.7.1 Dry ice/carbon dioxide slurry........................................................................ 1.7.2 Clathrate slurry.............................................................................................. 1.7.3 Micro-emulsion slurry................................................................................... 1.7.4 Shape-stabilized PCM slurry......................................................................... 1.7.5 Microencapsulated PCM slurry..................................................................... 1.7.6 Polyethylene pellets....................................................................................... Literature cited in Chapter 1...........................................................................................

11 11 12 12 12 13 13 14 14 15 15 15 16 16 17 17 17 18 18

2. Ice Creation, Thermophysical Properties of Ice Slurries and Other Characteristics ...................................................................................... 19 2.1 The formation of ice.................................................................................................. 19 2.1.1 Introduction ................................................................................................... 19 2.1.2 Metastable state – supercooled water............................................................ 19 2.1.3 Nucleation ..................................................................................................... 19 2.1.4 Effect of additives ......................................................................................... 24 2.2 Crystal growth ........................................................................................................... 24 2.2.1 Initial crystal growth ..................................................................................... 24 2.2.2 Further processes affecting the crystal size................................................... 26 2.3 Types of ice crystals and ice particles...................................................................... 29 2.3.1 Shape parameters........................................................................................... 30 2.3.2. Ice particle model .......................................................................................... 32 2.3.3 Measurements and statistics .......................................................................... 33 2.4 Properties of aqueous solutions and ice ................................................................... 33 2.4.1 Introduction ................................................................................................... 33 2.4.2 Thermophysical properties of aqueous solutions .......................................... 34 2.4.3 Freezing-point temperature of aqueous solutions ......................................... 36 2.4.4 Thermophysical properties of ice.................................................................. 36 2.5 Physical properties of ice slurry .............................................................................. 37 2.5.1 Freezing point temperature and ice concentration ........................................ 37

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2.5.2 Viscosity ....................................................................................................... 2.5.3 Thermal conductivity ................................................................................... 2.5.4 Enthalpy and enthalpy phase diagrams of aqueous solutions ....................... 2.6 Safety, ecology and corrosion aspects of aqueous solutions ................................. 2.6.1 General characteristics of additives used as aqueous solutions .................... 2.6.2 General explanation of symbols ................................................................... 2.6.3 Comments on each type of aqueous solution ............................................... 2.6.4 Corrosion behaviour and material compatibility ......................................... Literature cited in Chapter 2 ......................................................................................... 3.

39 40 41 48 48 48 49 50 50

Fluid Dynamics ......................................................................................................... 55 3.1 Rheology .................................................................................................................. 55 3.1.1 State of the art of ice slurry rheology ........................................................... 59 3.2 Flows in tubes and pattern formation .................................................................... 60 3.2.1 State of the art of research on flow patterns.................................................. 61 3.2.2 Velocity profiles ........................................................................................... 64 3.2.3 Concentration profiles ................................................................................... 66 3.2.4 Critical deposition velocity ............................................................................ 67 3.2.5 Theoretical determination of flow patterns .................................................. 70 3.3 Pressure drop .......................................................................................................... 70 3.3.1 Isothermal, stationary, homogeneous ice-slurry flow .................................. 71 3.3.2 State of the art of ice-slurry pressure drops................................................... 73 3.3.3 Friction factor for laminar flow .................................................................... 74 3.3.4 Semi-empirical correlations for the turbulent ice-slurry friction factor........ 74 3.3.5 General empirical determination of the friction factor for ice-slurries ......... 75 3.3.6 Pressure drops of ice-slurry flows in heat exchangers ................................. 77 3.4 Time-dependent behaviour ..................................................................................... 78 Literature cited in Chapter 3........................................................................................... 79

4. Thermodynamics and Heat Transfer ................................................................. 83 4.1 Overview .................................................................................................................. 4.2 Basic definitions ...................................................................................................... 4.2.1 Effective enthalpy and effective specific heat .............................................. 4.2.2 Effective thermal conductivity ..................................................................... 4.2.3 Dimensionless numbers ................................................................................ 4.2.4 Reference temperatures and heat transfer coefficients ................................. 4.3 Measurement techniques ........................................................................................ 4.3.1 Introductory remarks .................................................................................... 4.3.2 Local ice fraction .......................................................................................... 4.3.3 Local ice slurry temperature ......................................................................... 4.3.4 Local ice slurry velocity ............................................................................... 4.4 Flow phenomena ..................................................................................................... 4.4.1 Velocity profile, mean velocity .................................................................... 4.4.2 Temperature profile, mean temperature in vertical channels ....................... 4.4.3 Local ice fraction profiles ............................................................................ 4.5 Heat transfer phenomena ....................................................................................... 4.5.1 A brief introduction ......................................................................................

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83 83 83 84 85 86 87 87 87 88 88 89 89 92 93 94 94


4.5.2 Pipes ............................................................................................................. 95 4.5.3 Heat transfer in rectangular channels ......................................................... 105 4.5.4 Heat transfer in rectangular channels with a bend ..................................... 113 4.6 Heat exchangers with stagnant flow .................................................................... 115 4.7 Industrial heat exchangers .................................................................................... 117 4.7.1 Brief introduction ....................................................................................... 117 4.7.2 Heat transfer correlations in compact heat exchangers .............................. 117 4.8 Conclusions and outlook ...................................................................................... 120 Literature cited in Chapter 4 ........................................................................................ 121

5. Ice Slurry Production ........................................................................................... 125 5.1 Fundamentals of ice slurry generation ................................................................. 125 5.1.1 Ice crystallization ........................................................................................... 125 5.1.2 Heat and mass transfer aspects ..................................................................... 126 5.1.3 Categories of ice slurry generator ................................................................. 126 5.2 Current and possible methods of ice slurry production ....................................... 128 5.2.1 Scraped surface ice slurry generator ............................................................. 128 5.2.2 Vacuum ice ................................................................................................... 137 5.2.3 Direct contact generators with immiscible refrigerant ................................. 139 5.2.4 Direct contact generators with immiscible liquid secondary refrigerant ...... 142 5.2.5 Supercooled brine method ............................................................................ 143 5.2.6 Hydro-scraped ice slurry generator .............................................................. 146 5.2.7 Special coating of generator surface to avoid ice sticking to surface ........... 147 5.2.8 Fluidized bed crystallizer .............................................................................. 152 5.2.9 High pressure ice slurry generator ................................................................ 154 5.2.10 Recuperative ice making ............................................................................ 158 Literature cited in Chapter 5 ........................................................................................ 161

6. Transport .................................................................................................................. 167 6.1 Advantage of transport characteristics of ice slurries over conventional fluids.......................................................................................... 167 6.2 Design of transport systems ................................................................................... 167 6.2.1 General considerations................................................................................... 167 6.2.2 Single-tube versus dual-tube systems ........................................................... 168 6.2.3 Considerations of defrosting ......................................................................... 168 6.2.4 Pipe Materials ............................................................................................... 170 6.2.5 Calculation of pressure drops ........................................................................ 170 6.2.6 Avoidance and influence of phase separation ............................................... 170 6.3 Transport capacity ................................................................................................. 174 6.3.1 Calculation of transport capacity .................................................................. 174 6.3.2 Pipe selection chart ....................................................................................... 175 6.4 Pumping ................................................................................................................. 176 6.4.1 Centrifugal pumps and their application ranges ........................................... 176 6.4.2 Other pumps for ice slurry ............................................................................ 181 6.4.3 Calculation guidelines using manufacturer’s data ........................................ 185 6.4.4 Long term performance test .......................................................................... 189 6.4.5 Internal build up of ice clusters in centrifugal pumps ................................... 190 6.4.6 Corrosion and Erosion .................................................................................. 191

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6.4.7 Problems at standstill .................................................................................... 191 6.5 Fittings and related pressure loss coefficients ..................................................... 192 6.5.1 Test rig set up ................................................................................................ 192 6.5.2 Design of pressure taps ................................................................................. 193 6.5.3 Data treatment ............................................................................................... 193 6.5.4 Experiments and results ................................................................................ 195 6.5.5 Comparison of measured values of ice slurries and single phase fluids ....... 198 6.6 Valves ..................................................................................................................... 199 6.7 Insulation ............................................................................................................... 199 6.8 Critical conditions ................................................................................................. 199 6.9 Quick guide to ice slurry installation and operation in order to avoid blockage .................................................................................................... 200 6.9.1 Homogeneously mixed storage ...................................................................... 200 6.9.2 Transport system ........................................................................................... 200 Literature cited in Chapter 6 ........................................................................................ 201

7. Storing/Melting and Mixing ............................................................................... 203 7.1 Storing vessels ....................................................................................................... 7.1.1 Storing methods/devices and processes ........................................................ 7.1.2 Melting methods/devices and processes ....................................................... 7.2 Mixing tanks .......................................................................................................... 7.2.1 Mixing methods/devices and processes ........................................................ 7.2.2 Stratification in mixing tanks ....................................................................... 7.2.3 Power consumption in Newtonian range ...................................................... 7.2.4 Power consumption for highly-viscous range .............................................. 7.3 Numerical modelling for storage tank design ...................................................... 7.3.1 Physical modelling of accumulation/piling and melting ............................... 7.3.2 Mathematical modelling ............................................................................... 7.3.3 Confirmation of modelling ............................................................................ 7.4 Numerical modelling for mixing tank design ...................................................... 7.4.1 Physical modelling of flow and stratification ............................................... 7.4.2 Mathematical modelling ............................................................................... 7.4.3 Confirmation of modelling ............................................................................ Literature cited in Chapter 7 ........................................................................................

203 203 206 207 207 208 209 209 209 209 211 215 219 219 220 220 221

8. Melting Ice Slurry in Heat Exchangers ........................................................... 223 8.1 Plate heat exchangers ........................................................................................... 223 8.1.1 Test rig set up ............................................................................................. 225 8.1.2 Measuring equipment ................................................................................. 227 8.1.3 Heat transfer results .................................................................................... 227 8.1.4 Correlation for heat transfer ....................................................................... 229 8.1.5 Pressure drop results .................................................................................. 231 8.1.6 Correlation for pressure drop ..................................................................... 232 8.1.7 Observations ................................................................................................ 233 8.1.8 Minimum flow rate .................................................................................... 234 8.2 Air coolers .............................................................................................................. 235 8.2.1 Test rig set up ............................................................................................. 236 8.2.2 Heat transfer results ................................................................................... 237

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8.2.3 Correlation for heat transfer ....................................................................... 8.2.4 Pressure drop results .................................................................................. 8.2.5 Correlation for pressure drop ..................................................................... 8.2.6 Comparison between single-phase media and ice slurry ........................... 8.2.7 Minimum flow rate .................................................................................... 8.3 Observations .......................................................................................................... 8.4 Conclusions ........................................................................................................... Literature cited in Chapter 8 ........................................................................................

239 239 240 242 243 244 248 249

9. Direct Contact Chilling and Freezing of Foods in Ice Slurries .............. 251 9.1 State of the art and conventional modes of food refrigeration ........................... 251 9.2 Unfreezable liquids and pumpable ice slurries as refrigerating media and fluidizing agents ............................................................................................. 253 9.3 Cooling of fish with ice slurries ............................................................................. 259 9.4 Ice-slurry-based cooling of fruits and vegetables ................................................ 263 Literature cited in Chapter 9 ........................................................................................ 269

10. The Control of Ice Slurry Systems .................................................................... 273 10.1 Introduction ........................................................................................................ 10.2 General organization of an ice slurry system .................................................... 10.3 What is to be controlled ...................................................................................... 10.3.1 Control of consumer units ..................................................................... 10.3.2 Control of the storage tank .................................................................... 10.3.3 Control of the ice slurry generator ......................................................... 10.3.4 Control of the primary refrigerating unit ............................................... 10.4 Influence of the temperature and solute concentration on the control parameters ................................................................................... 10.5 Consequences of the uncertainty about the ice concentration on the control of the system ................................................................................ 10.6 Conclusions ......................................................................................................... Literature cited in Chapter 10 ......................................................................................

273 273 274 274 276 276 280 280 283 285 285

11. Optimization of Ice Slurry systems ................................................................. 287 11.1 Criteria ................................................................................................................. 287 11.2 Methods ................................................................................................................ 288 Literature cited in Chapter 11 ...................................................................................... 289

12. Present and Future Applications ...................................................................... 291 12.1 Introduction .......................................................................................................... 291 12.2 Comfort cooling .................................................................................................... 291 12.2.1 Comfort cooling of buildings ..................................................................... 291 12.2.2 Applications to office building .................................................................. 292 12.2.3 Applications to institutional buildings ........................................................ 297 12.2.4 Applications to commercial buildings ....................................................... 299 12.2.5 Mine cooling .............................................................................................. 301

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12.3 Food processing .................................................................................................... 12.3.1 Rapid cooling of vegetables ....................................................................... 12.3.2 Fish processing ........................................................................................... 12.3.3 Meat processing .......................................................................................... 12.3.4 Dairy processing ........................................................................................ 12.3.5 Brewery ...................................................................................................... 12.3.6 Retail food applications ............................................................................. 12.4 Possible future applications ................................................................................. 12.4.1 Ice pigging .................................................................................................. 12.4.2 Medical applications .................................................................................. 12.4.3 Artificial snow ............................................................................................ 12.4.4 Transport refrigeration ............................................................................... 12.4.5 The use of ice slurry for fire fighting ......................................................... 12.5 Conclusions .......................................................................................................... Literature cited in Chapter 12 ......................................................................................

302 302 302 305 305 306 308 311 311 311 311 312 313 313 314

13. Conclusions and recommendations for further R&D ............................... 317 Appendix 1: List of authors .................................................................................... 321 Appendix 2: List of selected plants ....................................................................... 325 Appendix 3: List of symbols .................................................................................... 345 Appendix 4: List of figures ...................................................................................... 351 Appendix 5: List of tables ........................................................................................ 361

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IIF-IIR –Handbook on Ice Slurries – 2005

FOREWORD Ice slurries are a really promising technology, because of their advantages regarding the environment, which is the most important challenge ahead of us, along with safety of course. The selection of the refrigerant for refrigeration equipment is the key problem, particularly since the Montreal Protocol and the United Nations Convention for Climate Change: some refrigerants (CFCs, HCFCs) play a role in the depletion of the ozone layer, while others (HFCs), which are progressively replacing them, unfortunately also have important global warming potentials even if they do not deplete the ozone layer. The aim then is to reduce the refrigerant losses from equipment and then to reduce the refrigerant charge. A very efficient solution is the use of environmentally friendly secondary refrigerants. Some other refrigerants, such as ammonia or propane, which are environmentally friendly, need a lot of precautions for human safety: in a same manner, we then can combine a protected area with that refrigerant and a safe secondary refrigerant. Another important issue is the energy efficiency of the refrigeration equipment. Energy consumption accounts for about 80% (on the average) of the global warming impact of refrigeration and it uses about 15% of the total electricity produced worldwide. The final decision concerning the selection of the refrigerant regarding the impact on the environment has to take into account the Life Cycle Climate Performance (LCCP) of the refrigeration equipment, including the impact of energy consumption on climate. Ice slurry as a secondary refrigerant is a very interesting solution thanks to the high cooling capacity given by the latent heat of phase change. It is simple and environmentally friendly. We now have a lot of examples of use of this technology. However, we still need a lot of research, particularly on how to generate ice slurry in an efficient, reliable and economic way for use in a broader range of applications. The IIR set up its Working Party on Ice Slurries in 1998; this party has actively organized and continues to organize workshops in order to better improve and to implement this technology. This book is the result of years of collaboration and experience. It involved nearly 50 IIR experts and I want to thank all of them for their work, particularly Peter W. Egolf, Michael Kauffeld and Masahiro Kawaji, for their efficient coordination of such difficult and useful work. I hope that this book will be a really useful guide for all the industrial practitioners and scientists who want to know more on and to implement this technology in the future.

Didier Coulomb Director of the IIR

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PREFACE The role of secondary refrigerants in industrial and commercial refrigeration is growing as the focus on the reduction of greenhouse gas emissions increases. The transition from distributed refrigeration plants with large charges of primary refrigerant (ammonia or HCFC /HFC) is taking place in some countries and more indirect systems with compact chiller units and secondary refrigeration loops are now being installed. Based on a simple temperature analysis, the additional heat exchange introduced when using such indirect systems leads to increased energy consumption of approximately 10-20%. But such comparisons are not necessarily valid, as they seldom include inefficiencies due to poor superheat control and defrosting, pressure losses in refrigerant headers and suction lines of distributed directexpansion systems, nor do they take into account the greater flexibility of indirect systems. An indirect system can be improved if phase-change materials1 are applied instead of traditional single-phase secondary refrigerants. At temperatures below 0°C ice slurry facilitates such efficiency improvement as the energy consumption for pumps can be reduced and the required temperature difference in heat exchangers lowered thanks to some very attractive thermophysical properties of ice slurry. Although ice slurry has been known since the ancient Roman times, co-ordinated and focused research activities were launched. This Handbook summarizes the current knowledge on ice slurry. Approximately 50 international experts have combined their knowledge and jointly created this unique document. We hope that it will also be useful to other system designers, engineers or scientists working with ice slurry or interested in using ice slurry for various applications.

Karlsruhe, Toronto and Yverdon, December 2004

Michael Kauffeld, Masahiro Kawaji and Peter W. Egolf

1 )

This publication deals only with ice slurry made from purely liquid phase fluids, i.e. without solid particles other than ice. Hence the phase change-material described in this Handbook utilizes the phase change of water to and from ice (energy of fusion with H2O-molecules) solely. The authors are well aware of the multitude of other phase-change materials used in industry and being subject to research especially in the domain of thermal energy storage. Examples of other phase-change materials (PCMs) are waxes, polymers (sometimes also employing water as PCM), salts, etc. Even though this publication has been limited to ice slurry alone, similarities to other phase-change slurries might be found and hence this book might be helpful to those working with other phasechange materials as well.

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CHAPTER 1. SUMMARY OF ICE SLURRY TECHNOLOGY by Michael Kauffeld, Masahiro Kawaji and Peter W. Egolf

1.1 Introduction The use of ice for prolonging the storage life of foodstuffs dates back many millennia. Up until the middle of the last century all ice used for cooling was from natural sources (winter snow/ice or imported Arctic ice). Sometimes the natural snow was mixed with salt in order to reach lower temperatures. The production of ice cream is known to have been achieved using this technnique some thousand years ago in ancient Rome. With the introduction of a mechanical cold production technology, ice was and is still produced in different forms, e.g. blocks, cubes, tubes or flake ice. Most of these forms of ice need a certain degree of manual operation for transportation from one place to another, and have rather sharp edges that may damage the surfaces of products that need to be kept refrigerated in direct contact with the ice. Furthermore, they are usually quite coarse and show poor heat transfer characteristics when releasing the latent heat of fusion. The technical utilization of ice slurry – a mixture of small (typically 0.1 to 1 mm in diameter) ice crystals/particles 1 and a carrier fluid — a mixture of water and a freezing point depressant — allows the phase change material, “ice”, to be pumped to the point of application. Heat transfer characteristics are enhanced as well as product compatibility in the food industry. Characteristic of ice slurries is that the particles disappear in the melting process and have to be created again by a special ice slurry generator. In storage tanks the particles experience large buoyancy forces, which lead to a high degree of stratification of the ice slurry with a maximum ice content at the top of the tank. Therefore, usually a mixing device, or some other special equipment, is necessary to create homogeneous ice particle suspensions, which would guarantee the safe operation of a system without the occurrence of clogging in the tubes. In recent years, the development of commercial ice slurry systems has enabled the use of ice slurry in a wide range of applications. The simplicity of freezing water with an environmentally friendly additive (alcohol, salts, etc.) and obtaining very high enthalpy densities makes the application of ice slurries a promising technology for the future.

1.2 Existing technologies The key issue for using ice slurry is the reliable, energy efficient and cost effective (cheap) production of the ice slurry. Several variations of ice slurry production technologies exist. They will be described in detail in Chapter 5, but most of the commercial ice slurry generators can be classified into two categories depending on the mechanism of ice crystal nucleation: heterogeneous or homogeneous nucleation.

1

The terms “ice crystal” and “ice particle” are used in parallel throughout this publication. In general the smaller the particles, the more likely they are to be named “ice crystal”, as they usually consist of a homogeneous crystal matrix. Especially larger particles above 1 mm diameter are usually called “ice particles”.

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1.2.1 HETEROGENEOUS NUCLEATION Systems with mechanical scrapers or brushes produce ice slurry based on a heterogeneous nucleation process. This process is utilized in a refrigerating machine containing a special evaporator with a double cylinder or plate in which a part of the water/brine mixture is cooled at the wall. Then the ice crystals are created with a size of some tenths of millimetres, mechanically scraped away and accumulate in the suspension. Ice slurry generators of this type comprise the majority of the installed equipment. First prototypes are known from 1976 with related U.S. patents. An alternative ice removal technique applies fluidized bed technology (Gun, 2001). New developments aim at avoiding the scraping elements by alternating between different evaporators (Davies, 2002), coating the surface of the heat exchanger facing the ice slurry (Zwieg, 2002) or controlling the flow rate as well as the evaporation temperature (Barth, 2002). All of these new techniques utilise some form of hydro-scraping based on the drag forces associated with the fluid flow.

1.2.2 HOMOGENEOUS OR SPONTANEOUS NUCLEATION The ice slurry is created directly by injection and evaporation of a cold refrigerant in the basic brine solution. The gas expansion causes a homogeneous or spontaneous nucleation. The direct contact of the cold refrigerant and the secondary fluid leads to a high efficiency of these systems, because no additional heat exchangers (evaporators) are necessary. Because of the turbulent jet-like injection of the refrigerant, the ice crystals are finely dispersed in the liquid. Water itself can also be used as the refrigerant in this process. The system is then commonly called “vacuum ice”. An alternative way is to use a water-immiscible single-phase heat transfer fluid, which creates ice in direct contact when mixed with water. The heat transfer fluid is cooled in a separate refrigeration unit (chiller). Due to the additional heat transfer between the primary refrigerant, the heat transfer fluid and finally the water/ice, this process is assumed to be less efficient than the direct contact evaporation process described above. Yet another method that utilizes homogeneous nucleation is supercooling of water or brine and subsequent release of supercooling by ultrasonic or mechanical shock.

1.3 Modern ice slurry applications Ice slurry is used in many countries in various applications. The following trends can be seen on an international level. In China and in other developing countries of the Far East ice slurry is used for cooling of railway cars, where ice slurry fills the voids surrounding the cargo hold. This technology is similar to the 100-year-old technique of using block ice, but the ice slurry is much easier to handle. A similar system has been developed in Germany for catering vessels, which are used in passenger trains. The vessels are charged with ice slurry at the beginning of a journey and

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keep the food refrigerated for many hours. So far the system has only been applied in Switzerland, but other applications are about to follow. In Japan, ice slurry is mainly used in connection with air conditioning of large buildings. In most Japanese installations ice slurry is only used as an energy storage medium and is not pumped directly to the various air handling coils. Such direct application of ice slurry in airconditioning systems might be beneficial when combined with low temperature air distribution systems (tair ≅ 2°C). The low-temperature air would save fan energy, duct size and hence building height, but the thermal comfort and air quality perceived by occupants in the building must of course be ensured. Furthermore, condensation risks must be minimized. Chilean, Dutch and Icelandic fishermen (to mention just the major ones) use ice slurry for direct chilling of fish and other catches. The ice slurry is produced from seawater on board in small ice slurry plants. The ice slurry produced is then stored for up to 10 days in the fish hold or special ice slurry tanks. When the catch is taken on board it is mixed with the ice slurry (sometimes, drained ice slurry). Several years of practice have shown a prolonged storage life of such catch as well as a much better quality, and hence better prices for the catches may be obtained. Moreover, the application of ice slurry is now moving into fish processing factories onshore. Several commercial applications (bread, beer, and sausage production) are known in Germany. Ice slurry is used in air coils (sometimes air coils designed for direct expansion of HFC-refrigerants). At least one installation in Germany utilises ice slurry for air conditioning. Two supermarkets with an ice slurry system for the chilling temperature range are operated in Switzerland. In addition, two large-scale applications were reported: Zürich-Kloten Airport and a Pharma Park close to Lugano. Most installations mentioned in Appendix 2 use ice slurry generators of the scraped surface type. In many of the installations, initial investment costs are higher due to the type of ice slurry generator. Often their operating costs are similar to those of other refrigeration systems. Sometimes cost savings can be obtained by reduced energy costs (e.g. ice slurry storage in Japan) or in the form of a higher value of the chilled product (e.g. ice slurry for direct cooling of fish).

1.4 International Institute of Refrigeration (IIR) Working Party on Ice Slurries

1.4.1 SCIENTIFIC CHALLENGES The basic physical properties of ice slurries have not yet been fully investigated. However, commercial designs of refrigeration systems require that these properties be well understood, since they form the basis for most design calculations, e.g. the application of melting/freezing models, the Navier-Stokes equations with rheological models and also for simpler calculation methods designed for more practical use. New additives must be evaluated and tested for low-temperature applications, and the physical properties of the suspensions containing these additives must also be measured and published.

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There is still some slight variation in reported heat transfer characteristics, which have been experimentally determined by various research groups. Further discussions and detailed examination of published results are required, but there is also a need for setting up common standards for presenting new research results. For instance, the work of the various groups would benefit from the use of common definitions for dimensionless numbers, which may be calculated either from the well-defined properties of the ice free carrier liquid or from the actual properties of the ice slurry. Directly immersing foodstuffs in the ice slurry mixtures is another relevant topic of research, the results of which will be useful for the fishing industry and certain sectors of agriculture.

1.4.2 TECHNICAL CHALLENGES There are various methods of producing fine-crystalline ice suspensions and the ice slurry generators based on those methods should be subjected to long-term testing. Furthermore, the efficiency of different physical methods to produce the “liquid ice mixtures” should be evaluated, tested and compared. New methods of ice slurry production need to be continually developed. Heat transfer, time dependency (altering particle size distribution as a function of time, see also Chapter 3.4), pumping characteristics and the pressure drop in piping systems also require further investigations, while the hydraulic resistances of fittings and control valves, etc. for ice slurry flow must also be established theoretically and experimentally. Studies of cold storage behaviour and stratification of ice slurry must be continued. Are mixing devices in storage tanks necessary to counteract the buoyancy effects caused by the ice crystals in the aqueous solutions? The use of storage tanks reduces the required size of the ice slurry generator but increases the running periods of the refrigeration machines. One major advantage of ice slurries is their dual role as a transportation fluid and storage medium. Various measurement and control devices are available for ice transport systems, but special components for ice slurry must be developed and the performance of existing equipment should be further evaluated by making reliable comparisons.

1.4.3 OBJECTIVES OF THE WORKING PARTY The main objectives of the working party are to add new results to the currently available body of knowledge in application and design, and to help improve this new technology by exchanging information and know-how obtained by various members. Another objective is to promote positive developments in fine-crystalline ice slurry systems world wide. Positive efforts are achieved by:

1. 2.

Listing and studying current scientific and technical problems. Establishing and continuously updating a reference list of test facilities and experimental material of research projects concerning ice slurry systems. The current reference list is available on the World Wide Web at www.ex.ac.uk/ice.

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3.

4. 5. 6. 7.

Establishing and continuously updating a reference list of research publications concerning ice slurry systems. A reference list and important publications are also available on the web. Initiating demonstration plants to prove the reliability of ice slurry systems. Initiating further research, e.g. defining experiments involving collaborating group members. Organising meetings for all members and other persons interested in the topic. Maintaining web pages with continuously updated information about ice slurries and ice slurry systems.

Meetings are organized, preferably annually, where information is exchanged and latest findings in the field of ice slurry research are presented. The working party currently consists of approximately 70 international scientists and industrial representatives (as of December 2004). New members, who have knowledge of ice slurry and/or ice slurry systems and are willing to participate in the working party, are always welcome.

1.5 Research institutes Several research institutes conducting ice slurry research exist around the world. Please refer to Appendix 1: “List of Authors” of this handbook to see details of some of those research institutes/universities/manufacturers.

1.6 Conclusions and outlook on the use of ice slurry The industrial use of ice slurry began recently (about 25 years ago) but ice slurry has a great potential for the future. Ice slurries enable the use of indirect refrigeration systems with a small charge of the primary refrigerant as well as the possibility of thermal storage and associated money savings. Furthermore, the use of ice slurry enables direct-contact cooling or freezing of products. Ice slurry also has better transport properties in tubes and heat exchangers, i.e. an approximately 8-fold higher heat capacity than the traditional single-phase secondary refrigerant for similar flow rates. The tube diameter can consequently be reduced by about 50% and the velocity inside the tubes can be reduced by about 50%. As a result, the energy consumption by the pumps to pump the ice slurry is reduced to only about 1/8th of the energy consumption necessary to pump the traditional single-phase secondary refrigerant, if the viscosity is similar. At moderate heat fluxes, the heat transfer coefficient for ice slurries is increased by a factor of 50 to 100 % as compared to conventional secondary refrigerants. Therefore, ice slurry is believed to be a very promising secondary refrigerant with potential for widespread future use.

1.7 Other phase-change slurries (PCSs) Multifunctional (thermal) fluids and suspensions, also named “intelligent fluids”, yield new classes of fluids with improved (thermal) properties. These fluids can be designed to

15


optimally fulfil particular objectives. In refrigeration and air conditioning these can be enhanced thermal conductivity of a fluid, higher heat transfer coefficients, higher thermal energy storage capacity, temperature stabilization, reduced pressure drop, etc. The use of phase-change material (PCM) in a dispersed phase in a continuous carrier fluid leads — by its phase change and latent heat — to very high energy densities, whilst the pumpability of the fluid still remains. Such substances are named “phase-change slurries (PCS)”. Ice slurry is the best-known PCS, but restricted to temperatures below zero degrees Celsius. To overcome this restriction, at present, other types of PCS are being developed, e.g. micro-encapsulated PCS, clathrates (clathrates utilise a chemical reaction and are therefore not really phasechange slurries), shape-stabilized paraffins, etc. Nanofluids, e.g. fluids with dispersed metallic particles on a nano-scale, also show enhanced heat transport properties. An advantage is that the small particles - as a result of Brownian motion - do not lead to stratification, which is induced by buoyancy forces. Phase-change slurries are fluids with dispersed particles, which change phase at the melting temperature of the dispersed phase. If the fluids are mixtures, very often a temperature glide occurs, which is seen in the enthalpy density function h(T). Then h alters continuously as a function of the temperature T. The energy to build up a crystal of a solid in a freezing process is stored in the material and when the material — in the opposite process — is melted, this amount of thermal energy (named latent heat) is released again. In a water/ice transition the stored energy is high, namely 332 kJ/kg. Because the concentration of ice particles in technical applications usually is less than fifty percent, the enthalpy density can (at most) reach 166 kJ/kg. Other substances have slightly smaller enthalpy densities, but they are still of high technical interest. To this latent heat, a smaller fraction of sensible heat may be added. The energy storage capacity of phase change materials and slurries can be two to ten times higher compared with the conventional storage technology using water, depending on the material used and the operational temperature range of the engineering system.

1.7.1 DRY ICE/CARBON DIOXIDE SLURRY Recently, a Japanese researcher reported on an interesting two-phase fluid system for low temperature refrigeration, namely carbon dioxide with dry ice content (Inaba, 2003). The liquid carbon dioxide operates as a boiling secondary refrigerant. It can be cooled for example by an ammonia system. The dry ice (solid carbon dioxide) can also be mixed with a singlephase heat transfer fluid as described by Pettersen et al. (1994).

1.7.2 CLATHRATE SLURRY Clathrates or hydrate slurries are a crystalline compound substance of water (host molecules) and a low-boiling temperature gas (guest molecules) in a special molecular structure at a certain temperature and pressure (Inaba, 2000). The particle size is in the order of 5–50 µm. The clathrate can be separated into liquid water and the gas phase by heating. This is a chemical reaction with a high reaction enthalpy. Therefore, it is not absolutely correct to list the clathrates in this chapter on PCS.

16


1.7.3 MICRO-EMULSION SLURRY Water and liquid paraffin are immiscible. If an emulsifier, which is composed of a hydrophilic head group and a hydrophobic tail, is injected into water, the paraffin is finely dispersed. Only small amounts of emulsifier are necessary for this process. The quantity of emulsifier/surfactant determines the size of the paraffin particles. Different problems have to be solved by choosing the best additives, namely prevention of: • • •

Coagulation Coalescence Ostwald ripening

see e.g. (Hadjieva, 2003). The process of the growth of larger particles at the expense of smaller ones has to be avoided. This process, which is also observed in ice slurries, leads to an undesired change of some physical properties, e.g. shear stress (“viscosity”), effective thermal conductivity, etc. Usually the density, the enthalpy density and the specific heat are not influenced by such growth effects.

1.7.4 SHAPE-STABILIZED PCM SLURRY When a plastic material, e.g. polyethylene, is used as a stabilizing structure for the PCM, the slurry is referred to as shape-stabilized PCM slurry. It is necessary that the PCM is immiscible in the carrier fluid and in its liquid state does not leave the stabilizing structure, yielding an open container. A combination used in practice is water (up to 90% contained in the polymeric matrix) in oil as carrier fluid. Also gels and aero gels are used for this purpose. The heat transfer performance is better, compared with microencapsulated PCMs (see Chapter 1.7.5), because there is no additional plastic layer between the carrier fluid and PCM which presents an additional resistance for the heat flux. In some cases the polyethylene combs are irregular, e.g. of a dendritic nature.

1.7.5 MICROENCAPSULATED PCM SLURRY Micro-encapsulation techniques were well developed, mainly by the pharmaceutical industries, because they were used to produce tablets, copy papers, composites, powders, coatings, foams and fibres. Furthermore, they were applied in cloth manufacture for heat capacity enhancement (Colvin, 2003). Plastic microcapsules, containing a PCM, floating in a carrier fluid for thermal energy transportation (see for example Jahns, 2003) constitutes a newer application. The encapsulation has significant advantages, e.g. the PCM is completely encapsulated and, therefore, shows a higher thermal cycling resistance. Important is that the capsules are sufficiently resistant to the shear stresses occurring in pumps. The smaller the capsules, the higher is their resistance to destruction.

17


1.7.6 POLYETHYLENE PELLETS This technology is used rather rarely, but solid-solid transitions, e.g. of pentaelythrytohol pellets (Inaba, 2000), have the advantage that no encapsulation is necessary, because of their permanent solid state. Major research activities in Canada, Europe, Japan and the United States of America are directed towards the development of multifunctional and “intelligent” fluids. An example is the clathrate system for a Japanese air-conditioning application reported by Hayashi (2000). These developments will lead to highly improved fluids compared with the conventional substances. But so far only ice slurry has made its way to full-scale production. These applications have been mainly pioneered by the refrigeration and air-conditioning industry. This handbook is solely devoted to ice slurries and their technical applications.

Literature cited in Chapter 1 1.

Barth, M.: Hydro-scraped ice slurry generator. Proceedings of the Fifth IIR Workshop on Ice Slurries, Stockholm, Sweden, May 2002 2. Colvin, D. P. et al., Proceedings of the Phase Change Material and Slurry Scientific Conference and Business Forum, 107-121, Yverdon-les-Bains, Switzerland, April 2003 3. Davies, T.: A novel recuperative ice generator. Proceedings of the Fifth IIR Workshop on Ice Slurries, Stockholm, Sweden, May 2002 4. Gun, M. A. van der; Meewisse, J. W.; Infante Ferreira, C. A.: Ice production in a fluidized bed crystallizer. Proceedings of the Fourth IIR Workshop on Ice Slurries, Nov. 2001, Osaka, Japan 5. Hadjieva, M.; Gutzow, I.; Vassilev, T.: Proceedings of the Phase Change Material and Slurry Scientific Conference and Business Forum, 27-32, Yverdon-les-Bains, Switzerland, April 2003 6. Hayashi, K.; Takao, S.; Ogoshi, H.; Matsumoto, S.: Research and development on highdensity cold latent-heat medium transportation technology. Study based on NKK’s R&D project: Broad Area Energy Utilization Network System (Eco Energy City Project), Japan, 2000 7. Inaba, H.: Int. J. Therm. Sci. 39, 991-1003, 2000 8. Inaba, H.: Proceedings of the Phase Change Material and Slurry Scientific Conference and Business Forum, 3-13, Yverdon-les-Bains, Switzerland, April 2003 9. Jahns, E.: Proceedings of the Phase Change Material and Slurry Scientific Conference and Business Forum, 45-49, Yverdon-les-Bains, Switzerland, April 2003 10. Pettersen, J.; Jakobsen, A.: A dry ice slurry system for low temperature refrigeration. SINTEF Report STF11 A94059, Trondheim, Norway, 1994 11. Zwieg, T.; Cucarella, V.; Worch, H.: Novel bio-mimetically based ice-nucleating coatings for ice generation., Proceedings of the Fifth IIR Workshop on Ice Slurries, Stockholm, Sweden, May 2002

18


CHAPTER 2. ICE CREATION, THERMOPHYSICAL PROPERTIES OF ICE SLURRIES AND OTHER CHARACTERISTICS

2.1 The formation of ice by Thomas Zwieg

2.1.1 INTRODUCTION Crystallization of ice starts from a small nucleus, on which surface water molecules of the surrounding liquid phase are incorporated. The temporal and spatial scope of crystallization is characterized by two processes, nucleation and crystal growth.

2.1.2 METASTABLE STATE – SUPERCOOLED WATER The phase change from water or an aqueous solution to ice occurs via metastable states; the supersaturated state in the case of isothermal pressure variations, the supercooled state in the case of isobaric temperature variations, or a combination of both. In most applications the metastable liquid state is reached only by cooling. Within the supercooled water, clusters of water molecules, also called embryos, are formed in an ice-like, hexagonal configuration. These embryos have only relatively short lifetimes and decay again. Increasing the degree of super-cooling lowers the total free energy, so that at a certain level of super-cooling, ∆T, the embryos are more likely to grow than decay. When a critical embryo size is achieved, the embryo becomes a nucleus. Then the process of ice nucleation or conversion from metastable supercooled water into stable ice crystals starts (Lock 1990, Vali 1995).

2.1.3 NUCLEATION For nucleation two different mechanisms are distinguished; the homogeneous and the heterogeneous nucleation. In homogeneous nucleation embryos are formed internally in the supercooled liquid containing only water molecules. In heterogeneous nucleation a foreign substrate initiates nuclei formation (Fletscher 1970). The nucleation process correlates with a change in Gibbs free energy, which consists of two counteracting parts, the volume free energy ∆GV and the surface free energy ∆GS : ∆G = −∆GV + ∆GS

(2.1)

During the phase transition, energy is released because of the lower free energy in ice. This energy is proportional to the volume or number of molecules incorporated. The creation of a new surface, the interface between ice and water, needs energy. This energy demand is proportional to the surface area, A, and acts against the phase transition. For the very simplified model of a small nucleus with a spherical shape and the radius, r, the change in free energy becomes: 4 ∆G = −V ∆GV + A∆GS = − π r 3 ( ∆GV ) + 4π r 2γ iw (2.2) 3

where γiw is the surface tension between the ice embryo and the water.

19


For the transformation from liquid to solid the change in volume free energy ∆GV is: ∆GV = ∆H − T∆S = (H L − H S ) − T ( S L − S S ) (2.3) where the indices L and S represent the liquid and solid phase, respectively. If we assume that the free energies of the two phases are independent of pressure, and the temperature dependence is small, then: L H L − H S = L f and S L − S S = f (2.4) and (2.5) Tm where Lf presents the latent heat of fusion/crystallization and Tm the melting point. From 2.4 and 2.5, the following expression is obtained: ⎛ T ⎞ L f ∆T ∆GV = L f ⎜ 1 − ⎟ = Tm ⎝ Tm ⎠

(2.6)

Using a molecular approach the volume free energy can be described as:

∆GV = ∆µ = (µ i − µ w )

(2.7)

where µi and µw are the chemical potentials per molecule in the supercooled water and in ice respectively. Using (2.7), equation (2.2) can be expressed as: 4 ∆G = n∆µ ⋅ Aγ iw = πr 3 ρ n ∆µ + 4πr 2 γ iw 3

(2.8)

where n is the number of molecules; A is the surface area of the embryo; γiw is the surface tension between the ice embryo and water and ρn is the density of molecules per unit volume.

Figure 2.1 illustrates the qualitative influence of the radius of the nucleus on the change in Gibbs free energy. The radius, r, at which the slope ∂(∆G)/∂r = 0 is defined as the critical radius, r*. Differentiating equation (2.2) with respect to r, inserting equation (2.6) and setting ∂(∆G)/∂r = 0, r* can be expressed as: r* =

2γ iw 2γ iwTm 2γ iw ⋅ Tm = = Lm ⋅ ∆T ∆GV ∆H∆T

(2.9)

where r* corresponds to the above mentioned critical embryo size. Table 2.1 illustrates the relationship between temperature T, critical radius r* and the critical number of molecules inside the ice embryo, n*.

Figure 2.1. Critical nucleus radius in homogeneous nucleation

20


Table 2.1. Critical radius and number of molecules per embryo for homogeneous nucleation of ice (Vali, 1995) T (°C) –40 –20 –5

r* (nm) 0.8 1.8 7.0

n* 70 650 45 000

The energy barrier for a spherically shaped nucleus, also called the work of nucleation, is: ∆Gn * =

16π γ iw3 ⋅ Tm 2 3 ( L f ⋅ ∆T ) 2

(2.10)

Above the critical radius, d(∆G)/dr < 0, thus the nucleation process releases energy and spontaneous growth of the nucleus occurs. From Equations (2.9) and (2.10) it can be concluded that the critical embryo size and the energy barrier for spontaneous nucleation decrease significantly with an increasing degree of supercooling and decreasing equilibrium freezing temperature. At low degrees of supercooling, few large nuclei form and the nucleation speed is low. On the other hand, at high degrees of supercooling many small nuclei form and the nucleation speed is high. The rate of nucleation follows the Arrhenius equation and has the form: ⎛ ∆Gn * −∆G A ⎞ J = K exp⎜ − ⎟ kT ⎝ ⎠

(2.11)

where ∆GA is the free energy of activation for diffusion across the boundary separating liquid and crystal. Turnbull and Fisher (1949) made a formal derivation for the constant K. By applying (2.10) the rate of nucleation, J, is given by: J=

⎡ 16πγ iw3Tm 2 ⎤ nL kT ⎛ ∆GA ⎞ exp ⎜ − exp − ⎢ ⎥ ⎟ 2 h ⎝ kT ⎠ ⎢⎣ 3L f 2 ( ∆T ) kT ⎥⎦

(2.12)

with nL as the number of water molecules per unit volume. According to Fletcher (1970) [x] in the specific case of freezing of supercooled water, the term (NkT/h) ≈ 1035 cm-3 s-1. Using the activation energy for viscous flow of water for ∆GA, we find for the term ∆GA/kT ≈ 10 at –2°C, ≈ 15 at –22°C and ≈ 18 in the range –30 to –40°C. Thus for freezing of water at –2°C equation 2.12 can be expressed as: ⎛ 16πγ iw3Tm 2 J ≈ 10 exp ⎜ − ⎜ 3L 2 ( ∆T )2 kT f ⎝ 40

⎞ ⎟ cm-3 s-1 ⎟ ⎠

(2.13)

In this equation the strong dependence of the nucleation rate upon the degree of supercooling is apparent.

21


In practice, the majority of nucleation phenomena in liquids take place at degrees of supercooling significantly less than those predicted by the theory of homogeneous nucleation. This discrepancy is attributed to the presence of foreign surfaces e.g., cold walls or particles in contact with the aqueous solution. These surfaces partly offer the necessary embryo surface for nucleation, thus acting as nucleation catalysts. The volume-to-surface ratio will increase and the nucleus-liquid interface will be partially replaced with the nucleus-catalyst interface. In the case of heterogeneous nucleation the work of nucleation can be written as:

∆Ghet * = f (I p β ) ⋅ ∆Gn * , (f ≤ 1)

(2.14)

where Ip represents an interface parameter and β a geometrical factor. For the special case of nucleation at a flat and smooth wall depicted in Figure 2.2, the factor f can be expressed as: f =

1 (2 + cosθ ) ⋅ (1 − cosθ )2 4

(2.15)

where θ is the contact or wetting angle, which is a function of the surface free energies at the interface between the phases involved. The contact angle is described by Young's equation: cosθ =

γ ws − γ is γ wi

(2.16)

All values of θ < π reduce the critical nucleus size and energy barrier for nucleation. Thus, lower supercooling is necessary in a heterogeneous system. Homogeneous nucleation is the limiting case when the wetting angle, θ, increases to θ = π.

Figure 2.2. Geometrical and surface energy balances in heterogeneous nucleation The above treatment of heterogeneous nucleation is based entirely on simplified thermodynamic considerations. This theory suffers from a number of serious limitations. The main difficulty is that the factors such as the interaction and structure of the first monolayer of the liquid in intimate contact with the foreign surface, the crystallographic lattice misfit, the surface heterogeneity, defects and roughness and the type of bonding, are not taken into 22


consideration. The role of some of these influencing factors in the nucleation process is not yet completely understood. Fletcher (1970) included these factors in the general interfacial parameter Ip, used in Equation (2.14). The contact angle in Equation (2.16) as an experimental measure of the wetting behaviour of the liquid phase at the foreign surface is more a macroscopic than a microscopic parameter, thus would not be able to fully express influencing factors at a molecular level. The factors mentioned above will of course directly influence the surface free energy ∆GS and the volume free energy ∆GV. In order to visualise these factors they can be summarized in an additional free energy term ∆GSt, which expresses the strain introduced into the nucleus/growing crystal by the above mentioned factors. The Equation (2.1) for the Gibbs free energy can be re-written as: ∆G = ∆GV + ∆G S + ∆G St

(2.17)

The crystallographic lattice misfit δ between a nucleating surface and ice may be defined as: a − a0 (2.18) δ= a0 where a and a0 are the lattice parameters of the nucleating surface and ice respectively. As illustrated in Figure 2.3 this misfit will introduce a certain amount of dislocations and elastic strain ε in the ice.

Figure 2.3. Nucleation of an ice embryo on a crystalline substrate with a lattice misfit of approximately 10%. Dislocations (arrows) and elastic strain are introduced into the nucleus.[x, Flet] An increase in the concentration of dislocations will raise the magnitude of the interfacial energy γis which implies an increasing contact angle and decreasing nucleation efficiency of the nucleating surface. The strain in the ice embryo will raise the bulk free energy in the ice, which also lowers the ice nucleation efficiency of the foreign surface. Consequently the best nucleating substrate must have a lattice structure like or very similar to the ice.

23


A special case of heterogeneous nucleation is the secondary nucleation, where nucleation is induced on a seed crystal. Nucleation occurs at the surface of a prior existing crystal of the material crystallized. Please refer to Nývlt (1985) and Myerson (1992) for a detailed description. Similar to the heterogeneous system, nucleation can also be induced at lower supercooling by dynamic stimulation. The energy required to create the necessary embryo surface is supplied by friction, vibration or pressure pulses. Ice generation by the application of, for example, ultrasonic waves is well known.

2.1.4 EFFECT OF ADDITIVES The equilibrium behaviour of ice and water is changed by the presence of solutes. The entropy of an aqueous solution is always higher than that of pure water. If the ice formed from the solution is considered to be pure ice, which requires low freezing rates, the enthalpy change per mol will be the same as without an additive and therefore the freezing temperature to fit ∆G = 0 must decrease according to: Tm’ = Q / ∆S’ = ∆H / ∆S’ , where ∆S’ = Sas – Si

(2.19)

Here, Sas represents the entropy of the solution, and Si the entropy of ice. ∆S’ is larger than ∆S and therefore Tm’< Tm. During solidification the system will suffer an increase in the solute concentration. For example, sodium chloride (NaCl) is essentially insoluble in ice. At low freezing rates salt is rejected into the solution as ice forms. At high freezing rates, salt can no longer diffuse fast enough away from the interface and will be partially trapped in the ice. Thus, the structure and the properties of the ice formed will be altered.

2.2 Crystal growth by Thomas Zwieg, Didier Vuarnoz, Torben Hansen and Beat Frei

2.2.1 INITIAL CRYSTAL GROWTH Under the circumstances that a nucleus larger than the critical size is formed and the supercooling ∆T is not decreasing, the nucleus will grow further in size due to incorporation of additional water molecules at the surface. This process, the crystal growth, controls the final particle size distribution obtained in the mixture. Several models exist to describe the mechanism of crystal growth. They can be classified into pure thermodynamic models or models dealing with the actual kinetics of crystal growth. For a detailed review, refer to Nývlt (1985), Myerson (1992) or Hobbs (1974). The growth of ice in aqueous solutions may be governed by one or more of the following important factors: a) the transport of water molecules through the fluid towards the interface, b) the accommodation of these molecules on the ice surface, c) the removal of the heat of crystallization. A model that focuses on the transport of water molecules towards the interface is the diffusion layer model (Nývlt 1985, Myerson and Ginde 1993).

24


This model divides the crystal growth into two phases: a) Molecular diffusion through the boundary layer and b) Incorporation of molecules into the surface layer. These two phases are combined into one kinetic equation describing the crystal growth, dmc 1 1 1 = + = K G ⋅ A ⋅ ∆C with K G kd ki dt

and k d =

D

δ

(2.20)

where A is the surface area of the crystal, KG the overall mass transfer coefficient, kd and ki the mass transfer coefficients for diffusion and incorporation, ∆C the concentration changes in the boundary layer, D the diffusion coefficient and δ the boundary layer thickness. After adsorption of the water molecules on the crystal surface they diffuse two-dimensionally on the surface before being integrated into the ice lattice. This integration typically occurs at kink sites, steps, terraces or screw dislocations. Details regarding these phenomena are the subject of different thermodynamic models, e.g. models of Kossel, Stransky or Burton, Carbera and Frank (BCF-model). The crystal growth rate may be described as a linear function and related to the increase in the crystal mass over time, RG, introduced above: RG =

α 1 dmc ⋅ = 3⋅ ⋅ ρ ⋅G A dt β

(2.21)

where A is the surface area of the crystal, α and β volume and area shape factors, ρ the crystal density and G the linear growth rate (Myerson and Ginde 1992). The influence of heat of crystallization on crystal growth is discussed by Pronk et al. (2004). The ice growth habit or ice growth shape in an aqueous solution is reported to be dendritic or needle like (Fletcher 1970, Hobbs 1974, Lock 1990). It was shown that the ice crystals heterogeneously formed in a tube-and-shell ice slurry generator under flow conditions, were also of dendritic type (Zwieg 2002).

Figure 2.4. Ice crystals formed heterogeneously in a shell-and-tube ice slurry generator under forced flow conditions As illustrated in Figure 2.4 the branches of the dendrites grow under these circumstances faster on the upstream edge and slower on the downstream edge. The highest growth rates occur at the branches oriented at an angle of approximately 60° from the flow direction. The ice dendrites grow flat on the cooled surface, forming a thin, closely packed layer of ice. The further growth is also of dendritic type, now directed to the centre of the tube, increasing the layer thickness and decreasing the relative tube diameter.

25


2.2.2 FURTHER PROCESSES AFFECTING THE CRYSTAL SIZE Once the initial ice crystals are formed in the ice slurry generator, their shape and size are altered through a number of processes starting immediately after the initial crystallization process. These processes are called attrition, spheroidization, agglomeration and Ostwald ripening. All four processes are described in detail in the following paragraphs. The driving potential for all crystal growth mechanisms is the minimization of the Gibbs' free energy:

∆G = −SdT −Vdp+ ∑µdn + γdA

(2.22)

2.2.2.1 Attrition Attrition refers to the breaking off of small fragments, e.g. dendrite branches of a crystal. It occurs when the crystal is subjected to a stress. This can be due to high fluid shear during flow or mixing, or due to a collision with matter, e.g. other crystals, a mixing device, walls etc. All kinds of damaging mechanisms are included in attrition, including abrasion. Impact of attrition on the crystal size distribution can be found in the work of Pronk (2002). 2.2.2.2 Spheroidization Spheroidization is a crystal forming process, which occurs after the dendritic crystal has left the ice slurry generator. A sphere has a minimal surface area per unit volume. This is thermodynamically favourable, therefore, the dendritic ice crystals formed in ice slurry generators spheroidize during the transport to the storage tank or system, due to Ostwald ripening in combination with attrition. 2.2.2.3 Agglomeration When two or more crystals collide in a saturated suspension, they can adhere to each other and become one crystal. This process is called agglomeration. These crystals can further coalesce and sinter together, forming a larger stable crystal. The degree of agglomeration decreases with increasing intensity of agitation and increases due to high supersaturation. Vuarnoz et al. (2001) and Egolf et al. (2002) further showed the cluster problem in a realistic tank of about 1000 liters in volume. Kitamoto et al. (2001) proposed the use of chemicals or biological surfactants to reduce the agglomeration in ice slurry. 2.2.2.4 Ostwald ripening Ostwald ripening is a crystal coarsening process, which alters the crystal size distribution of a precipitate even under isothermal conditions. During ripening large crystals tend to grow and the surrounding small crystals show the tendency to dissolve. This spontaneous process occurs, because larger crystals (with their smaller surface area to volume ratio) are in a lower state of free energy ∆G. This phenomenon is described by the Gibbs-Thomson (OstwaldFreundlich) equation: ⎛1 1⎞ − ⎟⎟ r ⎝ 2 r1 ⎠

∆G = 2 ⋅ γ ⋅ Ω ⎜⎜

(2.23)

where γ is the crystal interfacial energy and Ω the atomic volume.

26


The difference in curvature is the driving force for the Ostwald ripening. Larger particles, having a larger radius r are thermodynamically favored during the coarsening. Along the perimeter of an ice crystal, differences in curvature are a source of atomic interactions through the ice/water interface and in the course of time lead to spheroidization of the crystals. If mass transport between the crystals occurs and the growth kinetics is diffusion controlled, all crystals of radius r=

β ⋅ Vm ⋅ γ c ⋅ c ∗

(

k ⋅T ⋅ c − c∗

)

(2.24)

are in equilibrium with the bulk solution; here, β is a surface shape factor, Vm the molar volume of the solute and γc the specific surface energy of the crystal, c the solubility of the crystal and c* the equilibrium solubility (Nývlt, 1985; Myerson and Ginde, 1993). Crystals with radii smaller than r tend to dissolve but larger than r tend to grow. The speed of the ripening process depends largely on the crystal size and the solubility. In the case of diffusion controlled growth kinetics, the linear growth velocity may be approximately described by: dr γ c ⋅ Vm2 ⋅ D ⋅ c ∗ ≈ dt 3⋅ k ⋅T ⋅ r 2

(2.25)

where D is the diffusion coefficient. Ripening occurs usually at low supersaturation. The growth kinetics is therefore more likely to be controlled by surface integration effects than by diffusion. Consequently ripening could be considerably slower than indicated by Equation 2.25. Pronk et al. (2002) showed experimentally that this Ostwald ripening is the dominant mechanism. The ripening process appears to be stronger in an ice slurry with a lower concentration of the freezing point depressant. Similar results were also found by Hansen et al. (2002). Ostwald ripening was found to be the predominant crystal growth mechanism during five days of storage in a 1 m³ storage tank. In a storage tank with a mixing device the crystal growth rate was found to increase due to convection, whereas non-moving layers of ice crystals grow due to diffusion. The crystal growth is an inherent property of the ice slurry system and cannot easily be controlled (Hansen et al., 2002). Ice crystal growth has been thoroughly studied in frozen food products and additives to decelerate ice crystal growth have been developed for use in, for example, the ice cream industry. Common crystal growth inhibitors also work by the same principle based on hydrogen bonding with ice (Hansen et al., 2002). Polar additives used for freeze protection can form hydrogen bonds with the water molecules. The freezing point depressing additives, propylene glycol and ethanol used in the Danish survey, are both polar. With their polar hydrophilic ends they form hydrogen bonds with ice crystals, while their non-polar hydrophobic ends reject water and ice molecules. The hydrogen bond is considered as an energy barrier reducing the agglomeration activity. In the study by Hansen et al. (2002), Tween 85 was only present at a concentration of 0.15% wt. As both ethanol and propylene glycol form hydrogen bonds with the ice, it is believed that the concentration of freezing point depressing agent is high in the concentration boundary layer (Hansen et al., 2002).

27


The re-crystallization rate was always found to depend on time to the power of 1/3 in the case of solely diffusion driven growth with mixtures of water and polar freezing point depressing agents at concentrations corresponding to freezing points of –4.5°C and –4.9°C, respectively (Hansen et al., 2002). Kang (1999) performed fundamental studies on hydrogen bonding effects on the morphology of ice and Yazaki (1997) investigated and modelled the molecular motion at the water/ice interface to predict the growth rate, which was found to have a maximum value close to the freezing point of water. Figure 2.5 shows a representative example of the development of the size distribution of crystals with time (Hansen et al., 2002). The results are in good agreement with the finding by Hagiwara (1996). The initial crystal diameter in the storage tank was distributed in a narrow band of ±50 µm around the mean crystal size of approximately 100 µm. At the end of the storage period (94 hours), the mean crystal diameter increased to approximately 480 µm, and the crystal size ranged from 250 to 700 µm. Ethanol Propylene glycol

14

40 Growth rate ( µm/h)

Frequency (%)

10 wt.% ice

12

45 hours 0 hours 22 hours

30

94 hours

20 10

10

30 wt.% ice - mixed

8

30 wt.% ice - heterogeneous

6

46 wt.% ice

4 2

0 0

100

200

300

400

500

600

700

0

Feret diameter (µm)

0

10

20

30

40

50

60

70

80

90

100

Time (h)

Figure 2.5.

a) Mean Feret diameter growth dependency on additive, ice concentration and storage type shows clearly the Ostwald ripening effect. b) Particle Feret diameter growth rate dependency on additive, ice concentration and storage type.

In the experiments performed by Hansen et al. (2002), the equation for the average particle diameter was formulated as: d Feret = E + B ⋅ τ C

(2.26)

where the coefficients E, B, C were determined according to the additive and type of the storage tank (Table 2.2).

28


Table 2.2. Parameters E, B and C Additive Propylene glycol Propylene glycol Propylene glycol Propylene glycol Ethanol Ethanol Ethanol Ethanol

Storage tank homogeneous homogeneous stratified stratified homogeneous homogeneous stratified stratified

Cice 10% 30% 30% 46% 10% 30% 30% 46%

E 100.7 162.6 113.2 126.5 118.9 199.7 92.8 144.3

B 28.6 11.4 7.7 7.6 25.6 8.4 21.1 4.6

C 0.53 0.60 0.68 0.59 0.62 0.70 0.49 0.72

R2 0.986 0.892 0.938 0.916 0.988 0.937 0.983 0.972

These results reveal three characteristic differences in the parametric influence on the crystal growth in the case of ice slurry: 1) the growth rate is always higher with ethanol compared to propylene glycol, 2) crystal growth rate is slower at higher ice concentrations, 3) the growth rate is higher in the homogeneously mixed storage. These findings revealed that contact with air from the surroundings did not influence the crystal growth rate (Hansen et al., 2002). In the agitated (homogeneous) storage, convection leads to growth rates which are approximately 60-70% higher than in the heterogeneous storage. The size distribution of ice particles influences the operation of ice slurry systems. Ice slurry with larger ice particles will require a greater stirring effort to obtain a homogeneous mixture. In heat exchangers the melting characteristics may also change (Hansen et al., 2002).

2.3 Types of ice crystals and ice particles by Didier Vuarnoz and Torben Hansen

Particle shape and size analysis is important in elementary particle and solid state physics, chemistry, pharmaceutical studies, biology, etc. (for an overview, see e.g. Kawashima, 1993 or Egolf, 1999). Because of the rather large size of the ice particles in ice slurries (30-300 µm), an ordinary optical microscopic method can be used to study particle characteristics, although a small heat input into the fluid occurs. The disadvantage of this technique is that two-dimensional projections of the particles are obtained, which show irregular shapes. The probability of observing one entire large particle in the field of view of the microscope is smaller than the probability of detecting a small one. Two methods have been developed to extract the ice concentration from photography (Sari, 2000) and (Fournaison, 2001). Nevertheless, these methods are not as simple and accurate as others used to determine the ice concentration. Numerous microscopy pictures of ice slurry particles have been published, e.g., by Fukusako et al. (1999), Bel (1996) and Kauffeld et al. (1999). Kawashima (1993) studied ice slurry flows (snow water mixtures) with a high-speed video camera. Bel (1996) reported that the ice crystals that have a hexagonal structure, become a little smoother and rounder under the attrition process. The major difficulty is to interpret the focussed or projected image from photography to obtain the three-dimensional structure. The first assumption is that the ice

29


particles are flat or round, but the particles may also undergo some metamorphoses, see section 2.2.2 and (Turian, 1992). Such mechanisms may explain the time behaviour, as illustrated in Figure 2.6. Many groups are equipped to perform photography of ice crystals (Hansen et al., 2002; Pronk, 2002 and Vuarnoz, 2001).

a) Only liquid

b) Air dissolved in the substance leaving it

c) First ice crystals appear

d) Crystals at the outlet of a scraper-type ice slurry generator

e) Ice particles after 11 min of storage

f) Ice particles after 10 hours of storage

g) Ice particles after 22 hours of storage

h) Ice particles during their melting process

i) Ice particles have totally disappeared

Figure 2.6. Ice crystal morphology during a freezing/melting cycle, a), b), c), h), and i) from EIVD-TiS laboratory, Switzerland; d) from DTI, Denmark; e), f), g) from Delft Univ., Netherlands (Pronk 2002)

2.3.1 SHAPE PARAMETERS Knowledge of geometrical characteristics of ice slurry particles and their time behaviour is believed to be an important key to understanding the deviation in the results found in numerous apparently comparable experimental investigations of thermophysical properties, pressure drop, heat transfer coefficients, viscosity, etc. (Hansen et al., 2002). The shape and size of the ice crystals in ice slurries depend on many parameters, and the shape of ice particles evolves throughout their lifespan.

30


Non-spherical particles and particle size distribution If the particles are non-spherical, their terminal settling velocity, e.g. in a storage tank, is lower than that of a spherical particle. Working with projections rather than a full volumetric analysis leads to a loss of information. The projected image of an individual ice crystal does not reveal its true shape and dimension.

The more spherical the ice crystals are, the more adequate it is to quantify the crystal dimensions in terms of the Feret diameter. The Feret diameter is defined as the diameter of a circle having the same area Ap as the projection of the ice crystal: 4 ⋅ Ap

DFeret =

(2.27)

π

Table 2.3. Effective particle diameters (Turian et al., 2002) dv ds dsv

Diameter of a sphere with the same volume as the particle Diameter of a sphere with the same surface area as the particle

1

⎛ 6 ⋅V ⎞ 3 dv = ⎜ ⎟ ⎝ π ⎠ ⎛S ⎞ ds = ⎜ ⎟ ⎝π ⎠

(2.23)

0 .5

(2.24)

2 Diameter of a sphere with the same external surface ⎛ V ⎞ dv d 6 = = ⋅ ⎟ ⎜ sv to vol. ratio as the particle 2 ⎝S⎠

(2.25)

ds

dd df dst

Diameter of a sphere with the same resistance to motion as the particle in the same fluid Diameter of a sphere with the same density and free falling velocity as the particle in the same fluid Free falling diameter of the particle in Stokes law region (Re < 0.2) d st =

⎛d 3 18 ⋅ η ⋅ w 0 = ⎜ v (ρ f − ρ ice )g ⎜⎝ d d

⎞ ⎟ ⎟ ⎠

(2.26)

There are a variety of methods for the determination of the effective particle diameter (see e.g. Turian et al. (1992) and Table 2.3. The ice particles in an ice slurry can vary in size from ~ 0.1 to ~ 0.7 mm, as shown by Hansen et al. (2002). Their size depends on the storage time. The equation for the average particle size determination is given by Turian et al. (1992): k

dm =

∑n d i

i =1

m i

/

∑n

(2.28)

i

where ni is the number of particles with a diameter between di and di+1 and m is the mth moment of the size distribution (Turian et al.,1992): d

length mean diameter

(2.29)

“surface” mean diameter

(2.30)

“volumetric” mean diameter

(2.31)

1

⎛⎜ d 2 ⎞⎟ 2 ⎝ ⎠ 1

⎛⎜ d 3 ⎞⎟ 3 ⎝ ⎠

31


d wm =

d4

“weighted-moment” mean diameter

d3

(2.32)

The latest findings on the distribution of ice particle sizes are those reported by Hansen et al. (2002), who arrived at the conclusion that an ice particle size distribution can be approximated by a normal distribution. The mean value and the standard deviation depend on the additive used, the storage type and the time.

2.3.2 ICE PARTICLE MODEL Modelling work facilitates correlation and extrapolation of results. The ice concentration may, for example, be determined from a few photographs. Another example of an ice particle model was presented by Egolf (1999) based on his physical properties model for ice slurry. Geometrical model Photographs show that in a quiescent (inactive) fluid the solid ice particles are randomly distributed throughout the carrier fluid. At present, to describe particles, two kinds of models are discussed. In one model the particle form is assumed to be given by two hemispheres connected to a small cylinder of length d. The second model assumes disk-shaped particles with a radius r and a thickness h. (see Figure 2.7a) and b) respectively).

a)

b)

l d

R

Ice particle

h

b

Figure 2.7. Ice particle shapes estimated from projected images: a) a spheroidal ice particle shape composed of two hemispheres connected by a cylinder of the same radius (applied by Vuarnoz and Egolf [2001]), b) disk-shaped ice particle model proposed by Pronk (2002)

The main objective is to determine the actual volume of the particles from microscopy images. One method was developed by Vuarnoz and Egolf (2001) for the case of spheroidal particles. They assumed that the particles are distributed in a homogenous and isotropic manner. After double space integration, the authors found that the actual distance d is 19% larger than the optically observed dsphere. This factor is taken into consideration by applying a correction to the two-dimensional observation to approximate three-dimensional size. Notice that the quantities d and l are affected by this factor but not the width b. The factor f = 1/1.19 = 0.84 is named the view factor. Based on this method it is possible to estimate the ice concentration in the ice slurry.

32


2.3.3 MEASUREMENTS AND STATISTICS Numerous researchers have investigated ice crystals by photographic methods. Sampling locations and age of the sample are of major importance, as shown by Vuarnoz et al. (2001), see also Figure 2.8a and b. Measurements were performed on two samples after two hours of storing the ice slurry with additional mixing. Samples were chosen from four different heights in the storage tank — two hundred ice particles were used to quantify the ice particle dimensions. It was observed that the size of the ice particles is not a clearly defined function of the temperature of the ice slurry (Vuarnoz et al., 2001). Ice content = 10.3 %

Ice content = 21.4 %

300

350

250

300

200

250

150

200

100

150

50

100

0

50 0

100

200

300

400

500

600

700

Length l (µ m)

0

100

200

300

400

500

600

700

Length l (µ m)

Figure 2.8. Ice particle size distribution data obtained for a 10 w/w% water-ethanol ice slurry after correction with a view factor. Shown are the data for (a) Ci = 10.3% and b) Ci = 21.4% ice concentration (Vuarnoz, 2001 and Egolf, 2002)

2.4 Properties of aqueous solutions and ice by Åke Melinder

2.4.1 INTRODUCTION In some applications, ice slurry is produced with pure water which is an excellent secondary fluid. However, when temperatures below 0°C are required, one or more freezing point depressant additives are used. Such binary or ternary aqueous solutions have long been used in single-phase indirect refrigeration systems to transport energy from the cooling unit to the evaporator. The same liquid mixtures may be used for ice slurry applications, where small ice crystals are formed and distributed to the cooling unit from which heat is removed when some or all of the ice crystals melt.

33


In order to choose a secondary fluid for ice slurry use and to make correct technical calculations of the ice slurry system there is a need to examine and evaluate thermophysical properties and other aspects of the aqueous solutions. There are several requirements that have to be fulfilled by an ideal secondary fluid. It should possess good thermophysical properties, making it possible to: • transport the required cooling capacity through small pipes or tubes at a small volumetric flow rate with a small temperature change over the cooling unit; • obtain good heat transfer, leading to small temperature differences at the location of heat transfer in the evaporator or object to be cooled; • be pumped with an acceptable pressure drop, in order to use a pump with small or moderate pumping power. Furthermore, it is important that the fluid does not cause any material corrosion problems. It should also be non-toxic, environmentally acceptable, non-flammable, safe to handle and being available at a reasonable price.

2.4.2 THERMOPHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS Aqueous solutions of ethyl alcohol (ethanol) and sodium chloride (sea water) have been used in most ice slurry applications in Europe. However, aqueous solutions of glycols, ammonia and various salts may also be of interest for various applications. From this point of view, the following seven aqueous solutions are considered for ice slurry use: ethyl alcohol, ethylene glycol, propylene glycol, ammonia, calcium chloride, sodium chloride and potassium formate. Alcohol, glycol and salt solutions (sea water) represent the major applications so far. The other solutions are used thanks to their favourable thermophysical properties. Also, other substances, e.g. sugars, are of course feasible for ice slurry use, even though they are not considered here. The following thermophysical properties are of importance when comparing different aqueous solutions: the freezing point temperature, density, viscosity, specific heat or enthalpy change and thermal conductivity. These property values can be obtained from Melinder (1997). Other thermophysical properties that are useful to know at times are the boiling point temperature, thermal expansion coefficient and surface tension. Brief comments are given on each of them here. For most of these aqueous solutions, values of these properties can be obtained from Melinder (1997). The freezing point temperature, ϑF, is the temperature at which ice crystals begin to form in equilibrium if there is no supercooling. In ice slurry applications the slope of the freezing point curve is important as it determines the ice concentration that can be obtained in equilibrium (see also 2.4.3). A low boiling point temperature of the aqueous solution can (even at moderate temperatures) create problems in a system, especially if the liquid is exposed to atmospheric air. This may pose a problem with high concentrations of alcohol in water. However, additive concentrations used in most ice slurry applications are quite low and this is usually not a problem (see Chart C14, Melinder, 1997).

34


The surface tension, σt, of a liquid is the force per unit length that acts to keep the surface as small as possible. A low surface tension may increase the tendency of the solution to leak out and may also increase the risk of foaming in the system and of cavitations in the pump. Ethyl alcohol has the lowest surface tension of the aqueous solutions followed by the glycols (and ammonia). The salt solutions have higher surface tensions than water (see Chart C15, Melinder, 1997). Knowing the correct mass density, ρ, is important for several reasons. The concentration of a certain known solution is often measured by checking the density. The density of aqueous solutions used is higher than the density of ice. In ice slurry systems this high density may cause a stratification of the fluid caused by the buoyancy forces on the ice particles. The mass density difference between ice and carrier fluid and hence the tendency to separate is the lowest with ethyl alcohol (and ammonia), followed by glycols, and most severe with salt solutions. It is important to determine the dynamic viscosity, µ, and/or the kinematic viscosity, ν = µ/ρ, of a liquid. The viscosity should not be too high at the operating temperature if the aqueous solution is to perform well. The viscosity is also used to calculate the Reynolds number, Re = (w⋅d)/ν, which determines the type of flow that will prevail, laminar, transitional or turbulent. Here w is the fluid velocity and d is a characteristic length, i.e. the tube diameter. The viscosity of (single phase) propylene glycol is the highest, followed by ethyl alcohol and ethylene glycol, while potassium formate and the chlorides show the lowest viscosities. The viscosity of ice slurry will, however, depend strongly on the ice content. A high value of the specific heat, cp, of the fluid is favourable as it affects the heat transfer coefficient and the volume flow rate needed for a desired cooling capacity. At the low concentrations usually used in ice slurry, the specific heat of ethyl alcohol is higher than that of water. The volumetric heat capacity (i.e. specific heat times the fluid density) is inversely proportional to the secondary fluid flow rate needed for a certain cooling capacity. A high value of thermal conductivity, k, is desirable as it contributes to good heat transfer and thereby decreases the temperature difference between the fluid and the tube wall. The chloride salts and potassium formate have generally a higher thermal conductivity than the other aqueous solutions. The thermal conductivity of ice slurry will increase with the ice concentration, but it is very difficult to measure the thermal conductivity of a two-phase fluid. The volumetric thermal expansion is of interest to designers of refrigeration systems in determining the size of expansion vessels. Curves of thermal volume expansion coefficient from freezing point to a certain temperature for various concentrations are given in Charts C1-11e in Melinder (1997), for most of the aqueous solutions. In ice slurry applications, one of the main purposes is to benefit from the latent heat or enthalpy difference when the ice is melting. The latent heat reduces the volumetric flow rate required for a desired cooling power. The latent heat available is reduced with increasing additive concentration. For aqueous solutions the available latent heat reaches its maximum at temperatures just below the freezing point and decreases at lower temperatures.

35


2.4.3 FREEZING-POINT TEMPERATURE OF AQUEOUS SOLUTIONS In Figure 2.9 the freezing point temperature is shown as a function of the additive concentration (cA). Freezing point curves are presented for different aqueous solutions. For low concentrations these curves are usually based on the values published in the CRC Handbook of Chemistry and Physics (1989) and for higher concentrations they are based on the polynomial equations given in Chapter 6 of Melinder (1997). In order to obtain and maintain ice slurry the operating temperature must be kept below the freezing point. When the temperature drops below the freezing temperature ice crystals consisting of pure water may start to freeze out. 0 Ethyl alcohol Ethylene glycol

Freezing point temperature in °C

-5

Propylene glycol Ammonia

-10

Calcium chloride Sodium chloride

-15

Potassium acetate Potassium formate

-20 -25 -30 -35 0

10

20

30

40

50

Mass concentration of additive, CA in % by weight

Figure 2.9. Freezing point temperature (ϑF) as a function of additive concentration (CA)

2.4.4 THERMOPHYSICAL PROPERTIES OF ICE In order to predict the thermophysical properties of ice slurries, it is necessary to know the properties of the pure substances, e.g. ice (water in its solid phase). The density of ice is lower than the density of water in the liquid phase (ice tends to float on the liquid surface). The density of ice, ρI, at the temperature, ϑ I (in °C),can be expressed as:

ρI = 917 – 0.13·ϑ I (kg/m3)

(2.33)

The thermal conductivity of ice at the temperature, ϑ I, is much higher than that of water in the liquid phase. This feature has a good influence on the performance of ice slurries. The thermal conductivity of ice, kI, as a function of temperature, ϑ I, can be described by:

36


kI = 2.21 – 0.012·ϑ I (W/m·K)

(2.34)

The equations for the density and the thermal conductivity are based on the data published in the Handbuch der Kältetechnik, VI/B (1988) and Handbook of Thermodynamic Tables and Charts (1976). The specific heat of ice at the temperature, ϑ I, is much lower than the specific heat of water in the liquid phase. The specific heat of ice, cp,I, as a function of temperature can be described by: cp,I = 2.12 + 0.008·ϑ I [kJ/(kg·K)]

(2.35)

The enthalpy of ice, hI, at the temperature, ϑ I, can then be calculated with the relation: hI(ϑ I) = –332.4 + ϑ I ·(2.12 + 0.008·ϑ I)

(2.36)

These equations are based on the heat of melting of ice (332.4 kJ/kg) as well as the specific heat values of ice, presented by Dickinson-Osborne, published in CRC Handbook of Chemistry and Physics (1989).

2.5 Physical properties of ice slurry By Åke Melinder and Oleg B. Tsvetkov (see specific list of symbols in Appendix 3)

Most properties of ice slurries can be derived from the individual properties of the aqueous solution and of ice by combining the respective properties in the correct ratio. The particle or ice fraction, often called ice concentration is here a crucial parameter. Nonetheless the viscosity, thermal conductivity and enthalpy of the ice slurry have to be determined more carefully as described in the following sections.

2.5.1

FREEZING POINT TEMPERATURE AND ICE CONCENTRATION

Figure 2.10 shows how the freezing point is changes with the composition of the mixture. The diagram can be used for any of the aqueous solutions, but let us use the example of a salt in water. An increased concentration of the freezing point depressant lowers the freezing point temperature. This continues until we reach the concentration where salt and water form an eutectic solution. The freezing point is raised when the concentration becomes higher than the eutectic. The over-eutectic part of the freezing point curve is generally of no interest for this application. Note that only certain solutions have well-defined eutectic points.

37


Temp. A

0

tF

F

tS

K

tE

S

E

0

c0

cS cE Conc. Figure 2.10. Freezing point diagram (schematic)

Let us assume a solution with the concentration c0 and note what happens when it is cooled down from A to the freezing point F (c0, tF) and below that temperature. If the temperature is decreased below the freezing point and the process takes place in equilibrium, a separation of the mixture takes place. Ice crystals that ideally consist of pure water freeze out and are separated from the rest of the solution and the concentration of the freezing point depressant in the remaining solution rises as a consequence. When the temperature has been lowered so that it corresponds to K in Figure 2.10, there are ice crystals with the condition (c = 0, tS) as well as solution with the condition (cS, tS). A consequence of this is that the solution does not freeze to a solid mass when the freezing point is passed, but an ice slurry is formed. Only when the temperature goes down to the eutectic temperature, would the solution fully solidify. We need also to remember that in practice sub-cooling phenomena often occur. The first ice crystals are often not formed until the solution temperature falls to one or two degrees below the freezing point, as indicated by the freezing point curve. When some ice crystals have been formed, the continuation of the process seems easier to take place in equilibrium. The concentration of the remaining solution is given by a mass balance based on the condition that the mixture has an unchanged total amount of salt. Let us refer to the mass of pure ice by mI and the mass of solution by mS, the concentration of which is cS. Then the amount of salt is mS·cS. In the original solution the salt amount was evidently c0·(mI+mS). As the amount of salt has not changed, it follows that mScS = c0(mI+mS), which also can be written as mS(cS-c0) = mIc0. The ice concentration, or mass fraction of ice, cI, can then easily be calculated from: cI = mI/(mI+mS) = (cS-c0)/cS

(2.37)

Some extensive studies on ice slurry properties, such as those by Bel et al. (1996) and Guilpart et al. (1999), present ice concentration as a function of the temperature for various concentrations of the freezing point depressant substance, usually for ethyl alcohol-water. Suitable equations for ice slurries are also given in Kauffeld, et al. (1999) and Lottin, et al. (2000).

38


Figure 2.11 gives in the same manner ice concentration (mass fraction of ice) as a function of the temperature for various concentrations of the freezing point depressant substance for aqueous solutions of sodium chloride and ethyl alcohol. Property values are taken from CRC Handbook of Chemistry and Physics (1989) and an Excel programme based on equations and coefficients (not valid for low concentrations) in Melinder (1997b). Sodium chloride-water

Ethyl alcohol-water

0,6

0,6 0,55 Ice concentration [kg ice/ kg tot.] .

Ice concentration [kg ice/ kg tot.] .

0,55 0,5 0,45 0,4 0,35 0,3 0,25 0,2 0,15 0,1

0,5 0,45 0,4 0,35 0,3 0,25 0,2 0,15 0,1 0,05

0,05

0

0

-25 -25

-20 -15 -10 -5 Ice slurry temperature [°C]

-20

0

-15

-10

-5

0

Ice slurry temperature [°C] Initial conc. of additive [kg add./ kg tot.]

Initial conc. of additive [kg add./ kg tot.] 0,03 0,13

0,05 0,15

0,08 0,18

0,10

0,05

0,10

0,15

0,20

0,20

0,25

0,30

Figure 2.11. Ice concentration as function of temperature for two types of aqueous solutions In 2.5.2 and 2.5.3 the volume fraction of particles, c, is introduced, corresponding to a volumetric ice fraction, cI,vol = cI/((cI+(1-cI)ρI/ρCS), where cI is the mass ice fraction, ρI is the density of ice and ρCS is the density of the concentrated solution. The density, ρ, of ice slurries may be estimated with a mixing equation ρ = 1/[(cI/ρI)+(1-cI)/ρCS]. 2.5.2 VISCOSITY The shear viscosity of a concentrated suspension, taking into account the hydrodynamic interaction of particles, particle rotation, collision between particles, agglomerate formation, and so on, can be expressed by a theoretical equation in a power series (Thomas, 1965):

η * / η1 = 1 + a1c + a2c 2 ± a3c 3 ± ... .

(2.38)

The constant a1 is generally assumed to have the value determined by Einstein, a1 = 2.5 . Based on many experimental investigations of the viscosity of suspensions it was shown that the term 1 + 2.5 ⋅ c + 10.05 ⋅ c 2 accounts for over 97.5% of the values of the relative viscosity η * / η1 for volume fractions of particles, c, below 25% ( c < 0.25). For values of c > 0.25 satisfactory results were obtained by Thomas (1965):

39


η * / η1 = 1 + 2.5 ⋅ c + 10.05 ⋅ c 2 + ∆

(2.39)

where ∆ = A ⋅ e B⋅c , A = 0.0273, B = 16.6, η * is shear viscosity of the suspension, and η1 is shear viscosity of a matrix. For two-phase mixtures like ice-slurry the background shear viscosity η1 is the viscosity of the liquid solution. Viscosity values of many aqueous solutions can be obtained from Tables D1-11 in Melinder (1997a, b). Some literature data for the shear viscosity of solutions are also given in Tvsetkov (2001) and Vargaftic (1972). The following numerical values for predicting the reduced relative viscosity for c = 0.1 and c = 0.2 were defined as:

η * / η1 = 1 + 2.5 ⋅ 0.1 + 10.05(0.1) 2 + 0.00273 exp(16.6 ⋅ 0.1) = 1 + 0.25 + 0.1005 + 0.014 = 1.365 for c = 0.1 , and

η * / η1 = 1 + 2.5 ⋅ 0.2 + 10.05(0.2) 2 + 0.00273 exp(16.6 ⋅ 0.2) = 1 + 0.5 + 0.402 + 0.076 = 1.978 for c = 0.2 . Particularly important are questions pertaining to the non-Newtonian and viscoelastic behaviour of ice slurry. Many viscosity measurements of ice slurry as a function of the ice concentration have shown that ice slurry behaves like a Newtonian fluid for ice concentrations lower than 20% vol. (c < 0.2).

2.5.3 THERMAL CONDUCTIVITY The theory of the heat conduction phenomena through a random suspension of spherical particles in a matrix of uniform thermal conductivity has suggested that the volume fraction of the particles is small enough to make all interactions between the spheres negligible. For this kind of suspension an effective thermal conductivity k * in the Maxwell approach can be represented by, k * k 1 = 1 + 3βc

(2.40)

where: β = (α − 1) (α + 2), α = k 2 k1 , c is the volume fraction of the particles (spheres), k1 is the thermal conductivity of a matrix, and k 2 is the thermal conductivity of the spheres. However, the validity of equation (2.33) is restricted to a very small volume fraction of particles. To represent the actual behaviour of the thermal conductivity including the effect of interactions between spheres, the following approximation of k * has been proposed (Jeffrey, 1972). k * k 1 = 1 + 3β c + 3β 2 c 2 (1 + 2δ

α −1 ) α +2

(2.41)

The information about the coefficients δ , β and α is summarized in Table 2.4. For the iceslurry models the background conductivity k1 is the thermal conductivity of the liquid water solution or of another secondary refrigerant, and k 2 is the thermal conductivity of ice. The equation for ice by (Bobkov, (1977) of the form:

40


k 2 = k I = 2.22(1 − 0.0015ϑ ) has been used for Table 2.4. Here k I is given in Wm-1K-1, and ϑ in °C.

α β δ

Table 2.4. Coefficients in Eq. (2.40) for k * k 1 0.1 0.5 1.0 2.0 5.0 -0.429 -0.200 0 0.25 0.571 0.21 0.21 0.21 0.22 0.22

(2.42)

50.0 0.942 0.25

Thermal conductivity values of many aqueous solutions can be obtained from Tables D1-11 in Melinder (1997a,b). The thermal conductivities k1 of some actual water solutions are given in Tvsetkov (2001) and Vargaftic (1972). Using Table 2.4 it is possible to calculate α (which varies from about 17 to 4) and estimate k * k 1 according to Eq. (2.41). For example, if α is assumed to be equal to 5, the values of β and δ from Table 2.4 are as follows: β = 0.571, δ = 0.22. This leads to the relative thermal conductivity value of:

k * k 1 = 1 + 3 ⋅ 0.571 ⋅ 0.1 + 3(0.571) 2 (0.1) 2 (1 + 2 ⋅ 0.22

5 −1 ) = 1 + 0.1713 + 0.00978 ⋅ 1.25 = 1.183 5+2

where c = 0.1 .

2.5.4 ENTHALPY AND ENTHALPY PHASE DIAGRAMS OF AQUEOUS SOLUTIONS The secondary fluid flow rate required to achieve a cooling capacity of Q& (in kW) in an indirect system with a single-phase fluid can be calculated by the following relation: Q& = m& ⋅ c p ⋅ ∆ϑ = V& ⋅ ρ ⋅ c p ⋅ ∆ϑ

(2.43)

For an ice slurry system, it is more suitable to apply the relation: Q& = m& ⋅ ∆h = V& ⋅ ρ ⋅ ∆h

(2.44)

Both sensible heat and latent heat of melting are included in the enthalpy difference, ∆h. In these relations, m& is the fluid mass flow rate, V& is the volumetric flow rate, ∆ϑ is the temperature change between the fluid entering and exiting the cooling unit, ρ is the fluid density and cp is its specific heat. The “heat transport capability" of ice slurries in equilibrium is proportional to the enthalpy difference, ∆h, obtained for a certain temperature change between the fluid entering and exiting the cooling unit. It is much higher for an ice slurry than for mono-phase aqueous solutions, as there is a benefit from the latent heat of melting of ice crystals, which reduces the fluid flow rate required for a given cooling capacity and also the temperature change. This “heat transport capability” depends partly on the specific heat of the fluid, but more on the amount of ice that will melt, i.e., on the ice concentration of the ice slurry that enters the cooling unit (Melinder, 2002b).

41


A way to visualize the benefits from the latent heat or enthalpy difference in the melting process of ice may be achieved by studying an enthalpy-phase diagram of the aqueous solution used. The amount of heat exchanged in the freezing process can be estimated if we have access to enthalpy values, for instance from such enthalpy-phase diagrams with some added features. Such diagrams can help us estimate at what additive concentrations and temperatures we will get the most benefit. Such enthalpy-phase diagrams are given for seven aqueous solutions in Figures 2.13 to 2.19. These diagrams are taken from Melinder (2002a) where also the enthalpy difference between certain temperatures and for various freezing points is given. For calculation purposes we choose to view an ice slurry solution as consisting of small ice crystals of pure water that freeze out, and the rest of the solution with a higher concentration of the freezing point depressant. In order to estimate enthalpy values of an aqueous solution with ice particles we need freezing point data, values of specific heat as well as enthalpy values of ice and heat of mixing of the solution. The heat of mixing can, in the diagrams, be seen as the variation in enthalpy values with the concentration of a reference isothermal line (ϑR = 0°C, 10°C or 25°C). The enthalpy of the ice slurry, h, at point K in Figure 2.12, can be expressed by the following function (see Figure 2.12): h = h(K) = hI (ϑCS)·cI + hCS(cCS, ϑCS)·(1 – cI) where

hI(ϑCS) = hH – hD = hH – hG + (hG – hD)

(2.45) (2.46)

ϑCS

hCS(cCS, ϑCS) = h0,R + ∆hM(cCS, ϑR) + ∫ (c p ·dϑ )

(2.47)

ϑR

The enthalpy difference between D and G, the heat of melting of water, is hD-hG = 332.4 kJ/kg. The enthalpy of ice at various temperatures shown in Figures 2.13-2.19 has been estimated using Eq. 2.36. In Eq. 2.47, the enthalpy of water at the reference temperature, h0,R is defined as: h0,R (0°C) = 0 kJ/kg and h0,R (25°C) ≈ 104.8 kJ/kg. Point I in Figure 2.12 corresponds to the heat of mixing value, ∆hM(cCS, ϑR = 0°C). The sources of heat of mixing values, ∆hM, and the reference temperature, ϑR, for each diagram are as follows: Figures 2.12 and 2.13 - Sodium chloride (ϑR = 0°C): ∆hM from Bošnjakovic (1961); Figure 2.14 - Ethylene glycol (ϑR = 25°C): ∆hM from Heats of Mixing Data Collection (1986); Figure 2.15 - Propylene glycol (ϑR = 25°C): ∆hM from Heats of Mixing Data Collection (1986); Figure 2.16 - Ethyl alcohol (ϑR = 0°C): ∆hM from Landolt-Börnstein, (1976); Figure 2.17 - Ammonia (ϑR = 10°C): ∆hM from Landolt-Börnstein, (1976); Figure 2.18 - Potassium formate (ϑR = 25°C): ∆hM from Norsk Hydro Research Center (2001); Figure 2.19 - Calcium chloride (ϑR = 0°C): ∆hM from Bošnjakovic (1961). To illustrate this type of diagrams, let us examine Figure 2.12 for a mixture of sodium chloride-water. The concentration, cA, refers here to the concentration of pure sodium chloride in water. The vertical axis gives the enthalpy, h, expressed in kJ/kg mixture. The freezing point curve is represented in the figure by the bold line, htF, or D – E, where E is the eutectic 42


point. The diagram also shows some (thin) isothermal lines (20°C, 10°C, 0°C, –2°C, –4°C, etc.). Let us follow as an example the cooling process from point A where ϑA = 0°C for a mixture with the freezing point temperature ϑF = –5°C. The additive concentration is then cA ≈ 0.079 (7.9% NaCl by wt). The temperature decreases when heat is removed from the mixture and the freezing point is passed at point F and it has reached ϑK = –10°C at point K. Small ice particles can be formed in an ice generator device during such cooling below the freezing point of a mixture with lower concentration than the eutectic. As the ice slurry solution can be viewed as consisting of two components: i) ice crystals of pure water that freeze out and the rest of the solution with a higher concentration of the additive, the point K thus represents a condition of mixture between pure ice of –10°C (at point H), and ii) a concentrated solution of the condition at C (cCS ≈ 0.141, ϑF = –10°C). The amount of heat that has to be removed for each kg of original solution can be seen as the enthalpy difference hA-hB ≈ 176 kJ/kg. Of this enthalpy difference only 10% is from the cooling of the liquid from 0°C to –5°C (between A and F), while 90% is from the cooling from –5°C to –10°C between F and K where the freezing of ice particles takes place (see dashed line A - F - K). This illustrates well the potential for ice slurries, e.g., for cooling cabinet applications, and the potential is greater for even lower additive concentrations and at temperatures just below the freezing point. The lines for ice concentration are obtained by dividing each two-phase isothermal line in parts between the freezing point curve and the corresponding enthalpy value of ice. The ice concentration that can be expected at K is given in the figure as cI ≈ 0.43 (or 43% ice) (see Melinder, 2001). The enthalpy lines in Figures 2.13-2.19 connecting the temperatures 2, 5 and 10 Kelvin below the freezing points, are marked htF-2, htF-5, and htF-10. To see how they have been made, note in Figure 2.12 the dashed lines for htF -htF-5 for the freezing points tF (ϑF) = –3°C, –5°C, –7°C and –10°C (the line for –5°C continues up to 0°C). These enthalpy lines can help us estimate the equilibrium potential of performance of the aqueous solution when used as an ice slurry. A large enthalpy difference indicates a big potential for its “heat transport capability”.

43


100

20°C

100

.20°C

20°C

20°C

10°C

10°C

0°C

0°C -5°C -10°C

Liquid only 50

10°C

D 0

0°C

-50

50

0°C

A F

-2°C

htF

-4°C -6°C

-10°C

cI = 0,2

L

0

-10°C

-2°C -14°C -20°C

-50

E

cI = Ice conc.

-100

htF-5

cI = 0,4

Enthalpy, h [kJ/kg] .

Enthalpy, h [kJ/kg] .

10°C

-21°C

-150 K -200

cI = 0,6 Eutectic area ≈ -21°C cI = 0,8

-6°C -8°C

-10°C -15°C

cI = 0,2

E

htF-2 -20°C

-100

cI = Ice conc. cI = 0,4

-21°C

htF-5

-150

htF-10 cI = 0,6

-200

-250

htF -4°C

Eutectic area ≈ -21°C

-8°C M

-300

-250

cI = 0,8 G

-21°C

Solid area

-350 H I -400

-300 -21°C

Melinder, 2004

Melinder, 2004

-350 0

0,05

0,1

0,15

0,2

0,25

Concentration [kg NaCl / kg solution]

Figure 2.12. Schematic enthalpy phase diagram (NaCl - H2O)

0

0,05 0,1 0,15 0,2 Concentration sodium chloride, (cA = cNaCl)

0,25

Figure 2.13. Enthalpy phase diagram for sodium chloride - water


100

100 20°C

Melinder, 2002

Melinder, 2002

20°C

20°C 10°C

-2°C

-4°C

htF

-5°C

htF-2

cI=Ice conc.

-100

cI=0,4

-50

-15°C

-20°C

htF-5

-150 -25°C

cI=0,2

-5°C -4°C htF -6°C -8°C -10°C -5°C

cI=Ice conc.

-100

cI=0,4

htF-2 htF-5

-150

-10°C -15°C

-20°C -25°C

htF-10 -200

0°C -2°C

-10°C

-6°C -8°C -10°C

10°C

0°C

0

0°C -5°C

-50 cI=0,2

10°C

10°C

0°C

0

Enthalpy, kJ/kg

50

Enthalpy, kJ/kg

50

-30°C

cI=0,6

-200

htF-10

cI=0,6

-30°C

-35°C -40°C

-250

-35°C -40°C

-250 cI=0,8

cI=0,8 -300

-300

-350

-350 0

0,05

0,1

0,15

0,2

0,25

0,3

0

0,35

0,2

0,3

0,4

Concentration propylene glycol, (cA = cPG)

Concentration ethylene glycol, (cA = cEG)

Figure 2.14. Enthalpy phase diagram for ethylene glycol – water

0,1

Figure 2.15. Enthalpy phase diagram for propylene glycol – water

45


100

100 Melinder, 2002

Melinder, 2002

20°C

50

50

20°C

30°C

10°C

10°C 10°C

0

cI=Ice conc.

-50

htF -8°C

Enthalpy, kJ/kg

-100

-5°C

-6°C

-2°C

0°C

-5°C

-4°C

cI=0,2

-10°C

-10°C

htF-2

-15°C

cI=0,4

-150

-20°C

htF-5 -200

20°C 0°C

-2°C

-50

Enthalpy, kJ/kg

0

0°C

cI=0,6

-250

-5°C

-100

cI=Ice conc.

-10°C

cI=0,4

-150

0°C

htF

-8°C

-10°C

htF-2

-15°C

htF-5

cI=0,6

-250

-30°C

cI=0,8

-5°C -6°C

cI=0,2

-200

-25°C

htF-10

10°C

-4°C

-20°C

htF-10

-35°C

-25°C

cI=0,8

-300

-300

-350

-350

-30°C -35°C

0

0,05

0,1

0,15

0,2

0,25

0,3

Concentration ethyl alcohol, (cA = cEA )

Figure 2.16. Enthalpy phase diagram for ethyl alcohol – water

-40°C

0

0,02

0,04

0,06

0,08

0,1

0,12

Concentration ammonia, (cA = cNH3)

Figure 2.17. Enthalpy phase diagram for ammonia - water

46

0,14


100

100 Melinder, 2002

20°C 10°C

0

0°C

0°C -5°C

-2°C

-4°C

-6°C

Enthalpy, kJ/kg

-50 cI=0,2

-5°C

htF

10°C

-10°C

20°C

-8°C-10°C

htF-2

-50

-15°C -20°C

htF-5 cI=0,4

-25°C

-150 htF-10 -200

30°C

0

cI=Ice conc.

-100

50

10°C

Enthalpy, kJ/kg

50

Melinder, 2002

-2°C

cI=0,2 -100

0°C -4°C

htF

cI=Ice conc. -5°C -6°C

-8°C

htF-2 -10°C

cI=0,4

-150

10°C

-15°C

-200

-35°C

htF-5

cI=0,6

-40°C

-250

htF-10

-250 cI=0,8 -300

-350

-350 0,1

0,15

0,2

0,25

0,3

0

Concentration potassium formate, (cA = cKFo )

Figure 2.18. Enthalpy phase diagram for potassium formate - water

0,04

-20°C -25°C

cI=0,8

-300

0,05

-5°C -10°C

-30°C

cI=0,6

0

0°C

30°C

0,08

0,12

0,16

0,2

Concentration calcium chloride , (cA = cCaCl2)

Figure 2.19. Enthalpy phase diagram for calcium chloride - water

47


2.6 Safety, ecology and corrosion aspects of aqueous solutions by Cecilia Hägg and Åke Melinder

2.6.1. GENERAL CHARACTERISTICS OF ADDITIVES USED AS AQUEOUS SOLUTIONS A number of characteristics relating to safety, ecology and corrosion of aqueous solutions need consideration. Some important aspects are flammability, toxicity, acidity, corrosiveness and material compatibility. A study on some of these general characteristics of the additives in aqueous solutions has been done and some results are listed in Table 2.5. A general explanation of the symbols is given after the table. Comments are then given for each type of aqueous solution followed by some remarks on corrosion behaviour and material compatibility. These general characteristics can be viewed as valid for single-phase as well as two-phase ice slurry applications though the concentrations needed for ice slurry are lower than for single-phase.

Calcium Chloride

Potassium Acetate

Potassium Formate

Potassium Carbonate

Flash point

Ammonia

Explosion limit

Methyl Alcohol

LD 50 oral rat

Ethyl Alcohol

WGK

Propylene Glycol

Health Flammability Reactivity Hazard marks Poison Class CH

Ethylene Glycol

Table 2.5. General characteristics of the listed additives

1 1 0 Xn

0 1 0 -

0 3 0 F

1 3 0 F, T

3 1 0 C, N

Xi

1 0 0 -

-

2 0 0 Xn

4

F

F

3

-

F

5

-

4

1

2

1

1

0

1

5628

350

1000

32050

5500

1870

5.5-44

-

-

-

-

-

-

-

-

>250

-

-

1 4700 1.812.8 116

1 1 194006200 36000 2.43.5-15 17.4 99 12

2.6.2. GENERAL EXPLANATION OF SYMBOLS The values for Health, Flammability and Reactivity range from 0 to 3. For instance, flammability 0 means that the chemical is not flammable at all and flammability 3 means highly flammable. Descriptions of the Hazard marks are: Xn means harmful, Xi means irritating, F means flammable, T means toxic, C means corrosive, and N means dangerous for the environment. Poison class CH is a classification of the chemicals according to Swiss toxicity law. Descriptions of the symbols are: 3 means strong toxins, 4 means substances and products that must be considered harmful, 5 means substances and products with a low hazard potential and F means not subject to toxicity classification.

48


WGK is a classification, according to the national regulation of the Federal Republic of Germany, of the degree of water pollution. The denominations are: WGK 1 means slightly water polluting substance and WGK 2 means water polluting substance. LD 50 oral rat is a toxicological value of lethal dose. It states the dose in mg of substance per kg (of animal weight) that kills 50% of the laboratory test animals. The greater the LD50 value, the lower the toxicity of a substance. Substances, with an LD50 value greater than 2000 mg/kg are not classified as harmful. The LD50 values given by manufacturers are often those obtained from literature for pure substances, and do not include the effects caused by the inhibitors and stabilizers (Lethal dose for human; see 2.6.3). Explosion limit is given in volume percent and flash point is measured in ºC, both for pure substances. The above information is mainly based on Merck Chemical Databases and Hazardous Substances Databank (HSB).

2.6.3. COMMENTS ON EACH TYPE OF AQUEOUS SOLUTION Ethylene glycol (EG) is highly toxic for humans. The minimum lethal dose for humans is 11.5 ml/kg or approximately 100 ml concentrated glycol in an adult. Short-term exposure can result in irritation to eyes, skin and respiratory tract. Repeated or long-term exposure can bring about effects on the central nervous system and eyes. EG is slightly flammable. EG has good thermo-physical properties for cooling applications. Propylene glycol (PG) is slightly water polluting and practically non-toxic to humans. The minimum lethal dose for human adults is more than 15 times greater than that of ethylene glycol. Propylene glycol has a low fire hazard when exposed to heat or flame. Propylene glycol without suitable corrosion inhibitors can show a rather low pH value that might affect the corrosion potential. PG has a very high viscosity at low temperatures. Ethyl alcohol (ethanol) is highly flammable and is dangerous when exposed to heat and flame. Vapours may form explosive mixtures with air. Most vapours are heavier than air. Ethyl alcohol has a very low surface tension, which may cause leakage in sealing devices and foaming. Mixtures of ethyl alcohol and water are considered non-flammable at concentrations normally used as ice slurry. Classified as a substance with a fire risk at higher concentrations because of the low flash point. May cause intoxication if consumed, denaturants added in many countries. Exhibits high viscosity at low temperatures. Methyl alcohol (methanol) is listed in Table 2.5 but should not be used in commercial applications. It is highly toxic and may be fatal if inhaled, ingested or absorbed through skin. Ammonia has a conspicuous smell, can cause strong irritation to eyes, skin and the respiratory tract. Death can result if rapid escape is not possible. Swallowing liquid ammonia is corrosive to mouth, throat and stomach. Exposures to high concentration can cause temporary blindness and eye damage. Ammonia is highly toxic to aquatic organisms. Ammonia vapour is lighter than air and there is a flammability risk. In spillage or disposal most of the quantity evaporates into the atmosphere where it quickly decomposes. Calcium chloride is not toxic, but causes irritation to nose and throat when inhaled and to eyes when in contact.

49


Potassium acetate has a low hazard potential. Inhalation may cause mild irritation. The pH values given for commercial products of potassium acetate are 8-11 (see also 2.6.4). Potassium formate does not cause any skin, eye or respiratory irritation. The pH values given for commercial products of potassium formate are 9 – 12 (See also 2.6.4).

2.6.4. CORROSION BEHAVIOUR AND MATERIAL COMPATIBILITY Ethylene glycol, propylene glycol and ethyl alcohol: glycols seem to cause less general corrosion on carbon steel than alcohols. The corrosion potential for these solutions is comparatively the same as for the water the glycol has been mixed with. This means that almost the same construction materials can be used for these solutions as the system for water. However, after a long time use, the glycols tend to become slightly acidic because of oxidation or decomposition, which implies an increase in the corrosion potential. Ammonia is not compatible with copper. Ammonia is not compatible with elastomers made from 100% soft rubber, isoprene (IR), natural rubber (GRS), polyurethane (AU) and silicon rubbers (Schweitzer, 1996). Calcium and sodium chloride based aqueous solutions show great signs of corrosion on carbon steel when oxygen is present. They can cause pitting and crevice corrosion, as the spot-like corrosion of stainless steel in seawater or sodium chloride solution. Chlorides require buffering and at least two strong inhibitors, which have bad impact on the environment. Corrosion inhibitors with chromates may cause a health risk. For chloride-based solutions, it should be sufficient to use the same construction materials as for seawater. Calcium chloride is not compatible with elastomers made from 100% soft rubber (Schweitzer, 1996). Potassium acetate, potassium formate (and mixtures of these): parts containing zinc, zinc alloys (such as galvanised surfaces) or aluminium should be avoided in systems with potassium formate or potassium acetate solutions that have high pH-values (see 2.6.3). However, the corrosion of aluminum by these organic salt solutions can be reduced by means of inhibitors. Potassium acetate is not compatible with elastomers made from 100% polyether-urethane (EU) (Schweitzer, 1996).

Literature cited in Chapter 2

1. Aittomäki, A., Kianta, J, Indirect Refrigeration Systems Design Guide Book, Tampere, 2003. 2. Allen, T.: Particle Size Measurement, Fourth Edition, Chapman and Hall, ISBN 0 412 35 070, 1992. 3. ASHRAE, ASHRAE handbook fundamentals, ISBN 1-883413-88-5, 2001. 4. BASF, Glythermin®, Glycol-based heat- transfer fluids for heating and cooling system. Brochure. 5. Bel, O.: Contribution à l’étude du comportement thermo-hydraulique d’un mélange diphasique dans une boucle frigorifique à stockage d’énergie. Ph.D.-thesis, No. 96 ISAL 0088, L’Institut National des Sciences Appliquées de Lyon, France, 1996.

50


6. Bel, O., Lallemand, A. Study of a two-phase secondary refrigerant. 1. Intrinsic thermophysical properties of an ice slurry, Int. Journal of Refrigeration, IIR/IIF, Paris, , 22 p.164-174, 1999. 7. Bobkov V.A., Production and Application of Ice, Foods Industry Publ. House, Moscow, p. 232, 1977. 8. Bošnjaković, F., Technische Thermodynamik, II Teil, Band 12, in Wärmelehre und Wärmevirtschaft in Einzeldarstellung, Dresden/Leipzig, 1961. 9. CRC Handbook of Chemistry and Physics (edited by Weast, R.C.), 1989. 10. Egolf, P. W., Brühlmeier, J., Özvegyi, F., Abächerli, F., Renold, P.: Kältespeicherungseigenschaften und Strömungsverhalten von binärem Eis. Forschungsbericht zuhanden der Stiftung zur Förderung des Zentralschweizerischen Technikums, June 1996. 11. Egolf, P. W., Frei, B.: The Continuous-prop erties Model for Melting and Freezing applied to Fine-crystalline Ice Slurries. First IIRWorkshop on Ice Slurries, Yverdon-lesBains, Switzerland, p. 25-40, May 1999. 12. Egolf, P. W., Sari, O., Meili, F., Moser, Ph., Vuarnoz, D.: Heat Transfer of Ice Slurries in Pipes. First IIR Workshop on Ice Slurries, Yverdon-les-Bains, Switzerland, p. 106-123, May 1999. 13. Egolf, P.W., Vuarnoz, D., Ata-Caesar, D., Kitanovski, A.: Front Propagation of Ice Slurry Stratification Processes. Fifth IIR Workshop on Ice Slurries, Stockholm, Sweden, May 2002. 14. Fletcher, N.H.: The Chemical Physics of Ice, Cambridge University Press, 1970. 15. Fournaison, L., Chourot, J.M., Guilpart, J.: Different ice mass fraction measurement methods, Fourth IIR Workshop on Ice Slurries, Osaka, Japan, 2001. 16. Fukusako, S., Kozawa, Y., Yamada, M., Tanino, M.: Research and Development Activities on Ice Slurries in Japan. First IIR Workshop on Ice Slurries, Yverdon-les-Bains, Switzerland, p. 83-105, May 1999. 17. Guilpart J., Fournaison L., Ben Lakhdar, M.A. Calculation method of ice slurries thermophysical properties - application to water/ethanol mixture, Int. Congress of Refrigeration, IIR/IIF, Sydney, 1999. 18. Hagiwara, T.; Hartel, R. W., Effect of Sweetener, Stabilizer, and Storage Temperature of Ice Recrystallization in Ice Cream. Journal of Dairy Science, vol. 79: 735-744, 1996. 19. Handbook of Thermodynamic Tables and Charts; Raznjevic, K., 1976. 20. Handbuch der Kältetechnik, VI/B (edited by Steimle, F.), 1988. 21. Hansen, T.M, Radosevic, M.; Kauffeld, M.: Behavior of Ice Slurry in Thermal Storage Systems, ASHRAE Research Project 1166, published 2002. 22. Hazardous Substances Databank (HSB), Database of the National Library of Medicine’s TOXINET system, http://toxnet.nlm.nih.gov, 06/10/02. 23. Heats of Mixing Data Collection, 1. Binary Systems, Christensen, J. J, Gmehling, J., Rasmussen, P., Weidlich, U., 1986. 24. Hobbs, P.V.: Ice Physics, Oxford University Press, 1974. 25. Inada, T; Lu, S. S.; Grandum, S.; Yabe, A.; Zhang, X.,. Microscale Analysis of Effective Additives for Inhibiting Recrystallization in Ice Slurries Second IIR .Workshop on Ice Slurries. Paris, France, May 2000. 26. Jeffrey D.J., Conduction through a random suspension of spheres, Proc. Roy. Soc., London A, vol. 335: p. 355-367, 1972. 27. Kang, C.; Okawa, S., Recent Study on Ice Melting and Water Freezing Using Molecular Dynamics Method.1st report: Recent Study on Molecular Dynamics Method for Water/Ice Behavior. Transactions of the JSRAE 16(1): 1-10, 1999.

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28. Kauffeld, M., Christensen, K. G., Lund, S., Hansen, T. M.: Experience with Ice Slurry. First IIR Workshop on Ice Slurries, Yverdon-les-Bains, Switzerland, p. 42-73, May 1999. 29. Kawashima, T., Saqsaki, M., Takahashi, H.: Experimental Studies of Snow-water Mixture Flows in Horizontal Pipes. Twelfth Int. Conf. on Slurry Handling and Pipeline Transport, Hydrotransport 12, Mechanical Engineering Publications Limited, London, 1993. 30. Kossel, Stransky or Burton, Carbera and Frank (BCF-model), Chapter 2 in: Myerson, A.S.: Handbook of Industrial Crystallization, Butterworth-Heinemann, 1993. 31. Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology, Group IV, Vol. 2. Heats of Mixing and Solution, 1976. 32. List, R.: Private Communication. 2000. 33. Lock, G.S.H.: The growth and decay of ice, Cambridge University Press, 1990. 34. Lottin, O., Epiard, C. Thermodynamic properties of some currently used water - antifreeze mixtures when used as ice slurries, Eighth Int. Refrigeration, Purdue, USA, p.391-398, 2000 35. Melinder, Å.: Köldbärare för värmepumptillämpningar, Rapport R114:1985, Byggforskningsrådet, Stockholm 1985. 36. Melinder, Å., Berendson, J., Granryd, E., Köldbärare för värmepumpstillämpningar, Rapport R18:1989, Byggforskningsrådet, Stockholm, 1989. 37. Melinder, Å., Thermophysical properties of liquid secondary refrigerants, Tables and Diagrams for the Refrigeration Industry, Paris, IIF/IIR, 1997. 38. Melinder, Å. Thermophysical properties of liquid secondary refrigerants, Charts and Tables, Stockholm, Swedish Society of Refrigeration, 1997. 39. Melinder, Å., Enthalpy-phase diagrams as an aid in estimating the performance of ice slurries, Fourth IIR Workshop on Ice Slurries, Osaka, Nov. 2001. 40. Melinder, Å., Enthalpy-phase diagrams of aqueous solutions for ice slurry applications, Fifth IIR Workshop on Ice Slurries, Stockholm, May 2002a. 41. Melinder, Å., Influence of temperature on latent heat benefits in ice slurry applications, Zero leakage – Minimum Charge, IIF/IIR, Stockholm, 2002b. 42. Melinder, Å., Estimating the ”transport capability” of ice slurries with the aid of enhanced enthalpy-phase diagrams, Fifth Gustav Lorenzen Conference on Natural Fluids, IIF/IIR, Guangzhou, 2002c. 43. Merck, Merck Chemical Database, www.merck.de, 06/10/02. 44. Myerson, A.S; Ginde in Myerson, A.S.: Handbook of Industrial Crystallization. Butterworth-Heinemann series in chemical engineering, 1992. 45. Norsk Hydro Research Centre, Internal report, 2001. 46. Nývlt: The Kinetics of Industrial Crystallization, Elsevier, 1985. 47. Pronk, P., Infante Ferreira, C.A., Witkamp G.C.: Effects of Long-Term Ice Slurry Storage on Crystal Size Distribution. Fifth IIR Workshop on Ice Slurries, Stockholm, Sweden, May 2002. 48. Sari, O., Meili, F., Vuarnoz, D., Moser, Ph., Egolf, P. W.: Thermodynamique d’un écoulement de coulis de glace dans un tube à flux de chaleur constant. 2000 EUREKA FIFE, research report No. 6, March 2000. 49. Sari, O., Meili, F., Vuarnoz, D., Moser, Ph., Egolf, P. W.: Thermodynamics of Moving and Melting Ice Slurries. Second IIR Workshop on Ice Slurries, Paris, France, May 2000. 50. Schweitzer, Philip A., Corrosion engineering handbook, ISBN 0-8247-9709-4, New York, 1996. 51. Thomas D.G., Transport characteristics of suspension, J. Colloid. Sci., vol. 20: p. 267277, 1965. 52. Tsvetkov O.B., Laptev Ju. A., Kolodiaznaia V.S., One-and two-phase refrigerating liquid media, Kholodilnaja Teknika, no. 10: p. 8-12, 2001.

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53. Turian, R.M. et al: Settling and Rheology of Suspensions of Narrow-Sized Coal Particles. AIChE Journal, Vol. 38, No. 7, pp. 969-987, 1992. 54. Turnbull, D.; Fisher, J.C.: Rate of nucleation in condensed systems. Journal of Chemical Physics 17: p. 71-73, 1949. 55. Vali, G.: Principles of Ice Nucleation, in: Lee, R.E.; Warren, G.J.; Gusta, L.V.: Biological Ice Nucleation and its Application, APS Press, 1995. 56. Vargaftic, N.B., Thermophysical properties of gases and liquids. Handbook, Nauka Publ. House, Moscow, 1972. 57. Vuarnoz, D., Sari, O., Egolf, P.W.: Correlations between Temperature and Particle Distributions of Ice Slurry in a Storage Tank. Fourth IIR Workshop on Ice Slurries, Osaka, Japan, Nov. 2001. 58. Washington, C.: Particle Size Analysis in the Pharmaceutics and Other Industries, Ellis Horwood Publishing Company, 1993. 59. Yazaki, T.; Okawa, S.; Saito, Akio: “Molecular Dynamics Simulation Study of Ice Crystal Growth”, Trans. of the JSRAE, Vol. 14, No. 2, pp. 179-190, 1997. 60. Zwieg, T.; Cucarella, V.; Worch, H.: Novel bio-mimetically based ice-nucleating coatings for ice generation., Fifth IIR Workshop on Ice Slurries, Stockholm, May 2002.

53

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CHAPTER 3.

FLUID DYNAMICS

The operation of ice slurry systems aimed at the transfer of mass and heat between system components, depends on the governing principles of fluid dynamics. Without a thorough understanding of process hydrodynamics, the design of any ice slurry system becomes an art, specific to the particular application. Fluid dynamics are involved in pumping and transportation, sedimentation, mixing and separation, filtration and fluidized bed operations. Unlike gases, which are nature’s simplest substances, liquids are more complex in behaviour, and hence, cannot be described by a simple thermodynamic relation. If this is true for simple, single-component liquids, the situation is even more complex for ice slurry. Ice slurry is a mixture of a liquid phase (which again may consist of several components) and solid particles in the form of ice, which even grow and decay during operation. This chapter covers the rheology of ice slurry, i.e. the deformation of the fluid under the action of stress, flows in tubes and their patterns, pressure drop and the time-dependent behaviour of ice slurry due to the growth and decay of the ice particles.

3.1 Rheology by Christian Doetsch, Andrej Kitanovski, Torben Hansen and Beat Frei (see specific list of symbols in Appendix 3) Homogeneous suspensions are frequently described as single-phase, isotropic fluids with modified rheological behaviour. But instead of the viscosity of the liquid (ηL), a modified socalled effective viscosity of the suspension (ηeff) is used. Many different models have been used for the suspension viscosity determination. Most of them essentially extend the work of Einstein on spheres and his equation for viscosity (C < 0.01) (Barnes, 1989): ηeff = η L (1 + 2.5 ⋅ C )

(3.1)

where C is the concentration (or volume fraction) of the solid phase in a solid-liquid mixture. In eqn. 3.1, there is no effect of particle size, nor of particle position, because the theory neglects the effects of other particles. Several other models for viscosity determination have been developed, as shown in Table 3.1. The most popular determination of the suspension viscosity, which comprises not only the concentration of the solid phase, but also the interaction between the solid particles, is based on the well-known Thomas equation (Thomas 1965):

(

η eff = η L 1 + 2.5C + 10.05C 2 + 0.00273e16.6C

55

)

(3.10)


Table 3.1. Formulae for viscosities of Newtonian suspensions as a function of the volume fraction C of the solid phase (Darby 1986) ⎛ 1 + 0.5 ⋅ C − 0.5 ⋅ C 2 Guth and η eff = η L ⎜⎜ 2 Simha ⎝ 1 − 2 ⋅ C − 9 .6 ⋅ C

Vand

⎞ ⎟ ⎟ ⎠

⎛ 2. 5 ⋅ C ⎞ ⎟ ⎝ 1 − 0.609 ⋅ C ⎠

η eff = η L ⋅ exp⎜

⎛ 2. 5 ⋅ C + 2. 7 ⋅ C 2 ⎞ ⎟ ⎟ ⎝ 1 − 0.609 ⋅ C ⎠

η eff = η L ⋅ exp⎜⎜

⎛ 2. 5 ⋅ C ⎞ ⎟ ⎝1 − K ⋅C ⎠

Mooney

η eff = η L ⋅ exp⎜

Simha

η eff = η L ⎜⎜1 + 1.5 ⋅ C ⎜1 +

⎛

⎛

⎝

⎝

0.75 < K < 1.5

⎞ 25 ⋅ C ⎞ ⎟.......⎟⎟ 3 4f ⎠ ⎠

1 1000 a relation is given by Hanks (1996):

(

λ = λαL + λTα

)α

1

(3.59)

where the laminar component, λL, is calculated by using an equation from Table 3.4. The turbulent component (term), λT, in Eq. (3.59) is calculated by:

λT =

4 ⋅ 10 a Re

0.193

[

(

a = −1.378 ⋅ 1 + 0.14 ⋅ exp − 2.9 ⋅ 10 −5 ⋅ ReB

)] m = 1.7 + 40000 Re

(3.60)

B

Calculations by Kitanovski (2002) show that Eq. (3.58) may also be useful in combination with the Casson model.

72


3.3.2 STATE OF THE ART OF ICE SLURRY PRESSURE DROPS Earlier investigations did not consider rheological models as a basis for the friction factor evaluation of laminar and turbulent ice slurry flows. Usually only empirical correlations were determined. Snoek (1993) did not notice large pressure drop differences in flows with ice concentrations Cr < 0.1. However, higher ice concentrations resulted in higher pressure drops. Minimal pressure drops occur at velocities at which the transition between heterogeneous flow and a flow with a moving bed occurs. Winters and Kooy (as reported by Snoek, 1993) investigated the pressure drop of ice slurry at velocities above 3 m/s and ice concentrations over 20%. They did not observe a large difference between the pressure drop of the ice slurry and that of the carrier fluid (water). However, higher pressure drops are observed with ice slurry than with pure water, at velocities lower than 1 m/s. Larkin and Young (as reported by Snoek, 1993) as well as Sellgren (1986) discovered that at velocities in the range 1.0 to 1.5 m/s, the friction factor of the ice slurry (dp = 1.2 cm and Cr < 0.15) is close to that of pure water. For lower velocities, Sellgren (1986) observed a separation of two phases and an increase in the pressure losses. Larkin and Young (as reported by Snoek, 1993) performed experiments at ice concentrations 0 < Cr < 0.25, but did not report large alterations in the results. At higher velocities the pressure drop rapidly increases. They also observed a separation of two phases at lower velocities. Knodel et al. in France (as reported by Snoek 1993) reported on reduced pressure drops at higher ice concentrations. Their ice slurry contained large ice particles (3-6 mm), the velocities varied from v = 1.5 to 3.5 m/s and the ice concentration was 0 < Cr < 0.15. Takahashi (1993) also conducted experiments on pressure drops of ice slurry, which contained pure water and crushed ice (dp = 12.5 mm) at a concentration of Cr = 0.25. The results showed higher pressure drops for ice slurry than for water at normal operational conditions. At high velocities the pressure drop of ice slurry was even lower than that of water. This could be explained by a drag reducing effect. Early investigations showed large deviations in experimental data. The ice particles in these experiments were rather large, so the results cannot be applied to modern fine-crystalline ice slurries. Today ice particles in ice slurry systems have a characteristic size between dp = 0.1 to 1 mm. There are also different additives in use nowadays that were not used previously. Frei and Egolf (2000) observed a change in the pressure drop as a function of time during pressure drop measurement. Even when the influence of a super-cooled or preheated carrier fluid was eliminated, the pressure drop decreased with time to an asymptotic value, now recognised as the time dependent behaviour of the shape and size of ice crystals. During the last few years numerous researchers performed a large number of experiments to obtain pressure drop data. Some of their work has been reported in the following references: Knodel et al. (2000), Chaer et al. (2000/2001), Frei and Egolf (2000), Jensen et al. (2000), Tassou et al. (2001), Guilpart et al. (1999), Hansen and Kauffeld (2000), Doetsch (2001), Dong Wong Lee et al. (2002), Reghem (2002), Bel (1996), Christensen et al. (1997), Bellas et al. (2002), and Egolf et al. (2001). Some of them presented empirical equations, while others gave semi-empirical equations, which were based on rheological models, mostly the Bingham or the Casson model. Even in recent experiments on pressure drops, there is a large difference between the individual pressure drop measurements and the corresponding shear stresses (Frei et al. 2000). There are many explanations for this phenomenon. One is due to the large amount of data, which is available. Others are due to the time behaviour (different particle sizes), different flow patterns (homogeneous-heterogeneous flow), material properties, geometrical parameters, the effect of a preheated or a superheated carrier fluid, and heat transfer, i.e. melting of ice particles during measurements.

73


3.3.3 FRICTION FACTOR FOR LAMINAR FLOW Usually, the friction factors are determined by equations listed in Table 3.4. They depend on rheological characteristics of the particular fluid or respective model. Therefore, each parameter of a model has to be determined experimentally. Usually they are obtained by the application of the Rabinowitch-Mooney equation (see Section 3.1). Several authors have decided to use such an approach. But it requires a large amount of experimental data; otherwise the friction factor correlations, determined for the rheological parameters, e.g. viscosity and yield stress, together with other correlations, lead to a high uncertainty. In such a case completely empirical models may give better results.

3.3.4 SEMI-EMPIRICAL CORRELATIONS FOR THE TURBULENT ICE-SLURRY FRICTION FACTOR Turbulent friction factor correlations are based on the rheological properties of a particular fluid and some experimental data as well. For ice slurry, Doetsch (2001) introduced a new correlation given by Eq. (3.61). He took the Casson model to describe the rheological behaviour of ice slurry. His correlation is based on an extended Blasius equation. A similar equation was also proposed by Thomas and reported by Wasp (1977) for Non-Newtonian fluids.

λ = 0.34179 ⋅ (Re C )−0.25793 ⋅ (Ca + 1)0.013532

(3.61)

Equation (3.61) is valid for Recritical < ReC < 40 000 (0 < Ca < 100 000) and applies to ice slurries with any kind of additives. Rheological properties of ice slurry with different additives are presented in Section 3.1. Using the experimental data of Hansen (the same data used to develop the equation in Table 3.5), Kitanovski (2002) applied two rheological models, the Casson and Bingham models, in order to determine which model best fits the experimental data. The yield stress parameter and viscosity parameter were determined for both models by using the Mooney-Rabinowitch equation. Jensen et al. (2000) used the same experimental data and Thomas (1965) equation for the determination of the “Bingham viscosity parameter”, which differs from the one used by Kitanovski, who obtained both parameters for both models from experimental data. The procedure of Kitanovski (2002) was in accordance with that of Doetsch (2001) for a Casson fluid. While Jensen’s data fitted within ±20% for 80% of all experimental data, Kitanovski has obtained a fit of ±15% for all experimental data for a Bingham fluid, and ±30% for all experimental data for a Casson fluid. We can conclude that it is very advantageous to determine both parameters of the Casson or Bingham model from experimental data, not using known equations for the suspension viscosity of the corresponding Newtonian fluids, such as the Thomas (1965) equation.

74


Figure 3.16. Darcy´s friction factor dependence on the Reynolds and the Casson numbers (Doetsch, 2001) Since Doetsch (2001) obtained a deviation of less than 5% for Ca < 1000, less than 10% for 1000 < Ca < 10 000 and less than 20% for Ca > 10 000, we can conclude that his semiempirical equation gives very good results and may be applied to any kind of turbulent ice slurry flow with any additive. However, it best applies when ice particles are rather small, i.e., dp = 0.1-0.5 mm, and of course under homogeneous flow conditions. 3.3.5 GENERAL EMPIRICAL DETERMINATION OF THE FRICTION FACTOR FOR ICE-SLURRIES Correlations based on a dimensional analysis yield normally better fits to experimental data than the semi-empirical approaches. However, extrapolation and interpolation using empirical correlations can lead to large deviations. In this section, only correlations which satisfy both laminar and turbulent flows are presented.

75


Table 3.5. Empirical correlations for the friction factor of ice slurry flows Performed by (year) Kitanovski (Experimental data from Hansen –DTI ) (2002) based on Turian´s work Reghem (2002) based on Turian´s work

Reghem (2002) based on Ogihara´s work

Specification of experiment

Equation

b ABS plastic pipe ⎞ 5 v2 b3 b4 ⎛ b2 ⎟ ⎜ f is = f f + b1 ⋅ C r ⋅ f f ⋅C D ⋅ inner diameters ⎜ D ⋅ g ⋅ s −1 ⎟ ⎠ ⎝ 12.8, 21, 27.7 mm 0 . 0791 v = 0.5-2 m/s ff = Re 0.25 Cr = 0-30% initial ethanol L concentration: ∆p = 2 ⋅ f ⋅ ρv 2 5, 10, 20% D dp ~ 300 µm Coefficients presented in Table 3.6 gen.: scraper d Plastic pipe ⎞ ⎛ λ is − λf v2 b c ⎜ ⎟ = a ⋅ C r ⋅ λf ⋅⋅ ε = inner diameters ⎜ D ⋅ g ⋅ s −1 ⎟ λf ⋅ C r ⎠ ⎝ 21.5, 44.6 mm 0.316 v = 0.1 to 3 m/s λf = Ref 0.25 Cr = 0-30% initial ethanol concentration: L ρv 2 ∆p = λis ⋅ 10% D 2 dp = 100-300 µm Coefficients presented in Table 3.7 gen.: scraper 1 Plastic pipe Re1 = Re⋅ K ⋅ Cr inner diameter 1+ 21.5 mm v v = 0.1 to 3 m/s 0.316 λis = homogeneous flow for Cr = 0-30% Re1 0.25 initial ethanol Re1 > 2100 concentration: 64 heterogeneous flow for λis = 10% Re1 dp = 100-300 µm Re1 < 2100 gen.: scraper

K = 9.75 L ρv 2 ∆p = λis ⋅ Snoek & Gupta (1993)

Pipe diameters 38-100 mm v = 0.96-3.53 m/s Cr = 0-31% initial glycol concentration 9.6-12.9% dp - not known gen.: scraper

Φ2 =

D 2 λis

λwater

Φ 2 = 1 + a ⋅ C r ⋅ (Reis ) c + d ⋅ C r e ⋅ D f b

λwater =

0.316 Rewater 0.25

∆p = λis ⋅

L ρv 2 D 2

Coefficients presented in Table 3.7

76

Uncertainty

Eq.

±15% for all experimen- (3.62) tal data (3.63)

(3.64)

±14% for all experimen- (3.65) tal data (3.66)

(3.67) ±6% for all experimen- (3.68) tal data in homogeneous flow regime (3.69) ±25% for all

experi(3.70) mental data for heterogeneous flow regime (3.71) ±10% for all experimen- (3.72) tal data (3.73) (3.74)

(3.75)


Table 3.6. Coefficients for empirical correlations for initial concentrations of the additive ethanol (Kitanovski, 2002) 5 wt-% ethanol

10 wt-% ethanol

20 wt-% ethanol

b1

0.00000039332

650.1835

912649.1

b2

0.45034198847

1.147015

0.621567

b3

4.02136479789

3.807498

3.722244

b4

3.84746019112

1.089962

0.092936

b5

–0.67864294281

–0.649095

–0.403264

Table 3.7. Coefficients for empirical correlations for two different additives (from Table 3.5) 10 wt-% ethanol - water (Reghem, 2002)

9.6 - 12.9 wt-% glycol - water (Snoek, 1993)

a

1640

0.1119

b

1.109

2.151

c

0.376

0.2422

d

–0.642

0.02415

e

/

0.3996

f

/

–0.2845

3.3.6 PRESSURE DROPS OF ICE-SLURRY FLOWS IN HEAT EXCHANGERS Contrary to isothermal flows, the pressure drop of ice slurries in heat exchangers must be determined considering heat transfer. The reason is that the ice slurry is melting in the heat exchangers, and the physical properties are therefore changing. Based on this phenomenon, a valuable theoretical study was performed by Egolf et al. (2001) who proposed an equation for an average pressure drop. The model applies to the transport of ice slurries through cylindrical heat exchangers, with small applied heat fluxes, R=

R in R ln in R out

⎛ R ⋅ ⎜⎜1 − out R in ⎝

⎞ ⎟⎟ ⎠

(3.76)

where R denotes the specific pressure drop of the inlet (Rin) and of the outlet (Rout): dp R in = − dx

= x =0

λin ρ in ⋅ v in D

⋅

2

2

and Rout

dp =− dx

= x =L

λout ρ out ⋅ v out D

⋅

2

2

(3.77a,b)

This approach is based on an exponential decrease in the pressure drop due to the transport and melting through the cylindrical heat exchanger. R( x ) = α exp( − β

x ) L

(3.78)

77


If one applies the arithmetic mean value between the inlet and the outlet to determine the average pressure drop, the error may be large. Note that in slow flow, stratification (or flow with a moving bed) may occur, but this is not the subject of this section. 10

R (Pa/m)

10

5

R (Pa/m) Example R (Pa/m) M odel

4

Mean specific pressure drop 1533 Pa/m

1000

100

10 0

0.2

0.4

0.6

0.8

1

x/L (-) Figure 3.17. The specific pressure drop R in a heat exchanger decreases approximately exponentially. In this example R changes from the inlet to the outlet by more than a factor of ten! “Example” denotes a step-by-step downstream calculation through the heat exchanger. “Model” denotes results obtained by applying Eq. (3.76) (Egolf et al., 2001) There have been several experiments performed on the pressure drop of ice slurry flows in heat exchangers, most notably those reported by Bellas et al., 2002; Tassou et al., 2001; Knodel et al., 2000; and Jensen et al., 2000.

3.4 Time dependent behaviour by Didier Vuarnoz, Torben Hansen and Beat Frei

In 1999 at the University of Applied Sciences of Central Switzerland a curious observation was made (Frei and Egolf, 2000). In a storage experiment at a constant ice slurry temperature (and density), a trough formed on the surface of the ice slurry — shaped around the shaft of the mixing element — and smoothly altered its form and depth with elapsed time. A first interpretation was that the viscosity of the fluid may have changed as a function of time. In further investigations of this phenomenon, the pressure drop in loops outside the storage vessel was measured, and remarkable changes in specific pressure drop with time and evaporator temperature were observed. After five cycles of partial melting and generation the difference in pressure drop in the discharge loop (after storage and mixing) vanished completely (see Figure 3.18) leading to the conclusion that storage and mixing have an influence on the behaviour of ice slurry. Knowledge of the geometrical characteristics of the ice particles in the ice slurry and time dependent behaviour is now known to be an important key to understanding the deviation in the results found in numerous apparently comparable experimental investigations of thermophysical properties, pressure drop, heat transfer coefficients, etc. The average size, the size

78


distribution and the geometrical characteristics of ice particles are known to affect the thermophysical properties of the ice slurry. The geometrical characteristics might depend on the method of ice generation or the ice crystal history of partial melting and re-crystallization (Hansen, 2002). Some mechanisms of alteration of the initial shapes of the ice particle are reviewed in Pronk (2002) and summarized in Chapter 2.2.2 of this handbook.

Figure 3.18. The specific pressure drop in a charge - and discharge - loop alters as a function of time and evaporator temperature at the same velocity and ice mass fraction (Frei and Egolf, 2000) Literature cited in Chapter 3

1.

Bagnold, R.A., Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc., A225, pp. 49-63, 1954. 2. Barnes, H.A.,: An Introduction to Rheology, Elsevier, Chapter 7, 1989. 3. Bel, O.: Contribution à létude du comportement thermo-hydraulique dún mélange diphasique dans une boucle frigorifique à stockage d´énergie. PhD Thesis, LÍnstitut National des Sciences Appliquees de Lyon, 1996. 4. Bellas, J. et al.: Heat transfer and pressure drop of ice slurries in plate heat exchangers. Applied Thermal Engineering, Volume 22, Issue 7, pp. 721-732, July 2002. 5. Chaer et al.: Flow Characteristics and Pressure Drop of Ice Slurries in Straight Tubes. Clima 2000/Napoli 2001 World Congress, Napoli, September 2001. 6. Christensen, K.G.; Kauffeld, M.: Heat Transfer Measurements with Ice Slurry, IIR, Heat Transfer Issues in Natural Refrigerants, November 1997. 7. Darby, R.: Hydrodynamics of slurries and suspensions. Encyclopedia of Fluid Mechanics, Vol. 5, Slurry flow technology, Chapter 2, pp. 49-92, 1986. 8. Doetsch, C.: Experimentelle Untersuchung und Modellierung des rheologischen Verhaltens von Ice Slurries. Ph.D. thesis, Fraunhofer Institut – UMSICHT, Fachbereich Chemietechnik der Universtät Dortmund, 2001. 9. Dong Won Lee et al.: Experimental study on flow and pressure drop of ice slurry for various pipes, Fifth IIR Workshop on Ice Slurries, Stockholm, May 2002. 10. Doron, P.; Barnea, D.: Flow pattern maps for solid-liquid flow in pipes, International Journal of Multiphase Flow, Vol. 22, No. 2, p. 273-283, 1996.

79


11. Doron, P.; Granica, D.; Barnea, D.: Slurry flow in horizontal pipes – experimental and modeling, International Journal of Multiphase Flow, Vol. 13, No. 4, pp. 535-547, 1987. 12. Egolf, P.W. et al.: Pressure drop and heat transfer in a cylindrical heat exchanger with ice slurry flow, Third IIR Workshop on Ice Slurries, Lucerne, pp. 77-84, May 2001. 13. Frei, B., Egolf, P.W., Viscometry applied to the Bingham Substance Ice SlurryProceedings of the Second IIR Workshop on Ice Slurries , pp. 48-59, Lucerne, Switzerland, 2000. 14. Guilpart, J. et al.: Experimental study and calculation method of transport characteristics of ice slurries, First IIR Workshop on Ice Slurries, Yverdon, pp. 74-82, 1999. 15. Hanks, R.W.: Principles of Slurry Pipeline Hydraulics, Encyclopedia of Fluid Dynamics, Vol.5, Slurry flow Technology, Gulf Publishing Company, pp. 213-276, 1986. 16. Hansen, T.M.; Radosevic, M.; Kauffeld, M., Behavior of Ice Slurry in Thermal Storage Systems, ASHRAE Research Project 1166, ASHRAE, 2002. 17. Hansen; T.M., Kauffeld, M.: Viscosity of ice slurry, Second IIR Workshop on Ice Slurries, Paris, France, May 2000. 18. Jensen, E.N. et al.: Pressure drop and heat transfer with ice slurry, IIR Conference, Purdue-USA, 2000. 19. Kawaji, M. et al., Ice slurry flow and heat transfer characteristics in vertical rectangular channels and simulation of mixing in a storage tank, Fourth IIR Workshop on Ice Slurries, Osaka, Japan, pp. 153-164, Nov. 2001. 20. Kitanovski, A. et al., Flow Patterns of ice slurry flows, Fifth IIR Workshop on Ice Slurries, Stockholm, May 2002. 21. Kitanovski, A., PhD thesis, Faculty of Mechanical Engineering, University of Ljubljana, 2003. 22. Kitanovski, A., Poredoš A., Concentration distribution and viscosity of ice slurry in heterogeneous flow, IIR Journal, Vol. 25, Issue 6, pp. 827-835, 2002. 23. Kitanovski, A.; Poredoš, A, Theory on concentration distribution of the ice slurry flow, Fourth IIR Workshop on Ice Slurries, Osaka, pp. 15-24, 2001. 24. Knodel, B.D. et al.: Heat transfer and pressure drop in ice water slurries. Applied Thermal Engineering, vol. 20, pp. 671-685, 2000. 25. Mooney, M.: Explicit Formulas for Slip and Fluidity, Journal of Rheology Bd. 2, pp. 210215, 1931. 26. Nasr-El-Din, H.; Shook, C.A.: The lateral variation of solids concentration in horizontal slurry pipeline flow, International Journal of Multiphase Flow, Vol. 13, No. 5, pp. 661670, 1987. 27. Pronk, P., Infante Ferreira, C.A., Witkamp G.C., Effects of Long-Term Ice Slurry Storage on Crystal Size Distribution. Proceedings of the Fifth IIR Workshop on Ice Slurries, Stockholm, Sweden, May 2002. 28. Rabinowitsch, B.: Über die Elastizität von Solen, Zeitschrift für physikalische Chemie, Vol. A 145, pp. 1-7, 1929. 29. Reghem, P., PhD thesis, University of Pau, 2002. 30. Richardson, J.F.; Zaki, W.N., Sedimentation and fliudisation: PART 1, Trans. I CHEM. E., vol. 32, pp. 35-53, 1954. 31. Roco, M.C.; Shook, C.A, New approach to predict concentration distribution in fine particle slurry flows, PCH, Vol. 8, No. 1, pp. 43-60, 1987. 32. Sari, O.; Meili, F.; Vuarnoz, D; Egolf, P.W., Thermodynamics of moving and melting ice slurries. Second IIR Workshop on Ice Slurries, Paris, May, pp. 140-153, 2000. 33. Sari, O.; Vuarnoz, D., Meili, F.; Egolf, P.W., Visualization of ice slurries and ice slurry flows, Second IIR Workshop on Ice Slurries Paris , May, pp. 68-80, 2000.

80


34. Sasaki, M.; Kawashima, T.; Takahashi, H.: Dynamics of snow-water flow in pipelines, Slurry Handling and Pipeline Transport, Hydrotransport 12, pp. 533-613, 1993. 35. Sellgren, A.: Hydraulic Behaviour of Ice Particles in Water, Hydrotransport 10, International Conference on Slurry Handling and Pipeline Transport, pp. 213-217, 1986. 36. Shook, C.A., Roco, M.C., Slurry Flow – Principles and Practice, Butterworth – Heinemann, 1991. 37. Snoek, C.W.: The design and operation of ice slurry based district cooling systems, IEANovem, 1993. 38. Stamatiou, E.; Kawaji, M.; Goldstein, V.: Ice Fraction Measurements in ice slurry flow through a vertical rectangular channel heated from one side, Fifth IIR Workshop on Ice Slurries, Stockholm May 2002. 39. Steffe, J.F.: Rheological methods in food process engineering. Second edition, Freeman press, 1992. 40. Takahashi et al., Flow properties for slurries of particles with densities close to that of water, ASME, Liquid-Solid flows, vol. 118, pp. 103-108, 1991. 41. Takahashi et al.: A laboratory study of pressure loss and pressure fluctuation for ice water slurry flows in a horizontal pipe, Hydrotransport 12, pp. 497-511, 1993. 42. Tassou, S. et al.: Comparison Of The Performance Of Ice Slurry And Traditional Primary And Secondary Refrigerants In Refrigerated Food Display Cabinet Cooling Coils, Fourth IIR Workshop on Ice Slurries, Osaka, November 2001 43. Thomas, D.G.: Transport characteristics of suspensions. Journal of Colloid Science, no. 20, pp. 267-277, 1965 44. Turian, R.M.; Yuan, T.F.: Flow of slurries in pipelines, AIChE J. 23, p. 232-243, 1977 45. Vuarnoz, D.; Meili, F.; Moser, Ph.; Sari, O.; Egolf, P.W, Fluid and Flow Visualizations of Ice Slurries, Eureka Project FIFE, research report No. 8, University of Applied Sciences of Western Switzerland, 2000 46. Wasp, E.J.: Solid-Liquid Flow, Slurry Pipeline Transportation, Series on Bulk Material Handlings, Vol. 1, No. 4, 1977

81

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CHAPTER 4. THERMODYNAMICS AND HEAT TRANSFER by Peter W. Egolf, Andrej Kitanovski, Derrick Ata-Caesar, Osmann Sari, Alen Sarlah, Evangelos Stamatiou, Masahiro Kawaji, Jean-Pierre Bedecarrats and Francoise Strub (see specific list of symbols in Appendix 3)

4.1 Overview The derivation of a macroscopic theory for ice slurry flows leads to very complex multicomponent and multi-phase mass, momentum and energy conservation equations. Therefore, most of the existing theoretical work — which is related to heat transfer to and from ice slurries — is based on rather simple models, which consider ice slurry to be a homogeneous mixture of a carrier fluid and a large number of small ice particles. Experiments on heat transfer with ice slurries have shown that simple models usually only roughly describe the heat transfer phenomena, which are occurring during the melting of ice particles. As in other cases of fluid dynamics, analytical physical laws are available only for laminar flows. Such derivations were initiated by Graetz, who studied the thermodynamics of Bingham fluids in tubes. For the description of transitional flow and turbulent flow, by mathematical approximation techniques, numerous empirical equations have been derived, in order to describe heat transfer in heat exchangers (with different geometries) from the hot walls to ice slurries. Simultaneous measurements of temperature distributions and ice concentration fields during melting have shown that a thermal equilibrium between the carrier fluid and the ice particles is not always obtained. There is considerable lack of agreement between the experimental results reported by researchers from different laboratories. Qualitative and minor results were mostly obtained in cases where the concentration of the ice was determined by applying the equilibrium temperature/ice concentration functions and not by the indirect method of measuring the density. The latter method shows a high accuracy, especially when the Coriolis principle is applied. Furthermore, a heterogeneous distribution of ice particles — due to buoyancy — has in some cases led to experimental results which are difficult to classify. Despite such indeterminism, numerous comprehensive articles on heat transfer mechanisms with phase change of various ice slurry flows exist. In this chapter, only the studies in which the ice slurries were investigated and the related thermodynamic phenomena are clearly described, are cited or presented.

4.2 Basic definitions

4.2.1 EFFECTIVE ENTHALPY AND EFFECTIVE SPECIFIC HEAT In order to describe the enthalpy of phase change materials, Egolf and Manz (1994) developed a macroscopic model to describe the behaviour of melting and freezing mixtures, the Continuous-Properties Model (CPM), which basically describes a continuous phase transition. Therefore, it is well suited to describing the overall thermodynamic behaviour of ice slurries. If in the temperature/specific enthalpy diagram the region of the continuous phase transition is chosen to be small, the model is also a good approximation for modelling the dynamics of substances with discontinuous phase transitions. But it may also take into account the occurrence of a mushy region near the eutectic point of a mixture. In reality, the width of this region depends on the dynamics of the problem. 83


The enthalpy and the specific heat of ice slurries may be calculated by applying appropriate equations for mixtures, which are presented in Chapter 2. 4.2 2 EFFECTIVE THERMAL CONDUCTIVITY For the effective thermal conductivity several models may be found, which are mainly derived from Jeffrey’s model (1973) (see Chapter 2). A selection of some of the principal models is presented in Table 4.1. Table 4.1. Some models for the effective thermal conductivity of suspensions Performed by

Equation

(

kis = kcf 1 + 3 ⋅ Cv ⋅ β + 3 ⋅ Cv2 ⋅ β 2 ⋅ γ Jeffrey (1973)

γ =1+

β

4 ki α= , kcf

+

3β α + 2 , ⋅ 16 2α + 3 α −1 , β= α +2

kcf ⋅ (1 − Cv ) + ki ⋅ Cv ⋅

Brailsford and Major (1964)

kis =

Wasp (1977)

kis = kcf ⋅ kis =

Ri =

0 ≤ α ≤ ∞.

3 ⋅ kcf 2 ⋅ kcf + ki

 3 ⋅ kcf   1 − Cv 1 −  2⋅k + k  cf i  

.

ki + 2 ⋅ kcf − 2 ⋅ Cv ⋅ (kcf − ki ) . ki + 2 ⋅ kcf + Cv ⋅ (kcf − ki )

(2 ⋅ k + k ) − 2 ⋅ (k − k )⋅ R (2 ⋅ k + k ) + (k − k )⋅ R cf

i

cf

Maxwell and Eucken (see Eucken, 1940)

)

cf

i

1  ρ  1 1 +  − 1 i  ρ cf  Ci

cf

i

i

i

Remarks This is the equation which up to the present has been applied in most calculations of the thermodynamic behaviour of ice slurries. This equation shows good agreement with experimental results, obtained from paraffin slurries (Shin et al., 2002).

,

i

.

A more comprehensive overview of formulae to calculate the effective thermal conductivities of suspensions was given by Bel (1996). All the macroscopic models, shown in Table 4.1, were derived for a homogeneous mixture of a carrier fluid and particles which are immiscible in the fluid. The effective thermal conductivity is the thermal conductivity of the mixture. This is a good approximation in the limit where the particle diameter tends towards zero and the number of particles approaches infinity, leaving the mass fraction of the particles unaltered. Please note that, depending on 84


the problem studied, a particle here may be a gas bubble, a liquid droplet or a solid particle. In the case of ice slurries it obviously is an ice particle. Nanofluids yield the best practical realization of this limit. In several models, as shown in Table 4.1, the effective thermal conductivity is calculated in analogy with the resistance of electric circuits. This procedure always leads to models combining the thermal conductivity of a carrier fluid and the thermal conductivity of the particles. This is performed in such a manner, that in the limit of zero particle fraction, the thermal conductivity of the carrier fluid results for the effective thermal conductivity. On the other hand, in the limit of particle fraction equal to unity, the thermal conductivity of the particles is obtained. In more sophisticated models the geometry of the particles is also considered. In the case of ice slurries at the melting temperature the particles do not only conduct heat, they also melt. If the phase transition is discontinuous the particles are ideal heat absorbers, and in a description of the effective thermal conductivity, the thermal conductivity of the particles cannot be important. Therefore, the models - developed for nonmelting suspensions - only apply approximately to ice slurries. At present at the University of Applied Sciences of Western Switzerland further clarifying work on the question of which situations and how the concept of an effective thermal conductivity applies to phase change slurries is in preparation. The problem of different thermal relaxation times of the carrier fluid and the small phase change material regions has to be addressed in future work.

4.2.3 DIMENSIONLESS NUMBERS In Table 4.2 some definitions of dimensionless numbers are presented. Some authors base them on the physical properties of the mixture and others on the properties of the carrier fluid. Table 4.2. Dimensionless numbers relevant to ice slurry fluid dynamics and thermodynamics

Nusselt number

h ⋅D Nuis = is h kis Reis =

Reynolds number

Graetz number

Nucf =

hcf ⋅ Dh k cf

All the physical properties correspond to the carrier fluid.

v is ⋅ Dh ⋅ ρ is

All the physical properties correspond to the The viscosity should homogenous ice be described by an appropriate rheological slurry mixture. model.

Pris =

Prandtl number

All the physical properties correspond to the homogeneous ice slurry mixture.

ηis

Re cf =

v cf ⋅ Dh ⋅ ρ cf

ηcf


c pis ⋅ηis

All the physical properties correspond to the The viscosity should homogenous ice be described by an appropriate rheological slurry mixture. model. All the physical ⋅ properties mis ⋅ c pis correspond to the Gzis = homogenous ice k is ⋅ x slurry mixture.

k is

Prcf =

c pcf ⋅ η cf k cf

⋅

Gz cf =

mcf ⋅ c pcf k cf ⋅ x



If the Bingham model is applied to describe the rheology of ice slurries, then the Hedstrom number (containing the critical shear stress) is also important. It is defined in Chapter 3.

85


4.2.4 REFERENCE TEMPERATURES AND HEAT TRANSFER COEFFICIENTS For the ice slurry flow in the heat exchanger illustrated in Figure 4.1, the local heat transfer coefficient, his,L, can be determined from knowledge of the thermal conductivity of the fluid, k, the temperature gradient (∂T ∂y ) y =0 at the wall, and mean temperature difference between the wall and the fluid (Tw,m − Tis ,m ) x :

his , x =

k − Tis ,m ) x

(Tw ,m

 ∂T  .    ∂y  x , y =0

(4.1)

(∂T

∂y ) y =0

x y

u(y)

Adiabatic Wall

g C L

H Figure 4.1. Heat transfer from the wall to an ice-slurry in a vertical rectangular duct with a second kind boundary at the wall The peripheral mean wall temperature, Tw,m, and fluid bulk temperature, Tis,m, of an arbitrary cross section can be defined as (Shah and London, 1978):

Tw,m =

Tis ,m =

1 Tw ds . ℘ ∫Γ

∫

ρ ⋅ c p ⋅ u ⋅ T ⋅ dAc

Ac

∫

Ac

ρ ⋅ u ⋅ c p ⋅ dAc

(4.2)

.

(4.3)

The fluid bulk temperature, Tis,m, also referred to as the “mixing cup” or “flow average temperature” requires knowledge of the ice slurry density, mixture velocity distribution and temperature distribution across the flow channel of the heat exchanger. The average heat transfer coefficient is obtained by integrating the local heat transfer coefficient over the heat transfer surface in contact with the ice slurry. For cylindrical pipes and channels it follows that: L

his , L

1 = ∫ h sl , x ⋅ dx . L 0

(4.4)

86


The local Nusselt number is defined by: Nu x =

his , x ⋅ D , kis , x

(4.5)

where the effective thermal conductivity of the ice slurry is denoted by kis,x. Such relations are only valid when the ice slurry is considered as an ideal mixture of water with additives and small ice particles. The average Nusselt number is calculated by substituting the average heat transfer coefficient and effective thermal conductivity into the definition of the Nusselt number:

Nu L =

his , L D , k is , L

(4.6)

where the mean effective thermal conductivity is similarly to Eq. (4.4) defined by:

χ =

1 L

L

∫ χ (x ) dx ,

χ ∈ {his , x , k is , x }.

(4.7)

0

4.3 Measurement techniques 4.3.1 INTRODUCTORY REMARKS Some experimental methods, which were mainly applied by the research group at the University of Toronto (Kawaji et al., 2001; Stamatiou et al., 2001, 2002; Stamatiou and Kawaji, 2004a, 2004b), are first described in the following sections and sub-chapters. Other measurement techniques, which were used by other authors, are described in later sections or given in related references. 4.3.2 LOCAL ICE FRACTION The simplest measurement technique for determining the local ice fraction is by removing a sample through an opening in the channel wall and analyzing the sample using a batch or online calorimetry technique. Other solid fraction measurement techniques available are reviewed elsewhere (Shook and Rocco, 1991). In the direct sampling method used by Stamatiou et al. (2002) and Kawaji et al. (2001), the ice fraction distribution was obtained by manually traversing a 6.35-mm O.D. stainless steel (0.51 mm wall thickness), L-shaped sampling tube. The probe position was determined using a calibrated slide-potentiometer. The L-shaped sampling probe was sharpened at its opening, and was also slightly enlarged (7.6 mm O.D.) to allow for easy passage of ice crystals (see Figure 4.2). In addition, the ice fraction value was shown to be unaffected by an ice slurry sampling velocity deviating from its isokinetic sampling value due to the presence of very fine ice slurry crystals that can follow the carrier fluid’s streamlines.

87


The ice slurry sample removed by the sampling probe was passed through a custom-made online calorimeter unit that was instrumented and properly calibrated to determine the local ice fraction (see Figure 4.3). The ice fraction distribution near the heated brass wall was obtained by traversing the sampling probe at an axial elevation of L/Dh ≈ 20 located mid-width (z/W=0.50) through the rectangular flow channel. Front Acrylic Wall

Back Brass Plate 25.4 mm

T-type T/C Traversing ISP

Wall T/C

Copper Coils

5.33-mm I.D. S.S. 304 Tube I.F. Profile Acrylic rod A

Ball Valve

Sample to calorimeter

A’

7.6 mm I.D.

Unheated or Heated Wall Ice Slurry

Figure 4.2. Local ice fraction distribution measurement at L/Dh≈19.

Figure 4.3. Calorimeter (680 W) for on-line ice fraction measurements

4.3.3 LOCAL ICE SLURRY TEMPERATURE Local ice slurry temperature measurements were obtained by traversing a 1.56-mm O.D. Ttype thermocouple across the heated flow channel. Temperature recordings were made at six selected transverse locations between the vertical heated brass plate and an acrylic wall over the channel gap of 25.4 mm (see Figure 4.4). The thermocouple probe was placed mid-width (z/W=0.50) through the rectangular channel at an axial elevation of L/Dh ≈ 20 as measured from the inlet of the heated brass section.

4.3.4 LOCAL ICE SLURRY VELOCITY Local ice slurry velocity profile measurements were conducted using an L-shaped hot film probe (TSI, Model: 1231AR) placed at the mid-width (z/W = 0.50) of the rectangular channel at the axial elevation of L/Dh ≈ 20. The hot film probe was connected to a Dantec CTA bridge anemometer (Dantec, Model: 56C17) with a fixed bridge ratio of 4:8. The hot film probe was traversed across the flow channel and local velocity measurements were made at six different selected locations across the gap between the heated wall and an opposite wall (see Figure 4.4). The output voltage signal from the hot film probe was recorded at a sampling frequency of 5 Hz using a data acquisition system. The hot film probe was initially calibrated at different ice fractions and velocities using a rotating pool of ice slurry in a circular container placed on a turntable. The hot film

88


anemometer calibration data were used to obtain the velocity profile at specific ice fractions during the melting experiments. More details of the hot film calibration method are given elsewhere (Stamatiou, 2003). Front Acrylic Wall

Back wall brass plate

0.0127 m

T-type T/C

Wall T/C

Traversing probe Copper Coils velocity profile

HWA probe

Signal to anemometer

C L Unheated or Heated Wall Ice Slurry

Figure 4.4. Local temperature and velocity measurements (side view)

4.4 Flow Phenomena

4.4.1 VELOCITY PROFILE, MEAN VELOCITY

4.4.1.1 Introduction Local measurements of ice slurry velocity profiles were made under adiabatic and non adiabatic flow conditions in a vertical rectangular channel using hot wire anemometry (HWA) with an L-shaped hot film probe (Stamatiou and Kawaji, 2004a). These measurements were carried out in a 0.61 m (L) x 0.31 m (W) x 0.025 m (gap, H) rectangular channel at relatively low ice slurry velocities of uis ~ 0.10 to 0.15 m/s and volume ice fractions of up to 10%.

4.4.1.2 Adiabatic ice slurry velocity measurements Figures 4.5 and 4.6 show the experimental results obtained by traversing the hot film probe in the vertical rectangular duct under adiabatic conditions at the axial location of L/Dh ~ 19.6. It is evident that the ice crystals have an effect of producing a blunt velocity profile that deviates considerably from the profile measured in a single-phase flow (volumetric ice fraction Φv=0.0%). In these figures, the laminar velocity profile for a power law fluid between two infinitely long parallel plates (α*=H/W=∞) given by Eq. (4.8) is also plotted (Hartnett and Kostic, 1989; Skelland, 1967).

89


n +1   u( y' ) 2n + 1   2 y'  n  = 1−   V n +1   H    

(4.8)

In Eq. (4.8), n is the power law index and y’ is the distance measured from the mid-plane of the flow channel. The power law index n was determined by best fitting eq. (4.8) to the experimental data. Most of the ice slurry HWA results shown were best predicted by n = 0.25, while the singlephase CFD calculation (PHOENICS code) with Thomas’s viscosity correlation (1965) failed to predict the present HWA measurements. The power law index of 0.25 suggests that the ice slurry flow may be interpreted as a pseudoplastic or shear-thinning fluid, which is similar to the behavior reported by Ben-Lakhdar et al. (1999) based on pressure drop measurements. For dilute ice slurry mixtures with ice fractions lower than 2% by volume, the non-Newtonian flow characteristics disappeared. As Figures 4.5 and 4.6 illustrate, the power law model can predict the ice slurry velocity profiles for volume ice fractions between 2% and 9%. Although other researchers have interpreted their ice slurry flows as Bingham plastic or Casson fluids from pressure drop measurements (Ayel et al., 2003), only the power law model was used to fit the ice slurry velocity profile data as it is the most widely used and simplest model to apply and can adequately describe the data. In the work of Stamatiou and Kawaji (2004a), the nonNewtonian flow characteristics of ice slurries were detected at low ice fractions (Φv ≥ 2%) since the hot-film anemometer is a much more sensitive instrument than a conventional pressure-drop measurement equipment. Although the above results indicate that the non-Newtonian flow characteristics depend on the ice fraction, various other parameters such as the ice crystal size, shape, distribution, ice slurry and carrier fluid densities, as well as the surface forces may also affect the deviation from Newtonian flow (Darby, 1986).

1.50

1.40

1.40 1.30 1.20

1.20

Φv

1.10

1.00

1.00

0.80

0.80 Φv(%)

0.70

Recf

[m s ]

-1

V [m s ]

0.60

2.4% 1980 2130 0.080 0.110 4.1% 1890 2140 0.081 0.102 5.9% 1780 2130 0.081 0.095 0.2% 2140 2160 0.081 0.105 0.0% 2180 0.082 0.103 Eq. (4.4.2-2); n =0.25 PHOENICS k-ε; µsl =2.0 mPa.s (Φv=4.1%), V=0.098 m/s

0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.00

Resl

-1

u/V

u/V

0.90

Φv(%) Resl Recf [m s-1] V[m s-1] 6.0% 3400 4045 0.153 0.160 5.9% 1780 2130 0.081 0.095 9.0% 2900 3900 0.148 0.147 Eq. (4.4.2-2); n =0.25 PHOENICS k-ε; µsl=2.20 mPa.s, V=0.160 m/s

0.40

0.20

Single-phase empirical; Sun et al. (2002). 0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

y/H

0.00 0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

y/H

Figure 4.5. Velocity profile data for ΦV=0.0-6.0%, =0.080m/s, Recf,L~2200

90

Figure 4.6. Velocity profile data for Φv=6.0-9.0%, Recf,L~2100 & 4000


4.4.1.3 Non adiabatic ice slurry velocity measurements near a heated wall Figure 4.7 compares the dimensionless ice slurry velocity distributions near heated and unheated walls for runs conducted under similar ice fractions (Φv ~ 5-6%) and Reynolds numbers (Recf ~ 4000) but different wall heat fluxes, q”w. This figure also compares the HWA data with the adiabatic laminar velocity profile for a power law non-Newtonian fluid (Harnett and Kostic, 1989), and the velocity profile predicted using a PHOENICS code with Thomas’s viscosity correlation (1965) for a flow between two parallel plates. The local Reynolds number, heat flux and local Nusselt number for the melting runs are also given in this figure. The definition of the Reynolds number based on the carrier fluid (liquid) properties, Recf, was adopted. For these data, the average slurry velocity, V, obtained by integrating the area under the curve, matched the average ice slurry velocity, , measured using an electromagnetic flow meter to within 5%. These velocity profile data suggest that when a wall heat flux is imposed, the flow near the heated wall decelerates in comparison to adiabatic ice slurry flow, while in the core region the velocity profile remains similar to that displayed in adiabatic ice slurry flow. The velocity reduction near the heated wall is due to the formation of an “ice-free” layer near the heated wall that has a greater density than the bulk ice slurry. When a higher heat flux is further imposed, the velocity near the heated wall is further decreased by about 10% as Figure 4.7 illustrates. Most of the velocity distribution data obtained displayed an approximately 10% reduction near the heated wall in comparison to adiabatic ice slurry flows suggesting that the flow decelerates near the heated wall in a vertical upward flow.

1.40

1.20

1.00

u ( y ') 2n + 1 ⎡ n +1/ n ⎤ = 1 − ( 2 y '/ H ) ⎦ V n ⎣

u/V

0.80

0.60

0.40

0.20

0.00 0.00

Φv

Resl

Recf

<usl> [m/s]

V

q"w

[m/s]

[kW/m2]

6.0% 3400 4045 0.153 0.160 9.0% 2910 3900 0.148 0.147 7.6% 3090 3920 0.149 0.146 6.3% 3200 3860 0.146 0.157 3.1% 3700 4050 0.153 0.138 Ref. [10]; n =0.25 PHOENICS, k-ε; µsl=2.2cP, V=0.16 m/s 0.20

0.40

0.60

0.00 25.5 25.0 25.3 24.2

Nucf,L 234 214 206 178

0.80

1.00

y/H Heated Brass Wall

Front Acrylic Wall

Figure 4.7. Typical ice slurry velocity profiles near a heated wall

91


4.4.2 TEMPERATURE PROFILE, MEAN TEMPERATURE IN VERTICAL CHANNELS

Figure 4.8 shows typical dimensionless ice slurry temperature distributions across a heated channel (α∗ = 1:12) for Recf ~ 3800 and volume ice fractions up to 26%. In Figure 4.9, the dimensionless ice slurry temperature distributions obtained in a narrow heated channel (α* = 1:8) are given at turbulent flow velocities (usl = 0.50 m/s), Recf ~ 6600 and volume ice fractions up to 23%. These temperature distribution measurements were made at the axial location of x/D h= 7 by traversing a single T-type thermocouple probe across the flow channel between the vertically heated brass plate (y/H = 0) and an adiabatic acrylic (y/H = 1.0) wall. The results are expressed in terms of a dimensionless fluid temperature, θ = T − Tsl Tsl ,in − Tw , as adopted by Hartnett and Kostic (1989). The temperature data shown in these figures represent the timeaveraged temperatures of 20 data points obtained over a period of approximately 10 sec for a specified ice fraction. Also, the temperature rise near the acrylic wall (y/H ≥ 0.7) is considered to be anomalous due to the heat conduction along the thermocouple sheath. Nonetheless, the temperature data for y/H

[%]

[m/s]

2.5% 5.1% 11.2% 15.7% 20.4% 22.2% 26.4%

Resl

Recf Thw,m q"w Nucf,L o

[ C]

0.147 0.147 0.147 0.141 0.142 0.144 0.143

3620 3330 2630 2170 1800 1700 1400

0.40

θ=(T-Tw)/(Tsl,in-Tw)

θ=(T-Tw)/(Tsl,in-Tw)

0.95

3900 3880 3800 3700 3720 3770 3700

0.60

39.3 40.1 40.4 40.4 40.2 40.1 38.7

2

[kW/m ]

23.6 24.3 25.3 25.7 25.8 26.6 26.3

123 127 128 137 130 153 144

0.80

0.90

Xs [%]

0.70 0.00

1.00

y/H

5.9% 9.3% 12.7% 14.8% 20.5%

0.80

0.10

0.20

0.30

Φv

<usl>

[%]

[m/s]

6.6% 10.5% 14.2% 16.5% 22.7%

0.40

0.519 0.530 0.520 0.504 0.517

0.50

Resl

Recf Thw,m q"w Nucf,L

6170 4800 4070 3600 2850

0.60

6650 6700 6600 6350 6500

[oC]

[kW/m2]

41.6 40.1 39.9 41.0 39.8

39.7 38.8 38.9 41.7 45.5

0.70

0.80

109 114 123 138 171

0.90

1.00

y/H Heated Brass Wall

Front Acrylic Wall

Heated Brass Wall

Front Acrylic Wall

Figure 4.8. Ice slurry temperature distributions for Figure 4.9. Ice slurry temperature distributions for Recf=6600 and α*=H/W=1:8 (H=12.7 mm) Recf=3800 and α*=H/W=1:12 (H=25.4 mm)

92


4.4.3 LOCAL ICE FRACTION PROFILES

4.4.3.1 Adiabatic ice fraction distributions Figure 4.10 shows typical ice fraction profiles (Φ/Φm values) measured by Stamatiou et al. (2002) using an on-line ice fraction sampling probe as described in section 4.3, for mean volume ice fractions ranging from Φv ~ 6.0 to 11%. These ice fraction measurements were conducted at similar ice slurry sampling velocities, Uo. The transverse location, y/H, represents the distance measured from the brass wall to the centre of the sampling probe. Here, Φm represents the average ice fraction of the local measurements. In Figure 4.10, a small variation in the ice fraction distribution is noted across the flow channel for dilute slurries (Φv 10%, the ice fraction distribution becomes flatter than that displayed for the lower ice fraction range, 3% Recf,L 0.146 0.147 0.149 0.149 0.148

0.50

0.60

1.92 1.80 1.85 1.75 1.75

0.70

3840 3850 3930 3910 3890

0.80

ΦV[%] 0.80

0.90

0.70 0.00

1.00

y/H

16.1 14.5 13.0

0.10

0.20

0.30

Tsl,L [oC]

usl [m s-1]

-4.07 -4.40 -4.43

0.146 0.146 0.146

0.40

0.50

Uo/<usl> Recf,L 1.35 1.32 1.23

0.60

0.70

3806 3820 3825

0.80

0.90

1.00

y/H

Figure 4.10. Effect of Φv (6-11%) on the ice Figure 4.11. Effect of Φv on the ice fraction distribution at Uo/ ~ 1.3 fraction distribution at Uo/ ~ 1.8

4.4.3.2 Ice fraction distributions near a heated wall It is of further interest to examine the ice fraction distributions near a heated wall since it has been previously observed that the local heat transfer characteristics could be markedly affected by local ice fraction variations (Horibe et al., 2001; Kawanami et al., 1998).

Figure 4.12 shows the effect of average ice fraction on the normalized local ice fraction distribution (Φ/Φm) near a heated wall at Recf ~ 3800 and q”w ~ 24 kW/m2 (Stamatiou et al., 2002; Stamatiou and Kawaji, 2004b). It can be observed that the ice fraction in the vicinity of the heated wall is approximately 5% to 20% lower than in the bulk. Furthermore, the wall 93


peaking phenomenon previously shown to occur near the adiabatic walls in dilute ice slurries (Φv < 8%), disappears near the heated boundary (y/H = 0) but remains near the other adiabatic wall (y/H ~ 0.75). At the nearly adiabatic wall, the ice fraction profile is similar to that obtained under adiabatic conditions, i.e., wall peaking appears in runs with small average ice fractions (3% < Φv < 8%). At higher mean ice fractions (i.e., Φv > 10%), however, the peaking phenomenon disappears. As seen in Figure 4.12, the local ice fraction near the heated wall does not show any systematic variation with increasing ice fraction in the free-stream. The latter result may suggest that even at low ice fractions and mean velocities, the “ice-free” zone remains thin as the ice crystals in vertical flows disperse uniformly across the heated channel. In comparison to adiabatic ice fraction profiles, however, the ice fraction reduction near the heated wall in dilute slurries (Φv < 8%) is approximately 30% to 40% greater than in the more concentrated ice slurries (Φv > 10%). In the more concentrated ice slurries (Φv > 10%), the ice crystals are more closely packed so that the ice fraction reduction near the heated wall is only 10 to 20% in comparison to the adiabatic ice fraction profiles. This, in turn, would impact the local heat transfer coefficient.

1.4

1.2

Φ/Φm

1.0

0.8

Φv

Recf

<usl > Uo/<usl>

3.3% 5.1% 7.6% 8.6% 8.8% 10.8% 11.7% 15.9% 18.1%

0.6

0.4

0.2

0.0 0.00

0.20

3900 3800 3830 3820 3840 3810 3840 3710 3760

0.40

0.149 0.143 0.145 0.145 0.146 0.145 0.145 0.141 0.144 0.60

q"w

Nucf,L

[ kW/m2 ]

[ m/s ]

2.3 1.8 1.2 2.0 1.4 1.7 1.5 1.5 1.3

22.5 23.7 24.4 24.8 24.6 25.4 24.0 25.5 25.1 0.80

139 153 157 158 153 167 171 174 161 1.00

y/H Front Acrylic Wall

Heated Brass Wall

Figure 4.12. Effect of Φv on ice fraction distribution at Recf ~ 3800 near a heated wall

4.5 Heat transfer phenomena

4.5.1 A BRIEF INTRODUCTION Numerous experiments have been performed to determine the local or averaged heat transfer coefficient and the corresponding Nusselt numbers for ice slurry flows through heat exchangers of different types. The following types of heat exchangers are discussed in further sub chapters:

94


• • • • •

Pipes Channels Channels with a bend Heat exchangers with stagnant flow Industrial heat exchangers.

4.5.2 PIPES Christensen and Kauffeld (1997) experimentally determined the average Nusselt number in flows through a cylindrical pipe (see Figure 4.13). A constant heat flux was provided to the inner pipe by condensing refrigerant R134a between two concentric tubes. The heat flux was varied between 6 and 14 kW/m2. The ice slurry was produced with an aqueous ethanol solution of initially 10 mass percent. The test section, constructed from a stainless steel tube, had an outer diameter of 26.9 mm, an inner diameter of 21.6 mm and a length of 1 m. The heat transfer coefficient, his,x, was determined by considering the temperature difference between the refrigerant R134a and the ice slurry. The Nusselt number for the ice slurry was determined as follows: A) For an ice concentration, Cv, above 5%: −0.192⋅ Nuis = 1 + 0.103 ⋅ Cv − 2.003 ⋅ Reis Nucf

(30−Cv ) 30

⋅ Cv

0.339⋅Reis ⋅10− 4

.

(4.9)

B) For an ice concentration, Cv, below 5%:

Nuis =1. Nucf

(4.10)

250

200

Nuis

150

100

v=1,0 m/s; D=0,018 m v=2,3 m/s; D=0,018 m v=1,0 m/s; D=0,023 m v=2,3 m/s; D=0,023 m

50

0 0

5

10

15

20

25

30

Cv (%) [%] Figure 4.13. Average Nusselt number for ice slurry flows through a pipe

95


The equations (4.9) and (4.10) are valid for the following parameter ranges:

• • • • •

0,7 < uis < 2.5 m/s 0 < Cv < 30% 18 < Dh < 25 mm 6 < q& < 14 kW/m2 Initial ethanol concentration ξe = 10%.

The authors found that the average Nusselt number increases with increasing ice mass fraction and Reynolds number. The increasing heat transfer coefficient with increasing ice mass fraction is explained by the melting of ice particles near the wall, and therefore, a decrease in the temperature gradient within the boundary layer. The dynamic viscosity of the ice slurry was determined by applying the Thomas model (see Chapter 3 or Thomas [1965]), and the ice slurry was considered as a Bingham fluid. The yield stress was determined from the data obtained in pressure drop experiments. The measured heat transfer coefficients increased from 3000 W/m2K for an ice mass fraction of 5% to 7000 W/m2K for a mass fraction of 25%. Jensen et al. (2000) performed a very similar experiment to that of Christensen and Kauffeld using condensing NH3 instead of the refrigerant R134a in the outer pipe. In Table 4.3 the parameters of their experiments are presented. Table 4.3. Test parameters (after Jensen et al., 2000)

Parameter Concentration of ethanol Ice concentration Pipe diameters (inner diam.) Velocities Heating power

Pressure loss 5, 10, 20 mass-% 5, 10, 15, 20, 25, 30 mass-% 12.8, 21, 27.7 mm 0.5, 1, 1.5, 2 m/s -

Heat transfer 10 mass-% 5, 10, 20, 30 mass-% 12, 16, 20 mm 0.5, 1, 1.5 m/s 500, 1000, 1500 W

The average heat transfer coefficient, his, was determined using the temperature differences between the refrigerant NH3 and the ice slurry. The average Nusselt number was determined as follows: For X > 0.01:

Nu is( A) Nucf

= 10.42 ⋅ Re

−0.5 cf

⎛ D 2 ⋅ ρ cf ⋅ τ 0 ⎞ ⎟ ⋅⎜ ⎜ ⎟ η cf ⎝ ⎠

0.14

,

(4.11)

where

X=

τ0 . v ⋅ ρ cf

(4.12)

2

For X < 0.0015 it was assumed that the ice slurry behaves as a Newtonian fluid. Thus, it follows that:

Nu is( B ) Nucf

= 1.

(4.13)

96


For 0.0015 < X < 0.01 the following interpolation formula must be applied: Nuis = Nu is( A) ⋅ A + (1 − A) ⋅ Nu is( B ) ,

where:

A=

(4.14)

X − 0.0015 0.81 0.39 and Nucf = 0.0237 ⋅ Re cf ⋅ Prcf . 0.0085

(4.15)

The uncertainty in the experimentally determined Nusselt number is ±10%. These empirical formulae are valid for: • 0.5 < u is < 1.5m/s • 5 < Cv< 30% • 12 < Dh < 20mm • 1.6 < q& < 13kW/m2 • Initial ethanol concentration ξe = 10%. Knodel et al. (2000) measured the heat transfer rate in an ice slurry flow with a constant heat flux imposed by electrical heaters on a stainless steel tube of 24 mm inner diameter and 4596 mm length. The velocity of the ice slurry varied between 2.8 and 5 m/s. The experimental device was set up with two heaters, each having a 30 kW heating power. The ice slurry was produced with pure water. During each operation of the experimental loop, at different downstream positions, the local heat transfer coefficients were determined by evaluating the temperature difference between the pipe wall and the bulk temperature of the ice slurry which was kept constant at Tb = 0°C. For each cross section, the inner tube wall temperature was calculated using the energy conservation equation and the measured outer wall temperature. Then the heat transfer coefficient data were obtained as shown in Figure 4.14 and compared with Petukhov’s (1970) relation for the average Nusselt number:

Nucf =

⎛f⎞ ⎜ ⎟ Re cf Prcf ⎝8⎠ 1 2

(

)

, K1 = 1 + 3.4 ⋅ f cf ,

K 2 = 11.7 + 1.8 ⋅ Prcf

−

1 3

.

(4.16)

⎛f⎞ 2/3 K1 + K 2 ⎜ ⎟ Prcf − 1 ⎝8⎠

In Equation (4.16) all the quantities must be determined using the physical properties of the carrier fluid. The coefficient f stands for the friction factor and is calculated using:

f = (1.82 log10 Re cf − 1.64) . −2

(4.17)

For pipes of small diameters, the authors determined the following relation between the experimentally determined Nusselt number for the ice slurry flow and the one calculated using Eq.(4.15) as : Nuis (4.18) = 0.885 . Nucf The empirical equation above is valid for the following parameter ranges: • 4 < Cv < 11% • 3.8·104 < Re < 7.4·104 • Dh = 24 mm.

97


These equations are only valid for “pure water” as the carrier fluid. When the Nusselt number is evaluated using the properties of a 10 mass-% ethanol aqueous solution, it decreases with increasing ice mass fraction.

Figure 4.14. Nusselt number data for an ice slurry flow heated with a heat flux of 15 kW/m2 and 40 kW/m2 (Knodel et al., 2000)

Snoek and Bellamy (1997) performed heat transfer experiments with a 2 m long pipe of 15.74 mm internal diameter under the conditions summarized in Table 4.4. Table 4.4. Parameters of the experiments performed by Snoek and Bellamy (1997)

Variable Heat flux Velocity Glycol concentration Ice concentration

Range 28-114 5-12 8-10 4-33

Units kW/m2 m/s % %

The pipe was heated by electrical heaters to provide a constant heat flux. To describe the heat transfer rates Snoek and Bellamy applied the Dittus-Boelter (1930) equation for turbulent flow in a smooth pipe, where the ice slurry properties are used instead of the carrier fluid: hD− B ,is = 0.023

kis 0 ,8 Reis Pris0, 4 . D

(4.19)

After comparing the experimental results with the heat transfer coefficients calculated using equation (4.19), Snoek and Bellamy (1997) proposed the following correlation:

98


Θ = 0.924 + 0.076 ⋅ e

Θ=

his hD − B ,is

Cv 100

⎛C ⎞ − 6.43 ⋅ 10 ⎜ v ⎟ ⎝ 100 ⎠ −5

0.562

Reis

0.827

,

(4.20a)

(4.20b)

.

The predicted heat transfer coefficients are shown against the ice mass fraction in Figure 4.15. The accuracy of the proposed empirical model is ±10% when compared with their experimental results. They found that the heat transfer coefficient increases with increasing ice mass fraction (increase of 19% for Cv = 20%).

16000

22

(W/m K) K] αhis [W/m

12000 8000 v=5 m/s v=8 m/s

4000 0 0

10

20

30

Cv [%] (%) Figure 4.15. Calculated heat transfer coefficients obtained by using Equations (4.19) and (4.20)

Guilpart et al. (1999) worked with an aqueous ethanol solution (with an initial ethanol concentration of 11%) to produce ice slurry in their experimental device. The heat transfer section consisted of a copper tube of 30 mm inner diameter and 0.5 m length. The applied constant heat flux was varied between 0-12 kW/m2. The wall temperature profile in the downstream direction was measured with nine thermocouples, positioned at a distance of 2 mm from the inner wall. The heat transfer coefficients were determined by evaluating the difference between the wall temperature and the bulk fluid temperature measured at different equidistant downstream positions. From their experimental results, an equation describing the heat transfer for laminar ice slurry flow was proposed. It is of a Graetz-Nusselt type equation with an accuracy of approximately ±13%:

Nu(z ) = 38.3 ⋅ Gz

0.15

⎛C ⎞ ⋅⎜ v ⎟ ⎝ 100 ⎠

0.52

.

(4.21)

The Graetz number is calculated from: ⋅

Gz =

mis ⋅ c pis k is ⋅ z

=

π D 4

⋅

z

⋅ Re is ⋅ Pris .

(4.22)

99


The model equations are valid over the following parameter ranges: • •

0 < Cv < 35% 3 < Re < 2000.

The authors also introduced a dimensionless Cameron number, X+. Its value is related to the downstream position z by the following formula: z D = π . X+ = Re is ⋅ Pris 2 ⋅ Gzis 2

(4.23)

The predictions of Equations (4.21) – (4.23) are shown in Figure 4.16.

2 2

[W/mK)K] islocal(W/m αhis,local

3000

Cv=5% Cv=15% Cv=25%

2500 2000 1500 1000 500 0 0

0.0001

0.0002

0.0003

0.0004

0.0005

+

X [-] Figure 4.16. The local heat transfer coefficient calculated by applying Eq. (4.21) - (4.23)

Sari et al. (2000) performed experiments to determine the heat transfer rates in ice slurry flowing through an aluminium tube in a heat exchanger as shown in Figure 4.17. The cylindrical heat exchanger was equipped with four electrical heating elements (with a total power of 1.02 kW), which yielded a constant heat flux boundary condition. Between the heating elements the probes could be continuously driven into the fluid to measure temperature profiles in cross sections perpendicular to the tube axis. Temperature profiles were measured at the inlet, the outlet and at three axial locations in the intermediate region of the heat exchanger. In the cross sections at the inlet and outlet (sections 1 and 5, respectively), more measurements could be performed as shown in two cross sections each. In Figure 4.17, the possible positions of the temperature probes and the actual positions are clearly distinguished. The ice slurry was produced using an aqueous Talin solution with an initial Talin concentration of 10 mass-percent. In these experiments a constant heat flux of 14.1 kW/m2 was applied to the outer wall of the pipe. The heated section had a length of 1-meter and a

100


diameter of 23 mm. Experimental data on wall surface temperatures, fluid temperatures, mass flows, densities and inlet and outlet pressures were recorded. Rheological data were taken from experimental work, which had been published by Frei and Egolf (2000), whereas the ice concentration, the density and the overall specific heat were determined in accordance with the measurements and model calculations of Egolf and Frei (1999). The effective thermal conductivity was determined by applying Jeffrey’s model (see Table 4.1). In the paper of Sari et al. (2000), a perturbation analysis was performed to numerically determine the heat transfer rate in an ice slurry flow. The applicability of this model is limited to small heat fluxes. Even though the heat flux in the experiment was chosen to be low, the basic requirements for the validity of the perturbation model could be only approximately fulfilled. The reason is that a high temperature rise in a thermal boundary layer occurs, due to the low effective thermal conductivity of the ice slurry.

φ = 23mm, i

Aluminium tube: L= 1m,

q&

Electrical heaters: m& in ρin pin

1

Section 1

φ = 60mm e

2

Section 2

3

Section 3

4

Section 4

5 m& out ρout pout

Section 5

Surface temperature measurements Possibility of fluid temperature measurements Performed fluid temperature measurements Figure 4.17. Test section schematic and temperature measurement locations (Sari et al., 2000)

The numerical model was developed for laminar and turbulent flows by applying a simple turbulent Prandtl number concept for turbulent flow (Cebeci and Bradshaw, 1984). The numerical results for laminar flow showed that the heat transfer rate is rather small, because the thermal penetration depth is low. The reason is a small diffusivity perpendicular to the pipe wall compared to the high convection velocity in the flow direction in the heat exchanger. From these results, it was concluded that tube-like heat exchangers with laminar flow will not work very efficiently. The numerical programme to calculate turbulent ice slurry flows was based on an average turbulent eddy viscosity of εh = 6.4 mm2/s in order to get the best agreement between the calculated and measured temperature profiles. By multiplying εh by the specific heat and density, a “turbulent thermal conductivity” of 250 W/(m K) is obtained, which is 360 times higher than in the case of laminar flow (e.g. 0.7 W/(m K)). It is

101


not surprising that the “turbulent” convection heat transfer in a turbulent ice slurry flow is much more efficient than the molecular heat diffusion in a laminar flow. The mean temperature in the radial direction at a certain downstream location was determined by: R 1 (4.24) < T >r = 2π ∫ T (r )rdr Ac = πR 2 . Ac 0 The local heat transfer coefficient was then determined using the following formula: h( x ) =

q& ( x ) . Tw ( x )− < T > r ( x )

(4.25)

Numerically calculated temperature profiles (solid curves) are compared to measured profiles (black dots) in Figure 4.18. The cross sections 1 (x = 0 mm) to 5 (x = 1000 mm) correspond to the five sections shown in Figure 4.17. The flow direction is from the left to the right. At the inlet of the heat exchanger a constant temperature boundary condition was obtained. The surface temperatures of sections 2 to 4 are found to be higher and are not shown in these figures.

x = 0 mm

x = 250 mm

x = 500 mm

x = 750 mm

x = 1000 mm

Radial distance from center

10

5

0

-5

-10 -5.1 -4.9 -4.7 -4.5 -5.1 -4.9 -4.7 -4.5

-5.1 -4.9 -4.7 -4.5

-5.1 -4.9 -4.7 -4.5 -5.1

-4.9 -4.7

-4.5

Figure 4.18. Numerically calculated temperature profiles compared to measured profiles

The Nusselt number as a function of the Hedström number, characterizing the Bingham effect, is shown in Figure 4.19 for laminar flow. On the left, presented by a rectangular symbol, the Nusselt number for a water/ethanol system without any ice fraction, is shown. The Nusselt number as a function of the Hedström number is shown in Figure 4.20 for turbulent flow. The heat transfer coefficient is higher in turbulent flow than in laminar flow.

102


This can be seen by comparison of the results of Figures 4.19 and 4.20. This corresponds to the physical fact that turbulent fluctuations lead to an additional heat transport mechanism.

250

Nusselt number

200 150 100 Laminar Re=780-1620

50 0 0

5000 1000 1500 2000 2500 Hedström number

Figure 4.19. The Nusselt number as a function of the Hedström number for laminar flow

350

Nusselt number

300 250 200 Turbulent

150

Re =3890-4840

100 50 0 0

5000

1000 1500 Hedström number

2000

Figure 4.20. The Nusselt number as a function of the Hedström number for turbulent flow

In Equation (4.25), Tw(x) represents the wall temperature at position x. Figure 4.18 shows a comparison between the experimental and numerical results for turbulent flow. In Figures 4.19 and 4.20 the Nusselt numbers are presented as a function of the Hedstrom and Reynolds numbers. The circular symbols show the results obtained at different sections of the heat

103


exchanger. They are not specifically distinguished in this presentation. The black symbols show the mean values of each experimental series for a particular Reynolds number. The range of Reynolds numbers investigated is given in the figure. On the left, characterized by a large rectangular symbol, the Nusselt number for water/ethanol (without ice) is shown. This value is Nu = 4.3. For higher Hedström numbers, the Nusselt number increases, as expected by a physical explanation of an increasing melting process. The authors emphasized the importance of the effective thermal conductivity, the only relevant physical property that has not been measured yet. The laser flash method or the hot wire method with a Dirac heating pulse are being developed for such applications. In 2002, Bedecarrats studied the behaviour of polypropylene particles of 3 mm diameter and ice slurry with an aqueous ethanol solution of initially10 mass-% ethanol. The outer side of the heat exchanger pipe was heated with hot water. The temperature of the hot water was controlled at the location of the pipe entrance. The analysis of the experimental data was based on a modified Wilson method (Shah, 1990; Wilson, 1915), which was used to determine the values of heat transfer coefficients from the determination of the overall thermal resistance of the heat exchanger: R=

1 1 = = ∑ R j = Ri + Rw + Rd + Ro U o Ao U i Ai

(4.26)

and: ⎛r ⎞ ln⎜⎜ 2 ⎟⎟ 1 ⎝ r1 ⎠ + ⎛⎜ 1 + 1 ⎞⎟ + 1 , + R= hi Ai 2 ⋅ π ⋅ L ⋅ k ⎜⎝ hdi Ai hdo Ao ⎟⎠ ho Ao

(4.27)

where Ri denotes the inside film resistance, Rw the wall resistance, Rd the combined inside and outside fouling resistance, and R0 the outside film resistance. Wilson (1915) proposed his method, which was also described by Dittus and Boelter in 1930 and by Sieder and Tate in 1936. From these equations it may be shown that Ri is proportional to v-0.8. The effect of the velocity, v, on R0 occurs only indirectly (by an alteration of the average outside temperature) and is generally negligible. The effect on Rw and Rd is also negligible. Therefore, it follows that: R =

1 −0,8 ≈ C1 ⋅ (v ) + C 2 , U o ⋅ Ao

(4.28)

and: C2 = R0 + Rd + Rw .

(4.29)

The linear equation (4.29) has to be adapted to the outside film resistance and velocity by adjusting the two “constants”, C1 and C2. When the velocity approaches infinity, C1 represents the slope of the function and C2 is the intercept where v -0.8 = 0. Assuming a clean tube (Rd = 0) and taking the known value of Rw into consideration, ho can be defined by determining C2 from the graph. Once C2 has been determined, for a given velocity Ri is then determined by: Ri = R − C2 .

(4.30)

104


Measuring the heat flow and the logarithmic temperature difference between the fluid at the inlet and outlet, the overall resistance is determined by: •

Q U 0 ⋅ A0 = . ∆Tln

(4.31)

The authors have emphasized that an increase in ice mass fraction, while keeping the mass flow rate unaltered, increases the heat transfer coefficient, and an increase in the mass flow rate (at an unaltered ice concentration) also leads to an increase.

4.5.3 HEAT TRANSFER IN RECTANGULAR CHANNELS The thermal-hydraulic behavior of ice slurries in laminar and turbulent flows through noncircular channels is of special interest due to the wide application of such geometries in compact heat exchangers. Nonetheless, very few experimental and numerical investigations of ice slurries have been carried out in such geometries since the associated hydrodynamic and heat transfer phenomena are generally more complex than in circular pipes, and require twodimensional analysis. The following sections aim at presenting some fundamental aspects of the fluid mechanics and heat transfer properties of ice slurries in vertical rectangular channels. In 1998, Kawanami et al. performed an experiment with a horizontal rectangular duct of 1 m length and 60 mm width. It was designed with variable wall heights of 20, 40 and 60 mm. The top and bottom walls were electrically heated to guarantee a constant heat flux. An initial 20 mass-percent ethylene-glycol aqueous solution and a 20 mass-% ice concentration were chosen for these experiments. Four different heat fluxes of 2, 4, 6 and 8 kW/m2 were used and kept constant over the duration of each experiment. The average heat transfer coefficient was determined using the following equation: hx =

q& , Tw, x − Tis ,i

(4.32)

where Tw,x represents the wall temperature at the location x and Tis,i is the initial ice slurry temperature at the entrance to the heat exchanger, which is considered to be constant. Based on the results shown in Figure 4.21, the authors drew the following conclusions: •

At the lower wall the variation of the heat flux had less effect on the heat transfer coefficient than on the top wall. This was thought to be due to the stratification in the flow (heterogeneous flow) and a resulting smaller latent heat potential at the bottom of the channel. The applied heat served to increase the carrier fluid temperature in regions with mainly sensible heat absorption.

•

At the top wall the variation of the heat flux resulted in an increased heat transfer coefficient. This was due to a higher concentration of ice particles close to the top, and therefore, the temperature difference — as defined in Equation (4.32) — was small. According to Eq. (4.33) this results in an increase in the heat transfer coefficient.

105


Figure 4.21. Local heat transfer coefficients measured in a horizontal rectangular channel of height 60 mm. Other parameters are given in the figures (from Kawanami et al., 1998)

At the top wall, an increase in the ice slurry flow rate, while maintaining a certain heat flux, had less effect on the heat transfer coefficient than at the lower wall. The authors explained this by referring to less stratification in the flow at a higher ice slurry velocity. More ice particles would flow closer to the lower wall and so the heat transfer coefficient increases at higher velocities.

Figure 4.22. Flow patterns according to Kawanami et al. (1998) and some predictions of the IPF (ice packing factor) for different channel heights: a: H = 60 mm, b: H = 40 mm, c: H = 20 mm Kawanami et al. (1998) also studied the influence of the channel height on the heat transfer coefficient, while keeping the heat flux and the ice slurry flow rate constant. On both the bottom and top walls of the channel, the heat transfer coefficient decreases with the channel

106


height. For the same ice slurry flow rate, a higher channel wall leads to greater stratification of the ice slurry (see Figure 4.22). The authors explained this by assuming that a decreasing channel height increases the local velocity near the upper wall of the channel, inducing stronger mixing, and therefore, leading to a better heat transfer rate in this region. At the bottom of the channel, an increasing number of ice particles with the decreasing channel height is observed and this increases the heat transfer coefficient, because of the latent heat of the ice particles. Kawanami et al. (1998) determined the average heat transfer coefficient by applying Eq. (4.32). For different heat fluxes, they observed a significant difference in the heat transfer coefficients at the top and bottom walls of the channel. The higher curve, representing the greater heat transfer coefficient at the top wall, was related to the close contact of the ice particles and melting at the top wall in this region. For different velocities at a given heat flux and channel height, larger heat transfer coefficients were determined at the top of the channel. However, the slope of the curve representing the heat transfer coefficient versus velocity was higher for the lower wall of the channel. Increasing the velocity reduced the difference between the mean heat transfer coefficients at the top and the bottom walls. The variation in the channel height showed that the mean heat transfer coefficient was higher at the top channel wall, but both heat transfer coefficients decreased with the increasing channel height. By considering the difference in the heat transfer coefficients between the top and bottom channel walls, the authors proposed the following formula, which contains a dimensionless height and a dimensionless heat flux:

Num = 23.7 ⋅ Reis

0.15

⎛H⎞ ⋅⎜ ⎟ ⎝W ⎠

0.36

⋅ q *0.05 ,

(4.33)

where H is the height of the channel, W is its width and q* is the dimensionless heat flux defined using the latent heat of the ice, hm, in J/kg as follows: ⋅

q* =

q hm ⋅ ρ is ⋅ vis

,

(4.34)

The predicted mean heat transfer coefficients are shown in Figure 4.23. 650 600

2

αis his (W/m K)

2 K] [W/m

550 500 450 400 350 300 0.02

v=0,2 m/s; q*=3 kW/m2 v=0,7 m/s; q*=3 kW/m2 v=0,2 m/s; q*=7 kW/m2 v=0,7 m/s; q*=7 kW/m2

0.03

0.04

0.05

0.06

H [m]

H (m) Figure 4.23. Mean heat transfer coefficients calculated using Eqs. (4.33) and (4.34)

107


The accuracy of this empirical equation is ±20%, and it is valid for the following parameter values and ranges: • Cv = 20% • 0.1 < vis < 0.8 m/s • H = 20/40/60 mm • 2 < q& < 8 kW/m2. At the University of Applied Sciences of Western Switzerland, Kitanovski et al. (2003) studied heat transfer to an ice slurry of a 10% propylene-glycol solution. This ice slurry flowed through a rectangular, horizontal aluminium heat exchanger of 1-meter length. The hydraulic diameter was 23 mm, which is identical to the inner diameter of the tube heat exchanger used in the previous work of this research team. Two mass flow meters were installed, one before and the other after the heat exchanger. Temperatures at the inlet and outlet were measured with Pt-1000 sensors, while the vertical temperature profiles at discrete cross sections of the heat exchanger were measured with thermocouples. Low (1800 W/m2) and high (7200 W/m2) heat fluxes were used. For the low heat flux case, temperature distributions in the channel cross section were measured in the heat exchanger at five equidistant downstream locations (the first cross section at the inlet, and subsequent downstream locations in steps of 0.25 m). For the higher heat flux of 7200 W/m2, the temperature distribution was measured only at three axial locations (the first cross section at the inlet and in steps of 0.5 m). Simultaneously with the temperature measurements, the pressure drop was determined at four equidistant axial locations. The experimental data (temperature profiles) revealed a turbulent flow through the test section. Therefore, a thermal eddy diffusivity model was introduced in the numerical simulations. It is known that such local turbulence modelling cannot give an accurate description (see e.g. Egolf and Weiss, 2000). Nevertheless, in such a case, it yields a simple and valuable first approach. Figure 4.24 shows the temperature distributions in the downstream direction of this rectangular heat exchanger for the low heat flux case. The authors assumed that a perturbation analysis only approximately applies to such small heat fluxes, but they have not derived a criterion for this. Each temperature profile measurement was performed in a separate experiment and since the initial temperature conditions at the inlet were not always identical, they are specified in Figure 4.24 on the right-hand side of the curves.

Figure 4.24. Experimentally and numerically determined temperature profiles for a heat flux of 1800 W/m2 in a 1-meter long rectangular heat exchanger at a mass flow rate of 1.2 kg/s. The measurement locations were: x = 0.25 m, 0.5 m, 0.75 m and 1 m. Trapezoidal symbols denote experimental data, while small triangles and the fitted solid curves represent numerically calculated profiles

108


In Figure 4.25 the temperature profiles for the higher heat flux case are presented. A significant deviation between numerical and experimental temperature profiles is observed. The authors have explained that this is due to a failure of the perturbation analysis model at very high heat flux densities. In all cases the temperature distributions were not exactly axisymmetric. The reason is a stratification of the ice particle field. Ice particles have a lower density than the carrier fluid. This leads to higher ice concentrations at the top of the channel. Therefore, lower temperatures were observed in the higher layers. In all cases the flow was heterogeneous with an average velocity of approximately 0.75 m/s. As seen in Figures 4.24 and 4.25, there are low gradients of the temperature profiles T(y,x=const) towards the wall. The temperature measurements close to the wall are very difficult to perform. Therefore, these measurements have to be interpreted very carefully; as the authors have stated, they could even be erroneous.

Figure 4.25. Temperature profiles for a heat flux of 7200 W/m2 in a 1-meter long rectangular heat exchanger. The axial locations of the measurements are: x = 0.5 m and 1 m. Trapezoidal symbols denote experimental data and the solid curves represent numerically calculated profiles

Figure 4.26 shows the ratio of the thermal eddy diffusivity to thermal diffusivity related to molecular diffusion. The turbulent diffusivities were determined by fitting the numerical calculation results to the measured temperature profiles. Surprisingly these ratios decrease in downstream direction. The results for the low and high heat flux cases show qualitatively the same behaviour.

Figure 4.26. Ratios between the thermal eddy diffusivity and the thermal diffusivity at different axial locations in a rectangular heat exchanger for different heat fluxes. The data correspond to the results shown in Figures 4.24 and 4.25. The dotted line was drawn in analogy to the solid line. It must be confirmed by more measurements

109


The ratio of the thermal eddy diffusivity to the molecular diffusivity is large near the inlet of the heat exchanger and decreases continuously toward the outlet. A diffuser was mounted at 1-meter upstream of the heat exchanger inlet, with an inclination angle of 20°. It was assumed that in this diffuser strong turbulent fluctuations (eddies) were created, which then decayed when transported downstream. As a result even in isothermal flows the turbulent characteristics were not constant but varied as a function of the downstream location x. This explains the decreasing ratio of diffusivities. This observation was made by numerical investigations by altering the eddy diffusivity and applying curve fitting to the measured and calculated temperature profiles. A second important observation was a deviation between the measured temperatures at the outlet and the equilibrium ice fractions. The density measurements, which are a reliable measure of the ice concentration, showed higher ice fractions at the outlet than expected by temperature measurements. Temperatures above 0oC were observed, while the corresponding density measurements clearly showed a non-negligible ice fraction in the fluid. Therefore, overheating of the carrier fluid appears to have occurred, which may have influenced the measurements of the temperature sensors. This phenomenon has also been observed in other laboratories. It has also occurred in plate heat exchangers (e.g. see Frei and Boyman, 2003). Stamatiou and Kawaji (2004b) also studied heat transfer in rectangular channels with a constant heat flux. For the cross section of a rectangular duct shown in Figure 4.27, the dimensions H and W define the height and width, the ratio of which is the channel aspect ratio, α* = H/W. If α*→ ∞, it corresponds to a channel between two parallel plates, in which case the side walls will have an insignificant effect on the flow field. For flows in non-circular channels, the hydraulic diameter Dh of the duct is commonly used as the characteristic length (Cho et al., 1998). The hydraulic diameter for the rectangular duct of Figure 4.27 is defined as follows: Dh = 4 Ac P =

2( H ⋅ W ) (H + W )

(4.35)

where Ac is the flow cross sectional area and P is the wetted perimeter of the channel. y

H x

α*=H/W

W Figure 4.27. Geometrical dimensions of a rectangular duct

Heat Transfer Parameters The circumferentially averaged but axially local ice slurry heat transfer coefficient hsl,L for a constant wall heat flux, q w" , is defined by:

110


constant wall heat flux, q w" , is defined by: qw'' = his ,L (Tw,m − Tis ,m ) ,

(4.36)

where Tw,m is the mean wall temperature, and Tis,m is the bulk ice slurry temperature. The ice slurry heat transfer results are presented in terms of a dimensionless heat transfer coefficient known as the Nusselt number, Nu. The local ice slurry Nusselt number, Nucf,L, was evaluated based on the local heat transfer coefficient (his,L), the thermal conductivity of the carrier fluid (kcf), and the hydraulic diameter, Dh:

Nu cf , L =

his , L ⋅ Dh k cf

.

(4.37)

The average ice slurry Nusselt number, Nucf,m, was defined based on the carrier fluid properties, and was computed using the arithmetic mean of the local ice slurry Nusselt numbers (Stamatiou and Kawaji, 2004b).

Thermal Boundary Condition The thermal boundary condition H was investigated in which a uniform wall heat flux is applied axially at one heated wall, while the other walls are maintained at nearly adiabatic condition.

Comparison with Single-Phase Heat Transfer Data The Nusselt numbers can be compared with well known single-phase heat transfer correlations to examine the effect of ice crystals on the average heat transfer coefficient. These single-phase heat transfer correlations are summarized below.

Turbulent Single-Phase Convection The average ice slurry Nusselt numbers can be compared with well known single-phase convective heat transfer correlations for fully developed turbulent tube flow in the thermal entrance region given by Eq. (4.38) (Holman, 1998; Knudsen, 1958), ⎛D ⎞ Nu cf = 0.036 Recf0.8 ⋅ Prcf1 / 3 ⎜ h ⎟ ⎝ L ⎠

0.055

10
0.9

(2)η = 0.6

(a) Ice melting process in the spray method (lateral view)

Outlet Ice-rich Layer

Ice-rich

Layer

Water

Moving Inlet

(1)η < 0.3

Jet Flow

Jet Nozzle

(2)η = 0.6

(3)η > 0.9

(b) Ice melting process in the jet method (seen from above) Figure 7.4. Ice melting process in a tank

7.2 Mixing tanks 7.2.1 MIXING METHODS/DEVICES AND PROCESSES Mixing is applied in homogeneous storage tanks to avoid separation of the ice from the liquid phase. In heterogeneous storage tanks with harvested pure ice, external mixing of the ice with pre-cooled coolant in an agitated mixing tank is required before distribution by the transport system. Some examples of common mechanical agitation devices are: – Propellers with flat inclined blades or 3D-shaped blades – Agitators with cross bars – Agitators with a special shape Agitators can be installed vertically from above or horizontally through a side wall, or in the case of an immersed agitator, they are directly located in the storage medium and hence the driving unit must be totally sealed. A disadvantage of the latter option is that all the driving power including waste heat is dissipated as heat into the ice slurry.

207


A complete circulation of the tank contents is necessary for homogenous storage. That can be achieved with large diameter agitators at low rotational speeds and moderate power input. The mean flow in the tank can be supported by jet nozzles. There is no application known which exclusively uses jet nozzles for mixing in a homogeneous tank. The specific power input decreases with an increasing diameter ratio, Dagitator / Dtank , whereby the torque of the agitator shaft increases at the same time. Also the agitator location (height and distance from the centre of the tank) is important for its effectiveness. In cylindrical storage tanks with a centrally arranged agitator, special baffles might be necessary in order to achieve complete mixing. Tanks of cubic shape do not need these baffles, since the flow direction will be sufficiently disturbed by the tank walls resulting in good mixing. An upper limit on the average ice fraction in propeller-mixed storages is found to be 25 wt-% in available literature (Kakutami and Noburo, 1999). Up to 35 wt-% ice fraction has been reached by optimisation of propeller design and location as well as the propeller speed (Hansen et al., 2002). The main advantages of homogeneous ice slurry storage are reduced agglomeration of ice crystals and the easy discharge of the slurry. Good discharge performance and very good heat transfer rates are achieved due to the large specific surface area of the small ice crystals. Because of the limitation on the average ice fraction, homogenous ice storage systems have to be designed with a larger storage volume than heterogeneous storage systems.

7.2.2 STRATIFICATION IN MIXING TANKS In the following, stratification is defined as the separation of ice crystals and liquid as a result of different densities of the components. The ascent of the lighter ice crystals within the liquid proceeds all the time until stable stratification has been reached. This steady state condition implies that all ice particles are at the top of the tank and the maximum packing factor has been reached. That means each particle is in direct contact with the adjacent particles and not enough space exists between the particles to get any closer. This maximum packing factor depends on the crystal shape and size distribution. For spherical particles of uniform size, it is 74%. For ice slurry the value might be higher due to the dish-like shape and non-uniform size-distribution. There is a lack of knowledge on whether the particles and their shape in this packed layer are affected by the compressive force, which arises from the buoyancy force on the single particles. Stratification occurs in ice slurry tanks if no efforts are undertaken to keep the slurry mixed. That might be the case for a stationary agitator. The density driven process of separation of ice crystals and liquid depends on the following parameters: – – – –

density difference between ice and liquid ice crystal size and shape viscosity of the liquid overall ice concentration

208


For ascending ice particles in an unmixed storage tank laminar flow prevails. In an agitated storage tank, stratification can occur if the agitator is operated at too low a speed and power. Then usually a three-dimensional turbulent flow exists. For this case (Re > 104) the shape of the particles has only very little influence on the rate of ascent (Schempp, 1996). Particle distributions in a tank also have been calculated by Egolf et al. (2001) using a multicomponent approach.

7.2.3 POWER CONSUMPTION IN NEWTONIAN RANGE Propellers have been tested at the Danish Technological Institute (Hansen et al., 2002) and the power consumption was approximately 70 W per m³ storage volume. The required mixing power rises significantly above 30 wt-% ice and the practical limit for most applications therefore is considered to be between 30 and 35 wt-%. Values for specific power consumption in actual ice slurry applications are rather higher than the 70 W per m³ storage volume stated above (Huhn, 2003).

7.2.4 POWER CONSUMPTION FOR THE HIGHLY-VISCOUS RANGE Although the transition from the Newtonian to the Bingham behaviour has been reported to depend on both ice concentration and additive concentration (Nørgaard et al., 2000; Frei and Egolf, 2000), a widely applicable map of the transition from Newtonian to Bingham behaviour, and the magnitude of shear stress required are still lacking (Hansen et al., 2002). In the available literature, different values for the transition from the Newtonian range to “highviscous range” are found, varying between 20 and 30 wt-%. Higher ice fractions up to 52 wt-% in agitated homogeneous storage systems have been achieved at the Danish Technological Institute by applying a special spiral-shaped stirring device. Non-Newtonian behaviour can be assumed for this case. Mixing was possible, but a strongly increased power input was required compared to the case of ice fractions within the Newtonian range (up to 30 wt-%) and mixing with a propeller. An increase by a factor of 10 was reported.

7.3 Numerical modelling of storage tank design A numerical model has been applied to an actual design of supercooling-type ice storage systems (Tanino et al., 1995, 1997, 1999 and 2001). 7.3.1 PHYSICAL MODELLING OF ACCUMULATION/PILING AND MELTING The accumulation and piling of ice was modelled, as shown in Figure 7.5, in order to determine the overall properties of the ice storage process (the contour of ice-rich layer) and to make use of them in the actual design (Tanino et al., 1997; Kozawa and Tanino, 1999; Kozawa et al., 2001; Tanino and Kozawa, 2001). A two-dimensional cylindrical coordinate system was adopted, and the following assumptions were made:

209


(a) There is no heat transfer (b) Flow in the water region inside the tank is not considered. The time history of the contour of the ice-rich layer can be calculated, considering the mass conservation in the upper part of the ice-rich layer. The calculation procedure is as follows; (1) Calculate the velocity distribution of the water permeating through the ice-rich layer. (2) Estimate the quantity of ice accumulated in a given time interval. (3) Consider the deformation and increasing compactness of the ice-rich layer. (4) Determine the contour of the ice-rich layer, and repeat steps (1) to (4) at a new time step. Center axis

Center axis

z

z Supply opening Ice piling on upper surface Mz(r) Ice slurry

Ice content αice=2.5%

G

u v

Ice growing toward perimeter Mr moving Ice granules bed

v

Ice-rich layer

Ice piling on upper surface

Water velocity v

Ice growing up toward the upper space

Initial Water level Packing by self-weight

Shear stress

τi

Water Deformation by buoyancy and self-weight In the only water region, the effect of flow is not considered

Side wall

Side wall Ice-rich layer

Radius axis

Radius axis

r

(1)

r

(2)

Figure 7.5. Overview of ice storage model in a tank In the ice melting process, stored ice particles in the ice-rich layer melt, and the ice layer is rebuilt by breaking up and re-agglomerating, causing non-uniform thermohydraulic behaviour within the ice-rich layer. It is most important for the actual design to determine how the temperature of the cold water changes with time at the outlet of the tank. A one-dimensional model (Kozawa and Tanino, 1999; Tanino and Kozawa, 2001; Tanino and Kozawa, 2001) was adopted in the water depth direction as shown in Figure 7.6. In this model of the ice melting process, it was assumed that: (a) The ice particles in the ice layer are spherical in shape (b) Within each calculation element, the diameter of the ice particles changes with time, but they are spatially uniform (c) The number of ice particles within each calculation element is temporally constant (d) Water is completely mixed in the water region at the bottom of the ice layer. The time history of the cold water temperature at the outlet of the tank, in a computational 210


element, can be calculated using relationships between length, porosity, and ice particle radius. The calculation procedure is as follows: (1) Calculate the amount of ice melting within the ice-rich layer. (2) Calculate the spatial distribution of the temperature of the water permeating through the ice-rich layer, using the mass and energy conservation equations within the icerich layer. (3) Estimate the spatial distribution of porosity and ice particles radius within the icerich layer. (4) Calculate the temperature at the outlet of the tank. (5) Determine the water temperature at the inlet of the tank, and repeat steps (1) to (5) at a new time step. Water Inlet

r0

Water permeating in ice-rich layer

m

u Tl0

ε0

Water cooling in ice-rich layer

r0

r : Radius of an ice particle ε : porosity of ice-richlayer

lo

u r0

ε0

l : Calucration element

Tl0 Tout

Water mixing in only-water region

Water Outlet

Tl u

m

Tl u(b)

T (b)

Tl : Water temperature u : Water velocity Water Tout

Time = 0

l

u

r,ε Tl0

ε0

Tl

l

Tl0

Tl

u

l

m

Time = t

Thickness of ice-rich layer

lo

ε0

m

Ice melting in ice-rich layer

u lo

Thickness of ice-rich layer

lo

u r0

Spray nozzle

Tin

l

Ice Particle ( 0 Ž) r,ε

Tin

Only-water region

Ice-rich Layer

m : Mass rate of ice melting

Figure7.6. Overview of the ice melting model in a water-spraying system

7.3.2 MATHEMATICAL MODELLING For the accumulation and piling model of the ice storage process in Figure 7.5, Equation (7.1) expresses the mass conservation in a time interval (∆t) at the upper surface of the ice-rich layer, when the ice slurry supplied at the upper part of the centre axis flows in the radial direction (Figure 7.5) along the upper surface of the layer:

αiceG∆t = ∑ rr =0 Mz (r ) + Mr

(7.1)

Here, Mz(r) is the amount of ice accumulation in the vertical direction (the z direction in Figure 7.5) during time ∆t on the upper surface of the ice-rich layer. Mr is the amount of ice growing in the r direction during time ∆t along the perimeter of the ice-rich layer. The symbol

211


α denotes the content of the ice slurry and G is the mass flow rate of the ice slurry supplied from the supply opening. If the velocity of water permeating downward from the upper surface through the ice-rich layer is determined, the amounts of ice Mz(r) and Mr can be calculated. A continuity equation for water permeating through the ice-rich layer can be written as follows:

∂u u ∂v + + =0 ∂r r ∂z

(7.2)

Here, u and v are permeated water velocities through the ice-rich layer in r and z directions, respectively. The permeating water flow through the ice-rich layer is assumed to obey Darcy’s law, thus the velocities are expressed as follows:

u=−

κ ∂p µ l ∂r

v=−

(7.3a),

κ ∂p κ − ρl g µ l ∂z µ l

(7.3b)

where p is the pressure, g is the gravitational acceleration, and κ is the permeability of water in the ice-rich layer, and µl and ρl are the viscosity and the density of water, respectively. The boundary conditions for the pressure can de determined as follows:

p = p0 p = p0 – ρlgh dp/dr = 0

(interface between the ice-rich layer and the atmosphere) (interface between the ice-rich layer and the water) (central axis of symmetry)

where h is the water depth and p0 is the atmospheric pressure. The permeability of water in the floating ice-rich layer was determined from experiments by using a test cylinder (Tanino et al., 1997). In this model a constant value for the permeability (κ = 1.4 × 10-9m2) was adopted from the experimental data. A balance of forces in the floating ice-rich layer is considered to yield the deformation of the ice-rich layer due to the buoyancy force and the weight of the floating ice-rich layer. This means that the floating ice-rich layer is not solid but deforms by the shear stress due to the buoyancy and the weight of the cross section in the z direction. Separate cylindrical shells of the floating ice-rich layer are assumed to allow the movement in the z direction, where its buoyancy and its own weight are in balance. Equation (7.4) is used to calculate the shear stress.

τ i = Fi / 2πrili

(7.4)

(

)

Fi = ∫ r p 2π rl a (1 − ε )ρ i gdr − ∫ r p 2π rl b (1 − ε ) ρ l − ρ s gdr ri ri

where τi is the shear stress. The quantity ε is the porosity in the floating ice-rich layer (ε = 0.85), ρs is the density of ice, a subscript i denotes a position in the r direction, subscripts a and b represent the heights of the floating ice-rich layer above and below the water level, and a subscript p denotes the perimeter of the ice-rich layer.

212


It is assumed that the shear stress of 4.9 Pa can divide the floating ice-rich layer, which then leads to rearrangement and marching of the ice-rich layer. In the ice storage process, after the floating ice-rich layer reaches the bottom of the tank, the layer is compressed due to its own weight of accumulated ice. From ice packing experiments using test cylinders, the change in porosity due to the pressure by the weight of the accumulated ice-rich layer is determined as follows:

ε = 0.85 − 5 × 10 −5 ⋅ p press

(ppress 10 × 10 Pa)

(7.5 b)

3

where ε is the porosity of the ice-rich layer and ppress is the pressure given by the weight of the accumulated ice-rich layer. It is assumed that the relationship between the porosity and permeability of the compressed ice-rich layer can be described by the following equation: ⎧⎛ ε ⎪ κ = κ f ⋅ ⎨⎜⎜ ⎪⎩⎝ ε f

⎞ ⎟ ⎟ ⎠

3

⎛1 − ε f ⎜ ⎜ 1− ε ⎝

⎞ ⎟ ⎟ ⎠

2

a

⎫ ⎪ ⎬ , ⎪⎭

a = 0.1

(7.6)

where εf is the porosity of the floating ice-rich layer (εf =0.85) and κf is the permeability of water in the floating ice-rich layer (κf =1.4 × 10-9 m2). For the model describing ice melting in Figure 7.6, the changes in the length and porosity of the ice-rich layer and radius of the ice particle are calculated using the mass conservation equation (7.7). In this manner the reduction in the amount of ice in a computational element of the melting ice-rich layer is calculated. 3 M S = ρ S ⋅ l ⋅ A ⋅ (1 − ε ) = πr 3 nρ S 4

(7.7)

Here Ms denotes the mass of ice, l is the length of the computational element, ε is the porosity, r is the radius of the ice particles, n is the number of ice particles of radius r in the computational element, which is assumed to be constant in the ice melting process, A is the cross-sectional area of the tank and ρs denotes the density of ice. The relationship between the length and the porosity in the computational element is as follows:

ε = 1−

1 − ε0 l l0

(7.8)

Here, a subscript 0 denotes the initial condition, and n / (l•A ) = 1.6×105 for ε0 = 0.9. Because the temperature of ice is 0 °C in the supercooling-type ice storage system, the energy conservation in the ice-rich layer can be described by Equation (7.9), in which the thermal conduction term is neglected:

εcl ρl

∂Tl ∂T m (clT + hL ) + εcl ρ l u l = ∂t ∂z εAl 213

(7.9)


Here Tl and u are the temperature and velocity of the permeating water, respectively, m is the quantity of water produced by melting of ice in the ice-rich layer, cl is the specific heat of water, ρl is the density of water and hL denotes the latent heat of ice. The mass conservation in the ice-rich layer can be written as follows:

ερl

∂u m ερl dz = + ∂z Al l dt

(7.10)

Here dz/dt denotes the change in height due to the melting of ice. The time history of the temperature of the cold water taken from the ice storage tank can be calculated according to a heat balance in the water region below the ice layer. It is assumed that the water is completely mixed in the region. Then it follows:

∂H (Tout − Ts ) + H ∂Tout = u( b )Tl ( b ) − uoutTout ∂t ∂t

(7.11)

where Tout is the water temperature below the ice-rich layer at the outlet of the tank, H is the height of the water region below the ice-rich layer, Ts is the temperature of ice (0 °C), and a subscript (b) denotes a position in the boundary between the ice-rich layer and the water region. In the model the most important step is to estimate the amount of melting ice in the ice-rich layer correctly. The amount of melting ice is calculated as follows: m=−

αp =

dM S α p Ap ( Tl − TS ) = dt hL

λl

2r

(7.12a)

⋅ Nu

(7.12b)

Here αP is the heat transfer coefficient between the ice particles and the water, Ap is the surface area of ice particles in the calculation element, λl is the thermal conductivity of water and Nu is the Nusselt number for a sphere. Microscopically the interior of the ice-rich layer is not uniform at all positions; there exist "water paths" along the side wall of the tank and within the ice-rich layer, and the flow of permeating water within the ice-rich layer varies with time and space. Thus, how the area of effective heat transfer surface changes with respect to the quantity of water produced in the ice-rich layer was modelled as follows: Ap = C ⋅ 4πr 2 n

(7.12c)

C = C1 (ε ) ⋅ C2 (uavg ) ⋅ C3 (Lice )

(7.12d)

Here C is the product of the effective heat transfer area affected by the porosity within the icerich layer C1(ε), the velocity of the permeating water within the ice-rich layer C2(uavg) and the side wall surface of the ice storage tank C3(Lice). Formulae for these quantities are shown in Table 7.1.

214


Table 7.1. Ratio of effective heat transfer area Effect of porosity within ice-rich layer C1 (ε)

Effect of velocity of permeating water C2 (uavg) Effect of side wall surface of tank C3 (Lice)

C1 (ε ) = 0.2

(ε0.9)

(

C 2 u avg

)

⎛ u avg =⎜ ⎜ u avg 0 ⎝

⎞ ⎟ ⎟ ⎠

2

, uavg0=0.87mm/s

C3 ( Lice ) = (Lice / L0 )−2 , Lice: Initial

L0 = 0.7m

7.3.3 CONFIRMATION OF MODELLING The time history of the floating ice-rich layer was investigated experimentally with two mass flow rates, G = 0.33 and 0.92 kg/s, with a comparison of calculation results shown in Figure 7.7 (1). When G is small, (G = 0.33 kg/s), the contour of the floating ice-rich layer did not spread to the side wall and the water region was formed in the tank, as shown in picture (a). But when G is large, (G = 0.92 kg/s), as shown in picture (b), then the contour of the floating ice-rich layer maintains one-dimensionality in the direction of the water depth, with almost no formation of a water region. Thus it was possible to demonstrate with this calculation model the difference in the contours of the floating ice-rich layer due to differences in the mass flow rate G, as obtained in experiments. Figure 7.7 (2) presents a comparison of calculated and experimental results for the evolution in the contour of a compact ice-rich layer (the piled ice-rich layer) after the floating ice-rich layer reaches the bottom wall of the tank. The mass flow rate G = 1.11 kg/s is the condition under which a floating ice-rich layer is formed whose one-dimensionality in the direction of water depth is maintained (G > 0.92 kg/s). In this figure some difference is seen between the measured and calculated contours of the piled ice-rich layer. There was no big difference between the experimental and predicted results for the maximum thickness of the piled icerich layer in the center of the tank 80 minutes later (the time after the ice-rich layer reached the bottom of the tank).

215


10min 20min

0.4

20min

Ice-rich layer

0.3

0.6

0.4

0.6

Water

40min

0.5 Ice-rich layer 20min

0.4

0.5

20min

0.4 Ice-rich layer

30min

0.2

0.2

0.3

0.1

0.1

0

0.2 0.1

0.1

0.2

40min

0.1 46min

Water

0 0.5 0.4 0.3 0.2 0.1

0 0.5

0.3 0.4

0.2

40min

36min

0.4 0.3

10min

30min 30min

0 0.5

0.7

0.3

0.3

0.2 Water

0.6 0.5

Ice-rich layer

30min

0.1

0.7

0.8 Initial Water level

10min

10min

0.5

0.7

z,m

0.6

Initial Water level

z,m

0.7

z,m

0.8

0.8 Initial Water level

0

0.1

0.2

0.3

Water

0.4

0 0.5

r,m

r,m Experiment

Experiment

Prediction

(a) G= 0.33 kg/s (vavg = 4.2×10-4 m/s )

Prediction

(b) G= 0.92 kg/s (vavg = 1.17×10-3 m/s)

(1) Comparison of contours of floating ice-rich layer between experimental and calculation results Center axis

Side wall 1.2

1

Side wall 1.2

Suplly of Ice Slurry G =1.11kg/s G =1.11kg/s α ice =2.5% 80m in

Operatiom time=80min

1

70m in

60min 70min

60m in

40min 30min

0.8

Ice-rich layer 50m in 40m in

z ,m

0min

30m in

Initial water level

0.6

0.6

z z,m ,m

0.8

Ice-rich layer -30min

0.4

0.4

Operation time=

Ice-rich layer

-30min

-15min

0.2

0min

0 0.5

0.2

Operation time=0min Ice-rich layer reaching the bottom of tank

-15min

0 0.4

0.3

0.2

0.1

0

0.1

0.2

0.3

0.4

Bottom wall

0.5

rr r,m , ,mm

r ,m

Prediction

Experimant

(2) Comparison of contours of piled ice-rich layer between experimental and calculation results Figure 7.7. Comparison of prediction and measurement in an ice storage process

The design conditions of an ice storage tank for storing a prescribed amount of ice (thermal energy) can be determined by calculating the contour of the ice-rich layer based on this model. At first the ice slurry flow rate (for the effective use of the volume of the ice storage tank) and

216

z,m

0.8


the number and positions of the ice slurry supply openings are determined from the horizontal distribution of the floating ice-rich layer. Figure 7.8 shows both the calculation and experimental results on the relationship among the average downward superficial velocity of water inside the tank vavg, the ice packing factor (IPF), and the thickness of the ice-rich layer at the side wall in relation to the central axis of the tank Lmin/Lmax. The radius of the ice storage tank R is 0.5 m and the water depth h is 0.62m. As evident in the figure, vavg > 0.8 mm/s can be determined as the condition that allows the tank volume to be used effectively with the ice-rich layer spreading to the side wall and the water region remaining small (Lmin/Lmax>>0). 20

1

Lmin/Lmax(exp)

R=0.5m 16 G=0.33

0.92kg/s

0,8

12 Lmin/Lmax(exp)

0,6

8

0,4

IPF(exp) 4

0 IPF(exp) 0,2

0,2

IPF(cal) 0,4 0,6

Lmin/Lmax(cal)

0,8

1

Lmin/Lmax (-)

IPF (%)

h=0.62m

0 1,2

v avg (m/s) ×10

-3

Figure 7.8. Rate of utilisation of the volume of the ice storage tank Moreover, the height of the space above the initial water level in the tank (freeboard) is determined from the distribution in the height direction of the piled ice-rich layer. Figure 7.9 shows the predicted contour of the ice-rich layer for the actual design study in a large scale ice storage tank of size 8.8 × 8.5 × 4 m (length x width x height). Here, R is the equivalent radius of the cross-sectional area of the rectangular tank (1/2 the distance between the ice slurry supply openings). In the figure, predicted results are shown when the ice-rich layer reaches the side wall of the tank, and in 480 minutes of ice storage operation, approximately 0.4 m of ice piles up in the vertical direction from the initial water level. Through this calculation, the number of ice slurry supply openings required to store the prescribed quantity of ice and perform ice storage operation for 480 minutes could be determined. From such predicted contours of the ice-rich layer and the structure inside the tank (placement of girders and communicating openings to other tanks), the height of the available space at the top of the tank could be calculated as 1.2 m (water depth = 2.8 m).

217


4 Supply of Slurry Ice

Initial Water Level

480min

3

z,m

60min 120min

2

180min

Ice-rich Layer

240min

1

Water 0 0

1

2

3

4

R =4.9m

r,m (a) Predicted contours of an ice-rich layer in a large scale tank Supply of Ice Slurry

Ice-rich layer

(b) Ice-rich layer in an actual large scale tank Figure 7.9. Design conditions for ice storage

A comparison between the experimental and predicted results for the cold water temperature at the outlet of a flat tank in the ice melting process is presented in Figure 7.10. Tout(exp) is the experimental value, Tout(cal) is the calculated value according to this model, Lice is the calculated value of the thickness of the ice-rich layer, W is the flow rate of sprayed water, and IPF is the ice packing factor under charging conditions, which is averaged over an initial water volume. The experimental results can be well predicted by the model. Also shown in figure 7.10 is Tout(emp-rel) which is the value obtained from a simple empirical correlation developed assuming the temperature within the ice-rich layer to be at the freezing-point everywhere, and using the ice-rich layer cooling capacity obtained from an analysis of the experimental data (Tanino et al., 1995, Tanino et al., 1997 and Mito et al., 2001). These models of storing (accumulating/baling) and melting ice have been used for the design in over 20 actual supercooling-type ice storage systems in Japan. The sizes of the systems vary from 25 to 1120 m3 tank capacity and 25 to 1060 tons of refrigeration cooling capacity. Applications cover office buildings, colleges, commercial buildings, shopping centres, food distribution centres and factories.

218


Tank:2.5×2.0×2.4mH (Initial water level=1.6 mH) IPF=34% W=15 m 3/h Heat Lice Ice manufacturing =3 Heat load=71kw Tin

7

1.8

0.9

Lice ,m

T , •C

14

Tout(cal) Tout(emp-rel)

Tout(exp

0

0 0

120

240

t , min

Figure 7.10. Comparison of experimental and predicted results for cold water exit temperature from a flat water tank

7.4 Numerical modelling for mixing tank design

7.4.1 PHYSICAL MODELLING OF FLOW AND STRATIFICATION

In modelling the stratification process, the forces acting on the ice particles have to be in equilibrium. Then the velocity and the distribution of ice particles can be calculated. The forces acting on the ice particle are (Westphal, 1947): – gravity, – buoyancy, – drag force on the particle moving in the liquid. The rise velocity of an isolated particle can then be derived. It corresponds to the required local downward flow velocity of the liquid to keep the particle in balance and thus prevent stratification. To determine the drag force, a spherical particle shape and laminar flow at low Reynolds numbers are assumed. The ice particles are in practice not isolated but interact with each other. A downward flow of the liquid will occur, balancing the volume in the tank if the particles ascend. The effective rise velocity is then different from the local velocity between the particles and liquid. Therefore a correction for the rise velocity of a particle swarm dependent on the average ice concentration has to be applied. In agitated tanks with turbulent flow the rise velocity of the ice crystals is superposed with the mean flow of the liquid. A clear reduction in the local rise velocity of the particles in the liquid can result from this, but reliable quantitative results are rare even for particle loaded flows in general (Schempp, 1996).

219


7.4.2 MATHEMATICAL MODELLING The following three equations define mathematically the storage problem with buoyancyinduced motion of the ice particles in an ice slurry with diffusion, but without the occurrence of melting (Egolf et al., 2001):

r ∂ (ρˆ ice ) + div (ρˆ ice ⋅ v ice ) − D ⋅ ρ ⋅ ∆c ice = 0 (7.13) ∂t r Here, D is the diffusion constant, v the velocity vector and ρˆ the density of a component of the ice slurry. The initial condition is defined by a homogeneous ice fraction cice throughout the fluid domain Γ in the slurry tank. Thus the density is constant at time zero:

r

r

ρˆ ice (t = 0, x ) = ρˆ ice,0 = const, ∀x ∈ Γ

(7.14)

A further boundary condition is that no ice particles cross the bounding walls of the storage tank and the free surface of the ice slurry, which are denoted by ∂Γ .

[ρˆ ice ⋅ vrice − D ⋅ ∇ρˆ ice ] ⋅ γr(t, xr ) = 0,

r r ∀x, γ ∈ ∂Γ

(7.15)

Starting from laminar flow around a spherical particle at low Reynolds numbers the following r rise velocity vice is found. Here, vice is the vertical component of v . The complete derivation is given in (Egolf et al., 2001). The equation is valid for ice fractions up to 15-20%. For higher ice fractions the Bingham behaviour of ice slurry has to be taken into consideration. Results for that range are not known so far. 2 ⎧ g ⋅ Dpart (ρ slurry (T , c ice ) − ρ ice (T )) ⋅ , ⎪ η slurry (T , c ice ) v ice (T , c ice ) = ⎨ 18 ⎪ ⎩0,

c ice,max =

c ice < c ice,max

(7.16)

c ice ≥ c ice,max

ρ ice Vice,max ⋅ ρ V

Here c ice,max is the maximum ice concentration resulting from the maximum packing factor as described in section 7.2.2.

7.4.3 CONFIRMATION OF MODELLING Vuarnoz et al. (2001) performed experimental investigations on the stratification process with initial homogeneous ice particle fields of 10.3% and 21.4% ice fraction. Samples were taken from four different levels of an ice slurry tank with 1000 litre volume and investigated under a light-transmittance microscope. The experiments provided information on ice fraction distribution in the tank as a function of time and space.

220


The initial condition is obtained by stopping the mixer suddenly. The constant temperature profile in the tank remained during the stratification process. Thus, stratification cannot be determined by temperature measurements alone. The observation chamber had a height of 1mm. A frame of 2384 µm by 1603 µm enlarged with a microscope was photographed. Ice fraction was determined by evaluating the number and size of ice particles in the photograph. A front is defined as the interface between the mushy ice slurry and the ice-free liquid, which moves upward in the tank according to the level of extraction. After some time ice has accumulated at the top and the lower part of the tank contains pure liquid. At the top, particles cannot rise further and therefore ice fraction increases until maximum packing is reached. A second front in the ice concentration is the level where maximum packing has been just reached. This front propagates from the top of the tank downwards. Not much is known about this steady-state ice layer with the maximum ice fraction. As the buoyancy force continues to act, this layer may be further compressed. It might be that the ice crystals freeze slightly together in this layer. Another effect is documented by Egolf et al. (2002). From the photographs in (Vuarnoz et al., 2001) it was found that the ice particles had approximately an elliptical shape with a mean width to mean length ratio of 0.7. Assuming spherical ice particles with an identical volume in the numerical modelling, an equivalent diameter of 200 µm was obtained. The observed front propagation times could not be explained by the simulations with this diameter. Adjustment of the results is obtained by setting the diameter to 500 µm in the simulation. This assumption, that a small number of particles stick together resulting in clusters with a larger equivalent diameter, could be confirmed by analysing the photographs.


1. Egolf, P.W.; Vuarnoz, D.; Sari, O.: A model to calculate dynamical and steady-state behaviour of ice particles in ice slurry storage tanks. Fourth IIR Workshop on Ice Slurries, Osaka, Japan, November 2001. 2. Egolf, P.W.; Vuarnoz, D.; Sari, O.; Ata-Caezar, D.; Kitanovski, A.: Front propagation of ice slurry stratification process. Fifth IIR Workshop on Ice Slurries, Stockholm, Sweden, May 2002. 3. Frei, B.; Egolf, P.W.: Viscometry applied to the Bingham substance ice slurry. Second IIR Workshop on Ice Slurries, Paris, France, May 2000. 4. Hansen, T.M.; Radosevic, M.; Kauffeld, M.: Behaviour of ice slurry in thermal storage systems. ASHRAE Research Project - RP 1166, February 2002. 5. Huhn, R.: Untersuchung und Modellierung der Speicherung von pumpfähigen SoleEisgemischen in Pufferspeichern sowie der Eisbildung an Verdampferoberflächen. Forschungsrat Kältetechnik e.V., Bericht Nr. 88/02, Frankfurt (Main) 2003. 6. Kakutami, S.; Noburo, O.: Development of High Density Heat Transportation System. Refrigeration, Vol. 74, No. 856, pp. 28-35, 1999. 7. Kozawa, Y.; Aizawa, N.; Tanino, M.: Study on Ice Storing Characteristics in Dynamictype Ice Storage System by Using Supercooled Water, Effects of the supplying conditions of ice-slurry at deployment to District Cooling and Heating System, Third IIR Workshop on Ice Slurries, pp. 87-96, Lucerne 2001. 8. Kozawa, Y.; Tanino, M.: Ice-water Two-phase Flow Behavior in Ice Heat Storage System,

221


First IIR Workshop on Ice Slurries, pp. 146-156,Yverdon, Switzerland, 1999. 9. Mito, D.; Mikami, Y.; Tanino, M.; Kozawa, Y.: A New Ice-slurry Generator by using Actively Thermal-hydraulic Controlling both Supercooling and Releasing of Water, Fifth IIR Workshop on Ice Slurries, Stockholm, Sweden, May 2002. 10. Mito, D.; Tanino, M.; Kozawa, Y.; Okamura, A.: Application of a Dynamic –type Ice Storage System to the Intermittent Cooling Process in the Food Industry, Fourth IIR Workshop on Ice Slurries, pp.105-114, Osaka, Japan, November 2001. 11. Nørgaard, E.; Christensen, K.C.; Hansen, T.M. et al.: Heat transfer and pressure drop with ice slurry. 4th IIR Gustav Lorenzen Conference, Purdue, July 2000. 12. Riber, C.: Akkumumlering af sjapis. Danmarks Tekniske Universitet, January 1999. 13. Schempp, A.: Modellierung von Feststoffverteilung und Wärmeübergang in gerührten Fest/Flüssig-Systemen. Fortschritt-Berichte / VDI : Reihe 3, Verfahrenstechnik Nr. 430, VDI-Verl., Düsseldorf 1996. 14. Tanino, M.; Kozawa, Y.; Hijikata, K.; Nakabeppu, O.: Prediction of Ice Storage Process in Dynamic-type Ice Storage System, Proc. of 10th International Conference on Thermal Engineering and Thermogrammetry, pp. 321-326, Budapest, Hungary 1997. 15. Tanino, M.; Kozawa, Y.: Ice-water Two-phase Flow Behavior in Ice Heat Storage Systems, Int. Jour. of Refrigeration of IIR, 24(7); 638-652, 2001. 16. Tanino, M.; Kozawa, Y.; Mito, D.; Inada, T.: Development of Active Control Method for Supercooling Releasing of Water. Second IIR Workshop on Ice Slurries, pp. 127-138, Paris, France, May 2000. 17. Tanino, M.; Kozawa ,Y.: Performance Evaluation of an On-site Type Ice Storage System by using Ice Slurries Made of Super-cooled Water, Jour. of AIRAH, : 55(9); pp. 28-31, 2001. 18. Tanino, M.; Mito, D.; Kozawa, Y.: Recent Study on Ice Slurries, Jour. of AIRAH, 55(8); 17-18, 2001. 19. Tanino, M.; Moriya, M.; Kikuchi, S.; Shiraushi, H.; Okonogi, T.; Kozawa, Y.: An Ice Storage System Using Supercooled Water, 2st Report; Ice Storage and Melting Characteristics. Trans. of the Japanese Association of Refrigeration, 12(3), pp. 39-49 (in Japanese), 1995. 20. Tanino, M.; Moriya, M.; Okamura, A.; Yamazaki, K.; Okonogi, T.; Seki, Y.; Kozawa, Y.; Miyata, Y.; Ohta, M.: Development of Large-scaled Ice Storage System by Using Supercooled Water, Jour. of the Society of Heating, Air-conditioning and Sanitary Engineers of Japan, 71(11), pp. 73-83 (in Japanese), 1997. 21. Vuarnoz, D.; Sari, O.; Egolf, P.W.: Correlation between temperature and particle distribution of ice slurry in a storage tank. Fourth IIR Workshop on Ice Slurries, Osaka, Japan, November 2001. 22. Westphal, W.H.: Physik – Ein Lehrbuch von Wilhelm H. Westphal. 12. Auflage, Springer-Verlag, Berlin 1947.

222


CHAPTER 8. MELTING ICE SLURRY IN HEAT EXCHANGERS by Ebbe Nørgaard

Ice slurry is often used in indirect cooling applications where ice slurry is a refrigerant (in contrast to the direct contact applications especially known from the food and fish industry, see Chapter 9). When ice slurry is exchanging heat with another liquid, plate heat exchangers are a very common choice in current technology. But, because of their small flow channels, ice slurry flow may present a challenge for their use. Nevertheless, experience has shown that compact plate heat exchangers can be used with ice slurry. Actual experience and calculation methods are described in this chapter. Another topic of heat exchange is the cooling of air in fin-and-tube heat exchangers (also known as air coils). This chapter also covers these types of heat exchangers.

8.1 Plate heat exchangers A very compact and highly effective type of heat exchanger is the Compact Brazed Plate Heat Exchanger (CBE). Plate heat exchangers have found uses in many different applications. This section focuses on applications where CBE´s are used to cool secondary media with ice slurry, hence involving melting of ice particles. Because ice slurry has the latent heat stored in the media itself, a relatively high Log Mean Temperature Difference (LMTD) is achievable compared to single-phase media (see Figure 8.1). This means that the volumetric flow rate can be very low when the ice concentration is high compared to a single-phase medium. Furthermore ice slurry has good heat transfer characteristics. Applications where the use of plate heat exchangers and ice slurry as a coolant is considered feasible, are generally as intermediate heat exchangers. This could be in a cooling system with many different temperature demands or in a large distribution system where the energy consumption for transport is an important issue. Figures 8.2 and 8.3 illustrate some of these applications. In order to gain knowledge about the thermodynamic and hydraulic behaviour of ice slurry in plate heat exchangers and to create a foundation for dimensioning, three small scale copper brazed heat exchangers have been tested in a laboratory with ice slurry. The CBE´s tested had different geometry in order to find the optimal heat exchanger for ice slurry.

223


Figure 8.1. Illustration of a theoretical temperature difference between the two media that exchange energy. All the ice is melted in the heat exchanger

Ice generator

Chiller Ice Storage Tank

CBE

CBE

CBE

CBE

Building

Figure 8.2. A district cooling system where CBE´s are used as intermediate heat exchangers between the central refrigeration unit and the buildings to be cooled

224


S

Air cooled condensor

R

R

Propane

S

K1

S

C1 K2

Ice slurry R Icegenerator

K3 Ice creme (-32°C)

R

CBE

R

S

F1

S

S

C2

CO2 (-8°C)

S

F2

P2

P1/P2

F3

R

Figure 8.3. Sketch of a laboratory test plant where a CBE was used with ice slurry as a condenser in a cascade system with propane in the top cycle and carbon dioxide in the bottom cycle. The installation is designed for a supermarket application. The condensing pressure of the carbon dioxide was two bar lower than with the original single-phase media

8.1.1

TEST RIG SET-UP

A test rig for the examination of pressure drop and heat transfer in a plate heat exchanger was constructed. Three heat exchangers were tested: • • •

Ⓐ with 10 plates. Called B15 in Figure 8.6 and thereafter (connections: 4 channels with ice slurry and 5 channels with glycol 30 wt-%); Ⓑwith 10 plates. Called B10 in Figure 8.6 and thereafter (connections: 4 channels with ice slurry and 5 channels with glycol 30 wt-% and vice versa); Ⓒ with 28 plates Called B5 in Figure 8.6 and thereafter (connections: 13 channels with ice slurry and 14 channels with glycol 30 wt-%).

The physical dimensions of the three heat exchangers are illustrated in Figure 8.4.

225


35 70

283

35

113 183 462

70 70

•

Heat transfer area: • Heat transfer area: 0.26 m2 • Heat transfer area: 0.29 0.336 m2 m2 Ⓒ Ⓑ Ⓐ Figure 8.4. Dimensions of the three different heat exchangers tested

The ice slurry was generated by a standard ice slurry system with a scraped surface ice slurry generator and stored in a homogeneous storage facility. The ice concentration was controlled by on/off regulation of the ice generator, which allowed the ice content to vary within ± 2 wt%. A solution of 10 wt-% ethanol in water was used throughout the experiments (freezing point temperature = –4.5°C). A schematic of the test rig is shown in Figure 8.5. Thermocouple chain Return ice slurry

Controller for heater

dp

Buffer tank

Massflow meter

Electrical heater

Supply ice slurry Propylene glycol Volumeflow meter

Figure 8.5. Sketch of test rig On the ice slurry side (primary side), two pieces of transparent plastic pipe were placed just before and after the heat exchanger in order to visualise the flow of ice slurry through the heat exchanger. On the secondary fluid side an open storage tank was installed containing approximately 70 litres of 30 wt-% propylene glycol. A 6 kW electrical heater installed in the tank was activated by a relay, which was controlled by the temperature of the fluid in the tank. In that way the inlet temperature of the glycol could be kept at the desired level within ± 0.5 K.

226


8.1.2

MEASURING EQUIPMENT

The list of measuring equipment used in the experiments is shown in Table 8.1. Table 8.1. Measuring equipment Instrumentation Mass flow meter / density Volume flow meter

Differential pressure transmitter Absolute temperature ice slurry and brine Temperature Difference (ice slurry) Temperature Difference (Brine)

8.1.3

Type/make

Range

Accuracy

Sensor: Danfoss 2100 (DI15)/ Converter: Danfoss 3000 Sensor: Danfoss Mag 1100 (DN 10)/ Converter: Danfoss Mag 5000 Yokogawa Dpharp dp-transmitter Thermocouple Type T

280-5600 kg/h 100-2900 kg/m3

± 0.1% (of reading) or ± 3 kg/m3

0-1330 L/hr

± 0.15% fs (full scale)

0 – 400 kPa

± 0.075% fs

-200°C – 350°C

± 0.3 K

Thermocouple chain Type T / calibrated Thermocouple chain Type T / calibrated

0–3K

± 0.05 K

0–5K

± 0.05 K

HEAT TRANSFER RESULTS

In order to achieve equal flow conditions on the glycol side and thereby rule out that parameter in the data analysis, the brine flow rate (or Reynolds number) was kept almost constant throughout the experiments. This resulted in heat transfer coefficients on the glycol side in the range of 5000 – 8000 W/m2K. The variation was also caused by small variations in the flow rate, but it was mainly caused by the temperature dependent fluid properties. The experiments were planned so that all the ice was melted before leaving the heat exchanger, so as to get full benefit from the latent heat of the ice slurry. This means that the heat flux was also increased in line with increased flow rate and thereby the Reynolds number. The inlet temperature of the glycol was adjusted to the level where all the ice was melted. The heat transfer coefficients obtained are shown in Figure 8.6. Correlations are given in section 8.1.4.

227


5000

B10 30% 4ch

4500

B10 20% 4ch B10 10% 4ch

4000

B10 30% 5ch

h (W/m2K)

3500

B10 20% 5ch

3000

B10 10% 5ch

2500

B5 30% 13ch

2000

B5 20% 13ch

1500

B5 10% 13ch B15 30% 4ch

1000

B15 20% 4ch 500 0

25

50

75

100 125 150 175

B15 10% 4ch

Re (-)

Figure 8.6. Heat transfer coefficients on the ice slurry side obtained for all three CBE´s and plotted against the Reynolds number based on average ice slurry properties between the inlet and outlet conditions. The ice concentration shown in the legend is the inlet condition – the outlet concentration is always 0 wt-%. The channel number, “ch”, denotes channels with ice slurry The heat transfer coefficients show an almost linear increase when plotted against the Reynolds number, which indicates that the flow is laminar. The experiments with type (B15) show clearly that the heat transfer coefficient increases with increasing ice concentration. This tendency is not so clear with the other two exchangers (B5) and (B10). Unknown parameters in the experiments are the time dependent crystal size distribution and viscosity, and how much these factors influence the heat transfer characteristics of ice slurry. Heat transfer coefficients for two-phase fluids are known to show a dependency on the heat flux [kW/m2]. Figure 8.7 shows the relations among heat flux, Reynolds number and heat transfer coefficients obtained in the experiments.

228


7000

5000

h [W/m2K]

6000

4000

5000

3000

4000

h [W/m2K]

6000

7000

2000

3000

1000

2000 1000 0 20

15 Heat flux [kW/m2K]

10

5

0 0

25

0 150 125 100 75 [-] 50 Re

Figure 8.7. Heat transfer coefficients plotted against the heat flux and Reynolds number. R2 = 0.97 for the grid shown The plot shows that the heat flux has a positive effect on the heat transfer coefficient up to 1015 kW/m2. Above 15 kW/m2 there is only a slight increase in the heat transfer coefficient-heat flux slope, which indicates that the heat transfer process on the ice slurry side is dominated by the carrier fluid properties and constrained by the heat transfer between the carrier fluid and the ice particles.

8.1.4

CORRELATION FOR HEAT TRANSFER

All fluid properties used in the following correlations are average ice slurry properties between the inlet and outlet condition unless otherwise stated.

Q = m& 1 ⋅ C p1 ⋅ ∆t1 = m& 2 ⋅ C p 2 ⋅ ∆t 2 = K ⋅ A ⋅ LMTD

(8.1)

Q & m Cp

= = =

Heat capacity [kW] Mass flow rate [kg/s] Specific heat capacity [kW/(kg K)]

∆t A K LMTDsh

= = = =

Temperature change [K] Area [m²] Heat transfer coefficient [W/(m² K)] Logarithmic Mean Temperature Difference [K]. (Superheated - see section 8.3)

Fouling was not taken into account because the heat exchangers were new so the overall heat transfer coefficient, K, is defined as:

229


K=

(8.2)

1 1 + + h1 λ h2

film coefficient [W/(m² · K)] Wall thickness [m] Wall thermal conductivity [W/(m · K)]

= = =

h t λ

1 t

The film coefficient, h , is defined as:

h=

Nu ⋅ λ ⋅ψ ice dh

(8.3) ⎛η = ⎜ bulk ⎜η ⎝ cf

ψice

=

Two-phase correction factor, ψ ice

Nu λ dh

= = = = =

Nusselt number [-] Fluid thermal conductivity [W/(m K)] Hydraulic diameter [m] Ice slurry viscosity [Pa s] Carrier fluid viscosity [Pa s]

µ bulk µ cf

0.3

⎞ (Re + 6)0.125 ⎟ ⎟ ⎠

•

•

•

The correlation for the Nusselt number is given by the expression: Nu = C ⋅ Re n ⋅ Pr y (8.4) C n

= =

Empirical constant [-] Empirical exponent [-]

Re

=

Reynolds number [-] Re =

Pr

=

Prandtl number [-] Pr =

m& channel ⋅ 2 where w is the channel width in m w ⋅ η bulk C p ,cf ⋅ µ

λ 6.4

=

y

e Pr + 30 Prandtl number exponent [-], y = (about 1/3 for laminar flow and 0.4 for 3 turbulent flow)

From the experimental data the empirical values shown in Table 8.2 were found: Table 8.2. Empirical values obtained to correlate heat transfer results

C n

Ⓒ 0.73 0.42

Ⓑ 0.31 0.61

Ⓐ 0.28 0.57

The relation between the measured and calculated Nusselt numbers is shown in Figure 8.8.

230


35 +20%

Calculated Nusselt number (-)

30 -20%

25 20 15

B10 B15 B5

10 5 0 0

5

10

15

20

25

30

35

Measured Nusselt number (-)

Figure 8.8. Accuracy of heat transfer correlation 8.1.5 PRESSURE DROP RESULTS

∆p (Kpa)

In parallel with the heat transfer measurements the pressure drop was measured on the ice slurry side. The measurements are shown in Figure 8.9. 20

B10 30% 4ch

18

B10 20% 4ch

16

B10 10% 4ch

14

B10 30% 5ch

12

B10 20% 5ch

10

B10 10% 5ch

8

B5 30% 13ch

6

B5 20% 13ch

4

B5 10% 13ch

2

B15 30% 4ch

0

B15 20% 4ch

0

25

50

75

100

125

150

175

B15 10% 4ch

Re (-)

Figure 8.9. Pressure difference plotted against the Reynolds number. The ice concentration on the label shows the inlet condition – the outlet concentration is always 0 wt-% - and “ch” is short for channels with ice slurry

231


The pressure drop increased with increasing Reynolds number and ice concentration. The heat exchanger of type Ⓒ (B5) (short, narrow and many parallel channels) had the lowest pressure drop of the three heat exchangers tested and Ⓐ (B15) the highest (long, narrow and a few channels). In practical installations for a given capacity, the optimal heat exchanger with regard to energy consumption by distribution pumps and installation cost, is the heat exchanger that is the cheapest, most compact, has the lowest pressure drop and the highest heat transfer properties for a given capacity. The heat transfer and pressure drop results indicates that the optimal heat exchanger for ice slurry must be short and have many parallel channels like the typeⒸ (B5) or alternatively wide and short like the type Ⓑ(B10). 8.1.6 CORRELATION FOR PRESSURE DROP All fluid properties used in the following correlations are average ice slurry properties between the inlet and outlet conditions unless otherwise stated. ∆Pchannel =

m& channel ρ

= =

f (Re) ⋅ 1000

ρ

(8.5)

Channel mass flow rate [kg/s] Density [kg/m3]

φice

=

Two-phase correction factor, ϕ ice

f(Re)

=

e⎝

Re

=

Reynolds number, Re =

w

= =

Channel width [m] Ice slurry viscosity [Pa s]

⎛ ⎜ a+

ηbulk

[Pa]

2 & channel ⋅m ⋅ ϕ ice

b ⎞ ⎟ Re1.5 ⎠

⎛η = ⎜⎜ wall ⎝ η bulk

⎛ ⎜

⎞ ⎜⎝ ⎟ ⎟ ⎠

1. 2 ⎞ ⎟⎟ Re +6 ⎠

[1/m4] & channel ⋅ 2 m w ⋅ η bulk

•

From the experimental data the empirical values for the constants a and b were found for the three CBE’s, Ⓐ, Ⓑ and Ⓒ as shown in Table 8.3. Table 8.3. Empirical values obtained to correlate pressure drop results

a b

Ⓒ 17 110

Ⓑ 16 221

Ⓐ 17.6 181

The relation between the measured and calculated pressure drop values is shown in Figure 8.10.

232


20

Calculated pressure drop (kPa)

+25%

B10 B15 B5

15

-25%

10

5

0 0

5

10

15

20

Measured pressure drop (kPa)

Figure 8.10. Accuracy of pressure drop correlation Although not all data were well correlated, the correlation can predict the data within ± 25%. The viscosity of ice slurry is affected by the age of the ice slurry, which was not measured in the experiments. This might explain some of the larger deviations. However, additional experiments were carried out subsequently to investigate the relation between pressure drop and time. See section 8.3.

8.1.7 OBSERVATIONS

∆p (kPa)

In order to illustrate the effect of the latent heat stored in the solid ice particles a comparison between the measured pressure drop for ice slurry and calculated pressure drops for a 30 wt-% solution of propylene glycol in water has been carried out, see Figure 8.11. 60 50 40 30 20 10 0

B10 30 % ice B10 30% pg

0

1

2

3

4

5

6

7

8

Q (kW)

Figure 8.11. Pressure drop data plotted against the heat exchanger capacity. The ice concentration in the legend shows the inlet condition – the outlet concentration is 0 wt-%. The comparison is made with equal temperature differences on both primary and secondary sides and equal mass flow rates on the secondary side

233


Figure 8.11 shows that the pressure drop is 5 to 10 times higher with propylene glycol compared with ice slurry when the heat exchanger capacity is the basis for comparison.

A simple analysis has been made where the goal was to investigate how to optimally operate a CBE with regards to ice concentration, pressure drop and heat exchanger capacity. Figure 8.12 shows a plot of the power consumption required to transport the ice slurry through the heat exchanger against the transferred heat capacity. 25

B10 30% 4ch B10 20% 4ch

20

B10 10% 4ch

Ptransport [W]

B10 30% 5ch B10 20% 5ch

15

B10 10% 5ch B5 30% 13ch

10

B5 20% 13ch B5 10% 13ch

5

B15 30% 4ch B15 20% 4ch

0 0

2

4

6

B15 10% 4ch

Qperformance [kW]

Figure 8.12. Pumping power (Ptransport) required to transport the ice slurry through the CBE against the transferred heat capacity (Qperformance). The pump efficiency coefficient used to calculate the transport effect is assumed to be constant at 0.1 From the analysis it is evident that the optimal point of operation is when the inlet ice concentration is high. This becomes clearer as the capacity increases. The largest benefit is when the ice concentration is increased from 10 to 20 wt-% ice at the inlet. If the criterion for optimal operation is not low pressure drop but instead high performance, the flow rate should be increased so that the ice is not melted off completely at the outlet. In addition the inlet ice concentration should be as high as possible.

8.1.8 MINIMUM FLOW RATE Besides the heat transfer and pressure drop experiments another series of experiments was carried out, in order to create a map useful for operation because flow pulsation was observed in some cases. This happened when the flow rate was low in combination with high ice concentration. Each experiment was carried out at a constant flow rate and with increasing ice concentration from 0 to 30 wt-%. It was then observed at which ice concentration the flow began to pulsate 234


Reynolds number (-)

carried out for each heat exchanger with different flow rates. The results are shown in Figure 8.13. 50 45 40 35 30 25 20 15 10 5 0

B5 B15 B10

Stable flow conditions

Unstable flow conditions

0

5

10

15

20

25

30

Ice concentration (% wt.)

Figure 8.13: The relation between the Reynolds number and ice concentration where the flow begins to pulsate. If stable flow conditions are desired the point of operation should be above the dotted line. The experiments were carried out without any heat flux from the secondary side For plate heat exchangers Ⓒ (B5) and Ⓐ (B15) there is a constant lower limit at a Reynolds number of approximately 20, which should be always exceeded if stable flow conditions are desired. The results for heat exchanger Ⓑ (B10) showed a linearly increasing tendency, which indicates that when the ice concentration is high, higher Reynolds numbers are required in order to obtain stable flow conditions. Actual flow blockages were not observed at any time.

8.2

Air coolers

The use of ice slurry to cool air is applicable to many different industries. The main constraint when using ice slurry in air coolers is the temperature level, which is below 0°C. This means, for example, that the use of ice slurry in air conditioning systems is not straight forward because the cold air is generated at a lower temperature than required for this type of application. This results in larger energy consumption by the primary refrigeration plant than what is required to cool air with water at 7°C. On the other hand, the lower air temperature reduces the amount of air required for a given cooling load and hence air ducts and fans can be reduced in size resulting in lower investment and operating costs of the air handling system. Other applications where the use of ice slurry to cool air is more attractive are: • Supermarket display cabinets. • Cold storage for food products (meat, beer, dairy products, vegetables, etc.).

235


• •

Industrial air conditioning – such as providing cabin cooling for parked aircraft during static turn-around periods. Retro-fitting and refurbishment of existing pumped or DX cooling coils and plants, which for environmental or other reasons, are being replaced with a secondary cooling system.

In order to gain some fundamental knowledge about the behaviour of ice slurry in air coolers and to establish a foundation for sizing, some experiments have been conducted on two standard (single-phase) air coolers with different geometry.

8.2.1. TEST RIG SET UP The experiments were conducted in a closed air circuit loop containing air conditioning equipment, fan and an orifice to measure the air flow rate. Figure 8.14 shows a schematic of the air circuit.

Figure 8.14. Sketch of test rig. The ice slurry air coil is labelled 1

The temperatures of air entering and leaving the heat exchanger were measured with nine evenly distributed thermocouples in order to detect if there were any dead zones and if a blockage would occur. The relative humidity was measured at the inlet and outlet of the heat exchanger. On the ice slurry side the mass flow rate, inlet temperature and ice concentration were measured at the inlet using a Coriolis mass flow meter. The temperature and pressure differences on the ice slurry side were also measured. The capacity of the air cooler was calculated on the airside, which also by calculation led to the outlet ice concentration. In order to find the accuracy of this method a preliminary energy balance between the air and liquid streams was conducted with a single-phase fluid on the liquid side which resulted in a deviation of less than 10%. The list of measuring equipment used in the experiments is given in Table 8.4, while Table 8.5 gives the dimensions of the two tested coils.

236


Table 8.4. Measuring equipment Instrumentation

Type/make

Range

Mass flow meter / density/temperature

Sensor: Danfoss 2100 (DI15)/ Converter: Danfoss 6000 Differential Pressure Yokogawa Dpharp transmitter dp-transmitter Temperature difference Thermocouple chain Type T / calibrated Air volumetric flow rate Orifice (DIN1952) Relative humidity Vaisala Air temperature Thermocouple Type T / calibrated

Accuracy

0-3 K

± 0.1 % (of reading) or ± 0.2 % or ± 0.1 K ± 0.075 % of full scale (fs) ± 0.05 K

0.08-2 m3/s 0-100 % RH –5-30°C

± 0.5% ±2% ± 0.3 K

280-5600 kg/hr 960-1020 kg/m3 –30-100°C 0-100 kpa

Table 8.5 Coil dimensions Parameter No. of circuits Fin pitch Inner tube diameter Outer surface area Inner surface area Inner header diameter Rows deep Face area No. of Tubes

3/8” tube coil 14 2.5 mm 9.25 mm 32 m2 2.4 m2 18 mm 4 0.7 x 0.72 = 0.50 m2 112

12 mm tube coil 11 2.5 mm 11.6 mm 54 m2 2.3 m2 39 mm 4 0.72 x 0.72 = 0.52 m2 88

8.2.2. HEAT TRANSFER RESULTS Throughout the experiments the airflow was kept at a constant flow rate of 1.3 m3/s ≈ 2.7 m/s mean face velocity. The humidity of the air was only measured entering the 12 mm tube coil because dry cooling was assumed in the closed air circuit. It turned out that the circuit was not perfectly closed resulting in ice build-up on the air side of the coil. The heat transfer results for the 12 mm coil were corrected with the contribution of rim formation with comparable results on the 3/8” tube coil where the relative humidity was measured both entering and leaving the coil. Figure 8.15 shows the heat transfer results for both coils. The heat transfer coefficient is seen to increase with increasing Reynolds number and ice concentration.

237


h (W/m2K)

Heat transfer coefficient 30 % ice 3/8 20 % ice 3/8 10 % ice 3/8 10 % ice 12 20 % ice 12 30 % ice 12

5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0

250

500

750 1000 1250 1500 1750 2000 2250 2500 Re (-)

Figure 8.15. Heat transfer results for both coils. The ice concentration shown in the legend is the inlet ice concentration. The outlet ice concentration varied from 0-25 wt-%. The Reynolds number was calculated based on the average ice slurry properties between the inlet and outlet conditions. Furthermore the heat flux also varied between the experiments In order to investigate the influence of heat flux on the internal heat transfer coefficients a diagram was developed where the internal heat transfer coefficients are plotted against the heat flux and Nusselt number (Figure 8.16).

4500

3500

HTC [W/m^2K]

4000

3000

3500

2500

3000

2000

2500

HTC [W/m^2K]

4000

4500

1500

2000 1500 1000 .5 12 10 Heat f lux [kW

7 .5

5

/m^2]

5 5 5 45 0 4 35 0 -] 3 [ 2 0 Nu 20 5 1 10 5 5 2.

1000

Figure 8.16. Heat transfer results for both coils. The area refers to the inner surface area. The Nusselt number is the average of the inlet and outlet conditions Because the correlation coefficient (R2 value) is relatively low (0.71), unambiguous conclusions are difficult to draw. However, the plot indicates that the heat transfer coefficient is unaffected by the heat flux, although the experiments using the CBE´s showed some

238


relation between the heat flux and heat transfer coefficients. In the plate heat exchanger experiments, there was an effect of the heat flux up to 15 kW/m2 while the present results showed none. A likely explanation for this difference is that the Reynolds numbers in the air cooler were much higher than in the plate heat exchanger. In the air cooler experiments the boundary layer could have been dominated by the ice slurry properties, resulting in relatively high heat transfer coefficients.

8.2.3. CORRELATION FOR HEAT TRANSFER Using the correlation described in section 4.5.1 “Heat transfer in straight tubes” and average fluid properties between the inlet and outlet, it is possible to calculate the inner heat transfer coefficients within ±30 % deviation. See Figure 8.17.

Calculated HTC (W/m2k)

Accuracy of heat transfer correlation +30%

5000 4000

-30%

3000 2000

3/8" 12mm

1000 0 0

1000

2000

3000

4000

5000

Measured HTC (W/m2k)

Figure 8.17. Ice slurry side heat transfer results for both coils. The calculated values are based on the correlation described in section 8.1.4 and average fluid properties between the inlet and outlet. The air-side HTC is calculated from a correlation supplied by the manufacturer Because the inner heat transfer coefficient is so much higher than the air-side heat transfer coefficient, the overall heat transfer is more dependent on the air-side heat transfer coefficient.

8.2.4. PRESSURE DROP RESULTS In parallel with the heat transfer measurements the pressure drop on the ice slurry side was also measured as shown in Figure 8.18. The pressure drop increased with increasing Reynolds number and ice concentration. In general the pressure drop was higher in the 3/8” coil compared with the 12 mm coil due to the smaller tube diameter. The length of each pass was similar for both coils.

239


Pressure difference 30 % ice 3/8 20 % ice 3/8 10 % ice 3/8 10 % ice 12 20 % ice 12 30 % ice 12

80 ∆p (kPa)

60 40 20 0 0

250

500

750 1000 1250 1500 1750 2000 2250 2500 Re average (-)

Figure 8.18. Pressure drop results. The pressure loss in the connections is at maximum 8 kPa and included in the values shown. The ice concentration shown in the legend is the inlet ice concentration. The outlet ice concentration varied from 0-25 wt-%. The Reynolds number was calculated based on the average ice slurry properties between the inlet and outlet conditions. Furthermore the heat flux varied between the experiments

8.2.5. CORRELATION FOR PRESSURE DROP By correlating the experimental pressure drop data during melting, it was found that a standard Newtonian theory would be appropriate in combination with the coil manufacturer’s data. So, in contrast with pressure loss in transport tubes, where the flow is Bingham and Newtonian – the flow during melting is solely correlated as Newtonian. The length of the tubes was 0.7 m, which is short relative to the transport tubes, therefore, the velocity profile was not fully developed. The following information was provided by the manufacturer: When Re < 1500, the flow is considered laminar and the friction factor is λ = 64/Re. When Re > 1500, the flow is transitional/turbulent and λ = 0.2 Re0.2. •

The pressure loss in the return bends was turned into an equivalent length of a straight tube. The data given by the manufacturer did not perfectly match the measured pressure losses for ice slurry. From experiments on pressure loss in single components it was found that the friction coefficients for ice slurry are higher than the values tabulated for turbulent water flow. However, as the Reynolds number increases the friction factor for ice slurry flow decreases and approaches the tabulated values for turbulent flow of water. Because the friction loss in return bends can be higher for ice slurry than for a single-phase fluid, the pressure drop correlation was fitted by adjusting the equivalent length of the return bends. This was done independently of the ice concentration – which is a simplification. Table 8.6 shows the fitted values for ice slurry.

240


Table 8.6. Equivalent lengths of return bends. The values represent the equivalent length of each bend 12mm coil 3/8” coil 1.7 m 0.6 m Ice slurry (fitted value) The pressure drop in the supply and return headers was calculated solely from manufacturer’s correlation: dp h =

1 ⋅ ρ ⋅ ch2 2

⎛ λ ⋅ Lh ⋅ ⎜⎜ 0.85 + dh ⎝

⎞ ⎟⎟ ⎠

(8.6)

where the velocity and friction factor are calculated at the inlet (highest velocity). The pressure drop decreases through the coil as the ice is melted off. Therefore the pressure drop in the coils was calculated using the average of the inlet and outlet fluid properties and according to: dp in ,out =

1 ⋅ ρ in ,out ⋅ c in ,out 2 2

⎛ λ ⋅ L + Leq ,bend ⋅ ⎜⎜ d ⎝

⎞ ⎟ ⎟ ⎠

(8.7)

which results in: dp =

dp in + dp out + dp hin + dp h ,out 2

(8.8)

Calculated pressure drop (kPa)

Using the above correlation the measured pressure drop data were predicted theoretically within ± 15 %. See Figure 8.19.

70 +15%

12 mm 3/8"

60 50

-15%

40 30 20 10 0 0

10

20

30

40

50

60

70

Measured pressure drop (kPa)

Figure 8.19. Comparison of measured and calculated pressure drop

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8.2.6. COMPARISON BETWEEN SINGLE-PHASE MEDIA AND ICE SLURRY Using the manufacturer’s dimensioning software a comparison was made between the measured ice slurry results and a single-phase fluid as shown in Figure 8.20. Fluid Velocity v's Internal HTC´s

Internal HTC´s (W/m2K)

3500 3000

12 mm Tube 10 mm Tube

2500

10% Ethanol/Water 20% Ice Concentration

2000 1500 1000 500

30% Propylene glycol

0 0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Velocity (m/s)

Figure 8.20. Comparison of internal heat transfer coefficients between a single-phase fluid and ice slurry. The outlet ice concentration varied from 0-15 wt-% Ice slurry heat transfer coefficients were 3 to 4 times higher than those of the single-phase liquid. This difference means that the capacity of the air cooler is increased approximately by 5-10 % or the heat transfer area can be reduced by 5-10% (largest improvement when the flow velocity is low). In addition the average temperature difference is increased as a result of the phase change of the ice slurry. Consequently, the heat transfer area can be reduced by up to 30 % with ice slurry compared with a single-phase fluid. Furthermore, the circuitry on the liquid side does not have to be cross-counter because the temperature glide of ice slurry is low. This gives the designer an extra degree of freedom, which opens up the possibility for minimising production cost. A similar comparison was also carried out with respect to pressure drop as shown in Figure 8.21. At low velocities the pressure drop for ice slurry is almost equal to that of the singlephase fluid, but at higher velocities the pressure drop for ice slurry becomes twice as high as for the single-phase fluid.

242


Fluid Velocity v's Pressure Drop

Pressure Drop (kPa)

70 60

12 mm Tube

50

10 mm Tube

10% Ethanol/Water 20% Ice Concentration

40 30 20 10

30% Propylene Glycol

0 0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Velocity (m/s)

Figure 8.21. Comparison of pressure drop between a singlephase fluid and ice slurry. The outlet ice concentration varied from 0-15 wt-% 8.2.7. MINIMUM FLOW RATE Tube blockages were not observed at any time during the trials, but the flow can pulsate if the flow velocity is very low. At flow velocities higher than 0.5 m/s the flow is stable. This works also in the headers. Experiments carried out on a transparent air cooler showed that the ice crystals tend to agglomerate in the headers if the flow velocity is relatively low. Therefore, it is important to design the headers so that dead spots are avoided. Some examples are shown in Figure 8.22 to illustrate how to – and how not to – design the headers.

Figure 8.22. Illustration of appropriate/inappropriate header design

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8.3 Observations

Through the experiments carried out on both compact brazed heat exchangers (CBE´s) and air coolers it was discovered that there were still ice particles left in the fluid at the outlet from the heat exchanger although the temperature at the outlet was higher than the freezing point temperature. This phenomenon is defined as superheating of the carrier fluid (SH) and in reality it means that the liquid is in thermodynamic non-equilibrium with the ice particles. This was visually observed through transparent sections of pipe right after the heat exchangers. Further downstream of the return tubes, the ice crystals were melted and the temperature of the liquid decreased again and reached the freezing point temperature, which means that the liquid reached the equilibrium condition. See Figure 8.23.

Figure 8.23. Schematic of temperature development through a CBE and further downstream when superheating (SH) occurs For operating heat exchangers with multiple parallel passes, it is important that the distribution of ice slurry is uniform. If the distribution is non-uniform in the inlet distributor/header, the melt off rate will vary in the parallel passes which can create a temperature gradient at the outlet. This can affect a temperature measurement at the outlet if the probe is located immediately after the heat exchangers. In the CBE experiments it was deemed too difficult to measure the temperature at the outlet of each pass. It was, however, possible to conduct this measurement in the air cooler experiments. Therefore, the surface temperature was measured on six different tubes at the outlet of the pass just before the return header on the 3/8” coil, see Figure 8.24.

244


Figure 8.24. Location of thermocouples at the outlet of 6 parallel passes, just before the return header. Thermocouple no. 3 was not used. There were 14 passes in all The results are shown in Figure 8.25. 1

2.0

0

1.8

-1

1.5

-2

1.3

-3

1.0

-4

0.8

-5

0.5

-6

0.3

T [K]

T [°C]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Tube_1 Tube_2 Tube_4 Tube_5 Tube_6 Tube_7 -7Ice_on 0.0 Ice off SH Figure 8.25: Surface temperatures of six outlet tubes in 29 experiments. The ice slurry temperature was measured with a Pt 100 probe in the liquid both at the inlet and outlet. Those two measurements are labelled as “Ice On” and “Ice Off” respectively. SH stands for superheat and is the only measurement that refers to the right y-axis. The number at the top of the diagram identifies the number of experiments. Hence the data points in the columns under each number (1-29) correspond to one experiment

If the degree of super-heating is related to non-uniform distributions between the passes, the degree of superheating should be most severe when the difference between the surface temperatures of the outlet tubes is the largest. In experiment number 4, the difference between the highest and lowest tube surface temperatures was 3.0 K and the degree of superheating was 1.6 K (third highest), which is consistent with the theory. In experiment number 18, however, the tube temperature difference was 0.8 K and the degree of superheating was 1.8 K,

245


which does not correspond very well to this theory. Consequently, the degree of superheating is believed to be not solely dependent on the distribution of ice slurry in the header/distributor.

SH (K)

Plotting the degree of superheat against the melt off rate of ice slurry in the air cooler experiments shows some tendencies, see Figure 8.26. 30 % ice 3/8 20 % ice 3/8 10 % ice 3/8 10 % ice 12 20 % ice 12 30 % ice 12

2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 0

5

10

15

20

25

30

35

40

dxice (% wt.)

Figure 8.26. Super-heating of carrier fluid at the outlet. The parameter on the x-axis is the melt off rate, and the ice concentration in the legend is the inlet concentration. The numbers 3/8 and 12 identify the two different air coils tested and refer to the diameter of the tubes

The results showed that it is relatively difficult to melt off the last 5-10 wt-% ice. This is related to the heat transfer rate between the ice crystals and carrier fluid plus the thermal conductivity of the mixture. When the ice concentration was high, for example 30 wt-% vs. 0 wt-%, the heat conduction ability of the mixture is almost twice as high, which will lead to a quicker equalisation of any temperature differences in the mixture. Furthermore, the crystal size also influences the temperature difference required to melt off an ice crystal. The amount of time required to melt off ice crystals increases with the size of the crystals. The crystal sizes were not measured in the experiments but they probably varied between 50 and 1000 microns or more, because the ice slurry was stored over many days. According to Hansen et al. (ASHRAE, 2002) the sizes of ice crystals can increase from 50 to 700 microns over a 4-day period. In some of the experiments the ice slurry had been stored for at least a week or more. In addition the distribution of crystal sizes also increases over time (ASHRAE, 2002). When melting ice slurry, smaller crystals vanish before the larger ones because the ratio of surface area to volume increases, as the crystals become smaller. So, the crystals that were visible at the outlet of the heat exchangers were initially the largest. In the plate heat exchanger experiments the degree of superheating was generally a little higher than in the air coolers. These experiments were all planned so that all the ice would be melted at the outlet. This is consistent with the findings in the air cooler experiments that it

246


requires a relatively much larger heat transfer area to melt off the last 5-10 wt-% ice, see Figure 8.27. 3,0

B10 30% 4ch B10 20% 4ch

2,5

B10 10% 4ch B10 30% 5ch

SH (K)

2,0

B10 20% 5ch B10 10% 5ch

1,5

B5 30% 13ch B5 20% 13ch

1,0

B5 10% 13ch 0,5

B15 30% 4ch B15 20% 4ch

0,0 0

25

50

75

100

125

150

175

B15 10% 4ch

Re (-)

Figure 8.27. Superheating (SH) of the carrier fluid in all the CBE experiments plotted against the average Reynolds number

The experiments carried out on the A-type (B15) plate heat exchanger showed the lowest superheat and those carried out on the C-type (B5) the highest. There is no clear relation between the Reynolds number and the degree of superheating. Furthermore there is no clear relation among superheat and ice content, heat flux or the duration of ice particles inside the heat exchanger. At this point the only two likely explanations left are: 1) the particle size, which varied throughout the experiments, again in the range from 50 to 1000 microns; and 2) flow distribution problems between the parallel passes. Thus, a series of measurements were carried out on the C-type (B15) heat exchanger where the time dependency of heat transfer coefficient, pressure drop and degree of superheating was investigated. The duration of each experiment was 10-15 minutes after which the heat source was turned off leaving the ice crystals to grow in the accumulation tank. After a certain period another experiment was initiated and so on. The results are shown in Figure 8.28.

247

1800

4

1700

3

1600

2 HTC SH

1500 1400 0

10

20

30

SH (K)

h (W/m2K)


1 0 40

50

60

Time (h)

Figure 8.28. The experimental results on time dependency in the C-type (B5) heat exchanger (CBE) with constant mass flow rate and full melt off from an inlet concentration of 20 wt-%. Heat transfer coefficient (HTC) refers to the left y-axis labelled “h” and the superheat refers to the right y-axis labelled “SH”

Even with small ice crystals superheat can occur. There is, however, a tendency which shows an increase in the superheat of 30 % and a decrease of 10 % in the heat transfer coefficient as the crystals increase in size. Because the superheat is 2.5 K after only half an hour it can be concluded that the superheating phenomenon is not only caused by the delayed melt-off of relatively large ice crystals. The C-type (B5) heat exchanger showed the highest degree of superheat. It had 28 plates compared with 10 for both the A-type (B15) and B-type (B10). Hence it is likely that the superheat in plate heat exchangers is caused mainly by poor flow distribution between the parallel passes, although this was not actually measured in the experiments.

8.4 Conclusions

Three different plate heat exchanger models were tested with ice slurry. The results showed very low pressure drop and high heat transfer capacity compared to single-phase media. The optimal ice concentration was found to be between 20-30 wt-% at the inlet. The most efficient geometry of the three plate heat exchangers was the short/slim and the one that had the highest number of parallel passes. The heat transfer coefficients were not higher than what is obtainable with a single-phase fluid, because the Reynolds numbers were very low. The carrier fluid properties dominate the heat transfer characteristics at low Reynolds numbers, because the heat flux is relatively high in a plate heat exchanger compared with other types of heat exchangers. This means that the ice particles near the wall are quickly melted off leaving only the carrier fluid to dominate the heat transfer. A break point for the heat transfer coefficient exists around a heat flux value of 10-15 kW/m2 in the tested range of Reynolds numbers. The heat flux should not be lower than this value if optimal heat transfer performance on the ice slurry side is desired.

248


Correlations have been developed to calculate heat transfer coefficients and pressure drop in three different compact brazed heat exchangers. The analysis showed that it is impossible to convert constants obtained for a specific CBE geometry with single-phase fluids to those for an ice slurry. Hence it is necessary to find new constants for every new heat exchanger geometry if reasonable accuracy is required. Two air coolers designed for single-phase media have been tested with ice slurry and correlations have been developed. Analyses of the experimental results showed that at a constant flow velocity, the internal heat transfer coefficient was improved by a factor of three to four and the corresponding pressure drop was increased by a factor of up to two compared to a single-phase fluid. It was also found feasible to simplify the fluid circuitry in the air coil investigated and thereby reduce the production cost.


1.

ASHRAE Final Reports 1166: Behaviour of Ice Slurries in Thermal Storage Systems. Principal Investigator: Michael Kauffeld, Danish Technological Institute; Conducted: April 2000-Oct. 2001, published in 2002.

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CHAPTER 9.

DIRECT CONTACT CHILLING AND FREEZING OF FOODS IN ICE SLURRIES by Kostadin Fikiin, Ming-Jian Wang, Michael Kauffeld and Torben M. Hansen (see specific list of symbols in Appendix 3)

Ice slurry has received increasing attention and demand for refrigeration processes in different industries because of the widespread concerns over product quality, process efficiency and environmental friendliness. This chapter deals with the application of ice slurry technologies to direct contact chilling and freezing of foods. As a rule, direct contact cooling in ice slurries improves the product quality. To date this technology has mainly been used in the fish industry (by employing sea-water-based ice slurry) but its recent applications to the fruit and vegetable processing sectors revealed a very promising potential as well. Both laboratory and industrial trials demonstrated convincingly the superiority of the ice-slurry-based immersion methods over conventional modes of food refrigeration. Direct contact cooling by dried ice slurries has lately been applied in supermarket display cabinets. Ice slurry is thereby used similarly to flake ice, but the slurry handling is much easier because it can be pumped to the display cases and released via a hose, whereas the ice flakes have to be shovelled. Moreover, there are no traumatic effects on the food surface, which may occur when flakes are involved. Although the cooling ability of the ice slurry is very similar to that of flake ice in this particular application of dried ice slurry, ice slurry shows heat transfer benefits for the direct contact/immersion applications described below.

9.1.

State of the art and conventional modes of food refrigeration

Let us, for instance, illustrate the ice slurry capabilities for food freezing applications as compared with the most common techniques known so far. In the early 1900s, many people were experimenting with mechanical and chemical methods to preserve food. As an industrial process, quick freezing began its history some 70 years ago when Clarence Birdseye found a way to flash-freeze foods and deliver it to the public – one of the most important steps forward ever taken in the food industry. During his stay in the Arctic, Birdseye observed that the combination of ice, wind and low temperature almost instantly froze just-caught fish. More importantly, he also found that when such quick-frozen fish were cooked and eaten, they were scarcely different from the fresh fish in taste and texture. After years of work, Birdseye invented a system that packed dressed fish, meat or vegetables into waxedcardboard boxes, which were flash-frozen under pressure (US Patent No. 1,773,079, 1930). Then he turned to marketing and a number of ventures were initiated to manufacture, transport and sell frozen foods (e.g. construction of double-plate freezers and grocery display cases; lease of refrigerated boxcars for railway transport; and retail of frozen products in Springfield, Massachusetts, in 1930). These technological achievements constituted the world's first cold chain for frozen foods, which became shortly a legend (Fikiin, 2003). Thus, quick freezing has further been adopted as a widespread commercial method for longterm preservation of perishable foods, which improved both the health and convenience of virtually everyone in the industrialised countries. Freezing rate affects strongly the quality of frozen foods, in which the predominant water content should quickly be frozen in a fine-grain crystal structure in order to prevent damages to the cellular tissues and to inhibit rapidly the spoiling microbiological and enzymatic processes. 251


Basic heat transfer considerations (Fikiin, 2003) clearly suggest that the desired shortening of freezing duration and a resulting high throughput of refrigerating equipment could be achieved by means of: (i) lower refrigerating medium temperature (which generally requires greater investment and running costs for the refrigeration machines to be employed), (ii) enhanced surface heat transfer coefficients (by increased refrigerating medium velocity and boundary layer turbulence, involvement of surface phase-change effects and less packaging), and (iii) reduced size of the refrigerated objects (by freezing small products individually or appropriately cutting the large ones into small pieces). Air-blast and multiplate freezers are most widespread, while air fluidizing systems are used for individual quick freezing (IQF) of small products. The cryogenic IQF is still very restricted because of the high prices of the liquefied gases used. Fluidized-bed freezing systems Air fluidization has been studied extensively and used commercially, with increasing popularity, over the last forty years (Fikiin et al., 1965, 1966, 1970; Fikiin, 1969, 1979, 1980). This freezing principle possesses many attractive features, including: • High freezing rate due to the small sizes and thermal resistance of the IQF products, large overall heat transfer surface of the fluidized foods and high surface heat transfer coefficients. • Good quality of the frozen products, that have an attractive appearance and do not stick together. • Continuity and possibilities for complete automation of the freezing process. In spite of these advantages, fluidization freezing by air has some drawbacks, such as: • Necessity of two-stage refrigerating plants (often using large quantities of CFC-, HCFCor HFC-based refrigerants with significant ozone depletion or global warming potentials) to hold an evaporation temperature of about –45°C, which results in high investment and power costs. • Lower surface heat transfer coefficients and freezing rates in comparison with the immersion methods described below. • Need for a high speed and pressurized airflow, that results in large fan power consumption. • Some moisture losses from the product surface and rapid frosting of the air coolers, caused by the large temperature difference between the products and the evaporating refrigerant. • Excessive sensitivity of the process parameters to the product shape, mass and size, that requires careful control specific to every separate food commodity. Freezing by immersion The immersion freezing in non-boiling liquid refrigerating media is a well-known method having several important advantages: high heat transfer rate, fine ice crystals in foods, high throughput, low investments and operational costs (Woolrich, 1966; Tressler, 1968; Fleshland and Magnussen, 1990; Lucas and Raoult-Wack, 1998). The immersion applications have been limited because of the uncontrolled solute uptake by the refrigerated products and operational problems with the immersion liquids (high viscosity at low temperatures, difficulty in maintaining the medium at a definite constant concentration and free from organic contaminants). Recent achievements in heat and mass transfer, physical chemistry, fluid

252


dynamics and automatic process control make it possible to solve these problems and to develop advanced immersion individual quick freezing (immersion IQF) systems (Fikiin and Fikiin, 1998, 1999a, 2002, 2003a,b; Fikiin, 2003).

9.2.　Unfreezable liquids and pumpable ice slurries as refrigerating media and fluidizing agents The Hydro Fluidization Method (HFM) for fast freezing of foods was suggested and patented recently to overcome the drawbacks and to bring together the advantages of both air fluidization and immersion food freezing techniques (Fikiin, 1985, 1992, 1994). The HFM uses a circulating system that pumps the refrigerating liquid upwards, through orifices or nozzles, in a refrigerating vessel, thereby creating agitating jets. These form a fluidized bed of highly turbulent liquid and moving products, and thus evoke extremely high surface heat transfer coefficients. The principle of operation of an HFM freezing system is illustrated in Figure 9.1.

253


Figure 9.1. Possible arrangements of a HFM-based freezing system combining the advantages of both air fluidization and immersion food freezing techniques (Fikiin and Fikiin, 1998, 1999a): (1) charging funnel; (2) sprinkling tubular system; (3) refrigerating cylinder; (4) perforated screw; (5) double bottom; (6) perforated grate for draining; (8) sprinkling device for glazing; (7 and 9) netlike conveyor belt; (10 and 11) collector vats; (12) pump; (13 and 14) rough and fine filters; (15) cooler of refrigerating medium; (16) refrigeration plant Unfreezable liquid refrigerating media as fluidizing agents Although various immersion techniques have been known for a long time, until now hydrofluidization principles have not been used for chilling and freezing of foods. Experiments on HFM freezing of small fish and some vegetables through an aqueous solution

254


of sodium chloride showed a much higher freezing rate when compared with other IQF techniques (Fikiin, 1992, 1994). The maximum surface heat transfer coefficient achieved exceeded 900 W/(m2K), while this was 378 W/(m2K) when immersing in a flowing liquid, 432 W/(m2K) for sprinkling and 475 W/(m2K) for immersion with bubbling through (Fikiin and Pham, 1985). Even at a slight or moderate jet agitation and a comparatively high refrigerating medium temperature of about –16°C, scad fish were frozen from 25°C down to –10°C in the centre within 6-7 minutes, sprat fish and green beans within 3-4 minutes and green peas within 1-2 minutes. As an illustration Figure 9.2 shows recorded temperature histories during hydrofluidization freezing of scad and sprat fish, green beans and peppers.

b

a 30

30

25

25

Ambient temperature = –15/–16 o C Average jet velocity = 2 m s–1

o

Ambient temperature = –15/–16 C Average jet velocity = 2 m s–1

20 15

o

Temperature ( C)

15

o

Temperature ( C)

20

10 5 Centre 0 -5

Scad (28 g)

-10

10

Core

5

Peppers (30 g)

0 -5 -10

Surface

Surface

-15

-15

Green beans (11 g)

Sprat (7g) -20

-20

0

100 200 300 400 500 600 700 800

0

50

100

150

200

250

300

350

Time (s)

Time (s)

Figure 9.2. Experimental temperature histories during HFM freezing of some kinds of (a) fish and (b) vegetables, when using sodium chloride solution (without ice slurry) as a fluidizing agent (Fikiin, 1992; Fikiin and Fikiin, 1998, 1999a)

Two-phase ice slurries as fluidizing agents Pumpable ice slurries (known under different trade names, such as FLO-ICE, BINARY ICE, Slurry-ICE, Liquid ICE, Pumpable ICE or Fluid ICE) were proposed recently as environmentally benign secondary coolants circulated to the heat transfer equipment of refrigeration plants, instead of the traditional ozone-depleting CFC- or HCFC-based refrigerants (Paul, 1995; Ure, 1998, Egolf et al., 1996; Bel and Lallemand, 1999; Pearson and Brown, 1998). Promising attempts to refrigerate foods by immersion in such slurries have already been carried out. As already discussed, fish chilling in sea water-based ice slurries has good potential to replace the traditional use of ice flakes (Fikiin et al., 2002). A number of foods immersed in slurries with various ice contents are shown in Figure 9.3.

255


Figure 9.3. Different foods immersed in slurries with various ice concentrations: (a) fruits; (b) vegetables; (c) chickens; (d), (e) and (f) fish (Fikiin et al., 2002)

Fikiin and Fikiin (1998, 1999a) launched, therefore, the idea to enhance the advantages of hydrofluidization (described above) by employing two-phase ice suspensions as fluidizing media. Ice slurries possess a large energy potential as HFM refrigerating media whose small ice particles absorb latent heat when thawing on the product surface. Hence, the goal of ice slurry usage is to provide a high surface heat transfer coefficient (of the order of 1000-2000 W/(m2K) or more), shortened freezing time and uniform temperature distribution in the whole volume of the freezing apparatus. The combination of the HFM with the high heat transfer efficiency of the ice-slurry-based refrigerating media represents a new interdisciplinary research field whose development would advance essentially the refrigerated processing of foods. The HFM freezing with ice slurries can acquire a process rate approaching that of the cryogenic flash freezing modes. For instance, at a refrigerating ice-slurry temperature of –25°C and a heat transfer coefficient of 1000 W/(m2K), strawberries, apricots and plums can be frozen from 25°C down to an average final temperature of –18°C within 8-9 minutes; raspberries, cherries and morellos within 1.5 to 3 minutes; and green peas, blueberries and cranberries within about 1 minute only. The general layout of an ice-slurry-based system for hydrofluidization freezing is shown in Figure 9.4. Advantages of hydrofluidization freezing with ice slurries As described above, the novelty of the hydrofluidization method lies in the involvement of unfreezable liquids or pumpable ice slurries as fluidizing agents. It is well-known that the immersion freezing history began with the use of brines to freeze fish, vegetables and meat. Binary or ternary aqueous solutions containing soluble carbohydrates (e.g. sucrose, invert sugar, glucose [dextrose], fructose and other mono- and disaccharides) with additions of ethanol, salts, glycerol, etc., have been studied as possible immersion media. There are practically unlimited possibilities to combine constituents and to formulate appropriate

256


Figure 9.4. Schematic diagram of an ice-slurry-based hydrofluidization system HyFloFreeze® (Fikiin and Fikiin, 1998, 1999a)

multicomponent HFM refrigerating media based on single-phase liquids or two-phase ice slurries, which have to be both product- and environment-friendly and to possess a low enough viscosity in terms of pumpability and good hydrofluidization. The main advantages of hydrofluidization over the conventional freezing modes can be summarized as follows: •

•

The HFM facilitates a very high heat transfer rate with a small temperature difference (product to cooling medium). The evaporation temperature can be maintained much higher (at –25/–30°C) achievable by a single-stage refrigerating machine with much higher COP and nearly half the investment and energy costs as compared with the conventional air fluidization. Cold dissipation through the freezer walls is subsequently also lower. The water flow rate or fan power consumption for cooling the condenser decreases as well, due to the reduced mechanical work of the refrigeration unit running at higher evaporation temperature. The critical zone of water crystallization (from –1 to –8°C) is quickly passed through, which ensures a fine ice crystal structure in foods preventing the cellular tissues from perceptible damage.

257


• •

•

• •

•

The product surface freezes immediately in a solid crust that hampers the osmotic transfer and gives an excellent appearance. The water losses tend to zero, while in air freezing tunnels the moisture losses are usually 2-3%. Delicious new products can easily be formulated by using some selected product-friendly HFM media (for example, fruits frozen in syrup-type sugar solutions turn into dessert products with beneficial effects on colour, flavour and texture). Such media can also include appropriate antioxidants, flavourings and micronutrients to extend the shelf life of the products and to improve their nutritional value and sensory properties. The HFM freezers use environmentally friendly secondary coolants (for instance, syruptype aqueous solutions and ice slurries) and the primary refrigerant is closed in a small isolated system, in contrast to the common air fluidization freezers where large quantities of ozone depleting and/or high global warming potential CFCs, HCFCs or HFCs are circulated to remote evaporators with a much greater risk for emission to the environment. Fluidized state is acquired with low velocity and pressure of the fluid jets due to the Archimedes forces and buoyancy of the products, that lead to both energy savings and minimum mechanical action on the foods. The operation is continuous, easy to maintain, convenient for automation and the labour costs are substantially reduced. Further processing or packaging of the HFM-frozen products is considerably easier since they emerge from the freezer in a “free-flowing” state, i.e. do not stick together. Ice-slurry-based HFM agents may easily be integrated into systems for thermal energy storage, accumulating ice-slurry during the night at lower electricity costs.

The top view photos on Figure 9.5 show how a hydrofluidized bed of highly turbulent ice slurry is formed inside the HyFloFreeze® prototype's freezing compartment.

Figure 9.5. HyFloFreeze® prototype: hydrofluidized bed of highly turbulent ice slurry (Fikiin, 2003). International research co-operation Two main applications of the suggested HFM freezing technique can clearly be distinguished: (i) employment of unfreezable liquids as fluidizing agents and (ii) use of pumpable ice slurries as fluidizing media. This freezing principle provides an extremely high heat transfer rate, short freezing times, great throughput and better product quality at higher refrigerating temperatures. Thus, only about half the investment and power costs are necessary as compared with the popular individual quick freezing methods. Moreover, such

258


hydrofluidization freezing systems are less hazardous from an environmental viewpoint, since the primary refrigerant is limited to a small isolated circuit. The emerging HFM technology has attracted the attention of a number of academics and industrialists. The identification of optimal design specifications for HFM freezing systems requires an interdisciplinary approach by researchers with complementary skills. The HyFloFreeze project was, therefore, funded by the European Commission and performed by an international research consortium of six participating organisations (four universities and two SMEs) from Belgium, Bulgaria, Russia and the UK (Fikiin, 2003).

9.3. Cooling of fish with ice slurries The use of ice for extending the storage life of fish dates back many millennia. Up to the middle of the last century all ice used for fish cooling was from natural sources (winter snow or imported arctic ice). With the introduction of mechanical cold production, ice was and is produced in different forms, e.g. block, cube, tube or flake ice. Most of these forms need a certain degree of manual operation for transportation from one place to another, and have rather sharp edges capable of damaging the fish surface. Furthermore, they are usually quite coarse, resulting in poor heat transfer. The introduction of ice slurry for direct contact cooling of fish (Figure 9.6) presents several attractive features to the process operation over other forms of ice (Wang et al., 2000). For quality assurance it is essential that effective product cooling be provided throughout the entire production chain, from catch at sea, to storage, transportation, and processing. Cooling technologies employed often use refrigerated seawater and/or different types of fresh ice. Sea water systems placed on board large vessels maintain fish, by sea water circulation, at a mean temperature of about 2-4°C. Disadvantages of such systems are the volume taken up by the refrigeration machinery, difficult working conditions and salt uptake by the fish, especially in smaller species like sardine. Onboard smaller ships, fresh ice is normally loaded from harbour, stored and eventually mixed with the catch. The tendency of fresh ice to recrystallize and agglomerate in many cases limits the quality of icing, since the ice has to be loosened by manual means before mixing. Often large blocks of ice mixed with the fish result in uneven cooling rates. Bacterial growth is highly temperature-dependent. As a rule of thumb, the shelf life of fish kept at 0°C is more than doubled compared to +5°C; the closer to the freezing point of the fish, the better the product quality. Bearing in mind that bacterial growth rates can not be stopped, but only decelerated, it is also important to minimize the bacterial level by a rapid temperature drop in each part of the process. Possible freezing of the fish anticipated for chilling may result in decreased sensory perception (Sørensen, 1999) and should therefore be avoided. Intuitively, the use of ice slurry could improve cooling of fish by exploiting properties such as (Wang et al., 2000): • narrow approach to the freezing point of fish; • close to isothermal heat exchange during melt-off; • smooth surface preventing fish from damage; • easy dosing, mixing, handling and pumping; • possible drainage of salty water to minimize salt uptake.

259


a

b

Figure 9.6. Fish chilling in ice slurry (Fikiin et al., 2002): (a) land-based systems and (b) on-board systems (Liquid IceTM, Brontec, Iceland)

Because of its tiny ice crystals, ice slurry is soft and flexible for the chilled product. It effectively avoids any hot spots in the fish container, and provides excellent contact with fish without bruising. As fish are surrounded by numerous ice crystals, high cooling rate is achieved. This significantly retards bacterial growth and reduces fish tissue degradation. Analysis of cooling methods and process simulation Ice slurry for fish cooling and controlling temperature during storage can be implemented in different ways. In order to verify the aforementioned advantages of ice slurry a simulation model has been developed and related experiments have been carried out (Hansen et al., 1999). To simulate the cooling process and to check whether freezing occurs near the fish

260


surface, a differential heat conduction equation was solved by using finite-element-based CFD software:

div(k grad T)= ρ ⋅c p ∂T ∂τ

(9.1)

90

15

80

-20

70

-55

60

-90

50

-125

40

-160

30

-195

20

-230

10

Fat fish

0 White fish -30 -25

80 70

-265 -15

-10

-5

0

1.4

60

1.2 Fat fish

50

1

40

0.8

30

0.6

20

0.4

10

0.2

0

-300 -20

1.6

White fish

0 -30

5

Temperature (°C)

-20

-10

0

Temperature (°C)

Figure 9.7. Enthalpy-temperature curve from differential scanning calorimetry of cod fillets (Sørensen and Spange, 1999) and calculated thermophysical properties Based on the freezing curve, the enthalpy can be calculated as a function of temperature by assuming constant heat capacities of constitutient substances. For fat fish neglecting the effect of oil on crystallization may cause some errors. The specific heat capacity of fish is calculated as follows: ∆h = ∆T ⋅ (X d c p ,d + X oil c p ,oil + ( X w − X i ) c p , w + X i c p ,i ) + X i L

261

(9.2)

Thermal conductivity (W/m/K)

50

Specific heat capacity (kJ/kg/K)

100

Specific enthalpy (kJ/kg)

Frozen water content (%)

Thermal properties are calculated by considering that phase change of water will occur over a wide temperature interval (see Figure 9.7). The majority of water (70-90%) is mechanically trapped in and between cells, and is relatively easy to freeze. During freezing the salt content increases, resulting in a temperature glide of phase change. Individual freezing curves may vary among species, although the characteristics remain the same, i.e. thermo-physical properties are strongly influenced down to a temperature of approximately –10°C. The behaviour of phase change described has a large effect on the thermo-physical properties that vary with the temperature throughout a frozen fish. The composition of fish changes a lot among species and depends on the place and season of harvesting, which may also affect thermo-physical properties. White fish may be considered relatively stable containing about 80% water and 20% dry materials. For fatty fish like horse mackerel and sand eel, the content of dry materials may remain approximately 20% during the season whereas the oil content varies from 1 to 20%. Temperature-dependent thermo-physical properties for white fish (80% water) and fatty fish (70% water, 10% oil) are shown in Figure 9.7.


⎛ ∂h ⎞ ⎟⎟ c p = ⎜⎜ ⎝ ∂T ⎠P

(9.3)

The thermal conductivity, k, is determined by the assumption that the overall resistance to conduction is due to the resistance of parallel layers of each substance in parallel (=) or perpendicular (⊥) to the heat flow direction. It is further assumed that both cases are equally represented, i.e.:

k = ½(k = + k ⊥)

(9.4)

Experiments with artificial and real fish samples To eliminate biological and seasonal variation of fish properties when comparing cooling methods, artificial fish samples with thermophysical properties close to those of white fish have been made out of Karlsruhe food simulator (a mixture of methylcellulose, sodium chloride and water). The aim of the experiments was to compare cooling of fish in containers by using ice slurry or flake ice. The distribution of fish is assumed to be in perfect layers of fish and ice respectively. Three different cooling scenarios were set up, two of them representing an ideal distribution of either flake ice or ice slurry on top of each fish layer, and the third assuming larger re-crystallized/agglomerated blocks of ice covering only 25% of the total surface area, while liquid film heat transfer is present on the remaining surface. Measurements were made for an artificial fish model with thermocouples placed internally. The fish was placed between artificial dummies in the middle of the container. A total of 20% pure ice was employed for each experiment. Results obtained were compared with the data for horse mackerel. For modelling purposes, fish were assumed to be cylinders of infinite length with adiabatic contact lines between fish. Temperatures of flake ice and ice slurry were set to 0 and –3°C, respectively. The heat transfer coefficient between the ice particles and fish was estimated to be 750 W/(m²K), a value affected by the resistance of the melting liquid layer between the fish surface and ice. Liquid film heat transfer coefficient was assumed to be 50 W/(m²K). Figure 9.8 shows a reasonable agreement between calculated and measured temperature histories. However, it is also evident that a simple set of boundary conditions is not sufficient to describe the real situation in the container and some deviation may exist, especially for the time interval when almost all the ice has melted (1200 to 1600 seconds). Furthermore, it appears that the centre temperature decreases at a higher rate when using ice slurry at –3°C. This is even more obvious at the surface. The calculated temperature histories indicate that freezing does not occur at the outer shell if the ice slurry is kept at above –3°C. The final equilibrium temperature of the fish was approximately 1 K lower when using the same amount of ice slurry versus using flake ice. The difference is caused by the larger enthalpy change of the melting ice slurry.

262


20

0.0

20

18

0.0

18

16

0.0

Flake ice blocks

Horse mackerel, 15% ice

16

14 -0.0

12

-0.0

-0.0

0.0

0.0

0.0

Measurements

10 8

FEM model

Flake ice

6 Ice slurry

4

Temperature (°C)

Temperature (°C)

-0.0

14 12 10 8

Flake ice

6 4 Ice slurry

2

2

0

0 0

1200

2400

3600

Time (s)

0

1200

2400

Time (s)

Figure 9.8. Variation in centre temperature (left graph) measured in an artificial fish model (43 mm diameter) cooled in a container with ice slurry at –3°C and with flake ice at 0°C, together with calculated temperatures (initially 20% ice in the container). Temperature measurement (right graph) in horse mackerel cooled in a container with ice slurry and with flake ice (initially 15% ice in the container) The results from the experiments with the artificial fish model were comparable with those with horse mackerel. A similar tendency was found, i.e., faster temperature drop and about 1 K lower final temperature when using ice slurry. The end cooling temperature was, however, different because of the smaller amount of ice. If the distribution of flake ice is not ideal because of re-crystallized blocks, Figure 9.8 reveals that cooling with flake ice is less effective than with ice slurry. Cooling experiments with a fish model immersed into a flowing stream of ice slurry with different velocities and ice concentrations were also conducted to identify any advantages of pre-cooling before container storage. Measurements were performed for flow velocities of 0.1 and 0.2 m/s and at ice concentrations of 10, 20 and 30 wt-%. Results showed that there is no major difference in terms of cooling time for different combinations of these parameters. Compared with the immersed fish model, no significant difference was detected when cooling a container with perfect distribution.

9.4. Ice-slurry-based cooling of fruits and vegetables The ice-slurry cooling method for fish can also be employed for fruit and vegetables, along with other food commodities to be chilled or frozen. In many cases the uncontrolled uptake of solutes (salt or alcohol) on the product surface is more undesirable than for fish (unless osmotic phenomena are exploited to give added value to the product). Similar to the fish cooling, much faster heat transfer rates can be obtained. Most notable is the improvement when comparing previously air cooled products versus ice slurry cooled products. For instance, the Danish Technological Institute investigated the chilling and freezing of pig

263


carcasses in ice slurry with good results, while a number of researchers around the world performed promising experiments with various fruits and vegetables. When using suitable product-friendly media, the osmotic phenomena on the surface can be exploited to give added value to the products. In particular, by freezing of fruits in sugarethanol-based aqueous solutions or pumpable ice slurries new delicious dessert products can be formulated with beneficial effect on colour, flavour and texture due to the enzymeinhibiting action of the sugar (Fikiin and Fikiin, 1998, 1999). In addition, the take-up of food additives (antioxidants, flavourings, aromas and micronutrients) is improved, which can result in a better quality and extended shelf-life of the end product. Nevertheless, the available data for the physical properties and the performance of such secondary fluids in food freezing equipment are still too scarce. A set of predictive equations for the density, viscosity, thermal conductivity and specific heat capacity of sugar-ethanol aqueous refrigerating media are given by Fikiin et al. (2001). Sugar-ethanol aqueous solutions and ice slurries suitable for immersion freezing of fruits Several important criteria must be taken into consideration when selecting liqueur-type refrigerating liquids and ice-slurries pertinent for fruit freezing applications: (i) product friendliness with regard to the end product quality, (ii) environmental friendliness, (iii) suitable rheological properties in terms of good pumpability, and (iv) appropriate initial freezing temperature (Fikiin et al., 2001). A number of test solutions were therefore prepared at the St. Petersburg State University of Refrigeration and Food Technologies by using distilled and deionized water, pure ethanol of food-admissible class and sugar (sucrose or glucose). Solution compositions and freezing points are presented in Table 9.1. The estimated uncertainty in the mass fraction data was ±0.1%. Table 9.1. Compositions and initial freezing temperatures of the studied solutions Solution Number

Composition (mass fraction) water, xw ethanol, xe sucrose, xs

1 2 3 4 5 6 7 8 9

0.55 0.60 0.65 0.55 0.60 0.65 0.55 0.60 0.65

Solution No.

water, xw

10

0.60

0.25 0.25 0.25 0.20 0.20 0.20 0.15 0.15 0.15

0.20 0.15 0.10 0.25 0.20 0.15 0.30 0.25 0.20

ethanol, xe glucose, xs 0.25

0.15

tf (°C) –28.0 –25.0 –22.0 –26.5 –23.5 –19.5 –23.0 –20.0 –16.5

tf (°C) –24.5

An international taste panel considered that solutions No. 1, 2 and 10 posessed the best sensory and physical properties, but some other solutions (such as No. 4, 5 and 6) were also acceptable.

264


Predictive equations for the thermophysical and rheological properties of sugar-ethanol aqueous solutions and ice slurries A series of experiments were carried out and some theoretical approaches were employed to determine basic thermal and rheological properties of the studied single- and two-phase refrigerating media and to establish resulting regression relationships. The following assumptions were made when deriving the predictive equations: (i) water is the only freezable component of the solution (because, at atmospheric pressure, all the ethanol remains unfrozen above –114.5°C), (ii) the temperature-dependent properties of the liquid solution are extrapolated below the initial freezing point to estimate the unfrozen fraction properties, and (iii) the ice fraction variation with the temperature conforms with the Raoult’s Law (Fikiin et al., 2001). Initial freezing temperature Typical gradients of the time-temperature curves during slow freezing or thawing (∼0.5°C/min) were registered to measure the initial freezing points of the studied solutions (Table 9.1) and the following empirical equations were then established by a regression analysis:

tf = a0 + a1. xe + a2.xs + a12.xe.xs

(9.4)

where 0.15 ≤ xe ≤ 0.25, 0.10 ≤ xs≤ 0.30, and a0 = 10.9, a1 = –103.33, a2 = –51.67 and a12 = –66.67. Density The liquid densities were determined by a piezometric technique, which was previously tested with reference liquids (water, ethanol and other well-investigated solutions). The resulting regression equation is:

ρl = (b0 + b1 xe + b2 xs + b12 xe xs) + (c0 + c1 xe + c2 xs + c12 xe xs) t

(9.5)

for tf ≤ t ≤ 21°C, 0.15 ≤ xe ≤ 0.25, 0.10 ≤ xs≤ 0.30 and coefficients are given in Table 9.2. Table 9.2. Coefficients of Eq. (9.5) b0 981.8

b1 –67.556

b2 481.111

b12 –255.556

c0 0.30483

c1 c2 –3.10689 –2.06289

c12 9.18444

Furthermore, the ice-slurry density can be expressed as follows:

ρis = [xi / ρi + (1 – xi)/ ρl ] –1

(9.6)

where xi is the mass fraction of ice, the ice density ρi = 916.8 (1 – 0.00015 t) and ρl is determined by Eq. (9.5) for xs = xsin / [1 – (1 – tf / t) xwin ] and xe = xein / [1 – (1 – tf / t) xwin ]. Viscosity Measurements of the liquid viscosity were carried out by using glass capillary viscometers and the results obtained were approximated by the following equation:

265


ηl = D + E t + F t 2

(9.7)

where: D = d0 + d1 xe + d2 xs + d12 xe xs, E = e0 + e1 xe + e2 xs + e12 xe xs, F = f0 + f1 xe + f2 xs + f12 xes, tf ≤ t ≤ 21°C, 0.15 ≤ xe ≤ 0.25 and 0.10 ≤ xs ≤ 0.30. The empirical coefficients are given in Table 9.3. Table 9.3. Coefficients of Eq. (9.7) –17.325 79.222 100.822 –181.778

d0 d1 d2 d12

1.556 –6.162 –7.486 15.611

e0 e1 e2 e12

f0 f1 f2 f12

–0.04318 0.15612 0.18694 –0.40644

The model of Thomas (1965), valid for ice particle diameters between 0.1 and 45 µm, can further be employed to evaluate the apparent viscosity of the ice slurry (please refer to Chapter 3 for a detailed description of rheological ice slurry properties):

ηis = ηl [1 + 2.5 ϕi + 10.05 ϕi2 + 0.00273 exp (16.6 ϕi)]

(9.8)

where the volumetric ice fraction ϕi = xi [ xi + (1 – xi) (ρi / ρl) ]–1 may vary between 0 and 0.625, while ηl is calculated by Eq. (9.7) for xs = xsin / [1 – (1 – tf /t) xwin ] and xe = xein / [1 – (1 – tf /t) xwin ]. Thermal conductivity As is well-known, the thermal conductivity of a ternary solution does not comply with the additive principle and cannot, therefore, be rigorously expressed through the properties of the different constituents. Nonetheless, by using a quasi-binary assumption the overall liquid conductivity could be considered as a compound function of the conductivities of ethanol and water-sugar system. It turned out that the liquid thermal conductivity predominantly depends on the ethanol content and could roughly be estimated on the basis of the ethanol fraction only:

kl = (i0 + i1 xe + i2 xe2) + (l0 + l1 xe + l2 xe2) t

(9.9)

for tf ≤ t ≤ 20°C, 0.10 ≤ xe ≤ 0.35 and equation coefficients are shown in Table 9.4. Table 9.4. Coefficients of Eq. (9.9) i0 0.50686

I1 –0.573278

i2 0.2401997

l0 0.001347

l1 –0.0028111

l2 0.0011861

In accordance with the Maxwell model, the apparent thermal conductivity of the ice slurry could be written in the form of Jeffrey (1973):

kis = kl (1 + 3 ϕi β + 3 ϕi2 β 2 χ)

266

(9.10)


where χ = 1 + 0.25 β + 0.1875 β [ (α + 2) / (2 α + 3) ], β = (α – 1) / (α + 2), α = ki / kl , ki = 2.22 (1 – 0.0015 t), ϕi is as in Eq. (9.8), and kl is calculated by Eq. (9.9) for xe = xein / [1 – (1 – tf / t) xwin ]. The dimensionless apparent ice-slurry viscosity, η* = ηis / ηl , and thermal conductivity, k* = kis / kl , determined by Eqs (9.8) and (9.10) as a function of the volumetric ice fraction, ϕi, are shown in Figure 9.9.

η∗ and λ∗

2,5

2

η∗

λ∗

1,5

1

0,5 0

0,05

0,1

0,15

0,2

Volumetric fraction of ice (ϕi)

Figure 9.9. Dimensionless apparent viscosity, η* = ηis / ηl, and thermal conductivity, k* = kis / kl, versus ϕi. (The notation for thermal conductivity in the figure follows the symbol tradition of Continental Europe, i.e. “λ” is used instead of “k”) Specific heat capacity General thermodynamic considerations make it possible to determine the specific heat capacity of ternary solutions on the basis of the heat capacities of the solution components. The data obtained for liquid sugar-alcohol aqueous solutions were fitted by the following regression equation:

cp,l = (m0 + m1 xe + m2 xs + m12 xe xs) + (n0 + n1 xe + n2 xs + n12 xe xs) t

(9.11)

for tf ≤ t ≤ 20°C, 0.15 ≤ xe ≤ 0.25, 0.10 ≤ xs ≤ 0.30 and empirical coefficients are presented in Table 9.5. Table 9.5. Coefficients of Eq. (9.11) m0 4.192

m1 –1.9272

m2 –2.8172

m12 0.0910

n0 n1 n2 0.000020 0.005075 0.002675

n12 0.000459

The apparent specific heat capacity of ice slurries and other water-containing systems can easily be evaluated as follows (Fikiin and Fikiin, 1999b):

267


cp,is = cp,l – d [ xi L ] / d t

(9.12)

where L = 334.2 + 2.12 t + 0.0042 t 2 , xi = xwin (1 – tf / t) and cl is determined through Eq. (9.11) for xs = xsin / [1 – (1 – tf / t) xwin ] and xe = xein / [1 – (1 – tf / t) xwin]. It is obvious that t < tf in all the ice-slurry related equations, Eqs (9.6), (9.8), (9.10) and (9.12). A small-size prototype of HFM freezer for testing, demonstration and promotion of the HFM technology is under investigation at the Technical University of Sofia and Interobmen Ltd. – Plovdiv (Bulgaria). The hydrofluidization, conveyor and driving systems of the prototype are shown in Figure 9.10.

a

b

Figure 9.10. Hydrofluidization, conveyor and driving systems of the HyFloFreeze® prototype (Technical University of Sofia and Interobmen Ltd.): (a) top view, (b) overall view The following initial design specifications were used when putting together the prototype freezer: (i) starting selection of fruits to be frozen: strawberries, raspberries, plums, apricots, morellos, cherries, blueberries and cranberries; (ii) refrigerating media: unfreezable liquids or pumpable ice slurries based on sugar-ethanol aqueous solutions, (iii) refrigerating medium temperature: –25/–30°C, (iv) evaporation temperature of the refrigerant: –30/–35°C, (v) throughput: 20-50 kg per hour (depending on the product); (vi) final temperature in the frozen food centre: –12/–15°C; (vii) final average temperature of the product: –18/–20°C; (viii) principle of operation: enhanced hydrofluidization throughout the whole freezer by

268


directed jets of fluidizing agent; and (ix) conveyor system: electronic regulation of the driving motor revolutions for smooth variation of the conveyor speed and product residence time depending on the individual freezing duration for each product. The ice-slurry-based HFM technology possesses a series of advantages over the conventional IQF modes, which can be summarised as follows (Fikiin and Fikiin, 1998, 1999; Fikiin et al., 2001): •

Frozen fruit quality: high freezing rate; fine-grain crystal structure; sharp reduction of the surface mass transfer; enzyme-inhibiting action of the sugar; easy incorporation of antioxidants, flavourings, aromas and micronutrients and formulation of delicious dessert-type frozen foods with extended shelf-life and improved nutritional value and sensory properties.

•

Energy and economic efficiency: higher refrigerating and evaporation temperatures; possibility for single-stage refrigeration machine with reduced investment, maintenance and energy costs; easy connection with systems for thermal energy storage; high throughput and cost efficiency.

•

Environmental friendliness: use of environmentally friendly secondary coolants (syruptype solutions or ice-slurries) and primary refrigerant closed in a small isolated system.

At some temperatures and concentrations, the pumping of sugar-ethanol-based slurry through the hydraulic circuit and perforated bottom may be accompanied by intense foaming (Figure 9.5). Preliminary tests revealed that this adverse effect could be overcome by adding suitable antifoaming agents.

Literature cited in chapter 9 1.

2.

3. 4.

5. 6.

7. 8.

Bel, O.; Lallemand, A. : Etude d’un fluide frigoporteur diphasique: 1 – Caractéristiques thermophysiques intrinsèques d’un coulis de glace; et 2 – Analyse expérimentale du comportement thermique et rhéologique. Int. J. Refrig., Vol. 22, No. 3: pp. 164-187, 1999. Egolf, P.W.; Brühlmeier, J.; Özvegyi, F.; Abächerli, F.; Renold, P.: Properties of ice slurry. Proc. IIR Conf. Applications of Natural Refrigerants, Aarhus, Denmark 1996, IIF/IIR: pp. 517-526, 1996. Fikiin, A.G.: Congélation de fruits et de légumes par fluidisation. Proc. Budapest Conf., IIF/IIR: pp. 197-203, 1969. Fikiin, A.G. : Bases théoriques du procédé de fluidisation lors de l’intensification de la congélation des fruits et des légumes. Proc. 15th Int. Congress Refrig., Venice, Vol. 4: pp. 221-230, 1979. Fikiin, A.G.: Physical conditions of fluidized-bed freezing of fruits and vegetables. Kholodilnaya Tekhnika / Refrig. Engng, No. 7: pp. 59-61 (in Russian), 1980. Fikiin, A.G.: Method and system for immersion cooling and freezing of foodstuffs by hydrofluidization. Invention Certificate No. 40164, Bulgarian Patent Agency INRA, 1985. Fikiin, A.G.: New method and fluidized water system for intensive chilling and freezing of fish. Food Control, Vol. 3, No. 3: pp. 153-160, 1992. Fikiin, A.G.: Quick freezing of vegetables by hydrofluidization. In New Applications of Refrigeration to Fruit and Vegetables Processing – Proceedings of IIR Conference,

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9.

10.

11.

12. 13.

14.

15.

16.

17.

18.

19.

20.

21.

Istanbul (Turkey), Refrigeration Science and Technology, International Institute of Refrigeration, 1994-3: pp. 85-91,1994. Fikiin, A.G.; Pham, V.H.: System for examination of heat transfer regimes during hydrorefrigeration of foodstuffs. Invention Certificate No. 39749, Bulgarian Patent Agency INRA, 1985. Fikiin, A.G.; Ditchev, S.P.; Fikiina, I.K.: Principal parameters characterising the fluidization of fruit and vegetable layers. Kholodilnaya Tekhnika / Refrig. Engng, No. 11, pp. 33-37 (in Russian), 1966. Fikiin, A.G.; Ditchev, S.P.; Karagerov, D.I.: Fluidized bed freezing system for fruits and vegetables with various dimensions. Invention Certificate No. 10967, Bulgarian Patent Agency INRA, 1965. Fikiin, A.G.; Ditchev, S.P.; Karagerov, D.I.: Fluidized bed freezing apparatus AZF. Kholodilnaya Tekhnika / Refrig. Engng, No. 7, pp. 55-58 (in Russian), 1970. Fikiin K.A.: Novelties of Food Freezing Research in Europe and Beyond. Flair-Flow Europe Synthetic Brochure for SMEs No.10 (ISBN: 2-7380-1145-4), INRA: Institut National de la Recherche Agronomique, Paris (France), 55p., 2003. Fikiin, K.A.; Fikiin, A.G.: Individual quick freezing of foods by hydrofluidization and pumpable ice slurries. In Advances in the Refrigeration Systems, Food Technologies and Cold Chain, Ed.: K. Fikiin, Proceedings of IIR Conference, Sofia (Bulgaria), Refrigeration Science and Technology, International Institute of Refrigeration, 1998-6: pp. 319-326 (published also in the AIRAH Journal, 2001, Vol. 55, No. 11, pp. 15-18), 1998. Fikiin, K.A.; Fikiin, A.G.: Novel cost-effective ice-slurry-based technology for individual quick freezing of foods by hydrofluidization. CD-Rom Proceedings of the 20th International Congress of Refrigeration, Sydney (Australia), ICR Paper No. 271, 1999a. Fikiin K.A.; Fikiin A.G.: Predictive equations for thermophysical properties and enthalpy during cooling and freezing of food materials. Journal of Food Engineering, Vol. 40, No. 1-2, pp. 1-6, 1999b. Fikiin, K.A.; Fikiin A.G: Congelación individual rápida de alimentos por hidrofluidificación y compuestos de hielo. Frío, Calor y Aire Acondicionado (Madrid), Vol. 30, No. 334, pp. 22-27, 2002. Fikiin, K.A.; Fikiin A.G.: Quick freezing of foods by hydrofluidization and pumpable ice suspensions. Kholodilnaya Tekhnika / Refrig. Engng, No. 1, pp. 22-25 (in Russian), 2003a. Fikiin K.A.; Fikiin A.G.: L'Ice Slurry (ghiaccio binario) per una surgelazione veloce degli alimenti – Surgelamento singolo degli alimenti mediante idrofluidizzazione. Industria & Formazione per il Tecnico della Refrigerazione e Climatizzazione (Milano), No. 3, pp. 36-39, 2003b. Fikiin, K.A.; Kaloyanov, N.G.; Filatova, T.A.; Sokolov, V.N.: Fine-crystalline ice slurries as a basis of advanced industrial technologies: State of the art and future prospects. Refrigeration Business (Moscow), No. 7, pp. 4-11 (in Russian), 2002. Fikiin, K.A.; Tsvetkov, O.B.; Laptev, Yu.A.; Fikiin, A.G.; Kolodyaznaya, V.S.: Thermophysical and engineering issues of the immersion freezing of fruits in ice slurries based on sugar-ethanol aqueous solutions. Proceedings of the Third IIR Workshop on Ice Slurries, Lucerne (Switzerland). International Institute of Refrigeration, pp.147-154, 2001. (published also in EcoLibrium – Journal of AIRAH: Australian Institute of Refrigeration, Air Conditioning and Heating, Vol. 2, No. 7, pp. 1015, 2003.)

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22. Fleshland, O.; Magnussen, O. M.: Chilling of farmed fish. Proc. Aberdeen Conf., IIF/IIR, pp. 185-192, 1990. 23. Hansen, T.; Wang, M.J.; Kauffeld, M.; Christensen, K.G.; Goldstein, V.: Application of ice slurry technology in fishery. XXth Int. Cong. of Refr., Sydney, Australia, 19-24 September, 1999. 24. Jeffrey D.J.: Conduction through a random suspension of spheres, Proceedings of the Royal Society London, Vol. A 335: pp. 355-367, 1973. 25. Lucas, T.; Raoult-Wack, A.L.: Immersion chilling and freezing in aqueous refrigerating media: review and future trends. Int. J. Refrig., Vol. 21, No. 6: pp. 419-429, 1998. 26. Paul, J.: Binary ice as a secondary refrigerant. Proc. 19th Int. Congress Refrig., The Hague, Vol. 4b: pp. 947-954, 1995. 27. Pearson, S.F.; Brown J.: Use of pumpable ice to minimise salt uptake during immersion freezing. Proc. Oslo Conf., IIF/IIR: pp. 712-722, 1998. 28. Sokolov, V.N.; Fikiin K.A.; Kaloyanov, N.G.: Advantages, production and applications of pumpable ice slurries as secondary refrigerants. BulKToMM Machine Mechanics, Vol. 44, pp. 26-31 (in Russian), 2002. 29. Sørensen, B.S.: Resultater fra brug af kvalitetsindikatorer i modelforsøg, Workshop i kvalitetsindikatorer, Danish Institute for Fisheries Research, 1999. 30. Thomas, D.G.: Transport characteristics of suspension – VIII: A note on the viscosity of Newtonian suspension of uniform spherical particles, Journal of Colloid Science, Vol. 20: pp. 267-277, 1965. 31. Tressler, D.K.: Food freezing systems. In: Tressler, D.K., Van Arsdel, W.B., Copley, M.J. The Freezing Preservation of Foods, Vol. 1, The AVI Publishing Co., Westport, Connecticut: pp. 120-152, 1968. 32. Ure, Z.: Slurry-ice based cooling systems. Proc. Sofia Conf., IIF/IIR: pp. 172-179, 1998. 33. Woolrich, W.R.: Handbook of Refrigerating Engineering, Vol. 2: Applications. The Avi Publishing Co., Westport, Connecticut, 434 , 1966. 34. Wang, M.J.; Hansen, T.M.; Kauffeld, M.; Goldstein, V.: Slurry Ice in Fish Preservation. Infofish International 2, pp. 42-46, 2000.

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CHAPTER 10. THE CONTROL OF ICE SLURRY SYSTEMS By Jacques Guilpart and Laurence Fournaison 10.1 Introduction As described in this Handbook, ice slurry systems are of utmost interest thanks to their wide range of applications and to their good performance. Many authors have described the advantages and drawbacks of this two-phase secondary fluid based on a pure thermal and hydraulic analysis, but literature dedicated to the control of these systems is quite scarce. This chapter aims to describe some possible and commonly used control principles for ice slurry systems. These principles depend on considerations outlined in this chapter, a main concern is the strategy of operational modes of the ice slurry system. Two main operation mode strategies for an application of ice slurry systems exist:

The first consists of using the ice slurry tank as a simple energy storage system, without paying attention to the ice-liquid phase separation inside the tank. In this case, the residual pure liquid should be pumped from the bottom of the tank and used in a very classical single-phase secondary fluid loop. Many systems dedicated to air conditioning are based on this strategy, especially in Japan (Wang et al., 1999).

The second strategy consists of taking advantage of the latent heat contained in the ice crystals of the slurry at the point of consumption or use. In this case, the slurry has to be maintained as homogeneous as possible in order to be pumped in the secondary loop. Of course, the design of this loop has to deal with the particular thermal and rheological behaviour of the slurry. Many systems dedicated to supermarkets or food process applications are based on this principle (Kauffeld et al., 1999; Wang et al., 2002).

Depending on the chosen strategy, this chapter aims to describe the classical concepts applied to control ice slurry systems. It will be shown that, despite some particularities related to the eventual use of ice slurry in the secondary loop and in heat exchangers, the control of these systems remains nearly as simple as the control of classical secondary loops working with single-phase fluids. 10.2 General organization of an ice slurry system Compared with a classical secondary fluid loop, the energy storage capability of ice slurry often calls for storage tanks designed to shave the peak demand in cooling. Consequently, an ice slurry system comprises an ice slurry generator charging a storage tank. Depending on the application the liquid or the ice slurry is then pumped from the storage tank to the consumer units, which are in a classical hydraulic loop with discharge and return lines as shown in Figure 10.1. In Figures 10.1a and 10.1b, two possibilities are represented with dotted lines: the use of single-phase residual liquid pumped from the bottom of a non-agitated tank and the use of ice slurry pumped from the middle of an agitated tank. A “mono-tube dynamic®” circuit could also be installed (Figure 10.1b): as the temperature during the melting of the ice remains almost constant in the slurry, this type of distribution loop is well adapted to servicing the consumer units.

273

Primary Secondary refrigerant refrigerant loop loop

Ice generator

Storage tank

Ice generator

Secondary refrigerant loop

Storage tank


Primary refrigerant loop

Figure 10.1b

Secondary refrigerant loop

Ice generator

Storage tank

Figure 10.1a


Figure 10.1c Figure 10.1. Some possible designs of an ice slurry system There are some additional differences between single-phase fluid and ice slurry secondary loops besides the ice slurry generator and storage tank. The heat exchangers of the consumer units working with ice slurries have to be supplied using small local pumps (classical centrifugal pumps are sufficient). It has also to be emphasised that the control of these terminal units cannot be based on three way valves or throttling devices, because of the risk of blocking the flow channels with plugs of ice. With the exception of these differences, an ice slurry system is designed as a classical secondary loop. A major consequence of this is that if a secondary fluid loop is designed to operate with ice slurry, it would work as well with a single-phase secondary fluid. 10.3 What is to be controlled? Figure 10.1 shows that, whatever the organisation of the system is, four basic elements have to be controlled in order to control the whole system: (i) the consumer units, (ii) the storage tank, (iii) the ice slurry generator, and (iv) the primary refrigerating unit. 10.3.1 CONTROL OF CONSUMER UNITS For the reasons cited above (necessity to use local feeding pumps), and considering that the heat exchangers can work with ice slurry as well as single-phase coolants, the control of the terminal consumer units can be easily set up: a simple ON-OFF control of the feeding pumps gives reliable results, although a variable speed control of the pumps will result in energy savings. A simple thermostat for measuring the process temperature (cold room, display cabinet, etc.) is sufficient. The functional scheme of the control of terminal units is presented in Figure 10.2.

274


Y

terminal unit

X

T

Figure 10.2. Functional scheme of the control of terminal consumer units The terminal supply pump can be combined with a solenoid valve, but in most cases this is not mandatory. Often the defrost strategy to be used is the same as those which are adopted for single-phase fluids (clock, thermostat, differential pressure controller, electric resistances, whole loop heating with an electric device or hot gas method, etc…). An example of the defrosting system is presented in Figure 10.3. The heating device C should be an electric resistance-type or a hot gas system.

Storage tank

B C

Ice generator

A

A B C

A

Normal cycle OPEN CLOSE OFF

Defrost CLOSE OPEN ON

Figure 10.3. Defrost system based on simultaneous defrosting of consumer units However, a more suitable and adaptable defrosting strategy can be set up by defrosting consumer units independently. This can be performed by locally warming the coolant in the primary loop. On one hand this kind of set up is more expensive in terms of investment (as every consumer unit has to be equipped with a heating device), but on the other hand better energy efficiency of this alternative method leads to substantial savings. Figure 10.4 illustrates a possible design of such a defrosting system. In some applications, e.g. medium product temperature at +5°C, the heating element might be avoided and defrosting is achieved by simply stopping the ice slurry flow.

C

terminal unit

B

A

A B C

Cooling demand Yes No OPEN CLOSE ON OFF OFF OFF

Figure 10.4. Example of a local defrost set up

275

Defrost CLOSE ON ON


To conclude, the control of terminal consumer units in an ice slurry loop is easily realized and is similar to the control principle applied in classical secondary refrigerant systems. It has to be based on “ON-OFF” actuators to avoid the problem of plugging, which occurs if proportional actuators such as three way valves or throttling devices are used. 10.3.2 CONTROL OF THE STORAGE TANK Because the storage tank “only” accumulates or releases thermal energy, it should be considered as a passive element, which does not need any specific control, except for safety assessments. The list of safety devices presented below is not exhaustive and can be extended according to the specific characteristics of the storage and the distribution devices:

Maximum power of the agitator. Different authors recommend a power between 25 to 70 W/m3 for maintaining an acceptable degree of homogeneity of the stored ice (Kauffeld et al., 1999; Ben Lakhdar et al., 2001). In some applications no agitator is required and ice-liquid phase separation is used as a process advantage (for instance, for harvesting fairly dry ice at the top of the tank or using single-phase liquid in air conditioning loops). High-low level measurements in the tank. Discharge pressure of the two pumps (distribution loop and ice slurry generator) to detect eventual plugging or cutting off of the circuits. Ice slurry temperature measurement in the tank and/or at the outlet of the tank. Note that what this temperature represents is quite difficult to interpret, depending on the homogeneity of the ice slurry.

To conclude, the control of the storage tank is not a major problem if one considers that it is just a passive element. But the problem is totally different if one wants to control the stored thermal energy inside the receiver: this consideration will be discussed below, at the same time as the influence of the consequences of the ice and temperature distributions inside the storage tank. 10.3.3 CONTROL OF THE ICE SLURRY GENERATOR 10.3.3.1 General considerations The role of the ice slurry generator is to create ice crystals in the coolant. The ice mass fraction at the outlet of the generator depends on different parameters and can be approximately evaluated by:

x 0 = xi +

1 Φ0  + c p ⋅ ∆T   L  m& 

(10.1)

where xo and xi are respectively the ice mass fractions at the outlet and inlet of the ice slurry generator, cp is the specific heat capacity (kJ/kg K) of the carrier liquid (which should be assumed to be constant as a first approximation), L is the latent heat of ice (333 kJ/kg), Φ0 (kW) is the refrigerating capacity of the primary refrigerating unit, m& (kg/s) is the mass flow rate of the secondary refrigerant (the ice slurry) in the ice slurry generator and ∆T (K) is its 276


temperature drop. While the outlet temperature is greater than the melting point of the coolant, ice fraction remains at zero, xo = xi = 0. In this case, the ice slurry generator works as a chiller without incurring any damage. Figure 10.5 shows the relationships between different input parameters for an ethanol-water system. This chart is based on the calculation method for thermophysical properties proposed by Guilpart et al. (1999) and Ben Lakhdar (1998). The values obtained with this method are consistent with Bel and Lallemand (1999) in the two-phase domain and with Melinder (1997) in the single-phase domain. Figure 10.6 explains how to deal with Figure 10.5. For instance, if the intention is to work with a 3% ice slurry (“In” at 3% ice in Figure 10.6) made from a 15% initial ethanol solution (X = 0.15) the temperature has to reach –7.3°C (“Out 1” in Figure 10.6), corresponding to an enthalpy of –79 kJ/kg. If this mixture is used at the inlet of an ice slurry generator designed to Φ provide the ratio 0 equal to –100 kJ/kg, the outlet enthalpy of –179 kJ/kg corresponds to a m& temperature of –12.5°C (“Out 2”) and to an ice concentration of 31% (“Out 3”). Ice concentration (w/w) 0

0.1

0.2

0.3

0.4

0.5

0

-100

-150 X

X =

-35

-30

-25

-20

X

=

0. 2

=

0. 1

X=

X=

0. 1

=

0.2

0.

3

3 0.

-200

X

Enthalpy (kJ/kg)

-50

-15

-10

-5

0

5

Temperature (°C)

Figure 10.5. Thermal characteristics with main parameters of a water/ethanol mixture

277

0.6


Out 1 : -7.3 °C

In : 3% ice 0

0.1

0.2

0.3

0.4

0.5

0.6

0

∆h = 100 kJ/kg

-50

-100 in

-150

=

0. 15

X=

0. 1

5

-200

:X

-35

-30

-25

-20

-15

-10

-5

0

Out 2 : -12.5 °C

5

Out 3 : 31% ice

Figure 10.6. Use of the diagram presented in Figure 10.5 (cf. text) 10.3.3.2 Different possible control strategies

Three main control strategies of ice slurry generators may be envisaged. Today, all these possible strategies are based on the measurement of a temperature, assuming that the dependence between the temperature and the ice concentration is known. This assumption is quite approximate (Fournaison et al., 2001), but it still remains the simplest and cheapest solution. These three strategies are: 1. The control of the ice concentration at the outlet of the ice slurry generator. This strategy is possible while using ON-OFF or HIGH-LOW control of the primary refrigerating unit based on the outlet temperature measurement (see Figure 10.7a). This strategy is quite safe for the ice slurry generator, but it does not take into account the ice fraction contained in the storage tank. 2. The control of the ice concentration in the ice slurry tank, which is supposed to be the same as at the inlet of the ice slurry generator. This strategy is an interesting solution, only if the medium in the storage tank is perfectly agitated, which is seldom encountered in practice (cf. Figure 10.7b). 3. The control of the ice concentration increase in the ice slurry generator while using Φ variable flow rates of the secondary fluid (modification of the 0 ratio at constant m& Φ0) and/or a high/low control of the primary refrigerant loop. The input values for this control are the temperature decrease, necessarily associated with a low temperature limit at the outlet (cf. Figure 10.7c).

278


ON / OFF or HI / LOW

ON / OFF or HI / LOW

Ice generator

Storage tank

Storage tank

Ice generator

T


(b) Storage tank

Ice generator

(a)



(c) Figure 10.7. Some different possible strategies to control an ice slurry generator The first strategy is mainly used because it is inexpensive, easy to install and ensures safe running conditions for the ice slurry generator. It is only an accurate method if the solute concentration at the inlet of the ice slurry generator is constant and well known, and if the temperature measurement is accurate enough. It is emphasized that these two conditions sometimes remain difficult to be verified in industrial conditions. The behaviour of the storage tank is particularly important: in this system, the ice-liquid phase separation leads to a variation of ice concentration. Therefore the significance of the temperature measurement is apparent. As mentioned in the introduction, the problem of ice-liquid phase separation is somehow related to the overall strategy of operating the ice slurry installation: 1. If ice slurry appears in pipes and heat exchangers the storage tank has to be a perfectly agitated vessel to ensure a homogenous ice distribution (Figure 10.8a). This method is used in applications near 0°C such as certain cold rooms, display cabinets and food processing. 2. The ice slurry tank is only considered as an energy storage tank, and the secondary loop is charged with a single-phase or low ice concentration coolant (Figure 10.8b and 10.8c). In this case ice-liquid phase separation implies a variation of the residual liquid concentration, resulting in a variation of the melting point of the coolant. This system is often used for applications requiring large storage tanks, such as air conditioning of buildings for instance. 3. The highly concentrated ice at the top of the storage tank is harvested and either used as “dry” ice (Figure 10.8d), or mixed with the liquid coming back from the process (Figure 10.8e). The first case is often encountered in direct cooling in the food industry, e.g., for chilling shrimps and/or fish (Wang et al., 2002). In these applications, sea water (NaCl brine) is used and the brine is not recycled (the system is

279


Dry ice

Poor layer

b) Partially agitated tank and use of concentrated slurry

Mixing device

c) Storage tank without agitation and use of ice slurry at a low concentration

Ice generator

Ice generator

a) perfectly agitated tank and use of homogeneous ice slurry

Rich layer

Ice generator

Ice generator

Ice generator

charged with fresh sea water). The second case corresponds to marginal applications for which the temperature of the process has to be variable.

drain

Fresh brine

d) Use of dry ice

e) Mixing device

Figure 10.8. Different operational modes of ice slurry systems In most cases the industrial applications lie between the “perfectly agitated” storage tank and the “perfectly separated” rich and poor layers of ice slurry in the storage tank. 10.3.4 CONTROL OF THE PRIMARY REFRIGERATION UNIT The primary refrigeration unit can be controlled in an on/off manner or by varying the evaporation temperature gradually in order to adjust the ice making capacity according to Equation 10.1. Any capacity control, used in conventional refrigeration units, might be applied, e.g. speed controls of the compressor, thermostatic expansion valve, and automatic solenoid expansion valve. 10.4 Influence of the temperature and solute concentration on the control parameters If the ice slurry in the tank is perfectly agitated, the temperature of the slurry may be considered to be constant. The temperature only depends on the nature of the freezing depressant, on its initial concentration and on the ice mass fraction. According to the solid/liquid equilibrium curve, this temperature perfectly defines ice concentration of the ice slurry. Usually ice concentrations between 0.1 and 0.3 wt-% are used. Figure 10.9 shows for an ethanol/water mixture the relationships existing among the temperature, the initial solute concentration and the ice concentration. 280


1.2

Ice mass fraction

1.0

0.8

0.6

0.4

0.2

0.0 -50

-40

-30

-20

-10

0

10

Temperature (°C) Initial ethanol mass fraction

0

0.05

0.1

0.15

0.2

0.25

0.3

0.4

0.5

Figure 10.9. Ice concentration versus temperature and solute concentration for ethanol/water mixtures According to Fournaison et al. (2001) and Figure 10.9, especially at low solute concentrations, a low accuracy in the temperature measurements leads to an even lower accuracy in the ice concentration. The initial solute concentration also plays a major role. Consequently, the control of ice slurry systems has to be based on accurate knowledge of both the temperature and the solute concentration. Table 10.1 describes the common accuracies that should be expected in laboratory conditions and in industrial conditions: Table 10.1. Expected accuracy in measurements under different conditions Laboratory conditions Industrial conditions Temperature measurement ± 0.1 K ± 0.5 K Solute concentration measurement 1% 5% These accuracies required show that the determination of the ice concentration by temperature measurement is sometimes impossible, see also Figure 10.10. Absolute error on ice concentration

0.3

0.2

0.1 Maximum absolute error X i = 0.30

0 -30

X i = 0.20 X i = 0.10

Xi=

-20

0.15 X i = 0.05

-10

0

Température (°C)

Figure 10.10. Absolute error in ice concentration measurements under industrial conditions when working with water/ethanol ice slurries

281


Figure 10.10 clearly shows that, e.g. for a solution of 5 wt-% ethanol at –2.5°C, it is almost impossible to predict the ice concentration by temperature measurement. It also shows that: • the maximum absolute error obtained in the ice concentration determination occurs close to the freezing point, • it is not reasonable to expect precise ice concentration determination, if the temperature is two to three degrees below 0°C, • the lower the temperature is, the better is the accuracy, • a high solute concentration implies a low error in the ice concentration determination.

These considerations are also valid for other solutes as shown in Figure 10.11.

Maximum absolute error on ice concentration

0.1 0.09 0.08 Industrial conditions

0.07 0.06 0.05

ammonia

0.04

ethanol propylglyc

0.03 0.02

Laboratory conditions

0.01 0 -35

-30

-25

-20

-15

-10

-5

0

Temperature (°C)

Figure 10.11. Maximum error in the ice concentration determination versus the temperature for different operating conditions Figure 10.11 indicates that, even under laboratory conditions and at low temperatures, the maximum absolute error made in the ice concentration determination cannot be lower than 1% (6% in industrial conditions). The reduction in this maximum error is possible, if more concentrated brines are used and in proportion the freezing point and consequently the ice concentration at a given temperature are reduced. Figure 10.11 also indicates that a higher temperature gives larger uncertainty in the ice concentration measurement. It appears that the control of ice slurry systems tends to be impossible at temperatures just below 0°C down to –3 or –4°C. This becomes evident when the uncertainty in the ice concentration measurement is equal to or greater than the basic value taken for controlling the system. Figure 10.12 shows the operating range of an ethanol/water ice slurry system. The ice concentration set-point is located between Xi = 0.1 and Xi = 0.3. This figure shows the degree of freedom in ethanol concentration and temperature one has in reaching this target.

The dotted lines surrounding the curves for Xi = 0.1 and Xi = 0.3 represent the ice mass fraction uncertainty due to the temperature and concentration measurements for the solution under industrial conditions. It appears that the control of ice concentrations at temperatures

282


higher than –4.1°C and/or ethanol concentrations lower than 8% is very difficult, and becomes even impossible at about 0°C. 0.2 0.18

Fre ezin gp oin t Xi = 0.1

ethanol concentration (W/W)

0.16 0.14

Xi =

0.12

0.3

0.1 Xi = 0.5

0.08 0.06 0.04 0.02 0 -10

-9

-8

-7

-6

-5

-4

-3

-2

-1

Temperature (°C)

Figure 10.12. Operating range of an ethanol/water ice slurry system On the other hand, the lower the temperature is and the higher the solute concentration is, the easier it becomes to control the ice concentration. 10.5 Consequences of the uncertainty in ice concentration on the control of the system Whatever the operational mode of the ice slurry installation is, it usually involves an increase in the solute concentration at the inlet of the ice slurry generator. This is the case for an imperfectly agitated storage tank where ice, i.e. frozen water, accumulates. It is also the case of a perfect ice separator (ice-rich and poor layers as illustrated in Figure 10.8). In all cases, the residual mother liquor is enriched in solute. According to the discussion above, this solute concentration shift helps to facilitate control of the ice slurry generator. At the same time, the temperature set point is reached at a lower ice concentration and that leads to a safer running condition. In the worst case (cf. Figure 10.13), if the solute concentration reaches a too high a value, the ice slurry generator would operate as a classical chiller, without any damage as mentioned above. In this case, the performance degradation simply implies an increase in the running time of the primary refrigeration loop. Consequently, it can be said that, even if the ice concentration control in the ice generation process is only approximately performed, the consequence on the global control of the system is not significant. For instance, if using an initially 10% ethanol mixture, a control scheme based on a classic thermostat (differential of ± 1 K) with a set point fixed at –6°C ensures a safe operating range as shown in Figure 10.13.

283


0.2 0.18

Fre

ethanol concentration (W/W)

0.16

ezin g

Xi = 0.1

C poi

Possible running range (monophasic coolant)

nt

0.14 Ice slurry running range

Xi = 0.3

0.12 0.1

Xi = 0.5

0.08

D

B A

0.06 0.04 0.02 0 -10

-9

-8

-7

-5

-4

-3

-2

-1

-6 Set point + - 1K

Figure 10.13. Operating range for an ice slurry loop working with an initial 10% ethanol/water mixture with a thermostat set point at –6°C ± 1 K The operating points shown in Figure 10.13 are as follows. Point A: designed operating set point: ice concentration Xi = 25% at –6°C Point B: maximum ice concentration (Xi = .35) obtained at the cut off of the thermostat. Point C: if some ice is accumulated in the ice slurry tank or anywhere else in the secondary loop, the concentration of the residual liquid increases. The ice slurry generator continues to run until the temperature of –7°C is reached (cut off of the thermostat). No ice is produced if the ethanol concentration reaches 15% or more (classical chilling mode). Point D: if the thermal load is too large, there is no more ice in the secondary loop. The initial ethanol concentration reaches the initial value of 10%. The ice slurry generator produces some ice while the temperature is less than –4.2°C. If the thermal load is too high, the primary refrigeration loop continues to run, even without ice production (classical chilling mode). To conclude with this example, the ice slurry loop cannot work below 10% of ethanol or below –7°C. Consequently, the maximum possible ice concentration is 35%, which is a safe running condition. From Figure 10.13, it is easy to see that the running range of an ice slurry loop is very small at temperatures above –3°C and that a very high ice concentration should rapidly occur at this temperature. The one situation to avoid is dilution of the initial mixture. This could happen, for instance, while refilling the installation with pure water. This situation would indeed have a major consequence leading to the system running with too high an ice concentration and the risk of plugging of the circuits. It should be emphasized that low solute concentrations could also lead to mechanical problems in certain ice slurry generators, which are not designed to be operated as flake ice slurry generators.

284


10.6 Conclusions The control of ice slurry secondary loops does not fundamentally differ from the control of classical indirect cooling systems. It only has to be based on the use of small local pumps for feeding the heat exchangers, and ON-OFF actuators to avoid the problem of plugging when using proportional actuators as three way valves or throttling devices. In practical situations, the control of the ice slurry generator should be based on the measurement of the inlet, or preferably, of the outlet temperature, even if the consequent accuracy on the ice concentration is only approximate. A judicious set up of the thermostat is able to ensure a safe running condition of the ice slurry generator. One must nevertheless emphasise that this control principle is not accurate enough to measure the refrigerating capacity (and/or the energy) delivered by the system. Special care has to be taken for systems running with low secondary fluid concentrations. Under those conditions, plugging of the ice slurry distribution loop and possibly mechanical damage to the ice slurry generator could occur. Therefore, it is not recommended to operate in the ice slurry domain at temperatures higher than –3 to –4°C. Literature cited in Chapter 10 1. 2. 3. 4. 5. 6. 7.

8. 9.

Bel O.; Lallemand A.: Study of a two phase secondary refrigerant. 1- intrinsic thermophysical properties of an ice slurry. Int. Journal of Refrigeration, Vol. 22, No. 3, pp. 164-187, 1999. Ben Lakhdar M.A.: Comportement thermohydraulique d’un fluide frigoporteur diphasique : le coulis de glace. Etude théorique et expérimentale. PhD thesis. INSA de Lyon, 1998. Ben Lakhdar M.A.; Blain G.; Compingt A. et al.: Direct expansion and indirect refrigeration with ice slurry. Third IIR Workshop on Ice Slurries, Lucerne, May 2001. Fournaison L.; Chourot J.M.; Faucheux M.; Guilpart J.: Ice fraction error calculation in ice slurries. Third IIR Workshop on Ice Slurries, Lucerne, May 2001. Guilpart J.; Fournaison L.; Ben Lakdhar M.A.: Calculation method of thermophysical properties for ice slurries, application to Water / ethanol mixture. XXth IIR International Congress of Refrigeration, Sydney, 1999. Kauffeld M.; Christensen K.; Lund S.; Hansen T.: Experience with ice slurry. First IIR Workshop on Ice Slurries, Yverdon les Bains, May 1999. Melinder A.: Thermophysical properties of liquid secondary refrigerants, Tables and diagrams for the refrigeration industry, IIF-IIR, Paris, 1997. Wang M.J.; Lopez, G.; Goldstein, V.: Ice slurry for shrimp and processing. Fifth IIR Workshop on Ice Slurries, Stockholm, May 2002. Wang M.J.; Inoue Y.; Goldstein V.: Ice thermal storage in modern buildings, XXth IIR International Congress of Refrigeration, Sydney, 1999.

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CHAPTER 11. OPTIMIZATION OF ICE SLURRY SYSTEMS by G. Grazzini, S. Pazzi

Ice slurry is used as a heat carrier and as a fluid useful for energy storage. The optimization of ice slurry systems refers to systems with components producing temperature differences, heat transfer and energy storage. There has not been much written about optimization of ice slurry systems, hence this chapter presents a brief general guide to optimization in general and optimization of energy systems in particular. Optimisation is a design or managing method used to obtain the best value of the defined system's goal (or goals). This can be expressed as an objective function which can be minimized or maximized. A set of unknowns or variables, subject to constraints allowing some values but excluding others, controls the values that the objective function can assume. The systems considered always have physical constraints and often the user needs to optimize a number of different objectives simultaneously.

11.1 Criteria Many different criteria can be used to build the objective function. Some common criteria are as follows. To evaluate the economic suitability of a project it is necessary to build some evaluation indices. These indices are used to evaluate the profitability of an investment and compare alternative investments. The most commonly used are: The Payback Period, which is defined as the length of time required for the cash inflows received from a project to recover the original cash outlay of the initial investment. A Net Present Value (NP) criterion estimates the actual value of all the cash flows during the lifetime of the project. Internal Rate of Return (IRR) calculates an interest rate that is characteristic of the project being considered. Mathematically the Internal Rate of Return (IRR) is the interest rate that makes the Net Present Value of the investment equal to zero. For more detailed information on the estimation of financial parameters related to plant design, readers should consult Tsatsaronis (2000a), Bejan et al. (1996) and their references. Economics often does not consider physical constraints. Energy is the physical parameter that obviously appears when dealing with an energy system. The objective function then should be the energy needs that have to be minimized. In cooling systems the parameter usually considered is the COP (Coefficient Of Performance), defined as the ratio between the cooling effect and the energy employed to obtain it. For irreversible systems a maximum exists for this parameter (Grazzini, 1993) so the COP function can be assumed as the objective to be maximized. When applied to complex systems the parameter should include all useful energy, including pressure losses in pipes.

287


The COP is defined from the first law of thermodynamics. In order to evaluate the temperature level of heat exchange, the second law also has to be considered. For this purpose the concept of exergy was introduced. When two thermodynamic systems are placed in communication, theoretically work can be developed as the two come into equilibrium. When one of the two systems is conveniently idealized and used as a reference environment, the other being some system of interest, exergy is defined as the maximum theoretical useful work obtainable as the systems interact to equilibrium. Alternatively, exergy is the minimum theoretical useful work required to bring a system from equilibrium with the environment to a specified state. For more detailed information on the exergy and exergy analysis, readers should consult the references by Moran (2000), Moran and Shapiro (2000), Bejan et al. (1996), Kotas (1995), Lozano and Valero (1993), Szargut et al. (1988). A thermodynamic optimization produced a design that was very different from an economically optimal one. The objective of thermoeconomic or exergoeconomic optimization is to minimize costs, both economic and related to destruction and loss of exergy. The goal is pursued with the association of a cost rate to each exergy transfer. For more detailed information on thermoeconomic or exergoeconomic analysis, readers should consult the references to work by Tsatsaronis (2000), Bejan et al.(1996), Lozano et. al. (1994), Evans (1980). Purely thermodynamic methods were proposed as the equipartition of entropy production (Tondeur and Kvaalen, 1986) and entropy minimization (Bejan, 1996), but they appear to be equivalent (Bejan and Tondeur, 1998). The same applies to finite-time, finite-seize, finiteresources and endoreversible (exoirreversible) thermodynamics (Bejan, 1996). Life Cycle Analysis (LCA) was developed in the 1970s to assess the environmental impact of a process (for a review see Frankl and Gamberale, 1998). The method started from a balance between the energy output and the energy used over the entire useful life of the system, including the total amount of energy and materials employed in a fabrication process, in the maintenance and in the decommissioning. LCA has been extended to include labour, environmental damage and recycling, so actually the acronym is used very often for Life Cycle Assessment considering all environmental impacts such as climate change, ozone depletion, etc. (EPA, 1994; ISO, 1998). Being LCA based on First-Law Analysis it fails to account for different types of energy carriers. Szargut (1990) introduced exergy in the procedure and Sciubba (2001) proposed Extended Exergy Accounting incorporating the above described approaches and thermoeconomic analysis.

11.2 Methods Optimization problems are made up of three basic ingredients: • • •

An objective function which has to be minimized or maximized. A set of unknowns or variables which affect the value of the objective function. An eventual set of constraints that allow the unknowns to take on certain values but exclude others.

288


•

An eventual set of constraints that allow the unknowns to take on certain values but exclude others.

Optimization algorithms can be divided into two main categories: unconstrained and constrained. The first category looks for the optimum of a specified objective function reference to the range of variation of the input parameters. The latter category optimizes the target function assuming a well defined set of constraints for the input parameters which represent the independent variables for the objective function. When dealing with non-linearly constrained optimization, other methods should be used. The sequential quadratic programming (sequential QP) algorithm, for example, is a generalization of Newton's method for unconstrained optimization in that it finds a step away from the current point by minimizing a quadratic model of the problem (Fletcher, 2000). More detailed information on the above mentioned optimization methods and other algorithms can be found, apart from the quoted references, at the Web site: http://www-fp.mcs.anl.gov/otc/Guide/OptWeb/. Genetic algorithms (Goldberg, 1989) optimize a function exploiting the principles of natural evolution. Evolutionary strategies (Baech, 1996; Baech et al., 1997) are based on the same principles of genetic algorithms but differ from these in that the best individuals are not crossed. Engineering problems are often characterized by a high degree of complexity which may imply time-consuming computations for target function evaluation. That is why optimization algorithms are commonly coupled to approximators such as Neural Networks (Dayoff, 1990) or Lazy Learning (Aha, 1997, Atkeson, 1997) algorithms. The open literature presents several studies dealing with the coupling of optimization algorithms and local or global approximators to solve engineering problems (Cosentino et al., 2001).

Literature cited in Chapter 11 1. Aha, D.W., Editorial, Artificial Intelligence Review, Special Issue on Lazy Learning , 1997 2. Atkeson, C.G., Moore, A.W., Schaal, S., Locally weighted learning, Artificial Intell. Review, 11: p. 11-73, 1997. 3. Baech, Th.: Evolutionary Algorithms in Theory and Practice, Oxford University Press, New York, 1996. 4. Baech, Th.; Fogel, D.B.; Michalewicz Z. (eds): Handbook of Evolutionary Computation, Oxford Univ. Press, New York, and Inst. of Physics Pub., Bristol, 1997. 5. Bejan, A., Entropy generation minimization., CRC Press Boca raton, FL, USA, 1996. 6. Bejan, A., Entropy generation minimization: the new thermodynamics of finite-seize devices and finite-time processes. J. of Applied Physics 79: p.1191-1218, 1996. 7. Bejan, A.; Tsatsaronis, G.; Moran, M.J.: Thermal design and optimization, John Wiley & Sons, Inc., New York, 1996. 8. Cosentino, R., Alsalihi, Z., Van Den Braembussche, R., Expert System for Radial Impeller Optimization, ATI-CST-039/01, 4th Europ. Conf. on Turbom., March 2001, Florence, Italy. 9. Dayoff, J., Neural Network Architectures. An Introduction, Van Nostrand Reinhold, 1990. 10. Evans, R.L., Thermoeconomic Isolation and Essergy Analysis, Energy 5, n.8-9, 1980.

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11. Fletcher, R., Practical Methods of Optimization, John Wiley & Sons, New York, U.S. , 2000. 12. Frankl, P., Gamberale, M., The methodology of LCA and its application to the energy sector, Proc. Advances in En. Stud., P. Venere, Italy, 1998. 13. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, 1989. 14. Grazzini, G.: Irreversible refrigerators with isothermal heat exchanges, Int. J. of Refrig., 16, No.2, pp.101-106, 1993. 15. Kotas T.: The Exergy Method of Thermal Plant Analysis, Butterworths, 1995. 16. Lozano M.A.; Valero A.: Theory of exergetic costs, Energy, Vol. 18, no.9, pp.939-960, 1993. 17. Moran, M.J.: Exergy analysis. In: F. Kreith ed. The CRC Handbook of Thermal Engineering, 1-69-77, CRC Press, Boca Raton, FL, USA, 2000. 18. Moran, M.J.; Shapiro, H.N.: Fundamentals of Engineering Thermodynamics, 4th ed., John Wiley & Sons, New York, 2000. 19. Sciubba, E., Beyond Thermo-Economics? The concept of Extended Exergy Accounting and its Application to the Analysis and design of Thermal Systems, Int. J. Ex. 1, n.1, 2001. 20. Szargut, J., Analysis of cumulative exergy consumption and cumulative exergy losses. In: Sieniytycz, S., Salamon, P., (Eds), Finite Time Thermodynamics and Thermoeconomics, Taylor and Francis, New York, 278-302, 1990. 21. Szargut, J.; Morris, D.R.; Steward, F.R.: Exergy Analysis of Thermal, Chemical and Metallurgical Processes, Hemisphere, New York, 1988. 22. Tondeur, D., Kvaalen, E., Equipartition of entropy production. An optimality criterion for transfer and separation processes. Ind. Eng. Chem. Res. 26,50-56, 1986. 23. Tsatsaronis G.: Exergoeconomics. In: F. Kreith ed. The CRC Handbook of Thermal Engineering, 1-88-94, CRC Press, Boca Raton, FL, USA, 2000.

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CHAPTER 12. PRESENT AND FUTURE APPLICATIONS by Savvas Tassou1, John Bellas, Issa Chaer, Thomas Davies, Thorsten Behnert, Ming-Jian Wang, Vladimir Goldstein

12.1

Introduction

Recent improvements in ice slurry generator technology and advanced design concepts have made ice slurries a competitive alternative to conventional secondary refrigeration systems and sometimes even to conventional direct expansion refrigeration systems. Many ice slurry plants have, for a number of years now, been successfully employed in many applications, from comfort cooling and commercial refrigeration to industrial production processes and medicine. These plants vary in size from small installations in specialist applications of a few kW cooling capacity to very large systems for high rise buildings, ships and factories of MW cooling demand. This chapter provides examples of existing ice slurry cooling applications, and highlights areas of research and development that could lead to future applications. The material presented is a compilation of information published in the open literature by designers, consultants, manufacturers and users of the technology. The examples cover applications worldwide and more attention is placed on applications where detailed information and analysis have been presented in the literature. In certain applications, reference is made to the manufacturer of the ice slurry generator but this does not imply any endorsement or judgement on the performance of the particular ice generation technology or product. The applications presented in this chapter are grouped into three main sections: Comfort cooling covers applications in office and institutional buildings as well as other commercial and industrial facilities such as the Kyoto train station complex, and district and mine cooling. The second section covers applications in the food industry including food processing, storage, transport and retail. The third section covers special and future applications that may result from ongoing research and development work.

12.2

Comfort Cooling

12.2.1 COMFORT COOLING OF BUILDINGS Ice slurry cooling systems have been installed in many buildings world wide for airconditioning purposes. In most cases, the ice slurry production system has been combined with a storage system to store energy during the night and use it during the day to meet the peak load. The result is that smaller refrigeration systems (chillers) can be used, usually with a capacity of 20-50% of the peak cooling load. Additionally, operational savings can be made where off-peak electricity tariffs are available. An ice slurry-based air conditioning system usually employs three independent circuits. A refrigerant circuit, an ice slurry circuit between the ice slurry generator, the storage tank and a heat exchanger and a chilled-water circuit between the ice slurry system and the load. An 1

The lead author of Chapter 12, Savvas Tassou, would like to acknowledge M. Tanino and Y. Kozawa for contributing material on the Kyoto Station building, T. Kuriyama for material on the CAPCOM building, Z. Ure for material on ice slurry applications, and P. Mueller Co. for the permission to use material and pictures from their ice slurry projects.

291


alternative arrangement is to pump the slurry from the tank directly to the load. Depending on the plant design single-phase fluid or ice slurry is distributed in the building or factory. A third design concept is to use the ice slurry as the heat sink in the circulation of a common refrigerant by gravity between the condenser and evaporator within a conventional refrigeration system (Wang and Kusumoto, 2001). In many cases, thanks to the low temperature of ice slurries a cold air distribution system has been used, resulting in reductions in the size of the ducting and piping, and capital cost. The above system configurations are discussed in greater detail in the application examples given in the following sections.

12.2.2 APPLICATIONS TO OFFICE BUILDINGS a) CAPCOM building The CAPCOM building is situated in Osaka, Japan and houses the research and development section of the software manufacturer CAPCOM. It was completed in March 1996 and consists of 20 storeys with a total floor area of 16 784 m2. Figure 12.1 shows a schematic of the building. The company’s offices are located from the 2nd to the 16th floor, occupying an area of 570 m2 on each floor. The heating load of the offices was calculated to be 151 W/m2, relatively higher than average, mainly due to the heat generated by the computers in the offices.

16th Floor

17th Floor: Rest room, Outdoor units

Area covered by one VAV unit Perimeter Air-conditioner

3rd to 16th Floor (Office Floors) Office Air-Conditioners 1th Floor 3rd Floor

Perimeter Air-conditioner

1st Floor

Plan of typical office floor of the building

Figure 12.1.

CAPCOM building 292


A gas-driven absorption refrigeration system is employed to provide cooling to the perimeter areas. Cooling to the internal areas is provided by an ice slurry cooling system consisting of two ice slurry units of 272 kW cooling capacity each. The ice generated by the ice slurry machines, which are located on the 17th floor, is stored in two storage tanks. The ice slurry from the tanks is pumped through an ice slurry separator which controls the ice fraction of the slurry to 20%, to air handling units on each floor as shown in Figure 12.2. Each of the 15 office floors is served by two air handling units of 9000 m3/h flow capacity each, which in turn serve six variable air volume (VAV) terminal devices. Ice Slurry Separators

Ice maker

Ice maker

Storage Tank

Storage Tank

Water/Alcohol

Water/Alcohol

Pump Floor 17

Ice slurry supply

Ice slurry return

Floor 16

Floor 15

AHU

AHU

Floor 2

Water and Hot Water Coil

Ice Slurry Coils

Water and Hot Water Coil

Figure 12.2. A schematic diagram of the ice slurry cooling system The low temperature of the ice slurry also offered the option of using a cooler air distribution temperature of 12°C instead of 15°C, which is the normal design practice in Japan. This reduced the air flow requirement from 41 m3/(m2h) down to 32 m3/(m2h), resulting in capital and operating cost savings due to the smaller size of equipment and the lower power 293


requirement for air distribution. Moreover, the cold air supply temperature offered lower humidity for the space and hence a more comfortable working environment. More details on the building and ice slurry system can be found in Kuriyama and Sawahata (2001). Power consumption for the ice slurry generators, pumps and air circulation fans was measured from July 15 to September 27, 1996. The results were compared with predicted energy consumption for an equivalent conventional ice thermal storage system and high temperature air distribution for the building. The ice slurry plant was found to have a 22 MWh higher energy consumption than the conventional plant, but hydraulic and air distribution costs were found to be lower by 47 MWh for the ice slurry plant, resulting in 25 MWh savings which represent 4% savings in the overall energy consumption of the building. b) Herbis Osaka Building The Herbis Osaka Building, in Osaka, Japan, was completed in February 1997. The building has five underground floors, forty floors above ground and one tower floor. The total height of the building complex is 181 m and the total floor area is 136 823 m2. It houses offices, a hotel, exhibition halls, shops, parking places, etc. The building is described in detail by Wang and Kusumoto (2001). The heating and cooling requirements of the building are satisfied by a “Crystal Liquid Ice Thermal Storage System with Heat Recovery” (CLIS-HR). The whole installation includes 31 units of heat recovery ice slurry generators of 260 kW capacity each and 16 sets of ice storage tanks of either 70 m3 or 140 m3 capacity, having a total thermal storage capacity of 80 750 kWh. A schematic diagram of the system is shown in Figure 12.3. The ice slurry system is utilised to drive a gravity based refrigeration system using R134a as a refrigerant. The refrigeration system employs two closed circuits, a warm and a cold circuit, each employing a condenser coil, an evaporator coil and an expansion valve. The evaporator of the cold circuit and the condenser of the warm circuit are of the plate fin type and are placed in the air handling unit which provides conditioned air to the building. Ice slurry generated by the super-chilling process is stored in a tank and from there it is pumped to the condenser of the cold refrigerant circuit. Refrigerant vapour from the evaporator coil condenses in the condenser of the cold circuit and the liquid refrigerant is then expanded as it flows through the expansion valve back to the evaporator where it evaporates and cools the air flowing through the air handling unit. In the warm circuit, heat rejected by the super chiller ice slurry generator is pumped to the evaporator coil of the warm refrigerant circuit. Refrigerant liquid from the condenser coil in the air handling unit expands as it flows through the expansion valve and then evaporates at a relatively high temperature in the evaporator by drawing heat from the hot water circulated from the ice slurry generator. The refrigerant vapour from the evaporator then passes to the condenser where it rejects heat to air flowing through the air handling unit for space heating.

294


Air Cooling

Condenser for Air Cooling Mode Ice Storage Tank

Mode Freon (Vapour)

Superchiller Pump Freon (Vapour)

Cold Air Liquid Hot Air

Air Heating Mode

Ice Slurry

Hot Water

Air Conditioner Condenser for Air Heating Mode

Figure 12.3. A schematic of the Herbis building thermal storage system The natural circulation of refrigerant requires considerably less power for operation compared to conventional vapour compression systems. From energy consumption records for the building during the first three years of its operation, it was concluded that the ice thermal storage system reduced the peak load of the building by about one third (Wang and Kusumoto, 2001). It was also identified that 60% of the total annual cooling and heating requirement could be met from night-time operation and thermal storage using off peak electricity tariffs, which resulted in significant operating cost savings.

c) Techno-Mart 21 Complex, Seoul, Korea The “Techno-Mart 21” complex (Figure 12.4) is one of the largest commercial buildings in Korea, housing a 10-storey shopping centre and a 39 storey-office tower. The total floor area is 260 100 m2. The peak cooling load of the building is 36 270 kW and is met by a 14 068 kW ice slurry cooling system. The plant consists of eight scraped type ice slurry units (Figure 12.5) with a capacity of 1759 kW each and a 3400 m3 storage tank (Figure 12.6).

295


Figure 12.4. The “Techno-Mart 21” building. (Information courtesy of P. Mueller Co.)

Figure 12.5. One of the eight ice-slurry units (1,759 kW) installed in the building. (Information courtesy of P. Mueller Co)

Each ice slurry unit consists of four ice slurry generators. The compressor/condenser package consists of four screw compressors with water-cooled condensers. The units are located on top of the storage tank and drop the ice slurry directly into the tank as shown in Figure 12.7. According to the manufacturer, due to the large difference between peak and off peak electricity tariffs, operation of the ice slurry thermal energy storage system during off peak, leads to substantial energy savings which resulted in a payback period of 1.1 years compared to a conventional cooling system (EPS Ltd., 2003a).

Figure 12.6. The inside of the tank showing spray nozzles at the top of the tank (Information Courtesy of Paul Mueller Co.)

296

Figure 12.7. Ice slurry generator discharge into the tank (Information Courtesy of Paul Mueller Co.)


12.2.3 APPLICATIONS TO INSTITUTIONAL BUILDINGS a) Stuart C. Siegel Centre, Virginia, USA The Stuart C. Siegel Centre is a 17 600 m2 athletic complex at Virginia Commonwealth University in Richmond, Virginia, housing a 7500 seat basketball arena and several other facilities for sport activities and teaching purposes. The total peak design-cooling load of the centre was calculated to be 4536 kW. The peak load occurs only when the arena reaches full occupancy while for the rest of the operating hours the load is significantly lower. For this reason, an ice slurry thermal energy storage system was employed consisting of 6 ice machines of 225 kW capacity each (Figure 12.8).

Figure 12.8. Ice slurry generators at the Stuart Siegel Centre, Virginia. (Information Courtesy of Paul Mueller Co.) The ice slurry generated is stored in a tank and then pumped through a heat exchanger where it chills the water circulated to the cooling coils of the air handling units down to 2.2°C compared to 6.6°C for a conventional system. This low water temperature results in reduced HVAC component sizes and capital and operating cost savings. Savings in peak demand charges due to the utilisation of energy storage as well as savings arising from reduced pump and fan power consumption amounted to USD 75 000 per year. A fuller description of the system is given by Nelson et al. (1999). b) Middlesex University, UK The ice slurry air-conditioning system at the Bounds Green campus of Middlesex University was (in 2003) the largest application of an ice slurry system in the UK. The system, commissioned in 1999 has a capacity of 148 kW and replaced an old 372 kW direct expansion refrigeration system. The choice of the ice slurry system was based on its overall environmental performance including the use of a natural refrigerant in the primary plant. Table 12.1 illustrates the projected capital and running costs of competing cooling systems at the project planning stage (Everitt, 1999). The capital cost of the ice slurry system was estimated to be only slightly higher than that of an absorption cooling system but almost double that of a conventional vapour compression plant. However, due to the utilisation of relatively cheap night-time electricity tariffs, the annual fuel costs were projected to be two thirds those of the absorption system and only one third those of the vapour compression system, giving a pay back period over the vapour compression system of approximately eight years. 297


Table 12.1. Approximate comparative costs of competing cooling systems Capital Cost £ (Sterling)

Fuel cost £ p.a.

Fuel cost over 20yrs £

Capital + Fuel costs over 20 yrs

185 000

5518

110 000

295 000

179 000

8294

166 000

345 000

Conventional vapour compression plant

90 000

17 500

350 000

530 000*

High specification vapour compression plant

120 000

17 500

350 000

470 000

Type Ice slurry system with thermal storage Absorption cooling system

* includes more frequent replacement

The installed ice slurry plant (Figure 12.9) features two 75 kW ice slurry generators served from an ammonia chiller. The fluid used in the ice slurry section is a water-urea solution. The physical arrangement of the ice slurry system is illustrated in Figure 12.10. The ice slurry generators are positioned at the top of two storage tanks so that the ice generated by each machine can drop straight into the respective storage tank. The total storage capacity of the two tanks is 72 m3. When fully charged, the tanks can provide cooling for up to 24 hours, even if the cooling plant should fail. The ice slurry is generated mainly overnight and is stored in the tanks. When cooling is required, chilled solution from the bottom of the tank is pumped through a heat exchanger to maintain the chilled water flow at the required temperature. Flow in the main chilled water circuit is provided by a fixed speed pump supplying 11.2 l/s of water against a pressure of 350 kPa (Sims, 1999). A flow header with six circuits served by variable speed pumps connected to the building management system (BMS) distributes chilled water to various parts of the university building (lecture theatres, study rooms, laboratories and a computer centre). The speed of the pumps is controlled by the BMS in response to variations in load. Operation down to 50% of design flow is possible which should lead to significant energy savings (Rendall, 1999). The whole system was installed in two phases, I and II, and has been designed to allow for future expansion. Presently the system operates in conjunction with an old direct expansion chiller of 228 kW cooling capacity. When this chiller comes to the end of its life, chilled water heat exchangers connected to the ice slurry plant will replace it.

Figure 12.9. Ice slurry machine on top of the storage tanks at the left of the picture and air cooled condensers at the right. (Information Courtesy of Paul Mueller Co.) 298


System Return

Air Cooled Chiller

Inlet 10 °C Supply 6 °C

Heat Exchanger

Ice Slurry Machine

Air Cooled Condensing Unit

System Supply

Ice Slurry Tank Phase I

Inlet 6 °C Supply 2 °C

Heat Exchanger

Ice Slurry Machine

Air Cooled Condensing Unit

Ice Slurry Tank Phase II

Figure 12.10. A schematic diagram of the ice slurry cooling system at Middlesex University

12.2.4 APPLICATIONS TO COMMERCIAL BUILDINGS Kyoto Station Building The Kyoto Station Building shown in Figure 12.11 is a complex 19-storey building having a total floor area of 238,000 m2. The building houses a train station, a hotel, a theatre and several commercial facilities. The layout of the building is shown in Figure 12.12. The cooling needs of the building are satisfied by two separate systems (Ise et al., 2001): • An absorption system driven by steam generated by a co-generation system, and • An ice slurry plant powered by electricity from the co-generation system and supplemented from the city’s electrical network.

299


Figure 12.11. An aerial view of the Kyoto Station Building

Figure 12.12. Layout of the Kyoto Station Building

The ice slurry plant incorporates two sets of brine chillers of 1400 kW cooling capacity each, four sets of shell and tube super-coolers of 700 kW capacity each and two concrete tanks for the storage of ice slurry. The tanks are located below the building’s basement and have a storage capacity of 400 m3 each. Figure 12.13 shows a schematic diagram of the plant. Ice slurry is produced by the method of super-cooling. Water is super-cooled to a temperature of –2°C in the super-cooling heat exchanger. As it exits the super-cooler, a small portion, around 2.5%, changes into ice, while the remainder stays in the liquid phase. The ice slurry produced drops into the tank and due to the density difference, the ice is accumulated at the upper part of the tank while the water occupies the lower part, remaining at a temperature of approximately 0°C. The ice slurry production/storage takes place during the night (23:00 h to 08:00 h), and the ice slurry in the tank reaches progressively an ice concentration of 23% with a cooling capacity of about 40 GJ.

300


During daytime operation, water from the bottom of the tank is pumped to heat exchangers where it chills the water circulated in the cooling circuits throughout the building. The fluid temperature in these circuits is 7°C and the return temperature is 10°C. The electrical power consumption for night-time ice production was estimated to be 3960 MWh/year, which represents only 4.6% of the building’s total energy consumption. A comparison between the absorption and ice-slurry system showed the ice-slurry system to have 50% lower running costs compared to the absorption system.

0.5 °C

Super-cooled Water –2 °C

Water

Super-cooler -3 °C -6 °C

Heat exchanger

Pipe Releaser of super-cooling stateBrine

Pre-heater Refrigerator Pump

Supply of Ice-slurry

£

Ice Layer nozzle

Je t

Water 0 °C (Tap Water)

Water Layer

Figure 12.13. Schematic diagram of the ice slurry plant at Kyoto Station Building

12.2.5

MINE COOLING

One of the first industrial sectors to introduce ice slurries to satisfy cooling needs was the mining industry. The continuously increasing depth of the mines, the larger machines and the larger rock surfaces, resulted in higher temperatures in the tunnels and the pumping costs of chilled water increased significantly (Sheer et al., 1984; Hager et al., 1991). Nowadays, mines operate at depths of more than 3000 m where temperatures exceed 50°C. Ice slurries, having much greater cooling capacity than chilled water, can effectively provide the same cooling load with much lower flow rate offering significant savings in pumping cost and size of equipment. Kidd (1995) also indicated that in mine cooling, when water is pumped underground, its potential energy is converted into heat. For the case of a pilot study for the Vaal Reefs mine, this heat represented a temperature rise of 2.34°C per 1,000 m of pipe run which would reduce considerably the cooling capacity of the water. In the case of ice slurry the temperature will be maintained fairly constant by the melting ice.

301


Ophir and Koren (1999) describe the ice slurry plant at the Western Deep Level Gold Mine in South Africa. The ice slurry is produced by a Vacuum Freezing Vapour Compression process. Four units are employed with a 3 MW cooling capacity each, serving working areas at depths of 4000 m below ground. Each ice slurry unit consists of a large vapour compressor of 320 m3/sec volumetric displacement and a compression ratio of 8:1. Gravity is used for the vertical transportation of ice slurry whereas horizontal transportation is achieved by a pneumatic pumping system.

12.3

Food Processing

Ice slurries can be applied to many food processing applications. These include rapid cooling of vegetables and fish, processing of meat and dairy products, food storage, display and distribution.

12.3.1

RAPID COOLING OF VEGETABLES

In the rapid cooling of vegetables, ice slurry can be pumped at a low temperature, close to 0°C, to cooling coils and air is blown across the coils by centrifugal or axial flow fans onto the vegetables which are laid out in trays or a moving belt, in a similar way to a blast freezer. An example of a vegetable cooling facility is one in Boston Lincolnshire, UK. The plant consists of a 88 kW ice slurry generator and a 10 m3 storage tank and is designed to meet a peak load of 180 kW (EPS Ltd., 2003b).

12.3.2

FISH PROCESSING

Ice slurry is an excellent medium for fresh fish cooling. Wang et al. (1999) reported that tests carried out with artificial and real fish to compare the cooling performance of ice slurry and flake ice showed ice slurry to perform better than the traditionally used flake ice in preserving the quality of the product. In an ice-slurry fish cooling system, the fish is totally covered by the slurry leaving no air pockets between the product and ice as is the case with flake ice. As a result, the cooling of the fish is faster and the growth of bacteria is slower, resulting in longer product life. Comparative tests between ice slurry and flake ice for the cooling of different fish have been carried out by a number of investigators (Wang et al., 1999; Paul, 2002). Although the rate of cooling is a function of the shape and size of the fish as well as its thermophysical properties, in every case ice slurry was found to produce faster cooling. Figure 12.14 shows comparative curves for plaice (flatfish) cooled in boxes immersed in ice slurry (Paul, 2002). The results showed that the time required to cool the plaice down to 2°C was more than 3 times faster than the time required with flake ice.

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o

of the Fish, C

Temperature in the Center


18 16 14 12 10 8 6 4 2 0

Flake Ice Ice Slurry

0

10

20

30

40

50

60

Time, min

Figure 12.14. Cooling rate of ice slurry compared to flake ice (Paul, 2002) Ice slurry plants for the cooling of fish are in operation in many countries. An example of such a plant is the prawn cooling plant at the Isle of Harris in Scotland (EPS Ltd., 2003b). The system consists of a 10 kW ice slurry unit and a 6 m3 storage tank containing seawater. The chilled seawater is essential to maintaining the quality of live prawns which are stored in the tanks. Cooling of the seawater in the tank is provided by the ice slurry system which is pumped through a heat exchanger to cool the seawater, bringing the temperature in the tank very rapidly down to 8°C. After this, the temperature is reduced down to 4°C more slowly, using a specially designed controller. The 10 kW ice slurry generator and the storage capacity of the tank can meet a peak cooling load of 47 kW. Operation at night with off-peak electricity can also lead to energy savings compared to conventional non-storage refrigeration systems. A plant described by Wang et al. (1999), shown in Figure 12.15, consists of two ammonia based ice slurry generators, a 62 m3 storage tank with a top harvester machine, a 1.2 m3 ice remixing tank and ice slurry distribution network. The ice is generated in the ice machines and stored in the storage tank where the ice crystals are accumulated at the top, forming an ice rich layer with 70% ice concentration. Once the storage tank is full of ice, brine is injected into the tank and pushes the ice layer against the rotating blades of the harvester machine which removes the ice crystals from the ice bed into a delivery chute. The ice is then discharged into the ice-mixing tank, which is equipped with an agitator, where it is mixed with brine forming ice slurry of 30 to 35% ice concentration. The mixture is then pumped to several locations to accommodate the cooling requirements of the processing and transport operations.

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Figure 12.15. The ice slurry system of the fish processing plant The overall benefits of using ice slurry in the fish processing industry are obvious. While ice slurry is used through the entire operating process, a constant temperature of fish is maintained from the moment fish are received, to the moment they are finally canned. In addition, fish are chilled at a much faster rate than before. As a result, the quality of the product, such as the texture, colour and bacteria retardation is greatly improved. Automated fish handling with ice slurry improves the productivity of the plant, as the plant is able to deal with peak load without inducing too many shifts per day. Ice slurry systems have also been successfully implemented in either small boats or large vessels. Conventional on-board cooling technologies are often based on refrigerated seawater (RSW) systems and/or different types of fresh ice (e.g. flake ice). With RSW systems onboard large vessels, fish are kept in fish holds with a circulation of seawater, at a mean temperature of about 2 to 4°C. Some disadvantages of the system include: the volume of space taken up by the refrigeration machinery; temperature level; and salt uptake, especially in smaller species such as sardine. Onboard smaller ships, fresh ice is normally loaded at the harbour, stored and eventually mixed with the catch. The tendency of fresh ice to agglomerate limits in many cases the quality of icing, since the ice has to be loosened by manual means before mixing. Mechanical loosening with motor driven snails is also reported to be a major cause of injury on smaller fishing boats in some countries. Furthermore, large blocks of ice mixed with fish often result in uneven cooling rates. Last but not least, larger pieces of ice with its sometimes sharp edges often damage the fish. In addition, bacterial growth is extremely dependent on temperature. As a rule of thumb, the shelf life of fish kept at 0°C is more than double that of fish kept at 5°C; the closer to the freezing point of the fish, the better the product quality. Since bacterial growth rates cannot be stopped, but only decelerated, it is also important to minimize the bacterial level by a rapid 304


drop of temperature in each part of the process. Nevertheless, care should be exercised to avoid freezing of the fish as it may result in decreased saleability. On fishing vessels, ice slurry can provide significant improvements over conventional chilling methods, such as RSW or flake ice. Since ice slurry consists of small crystals, either in dry form or pumpable slurry, it provides excellent chilling of fish while avoiding freezing and at the same time preventing fish from bruising, because of the soft and flexible nature of ice slurry. In addition ice slurry is easy to dose and mix with the catch.

12.3.3

MEAT PROCESSING

Paul (1999) describes an ice slurry system installed in a meat-processing factory in Germany to cover all the cooling and air conditioning requirements of the 3800 m2 site. This includes cooling for processing and storage of the meat, display cabinets and comfort cooling for the offices. The peak cooling demand was calculated to be 385 kW. The installed plant has a 240 kW capacity and consists of two ice slurry generators of 120 kW each and a 36 m3 tank. The capital cost of the plant was 435 000 Euros, while an equivalent direct expansion plant would have cost 390,000 Euros. However, the annual operating cost of the ice slurry system was found to be 89,000 Euros compared to a projected operating cost for a conventional plant of 109,000 Euros, resulting in a payback period of just over two years.

12.3.4.

DAIRY PROCESSING

An ice slurry plant for cheese processing is described by Gladis (1997). The plant in Hanford, California, USA, is installed in a dairy factory with a daily production of 90 000 kg of cheddar cheese. The cooling loads of both slow and rapid cooling processes such as cheese starter cooling, whey protein concentration, filtration vessels, etc., are estimated to be 2546 kWh per day. The peak cooling demand occurs at 7:00 am when the initial cooling of the cheese starter takes place from 85°C down to 25.5°C. This process requires 265 kW of cooling load. Other simultaneous cooling demands in the factory bring the total peak load to 396 kW. This peak load occurs for only one hour during the day while for the remaining 23 hours the total cooling load varies between 56 and 148 kW, representing less than 40% of peak load. To reduce the peak demand, an ice slurry system was installed which consisted of an ice slurry generator of 106 kW capacity and a 24.6 m3 storage tank, capable of storing 763 kWh of energy (Figure 12.16). The load profile of the plant is shown in Figure 12.17. The ice slurry plant operates continuously and generates ice slurry of 5 to 10% ice concentration from an initial solution of water with 7% propylene glycol. The generated ice slurry is pumped to the storage tank where, due to density differences, the ice crystals and chilled solution separate and occupy the upper and lower parts of the tank, respectively. A chilled solution of approximately 0°C is pumped from the bottom of the tank to the heat exchangers and the “warm” solution returns to the tank and distributed through spray nozzles over the ice layer.

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Ice slurry generator

return

R-22 Vapour Compressor/

PHE

Ice slurry

Condensing unit R-22 Liquid

Spray Headers supply Ice Slurry Tank

Figure 12.16. A schematic of the cheese processing ice slurry plant

Cooling Load

Cooling Load, kW

400

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kWh stored

350

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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

hour of the day Figure 12.17. Load profile and storage tank capacity over a 24-hour period

12.3.5

BREWERY

An ice slurry plant has been installed for process cooling and bottling the beer in Kempten, Germany. This brewery produces 13 different kinds of beer. Nearly all German breweries use ammonia as refrigerant in the production and the cold storage of the beer. As a result of the geographic location in the centre of the city, and the safety and environmental requirements of the city, the brewery decided to decrease the amount of ammonia used in their process. This was the reason for the brewery to use ice slurry as a cold storage and transportation medium.

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In this way the amount of ammonia has been decreased and the ammonia charge of the cooling plant remains completely in the machinery room. All security devices against the occurrence of damages can also be limited to the machinery room. The ice storage system is placed at a distance of 50 m from the machinery room. There are two different circuits for producing and delivering the ice slurry as shown in Figure 12.18.

Figure 12.18. Circuit schematic of the brewery plant

For the ice generation two orbital rod ice slurry generators are used with 350 kW of cooling capacity. A pump discharges brine from the bottom of the storage tank to the top of the ice slurry generators. The discharged brine must be completely ice free for this type of ice slurry generator. Otherwise the ice slurry generators could freeze and stop the ice production. At the outlet of the ice slurry generator a secondary pump discharges the newly formed ice slurry back to the storage tank. The secondary pump is required, because the ice slurry generators are not pressurized. The volume of the storage tank is approximately 70 m³. The storage tank has two functions. The first is to accumulate the ice and to increase the ice concentration in the storage. The main result is that the ice slurry generators only produce ice during night time, and the ice concentration can be increased up to a maximum of 30 wt-%. Another function is to decouple the ice generation process from the consumer circuits. In order to obtain a homogeneous dispersion of the carrier fluid and ice crystals, jet nozzles and stirrers are used. From the storage tank, ice slurry is pumped through the consumer circuit at an ice concentration of 10 wt-%. This ice concentration is high enough to supply all the consumers with chilling. As a result of the low ice concentration, ice slurry acts like a Newtonian fluid. The consumer circuit is a two string system. There are three different branches for the consumers; each of them is supplied by a pump. Different heat exchangers are used in this plant. A plate heat exchanger is used for cooling the wort, an in-process product of the beer production. The wort must be cooled down in a short time and a small temperature range must be kept. The outlet temperature of ice slurry from these heat exchangers is high and without any ice crystals. To keep the temperature of the wort within the targeted temperature range, a

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part of the warm brine can be mixed by a 3 way valve with the cooled inlet stream. As a result of the warm outlet the wort cooler has its own return pipe. The fermentation and storage of the beer take place in special vessels, cooled by welded halfround tubes. Each vessel has its own pipe connected to the consumer circuit. The control of the plant is executed by a Siemens SPS, which also controls the refrigeration plant. Ice concentration in the storage tank and the pipe connected to the consumer branch is determined from the temperature measurement. The accuracy of estimating the ice concentration by measuring the temperature depends strongly on the initial additive concentration. So, it is essential to analyse the initial additive concentration. If the temperature in the storage tank remains under a certain preset value, i.e. the ice concentration remains above the desired value, the ice production process will be stopped. Experience has shown that this control meets the demand of an industrial plant.

12.3.6

RETAIL FOOD APPLICATIONS

Traditional centralized refrigeration systems in large retail food stores require considerable amounts of refrigerant. These systems are prone to leakage due to the large number of joints and the long distribution pipe-work. The use of ice-slurry as a secondary fluid in retail food stores can reduce considerably the refrigerant charge in the primary system without significantly increasing the overall power consumption, due to the much smaller quantities of slurry that has to be pumped in the secondary circuit compared to traditional single-phase secondary systems. Tassou et al. (2001) compared the performance of a refrigerated display cabinet evaporator coil both with ice slurry and R22. The results indicated that even though the temperature of ice slurry entering the coil was at least 2°C higher than the temperature of R22, the ice slurry was able to provide slightly better heat transfer performance than R22. Lueders (1999) presented a feasibility study for a supermarket that would employ an ice slurry thermal storage system to serve the medium and high temperature loads of the refrigerated fixtures and the HVAC requirements of a retail food store. A direct expansion system would be used only for the low temperature frozen food display cases (–23°C). Heat rejection from the low temperature DX circuit would be accomplished through a water-cooled condenser served from the ice slurry system. The ice slurry plant which will employ ammonia as primary refrigerant would consist of two ice slurry loops with separate ice slurry tanks. The first loop would be connected to the “high temperature” ice slurry tank and will accommodate the HVAC requirements of the building as well as the condensing requirements of the low temperature DX system using a liquid solution at –1°C pumped from the bottom of the tank. The second loop would be connected to the “medium temperature” ice slurry tank and would accommodate the loads of the medium and high temperature display cabinets (–4°C and 4.5°C, respectively) using slurry of 15% ice concentration, at temperatures between –9°C and –12°C. The proposed plant arrangement is shown in Figure 12.19.

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HVAC 22 οC

Ice cream cases, – 23 οC Freon “Low” temperature loop

Dairy cases 4.5οC Ice Slurry -9 οC/-12 οC

Glycol -1 οC Water-cooled condenser

Cases -4 οC

“High” temperature Ice slurry tank

“Medium” temperature Ice slurry tank

Receiver Ice slurry t Figure 12.19. A schematic diagram of a supermarket ice slurry system The author made a comparison of pumping requirements, flow rates and piping costs between the ice slurry system and a system using a single-phase secondary fluid as a heat transfer medium. It was proposed that the ice slurry system would result in an 82% reduction in secondary fluid flow (10.2 m3/h instead of 55.4 m3/h) producing 82% savings in pumping costs and 51% savings in piping costs. It was estimated that the capital cost of the ice slurry system would be 89% higher than that of a conventional DX system (369 751 USD compared to 195 840 USD). The ice slurry system was also found to produce a 3.5% increase in the energy consumption of the plant but it would be able to shift 80% of the peak hour energy consumption to off peak hours which would result in 49% savings in electricity costs resulting in a payback period of 4.4 years. A similar system has been proposed by Davies and Lowes (2002a), who suggested that using ice slurry to condense and sub-cool the refrigerant liquid of a conventional retail refrigeration system down to 0°C would lead to an increase in the COP of the vapour compression refrigeration system and produce running cost savings of the order of 20%. Controlling the flow of ice slurry in the condenser will control the condensing pressure of the refrigeration system and if off peak electricity is used to charge the ice slurry storage, the energy cost savings could rise to 30% compared to ambient air heat rejection. If ice slurry is produced at temperatures down to –10°C, the same system could also be used to satisfy the refrigeration load of the medium and high temperature cabinets in the store directly. With around 120 000 supermarkets of more than 400 m2 floor area in the world, a widespread application of such a system could lead to significant reductions in the energy consumption of the sector (Davies and Lowes, 2002a).

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One ice slurry systems manufacturer has recently developed an ice-slurry system for the preservation of fresh produce, which is traditionally stored and preserved in ice (Sunwell, 2003). In 2002 the company delivered a few deepchillTM ice generation and distribution systems to a large Canadian supermarket chain in Ontario. In this system ice crystals formed inside an ice slurry generator with a 23 kW ice making capacity are pumped into an insulated 3.5 m3 storage-dispenser tank where they remain suspended in water. Dry ice crystals from the top of the tank at a maximum rate of 3 ton/h are then mixed with a small amount of water and the mixture containing 60% ice is pumped with a positive displacement pump (3.7 kW power) through a piping system to the display cases where it is spread over the display surface with a flexible hose. The ice delivery control at the individual display counters allows the operator to fill the display cases by simply turning on the delivery system at the counter and pumping the ice slurry into the cases (Figure 12.20). After drainage ice crystals form a shining ice bed in the cases. Traditionally, supermarket display cases for seafood and produce are commonly filled early in the morning before the store is opened by manually shovelling ice into the trays. Pumping ice slurry directly into the display cases at the counter eliminates any possible contamination of the ice due to transporting and shovelling. The transportation of the ice in a sealed environment guarantees a clean product at the counter. In addition, automation of the ice distribution process with the ice slurry system means a significant reduction in labour and less chance of work-related injuries, which result in lower cost.

Figure 12.20. High density ice slurry being discharged into display cases (Photo courtesy of Sunwell)

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12.4

Possible future applications

12.4.1.

ICE PIGGING

In many industrial applications, components like pipes, ducts and heat exchangers, require frequent and efficient internal cleaning. This process, commonly known as “pigging” is usually accomplished using piston rings or other mechanical methods. However, mechanical pigging cannot perform well in cleaning components with complex geometry. Experimental and theoretical work carried out at Bristol University, UK (Quarini, 2002), to investigate the cleaning efficiency of ice slurry, showed slurry to be able to “pig” even very complex geometries. The tests were conducted with ice slurry of 10% ice concentration using either salt or sugar as freezing point depressants. Fouling materials tested included jam and fats (food industry), toothpaste (pharmaceutical product) and fine silt and sand (river water cooled exchangers). The ice slurry proved capable of removing fouling materials from pipes with sharp bends, orifice plates and even from heat exchangers. Further work is being carried out but the first results are very encouraging for a new field of application.

12.4.2

MEDICAL APPLICATIONS

Ten to twelve minutes after a cardiac arrest, brain cells start dying rapidly because of lack of blood flow to the brain. However, when the cells are cooled, their metabolism and their chemical processes slow dramatically. Researchers at Argonne National Laboratory’s Energy Laboratory working on developing methods for rapid cooling of the blood to sustain the heart and brain cells after cardiac arrests have proposed a new possible medical application for ice slurries (Argon National Laboratory). In this approach, a specially formulated ice-particle slurry of high fluidity engineered using chemicals compatible with human tissues would be pumped into the patient’s carotid arteries, jugular veins and lungs to rapidly lower the temperature of vital heart and brain tissues and induce localised hypothermia. In simulated head and heart cooling the technique has been shown to be able to cool the brain’s and heart’s core temperatures down to 25°C in ten minutes which is much faster than conventional methods. More work, however, is required on production and delivery of ice slurry before the technique becomes a standard approach in helping cardiac arrest and stroke victims. Ice slurry can also be used to treat bruising and relieve pain during sport or other activities. It can be used as a cold pack, providing better contact with the body than traditional ice packs, or for immersion cooling of bruised feet, hands, elbows, etc.

12.4.3

ARTIFICIAL SNOW

Paul (2002) notes that ice slurry could be an excellent kind of artificial snow for indoor skiing. It can provide a better skiing surface than the commonly used snow substitutes, with less energy consumption. A large-scale project in Germany is in progress for the construction of a 30,000 m2 skiing hall. All the cooling requirements of the centre, from snow production to air conditioning will be catered by ice slurry plants.

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12.4.4

TRANSPORT REFRIGERATION

Another application proposed by Paul (2002) is the use of ice slurry as the cooling medium in refrigerated vehicles. Since the efficient cooling of products with ice slurry is well established, vehicles with double walls containing ice slurry in the gap could be an alternative to conventional refrigerated vehicles. The ice-slurry vehicles could operate in a network with ice slurry filling and discharging stations. A feasibility study by the author showed the idea to be viable. This technology has been used since 1994 in refrigerated railroad cars in China. Here the ice slurry is charged into compartments under the roof of each car. A similar system, where chilling is provided by ice slurry contained in a double-walled container and recharged at service stations, was in operation on certain trains of the Swiss railway company. Here trolleys were chilled by ice slurry in the walls of the trolleys. Since autumn 2004 an experimental unit is producing ice slurry for delivery vans in Austria. The question came into discussion because some end users announced problems with their existing systems in 1999. Since then several systems have been examined. Some of the main points in question were: o reducing service and maintenance costs, o reducing the weight of the delivery vans, o easy handling, o use of existing refrigeration plants if possible, o environment and sustainable technology (no use of HFCs if possible), o fast availability of refrigeration energy, o multi-usage of the van because of different temperature requirements, o weight savings – reduction in the weight of the delivery van in comparison to existing systems and hence increasing the payload, o no additional technology (compressors, valves, pumps, etc.) used in the van. Ice slurry offered advantages in many of the above topics. The main idea was to “refuel ice slurry like gasoline at a gas station”.

Figure 12.21. Charging the unit

Figure 12.22. Refrigerated body for delivery vans

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The first test van in Austria is a small delivery van for frozen goods (Figures 12.21 and 12.22). This vehicle was chosen because it requires the highest cooling capacity due to the many stops during the operation where doors are opened and goods are taken out. The temperature is not allowed to rise above –18°C during the entire delivery period. The tests yielded interesting details. The design of the heat exchanger had to be adapted to practical requirements. In addition, changes were made to the ice generator and the pump. The lowest ice slurry temperature achieved so far is about –39°C. The tests have demonstrated the use of ice slurry for freezing applications, i.e. –18°C compartment temperature. The tests will be extended thanks to the promising results. The tests also showed that the heat exchanger required a special design, different to that used for other purposes in the past. A new heat exchanger is now under development. 12.4.5

THE USE OF ICE SLURRY FOR FIRE FIGHTING

The properties of ice slurries may be exploited to great effect when they are used in place of water to fight Class A fires i.e. non-fuel fires, which constitute the vast majority of fires (Lowes, 2002). Because ice slurries can easily be pumped up to ice concentrations of 30%, existing fire fighting equipment such as hoses and nozzles can be used in an ice-slurry fire fighting system provided the slurry is stored and pumped from an appropriately stirred holding tank. Slurry ice may also be used in conjunction with foaming agents. Most portable water pumps used by fire brigades use the water they pump as the coolant for the engine. In the case of ice slurry it would be better to employ an electric or air-cooled engine driven pump, to minimise melting in the slurry. Comparisons between the performance of water and ice slurry when tackling similar fires demonstrated that ice slurry extinguished the fire in less than half the time taken with water, and that the gas temperature in the test room was dramatically lower when using ice slurry. The amount of steam formed when using ice slurry was said to be very low and dense. Only a small volume of ice slurry was needed to extinguish the fire compared with the volume of water normally used. The tests were carried out using ice slurry produced from a water solution of 7% propylene glycol concentration giving an ice production temperature of –2°C. The slurry was stored in a stirred 1 m3 polypropylene shipping container and standard fire brigade suction hoses were employed to withdraw the slurry into a portable fire pump. The slurry was delivered at 9 bar through a standard fire brigade hose of 25 mm internal diameter. It has also been proposed that if sodium bicarbonate is used as the freezing point depressant in the manufacture of ice slurry and the resulting slurry is pumped onto a fire together with a weak solution of acetic acid, a copious carbon dioxide foam would be produced which may further enhance the effectiveness of the ice slurry in extinguishing fires (Davies and Lowes, 2002b).

12.5

Conclusions

In this chapter a number of applications of ice slurry technology to different sectors of commerce and industry have been described. The chapter also highlighted opportunities for possible future applications. Over recent years, the field of applications has increased due to

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advances in technology and increased understanding of the thermodynamic and thermophysical properties of ice slurries. The spread of applications covers all continents but the majority are concentrated in Europe and Japan. In Japan the interest has mainly been in air conditioning with thermal storage and electrical load shifting to off-peak periods. In Europe, the applications vary widely from air conditioning to immersion and process cooling. The capital cost and energy consumption of ice slurry generators are factors that currently inhibit a wider application of the technology. With further research and development and increase in the number of applications, the capital cost of the equipment is likely to decrease and this will increase further the attractiveness of the technology to potential users.

Literature cited in Chapter 12 1. Argonne National Laboratory: http/www.ipd.anl.gov/biotech/programmes/biomedical/iceslurry.html 2. Davies, T.W.; Lowes, A.R.: A high efficiency refrigeration system, Proc. of a conference on New Technologies in Commercial Refrigeration, IIR, Urbana, USA, pp. 93-100, 2002. 3. Davies, T.W.; Lowes, A.R.: Fire extinguishing system, UK Patent Application 0222022.6, 2002. 4. EPS Ltd.: 2003a, http://www.epsltd.co.uk/slurry_sites.pdf 5. EPS Ltd.: 2003b, http://www.epsltd.co.uk/slurryice1.htm 6. Everitt, N.: Ice Pick, Heat. Vent. Rev., vol.39, no.11, p. 19, 1999. 7. Gladis, S.: Ice Slurry Thermal Energy Storage for Cheese Process Cooling, ASHRAE Transactions , Vol.103, Part 2, 1997. 8. Hager, M.; Kamper, T.: The Hydraulic Transport of Ice for Mine-Cooling. Powder Handling & Processing, Vol. 3, no. 4, pp. 317-325, 1991. 9. Ise, H.; Tanino, M.; Kozawa, Y.: Ice Storage System in Kyoto Station Building. Information booklet for the Technical Tour of the Fourth IIR Workshop on Ice Slurries, pp. 11-16, Nov. 2001. 10. Kidd, J.: Slurry Ice Production in Gold Mining, The South African Mechanical Engineering, Vol. 45, pp. 11-13, 1995. 11. Kuriyama, T.; Sawahata, Y.: Slurry Ice Transportation and Cold Distribution System, Information booklet for the Technical Tour of the Fourth IIR Workshop on Ice Slurries, pp. 1-6, Nov. 2001. 12. Lowes, A.R.: Fire-fighting apparatus and a method of fighting fire, UK Patent Application 0206813.8, 2002. 13. Lueders, D.: Proc. of the 21st Annual Meeting of the International Meeting of Ammonia Refrigeration, pp. 301-326, 1999. 14. Nelson, K.; Pippin, J.; Dunlap, J.: University Ice Slurry System, presented at the IDEA College-University Conference New Orleans, Louisiana, U.S.A, 1999. 15. Ophir, A.; Koren, A.: Vacuum Freezing Vapor Compression Process (V.F.V.C.) for mine cooling, Proc. of the 20th International Congress of Refrigeration, IIF/IIR, vol. III, paper 508, Sydney, 1999. 16. Paul, J.: Innovative Applications of Pumpable Ice Slurry, presented before the Institute of Refrigeration at London, UK, 2002. 17. Paul, J.: Generation and Utilisation of Liquid Ice (Binary Ice), Proc. of the 20th International Congress of Refrigeration, IIF/IIR, vol. III, paper 495, 1999. 18. Rendall, S.: Future Air Conditioning, Bldg. Serv. Environ. Engr., vol. 22, no.11, p. 12, 1999. 314


19. Sheer, T.; Correia, R.M.; Chaplain E.J.; Hemp R.: Research into the use of ice for cooling deep mines, Proc. of the 3rd International Mine Ventilation Congress, pp. 277-282, 1984. 20. Sims, B.: Going Green, Building Services Journal, CIBSE Supplement, pp. 8-9, 1999. 21. Sunwell, http://www.sunwell.com/index1.html, 2003. 22. Tassou, S.A.; Chaer, I.; Bellas, J.; Terzis, G.: Comparison of the performance of Ice Slurry and Traditional Primary and Secondary Refrigerants in Refrigerated Food Display Cabinet Cooling Coil, 4th IIR Workshop on Ice Slurries, pp. 87-95, 2001. 23. Quarini, J.: Ice-Pigging to Reduce and Remove Fouling and to Achieve Clean-in- Place, Applied Thermal Engineering, Vol. 22, pp. 747-753, 2002. 24. Wang, M.J.; Hansen, T.M.; Kauffeld, M.; Christensen, K.G.; Goldstein, V.: Application of Ice Slurry Technology in Fishery, Proc. of the 20th International Congress of Refrigeration, IIF/IIR, vol. IV; paper 569, Sydney, 1999. 25. Wang, M.J.; Kusumoto, N.: Ice Based Thermal Storage in Multifunctional buildings, Heat and Mass Transfer, Vol. 37, pp. 594-604, 2001.

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CHAPTER 13. CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER R&D By Michael Kauffeld, Masahiro Kawaji and Peter W. Egolf

Multifunctional (thermal) fluids and suspensions, also named “intelligent fluids”, are new classes of fluids with improved (thermal) properties. These fluids can be designed to optimally fulfil particular objectives. In refrigeration and air conditioning this can be enhanced thermal conductivity of a fluid, better heat transfer characteristics, a higher thermal energy storage capacity, temperature stabilization, reduced pressure drop, etc. The use of phase change materials (PCM) as a dispersed phase in a continuous carrier fluid leads — due to its phase change (latent heat) — to very high energy densities, whereby the pumpability of the fluid is still maintained. Such substances are named “phase change slurries (PCS)”. Ice slurry is the best known PCS. It is restricted to temperatures below 0oC. Ice slurries and other phase change slurries as well, are fluids with dispersed particles, which undergo phase change at the melting temperature of the dispersed phase. If the fluids are mixtures, very often a temperature glide occurs, which is apparent as the enthalpy h changes continuously as a function of the temperature T. The energy to destroy a solid crystal during a melting process is stored in the material, and when the material — in the reverse process — is solidified, this amount of thermal energy (latent heat) is released again. In a water/ice transition the stored energy is 333 kJ/kg. Because the concentration of ice particles in a carrier fluid is usually less than 50% in technical applications, the specific enthalpy due to phase change will typically be smaller than 170 kJ/kg for ice slurries. In addition to this latent heat, a smaller fraction of sensible heat for cooling or heating of the carrier fluid and the ice crystals is involved. Thus, the energy storage of ice slurries can be eight to ten times higher compared with the conventional storage technology using chilled water, depending on the operational temperature range of the engineering systems. Furthermore, the pumping power can be reduced by up to 80% and at the same time heat transfer can be increased twofold when compared with single-phase liquid used as a secondary refrigerant. In fact, heat transfer for melting ice slurry is in the same range as for evaporating HFC refrigerants. One of the characteristics of ice slurries is that the particles disappear in the melting process and have to be created again by a special ice slurry generator. In storage tanks the particles experience significant buoyancy forces, which cause stratification of the ice at the top of the tank. Therefore, a mixing device or other special piece of equipment is usually necessary to create a homogeneous ice suspension in the storage tank, which guarantees safe system operation without the occurrence of tube clogging. The simplicity of freezing water with an environmentally friendly additive (alcohols, salts, etc.) and obtaining very high specific enthalpies make the application of ice slurries a promising technology for the future. Pervading the studies of the IIR Working Party on Ice Slurries and from the material in the foregoing chapters of this book, a few topics appear to be of relevance to future research and development: 1. Heat transfer in melting and freezing ice slurries with a range of additives 2. Ice slurry generators 3. Principles of ice storage operation 4. Suspensions with melting temperatures above 0°C 5. Air-conditioning systems with low supply air temperature 6. New applications

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1. Heat transfer of melting ice slurry The thermal behaviour of ice slurry in heat exchangers is important to understand in successfully utilising the distributed ice slurry. On the other hand, the heat transfer characteristics of ice slurry during generation are important for the optimum design of ice slurry generators. Future R & D should cover an experimental parametric study of the influences of ice concentration, additives, heat flux and velocity on the heat transfer coefficients. In relation to melt-off rates in storage tanks, a heat transfer model for hot fluid flow through a packed bed of ice slurry would also be useful in the design of thermal ice slurry systems. The effect of the time behaviour of ice particle size on the heat transfer properties should be quantified. 2. Ice slurry generators Many different ice slurry production techniques are known. All of them have advantages and drawbacks. The one feature that all of them have in common is the high price of the ice generator itself. In many ice slurry systems, the ice generator is the single most expensive component. Its price is often a barrier to people/companies when applying ice slurry systems. Future research and development should focus on less expensive and more reliable ice slurry production methods. 3. Principles of ice storage operation Compared with traditional (harvest and coil-based) ice storage systems, ice slurry offers a more dynamic type of storage. However, the application of ice slurry systems still remains relatively limited due to lower temperature as compared with pure water ice from e.g. harvesting systems, costly equipment and more complex storage layout. Intensive work is needed to develop more cost-effective ice slurry generators working at close to 0°C. To bring the technology one step closer to its real potential, it is of utmost importance to focus on the storage principles. Today, systems are in many cases constrained by their mode of operation and also are often unsuitable to fit into existing buildings and storage facilities. If the full potential of ice slurry is to be exploited, i.e. pumping ice slurry to heat exchangers, the storage tank must be either homogeneously mixed or a top harvester type where subsequent mixing with a carrier fluid is employed. The homogeneously mixed storage is used in many small ice slurry installations. The major drawbacks of this storage principle are relatively low maximum ice content (35 wt-%) allowed and a relatively high cost of the mixing devices when applied to large-scale applications. Future R & D should yield design principles that can be applied to existing storage facilities, e.g. both cylindrical and rectangular tanks, in heterogeneous, partially homogeneous or fully homogeneous mode. The maximum ice content of these storage systems must be quantified and in the case of the heterogeneous storage, the melt-off capacity, extraction temperatures and the feasibility of ice slurry extraction should be investigated at different: • flow rates, • return temperatures, • diffuser designs, • internal mixing principles. 318


4. Suspension/emulsion systems with melting temperatures above 0°C For many purposes, it is difficult to obtain good economy in ice bank plants, as the ice has to be produced at a lower temperature than that required at the cooling coils (point of cold utilization). Exergy is lost in this way in the production of ice. The selection of the optimum design for a storage system is based on a balance among savings in energy during production, savings in capital expenditure on refrigerating machines, reduction in operating costs and increases in investment in the storage tank as well as possibly increased energy consumption due to a lower evaporation temperature in the ice generator. As the storage tank may amount to a significant part of the total capital expenditure, it is essential that a high energy density can be obtained in the storage tank and that latent heat is utilised if the size has to be kept at a satisfactory level. It will thus be optimal to use a phase-change material (PCM) above 0°C in the same manner as ice slurry. A number of materials are available which meet the requirements for high energy density and melting point temperatures between e.g. 6°C and 10°C. Future R & D should investigate thermo-physical and thermodynamic properties as well as practical handling aspects of PCM suspensions/emulsions. The properties of the most applicable PCMs should be explored experimentally. The practical investigations must focus on feasible storage design, emulsification processes, bacteriology, material compatibility, surface deposition, rheology, heat transfer during phase change (melting and crystallization) and suspension properties. 5. Air-conditioning systems with low supply air temperature The supply air temperature of air conditioning systems can be reduced below the typical 12°C to 15°C. Typical low-temperature air supply temperatures are between 2°C and 7°C. Several researchers and companies have published investigations and results from installed systems, which show improved overall energy efficiency for cold air distribution systems. The power saved on the air side (reduced fan power due to reduced air-flow) is much greater than the increase in compressor power consumption due to a lower evaporation temperature. The installation costs are also reduced due to smaller fans, smaller ducts and reduced floor height (some authors quote a gain of stories and hence floor area in the same overall building height when applying cold air distribution systems). Typically, low-temperature air is produced with direct evaporation of refrigerant or with cold water very close to its freezing point. Ice slurry could be used in a beneficial manner to produce low-temperature air. Future R & D work should concentrate on ice slurry generation principles, which result in ice slurry temperatures close to 0°C. Heat transfer to the air should be studied, as it is expected that the ice slurry will have better heat transfer coefficients than cold water. Air coils might have smaller tubes with ice slurry facilitating lower pressure drop on the air side and hence reduced fan power.

6. New applications In addition, new applications outside the traditional refrigeration and air conditioning area may require more research. Chapter 12 mentions ice pigging for cleaning of complex systems, the in-situ cooling of the heart or brain after cardiac arrests and strokes, artificial snow

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production and fire fighting. But the refrigeration area still offers new applications for ice slurry, e.g. transport vehicle cooling. This Handbook presents current knowledge on ice slurries and the application of ice slurries. The material has been compiled by more than 50 leading scientists in this field from around the world. We all hope that the material presented will be helpful to others and will assist in increasing the acceptance of this very promising technology.

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Appendix 1: List of Authors (indicated by code in brackets – LA = Lead Author, CA = Co-Author) Derrick Ata-Caesar (CA 4) University of Applied Sciences of Western Switzerland Route de Cheseaux 1 CH-1401 Yverdon-les-Bains, Switzerland E-mail: [email protected]

Tom Davies (CA 5 - Reviewer) The University of Exeter, The Harrison Bldg. School of Engg. and Computer Science North Park Road Exeter, EX4 4QF, UK E-mail: [email protected]

Michel Barth (CA 5) Association Française du Froid 17, rue Guillaume Apollinaire 75006 – Paris, France E-mail: [email protected]

Christian Doetsch (CA 3) Fraunhofer Institut UMSICHT Osterfelder Strasse 3 D-46047 Oberhausen, Germany E-mail: [email protected]

Jean-Pierre Bedecarrats (CA 4) LTE – Université de Pau Avenue de l’Université, BP 1155 64013 – Pau Cedex, France E-mail: [email protected]

Peter W. Egolf (Editor, CA 1, LA 4 and CA 13) University of Applied Sciences of Western Switzerland Route de Cheseaux 1 CH-1401 Yverdon-les-Bains, Switzerland E-mail: [email protected]

Thorsten Behnert (CA 12) AximaRefrigeration GmbH Kemptener Str. 11-15 D-88131 Lindau/Bodensee, Germany E-mail: [email protected]

Kostadin Fikiin (LA 9) Refrigeration Science and Technology Division Technical University of Sofia 8 Kliment Ohridski Blvd. BG-1756 Sofia, Bulgaria E-mail: [email protected]

John Bellas (CA 12) Brunel University Department of Mechanical Engineering Uxbridge – Middlesex, UB83PH, UK E-mail: [email protected]

Laurence Fournaison (CA 2 and 10) Cemagref Parc de Tourvoie BP 44 F-92163 Antony, France E-Mail: [email protected]

Issa Chaer (CA 3 and 12) Brunel University Department of Mechanical Engineering Uxbridge Middlesex, UB8 3PH, UK E-mail: [email protected]

Beat Frei (CA 2, 3, 6 and 7) University of Applied Sciences Lucerne Technikumstrasse 21 CH-6048 Horw, Switzerland E-mail: [email protected]

Kim Gardø Christensen (CA 3 and 12) Danish Technological Institute Teknologiparken Kongsvang Allé 29 DK-8000 Aarhus C, Denmark E-mail: [email protected]

Vladimir Goldstein (CA 12) Sunwell Technologies Inc. 180 Caster Avenue Woodbridge, Ontario L4L 5Y7, Canada E-mail: [email protected]

Viktor Cucarella (CA 5.2.7) Technical University Dresden Faculty of Mechanical Engineering Institute of Material Science 01062 Dresden, Germany E-mail: [email protected]

Giuseppe Grazzini (LA 11) Università di Firenze Dipartimento di Energetica "S.Stecco" Via S. Marta 3

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IT-50139 Firenze, Italy E-mail: [email protected]

Yoshiyuki Kozawa (LA 7, CA 5 and 11) Takasago Thermal Engineering Co., Ltd. 3150 Iiyama 243-0213 Atsugi, Kanagawa Pref., Japan E-mail: [email protected]

Jacques Guilpart (LA 10) Cemagref Parc de Tourvoie BP 44 F-92163 Antony Cedex, France E-mail: [email protected]

Adrien Laude-Bousquet (CA 5) ALB 70, avenue de l’Europe 69480 – Anse, France E-mail: [email protected]

Torben Hansen (CA 2, 3 and 9, LA 6) Danish Technological Institute Teknologiparken Kongsvang Allé 29 DK-8000 Aarhus C, Denmark E-mail: [email protected]

M. Leprieur (CA 5) Dinan District – Pole Cristal 34 rue Bertrand Robidou - BP 357 22106 – Dinan Cedex, France E-mail: [email protected]

Robert Huhn (LA 7) Dresden University of Technology Institute of Power Engineering D-01062 Dresden, Germany E-mail: [email protected]

Jeroen Meewisse (CA 5) Delft University Michiel de Ruyterweg 37 NL-2628 BX Delft, The Netherlands E-mail: [email protected]

Cecilia Hägg (CA 2) Royal Inst. of Technology, KTH Dept. Energy Technology/ETT S-10044 Stockholm, Sweden E-mail: [email protected]

Åke Melinder (LA 2 - Reviewer) Royal Inst. of Technology, KTH Dept. Energy Technology/ETT S-10044 Stockholm, Sweden E-mail: [email protected]

Rob Jans (CA Appendix 2) Fri Jado Oude Kerkstraat 2 NL-4878 AA Etten-Leur, The Netherlands E-mail: [email protected]

D. Mito (CA 5) Takasago Thermal Engineering Co., Ltd. 3150 Iiyama 243-0213 Atsugi, Kanagawa Pref., Japan E-mail:

Michael Kauffeld (Editor and CA 1, 5, 6, 7, 8 and 9, LA 13) University of Applied Sciences Moltkestr. 30 D-76133 Karlsruhe, Germany E-mail: [email protected]

Ebbe Nørgaard Jensen (LA 8) Danish Technological Institute Teknologiparken Kongsvang Allé 29 DK-8000 Aarhus C, Denmark E-mail: [email protected]

Masahiro Kawaji (Editor, CA 1, 4 and 13, LA 5) University of Toronto 200 College St. Toronto, Ontario, M5S 3E5, Canada E-mail: [email protected]

S. Pazzi (CA 11) Università di Firenze Dipartimento di Energetica "S.Stecco" Via S. Marta 3 IT-50139 Firenze, Italy E-mail: [email protected]

Andrei Kitanovski (LA 3, LA 4, CA 2) University of Applied Sciences of Western Switzerland Route de Cheseaux 1 CH-1401 Yverdon-les-Bains, Switzerland E-mail: [email protected]

Pepijn Pronk (CA 5) Delft University of Technology Faculty of Mech Engg. and Marine Techn. Section Refrig. and Indoor Climate Control Mekelweg 2 NL-2628 CD Delft, The Netherlands E-mail: [email protected]

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Savvas Tassou (LA 12) Brunel University Kingston Lane Uxbridge, UB8 3PH, UK E-mail: [email protected]

Patrick Reghem (CA 3) University of Pau Avenue de l'Université F-64000 Pau, France E-mail: [email protected] Paul Rivet (CA appendix 2-A2, CA 12) MC international SA 16/18 Avenue Morane Saulnier F-78941 Velizy, France E-mail: [email protected]

Oleg B. Tsvetkov (CA 2) Chairman of the St. Petersburg Regional Branch Academician Lomonosov str. 9 191002 St. Petersburg, Russia E-mail: [email protected]

Pedro D. Sanz (CA 5) Department of Engineering Instituto del Frío (CSIC) Calle José Antonio Nováis, 10 Ciudad Universitaria E-28040 Madrid, Spain E-mail: [email protected]

Didier Vuarnoz (CA 2 and 3) University of Applied Sciences of Western Switzerland Route de Cheseaux 1 CH-1401 Yverdon-les-Bains, Switzerland E-mail: [email protected] Ming-Jian Wang (CA 5, 9 and 11) Sunwell Technologies Inc. 180 Caster Avenue Woodbridge, Ontario L4L 5Y7, Canada E-mail: [email protected]

Osmann Sari (CA 4) École d'Ingénieurs du Canton de Vaud Route de Cheseaux 1 CH-1401 Yverdon-les-Bains, Switzerland E-mail: [email protected]

Hartmut Worch (CA 5.2.7) Technical University Dresden Faculty of Mechanical Engineering Institute of Material Science 01062 Dresden, Germany E-mail: [email protected]

Alen Sarlah (CA 4) University of Ljubljana Faculty of Mechanical Engineering Askerceva 6 1000 Ljubljana, Slovenia E-mail: [email protected]

Thomas Zwieg (LA 2.1 and 2.2) Danish Technological Institut Kongsvang Allé 29 DK-8000 Aarhus C, Denmark E-mail: [email protected]

Evangelos Stamatiou (CA 4 and 5) University of Toronto 200 College St. Toronto, Ontario, M5S 3E5, Canada E-mail: [email protected] Françoise Strub (CA 4) Laboratoire La TEP UFR Sciences & Techniques BP 1155 - Avenue de l'Université 64013 – Pau Cedex, France E-mail: [email protected] Masayuki Tanino (CA 5 and 11) Takasago Thermal Engineering Co., Ltd. 3150 Iiyama 243-0213 Atsugi Kanagawa Pref., Japan E-mail: [email protected]

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Appendix 2: List of Selected Plants Table A1. List of ice slurry applications in various countries of the world (based on private communications by the IIR Ice Slurry Working Group) Country

Approximate number

Typical applications

Argentina

8–10

Fishing vessels, fish processing plant

Australia

3–4

Fishing vessels, fish processing plant, air conditioning

Barbados

1–2

On-board fish processing

Canada

7–8

Fish processing plants, produce packing, air conditioning

Chile

20–25

China

7–8

Fishing vessels, railway cargo cooling, air conditioning

Cuba

1–2

Hospital air conditioning and refrigeration

Denmark

2–3

Air conditioning, process cooling

Ecuador

1–3

Salmon farming

Faeroe Island

7–8

Fishing vessels

France

7–10

Air conditioning, supermarkets, fishing vessels, cold stores, catering

Germany

15–17

Replacement of CFC air-conditioning plants, retrofit of CFC air-conditioning systems, meat processing plants, breweries, food vendors, fish processing

Great Britain

8–10

Fishing vessels, air conditioning, cold stores, food cooling

Guatemala

1–2

Shrimp processing

Iceland

50–60

Japan

250–260

Korea

2

Fishing vessels, fish processing plants

Fishing vessels Building air conditioning, fisheries, cold storage, dairy production Building air conditioning, poultry processing plant

Mexico

2–3

Fish processing plants, railcar chilling

Namibia

4–6

Fishing vessels,

New Zealand

7–9

Fishing vessels, thermal storage

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Country Norway

Approximate number 20–30

Typical applications Fishing vessels, fish processing plants

Philippines

4–6

Poultry processing plants, chemical crystallization

Russia

1–3

Aircraft air conditioning

South Africa

22–23

Fishing processing plant, fishing vessels, mine cooling

Spain

8–9

Fishing vessels

Switzerland

4–6

Supermarkets, trolley cooling in passenger trains, ground cooling of airplanes, pharmaceutical production park

The Netherlands

15–20

Fishing vessels, cold store, supermarkets

USA

15–20

Fish processing plants, air conditioning (thermal storage), penguin enclosure, fire protection

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Table A2. a) France: scraped surface technology (reference LGL) by P. Rivet Year of installation

Type of installation

Specific technical data Refrigerant

1996 1997 1997 1998 1998 1998 2000

Mini supermarket (demonstration) Fishing vessels Supermakets (cold stores) Air conditioning Cold storage plant 0°C, Cold storage hall +12°C Fishing vessels Kitchen, refrigeration of meals

R22

Power

Ice storage 8 m3 0.5 m3

(kW) 14 and 4

Refrigeration Number of Capacity ice slurry max (kW) generators 20 and 5

R22 R507

Secondary fluid

4

Ethanol, –5°C Ethanol, –30°C See water

2

130

200

8

Ethanol, –4.8°C

R22

1 m3

10

20

1

Ethanol, –1.5°C

R22

28 m3

80

195

4

Ethanol, –2.4°C

5

Sea water

1

Ethanol, –3.5°C

1

Prop. Glycol, –4.5°C

2

Water-ethanol, –4.5°C

R22 R404A

8 m3

Table A2. b) France: brushed surface technology (reference LGL) by P. Rivet 2000 2001 2001

Supermarket, cold storage plant Dairies (milk and serum cooling) Supermarket (CO2), cold storage plant, ice machine

R22

6 m3

50

R404A

30 m3

120

R404A/CO2

50

327

300

CO2


Table A2. c) Worldwide: scraped surface technology installed by SUNWELL by Ming-Jian Wang Year of Installation 1990 1990 1993 1997 1994 1999

Type installation Building air conditioning for Crystal Tower, Osaka Broccoli packing plant, cooling and packing broccoli Shrimp processing plant, shrimp cooling and preservation Poultry processing plant cooling chicken Transport refrigeration cooling railroad cars Arctic habitat Crystal ice for penguin enclosure

Location

Primary Refrigerant

Ice Ice Storage Cold Output for Cold Output for Production Direct Cooling Indirect Cooling

Japan

R134A

Canada

R22

48 ton/day

2x50 ton ice

U.S.A.

R707

20 ton/day

60 ton ice

Philippines

R22

24 ton/day

42 ton ice

China

R22

85 ton/day

2 x 250 ton

U.S.A.

R22

16 ton/day

20 ton ice

32x130 kW 41680 kW-h

1999

Fish processing plant, Saury cooling and packing

Japan

R404A

96 ton/day

2001

Salmon processing plant Salmon cooling

Norway

R404A

15 ton/day

2002

Supermarket Ice for display cases

Canada

R404A

3.5 ton/day

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Chilled water Slurry at about 20% ice fraction Slurry at 30-40% ice fraction Slurry at 30-40% ice fraction Ice slurry with salt (5-25% fraction) Dry crystal ice

40 ton ice Slurry at 35-50% ice fraction Slurry at 60% ice 3.2 ton ice fraction, water drained afterwards 25 ton ice

Ice slurry with 15%/50% ice fraction; Chilled seawater


Table A2. d) Switzerland: Scraped surface technology by Peter W. Egolf Year of installation

Type of installation

Migros Lancy Onex, 1995, 1999 display cabinets & storage plants 2001

Pilot system

Specific technical data

Power

Refrigeration Number of capacity ice slurry max (kW) generators

Secondary fluid

Refrigerant

Ice storage

(kW)

R507

1 m3

90

92.4

26

Propylene glycol at 13%, 4.5°C

NH3

1.5 m3

10.9

15.5

4

Ethanol 10%, -3.8°C

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IIF-IIR – Handbook on Ice Slurries – 2005NOMFICHIER

Table A2. d) Ice-slurry Production and Storage Systems in Japan by Yoshiyuki Kozawa, Masayuki Tanino Liquefied ice systems Ice manufacturing mechanics (1) Continuous manufacturing of ice slurry by using scraped surface technology, (2) Storage of uniform sherbet in a tank by feeding of ice slurry.

Company / Characteristics Sunwell Japan Ltd. Takenaka Corporation Sekisui Plant System Co., Ltd.

(1) Heat Storage Medium: Water/Ice/ Alcohol (2) Designed Max. IPF: 50% (3) Saving energy and cost by feeding of ice slurry to secondary systems, Power of Pump: 30% of Cold Water Feeding, Size of Pipe: 50% of Cold Water System (4) Cold heat source in building air-conditioning, by means of natural circulation of Freon (Tokyo Electric Power Company, 1996) (5) Number of systems installed: 160 (Takenaka Corporation, 2000)

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Table A2. d) Ice-slurry Production and Storage Systems in Japan (continued) Ice manufacturing mechanics (1) Ice slurry manufacturing by means of repeated icing and de-icing modes in evaporator tubes, (2) Feeding of ice slurry into storage tanks.

Company / Characteristics Shimizu Corporation

(1) Heat Storage Medium: Water/Ice/Inorganic Compounds (2) Designed Max. IPF: 30% (3) Melting process with high performance due to transporting of ice slurry (4) Heat storage medium without rotting and algae (5) Number of systems installed: 1; volume of tank: 75 m3 (Tokyo Electric Power Company, 1996)

331


Table A2. d) Ice-slurry Production and Storage Systems in Japan (continued) Ice manufacturing mechanics (1) Ice slurry manufacturing by means of ice and de-ice cycles in ice makers, or by using rounding poles in ice makers, (2) Storage of uniform sherbet in a tank by feeding of ice slurry, (3) Feeding of ice slurry with certain ice content into secondary systems from ice storage tanks.

Ice manufacturing mechanics (1) Continuous manufacturing of ice slurry with about 100 µm ice particles, (2) Feeding of ice slurry into storage tanks.

Company / Characteristics Maekawa MFG. Co., Ltd. (4) Heat Storage Medium: Water/Ice/ Alcohol (5) Designed Max. IPF: 40% (6) Saving energy and cost by feeding ice slurry to secondary systems, Power of Pump: 30% of Cold Water Feeding, Size of Pipe: 50% of Cooled Water System (7) High response to heat load of air conditioning by controlling ice content (8) Number of systems installed for air conditioning: 1; volume of tank: 19 m3. Number of systems installed for warehouse cooling: 3 (Tokyo Electric Power Company, 1996) Company / Characteristics Mitsui Engineering & Shipbuilding Co., Ltd. (1) Heat Storage Medium: Water/Ice/Alcohol (2) Designed Max. IPF: 40% (3) Non-adhering ice particles on wall and/or surrounding ice particles by using the special type of brine (4) Number of systems installed: 5; total volume of tanks: 242 m3 (Tokyo Electric Power Company, 1996)

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Table A2. d) Ice-slurry Production and Storage Systems in Japan (continued) Supercooled water systems Ice manufacturing mechanics Company / Characteristics (1) Making supercooled water (–2°C) in a shell & tube-type supercooling heat exchanger, (2) Continuous manufacturing of ice slurry by release of supercooling, (3) Feeding of ice slurry into storage tanks.

Takasago Thermal Engineering Co., Ltd.

(1) Heat Storage Medium: Tap water and ice (2) Designed Max. IPF: 40% (3) Flexible system arrangement, especially no restriction as to shapes and locations of ice storage tanks (4) Temperature of tank wall > 0°C Non-freezing of water in concrete walls (Tokyo Electric Power Company, 1996) (5) Number of systems installed: 23; total volume of tanks: 8520 m3 (by Takasago Thermal Engineering as of 2002)

333


Table A2. d) Ice-slurry Production and Storage Systems in Japan (continued) Ice manufacturing mechanics (1) Making supercooled water (–2°C) in supercooling heat exchanger, (2) Continuous manufacturing of ice slurry by release of supercooling due to an ultrasonic wave, (3) Feeding of ice slurry into storage tanks.

Characteristics (1) New type of this system (Mito, D. et al., 2002)

Ice manufacturing mechanics (1) Making of supercooled water (–2°C) in a plate-type super-cooling heat exchanger, (2) Continuous manufacturing of ice slurry by release of supercooling due to the vibration of leaf spring, (3) Feeding of ice slurry into storage tanks.

Company / Characteristics Shinryo Corporation

(1) Heat Storage Medium: Tap water and ice (2) Designed Max. IPF: 50% (3) Compact-type supercooling heat exchanger (Nagato, H., 2001) (4) Number of systems installed: 6

334


Table A2. d) Ice-slurry Production and Storage Systems in Japan (continued) Ice manufacturing mechanics (1) Making supercooled water (–2°C) in a plate-type evaporator, (2) Continuous manufacturing of ice slurry by release of supercooling due to additional cooling by Peltier elements, (3) Feeding of ice slurry into storage tanks.

Company / Characteristics Shimizu Corporation

(1) Heat Storage Medium: Tap water and ice (2) Designed Max. IPF: 40% (3) Compact-type supercooling heat exchanger (4) Supercooled ice making heat pump unit (5) Number of systems installed: 1; volume of tank: 23 m3 (Kurihara, T., Kawashima, M., 2001)

Ice manufacturing mechanics (1) Making of supercooled water in an evaporator, (2) Continuous manufacturing of ice slurry by release of supercooling in storage tanks.

Company / Characteristics Mitsubishi Heavy Industries, Ltd.

(1) Heat Storage Medium: Tap water and ice (2) Designed Max. IPF: 40% (3) Oil-less turbo-type refrigeration unit, High COP (=120% of usual refrigeration unit (4) Number of systems installed: 1; volume of tank: 87 m3 (Kakutani, S., Osa, N., 1999)

335


Table A2. d) Ice-slurry Production and Storage Systems in Japan (continued) Ice manufacturing mechanics

Company / Characteristics

(1) Making of supercooled water in a plate-type super-cooling heat exchanger, (2) Continuous manufacturing of ice slurry by release of supercooling in storage tanks.

Nippon Steel Corporation

(1) (2) (3) (4)

Heat Storage Medium: Tap water and ice Designed Max. IPF: 40% Compact-type supercooling heat exchanger Number of systems installed: 15

Ice manufacturing mechanics (1) Making of supercooled water in an evaporator, (2) Continuous manufacturing of ice slurry by release of supercooling due to the additional cooling in a separated tank, (3) Feeding of ice slurry into storage tanks.

Company / Characteristics Daikin Industries, Ltd. (1) Heat Storage Medium: Tap water and ice (2) Designed Max. IPF: 40% (3) Ice storage unit of multi-zone air- conditioners for building uses (4) Number of units installed: 2000 (Information from Tokyo Electric Power Company [1999,6])

336


Table A2. d) Ice-slurry Production and Storage Systems in Japan (continued) Ice manufacturing mechanics (1) Making of supercooled water in a plate-type evaporator, (2) Continuous manufacturing of ice slurry by release of supercooling in storage tanks.

Company / Characteristics Toshiba Corporation

(1) (2) (3) (4)

Heat Storage Medium: Tap water and ice Designed Max. IPF: 40% Compact-type supercooling heat exchanger Ice storage unit of multi-zone air- conditioner for building uses (Toshiba Corporation, 1998) (5) Number of units installed: 160 (Reply of Toshiba Corporation to a questionnaire [1999, 1996])

337


Table A2. d) Ice-slurry Production and Storage Systems in Japan (continued) Ice harvest systems Ice manufacturing mechanics (1) Repeating of freezing and harvesting on ice making plates grouped into 4, (2) Storing of harvested ice in a water tank, (3) Transporting of ice slurry after adjusting ice content to secondary systems.

338


Obayashi Corporation

(1) Heat Storage Medium: Tap water and ice (2) Designed Max. IPF: 45% (3) Number of systems installed: 13; total volume of tanks: 835 m3 (Tokyo Electric Power Company, 1996)


Table A2. d) Ice-slurry Production and Storage Systems in Japan (continued) Ice scratch systems Ice manufacturing mechanics (1) Instantaneous freezing of water flowing on the inner surface of a cylindrical evaporator, (2) Making ice flakes of 0.5 mm thickness by scratching with a rotating scrubber, (3) Storing of ice flakes in a water tank.

Company / Characteristics Taikisha Ltd.


Ice manufacturing mechanics (1) Making of thin film ice of 2 mm thickness, (2) Scratching a thin film ice mechanically into a storage tank.

Company / Characteristics Sanki Engineering Co., Ltd.


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Table A2. d) Ice-slurry Production and Storage Systems in Japan (continued) Ice manufacturing mechanics


(1) Freezing of sprayed water to ice of about 1 mm thickness on a Hazama Corporation rotating evaporator drum, (2) Scratching down of ice by a blade installed outside the drum into a storage tank. (1) Heat Storage Medium: Tap water and ice (2) Designed Max. IPF: 40% (3) Number of systems installed: 1; volume of tank: 357 m3 (Tokyo Electric Power Company, 1996)

340


Table A2. d) Ice-slurry Production and Storage Systems in Japan (continued) Other Systems installed in Japan Ice manufacturing mechanics


(1) Freezing of water on low temperature organic compound droplets sprayed into a water tank due to direct heat exchange, (2) Accumulating gradually of fragile ice from the free surface of water in a tank.

Toshiba Corporation

(1) Heat Storage Medium: Tap water and ice (2) Designed Max. IPF: 40% (3) Simple ice manufacturing (Hashiguchi, M. et al., 1995) (4) Number of systems installed: 1; volume of tank: 960 m3 (Watanabe, Y. et al., 1997)

Ice manufacturing mechanics


(1) Ice manufacturing in the evaporator of a lithium bromide solution type absorption refrigerator.

Taikisha Ltd.

(1) Heat Storage Medium: Tap water and ice (2) Designed Max. IPF: 40% (3) Effective use of waste heat and cogeneration systems (Yoshida, T., Sasao, H., 1993) (4) Results of introduction: Laboratory stage as of 1999.6 (Reply of Taikisha to questionnaire)

341


Dutch supermarket with ice slurry technology by Rob Jans The project Paradijsvogel Supermarkt was Fri-Jado’s fourth ice slurry (flo-ice®) project and the third in Holland. The supermarket is located in Amsterdam and owned by Mr Slot, who is a franchisee under the C1000 banner (Schuitema). The installation has been in operation since autumn 2000. It was a market introduction project, because Fri-Jado offers a mature, fully developed technique, proven energy savings up to 20% and patented techniques with regard to generation and application. The objectives of the projects were as follows: • • •

demonstrating technical fulfilment; reduction of annual direct emission of synthetic refrigerant: from 9.25 kg (comparable conventional installation) to 1.2 kg (ice slurry system); energy saving of at least 16% compared with a conventional installation.

In the supermarket with a sales area of 1250 m2 three different circuits were used: • • •

a circuit for cold generation HFC-404A is used; an ice slurry distribution circuit for cooling (ethanol/water ice slurry at –5°C); a separate conventional circuit for freezing.

Ice slurry is generated in a scraped-surface ice slurry generator and transferred to a cold buffer where the ice slurry is stored. In the daytime the generation of the cold buffer continues. The buffer gradually decreases because of a larger cold demand than the installation generates in the daytime. Technical details: Object-load (25°C/60%) Compressor capacity (–12°C/+43°C) Refrigerant Liquid supply Cold-storage tank Ice scrapers Liquid flow through objects Maximum ice concentration Low-temperature-system Object load (25°C/60%)

kW kW m3 kWh n kWh m3 % kW

342

98.0 80.1 HFC-404A Gravity 6 154 5 65 11 30 Cascade Refrigerant 11.4


The most important results of the project are: • • • •

Mechanical problems concerning the scrapers and adjustment problems, which arose in previous projects, have been solved definitively; One malfunction has occurred, which originated with a supplier. This experience is taken into account with future deliveries of the parts concerned; Energy savings add up to 17.6%; the savings on the energy bill, which will be calculated at the end of 2000, were even higher due to a lower night rate; In accordance with a theoretical approach a reduction of 86.2% in direct emissions is effected compared with a conventional installation. A practical approach (registration of added refrigerant) results in a leak percentage of 0%.

Consequently, the project was technically successful and the objectives set were realized. Therefore, the project offers an outstanding reference to demonstrate the good functioning of the ice slurry technology used. However, the implementation of ice slurry installations with scraper technology is not acceptable from a commercial point of view. Therefore Fri-Jado will start a feasibility study concerning ice slurry with vacuum technology, in which the expensive scrapers are replaced by a vacuum system. The resulting price reduction is a focus of the study. Finally, there are good possibilities to introduce natural refrigerants in Dutch supermarkets, because the use of refrigerants is limited to the engine room.

Literature cited in Appendix 2 1.

2. 3.

4.

5. 6. 7. 8.

9.

Hashiguchi, M.; Kamakura, K.; Okazaki, T.; Watanabe, Y.; Yamashita, K.; Takayanagi, M.: Development of an Ice Storage System Using Direct-contact Heat Transfer between Water and Water-insoluble Antifreeze, Proc. of Annual Conf. of the Soc. of Heating, Airconditioning and Sanitary Engineers of Japan: pp. 505-508, 1995. Kakutani, S.; Osa, N.: Development of High Density Heat Transportation System, Jour. of the JSRAE, 74-856, p. 28-3, 1999. Kurihara, T.; Kawashima, M.: Dynamic ice storage system using supercooled water, Introductions of heat pump and thermal storage unit for commercial use, Fourth IIR workshop on ice slurries, pp. 61-69, 2001. Mito, D.; Mikami, Y.; Tanino, M.; Kozawa, Y.: A new ice-slurry generator by using actively thermal-hydraulic controlling both supercooling and releasing water, Fifth IIR Workshop on Ice Slurries, Stockholm, May 2002. Nagato, H.: A dynamic ice storage system with a closed ice making device using supercooled water, Fourth IIR workshop on ice slurries, pp. 97-103, 2001. Takenaka Corporation, Catalogue of “Full Storage”, 2000. Tokyo Electric Power Company, Heating and Cooling for Air-conditioning by Heatpump, 54, 1996. Watanabe, Y.; Shingu, H.; Goto, K.; Yoshino, H.; Tamaya, S.; Nakatsu, Y.: Characteristics of melt-ability of Huge Ice Storage System for Gas-turbine inlet air cooling, Proc. of Annual Conf. of the Heat transfer Soc. of Japan, pp. 715-716, 1997. Yoshida, T.; Sasao, H.: Development of Absorption Ice-maker for Ice-slurry, Part1; Experiment of Ice-maker, Proc. of Annual Conf. of the Soc. of Heating, Air-conditioning and Sanitary Engineers of Japan, pp.401-404, 1993.

343


Appendix 3: List of symbols List of symbols Chapter 2 Symbol:

Unit [Rat. Inch Pounds]

Unit [SI]

a B C c cp C C CD d D E f f F g g G h H H He k k K l m, M p Pr q Q r r, R Re R2 s t T U v V x x

Btu lb-1 °F-1 µS/inch ft or microns ft or microns s-1 lb ft s-2 ft s-2 Btu/lb Btu/lb ft Btu Btu lb-1 F-1 lb s-2 ft³ s-1 ft lb psi Btu/h TR Ω inch ft or microns Btu lb-1 F-1 s °F ft s-1 ft3 ft

J kg-1 K-1 µS/cm m or microns m or microns s-1 kg m s-2 m s-2 J/kg J/kg m J J kg-1 K-1 kg s-2 m³ s-1 m kg kPa W W Ω cm m or microns J kg-1 K-1 s °C m s-1 m3 m

Parameter, coefficient Coefficient Coefficient Volumetric fraction Specific heat capacity Volume concentration Electrical conductivity Coefficient of drag Distance Diameter Coefficient Frequency Function Force Function Gravity Gibbs free energy Enthalpy Height of liquid column Enthalpy Hedström number Boltzmann constant Spring constant Ripening constant length Mass Pressure Prandtl number Power Refrigeration capacity Resistivity Radius Reynolds number Coefficient of determination Entropy Time Temperature Uncertainty of measurement Velocity Volume Concentration (weight fraction) Distance

345


Greek symbols: α Heat transfer coefficient δ Infinitesimal difference ∆ Difference λ Thermal conductivity γ Specific surface free energy µ Chemical potential ν Kinematic viscosity ω Angular velocity Ω Atomic volume ρ Density τ Time Θ Wetting angle ξ Temperature compensation for electrical conductivity χ Specific ice slurry property Subscripts: 0 1 2 add c C cf end fl ice hw ls L mix n R slurry S V w

Overall Different states Different states Additive Coriolis Catalyst Carrier fluid Final state Fluid Ice Hot water Latent melting Liquid Mixing heat Nucleus Resonance Ice Slurry solid volume Water

Superscript: * Diluted

346

Btu h-1 ft-2 °F-1 Btu h-1 ft-1 °F-1 Btu lb-1 ft-2 Btu lb-1 ft² s-1 s-1 ft³ lb ft-3 s % K-1

W m-2 K-1 W m-1 K-1 J kg-1 m-2 J kg-1 m² s-1 s-1 m³ kg m-3 s % K-1

-

-


List of symbols Chapter 2.5 (Tsvetkov) c – volume fraction of ice k – thermal conductivity, Wm-1 K-1 a, A, B – coefficients Greek symbols: η – dynamic viscosity, Pa⋅s ϑ – temperature, 0 C α , β , δ – coefficients Index * – effective 2,s – ice 1 – liquid

List of symbols Chapter 3.1 C D L p v

[-, %] [m] [m] [Pa] [ms-1 ]

Greek symbols: [Pas] η [Pa] τ [Pa] τ0 Index app B C eff K L max n ∞ 0

concentration pipe diameter pipe lenght pressure velocity

dynamic viscosity shear stress yield stress

apparent Bingham Casson effective arbitrary constant liquid maximum power index limiting viscosity at ininite shear rate limiting viscosity at zero shear rate

347


List of symbols Chapter 4 Standard A C C cp D f h h H k L m

q&

Surface Concentration Constant Specific heat Diameter Friction factor Enthalpy density Heat transfer coefficient Height Thermal conductivity Length Mass Mass flow Power law index Wetted perimeter Heat flux density

q’’ r R R T t u U U v V V x,z y

Heat flux density Radial coordinate Radius Thermal resistance Temperature Time Velocity Velocity Overall heat transfer coef. Velocity Velocity Volume Downstream coordinate Vertical coordinate

m& n P

Subscripts m2 m 3 m -3 /kg kg -1 J kg -1 K-1 m J kg -1 W m-2 K-1 m W m-1 K-1 m kg kg s -1 m

C Cf e h in i is ln m V w

W m-2 W m-2 m m K/W K s m s -1 m s -1 W m-2 K m s -1 m s -1 m3 m m

Χ Gr He Nu Pr Re

Dimensionless numbers +

Greek symbols α α∗ δ εh φ Φ η Θ ρ ϑ τ0 ξ

Thermal diffusivity Channel aspect ratio Thermal bound. lay. thick Thermal eddy diffusivity Angle Local ice fraction Viscosity Correction factor Density Τemperature Critical shear stress Mass concentration

Cross section Carrier fluid Ethanol Hydraulic Inlet Ice Ice slurry Logarithmic Mean value Volumetric Wall, water

m2 s -1 m m2 s -1 ° Pa s kg m-3 °C Pa kg kg -1

348

Cameron number Graetz number Hedström number Nusselt number Prandtl number Reynolds number


List of symbols Chapter 9

Subscripts c D x, X h k L t, T tf

–1

–1

Specific heat capacity (kJ kg K ) Diameter of ice particles (µm) Mass fraction (kg kg–1 ) Enthalpy per unit mass (kJ kg–1 ) Thermal conductivity (W m–1 K–1 ) Latent heat of water freezing/thawing (kJ kg–1 ) Temperature (o C or K) Initial freezing temperature (o C)

e d i is l oil p s w

ethanol dry matters ice ice slurry liquid solution fat matters (oil) at constant pressure sugar water

Greek letters

Superscripts

η λ ρ τ ϕ

in

Dynamic viscosity (mPa s) Thermal conductivity (W m–1 K–1 ) Density (kg m–3 ) Time (s) Volumetric fraction (m3 m–3 )

initial

Acronyms CFC COP HCFC

ChloroFluoroCarbon Coefficient of Performance HydroChloroFluoroCarbon

HFC HFM IQF

349

HydroFluoroCarbon HydroFluidisation Method Individual Quick Freezing


APPENDIX 4: LIST OF FIGURES

CHAPTER 2 Figures 2.1 2.2 2.3

2.4 2.5

2.6

2.7

2.8

2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19

CHAPTER 3 Figures 3.1

3.2 3.3

Critical nucleus radius in homogeneous nucleation Geometrical and surface energy balances in heterogeneous nucleation Nucleation of an ice embryo on a crystalline substrate with a lattice misfit of approximately 10%. Dislocations (arrows) and elastic strain are introduced into the nucleus [x, Flet] Ice crystals formed heterogeneously in a shell-and-tube ice slurry generator under forced flow conditions a) Mean Feret diameter growth dependency on additive, ice concentration and storage type shows clearly the Ostwald ripening effect b) Particle Feret diameter growth rate dependency on additive, ice concentration and storage type Ice crystal morphology during a freezing/melting cycle, a), b), c), h), and i) from EIVD-TiS laboratory, Switzerland; d) from DTI, Denmark, and e), f), g) from Delft Univ., Netherlands (Pronk 2002) Ice particle shapes estimated from projected images: a) a spheroidal ice particle shape composed of two hemispheres connected by a cylinder of the same radius (applied by Vuarnoz and Egolf [2001], b) disk-shaped ice particle model proposed by Pronk (2002) Ice particle size distribution data obtained for a 10 w/w% water-ethanol ice slurry after correction with a view factor. Shown are the data for a) Ci=10.3% and b) Ci=21.4% ice concentration (Vuarnoz, 2001 and Egolf, 2002) Freezing point temperature (ϑF) as a function of additive concentration (CA) Freezing point diagram (schematic) Ice concentration as function of temperature for two types of aqueous solutions Schematic enthalpy phase diagram (NaCl-H2O) Enthalpy phase diagram for sodium chloride-water Enthalpy phase diagram for ethylene glycol-water Enthalpy phase diagram for propylene glycol-water Enthalpy phase diagram for ethyl alcohol-water Enthalpy phase diagram for ammonia-water Enthalpy phase diagram for potassium formate-water Enthalpy phase diagram for calcium chloride-water

Eight different series of measurements of the effective viscosity, performed at CEMAGREF, DTI and UASCS with rotary and online viscometry. The solid curve shows a model calculation presented by Christensen et al. (1997) (see Frei and Egolf 2000) Rheogram for typical fluids with and without a minimum yield stress (τ0) and shear thickening (n > 1) or shear thinning behaviour (n < 1) Casson parameters ηC and τC with a dependence on the viscosity of the Carrier fluid (2 mPas < ηL < 10 mPas) and the ice particle concentration (0-45%) (Doetsch, 2001)

351


3.4 3.5

3.6

3.7

3.8

3.9

3.10 3.11

3.12 3.13 3.14 3.15 3.16 3.17

3.18

CHAPTER 4 Figures 4.1 4.2 4.3 4.4

Flow patterns of suspensions with S < 1 (see list of symbols) Visualization of ice slurry flows only allows a qualitative determination of flow patterns (10% water-ethanol mixture, dp ~ 0.1 mm, Di = 44.6 mm, case A: C = 5%, v = 0.1 m/s, case B: C = 10%, v = 0.2 m/s). Work performed by P. Reghem et al. at Pau University Visualization of ice slurry flows does not allow a very accurate determination of flow patterns (10 % water-ethanol mixture, dp = 0.2 ~ 0.4 mm, Di = 20 mm, rectangular pipe, case A: C = 7.6%, v = 0.54 m/s, case B: C = 7.5%, v = 0.23 m/s, case C: C = 7.5%, v = 0.15 m/s). Work performed by Didier Vuarnoz et al. at EIVD Flow pattern diagrams from three different experiments performed at LTE Pau University and the Danish Technological Institute (DN 50, 10% waterethanol) Flow pattern “diagrams” performed at the Korean Institute of Energy Research (Di = 24 mm, 6.5% ethylene glycol-water, d p = 0.27 mm) (Dong Won Lee et al., 2002) Velocity profiles of ice slurry flows (7% ethanol-water mixture, Cr = ~20%, DN 50, dp ~ 0.1 mm, dashed lines are approximate predictions (Kitanovski et al., 2002) Ice particle velocity profiles for ice slurry flow (11% ethanol-water mixture, Cr = 12, 10, 11%, DN 25, dp ~ 0.1 mm) measured by Vuarnoz et al. (2000) Concentration profiles of ice slurry flows in a horizontal pipe calculated with eq. 3.40 (D = 27.2 mm, dp = 1 mm, 10% water-ethanol) (Kitanovski et al., 2002) Deposition velocities for ice slurry flow – theoretical model (10% ethanolwater) (Kitanovski, 2002) Deposition velocities obtained from an empirical function (eq. [3.43]). (Kitanovski et al., 2002) Flow pattern diagram for ice slurry flows obtained by applying a theoretical model (DN 50, 10% water-ethanol) (Kitanovski et al., 2002) Critical Reynolds number as a function of the Hedstrom number (Eq. 3.55 + 3.56) Darcy´s friction factor dependence on the Reynolds and the Casson numbers (Doetsch, 2001) The specific pressure drop R in a heat exchanger decreases approximately exponentially. In this example R changes from the inlet to the outlet by more than a factor of ten! “Example” denotes a step-by-step downstream calculation through the heat exchanger. “Model” denotes results obtained by applying Eq. (3.76) (Egolf et al., 2001) The specific pressure drop in a charge - and discharge - loop alters as a function of time and evaporator temperature at the same velocity and ice mass fraction (Frei and Egolf, 2000)

Heat transfer from the wall to an ice-slurry in a vertical rectangular duct with a second kind boundary at the wall Local ice fraction distribution measurement at L/Dh≈19 Calorimeter (680 W) for on-line ice fraction measurements Local temperature and velocity measurements (side view)

352


4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21

4.22

4.23 4.24

4.25

4.26

4.27 4.28 4.29 4.30

Velocity profile data for ΦV=0.0-6.0%, =0.080m/s, Recf,L~2200 Velocity profile data for Φv=6.0-9.0%, Recf,L~2100 & 4000 Typical ice slurry velocity profiles near a heated wall Ice slurry temperature distributions for Recf=3800 and α*=H/W=1:12 (H=25.4 mm) Ice slurry temperature distributions for Recf=6600 and α*=H/W=1:8 (H=12.7 mm) Effect of Φv (6-11%) on the ice fraction distribution at Uo/ ~ 1.8 Effect of Φv on the ice fraction distribution at Uo/ ~ 1.3 Effect of Φv on ice fraction distribution at Recf ~ 3800 near a heated wall Average Nusselt number for ice slurry flows through a pipe Nusselt number data for an ice slurry flow heated with a heat flux of 15 kW/m2 and 40 kW/m2 (Knodel et al., 2000) Calculated heat transfer coefficients obtained by using Equations (4.19) and (4.20) The local heat transfer coefficient calculated by applying Eq. (4.21) - (4.23) Test section schematic and temperature measurement locations (Sari et al., 2000) Numerically calculated temperature profiles compared to measured profiles The Nusselt number as a function of the Hedström number for laminar flow The Nusselt number as a function of the Hedström number for turbulent flow Local heat transfer coefficients measured in a horizontal rectangular channel of height 60 mm. Other parameters are given in the figures (from Kawanami et al., 1998) Flow patterns according to Kawanami et al. (1998) and some predictions of the IPF (ice packing factor) for different channel heights: a: H = 60 mm, b: H = 40 mm, c: H = 20 mm Mean heat transfer coefficients calculated using Eqs. (4.33) and (4.34) Experimentally and numerically determined temperature profiles for a heat flux of 1800 W/m2 in a 1-meter long rectangular heat exchanger at a mass flow rate of 1.2 kg/s. The measurement locations were: x = 0.25 m, 0.5 m, 0.75 m and 1 m. Trapezoidal symbols denote experimental data, while small triangles and the fitted solid curves represent numerically calculated profiles Temperature profiles for a heat flux of 7200 W/m2 in a 1-meter long rectangular heat exchanger. The axial locations of the measurements are: x = 0.5 m and 1 m. Trapezoidal symbols denote experimental data and the solid curves represent numerically calculated profiles Ratios between the thermal eddy diffusivity and the thermal diffusivity at different axial locations in a rectangular heat exchanger for different heat fluxes. The data correspond to the results shown in Figures 4.24 and 4.25. The dotted line was drawn in analogy to the solid line. It must be confirmed by more measurements Geometrical dimensions of a rectangular duct Nucf,m as a function of Recf,m and Xs,m at Thw,m ~ 41.0oC and α*=1:8 (Stamatiou, 2003) Nucf,m as a function of Recf,m and Xs,m at Thw,m ~ 14.8oC and α*=1:8 (Stamatiou, 2003) Schematic of the flow model (Kawanami et al., 2001)

353


4.31 4.32 4.33 4.34

4.35 4.36 4.37

CHAPTER 5 Figures 5.1a 5.1b 5.1c 5.1d 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16

5.17 5.18

5.19

5.20

Local (above) and mean (below) heat transfer coefficients for the concave and convex curved walls (Kawanami et al., 2001) Melting behaviour of an ice slurry with an ice fraction of Ci=20 mass-% and heat flux of q& =2.4 kW/m2 after: a) 5 min, b) 15 min, c) 25 min Melting mechanisms as described and explained by Kawanami et al. (1999) Melting behaviour and temperature distribution for Ci=20 mass%, a) q·t = 2.88x106 J/m2; d) q = 800 W/m2; b and e) 1600 W/m2, c and f) 2400 W/m2 (Kawanami et al., 1999) Comparison of experimental results and proposed empirical correlations for convective heat transfer to ice slurries (Stamatiou and Kawaji, 2004b) An alternative heat transfer correlation for turbulent ice slurry flow (Stamatiou and Kawaji, 2004b) Comparison of local Nusselt number data with predictions for laminar nonNewtonian heat transfer to ice slurries (Stamatiou and Kawaji, 2004b)

Scraped-surface ice slurry generator (Courtesy of Sunwell) Orbital rod ice slurry generator (Courtesy of Paul Muller Co.) Scraped-surface ice slurry generator (Courtesy of Integral) Scraped-surface ice slurry generator with helical screw – originally designed for the production of flake ice (Courtesy of Ziegra) Schematic of an ice slurry generation system Double-walled tubular ice slurry generators with an envelope Disk type scraped-surface ice slurry generator with an envelope The internal circuits of a refrigerating disk Photo of an 80-kW ice slurry generator with staggered disks Staggered brushes Immersed disk type scraped-surface ice slurry generator Ice slurry generation with water as refrigerant (also known as vacuum ice) Vacuum ice system with water vapour removal by freeze-out (Zakeri, 1996) Schematic diagram of direct contact ice slurry generator (Wobst, 1999) Ice slurry generator based on direct contact evaporation (Coldeco®) Direct contact liquid coolant type ice slurry generator Current and possible systems of supercooled brine method in Japan Ice slurry production process using the supercooled water method in an ice storage system Actual numbers of equipment and installed refrigeration capacity of ice storage systems using the supercooled method in Japan (System (A), system (B) and system (C) of Figure 5.14) Schematic of a hydro-scraped ice slurry generator Representative scheme of the INP arrangement at the cell membrane of INA-bacteria. Hydrophilic residues act as nucleating sites, matching an icelike structure. Neighbouring hydrophobic residues surround the nucleation site, preventing ice sticking on the cell membrane Aluminium oxide modified by applying the sol-gel technology. Red colour (wavy line in the centre) represents hydrophilic residues and blue colour (two outer wavy lines on either side of the red curve) represents hydrophobic residues Sketches of the ice formation process over different coating materials

354


5.21 5.22 5.23 5.24

5.25

CHAPTER 6 Figures 6.1 6.2 6.3 6.4

6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14 6.15 6.16 6.17 6.18 6.19 6.20 6.21 6.22 6.23

Particle/Ice Removal Mechanism Fluidized bed heat High-pressure shift freezing of an agar gel cylinder from 210 MPa and –21ºC Refrigeration circuit for recuperative ice slurry generator A turbo-chiller plate of about 10 kW capacity, 1.5 m wide, 1 m high made from two sheets of 1 mm thick stainless steel plate welded together, with refrigerant entry/exit at the top and at the bottom to the right A turbo-chiller plate of about 10 kW capacity, 1.5 m wide, 1 m high made from two sheets of 1 mm thick stainless steel plate welded together,with refrigerant entry/exit at the top and at the bottom to the right

Example of reduced total pipe length by using a single pipe system Centralized warm liquid defrosting systems Local warm liquid defrosting systems Separated flow regimes. Left: measurement of separation velocities in a horizontal 50 mm pipe based on visual inspection. Right: ice concentration profiles (dashed lines) and velocity profiles (solid lines) for moving bed, stratified and homogeneous flow (top to bottom). (Hansen and Noergaard). (This reference is missing in the List of References) T-junction with a vertical upward facing branch without flow, i.e. the valve is closed Vertical T-junction without flow in the left branch Flow in parallel valve sections, experiment 14A. (Hansen, Radosevic, Kauffeld, 2002) Enthalpy of ice slurry depends on ice fraction and additive concentration Transport capacity (kW of cooling at full melt off) in pipes (Drør : Inner pipe diameter) The experimental set-up at the Danish Technological Institute and a sketch of a Grundfos CR pump Performance curves of a Grundfos CR 2-50 pump working with ice slurry Stage efficiency and power consumption curves of a Grundfos CR 2-50 pump working at 2800 rpm with ice slurry Stage efficiency of a Grundfos CR5-11 pump working at 2800 rpm with ice slurry Design of centrifugal pump to be immersed in to the ice storage Control loop circulation pump (combined UPE and a SP pump: UPESP1A3) Screw pump Pump characteristics for the screw pump in Fig. 6.16 Electrical power input, P (denoted “E” in the figure) against volumetric flow . rate V (denoted “Q” in the figure) for the screw pump shown in Figure 6.16 Overall efficiency for the screw pump shown in Figure 6.16 Side channel pump Pump total head for the side channel pump shown in Figure 6.20 Pump total head for the side channel pump shown in Figure 6.20 Overall efficiency of the side channel pump show in Figure 6.20

355


6.24 6.25

6.26 6.27 6.28 6.29 6.30 6.31 6.32 6.33 6.34 6.35 6.36

6.37

6.38

CHAPTER 7 Figures 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10

Measured performance curves compared to manufacturer’s data based on Jeffrey’s viscosity model (Grundfos pump CR 2-50 at 2800 rpm) Measured performance curves compared to manufacturer’s data based on Jeffrey’s viscosity model (30 wt-% ice, Grundfos pump CR 2-50 with variable speed). Cross bars indicate manufacturer’s tolerance Relative performance curves of the tested centrifugal pumps at 2800 rpm Comparison of measured relative performance of the CR5 centrifugal pump (2800 rpm) with and without ice particles Density of the ice slurry during the 24-hour test, 20% ice = 969 kg/m3 .

24 hour performance test of the CR5-11(Grundfos) at 0.33 x V 0 with 20 wt% ice Typical locations of the ice slurry clustering, photo taken from inlet side Flow rate over time of the pump shown in Figure 6.30 with 10 and 30 wt-% ice fraction Test section used in the experiments. The dots show the pressure measurement locations Pressure taps (Dimensions in millimetres) Typical axial pressure profile along a piping system containing a fitting Experimental results on pressure loss measurements in ABS-fittings The left figure shows a sketch of the possible flow pattern with ice slurry when the flow is highly turbulent, while the right sketch shows a possible flow pattern when the flow is laminar or of Bingham type Measured pressure loss coefficients for 90° bends with 10 and 30 wt-% ice fraction in a water/glycol carrier fluid. The diagram shows a clear relation between the loss coefficients and the Reynolds number. As the Reynolds number is increased the value of the loss coefficient approaches the tabulated value. Even the experiments without ice slightly show this trend The loss coefficients plotted against the Reynolds number and the ice concentration. This correlation has a R2 value of 0.96 compared to 0.84 for the correlation shown in Figure 6.37. Therefore it is concluded that the presence of solid particles in the fluid influences the loss coefficient negatively by a factor of 2 to 3

Overview of different categories of storage strategies (Hansen et al., 2002) Examples of some typical storage layout principles (Hansen et al., 2002) Ice storage process in a tank (seen from the side) Ice melting process in a tank Overview of ice storage model in a tank Overview of the ice melting model in a water-spraying system Comparison of prediction and measurement in an ice storage process Rate of utilisation of the volume of the ice storage tank Design conditions for ice storage Comparison of experimental and predicted results for cold water exit temperature from a flat water tank

356


CHAPTER 8 Figures 8.1 8.2

8.3

8.4 8.5 8.6

8.7 8.8 8.9

8.10 8.11

8.12

8.13

8.14 8.15

8.16 8.17

Illustration of a theoretical temperature difference between the two media that exchange energy. All the ice is melted in the heat exchanger A district cooling system where CBE´s are used as intermediate heat exchangers between the central refrigeration unit and the buildings to be cooled Sketch of a laboratory test plant where a CBE was used with ice slurry as a condenser in a cascade system with propane in the top cycle and carbon dioxide in the bottom cycle. The installation is designed for a supermarket application. The condensing pressure of the carbon dioxide was two bar lower than with the original single-phase media Dimensions of the three different heat exchangers tested Sketch of test rig Heat transfer coefficients on the ice slurry side obtained for all three CBE´s and plotted against the Reynolds number based on average ice slurry properties between the inlet and outlet conditions. The ice concentration shown in the legend is the inlet condition – the outlet concentration is always 0 wt-%. The channel number, “ch”, denotes channels with ice slurry Heat transfer coefficients plotted against the heat flux and Reynolds number. R2 = 0.97 for the grid shown Accuracy of heat transfer correlation Pressure difference plotted against the Reynolds number. The ice concentration on the label shows the inlet condition – the outlet concentration is always 0 wt-% - and “ch” is short for channels with ice slurry Accuracy of pressure drop correlation Pressure drop data plotted against the heat exchanger capacity. The ice concentration in the legend shows the inlet condition – the outlet concentration is 0 wt-%. The comparison is made with equal temperature differences on both primary and secondary sides and equal mass flow rates on the secondary side Pumping power (Ptransport) required to transport the ice slurry through the CBE against the transferred heat capacity (Qperformance). The pump efficiency coefficient used to calculate the transport effect is assumed to be constant at 0.1 The relation between the Reynolds number and ice concentration where the flow begins to pulsate. If stable flow conditions are desired the point of operation should be above the dotted line. The experiments were carried out without any heat flux from the secondary side Sketch of test rig. The ice slurry air coil is labelled 1 Heat transfer results for both coils. The ice concentration shown in the legend is the inlet ice concentration. The outlet ice concentration varied from 0-25 wt-%. The Reynolds number was calculated based on the average ice slurry properties between the inlet and outlet conditions. Furthermore the heat flux also varied between the experiments Heat transfer results for both coils. The area refers to the inner surface area. The Nusselt number is the average of the inlet and outlet conditions Ice slurry side heat transfer results for both coils. The calculated values are based on the correlation described in section 8.1.4 and average fluid

357


8.18

8.19 8.20 8.21 8.22 8.23 8.24 8.25

8.26

8.27 8.28

CHAPTER 9 Figures 9.1

9.2

properties between the inlet and outlet. The air-side HTC is calculated from a correlation supplied by the manufacturer Pressure drop results. The pressure loss in the connections is at maximum 8 kPa and included in the values shown. The ice concentration shown in the legend is the inlet ice concentration. The outlet ice concentration varied from 0-25 wt-%. The Reynolds number was calculated based on the average ice slurry properties between the inlet and outlet conditions. Furthermore the heat flux varied between the experiments Comparison of measured and calculated pressure drop Comparison of internal heat transfer coefficients between a single-phase fluid and ice slurry. The outlet ice concentration varied from 0-15 wt-% Comparison of pressure drop between a singlephase fluid and ice slurry.The outlet ice concentration varied from 0-15 wt-% Illustration of appropriate/inappropriate header design Schematic of temperature development through a CBE and further downstream when superheating (SH) occurs Location of thermocouples at the outlet of 6 parallel passes, just before the return header. Thermocouple no. 3 was not used. There were 14 passes in all Surface temperatures of six outlet tubes in 29 experiments.The ice slurry temperature was measured with a Pt 100 probe in the liquid both at the inlet and outlet. Those two measurements are labelled as “Ice On” and “Ice Off” respectively. SH stands for superheat and is the only measurement that refers to the right y-axis. The number at the top of the diagram identifies the number of experiments. Hence the data points in the columns under each number (1-29) correspond to one experiment Super-heating of carrier fluid at the outlet. The parameter on the x-axis is the melt off rate, and the ice concentration in the legend is the inlet concentration. The numbers 3/8 and 12 identify the two different air coils tested and refer to the diameter of the tubes Superheating (SH) of the carrier fluid in all the CBE experiments plotted against the average Reynolds number The experimental results on time dependency in the C-type (B5) heat exchanger (CBE) with constant mass flow rate and full melt off from an inlet concentration of 20 wt-%. Heat transfer coefficient (HTC) refers to the left y-axis labelled “h” and the superheat refers to the right y-axis labelled “SH”

Possible arrangements of a HFM-based freezing system combining the advantages of both air fluidization and immersion food freezing techniques (Fikiin and Fikiin, 1998, 1999a): (1) charging funnel; (2) sprinkling tubular system; (3) refrigerating cylinder; (4) perforated screw; (5) double bottom; (6) perforated grate for draining; (8) sprinkling device for glazing; (7 and 9) netlike conveyor belt; (10 and 11) collector vats; (12) pump; (13 and 14) rough and fine filters; (15) cooler of refrigerating medium; (16) refrigeration plant Experimental temperature histories during HFM freezing of some kinds of (a) fish and (b) vegetables, when using sodium chloride solution (without

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9.3 9.4 9.5 9.6 9.7

9.8

9.9

9.10

CHAPTER 10 Figures 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 10.10 10.11 10.12 10.13

ice slurry) as a fluidizing agent (Fikiin, 1992; Fikiin and Fikiin, 1998, 1999a) Different foods immersed in slurries with various ice concentrations: (a) fruits; (b) vegetables; (c) chickens; (d), (e) and (f) fish (Fikiin et al., 2002) Schematic diagram of an ice-slurry-based hydrofluidization system HyFloFreeze® (Fikiin and Fikiin, 1998, 1999a) HyFloFreeze® prototype: hydrofluidized bed of highly turbulent ice slurry(Fikiin, 2003) Fish chilling in ice slurry (Fikiin et al., 2002): (a) land-based systems and (b) on-board systems (Liquid IceTM, Brontec, Iceland) Enthalpy-temperature curve from differential scanning calorimetry of cod fillets (Sørensen and Spange, 1999) and calculated thermophysical properties Variation in centre temperature (left graph) measured in an artificial fish model (43 mm diameter) cooled in a container with ice slurry at –3°C and with flake ice at 0°C, together with calculated temperatures (initially 20% ice in the container). Temperature measurement (right graph) in horse mackerel cooled in a container with ice slurry and with flake ice (initially 15% ice in the container) Dimensionless apparent viscosity, η* = ηis / ηl, and thermal conductivity, k* = kis / kl, versus ϕi. (Note the symbol used for thermal conductivity in the figure follows the German symbol tradition, i.e. “λ” is used instead of “k”) Hydrofluidization, conveyor and driving systems of the HyFloFreeze® prototype (Technical University of Sofia and Interobmen Ltd.): (a) top view, (b) overall view

Some possible designs of an ice slurry system Functional scheme of the control of terminal consumer units Defrost system based on simultaneous defrosting of consumer units Example of a local defrost set up Thermal characteristics with main parameters of a water/ethanol mixture Use of the diagram presented in Figure 10.5 (cf. text) Some different possible strategies to control an ice slurry generator Different operational modes of ice slurry systems Ice concentration versus temperature and solute concentration for ethanol/water mixtures Absolute error in ice concentration measurements under industrial conditions when working with water/ethanol ice slurries Maximum error in the ice concentration determination versus the temperature for different operating conditions Operating range of an ethanol/water ice slurry system Operating range for an ice slurry loop working with an initial 10% ethanol/water mixture with a thermostat set point at –6°C ± 1 K

CHAPTER 12 Figures 12.1 CAPCOM building 12.2 A schematic diagram of the ice slurry cooling system

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12.3 12.4 12.5 12.6 12.7 12.8 12.9

12.10 12.11 12.12 12.13 12.14 12.15 12.16 12.17 12.18 12.19 12.20 12.21 12.22

A schematic of the Herbis building thermal storage system The “Techno-Mart 21” building (Information courtesy of P. Mueller Co.) One of the eight ice-slurry units (1,759 kW) installed in the building (Information courtesy of P. Mueller Co.) The inside of the tank showing spray nozzles at the top of the tank (Information courtesy of Paul Mueller Co.) Ice slurry generator discharge into the tank (Information courtesy of Paul Mueller Co.) Ice slurry generators at the Stuart Siegel Centre, Virginia (Information Courtesy of Paul Mueller Co.) Ice slurry machine on top of the storage tanks at the left of the picture and air cooled condensers at the right (Information Courtesy of Paul Mueller Co.) A schematic diagram of the ice slurry cooling system at Middlesex University An aerial view of the Kyoto Station Building Layout of the Kyoto Station Building Schematic diagram of the ice slurry plant at Kyoto Station Building Cooling rate of ice slurry compared to flake ice (Paul, 2002) The ice slurry system of the fish processing plant A schematic of the cheese processing ice slurry plant Load profile and storage tank capacity over a 24-hour period Circuit schematic of the brewery plant A schematic diagram of a supermarket ice slurry system High density ice slurry being discharged into display cases (Photo courtesy of Sunwell) Charging the unit Refrigerated body for delivery vans

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APPENDIX 5: LIST OF TABLES

CHAPTER 2 Tables 2.1 2.2 2.3 2.4 2.5

CHAPTER 3 Tables 3.1 3.2 3.3 3.4 3.5 3.6 3.7

CHAPTER 4 Tables 4.1 4.2 4.3 4.4

CHAPTER 5 Tables 5.1 5.2 5.3

CHAPTER 6 Tables 6.1 6.2 6.3

Critical radius and number of molecules per embryo for homogeneous nucleation of ice (Vali, 1995) Parameters E, B and C Effective particle diameters (Turian et al., 2002) Coefficients in equation (2.40) for k * k 1 General characteristics of the listed additives

Formulae for viscosities of Newtonian suspensions as a function of the volume fraction C of the solid phase (Darby 1986) Different models for laminar suspension flows (Darby, 1986; Hanks, 1986; Steffe, 1992) The maximum packing fraction of various arrangements of dispersed spheres (Barnes, 1989) Friction factors for Bingham, Power Law and Casson models. Laminar flow is assumed (Darby, 1986) Empirical correlations for the friction factor of ice slurry flows Coefficients for empirical correlations for initial concentrations of the additive ethanol (Kitanovski, 2002) Coefficients for empirical correlations for two different additives (from Table 3.5)

Some models for the effective thermal conductivity of suspensions Dimensionless numbers relevant to ice slurry fluid dynamics and thermodynamics Test parameters (after Jensen et al., 2000) Parameters of the experiments performed by Snoek and Bellamy (1997)

Typical specifications for ice slurry generators Percentage of ice instantaneously produced in different adiabatic and isentropic HPSF processes, obtained by mathematical modelling Approach to the experimental case. Supercooling and percentage of ice instantaneously obtained by a heat balance calculation

Centrifugal pumps tested with ice slurry; the manufacturer’s (Grundfos) product name/number is used List of components Pressure loss coefficients calculated with reference to the dynamic pressure in the actual cross section including the length of the fitting. For the reducer,

361


the reference dynamic pressure is downstream of the fitting. For the expansion, the reference dynamic pressure is upstream of the fitting. Danvak (1992) and VDI (1991) refer to the respective Danish and German engineering reference books

CHAPTER 7 Table 7.1

CHAPTER 8 Tables 8.1 8.2 8.3 8.4 8.5 8.6

CHAPTER 9 Tables 9.1 9.2 9.3 9.4 9.5

Ratio of effective heat transfer area

Measuring equipment Empirical values obtained to correlate heat transfer results Empirical values obtained to correlate pressure drop results Measuring equipment Coil dimensions Equivalent lengths of return bends. The values represent the equivalent length of each bend

Compositions and initial freezing temperatures of the studied solutions Coefficients of equation (9.5) Coefficients of equation (9.7) Coefficients of equation (9.9) Coefficients of equation (9.11)

CHAPTER 10 Table 10.1 Expected accuracy in measurements under different conditions

362

Michael Kauffeld Prof. Dr.-Ing. Michael Kauffeld, born in 1962, studied mechanical engineering at the University of Hannover, Germany and at the Catholic University of America, Washington, D.C. He holds a Master degree and Doctorate in mechanical engineering from the University of Hannover. Since 1986, he has worked with a variety of development projects within the field of refrigeration. First at the National Institute of Standards and Technology (NIST), USA, where he investigated energy savings through the use of zeotropic refrigerant mixtures in air conditioners and heat pumps. Then at the University of Hannover, Germany, where he continued to work with refrigerant mixtures and in addition studied the use of air as refrigerant. From 1992 to 1994, he was responsible for various heat exchanger development projects at a Norwegian aluminium manufacturer. He joined the Danish Technological Institute (DTI) in 1994, where he worked as project manager. Most of his work at DTI has focused on natural working fluids, such as air, water, ammonia, carbon dioxide, hydrocarbons and ice slurry. For 4 years, he acted as leader of the Ice Slurry Center, which joined the forces of fifteen companies, a university institute and the Danish Technological Institute in order to investigate the potentials of ice slurry in refrigeration systems. He has worked on the formulation of refrigerant management plans for Uruguay, Jamaica and Syria. Since 1997, he serves on the UNEP Refrigeration, Air Conditioning and Heat Pumps Technical Options Committee and served on the UNEP TEAP Task Force on Global Warming. He is president of the Ice Slurry Working Group and vice president of commission B2 of the International Institute of Refrigeration (IIR). Michael Kauffeld has written more than 100 scientific publications and filed several patents. Since 1 September 2002, he is professor for thermodynamics, refrigeration and air conditioning at the Karlsruhe University of Applied Sciences. Masahiro Kawaji Masahiro Kawaji is a Professor in the Department of Chemical Engineering and Applied Chemistry at the University of Toronto in Canada. He received B.A.Sc. from the University of Toronto in 1978, M.S. (1979) and Ph.D. (1984) from the University of California, Berkeley. After working on nuclear reactor thermal hydraulics research at the Japan Atomic Energy Research Institute for three years, he moved to the University of Toronto as an Assistant Professor in 1986. He became a full Professor in 1993 and served as an Associate Chair of his Department during 1995-97. In the past nineteen years at the University of Toronto, Professor Kawaji has conducted both fundamental and applied research covering various multi-phase flow and heat transfer problems including those related to HVAC and refrigeration, ice-slurry production and utilization, nuclear and chemical reactors, heat exchangers, Kraft Recovery boilers, mini and microchannels, and microgravity-related phenomena. His work has been published in more than 170 refereed journal and conference papers. He is a fellow of the Chemical Institute of Canada and received the Jules Stachiewics Medal for contributions to the heat transfer research. He is currently serving as vice-president of the Ice Slurry Working Group of the International Institute of Refrigeration (IIR), and a member of the scientific committees of the International Center for Heat and Mass Transfer and many international conferences. He is also serving as a regional editor of International Journal of Transport Phenomena and on the editorial boards of International Journal of Multiphase Flow and Journal of Process Mechanical Engineering. Peter W. Egolf Peter W. Egolf made an apprenticeship in the enterprise Gebrüder Sulzer AG in Aarau as a heating designer. Then he studied at the University of Applied Sciences of Central Switzerland, where he obtained his engineer’s diploma with a prize of the Swiss Association of Heating and Air-conditioning Companies. After working in an industrial R&D laboratory at Hesco in Rüti he studied physics at the Swiss Federal Institute of Technology (ETH Zurich). In 1984 he obtained his diploma contributing with a work in Dynamical Meteorology. Then he entered a R&D division at Gebrüder Sulzer AG in Winterthur, where he invented and investigated new (industrial) air conditioning systems. At an advanced age he had the opportunity to make a PhD in a Noble Laureate family (Nernst–Mendelsohn –Olsen–Rohrer) in low-temperature physics, studying nonlinear entropy and suface waves of superfluid He II. During this time he had a collaboration with I. Khalatnikov (Director of the Landau Institute for Theoretical Physics in Moscow) on the Langrange-Hamilton description of the free surface of the quantum fluid He II. During his PhD time, in 1988, he won a Research and Innovation Exhibition Award of the Swiss Federal Institute of Technology and obtained his PhD at this institute in 1990. After that a ten years employment at the Swiss Federal Institute for Materials Testing and Research followed in the field of energy and buildings. Egolf became a specialist for phase change materials (PCM) research, developing a macroscopic model: The Continuous-Properties Model for Melting and Freezing (1994) and obtained - together with Heinrich Manz – an award of building technology for a translucent solar wall system for day lighting and thermal heat storage with PCM. Also in 1994 he invented the Difference-Quotient Turbulence Model. In the same year he entered the field of research on ice slurries and he won in 1996, together with Joseph Brühlmeier and Osmann Sari, the Swiss Technology Award. Simultaneously they were awarded a Special Prize of the Swiss Bank Society for their approach to this environmental friendly technology. In 1998 Egolf created the Working Party on Ice Slurries of the International Institute of Refrigeration (IIR) and was its First President. Since 2000 he is the head of the Theory and Numerics Division (SIT) of the Thermics Institute at the University of Applied Sciences of Western Switzerland. Recently he initiated a second new Working Party of the IIR, namely on Magnetic Refrigeration (at Room Temperature), and he is currently serving as its President. He was a main organizer of eight scientific conferences. Furthermore, he is the regional French-Swiss coordinator of the Swiss national competence network BRENET and a regional Editor of the International Journal of Refrigeration. Egolf is a member of the Swiss Physical Society (SPG) and the Swiss Association of Cold (SVK). He is author of the IIR Technical Note on Ice Slurry, a Promising Technology. At present - for the Edition Elsevier - he is writing a book with a mathematical background and the title: Ice Slurries.

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