Engineering Data on Mixing

Engineering Data on Mixing by Reiji Mezaki, Masafumi Mochizuki, Kohei Ogawa

•

ISBN: 0444828028

•

Publisher: Elsevier Science & Technology Books

•

Pub. Date: January 2000

Preface This book is a compilation of the engineering data on mixing, which have appeared in the major technical journals of chemical engineering and bioengineering since 1975. That year marked the beginning of a period of rapid advancement in the science and technology of mixing, with rather reliable results for both theoretical and experimental studies. In addition, we have included some important earlier articles which have been and are still being referred to. Mixing is a basic technology important in a wide variety of industries. Many numbers of tanks equipped with various types of agitators have been used for mixing all kinds of materials since ancient times. Yet designs of both agitators and tanks still depend primarily on art and experience. In the light of this fact we felt that the data on mixing should be compiled and presented in a systematic manner for assistance in design and analysis of agitated tanks , and to provide easier access to mixing data for various engineering activities. Of course, computeraided searches of pertinent data bases can be of assistance to chemical engineers and bioengineers in their studies. However, computer surveys of data bases are sometimes timeconsuming and often costly. Furthermore inadequate selection of key words can jeopardize the searches. In view of these objections, we offer this book in the hope that it will be useful to those who desire to conduct an efficient and accurate survey of the mixing data of interest to them. No attempts were made to verify the mixing data given by the various investigators. We have simply indicated the limitations of correlations and data when they are available. The use of uniform units might have been appreciated by users of this book. However, we have elected to use the original units as given by the various authors, lest errors be introduced in the conversion process. In Chapter 1 we present a variety of results for the experimental measurements of flow patterns in stirred tanks. Most of the measurements were made by using modem LaserDoppler techniques. This chapter is useful for the prediction of flow patterns in tanks with many different geometries, various types of agitators, and fluids of diverse physical and rheological properties. Here can also be found valuable data for the validation of results obtained by CFD simulations. Chapters 2 through 5 deal with data for traditional chemical engineering subjects. In Chapter 6 we sununarize a number of scale-up relations developed over the years for various systems. They include liquid, solid-liquid, liquid-liquid, gas-liquid, and solid-liquid-gas systems. Chapter 7 provides data related to multiphase processes. We wish to call attention to two sections: Section 7.4.1 Drop size and drop-size distributions Section 7.4.2 Bubble size and bubble-size distributions These two subjects have not been treated systematically either in text books or in handbooks on stirred-tank mixing, although the results of both experimental and theoretical investigations have been reported on many occasions. Chapter 8 deals with gas-inducing mechanically agitated systems. The applications of this type of agitation system will become increasingly attractivefromthe standpoint of rationahzation of stirred-tank operations as well as environmental protection. A review of this book will reveal many important research subjects that fall in the domain of stirred-tank mixing. We examined over nine hundred technical articles published since 1950. From this activity we could draw two important conclusions: (1) First, about 95% of the results reported in those articles were obtained by employing vessels whose diameters were less than 0.5 m. In industry, vessels with appreciably greater diameters are in daily use, and many more vessels will be designed andfabricatedfor future use. In view of thisfact,much of the accumulated data and associated theory based on small- scale experiments will probably be

VI

inadequate for prediction of the performance of industrial-scale vessels. More data are undoubtedly needed to narrow the gap originating from this mismatch of equipment sizes. More specifically, advanced scale-up techniques, not rules, should be developed for precise prediction. In this respect it would be of great help if industries were cooperative in furnishing unsuccessful, as well as successful, examples of scale-up. (2) Secondly, there is a striking shortage of mixing data for systems in which highly viscous, non-Newtonian fluids are studied. It may be true that conventional agitated tanks are not satisfactory for such fluids. However, the authors of this book feel that many challenges still exist in this area. In this book we have excluded from consideration two important subjects related to mixing: reactions and crystallization in stirred tanks. Most of the articles treating those subjects were found to place more emphasis on the development of rate expressions for the reactions or crystallization. Here, we have aimed to compile data correlating process parameters with agitated-tank geometry and the physical properties of the relevant fluids. For this reason we feel that reactions and crystallization should be treated differently. It should be noted that several important journals issued in Russia, in Eastern Europe, and in the People's Republic of China were not considered in our search for mixing data. This is mainly because of difficulties in obtaining the original journals as well as the Englishlanguage versions. However, the authors sincerely hope that the pubhcation of this book will encourage other interested persons to compile mixing data published in the geographical regions mentioned above. Perhaps in this way some collaborative efforts will result in a substantially more complete compilation of engineering mixing data. It is inevitable that errors, omissions, and misunderstandings will arise in a work of this type. The authors will be grateful if readers would take the time and trouble to point these out to us. The authors would like to thank Professor R. B. Bird of the University of Wisconsin, who aided with advice and suggestions in reviewing and editing the title and preface to this book. Acknowledgment is also made to the staff members of Shinzan Sha, in particular, to Mr. K. Shinoe for his constructive advice during the preparation of the manuscript of this book, and to Ms. H. Tomita for the preparation of the camera-ready manuscript. Without their efforts this book could not have become a reality. August, 1999 Reiji Mezaki Masafumi Mochizuki Kohei Ogawa

Table of Contents

Preface, Pages v-vi Chapter 1 - Flow patterns, Pages 1-84 Chapter 2 - Mixing time, Pages 85-115 Chapter 3 - Power draw and consumption, Pages 117-238 Chapter 4 - Heat transfer, Pages 239-304 Chapter 5 - Mass Transfer, Pages 305-468 Chapter 6 - Scale-up rules, Pages 469-512 Chapter 7 - Other subjects related to multi-phase systems, Pages 513-731 Chapter 8 - Gas-inducing mechanically agitated systems, Pages 733-764 Author index, Pages 765-769

Chapter 1 . Flow patterns 1.1 Single phase Peters, D. C. and Smith, J. M., Ttans. Instn. Chem. Engrs., 45, T360 (1967) Fluid Flow in the Region of Anchor Agitator Blades Experimental apparatus Vessel Type: flat-bottomed Diameter: 12.08 in Height: 18 in Liquid contained Height: 14 in Impeller Type: anchor Width of agitator blade: 1.0 in Wall/blade clearance: runs2A 0.125 in runs2C 0.50 in Working fluids and their physical properties No. ^ (poise) p (g/cm^) 1 lubricating oil 1.5 - 2.5 0.865 2 lubricating oil 0.885 6.8 - 10.4 1.25 3 glycerol (3% water) 5.6 - 9.75 4 silicone oil (MS200) 125 - 131 0.96 0.98 290 ~ 318 5 silicone oil (MS200) n /j(gs" Vcm) p(g/cm^) 0.7 1.01 6 1% polyacrylamide (aq.) 2.12 - 2.57 0.46 - 0.54 7 2% 40.4 - 50.4 1.02 308-460 1.04 0.30 - 0.38 8 4% Reynolds numbers were computed using temperature-corrected viscosity data. F l o w measurement technique Photography 18 1 Results ' 1 ' ' « ' ' ' LJ-' f

Tank: 22.9 cm diameter Anchor: 19.5 cm diameter, 2.5 cm wide, 90 rev/min Fluid: Silicone oils, 60 poise and 180 poise

^^^-^^V^J t-

Velocity components perpendicular to radii, along. normal to, and at 30*^ to agitator blade

Hi)) ^^^Sr/w/y

t«t-

feCX^^^y^vy*!?^^^^

IS^^^^^r^'^^'

Velocity profiles andflowpatterns (Beckner, J. L., Ph. D. Thesis, 1965. University of Wales)

Chapter 1. Flow pattoms

\'-.

X

16 p.p.s. (some points at 8 p.p.s.) NiRe)=21A, Run3-2C-10

y

25.4 p.p.s. (some points at 12.7 p.p.s.) iV(i?«)=105.3, Run3-2C-30

33.4 p.p.s. and 63.4 p.p.s. i\^(/?e)=143.4, Run3-2C-60 Flow patterns with glycerol

1.1 Single phas«

^"

. . .

• . -^A* • .

/f.-

•

r''

*

. >r;*,

7

•..

'.

•M-Ji'.i'V^

•••..

y

.

/ 32.0p.p.s. N*(Me)=l2.9, Run7-2C-40

64.0 p.p.s (some points at 32 p.p.s.) iV*(/?^)=25.5, Run7-2C-80

'- -r - ^-. *

Note: Cxeneralized Reynolds numbers are based on a power law (expression for the shear rate/shear stress relationship as used by Beckner) Flow patterns with 2% aqueous polyacrylamide, 1 in. blade, 0.5 in clearance

/ 64.0 p.p.s (some points at 32 p.p.s.) N*(Jie)=3lA, Run7-2C-100

Notation a geometrical constant c clearance between blades and wall D paddle diameter DT tank diameter k usual power law characterization parameter n usual power law characterization parameter N rotational speed of stirrer p density of fluid /i viscosity of fluid

The normal Reynolds number: NiHe)=N^Dpln The Reynolds nimiber for power-law fluids: N*{Re)=N^~''D^p/[k[a(\-n)Y'\ a=37-120 C/DT

Chapter 1. Plow patterns

Cooper, R. C. and Wolf, D., Can. J. ofChem. Eng., 46,94 (1968) Velocity Profiles and Pumping Capacities for Turbine Type Impellers Experimental apparatus Vessel Type: flat-bottomed Diameter: 15 in Height: 20 in Baffle Number: 4 Width: IV2 in Impeller Type: 6 and 10 bladed turbines Dimension: Turbine No.

Blade diameter in.

Blade width in.

Blade length in.

No of Blades

1 2 3 4 5 6 7 8 9 10 11 12

3 4 5 6 9 9 4 4 4 4 4 4

0.6 0.8 1.0 1.2 1.8 3.6 0.6 1.0 1.2 1.4 1.6 0.8

0.75 1.0 1.25 1.5 2.25 2.25 1.0 1.0 1.0 1.0 1.0 1.0

6 6 6 6 6 6 6 6 6 6 6 10

Working fluids Water and air Flow measurement technique Hot-wire anemometry and three-directional pressure measurement

1.1 Siiigl* phas«

Results

J

2

.4

.«

.B

LO

Normalized radial velocity profiles for various turbine sizes and various rotational speeds in water.

Notation VR W Z

radial velocity component turbine blade width vertical distance

Radial velocity profiles at different radial distances (4-in. turbine in water).

Chapter 1. Flow patterns

Bourne, J. R. and Butler, H., Trans. Instn. Chem. Engrs., 47, Til (1969) An Analysis of the Flow Produced by Helical Ribbon Impellers Experimental apparatus Dimensions of vessels and impellers Type: flat-bottomed Volume: (1) 6 gals (2) 160 gals Geometry

The geometry of the helicalribbonmixer Summery of principal dimensions Impeller number 1 2 3 4 5

d (in) 10.303 11.030 11.142 11.370 34.34

d D 0.889 0.952 0.962 0.981 0.954

h D 1.06 1.06 1.06 1.06 1.06

W D 0.108 0.108 0.108 0.108 0.104

s D 0.345 0.345 0.345 0.345 0.345

Zo D 1.22 1.2L' 1.22 1.22 1.22

Working fluids and their physical properties Pseudoplastic fluids: aqueous solutions of sodium carboxy methyl cellulose (CMC) and hydroxypropyl methyl cellulose (Celacol) apparent viscosities 1 ~ 500 poise at concentrations up to 3 w/w% and shear rates of 1 3001/s

1.1 Single phase

Flow-measurement technique Observations of solid tracers and cine-photography Results

[T

p0-15

T"

Y

Y U

0-03 L

I

I

1

I

i

A*

xa Y4 4*0 D20

+ 30 X«0

0-15

_

/

/

7

vso 1

1 0-A

i

i 0-6

Is

0-09 h

Y Y Y

/ 1

J ,„-J.,..J

NOTE > No values of r^/Ni bclwtcn 0 ondOOS

X: Howflex SP D:2'95< Celacol

y;2'65%Celacol + :2-3% Celacol A; 2-0% Celacol Y: 1-65% Celacol

The distribution of axialfluidvelocities in the core for impeller 2 pumping upwards

Notation d D h N r Ri 5 Vt W Zo

Y

/

1

outside diameter of ribbon inside diameter of tank height of ribbon rotational speed of impeUer radial coordinate inside radius of ribbon pitch of ribbon axial fluid velocity width of ribbon static height of liquid in tank

1

'i X-t-

i

1

!

r---T— • r - —

0-03

X

V

Y Y

y

20A X40 i^AO 20 XS YCO X20 Y40 Y X O30 SX20 •f20 _ • A80 ^20 Y l AAO O30 o e+goao 3p V, YS X20 •''J, Y20 V«0 O30 V20 30 X a oso aso vioo oso 30o3o ^ 3 0 YIO 030 X20 X20 lOOA S^OW VW 20X O60 vco 0*0 AID

1

1

o-iep-

1

^

yi

Y

\"

Y Y Y Y Y

X

1

-t-

X+ X + XO X \ XX + x \ O x \ + X X X X \ /+ X+ X O X + \ / X X^ X X +X + \ /x+ + X+ X ^ X+ X+ X+ X + X X Xf + Xo X X X+ + X \ o o x+ X X^ O y ^ H -»ox / X

xAxo x j X

/

X

\ "H

Y x^l y / V/ X X

z/

X

H

\

\

. .

J 0-A

l_ . 1 0-6

1

J

_LAI

+ : impeller I X: impeller 2 o: impellers

The distribution of axialfluidvelocities in the core for impeUers 1,2 and 5 (6 gal and 160 gal tanks) pumping downwards

Chapter 1. Flowpatt«ms

Takashima, I. and Mochizuki, M.J. Chem. Eng. Japan, 4,66 (1971) Tomographic Observations of the Flow Around Agitator Impeller Experimental apparatus Vessel Type: flat-bottomed Diameter: 450 mm Height: 600 mm Liquid contained Height: 520 mm Baffle Number: 4 Width: 45 mm Impeller Type: radial flow turbine Diameter: 150 mm Number of impellers: 1 Number of blades on impeller: 8 Width of impeller blade (parallel to shaft): 34 nun Off-bottom clearance: 260 mm

Results

Flow profile in each sectional zone of various types of 8 blades turbine agitator

1.1 Single phas«

Double helical flow model for agitator blade Notation u tangential velocity at blade tip V absolute velocity of flow observed on the fixed coordinate Vr radial velocity of flow w relative velocity of flow observed on the rotating coordinate *P angle of the blade (see attached figure) Fb circulation of bound vortex around the blade 0 Vr/u flow coefficient CD angular velocity of impeller Subscript 2 outer point of flow from the impeller

Chapter 1.

10

Flow patterns

Murakami, Y., Fujimoto, K., Shimada, T, Yamada, A. and Asano, K.,/. Chem. Eng. Japan, 5,297 (1972) Evaluation of Performance of Mixing Apparatus for High Viscosity Fluids Vessel and impeller geometry

Impellers and vessels (a) anchor (b) paddle (c) helical ribbon (d) mixing apparatus with two agitator axes having multidisks Z>=12.2cm, H=D, rf=0.90D and 0.95A 6=0.1Z), 1)^=6.0 and 9.0 cm, /=0.5/)rf and 0.22Drf

Working fluids and their physical properties Liquid: aqueous solutions of com syrup Viscosity: about 200 poise

Flow measurement technique Photography

Results

t " II h t It I

0

0.5

h I i i I MM I 0 0.5 1.0

1.0

--*' V Q

XTTnd

*"•* V Q

Anchor-tangential velocity ll-H' RE - 0.07

11

[ol 1

j

XjlfUlDK

Sg

• /S>KP1 /"^ W?nfK 1

^Tind

Paddle-tangential velocity

Lfflll^

I

0 0.5 1.0 "adn

Helical ribbon (velocity profiles)

1.1 Single phase

11

Mixing apparatus with two agitator axes having multidisks (velocity profiles at a section 6 mm apartfromthe disk at 15 mm space intervals) ^CIRCULAR ANNULUS . KEILSPALT MASCHINEN CIRCULAR ANNULUS (ROTATING CYLINDER) ECCENTRIC

CYLINDERS

HELICAL RIBBON WITH SCRAPE MIXER WITH TWO AGITATOR AXES HAVING DISKS

|CL>

s

EXTRUDER

Q

\ -

C & R REACTOf ELICAL SCREki (NAGATA)

HELICAL SCREW (GRAY)

0.01 0.02 0.0^

0.1

1 -K , C / D ,

0.2 I/D^

Shear characteristics

Notation b blade width of helical ribbon, cm d impeller diameter, cm D vessel diameter, cm Dd disk diameter, cm gr gravitational conversion factor, g cm/G sec^ / distance between disks, cm n rotational speed, 1/sec Pv power consumption/unit volume, Gcm/seccm^ Vb, V2 tangential and axial velocity, cm/sec 77 liquid viscosity, poise K ratio of impeller diameter to vessel diameter

Chapter 1. Flow pattoms

12

Ito, S., Ogawa, K. and Yoshida, N.,/. Chem. Eng. Japan, 8,206 (1975) Turbulence in Impeller Stream in a Stirred Vessel Experimental apparatus Vessel Type: flat-bottomed Diameter: 312 mm Liquid contained Height: 312 mm Baffle Number: 4 Width: 10.4 mm Impeller Type: a standard six-bladed turbine Diameter: 104 nmi Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 26 nrni Width of impeller blade (parallel to shaft): 20.8 nmi Off-bottom clearance: 156 mm Working fluids and their physical properties an aqueous solutions of K4Fe (CKk and KaFe (CN)6. The kinematic viscosities of the solutions are the same as that of water Flow measurement technique Measurement of diffusional mass transfer rate using a multi-electrode Experimental conditions Impeller speed: 60,90 and 120 rpm Results

Notation r_ radial position, mm Ui mean velocity of i component, cm/sec UT impeller tip velocity, cm/sec 2 axial position, mm

65

75

85 95 105 r, mm

Turbulence intensity

Subscript r, z, G radial, axial, tangential component

t15

125

1.1

13

Van't Riet, K. and Smith, J. M., Chem. Eng. ScL, 30,1093 (1975) The Trailing Vortex System Produced by Rushton Turbine Agitators Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 44 cm (2) 120 cm Baffle Number: 2 Impeller Type: six-bladed disc turbine Diameter: (1) 17.6 (2) 48 cm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): Z)/4 Width of impeller blade (parallel to shaft): D/5 Working fluids and their physical properties Fluid: tap water and water/glycerin solutions Tracer: polystyrene particles (diameter 0.5 mm) Flow measurement technique Photography Experimental conditions Direction of Impeller speed: 5 rps Results

rototion

Schematic thee dimensional view of the trailing vortex pair.

Dirtetion

Schematic two dimensional view of theflowin the stirrer blade region. S, stagnation point.

Chapter 1 . Flow patterns

14 , Blode

>^=r/3, C=r/2, N=3Q0 rpm. (b) />=r/3, C=r/4, Ar=300 rpm

Notation T cylinder diameter, nmi

(a)

(b)

Chapter 1 . Flowpatt«ms

24

Kamiwano, M. Saito, E and Kaminoyama, M., Kagaku Kougaku Ronbunshu, 14,316 (1988) Flow Pattern and Apparent Viscosity of Pseudo-plastic Liquid in a Stirred Experimental apparatus Vessel Type: flat-bottomed Diameter: (1)0.1 (2)0.2 (3)0.3 (4) 0.4 m Liquid contained Height: (1)0.1 (2)0.2 (3)0.4 (4) 0.4 m Impeller Type: six-bladed flat turbine Diameter: (1) 0.05 (2)0.10 (4) 0.20 m (3)0.15 Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: (1)0.05 (2)0.10 (3)0.15 (4) 0.20 m Working fluid Pseudoplastic: 1.2 wt% aqueous solution of hydroxyethyl cellulose Experimental conditions Rotational speed of impeller (1/sec) (1)16.7 (2)6.88 (3)4.03 (4)2.72 Flow measurement technique Image sensor velocimetry Results

-I 1.4

V-2 =0.2 m, n=6.88s~*)

Notation D vessel diameter, m n impeller rotational speed, 1/sec R radius of vessel, m V flow velocity, m/sec Z height of vessel, m Subscript r, 9t, z

axes of cylindrical coordinate

-R=0.lVBottom o( vessel 0.5 m/5

Flow pattern represented by dimensional vector in r-z plane (D=0.2 m, «=6.88 s"*)

Chapter 1. Flow patterns

26

Winardi,S., Nakao, S. and Nagase, Y.,/. Chem. Eng. Japan, 21,503, (1988) Pattern Recognition in Flow Visualization around a Paddle Impeller Experimental apparatus Vessel Type: flat-bottomed Diameter: 460 mm Liquid contained Height: 400 ram Baffle Number: 4 Width: 40 mm Impeller Type: four-bladed paddle impeller Diameter: 160 mm Number of impellers: 1 Number of blades on impeller: 4 Width of impeller blade (parallel to shaft): 40 mm Off-bottom clearance: 200 mm Working fluid Water Flow measurement technique Photography Experimental conditions Impeller rotational speed: 120 rpm Results

//

x>-. \ .

-- .

Lli "^^

--

4

Icl ; »''

**••" \\i....

I

! I i

"^—1«

: J 5 \ \m.y' / I I-jJ / •

J

rrtS

I

...^^

(a) Discharge pattern, TD (b) Cross pass pattern, TP; x mark indicates disappearance of a particle from the impeller (c) Asymmetric Discharge patten, UD (d) Illustration of Weak Discharge patten, WD (e) Illustration of Weak Cross-pass patten, WP

1.1 Single phas«

27

Komori, S. and Murakami, Y.,AIChE Journal, 34,932 (1988) Turbulent Mixing in Baffled Stirred Tanks with Vertical-Blade Impellers Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.29 m Height: 0.7 m Liquid contained Height:/) and 2Z) Baffle Number: 4 Width: 0.029 m Impeller Type: four-bladed paddle Diameter: 0.145 m Number of impellers: 1 and 2 Number of blades on impeller: 4 Blade width: 0.029 m Blade thickness: 0.003 m ^^o^P A B C D E

S H H=2D H=2D H=2D H=^D H=D

im^ers 2 2 1 2 1

Working fluid Water Flow measurement technique Laser-Doppler velocimetry Experimental conditions Impeller speed: 60,120 and 150 rpm

^/^ 0.14--1.70 1.0 0.10-0.60 z

^-/^ 1.0 - 0.5L/Z) 0.06-0.90 0.10-1.50 0.5 (1.0 - 0.5L/Z)) 0.06 - 0.90

Chapter 1 . Flow p a t t o m s

28

Results 0.004

2S0 Afl-2.0s'^ on»1.0s*^ 200

O.OOC

o *- 150

L/0-0.2

tlg/D*1.0 1/0-0.3 VI>*^-2 hj,/0«0.425 ^

100

0.001 J 0.01

0.02

50h O

O

OL (Al

(Bl (C) (0) CxpertaenUI Group

0.04 ^0.0« ^0.08 0.10 0.20

(CI

Maximum (highest) mixing efficiency and minimum energy consumption for each experimental group

1 . * » . l I:..**-"*.Ill

3,..«V«*>N^^^I

];.......—;;] a::::!!" -*•

\3:»r»»«....,,. ''"-'ii j.'.*.»%*«...,^,.

in • e.i V D • 0.7

Velocity vectors and flow patterns in a double-impeller tank, H-2D, «=150 rpm (group A) (a) with lowest mixing efficiency, (b) with highest mixing efficiency

1.1 Single phase

29

Velocity vectors andflowpatterns in a double-impeller tank, H=2D, «=150 rpm (group B) (a) with lowest mixing efficiency, (b) with highest mixing efficiency 1 1 1 [ 1 11 i 11111 1 1surtlng Point il 11 {11 i 1 JJWHTTI

'i 11 ^n i 1 i 1 ^ij i 1 il LTI1111 (IIX1

'ft/ SMK

'1 W w iVw mII 1 111iII11 i1111 ;[illlJIJ||||/|| TTTrTTT^MTtvn

jJflTjT

m

•lii'inuiiii^i •llliSlllllli:!!

lUifmTmil^

PW™ iJirm]

1

j 1111 [ I TTl [TtJ 1

!| 1 1111 111 111 I'l ill J1 1111111 1M 1 III \TI\

3 m l

J^illJITriTnfllll iJinJIjLH

Tracer traveling path and lattices which indicate velocity-measiuement points in a double-impeller tank, H==2D, n=150 rpm (group A)

Notation D Ettox hb H L n P' 6 P- 6mn

tank diameter maximum value of mixing efficiency vertical distance between bottom of a tank and center of lower impeller water depth vertical distance between double impellers impeller rotational speed energy consumption minimum value of energy consumption P- 6

Chapter 1 . Flow patterns

30

Wu, H. and Patterson, G. K., Chem. Eng. Scu, 44,2207 (1989) Laser-Doppler Measurements of Turbulent-Flow Parameters in a Stirred Mixer Experimental apparatus Vessel Type: flat-bottomed Diameter: 27 cm Height: 27 cm Liquid contained Height: 27 cm Baffle Number: 4 Width: lO/T Impeller Type: six-bladed disk turbine Diameter: 9.3 cm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): D/4 Width of impeller blade (parallel to shaft): D/5 Off-bottom clearance: T/3 Working fluid Water Flow measurement technique Laser-Doppler velocimetry Experimental conditions Impeller speed: 100, 200 and 300 rpm Results 200 rpm r(cm) D 50 o 6.0 A 7.0 • 7.7 0 90 V J0.5

1 ))J3

•^•v>

>

I

>

I

0.1

02

0.3

0.4

09

0.$

07

08

Ua/U,ip

Mean radial velocity profiles at various radial positions.

Mean tangential velocity profiles at various radial positions.

1.1

Single phase

31 -T-

-r-

-r-

r»5cm total random O O too rpm

-^V,o

-0.05

0.00

0.05

0.10

0.15

0.20

000

Mean axial velocity profiles at various radial positions,

0.00

0.05

0.10

0.15

020

025

Profile of tangential turbulence intensity near the impeller tip.

0.30

0.05

0.iO

015

0.20

impeller diameter radical coordinate tank diameter fluctuation velocity mean velocity impeller tip velocity impeller blade width axial coordinate

0.30 0.35 Ur'/Uiip

Profile of radial turbulence intensity near the impeller tip.

055

0.00

0.05

0.10

015

020

025

030 035 u;/u,ip

Profile of axial turbulence intensity near the impeller tip.

Notation D r T u U Uiip w z

025

1 Subscripts r, 6,2 radial, tangential, axial 1 Superscript root-mean-square value

Chapter 1 . Flow patterns

32

Ranade, V V and Joshi, J. B., Ttam. Instn. Chem. Engrs., 68, Pirt A. 19 (1990) Flow Generated by a Disc Turbine: Part I Experimental Experimental apparatus Vessel Type: flat-bottomed Diameter: 300 and 500 mm

Baffle Number: 4 Width: r / 4

Impeller Type: six-bladed disc turbine Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: H/2 Vessel Impeller diameter, diameter, Z), nmi r, mm 300 100 500 168

Disc diameter,

Disc thickness,

Blade thickness.

mm 67 117

mm 2.7 3.7

mm 2.0 2.7

Blade width=i)/5. Blade length=Z)/4. Hub diameter=25 mm. Hub height=25 mm. Shaft diameter=19 mm.

Working fluid Tap water Flow measurement technique Laser-Doppler anemometry Results

0

0*1 0*2 0*1 0*4 0*1 0«l 0*7 0*t 0*1 OIMCMSIONLESS RAOIAL COOHOINATE , ( r- R,)/(l^fl, I

!•(

Radial profile of maximum mean radial velocity in the impeller stream.

1.1 Single phase

Curve

33

Reference

1 2 3 4 5 6 nt work

T mm 292 381 290 1,000 270 89 300

D mm 101.6 101.6 96.7 333.3 93.0 30.4 100.0

Measurement Technique Streak photography Hot wire anemometer Laser Doppler anemometer Hotfilmanemometer Laser Doppler anemometer Laser Doppler anemometer Laser Doppler anemometer

1. Cutter, L A.. \9&I,AIChEJ, 4:485. 2. Cooper, R. G. and Wolf, D., 1968, CanJCkem EngScu 46:96. 3. Van der Molen, K. and Van Maanen, H. R. E., 1978, Chem Eng Sci, 33:1161. 4. Drbohlav, J., Fort, L, Maca, K. and Placek, J., 1978, CoU Czech Chem Commun, 43:3148. 5. Wu,. H. and Patterson, G. K., 1987. Private Communications. 6. Chen, K. Y, Hajduk, J. C, and Johnson, J. W. 1988, Chem Eng Commun, 72:141.

0»%

0*2 0«} 0>4 0*f 0«« ••? 0*ft OtMCHSIOMLKSS RADIAL COOHOINATE f r - l t | ] / | l | . f l , |

Radial profile of maximum mean tangential velocity in the impeller stream.

Notation D impeller diameter, m H height of vessel, m N impeller rotational speed, 1/sec Q flow rate, mVsec r radial coordinate, m R tank radius, m Ri impeller radius, m T tank diameter, m U mean velocity, m/sec Utip impeller tip velocity, m/sec V tangential mean velocity, m/sec 2 axial coordinate, m

0 0.1 0-2 OO 0*4 0*S 0*1 MMCNStOflLESS RADIAL COORDINATE (r-R||/(R-R|)

Radial profile of radial pumping capacity.

Chapter 1. Flow pattoms

34

Kaminoyama, M., Saito, F. and Kamiwano, M.J. Chem. Eng. Japan, 23,214 (1990) Flow Analogy of Pseudoplastic Liquid in Geometrically Similar Stirred Vessels Based on Numerical Analysis Experimental apparatus Dimensions of vessel and impeller Vessel type: flat-bottomed Baffle: non-baffle Impeller: (1) six-bladed turbine Number of impeller: ( 1 ) 1

(2) paddle (3) anchor (2) 1 (3) 1 onolysed region

analysed region

'fh d/DaO.5 H/D-1.0 H/D=0.5 bw/D=OJ bl/D=0.125 ds/O = 0.0^

.Ks21 H/D«1.0 h 70=0.5 ds/0 = 0.0^

P-j (a) onolysed region

Ks20

Ksit

I• 112

d/DsO.9 H/0=:1,o bwl/DsO.l bvv2/D=0l tt»'2 ds/DsQ.O^

Schematic diagrams of mixers and analyzed regions: (a) turbine impeller mixer; (b) paddle impeller mixer; (c) anchor impeller mixer

1.1 Single phase

35

Working fluid A highly viscous pseudoplastic Ellis liquid Computational results

1t

shofl

vessel wall

impeller

O.Sm/5

J=l

I.OwA

J=A (a)

K=n

K= l (b)

Velocity vector distributions in turbine mixer (Z)=0.2m,«=3.33s"'): (a) on r-z plane a t / = l and 4; (b) on r-0 plane at/C=l and 11

Velocity vector distributions in paddle mixer (Z>=0.2 m, «=3.33 s *): (a) on r-z plane a t / = l and 4; (b) on r-d plane at ^=11 and 21

Chapter 1 . Flow patterns

36

Velocity vector distributions in anchor mixer (Z)=0.2 m, «=0.83 s *): (a) on r-z plane a t / = l , 5 and 9; (b) on r-0 plane at/C=l, 11 and 20

Notation hi blade length bw blade width impeller diameter d ds shaft diameter D vessel diameter h impeller height (off-bottom clearance) H liquid height / mesh number in Q direction K mesh number in z direction 0) rotational speed

1.1 SingI* phase

37

Jaworski, Z., Nienow, A. W, Koutsakos, E., Dyster, K. and Bujalski, W, Trans. Instn. Chem. Engrs., 69, P^t A, 313 (1991) An LDA Study of Turbulent Flow in a Baffled Vessel Agitated by a Pitched Blade Turbine Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.146 m Liquid contained Height: 0.146 m Baffle Number: 4 Width: T/10 Impeller Type: 45° pitched bladed turbine Diameter: T/3 Number of impellers: 1 Number of blades on impeller: 6 Projected height of impeller blade: D/5 Off-bottom clearance: 7/4 or T/2 Working fluid Water Flow measurement technique Laser-Doppler anemometry Experimental conditions Impeller speed: 101/sec Temperature: 20°C Reynolds number: 24,000 Results Notation C impeller off-bottom distance, m H liquid depth in vessel, m R dimension less radial coordinate T vessel diameter, m V dimensionless mean velocity V dimensionless r.m.s. fluctuating velocity Z dimensionless axial coordinate Subscripts R radial component RZ dimensionless resultant for (r-z) Z axial component

Dimensionless velocity profiles for C/H=l/4: (a) VR against Z ; (b) Vz against R.

33

Chapter 1. Flow patterns

Dyster, K. N., Koustakos, E., Jaworksi, Z. and Nienow, A. W, Trans. Instn. Chem. Engrs., 71, P ^ A. 11 (1993) An LDA Study of the Radial Discharge Velocities Generated by a Rushton Turbine: Newton Fluids, J?e > 5 Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.150 m Liquid contained Height: 0.150 m Baffle Number: 4 Width: r / 1 0 Impeller Type: six-bladed Rushton turbine Diameter: T/3 or T/2 Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): D/4 Width of impeller blade (parallel to shaft): D/5 Off-bottom clearance: T/2 Working fluids and their physical properties ^, J ^*"^^ Water Polyethylene glycol Glucose solution Glycerol solution 100% Glycerol

Refractive Index 1.333 1.359 1.475 1.457 1.471

Density (kg/mO 1,000 1.064 1,330 1,260 1,260

Viscosity (Pasec) 1X 10~^ 8.85 X10"^ 105x10^ 0.248 1.16

Flow measurement technique Laser-Doppler anemometry Experimental conditions Impeller speed: 50 -^ 800 rpm Results

W

(I)

Flow pattern (vector plots) generated by disc turbine-disc turbine (DT-DT) combination.

No. A B C D E F

C,m 0.2 0.1 0.15 0.2 0.15 0.112

IC,m 0.05 0.1 0.1 0.1 0.15 0.225

Nomenclature DDl DD2 DD3 DD4 DD5 DD6

1.1 Single phase

43

, ^ . . N \ \ \

\lt il 1

H "

fTT/TliiiJ //Ut MM I

lY|U''"

v\\

•;,

•lli ^//i

Iff/j////,. M

1

||l\lliw •'

1 Ml 111 /111 m .

nii/j///i..j

l/lli//// nwwvv

I Ml///""

l-'-^

rrrAi) if,.,'l\ innnii 1 Mj \ / u n M M.

% //

Flow pattern (vector plots) generated by disc turbine-pitched blade downflow turbine (DT-PTD) combination. No. 1 2 3 4 5 6

C,m 0.2 0.1 0.15 0.2 0.15 0.112

/Cm 0.05 0.1 0.1 0.1 0.15 0.225

Nomenclature DPI DP2 DP3 DP4 DP5 DP6

Notation C D H IC N Np P T w p

clearance of the bottom impeller, m or mm impeller diameter, m height of liquid from bottom, m or mm clearance between the centers of the two impellers, m or mm impeller speed, 1/sec power number, P/N^D^ impeller power consumption, W vessel diameter, m blade width of PTD, m liquid density, kg/m^

Chapter 1. Flow patterns

44

Moore, L. R T, Cossor, G. and Baker, M. R., Chem. Eng. Sa., 50,2467 (1995) Velocity Distributions in a Stirred Tank Containing a Yield Stress Fluid Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.147 m Baffle Number: 4 Width: 0.0147 m Impeller Type: (1) 45° pitched blade with six-blades (2) a six-bladed standard Rushton disc turbme Diameter: (1)49 mm (2) 50 mm Number of impellers: (1) 1 (2) 1 Number of blades on impeller: (1) 6 (2) 6 Length of impeller blade (perpendicular to shaft): (1) - (2) 12.5 nmi Width of impeller blade (parallel to shaft): (1) 6.8 nun (2) 10.0 mm Thickness of impeller blade: (1) 1.5 mm (2) 1.5 mm

Working fluid and its physical properties an aquenous solution of 0.17 wt% of a carboxy-vinyl polymer Model

Yield stress Ty

Herschel-Bulkley Power law

18.9 Pas

4.6 12.1

0.46 0.29

Flow measurement technique Laser-Doppler velocimetry

Results

Radial distribution of radial velocity for the pitched-blade turbine: (D)z*=0.41; (O)z*=0.24; (+)2:*=0.0; (•)z*=-0.24; (•)z*=-0.41.

1.1 Single phase

Radial distribution of axial velocity for the pitched-blade turbine: (n)z*=0.41; (O)2:*=0.24; (+)z*=0.0; (•)z*=-0.24; (•)z*=-0.41.

Radial distribution of tangential velocity for the pitched-blade turbine: (n)z*=0.41; (O)z*=0.24; (+)z*=0.0; (•)z*=-0.24; (•)z*=-0.41.

Notation D impeller diameter, m r radial coordinate r* dimension less radial coordinate, r/ru dimensionless r\ impeller tip radius, m T tank diameter, m z* dimensionless axial coordinate

45

46

Chapter 1. Flow patt«ms

Mavros, P. Xuereb, C. and Bertrand, J., Trans. Instn. Chem. Erie's., 74, Part A, 658 (1996) Determination of 3-D Flow Fields in Agitated Vessels by Laser-Doppler Velocimetry: Effect of Impeller TVpe and Liquid Viscosity on Liquid Flow Patterns Experimental apparatus Vessel Type: dish-bottomed Diameter: T Height HiH^T Baffle Number: 4 Width: T/IO Impeller Type: (1) a standard Rushton turbine (RU) (2) a three-blade Lightnin A310 (3) a MixelTT agitator

c (a)

^

^ ^

5

(b)

The Mixel TT agitator; (a) plane view; (b) front view. D=95 mm; blade height 24 mm Diameter, D: (1), (2), (3)Z)/r=0.5 Off-bottom clearance: T/3 Working fluid and its physical properties 1% (w/w) of carboxymethyl cellulose (CMC) T [mPa]=41.2 f'^'^ Flow measurement technique Laser-Doppler velocimetry

1.1 Single phase

47

Results

v/v;^^=o.4o I/ / '

' * \

\\»

II 11 • • I » • '

U I I M I ''^

\\ i * I '

•7TTH4T^ • / / / / / / ,. .//Ml I -

;;iiiiu (b)

(a)

**

I

•

t

V

•

.\N>^s;^

\\\

*^* \ \ \ \

^^=f

il

A\ ^

^/ // M / .;

(d)

(c)

(e)

(t)

Pseudo-2D maps of composite axial andradialvelocities, (a-^c) plain waterflowpatterns; (d~f) flow patterns in 1% CMC solution, (a, d) Rushton turbine; (b, e) Mbcel TT; (c, f) Lightnin A310

Chapter 1 . Flow patterns

48

0.20

•

'

'

1

— • — h • Ofh^+S

RU

—O-h-C-S

0.15 0.10

\

f S.

(•) "

0.05 fldgeof impalle r

0.00 •0.05 .n in 0.20

I

1

I

I

1

!

1 1. . 1 L,

'

I

'

•

'

1

i

'

'

1

1

1

•

1

•

> •

1

'

'

'

1

'

'

•

1

'

'

NRU --0—h.C-5

0.15

I

0.10 0.05

1 '

'

• i

' • ' 1

F

—O—NLA.h-C-5p

y » ^

0.40

1.

0.00

0.20 0.00

•dgeof impalier

>0.05 .n in

0.60

(b) i

'

—•—LA.h-C-5 W

-0.20

} ,

1

20

.

.

.

.

.

40

.

.

-0.40

I «

80

60 r(nim]

100

Axial velocity measurements for the Rushton turbine 5 mm above and beneath the agitator blades, (a) water; (b) 1% CMC solution 95 90 85

' I ' ' • 1 •••

1 •

- I

U

1 •t

1 1

i

20

III

1 • *

1

40

1

1

.

1

60 r|mmj

1

I

1

1

80

•

1

•

1

100

Axial velocity profiles 5 mm below the agitators; (a) Mixel TT; (b) Lightnin A310. TT, LA: water; NTT, NLA: 1% CMC solution

•'"T^

-NLA -NTT

80 75 70 65 60 55 100

(a) Radial velocity profiles off the edge (Ar=9.5 nun) of the impellers; (b) axial velocity profiles 5 mm above the agitator blades

Notation C impeller off-bottom clearance, m D impeller diameter, m hb agitator blade height, m T tank diameter, m V fluid velocity, m/sec Y shear rate, Hz Subscripts r radial tip tip

1.1 Single phase

49

Rutherford, K., Lee, K. C, Mahmoudi, S. M. S. and Yianneskis. M.^AIChE Journal, 42,332 (1996) Hydrodynamic Characteristics of Dual Rushton Impeller Stirred Vessels Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 294 mm (2) 100 mm Liquid contained Height: (1)294 mm (2) 100 mm Baffle Number: 4 Width: 0.1 T Impeller Type: Rushton impeller Diameter: T/3 Number of impellers: 2 Number of blades on impeller: 6 Impeller clearance and separation: 01=0.257 and C2=0.50T; 01=0.337 and €2=0.337; 01=0.157 and C2=0.50r Working fluid Distilled water Flow measurement technique Flow visualization and Laser-Doppler anemometry Experimental conditions Impeller rotational speed: 250 rpm (Vi^^=1.28 m/sec) in vessel (1) 2,165 rpm (Vi,>=3.77 m/sec) in vessel (2) Results VHP

^ .\ , .

• / • I

' *

» V * J

w 111 ' '/ ' '/ "

•^

^ f

S.'
C:--'' Vector plot of mean velocity vectors in the R-Z plane for CHE3.

•jMfcJ>Jil»5MML-J

Vector plot of mean velocity vectors in the R-Z plane for PMT.

0.2 r 0.0 ^

^2 y?9W W M . f ? 999

2..

N

>

Fluctuating velocity profiles for CHE3.

Fluctuating velocity profiles for PMT.

54

Chapter 1. Flow patterns

Notation D impeller diameter, m H liquid height in tank, m N impeller rotational speed, 1/sec r radial coordinate, m R dimensionless radial coordinate, r/T, dimensionless T tank diameter, m d mean velocity, m/sec V' rms fluctuating velocity, m/sec V dimensionless mean velocity, v/nDN, dimensionless V dimensionless rmsfluctuatingvelocity, v'/nDN, dimensionless z axial coordinate, m Z dimensionless axial coordinate, z/H Indices R radial component T tangential component Z axial component

1.1 SingI* phase

55

Hockey, R. M. and Nouri, J. M., Chem. Eng. Sd., 51,4405 (1996) Turbulent Flow in a Baffled Vessel Stirred by a 60° Pitched Blade Impeller Experimental apparatus Vessel Type: flat-bottomed Diameter: 294 mm Liquid contained Height: 294 mm Baffle Number: 4 Width: 29.4 mm Impeller Type: 60° pitched blade impeller Diameter: 98 mm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 49.0 mm Projected width of impeller blade (parallel to shaft): 18.5 mm Off-bottom clearance: 98 mm Working fluids water and two mixtures of water and maltose syrup Flow measurement technique Laser-Doppler velocimetry Experimental conditions Reynolds number (/?e=Z)^Wv)=48,000 Results

\i i

111111

& ^ ::^.

I 0.0

•

T" 1.0

2.0

3.0

Meanflowvelocities for Reynolds and power numbers of 48,000 and 2.2, respectively, in Q ^O"* plane: (a) axial and radial velocity vector; (b) tangential velocity profiles.

Chapter 1. Flow patterns

56

Notation D H N r R Vt z V

impeller diameter, m liquid height in the tank, m impeller rotational speed, 1/sec radial distance from the center of the tank impeller tip radius, m impeller tip velocity, itND, m/sec axial distancefromthe bottom of the tank fluid kinematic viscosity, mVsec

0.0

1.0

^ r/R

2.0

"1 3.0

Radial and tangential mean velocity vector mr-d plane for Reynolds and power numbers of 48,000 and 2.2, respectively, at different axial positions: (si)z=0,27H: (b)z=0.17^; ic)z=0.068H.

1.1 Singte phase

57

Harvey, A. D., Wood, S. R and Leng, D. E., Chem. Eng. Sci., 52,1479 (1997) Experimental and Computational Study of Multiple Impeller Flows Experimental apparatus Vessel Type: ellipsoidal-bottomed Height: 55.88 cm Baffle Number: 4 Width: 3.157 cm Thickness: 0.635 cm

Impeller

Type: 45° pitched-blade impeller Number of impellers: 4 Number of blades on impeller: 4 liquid level

baffle

4H

'Shaft

a) 2^2=3.58 Impeller 4(14)

b)z/Ra«353 c)z/R,=:2.89

]

d)2/R,»2.55

impeller 3 (IJ e) z/Rj= 2.21 f)2/Rj«1.87 g)z/R2-1.53

2(y h)z/Rj«1.19 Impeller dimensions and positioning for easel T „ _ Blade X-section ^P^"^' axu;)(cm)

1

r/R,

Schematic of multiple impeller configuration

1 2 3 4

0.318x1.75 0.318x4.13 0.238x2.54 0.318x2.54

Diameter (cm)

Height (cm)

9.207 22.860 17.780 12.383

5.73 18.82 30.73 42.48

Chapter 1. Flow patterns

58

Working fluid and its physical properties 85% (vol/vol) com syrup (viscosity = 928 cP; density = 1,000 kg/m^)

Flow measurement technique Laser-Doppler velocimetry

Experimental conditions Impeller rotational speed: 92 rpm

Results experiments

computations CASE1

|a)2/Rag3.58 b)2ma»3.23 C)zm,«2.89

/////"• //////^"

d)2m,«2.5S e)2/R,«2.21

]f)^^-

1.87

g)2ma«1.S3 h)z/Rgs1.19

Comparison of computed (left-handside) and experimental (right-handside) velocityfieldsfor case 1

1.1 Singl* phase

59

Case 1 velocity profiles for axial stations a-h

Notation / w

thickness of blade, cm width of blade, cm

60

Chapter 1. Flow patterns

Tanguy, R A„ Thibault, E, La Fuente, E. B-De., Espinosa-Solares, T. and Tecante, A., Chem. Eng. Sci., 52,1733, (1997) Mixing Performance Induced by Coaxial Flat Blade-Helical Ribbon Impellers Rotating at Different Speeds Experimental apparatus Vessel and impeller geometry

Mixer dimensions

Working fluids and their physical properties Aqueous Solutions of CMC, Gellan, and Xanthan n (shear thinning index) = 0.26 -- 0.64 consistency index = 2.95 — 21.55 Pas" density = 1,020 kg/m^

Circulation in the vicinity of the Rushton turbine

1.1 Singl* phas«

61

Computational Results

(a) Dispersion pattern induced by the dual impeller mixer. (b) Dispersion pattern induced by the helical ribbon only

0.04

?E

0.03 0.02 0.01

1 1 ^

0.00 -0.01 -0.02 -0.03 -0.12

-0.08

•0.04

0.00

0.04

0.08

0.12

0.08

0.12

Position (m)

(a) 0.04

t

0.03 0.02 f 0.01

I

0.00

(9

-0.01




..nil ^ ^ . / / M l 1 ..)

Feedingtube plane

90°-rotalcd plane

Batch (no flow)

Composite U„flowpattern; Rushton turbine, N=3 Hz, QL=6.41 min

30

1.1 Single phase

65

V/VHP=-OAO

Feedingtube plane

90°-n)tated plane

Batch (no flow)

Composite U„flowpattern; Mixel TT agitator, N=3 Hz, QL=SAI min *.

Notation N impeller rotational speed, Hz QL waterflowrate, ^/min U instantaneous velocity value, m/sec n mean velocity value, m/sec Vtip impeller tip speed, m/sec Indices r radial 2 axial q tangential

Chapter 1. Flow patterns

66

Schafer, M., Yianneskis, M., Wachter, R and Durst, F.,AIChE Journal, 44, 1233 (1998) Trailing Vortices around a 45° Pitched-Blade Impeller Experimental apparatus Vessel Type: flat-bottomed Diameter: 152 mm

Liquid contained Height: 152 mm Baffle Number: 4 Width: 15.2 mm Impeller Type: 45° pitched-blade impeller Diameter: 50 mm Number of impellers: 1 Number of blades on impeller: 4 Projected width of impeller blade: 10 mm Off-bottom clearance: 50 mm Working fluid and its physical properties Silicone oil (density = 1,039 kg/m^; dynamic viscosity = 0.0159 Pasec) Flow measurement technique Laser-Doppler anemometry Experimental conditions Impeller speed: 2,672 rev/min Results

Angle-resolved mean velocity vectors in the vicinity of the impeller blade in seven ^ planes: (a) 0=0^; (b) 0=2''; (c) 0=8«; (d) 0=30^

1.1 SingI* phase

67

0.5 v^

0.26 0.20

0.00

td)

Angle-resolved mean velocity vectors near the blade in four planes inclined at 45** to the horizontal plane. Each of these planes intersects the followmg ^ plane at midblade: (a) 0=80'* (-lO**); (b) 0=0**; (c) 0=4*»; and (d) 0=15^

Chapter 1 . Flow p a t t « m s

68

0.4

3.00-n

,

If

z/T

2.50 J

r/T

0.3 H

2.O0J I.50J

0.2 Jpeno^^oo^^oo^^^o^^^^^^^^ 0.1 H

i.ooJ

ii

0.50 J

^ ^ ^ ^ ^ t ' M i l l i-rn

0

20

40

1 60

1 80

Blade angle [°] (a)

r 100

120

0 00-i 0

50

100

J 15

Blade angle [°] (b)

(a) Variation of the nonnalized coordinates rIT, z/T of the vortex axis with blade angle 0; (b) variation of the vortex radius nonnalized with distance from the blade along the vortex axis {r*/d') with blade angle 0; (c) isosurface of vorticity at the edge of the trailing vortex behind an impeller blade.

Notation d' distance from the blade along the vortex axis, m D impeller diameter, m N impeller rotational speed, 1/min r radial coordinate: distance from the axis of the vessel, m r* trailing vortex radius, m T vessel diameter, m VHP impeller tip speed, nND/60, m / s e c z axial coordinate, m 0 the blade; 0 = 0 ° is the vertical plane through the middle of the leading blade

69

1.2 Multi phase 1.2.1 Solid-liquid systems Gosman, A. D., Lekakou, C, Politis, S., Issa, R. I. and Looney, M. K.,AIChE Journal, 38,1946 (1992) Multidimensional Modeling of Turbulent IWo-phase Flows in Stirred Vessels Experimental apparatus Vessel T)rpe: flat-bottomed Diameter: 0.294 m Liquid contained Height: 0.294 m Baffle Width: 0.0294 m Impeller Type: disc turbine Diameter: 0.098 m Number of impellers: 1 Off-bottom clearance: 0.098 m Working fluid, solid and its physical properties Fluid: water Solid: glass particles; density = 2,950 kg/cm^; mean diameter = 232.5 pm Computational conditions Impeller speed: 300 rpm Solid concentration: 0.02% Results

• * • • • • • •

I I '

'

•:•

i i i i i i i t « \ \ \ \ \ i t

« I

f I

I

I

I

I I I t t t \ \ t I

I I I

I t I

i

I M ' ' I * « t I I I I I I I 1111 n u M i 1/ / ' '•• ^ » M I I I I 11 M n 11 I I 11

I//'

M t l I I I M M t 11 I I i i I

1/ / ' . ' : • ' M I I I I I M I I I I I I M I I / I •:• ' I / I I I 1'i' / / / / I

\ \ -i' / / / / / ( \ \ ^t- ^ / / / I

i I t I n u l l I I 11 I M 1 M I 1 I I I II I 1 n i I I I 1 I II

\1'^-^-+ l^--

iaaa,j

/ '^^^\\ \ \ \ \\

' ' •*M \ \ \ \ W I \ *:• • M I I I 1 1 WW l \ \ - i - ' / / / / / I MIWI \ \ \ -;- - X / / / / / / M I I I \ \ \ N ^ | - . ^ ^ x / / / / / / / n 11II I I I \\\-^-J

^^y^^^y

% \ >.^-;,,

• • - ^ ^ ^ ^ ^ ^ > » • • • • / / / f t /

///

/ f/ ;/ I M M I

Velocity vectors @ 6=0°; scale: -* =0.82 m/s.

II

Chapter 1. Flow p«tt«ms

70

Velocity vectors @ jc=0.908ft scale: -> =0.15 m/s.

Velocity vectors @ x=Q.3H; scale: -> =0.63 m/s.

Notation /f Height of mixing vessel

1.2 Multiphase

71

Computational results 0.2S' Cro-

O O

ats-

0.10o 0.0S-

>^

O

_-.a

0.00-

.0.2

0.0

0.2

0.4

0.0

0.0

1.0

Mean velocity comparisons: (a) above the impeller @ Jf=0.1203 m (axial); (b) below the impeller @ jc=0.0757 m (axial); (c) impeller stream @/?=0.0515m (radial). o Nouri (1992). -o- predicted solid phase, — predicted liquid phase.

rms velocity comparisons: (a) above the impeller @ x=0.1203 m (axial); (b) below the impeller @ jc=0.0757 m (axial); (c) impeller stream @/?=0.0515m (radial). o Nouri (1992). -a- predicted solid phase, — predicted liquid phase.

Nouri, J. M. and Whitelaw, J. H., Int. J. MuUiphaseflow, 18,21 (1992).

72

Chapter 1. Flow pattoms

Pettersson, M. and Rasmuson, A. C.,AIChE Journal, 44,513 (1998) Hydrodynamics of Suspensions Agitated by Pitched-Blade Turbine Experimental apparatus Vessel Type: flat-bottomed Diameter: 210 mm Height: 210 mm Liquid contained Volume of liquid in vessel: 7 i Baffle Number: 4 Width: 22 mm Clearance of bafflefromwall: 7 nmi Clearance of bafflefrombottom: 8 mm Impeller Type: 45° pitched four-bladed turbine (downwards pumping) Diameter: 82 nun Number of mipellers: 1 Number of blades on impeller: 4 Length of impeller blade (perpendicular to shaft): 33 mm Projected height of impeller blade: 12 mm Off-bottom clearance: 70 mm Working fluid, solids and their physical properties Liquid: deionized water Solid: (1) seed particles: spherical metallic coated glass particles (density = 2.6 g/cm^; number mean size = 4 ^m) (2) process particles: glass beads (density = 2.42 g/cm^; mean size = 321 ± 9.6 ^m) Flow measurement technique Three-dimensional phase-Doppler anemometry Experimental conditions Impeller speed: 450,525, and 600 rpm Seed particles: 0.10 g; process particles: 0.06% by volume Results

Normalized 3-Dfluidmean velocity, N = 450 rpm.

1.2 Multiphase

73

80 100 0 (mm]

r 20 40 60 80 ndUl distance (mm]

100

Normalized rmsfluctuatingvelocities at A = - 1 0 mm. N = 450 rpm.

Normalized turbulent kinetic energy. N = 450 rpm.

3-D intensity of turbulence, N = 450 rpm.

Chapter 1. Flow patterns

74

-o-1^-A•«-

h=-30 mm h=-10mm| hslOrom h=30 mm

0.00H 0

40 80 radial distance [mmj

40 80 radial distance [mm]

radial distance [mm]

radial distance (mm] ^ 0.08 " i 0.06^ §

0.04 0.02

i" 0.00 J -fci^i 0

40 80 radial distance [mm]

Normalized Reynolds stresses. N = 450 rpm; ^ = 85°,

Notation Di

N Q

Tu U'i

u U'i'U'j

impeller diameter, m impeller speed, 1/sec turbulent kinetic enei:gy, mVsec^ 3-D intensity of turbulence, % normalizedfluctuatingvelocity, m/sec 3-D mean velocity, m/sec Reynolds stress, mVsec^ tangential component

»Hi-

-r 0 40 80 radial distance [mm]

1.2 MuKiphas«

75

1.2.2 Gas-liquid systems Ogawa, K., Yoshikawa, S. and Shiode, H., Kagaku Kougaku Ronbunshu, 18, 495 (1992) Flow Characteristics of Discharge Flow Region in a Stirred Vessel with Aeration Experimental apparatus Vessel Type: flat-bottomed Diameter: 312 mm Liquid contained Height: 312 mm Baffle Number: 4 Width: 31 mm Impeller Type: sixflat-bladeturbine Diameter: 104 mm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 26 mm Width of impeller blade (parallel to shaft): 20.8 mm Off-bottom clearance: 104 mm

Sparger Location: directly below the impeller Direction offlow:downwards

58 mm from vessel bottom

Working fluids and their physical properties Liquid: Kinematic viscosity (mVs) ion-exchanged water 1.03 x 10"^ 40 wt% glycerol aqueous solution 4.30 x 10~^ 60 wt% glycerol aqueous solution 4.30 x 10~® 0.5 wt% polyacrylamide aqueous solution (pseudoplastic viscosity = 0.132 Ns7m^; integer M = 0.647) Gas: air Flow measurement technique Electrode reaction velocimetry Experimental conditions Liquid

NiX/s)

0(^/min)

Test liquid

4

7 14 14 14

water, 40%G., 60%G., PAA water, 40%G., 60%G., PAA water, 40%G.,60%G., PAA water, 40%G., 60%G., PAA

5 6

Chapter 1. Flow patterns

76

Results

PA A no aeration

aeration

N=As-\0=lAI/min .,,

Contour line map of velocity for PPA aq.

r/D, l-l

0 0.5 r/0. l-l Velocity distribution for water

1.2 MultiphM*

77

^

Z1.2 o"

U

Oll/mtn)

1.^

Nn/&)

4

5

wQler

•

0

6 o

"T] l

o

h

Nl.O

0^

0.5 r/D, (-1

1.0

Relationship between axial position and radial position at where velocity takes maximum value for water Notation Di impeller diameter, m N impeller rotational speed, 1/sec Q airflowrate, i/min r radial position, m u velocity, m/sec Ut tip velocity of impeller, m / s e c Z axial position

Chapter 1. Plow patt«ms

78

Gosman, A. D., Lekakou, C, Politis. S., Issa, R. I. and Looney, M. K.,AIChE Journal, 38,1946 (1992) Multidimensional Modeling of Turbulent TWo-phase Flows in Stirred Vessels Experimental apparatus Vessel Type: flat-bottomed Diameter: 1.83 m Liquid contained Height: 1.67 m Baffle Width: 0.18 m Impeller Type: disc turbine Diameter: 0.915 m Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 0.41 m Sparger Air was injected from a 2.5 cm disc located on the vessel axis, 0.2 m from the base. Working fluids Liquid: water Gas: air Computational conditions Impeller speed: 70 rpm Air rate: 1,102 ^/min wall

Radial profiles of axial velocity at different axial stations @ ^=17.5**.

1.2 Multiphase

79

Gas phase profiles @ ^=15**; (a) jc=1.52 m; (b) Jif=1.04 m. D Revill and Irvine (1987), — predictions.

Gas phase profiles @ ^=15°; (c)ji:=0.41m;(d)x=0.12m. • Revill and Irvine (1987), — predictions.

Revill, B. K. and Irvine, K., ICI pec, private communication.(1987).

Notation X, r, 6 qrlindrical coordinate

Chapter 1. Flow patterns

80

Manikowski, M., Bodemeier, S., Liibbert, A., Bujalski, W. and Nienow, A. W, Can. J. ofChem. Eng., 72,769 (1994) Measurement of Gas and Liquid Flows in Stirred Tank Reactors with Multiple Agitators Experimental apparatus Vessel Type: flat-bottomed Diameter: 440 mm Height: S r Volume: 200 £ Number: 4 Width: 44 mm Clearance of bafQe from wall: 4.4 mm Impeller Type: (1) Rushton turbine (2) Rushton turbine (3) Lightnin A-315 impeller Diameter: (1) T/3 (2) 0.45 T (3) 0.43 r Impeller setup: three Rushton turbines turbine (1) x 3 two Lightnin impellers and one Rushton turbine impeller (3) x 2 + turbine (2) x 1 Location of impellers: |_

7S2

.

p.' i

1

r

[i

P

D

r' 1

1 i Vl52j r 1

D

.'•'l

4

»

«o

1 r^

D J

,

v^~

1012 1320

1 m

Schematic view of the stirred tank, dimensions in mm. On the left hand side of the impeller shaft, the gas sampling probe for gas transit tune measurements is shown. It can be moved parallel to the shaft On the right hand side, the arm is shown on which the probes of the ultrasound measuring device are mounted. The arm by which the probes can be swept between the reactor wall and the shaft isfixedto a steel tube attached to one of the bafQes, as shown on the right hand side of the figure. Sparger design Sparger position: fixed to the reactor bottom Holes: holes are arranged on a circle of 120 mm diameter

1.2 MuttiphaM

81

Working fluids and their physical properties Liquid: aqueous solutions of CMC Rheological properties of CMC solutions Concentration (% w/v) 0.8 1.2

K (Pas") 0.086 0.12

0.83 0.82

Gas: air Bubble velocity distribution measurement Ultrasound Doppler technique Experimental conditions Aeration rate: 4.0 mVhr (0.33 wm) Results 5 rev/s 6.7 rev/s

«J

8.3 rev/s

Rj

v\\\\\\\J

A 8J

8j

8j

iiwuV:' K\\\\\\\

\\\\\\\\

\\\\\\}

SJ

^J \\\\\\\\>^

^ i f

«J

RJ

KWWwi

\\\\\\\M

v[cm/sj

,.//

100

200

0

100

200

—r 200

Radius [mm] The patterns of the axial-radial components of the mean bubble velocities at 8.3,6.7, and 5 rev/s in a 0.2 % w/v CMC solution aerated at 4.0 mVh. Notation K consistency index, Pa(sec)'' n Flow behaviour index, dimensionless T tank diameter, m V mean bubble velocity, m/s y shear rate, 1/sec r shear stress. Pa

32

Chapter 1.

Plowpattams

Morud, K. E. and Hjertager, B. H., Chem. Eng. Scu, 51,233 (1996) LDA Measurements and CFD Modelling of Gas-Liquid Flow in a Stirred Vessel Experimental apparatus Vessel Type: dish-bottomed Diameter: 0.222 m Liquid contained Height: 0.222 m Volume of hquid in vessel: 7.5 i Baffle Number: 4 Width: O.ID Clearance of baffle from wall: 0.05Z) Impeller Type: six-bladed Rushton turbine Diameter: D/3 Number of impellers: 1 Number of blades on impeller: 6 Diameter of impeller disc: 0.243Z) Length of impeller blade (perpendicular to shaft): 0.09Z) Width of impeller blade (paraDel to shaft): 0.09Z) Off-bottom clearance: 0.47Z) Sparger Height: 0.108Z) Diameter: 0.108Z) Location: below the center hne of the impeller shaft Distance between the top of the sparger and the bottom of the vessel: D/5

Working fluids Fluid: distilled water containing 4 g NaCl/^ Gas: air

Flow measurement technique Laser-Doppler anemometry

Experimental conditions Impeller rotational speed (ppm): 360,400,540 and 720 Gas flow rate (WM): 0.09,0.49,0.75,1 and 1.33

1.2 Multiphase

83

Results

-I—•—I—'—r 0.2 0.4 0.6

0.0

0.8

1.0

(a)

Measuredradialgas velocity at the impeller height for different gas flow rates (a) Q=0.09 wm, (b) ©=0.49 wm. (c) Q=1.00 wm, (d) Q=1.33 wm.

g.e-

h«0.47 D 1.00 W M —4—720 RPM -e-540RPM — « ^ 400 RPM - B - 3 6 0 RPM

0.4-

2

0.2- ...

r,r'"

L-t-''-'-.

D

r:,-^

y^.-...'

0.0-

': :• 0 .0

,

'.-i'l-' '

1 02

•

1 0.4

'

1 0.6

'

1 0.6

• 1 .0

(c)

Measured axial gas velocity at the impeller height for different gas flow rates (a) Q=0.49 wm, (b) Q=0.75 wm, (c) ©=1.00 wm, (d) ©=1.33 wm.

84

h=0.72D 1.00 W M

-540RPM - 360 RPM

-L- 0.2 H

0.0

(a)

r'H

-I 0.2

(b)

'

1 0.4

'

1 ' '' I 0.6 O.B

1.0

rM-1

Measured tangential gas velocity at 1 wm (a) at the impeller level {h=0A7D), (b) above the impeller (h=0.72D).

1

Uog

T7

-Q H

(a)

Ho

t

Gas

(b)

(c)

GasflowrateQ=1.0 wm, (a) Vessel configuration, (b) Predicted gas pattern, (c) predicted gasfractioncontours.

Notation D h Ho 0 r R U V W Wiip U*

vessel diameter, m distance from vessel bottom, m initial liquid level, m gas flow rate, W M radial coordinate, m vessel radius axial velocity, m/sec radial velocity, m/sec tangential velocity, m/sec impeller tip velocity, m/sec U/WHP; F * = V/Wtip; W*= W/W^p;

r*=r/R

85

Chapter 2.

Mixing time

2.1 Single piiase Peters, D. C. and Smith, J. M., Can. J. ofChem. Eng., 47,268 (1969) Mixing in Anchor Agitated Vessels Experimental apparatus Vessel Type: flat-bottomed Diameter: 6,9 and 12 in Impeller Type: anchor Number of impeller: 1 Width of impeller blade: 1 in and 1.5 in Working fluid Polyacryl amide solution Measurement technique Use of iodine-thiosulfate reaction Results I2S CLEARANCE 2S'CLEARANCE so'CLEARANCE

40

40

fO

too

SPEED IN REVS/MIN. -

Mixing times for iodine-thiosulphate reaction (clearing). 1 % poly (acrylamide), 12-in. tank, 1-in. wide blade. *the blade-to-wall clearance.

Chapter 2. Mixing time

86

Carreau, P. J., Patterson, I. and Yap, C. Y., Can.]. ofChem. Eng., 54,135 (1976) Mixing of ^^scoelastic Fluids with Helical-Ribbon Agitators I — Mixing Time and Flow Patterns Experimental apparatus Vessel Type: (1) (2) flat-bottomed Diameter: (1) 6 (2) 10 in Height:(l)6 (2) 10 in Impeller Impeller

d (in.)

I II III IV V VI VII

5V8 5V8 5V8 4V8 5V8 8% 8%

h (in.)

ds (in.)

b (in.)

5%

V4 V4 V4 V4 V4

V,6 V,6 V,6 7,6 Vl6 V,6

5 3/8

5V8 5% 5V8 9V32 9V32

% %

—

Nt

D/d

l/d

w/d

p/d

2 2 2 2 1 2 2

1.11 1.11 1.11 1.37 1.11 1.11 1.11

4.48 3.00 4.12 4.00 4.39 4.44 4.69

0.0970 0.0970 0.195 0.121 0.0970 0.0990 0.0724

0.719 1.048 0.707 0.848 0.695 0.690 0.710

N.B. The blade of the impeller VII is made of circular tubing, all the others are made of flat ribbon. d - diameter of impeller h — height of impeller d, = diameter of shaft b = blade thickness Nh = number of blade D — inside tank diameter / = overall length of blade u) - blade width p = pitch .ds

2.1 Single phase

87

Working fluids and their physical properties Glycerol, 2% aqueous solution of sodium carboxyl methyl cellulose (CMC), and 1% aqueous solution of polyarylamide (Dow Chemical Separan AP-30) Properties of fluids Fluid

p, g/cm^ r]o, poises 9o, g/cm S R tu sec. A, sec*

Glycerol

2% CMC

1% Separan

1.25 5.68 — — — —

1.0 100.0 106.0 0.243 0.702 1.26 1.06

1.0 9.0 xlO^ 9.88x10^ 0.392 0.796 299.0 428.0

NOTES 1) 2) 3) 4)

M data taken at 25X. - 2 5 is the slope of log rj vs. log y at large / . (2-2/?) is the slope of log - (TU -T22) vs. log y at large y. Parameters rj*,, Oo* and ti were obtained by curvefittingthe rheological data to the model. 5) The values of A (elastic time constant) were estimated firom: ,.(Zi2a)-l] (Zi2a)a. = 2'"

Here a is a parameter associated with the behaviour of the dynamic viscosity and taken to be equal to 1/(1-25): X is the elastic characteristic time (largest "relaxation time") and Z ( ) is the Riemann zeta function.

Measurement technique Decoloration method: use of the reaction between iodine and thiosulfate in the presence of a starch solution. Results

• Q

^ • •

0

0

4X10

Impeller 1 11 III IV V VI

vu

Influence of impeller geometry on mixing time.

Chapter 2. Mixing tini*

88

3X10

N, RPM

Influence offluidproperties on mixing time.

Notation tm

r -(T11-T22)

p

mixing time, see effective rate of deformation, 1/sec zero shear viscosity, poise primary normal stress difference, dynes/cm^ density, g/cm^

2.1 Singl« phase

89

Brennan, D. J. and Lehrer, I. H., lyans. Instn., Chem. Engrs., 54,139, (1976) Impeller Mixing in Vessels Experimental Studies on the Influence of Some Parameters and Formulation of a General Mixing Time Equation Experimental apparatus Vessel Type Diameter (mm) Height (straight section of cylindrical vessel) (mm) Height (dish-section) (mm) Operating capacity (m^) BafQe width (nrni) Coil diameter (mm) b: bafQed, fb: flat-bottomed, he: with helical coil

b-fb 420 610

b-db 420 495

u-db-hc 420 505

u-db-cp 420 505

— 58.2x10-3 39 —

102 58.2x10-3 39 —

102 58.2x10-3 — 280

102 58.2x10-3 — —

u: unbaffled dp: dish-bottomed cp: with cylindrical probe

Impeller Type Diameter (nun) Number of impellers Number of blades d/D w/d

flat blade disk turbine flat blade turbme 63.5,76.0,100.0 and 102.0 land 2 land 2 6 6 0.15,0.18 and 0.24 0.125 and 0.20

Working fluids and their physical properties Newtonianfluidsof low viscosity

Measurement technique

Decoloration of methyl red indicator with neutralization of NaOH with HCl Experimental conditions and results Baffled vessels (1) Variable, impeller speed: 72 45**

0.325 0.325

0.346 0.346

0.231 0.231

— —

45**

45°

0.5 0.5

0.325 0.325

0.346 0.50

0.231 0.231

— —

45** 25**

0.5 0.5

6-Curved blade turbine 4-Curved blade open style turlrine 4-Pitched Wade turbine 4-Pitched Wade turbine with a draught tube 2-Pitched blade turbine 2-Pitched blade turbine with a draught tube VEGYTERVpropeUer

I ^—^-^ I Six-flat blade turbine

I ^—^r-^ I Sbc-curved blade turbine

4-Curved blade open style turbine

«c:^^5:o 3-Wade VEGYTERV propeller

4 & 2-pitched blade turbine Various types of agitators.

0.325

0.5 0.5 0.5

2.1

93

Working fluids and their physical properties Tap water, glycerin solutions, and com syrup solutions Physicochemical properties of liquids Liquid

Viscosity (Ns/m^xlO^)

Density (kg/m^)

0.894 4.75 9.90 31.52 14.56 61.70 408.74

997.1 1,122.8 1,158.1 1,197.2 1,185.4 1,249.5 1,312.8

Water Glycerin 45 volume % Glycerin 60 volume % Glycerin 75 volume % Com symp 45 volume % Com symp 60 volume % Com symp 75 volume % Results -I

1—I—r-

1 6-Curved| 4-Curved

•WeF pigcerln.

g

^

pm syrup

mw%

•ot iU^^^?j 10^ 2

4

6

8 10

4

6

8 10^^

4

6

8 10=

Re

Homogenization number as a function of Reynolds number: (1) 6-curved blade tiurbine, (2) 4K:urved blade open-style turbine (J)/T=0325, C/HL=0.5).

Chapter 2. Mixing time

94

n

i—i—I r r T I

1

1

1

I I r t ! •

•nrri

T

-A—

Wafer ^Vbl % Glycerine eoN^iyo

V

a

A T

7S^W%

10-

I

«Vbl% Com syrup 60\^l % 75Vbl%

• 0 1

Data of Havaset al."'''^' ' — D/T = 0.254, C / H L = 0.5 — 0 / T = 0.382. C / H L : 0.5 1

^jjSZjTSZSaj^—^—AAA A A A A ^

1,

10^2

I

681?

2

4

681?

2

t

>

Z

I

I

li

I

6 8 10^

2

Homogenization number as a function of Reynolds numberS-blade VEGYTERV propeller (Z)/r=0.325,

C/HL=0.5).

•I

T""

2

1

I

» » I I !•'

4 1 J-Pitched 1 4-Pitched 2-Pirched 4-Pitched »Ofauq^li] a A r V^ter • • A a A5Vbl% • Glycerine 60Vbl% B 1 o A • V • O 1 75Vbl*/o o V e • 1 SW5? m Gxn syrup A 1 A (D •• A 0 B 1 TSJE*

— 5 —

mw%

10 Ho

•

B K ^ c»^o^^B6v • • • • . . ^-.-.^-..-.-^...u^ . c 10 1?2 4 681? 2 4 6 8 1 0 ' 4 6 8 lO-*

|

Re Homogenization number as a function of Reynolds numben(l) 4-pitched blade turbine, (2) 2-pitched blade turbine, (3) 4-pitched blade turbine with a draught tube, (4) 2-pitched blade turbine with a draught tube (D/r=0.325,C//fi.=0.5).

2.1 SingI* phas«

Notation C distance between the impeller and the bottom of the tank, m D impeller diameter, m Dd impeller disk diameter, m HL liquid height, m Ho homogenization number, Ntm, dimensionless L length of impeller blade, m N impeller speed, 1/sec Re Reynolds number, ND^p/fi, dimensionless tm mixing time, sec T tank diameter, m W width of impeller blade, m 0 impeller blade angle, degree /I impeller viscosity, Nsec/m^ p impeller density, kg/m^

95

Chapter 2. Mixing tim*

96

Sano, Y. and Usui, H.,/. Chem. Eng. Japan, 18,47 (1985) Interrelations among Mixing Time^ Power Number and Discharge Flow Rate Number in Baffled Mixing Vessels Experimental apparatus Vessel Type: (1) (2) flat-bottomed Diameter (1)0.2 (2) 0.4 m Liquid contained Height: (1)0.2 (2) 0.4 m Baffle Number: (1) (2) 4 Width: (1)0.02 (2) 0.04 m Impeller Type d/D b/D np

turbine 0.4,0.5,0.6,0.7 0.1,0.15,0.2,0.3,0.4 2,4,6,8

paddle 0.3,0.4,0.5,0.6,0.7 0.05,0.10.0.15,0.20,0.30 2,4,6

Working fluid Tap water Experimental conditions 0.3 < d/D < 0.7 0.05 < b/D < 0.3 2 < w> < 8 Re>5x 10^ Measurement technique Measurement of electrical conductivity Results For paddles

1

i

1 d

Turbine (a: c: d = 5 : 2: 20)

neM= 2.1 (d/D)-'-^ ib/D)-^'^ nf^'' For turbines nftv= 3.8(rf/Z))-^«° (b/D)-"^' ni^'*' Notation a impeller length, m b impeller width, m c thickness of impeller disk, m d impeller diameter, m D vessel diameter, m n impeller rotational speed, 1/sec np number of impeller blades Re impeller Reynolds number, d ^n/v, dimensionless 6M mixing time, sec V kinematic viscosity of liquid, mVsec p liquid density, kg/m^

1

ch-

^J1 11' .,

Paddle

»- a - ^

1 -

•

1

2.1 S i n g I * plMis«

97

Takahashi, K., Yokota, T. and Konno, H.,/. Chem. Eng. Japan, 21,63 (1988) Mixing of Pseudoplastic Liquid in a Vessel Equipped with a Variety of HeUcal Ribbon Impellers Experimental apparatus Vessel and impeller geometries Vessel type: flat-bottomed Impeller type: helical ribbon ds ' "'""

Geometrical variables for helical-impellers

t

Bn

Geometry No. d (mm)

"7^

DHl DH2 DH3 DH4 DH5 DH6 DH7

::

X V)

1 ? z—i

d D

95.9 88.5 82.0 91.0 90.3 90.4 91.9

c/D

s/D

w/D

0.0208 0.0574 0.0900 0.0450 0.0482 0.0482 0.0405

0.926 0.909 0.912 0.621 0.455 0.930 0.921

0.100 0.100 0.100 0.100 0.100 0.152 0.200

D=H=100 mm, «^=2, rf,/Z)=0.0938

General configuration of a helicalribbonimpeller

Working fluids and their physical properties Liquid

n(-)

X(Pas")

3wt%HEC 4wt%HEC 5wt%HEC Com symp

0.768-0.832 0.718-'0.761 0.686-0.735 1

0.724-1.56 2.76-4.60 7.06-14.1 0.550-3.33

Results 0.405^rf/D^ 0.574, 0.455 =0.147, w=0.067,rf„=0.0159,Cba=0 012 3. Coils Name

Material

dc

he

du

dti

Cbc

ec

tic

CI C2 C3

Cr plated Cu Steel Copper

0.1827 0.1763 0.1887

0.205 0.2075 0.2175

0.0127(1/2") 0.00635(3/4") 0.00476(3/16")

0.0095 0.0043 0.0032

0.0275 0.0285 0.0175

0.0060 0.0064 0.0065

10.5 16.5 19.5

Characteristic parameters: D/d=l.e9, p/d=OM, A/rf=1.47, w/d=0A5,rf„/rf=0.106,Cba/d=OM,

2.1 SingI* phas«

103

Working fluids and their physical properties Properties of experimental liquids iu(Pas) n k P (kg/m^) (W/mK) Substance or m (Pas") (-) — 0.14 1.0 Glycerol 1,232. 0.213 1,235. 0.320 0.275 1,240. 0.315 0.310 0.408 1,246. 1,255. — 0.598 Vitrae oil HV32 0.055 856. 0.145 Mixture 0.200 873. 0.785 885. HV320 «• \w 2.48 1,383. 0.323 Com syrup CMC 1.0 0.564 0.748 996. 0.588 2.0 9.5 0.631 996. 0.575 Xanthan 0.75 6.27 0.122 995. 0.610 1.0 6.5 0.196 ^ 1.5 8.62 0.183 600mg/L 1,195. 0.356 Polyacrylamide 0.136 0.871 0.2 0.734 0.521 1.0 0.521 5.04 *Adjusted for desired viscosity. **Com syrup slightly diluted to avoid crystallization. Properties of distilled water used for solutions: //=9 x 10" Pa s, p=995.4 kg/m^ ife =0.610 W/mK, Cp=417J/kgK. Results (1) Mixing time Cone. (mass %) 89.0 91.5 93.5 95.0 97.5 100. * 100.

i

1

i 1

1

Cp

g/kg-K) — 2,515 2,480 2,451 — 1,901

1

2,358 4,177

1

1T

2,902

_J_

(Nt„U/(NL)N = 1+3.76 Wi"'*^ 0m<Wi i r i•*^A'U

M A t.e % CMC » CMC k CM O ATTJM L

1

III

iV!f^vi^

1

ijSBSf^BT-l

F ' ii A!

M

iT i1

Power-number-Reynolds-number curve for non-Newtonian fluids; all points in the crowded regions were not shown.

3.1 Single phas«

Metzner, A. B., Feehs, R. H., Ramos. H. L, Otto, R. E. and Tuthill, J. D., AIChE Journal 7,3 (1961) Agitation of Viscous Newtonian and Non-Newtonian Fluids Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.5-1.83 ft Baffle Number: 4 or 0 Width: 0.1 T Impeller Type:flatbladed turbine Diameter: 0.167-0.67 ft TID ratio: laminar region 1.3—5.5 transition region 2.0—5.5 Number of impellers: 1 Working fluids and their physical properties CMC, Attasol, Carobopol, Permagel and Pliovic Flow-behavior index 0.2—1.5 Apparent viscosity 1—180 poises Experimental conditions Power input: 0.4-176 hp/1,000 gal Impeller speed: 1.58—29 rev/sec Reynolds number: 2-1,760 Apparent viscosity: 1—180 poises

121

Chapter 3. Power draw and consumption

122

Results

1000

REYNOLDS NUMBER. D^Up/p,

Symbol

o

V

D

•

A A

O V



Fluid CMC Attasol Carbopol Carbopol Carbopol Carbopol Permagel Permagel Pliovic

n 0.34 0.38 0.26 0.20--0.26 0.30-0.54 0.18-0.29 0.16 0.21 1.5

Power number-Reynolds number correlation for non-Newtonianfluids:single,flatbladed turbine.

Notation D impeller diameter, ft gr dimensional conversion factor 32.2 ftlbM/sec^lbF n flow behavior index of a non-Newtonian fluid, dimensionless N rotational speed of impeller, 1/sec P power consumption, ft/6f/sec T tank diameter, ft /I viscosity, IbM/secft, //«is sometimes used to emphasize that the viscosity (or apparent viscosity of a non-Newtonian fluid is a function of shear rate) p density, Ibm/ft^

3.1 Singl* pluis«

123

Metzner, A. B., Feehs, R. H., Ramos. H. L, Otto, R. E. and Tuthill, J. D., AIChE Journal 7,3 (1961) Agitation of Viscous Newtonian and Non-Newtonian Fluids 1. Two flat-bladed turbines (1) Ranges of variables covered Variable T D T/D n M N

(ft.) (ft.) (poises) (rev./sec.)

NRe

Power dissipation (hp./l,000gal.)

Newtonian data

Non-Nertonian data

0.469-1.166 0.33'-1.00 1.023-3.50 1.0 1.48-184 0.03-16.8 0.10-480 0.04-230

0.469-1.166 0.33-1.00 1.023-3.50 0.14-0.72 2.41-200 0.08-17.3 0.146-620 0.06-175

Baffles, used as indicated on thefiguers,were of a width equal to 1/10 T,

(2) Results

1.0

10

100

REYNOLDS NUMBER, O ^ N / » / M SYMBOLS, T / O

h^^< 1 1.000 1 0.666 1 0.500 1 0.333

Lt66

0.786

RATIOS

0.698

1

0.662

0.496

1

1.166 O 1.75 O ^ i.iS

O

L048

•

1.023

•

2.33 ^ A 1.57 ° B 1.39 <J 3.50 > • 2.36

• • A « ^ BAFFLED TANK

0^ 2.10 ^ T

1.41


fc,l

REYNOLDS NUMBER, D ^ N / y ^

1,000

10.000

Chapter 3.

126

Power d m w and consumpticm

4. Double-pitch propellers (1) Ranges of variables covered Shaft position Curve TID A B C

II I

1.4-3.0 1.4-3.0 Newtonians

n

Power number-Reynolds number correlation for double-pitch propellers {n < 1.0).

(2) Results 100

j1

1 i 11 iffl

SI

-.(cm)

h(cm)

Al A2 A3 A4 A5

22.11 20.84 19.33 17.98 16.63

15.0 15.0 15.0 15.0 15.0

Along blade Projected

C/DT

2.38 2.38 2.38 2.38 2.38

3.22 3.22 3.22 3.22 3.22

0.0177 0.0454 0.0784 0.1078 0.1372

Working fluids and their physical properties Newtonian systems Code No. 1 10 4 11 5 2 7

Liquid Lubricating oil (British Petroleum, Llandarcy) Silicone liquid* Dilute golden syrup (Martineau's) Silicone liquid* Silicone liquid* Concentrated golden syrup Silicone liquid*

Viscosity (P)

Density (g/cw?)

6.8'-10.4

0.886

31.0-36.0 49.0-^56.0

0.98 1.364

55.0-61.0 173.0-183.0 385.0-707.0 501.0-618.0

0.98 0.967 1.374 0.967

Non-Newtonian systems Code No. 6 14 15 8 12 9 13

Liquid 10% aqueous CMC** 9.46% aqueous CMC** 7.16% aqueous CMC** 200/100,000 C.S. sihcone* Concentrated PBD*** Polymerised linseed oil Diluted PBD***

0.266-0.338 0.469 0.572-0.611 0.676-0.759 0.702 0.726 0.747-0.766

k (g cm~^ s""^)

Density (g/cnr)

1,763 567 100-115 943-2,293 1,900-2,475 1,117-1,986 934

1.043 L053 1.055 0.967 0.8 0.982 0.804

* Midland Silicones Ltd.: MS 200. ** Carcoxymethyl cellulose. *** Polybutradiene dissolved in ethylbenzene. Dilution was with methyl-cyclohexane. (International Synthetic Rubber Co. Ltd.)

132

Chapter 3. Pow«r draw and consumption

Results P

f c T

N^D^P{DT)

g J N^"D'P ] [* [a (!-«)]"•'J

a = 37-120[|-] Notation a C D DT

k n N P

r

p

T

geometric parameter clearance diameter of impeller diameter of tank constant in T=ky" exponent for power-law fluid rotational speed of impeller power input shear rate density shear stress

3.1 Single ph«s«

133

Bourne. J. R. and Butier, H., Trans. Instn. Chem. Engrs., 47, T263 (1969) Power Consumption of Helical Ribbon Impellers in Viscous Liquids. Experimental apparatus Vessel and agitator geometries Summary of Principal Dimensions Impeller number

dim)

dID

h/D

W/D

S/D

Zo/D

1 2 3 4 5 Nagata^ Rl R2 R3 R3' Gray2 Lightnin^ Hoogendoom and den Hartog"*

10.303 11.030 11.142 11.370 34.34

0.889 0.952 0.962 0.981 0.954

1.06 1.06 1.06 1.06 1.06

0.108 0.108 0.108 0.108 0.104

0.345 0.345 0.345 0.345 0.345

1.22 1.22 1.22 1.22 1.22

3.7 3.7 7.5 11.2 8.5 14 ft

0.94 0.94 0.95 0.95 0.95 —

0.9 0.9 0.95 0.95 0.89 2.2

0.11 0.11 0.10 0.10 0.06 0.09

0.7 1.05 0.95 0.95 0.68 0.56

1.0 1.0 1.0 1.0 1.1 —

9.1

0.96

0.9

0.087

0.58

1.5

1 2 3 4

Nagara, S. et al„ Chem. Eng, Oapan), 1957,21,278 Gray, J. B., Chem. Eng. Progr., 1963,59,55 Viscons Mixing Bulletin B531 Hoogendoom, C. J. et al., Chem. Eng. Sci., 1967,22,1689

Principal dimensions of tank and helical ribbon.

234

Chapter 3. Power draw and consumption

Results

__i£_

n

nil''*'-I)

Notation d D h k K / n N P Po Re p

outside diameter of ribbon inside diameter of tank height of ribbon hid consistency factor in the power law Did exponent in the power law rotational speed of ribbon power consumption dimensionless power number, PIpN ^d ^, dimensionless dimensionless Reynold number, pd W ^"7/iC, dimensionless density of liquid

3.1 Single phase

135

Novlk, V and Rieger, E, Trans. Instn. Chem. Engrs., 47, T335 (1969) Homogenization with Helical Screw Agitators Experimental apparatus Vessel and agitator geometries {Lff-fitf

17

\v

Mt>/O-0.1

Vessel Type Inner diameter (mm) Screw Diameter of screw (nmi) Pitch (mm) Liquid contained Height (mm)

o

„

flat-bottomed

flat-bottomed

100

150

60 60

94 94

100

150

Working fluids and their physical properties Water, glycerol and aqueous solutions of com symp and glycerol Viscosities of those Uquids = 1—10* cP

Results

Resultsfromscrew agitator with draught tube.

Chapter 3. Pow«r draw and consumption

136

10'

W A/'^—REYNOLDS NUMBER

Resultsfromscrew agitator in bafQed vessel.

A ( r , ~ REVNOLOS NUMBER

Resultsfromscrew agitator without baffles.

Notation d outer diameter of helical screw D inside diameter of tank Dt inside diameter of draught tube e offeet of agitator shaft from center of vessel H height of liquid N speed of agitator Np power number, P/pN ^d^, dimensionless P power consumption of agitator s pitch of screw Wb width of baffle fi viscosity of liquid p density of liquid 0 mixing time

3.1 Siiigl«phas«

137

Nagata, S., Nishikawa, M., Tada, H., Hirabayashi, H. and Gotoh, S.J. Chem. Eng. Japan, 3,237 (1970) Power Consumption of Mixing Impellers in Bingham Plastic Liquids Experimental apparatus Vessel Type: (1) (2) (3) flat-bottomed Diameter: (1) 20 (2) 30 (3) 40 cm Impeller Type d/D hID IID pitch

Ribbon 0.95 0.1 0.95 1.0

Anchor 0.5-0.95 0.1 0.5-0.95 —

Turbine 0.5 0.1 0.125 —

Paddle 0.3 -0.95 0.05-0.12 — —

s a) Ribbon

c) Turbine

d) Paddle

Working fluids and solids Dispersoids: CaCOa, MgCOs, kaolin, and Ti02 Dispersion media: city water, glycerin water solutions, machine oil and salad oil Results Np = {PN + KHe')Re-' -^aNy + I Determined coefficients a PN Ribbon 6.13 320 Anchor 4.80 200 6-Blade turbine 3.44 70 6-Blade turbine with baffles 3.44 70

/ 0.2 0.29 — 5.5

K 15 30 10 10

h 1/3 1/3 1/3 1/3

Chapter 3. Power draw and consumption

138

6 fi |03

6 t^r^2

2

A

6 6 ^Q4

10*

Np-Re" correlation forribbonmixer.

50

TOO

500

1000

iV>-/?^"correlation for 6 blade turbine.

5000

3.1 Single phase

Notation b blade width of impeller, cm d diameter of impeller, cm D diameter of mixing vessel, cm h constant, dimensionless He Hedstrom number, Ny{He"fy dimensionless / turbulent power number, dimensionless K proportionality constant / length of anchor arm, height of ribbon, or blade length of impeller, cm n impeller speed, 1/sec Np power number, d ^np/r}, dimensionless Ny yield stress power number, ty/pn^d ^, dimensionless Re" Reynolds number, d ^nplt], dimensionless a proportionality constant, dimensionless PN proportionality constant, dimensionless r] plastic viscosity, g / c m s e c p density, g/cm^ Ty yield stress for Bingham plastic fluids, g/cmsec^

239

Chapter 3. Power draw and consumption

140

Hall, K. R. and Godfrey, J. C, Trans. Instn. Chem. Engrs., 48, T201 (1970) Power Consumption by Helical Ribbon Impellers Experimental apparatus Vessel and impeller geometries Vessel type: flat-bottomed Impeller type: helical ribbon

Diagram of impeller and tank dimensions.

Impellers B (10 inch diam.) and A (IV2 inch diam.).

»c^:22iHr^i*.,

Impellers C, B, and D.

3.1 Single phas«

241

Impeller dimensions Impeller

D

dID

pid

h/d

eld

wid

NR

A B C D E

1.65 11.3 11.3 11.3 22.0

0.898 0.912 0.912 0.902 0.91

0.517 0.495 1.00 1.00 1.0

1.01 0.942 0.996 1.01 1.0

0.0575 0.0485 0.0485 0.0539 0.05

0.135 0.0971 0.0971 0.0981 0.1

1 1 2 1 2

For these impellers H=W2 D. D: inch.

Workingfluidsand their physical properties Newtonian fluids: aqueous solutions of com syrup (viscosities = 60—460 poise) non-Newtonian fluids: a commercial hydroxypropyl methyl cellulose at various concentrations in water

Results Po=^e6Re:\p/dr''^(NR){h/d){w/dfHc/dr'' tion fotaf* clearance between impeUer ribbon and vessel wall c d impeller diameter D diameter of mixing vessel gravitational conversion factor gc impeller height h fluid height H impeller speed, 1/sec N NR number of impeller ribbon pitch of impeller ribbon p p power consumption at impeller shaft {=27tNT) Po power number, Pgc/N^d^p, dimensionless Rea apparent Reynolds number, d^Np/^, dimensionless T torque at impeUer shaft w ribbon width apparent viscosity ^ density P

242

Chapter 3. Pow«r draw and consumption

Foft, L, Vale§ova, H. and Kudraa, V, Collect. Czech. Chem. Commun., 36,164 (1971) Studies on Mixing. XXVII. Liquid Circulation in a System with Axial Mixer and Radial Baffles Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 190 (2) 290 mm Liquid contained Height: (1)190 (2) 290 mm Baffle Number: 4 Width: 0.1 D Impeller Type: (1) propeller (2) paddle mixer with three inclined blades (3) paddle mixer with six inclined blades Number of impellers: (1)~(3) 1 Number of blades on impeller: (l)'-'(2) 3 (3) 6 D (nmi)

d (mm)

h2 (mm)

Rotational speed of mixer (rpm)

Propeller {s=d) and paddle mixer with three inclined blades (a=24°) 290 290 290 190 190 190

96.6 72.5 58.0 58.0 58.0 58.0

145.0 96.6 72.5 58.0 95.0 58.0

450-^1,000 800-1,800 1,000-2,000 900-1,600 900-1,600 900-1,600

Paddle mixer with six inclined blades (a=45°) 290 290 290 290 190 190 190

96.6 72.5 58.0 46.6 58.0 46.0 46.0

145.0 72.5 72.5 72.5 95.0 58.0 46.0

3 0 0 - 600 600-1,300 900-1,800 1,000-2,000 500-1,000 500-1,000 500-1,000

3.1 Single phas«

143

(a)

(b)

Mixer

(a) Three-blade paddle mixer with inclined blades, a=24*', A=0.2 d. (b) Six-blade paddle mixer with inclined blades, a=45*', /»=0.2 d.

Working fluids and their physical properties

Werking fluids Distilled water Distilled water Aqueous glycerol Aqueous glycerol Aqueous glycerol

r7(cP) 0.5 1.0 3.0 9.2 14.42

P(kg/m') 900 1,000 1,084 1,143 1,161

Results

for i?^> 1.0x10^ Mixer type PropeUer(5=(/) Three-blade paddle (a=24°) Six-blade paddle (a=45°)

B 0.592 0.387 1.014

Notation d mixer diameter, m D vessel diameter, m hz distance of the mixer rotor above the vessel bottom, m Kp pumping capacity, dimensionless n rotational speed of the mixer, 1/sec

f -0.146 0.130 -0.212

np

Re % ri P

0.026 0.060 0.166

number of impeller blades Reynolds number, nd^p/rf, dimensionless volumetric flow rate, mVsec dynamic viscosity of fluid, kg/msec liquid density, kg/m^

Chapter 3. Pow«r draw and consumption

144

Nienow, A. W. and Miles, D., Ind. Eng. Chem. Process. Des. Dev., 10,41 (1971) Impeller Power Numbers in Closed Vessels Experimental apparatus System Vessel Type Diameter (in) Height (in) Baffle Number Width (in)

(1)

(2)

flat-bottomed 6,12 6,12

1flat-bottomed 6,12 6,12

4 0.1 r

4 0.1 r

Impeller Type D/T C/Z DwID DJD x/Dw w/D Number of impellers Number of blades

(a) 1/4-3/4 1/6-3/4 1/5 1/4 0.05-0.44 1 6

(a): six-blade disk turbine (b): four-blade 45** pitched turbine (c): 2-bladeflatpaddle

Working fluid water Experimental conditions Impeller speed System (1): 40-2,400 rpm System (2): 20-1,000 rpm Temperature: 25°C

(b) 1/4-3/4 1/6-3/4 — — 1/4 1 4

(c) 1/4-3/4 1/6-3/4 1/4 — 1 2

3.1 Single phase

145

Results Power numbers for 2 x 10* < Nue < 10^ Identification, run no. r,in.

D/T

Air/water interface

Impeller clearance, C/Z V6(A)

V4(B)

VaCC)

V2(D)

VaCE)

ViiF)

x/D„

3.9 4.9 5.3 5.0 5.3

4.1 5.0 5.6

3.9 4.8 5.0

3.7 4.7 4.6

0.44 0.33 0.22 0.22 0.14 0.10 0.05

6-Blade Disk Turbine 1 2 3 4 5 6 7

6 6 6 6 6 12 12

V4 Va 72 72 V4 74 72

no no no yes no no no

3.6 4.4 4.6 4.2 4.3

3.8 4.7 4.9 4.8 5.0 5.5 5.5

Aerated Aerated Aerated

5.6 5.9 5.8

5.0

4.8

3.0 3.4 3.0 3.3 3.5

2.8 3.2 2.8

2.7 3.0 2.7

1.9 1.6 2.3 1.8 1.7

1.9 1.6 2.1

1.8 1.5 2.0

2-Blade Flat Paddles 8 9 10 11 12

6 6 6 12 12

74 72 V4 74 72

no no no no no

13 14 15 16 17

6 6 6 12 12

74 72

no no no no no

2.7 2.6 2.5

2.8 3.1 2.7 2.8 3.0

2.9 3.3 2.9

4-Blade, 45**-Pitch Turbine

VA

74 72

1.9 1.6 2.3

1.8 1.4 2.2 1.7 1.4

Notation C impeller clearance above the tank bottom, L D hnpeller diameter, L DL length of turbine blade, L Dw width of turbine blade or paddle blade, L N impeller speed, 1/T Np power number, P/pN^D^, dimensionless Nxe Rejmolds number, M) Vv, dimensionless P impeller power, MLVr^ T tank diameter, L w 45°-pitched turbine blade width, L X disk thickness, L Z liquid height, L V fluid kinematic viscosity, L^IT p fluid density, M/D

1.7 1.4 1.9

Chapter 3. Pow«r draw and consumption

146

Nagata, S., Nishikawa, M., Tada, H. and Gotoh, S.J. Chem. Eng. Japan, 4,72 (1971) Power Consumption of Mixing Impellers in Pseudoplastic Liquids Experimental apparatus Vessel Type: (1) (2) (3) flat-bottomed Diameter: (1) 20 (2) 30 (3) 40 cm

Impeller Type d/D b/D IID pitch

Ribbon 0.95 0.1 0.95 1.0

Anchor 0.5-^0.95 0.1 0.5-0.95 —

Turbine 0.5 0.1 0.125 —

Paddle 0.3 --0.95 0.05'-'0.12 —

a c) Turbine

a) Ribbon

d) Paddle

Working fluids and their physical properties Flow properties at high shear rate* Liquid Aqueous CMC LVNO. 1 Aqueous CMC WS-C Aqueous CMC HESS Aqueous PVAl Aqueous PVAc

Weight (%)

m

ik

0.3--6.2 0.5--4.5 1.0- -4.5 10--15 30--35

1.00- '0.270 0.72--0.432 0.668--0.436 0.71--0.57 0.72--0.64

0.01--690 13.1'-22.5 11.4--259 62- '340 7 1 - '220

•Aqueous CMC WS-C and HESS show the power-law behaviorfromthe low shear rate range (8-100 sec"') to the high shearrange(200-1,000 sec"*). However, the othersdod not obey the power-law

3.1 S i n g I * phase

147

Results

iCOO

fo

hv 1

['o

*"^

A-iiiC-.n.:- C^!C .^V'li»t:OtAvjj.JCu> PVAl Sc.ji.if.-n' [ r\'»\

!

IQU;

! i

i

ICC

i

1

Oj

"ojl^ ^'^

.

- I0.1

10

100

iOOO

10000

1X000

iV^-i?g'correlation for pseudoplastic liquids (Ribbon d/D=0.95).

Mite n o l i used K i t i v r 1 n c uf>d s""t' Ncwionians no 3.48% CMC sol. no J o 3.26^; CMC scl. X 2.84%CMC sol. r)f.) no + 2.51% CMC sol. A 2.40% CMC sol. no 1 V 2.51?; CMC sol. no no i 1.83% CMC sol1.67 % C N K : sol no Q no 1 0 1.50 "aCMi: sol. • 1.67% CMC sol. 4 B a ( f l e j . /d)]\ (t/d)-l

150

Chapter 3. Power draw and consumption

Notation a Ald^ surface area of the ribbon impeller A impeller diameter d de

E h k I n N NR

P Po Re s t w X P

equivalent diameter constant height of the hquid colunm consistency index in the power law equation impeller length flow behavior index in the power law equation rotational speed of the impeller number of impeller ribbons power consumption power number, P/d^N^p Reynolds number, d^N^~*^p/k impeller pitch vessel diameter impeller width t/de density

3.1 Single phas*

151

Chavan, V V and Ulbrecht, J., Ind. Eng. Chem. Process Des. Dev., 12,472 (1973) Power Correlation for Close-Clearance Helical Impellers in NonNewtonian Liquids Use of published data Impeller type Helical screw impellers with draught tube Helical ribbon impellers Combined ribbon-screw impellers Geometrical variables for the impellers

Helical screw impeller with a draught tube.

i

1

I

J

1

\

'1

i

IS T

A single-bladed helicalribbonimpeller and combinedribbon-screwimpeller.

Chapter 3. Pow«r draw and consumption

152

Geometrical Variables for Helical Screw Impellers with Draught Tube

No.

diem)

t/d

h/d

l/d

s/d

w/d

c/d

dr/d

Irld

Crid

G.l G.2 G.3 G.4 G.5 G.6 G.7

30.5 20.35 20.35 20.35 19.05 14.00 12.70

1.50 2.25 2.25 2.25 2.40 3.28 3.60

1.94 2.70 2.70 2.70 3.10 4.24 4.65

1.50 2.25 2.25 2.25 2.40 3.24 2.%

0.96 0.50 1.00 1.00 0.80 0.93 0.79

0.42 0.39 0.39 0.39 0.42 0.39 0.38

0.104 0.156 0.156 0.156 0.167 0.228 0.250

1.16 1.05 1.05 1.74 1.12 1.53 1.14

1.83 2.54 2.54 2.54 2.93 4.01 4.40

0.104 0.156 0.156 0.156 0.167 0.228 0.250

Geometrical Variables from Literature for Helical Screw Impellers with Draught Tube

No.

Ref.

G.l G.2 G.3 G.4 G.5 G.6 G.7 G8 G.9

Chavan,e/fl/.(1972) Chavan.«/a/.(1972) Chavan,^fl/.(1972) Chavan,«/a/.(1972) Chavan,g/fl/.(1972) Chavan,€^a/.(1972) Nagata,«/a/.(1957) Nagata,«/a/.(1957) Nagata,«/a/.(1957)

No.

Ref.

rf(cm)

t/d

h/d

l/d

s/d

w/d

c/d

dr/d

Ud

cjd

20.35 2035 19.05 2035 20.35 19.05 4.50 6.50 6.28

2.25 2.25 2.40 1.50 1.50 1.60 2.22 1.54 1.59

2.63 2.63 2.80 1.75 1.75 1.83 2.22 1.54 1.59

2.31 2.31 2.47 1.56 1.56 1.67 2.0 1.30 1.42

0.5 1.0 0.8 0.5 1.0 0.8 0.67 1.38 0.72

0.39 0.39 0.42 0.39 0.39 0.42

0.31 0.31 0.33 0.19 0.19 0.20 0.11 0.07 0.075

1.13 1.13 1.2 1.03 1.13 1.2 1.15 1.11 1.08

2.25 2.25 2.4 1.50 1.50 1.60 1.55 1.23 1.26

0.19 0.19 0.2 0.13 0.13 0.14 0.25 0.16 0.16

Geometrical Variables from Literature for Helical Ribbon Impellers

G.l G.2 G.3 G.4 G.5 G.6 G.7 G8 G.9 G.IO Gil G.12 G.13 G.14 G.15 G.16

d{cm)

Nagata,£/a/.(1972) Nagata,e^fl/.(1972) Nagata,€^ 0.45

Npo = 5.3 Npo = 3.80 M^v^-^

Notation Di impeller diameter, m DT tank diameter, m g gravitational acceleration, m/sec^ N rotational speed of impeller, 1/sec NF^ Froude number, N'^Dilg, dimensionless Npo power number in ungassed liquid, PogdpN^D?, dimensionless Po power consumed in agitation of ungassed liquid, kgm/sec p density of liquid, kg/m^

3.1 Single phase

161

Patterson, W. L, Carreau, R J. and Yap, C. Y.^AIChE Journal, 25,508 (1979) Mixing with Helical Ribbon Agitators. Part II Newtonian Fluids Experimental apparatus Vessel and impeller geometries Vessel type: flat-bottomed Impeller type: helical ribbon

Sketch of helicalribbonagitator system. Impeller characteristics Geometry Impeller

A B C D E F G H

I

n m IV V VI

vm VI

d

D

h

ds

(mm)

(mm)

(mm)

(mm)

fib

Did

lid

wid

Pid

0.130 0.130 0.130 0.105 0.130 0.222 0.219 0.222

0.145 0.145 0.145 0.145 0.145 0.248 0.248 0.291

0.137 0.137 0.137 0.137 0.137 0.234 0.238 0.234

6.35 6.35

2 2 2 2 1 2 2 2

1.11 1.11 1.11 1.37 1.11 1.11 1.12 1.30

4.48 3.00 4.12 4.00 4.39 4.44 4.75 4.44

0.097 0.097 0.195 0.121 0.097 0.099 0.072 0.099

0.719 1.048 0.707 0.848 0.695 0.690 0.724 0.690

635 6.35 6.35 9.53 9.53 9.53

Chapter 3. Power draw and consumption

162

Working fluids and their physical properties Fluid 100% glycerol 100% glycerol 100% glycerol Silicone oil Vitrea oil

P(kg/m^)

A/(Ns/m2)

1,254 1,254 1,259 1,100 869

0.568 0.708 0.800 0.137 0.193

Results siny + 1.8cosy] '^'

"d'Np

(1)

{jm

This equation can be simplified on the following grounds: 1. For commonly used helical ribbon agitators, w/d = 0.1, and yf=^ 15 deg. Therefore, we set (u;/(/)0i6 ~ 0.69, sin v^= 0.258, and cos y/^ 0.965. 2. Within the range of the experimental conditions, ReS'^ varies from 1.52 to 2.17. Hence, we take Re^^ = 1.82 as an average value. Equation (1) then reduces to

m

Na93

Np=24nt

d'Np

(2)

Notation d diameter of impeller, m ds diameter of impeller shaft, mm D diameter of vessel, m h height of impeller, m H height of liquid in vessel, m / length of impeller blade, m fib number of blades N rotational speed of impeller, 1/sec Np power number, P/pN ^d ^, dimensionless p impeller pitch P power consumed, W Re Reynolds number for mixing systems, d ^Nplji, dimensionless w blade width, m /x fluid viscosity, Nsec/m^ p fluid density, kg/m^ \lf blade inclination angle, degree

3.1 SingI* phas*

163

Yap, C. Y, Patterson, W. I. and Carreau, R J., AIChE Journal, 25,516 (1979) Mixing with Helical Ribbon Agitators Part III Non-Newtonian Fluids Experimental apparatus Vessel and impeller geometries Vessel type: flat-bottomed Impeller type: helical ribbon

Sketch of helical ribbon agitator system. Impeller characteristics Geometry Impeller A B C D E F G H

I

n m IV V VI

vm VI

d (mm)

D (mm)

h (mm)

(mm)

ftb

D/d

l/d

w/d

p/d

0.130 0.130 0.130 0.105 0.130 0.222 0.219 0.222

0.145 0.145 0.145 0.145 0.145 0.248 0.248 0.291

0.137 0.137 0.137 0.137 0.137 0.234 0.238 0.234

6.35 6.35 6.35 6.35 6.35 9.53 9.53 9.53

2 2 2 2 1 2 2 2

1.11 1.11 1.11 1.37 1.11 1.11 1.12 1.30

4.48 3.00 4.12 4.00 4.39 4.44 4.75 4.44

0.097 0.097 0.195 0.121 0.097 0.099 0.072 0.099

0.719 1.048 0.707 0.848 0.695 0.690 0.724 0.690

ds

254

Chapter 3. Pow«r draw and consumption

Working fluids and their physical properties Fluid 100% glycerol 100% glycerol Vitrea oil 1.0% Natrosol 250-HR 1.5% Natrosol 1.5% CMC-7H 2.0%CMC-7H 0.8%SeparanAP-30 1.0%SeparanAP-30 1.5% Separan** AP-30

P(kg/m3) 1,254 1,249

869 1,000 1,000 1,000 1,000 1,000 1,000 1,000

^ (Ns/m^) 0.568 0.800 0.193 1.07 24.0

2.5 10.0

340 1,100 1,200

S ~ — 0.235 0.381 0.175 0.244 0.382 0.392 0.417

^i(s)

A*(s)

~ —

— — — -

0.233 1.30 0.437 1.26 99.3

298 145

0.12 0.052 0.59 0.70 0.60

*The characteristic elastic time constant was calculated from Theological data at a shear rate equal to 10 s~* through the relation ^ = TU - Tzz/tn y. **Aged polymer powder. Results -1

Notation d ds D h H / Hb N Np p P Reg 5 ^1 w 7 r]e /x p Ti2 Til - T22

diameter of impeller, m diameter of impeller shaft, mm diameter of vessel, m height of impeller, m height of liquid in vessel, m length of impeller blade, m n u m b e r of blades rotational speed of impeller, 1/sec power number, P/pN^d^, dimensionless impeller pitch p o w e r consumed, W generahzed Reynolds number, d Wp/n^, dimensionless fluid rheologicd parameter, dimensionless fluid characteristic time, sec blade width, m shear rate, 1/sec effective viscosity, Nsec/m^ fluid viscosity,Nsec/m^ fluid density, kg/m? shear stress, N/m^ primary normal stress difference, N/m^

3.1 Singl«plMis«

165

Blasinski, H. and Rzyski, E., Chem. Eng. /., 19,157 (1980) Power Requirements of Helical Ribbon Mixers Use of published data Vessel and impeller geometries Vessel type: flat-bottomed Impeller type: helical ribbon

Xl 1/

-b

1^

1

I

1

Schema of the helicalribbonmixer.

J.

\

^ 1

f

0

Ref.

K

eld

Hid

pid

hid

hid

1 1 2 3 3 3 4 4 6 7 S 9 10 11 12 13 2 2 2 5 5 5 5 5 5 5 5

130 130 250 300 416 257 336 248 420 235 590 310 237 1,000 760 296 230 130 207 215 210 205 218 198 234 194 174

0.095 0.055 0.048 0.03 0.01 0.05 0.026 0.032 0.029 0.036 0.021 0.052 0.0375 0.01 0.026 0.026 0.057 0.054 0.048 0.017 0.035 0.055 0.035 0.035 0.035 0.035 0.035

1.19 1.11 1.12 1.06 1.02 1.10 1.052 1.064 1.412 1.072 1.008 1.103 1.64 1.02 1.28 1.158 1.136 1.13 1.12 1.034 1.071 1.111 1.071 1.071 1.071 1.071 1.071

1.28 1.1

1 1 0.996 1 1 1 1 0.96 0.941 1.036 0.915 0.966 1.03 1 1.11 1 1.01 1.01 0.942 0.862 0.893 0.926 0.893 0.893 0.893 0.893 0.893

0.114 0.103 0.0971 0.1 0.1 0.1 0.105 0.117 0.118 0.167 0.0905 0.1035 0.0875 0.1 0.11 0.1 0.135 0.0981 0.0971 0.103 0.107 0.111 0.142 0.071 0.107 0.107 0.107

0.745 0.753 0.57 0.61 0.772 1.25 0.5 0.362 1 0.517 1 0.495 0.431 0.446 0.446 0.446 0.446 0.357 0.596 0.892

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

IQQ

Chapter 3. Pow«r draw and consumption

Results For i?^ < 100

4 = 0.01 ~ 0.095, ^ = 1.02 ~ 1.64, 4 = 0-357 ~ 1.28, a d d - = 0.862--1.11, - = 0.071-0.167, « = lor2 d d X-O^/

\0.45/

\-0.63/r

\1.01/

\0.14

Poi?^ = 3 4 . l |eReferences 1. E. 0. Reher and R.B6hm, Chem. Tech., 22 (1970) 230. 2. K. R. HaU and J. C. Godfrey, Trans. Inst. Chem., 48 (1970) 201. 3. A. Mersmann, W. D. Einenkal and M. KSppel, Chem. Ing. Tech., 47 (1975) 953. 4. S. Nagata, Mixing, Kodansha, Tokyo, and Wiley, New York, 1975. 5. H. Blasiiiski, and Cz. Kuncewicz,Inz. Chem., 8 (1978) 807. 6. J. B. Gray, Chem. Eng. Prog., 59 (1963) 55. 7. M. D. Gluz and I. S. Pavlushenko, Zh. Pnkl Khim., 40 (1967) 1485. 8. C. J. Hoogedoom and A. P. den Hartog, Chem. Eng. Sci, 22 (1967) 1689. 9. R. T. Jounson, Ind. Eng. Chem. Proc. Des. Dev., 6 (1967) 340. 10. H. Ullrich and H. Schreiber, Chem. Ing. Tech., 39 (1967) 218. 11. M. Zlokamik, Chem. Ing. Tech., 39 (1%7) 539. 12. J. R. Bourne and H. Butler, Trans. Inst. Chem. Eng., 47 (1969) 263. 1.3 V. Nov^ and F. Rieger, Chem. Eng. J., 9 (1975) 63. Notation b width of ribbon blade, m D tank diameter, m d impeller diameter, m e clearance between impeller and tank wall, m H height of liquid level above tank bottom, m h height of impeller, m i number of helixes in impeller K Po Re, dimensionless N rotational velocity of impeller, 1/sec P mixing power input, W Po power number, P/N ^d ^p, dimensionless p pitch of heUcal impeller, m Re Reynolds number, Nd ^pl ry, dimensionless 77 viscosity of liquid, Pasec p density, kg/m^

3.1 Single phas«

167

Bertrand, J. Couderc, J. R and Angelino, H., Chem. Eng. Sci, 35,2157 (1980) Power Consumption, Pumping Capacity and Turbulence Intensity in Baffled Stirred Tanks; Comparison Between Several Turbines Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.40 m Liquid contained Height: 0.40 m Volume of liquid in vessel: 50.3 £ Baffle Number: 4 Width: 0.04 m Impeller Type System 1 Si System 2 S2 System 3 S3 System 4,5 S4, S5 System 6 Se Geometries

sixflatblade disk turbine (Figure 1) sixflatblade disk turbine (Figure 1) an impeller shown in Figure 2 an impeller shown in Figure 2 an impeller shown in Figure 3

H-T«400mm h«-|-«2CX)rrwn w«'jt«40mm

C^'-j-O'lOOmm !„•-*-•27 mm

L«-?-»33mm

Figure 1

Chapter 3. Pow«r draw and consumption

168

•4^S

S j system

S)^ system

S,ond £^ systems

^133 Figure 2

Off-bottom clearance: Si

S2

S3

S4

Ss

r/2

0.37

r/2

r/2

r/2

Working fluid water Experimental conditions and results Systems

5^"^^,^^ number u. Reynolds

S,

S,

14,700-67,800 *'»»'w u«,c»w 14,700-67,800

Power number NP Non-dimensional pumping coefficient NQ

5.1 - ^Q

14.700-67,800

14.700-67,800

10,100-46,400

4.9

4.2

3.4

9.2

1.61

1.11

0.65

131

Notation D Dc h H Ip Ig N Np NQ

agitator diameter, m agitator disk diameter, m agitator level in the tank, m water level in the tank, m width of the blades, m height of the blades, m agitator rotational speed, 1/sec power number, P/p7^^^Z)^ dimensionless pumping coefficient, Q/ND^^ dimensionless

P Q

Re T w A^ P

e

power input, kgmVsec^ piunping capacity, mVsec Reynolds number, ND^p/fi, dimensionless tank diameter, m baffle width, m viscosity, kg/msec density, kg/w? flow angle, degree

3.1 SingI* phas«

169

Takahashi, K., Aral, K. and Saito, S.J. Chem. Eng. Japan, 13,147 (1980) Power Correlation for Anchor and Helical Ribbon Impellers in Highly Viscous Liquids Experimental apparatus Vessel Type: flat-bottomed Diameter: 12.80 cm Height: 12.80 cm

Impeller Type Diameter (cm) Height (cm)

helical ribbon 10.28-12.00 12.50 0.102 0.094

anchor 11.52-12.67 11.50 0.102 0.094

w/D dJD

^

g4

^

w

1 1 J

!

1 1 LJ

d D

^

•i

1 1

L»h/sineB

Geometrical configurations of anchor and helicalribbonimpellers.

Cjeometrical variables of anchor and helical ribbon impellers

Geometry Anchor impellers

HeUcal ribbon impellers

No. ACl AC2 AC3 AC4 AC5 DHl DH2 DH3 DH4 DH5

d

c/D

11.52 12.16 12.48 12.54 12.67

0.0500 0.0250 0.0125 0.0100 0.0050

12.00 11.24 10.28 11.29 11.38

0.031 0.061 0.098 0.059 0.055

D/s

L

1.02 1.02 1.02 1.54 2.05

39.72 37.46 34.63 54.65 72.59

270

Chapter 3. Power draw and consumption

Workingfluidsand their physical properties Aqueous solutions of com syrup viscosities: lO-^-SOO poise Results For anchor impellers NpRe^

}^^I^ k.f{D/c) 21n{4 + 8c/f(;)-l d ^

where /(Z)/c) = l+0.00735(Z)/c)°-*^ For anchor and helical ribbon impellers 2hi(4+8c/M;)-l d where sin^fl=s/-J(;r(/)^ + 5^ Notation c clearance between impeller and vessel wall, cm d impeller diameter, cm ds shaft diameter, cm D vessel diameter, cm gr gravitational constant, gcm/Gsec^ height of blade, cm h H height of vessel, cm L length of blade, h/sin GB, cm Hp number of blades N rotational speed of the impeller, 1/sec Np power number, PgclpN^d^, dimensionless P power consumption, Gem/sec Re Reynolds number, d^Np/^f dimensionless s impeller pitch, cm w blade width, cm GB blade angle, rad jix viscosity, g/cmsec p density, g/cm^

3.1 Singl« phas»

271

Gray, D. J., Treybal, R. E. and Baraett, S. M., AIChE Journal, 28,195 (1982) Mixing of Single and Two Phase Systems: Power Consumption of Impellers Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.0287 m Baffle Number: 4 Width: 0.287 m Impeller Type: sixflat-bladedisc turbine Diameter: 0.0906 Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: C/D=^ 0.5,1.167 and 1.5 Working fluid Water Results 7V^ = 5.17(C/Z))°-2^

for

C/D 1.1

Notation C impeller height off the tank bottom, m D impeller diameter, m gc gravitational constant, kgm/kgf sec^ Po mechanical agitation power in ungassed Uquid, W N impeller rotational speed, 1/sec Np power number, Pagc/pN^D^, dimensionless p liquid density, kg/m^

Chapter 3. Pow«r draw and consumption

172

Takase, H., Unno, H. and Akehata, T, Kagaku Kogaku Ronbunshu, 8,560 (1982) Power Consumption of Surface Aerator in a Square Tank Experimental apparatus Vessel and impeller geometries System

(1)

Vessel Type Length and width (m) Water depth (m) Impeller Type Diameter of disk (m) di

(3)

flat-bottomed square tank 0.2 0.075-0.2

0.3 0.075-0.3

0.5 0.075-0.5

disk with six blades underneath the disk 0.03,0.06

0.03,0.06,0.12

0.06,0.12

20:7:2

ilbiWd

Number of impellers Number of bladed Off-top clearance (m)

(2)

1 6 0,0.01,0.02

1 6 0,0.01,0.02

0.03 5.00-41.7

0.06 1.67-16.7

0.03 5.00-41.7

0.06 1.67-16.7

0.12 0.83-6.67

0.06 1.67-16.7

0.12 0.83-6.67

1 6 0,0.01,0.02

Working fluid Tap water Experimental conditions System (1) di(m) Impeller speed (rps) System (2) di(m)

Impeller speed (rps) System (3) di(m)

Impeller speed (rps)

3.1

173

Results Below the critical Reynolds number H/W 0.75 Z)

—

Working fluids and their physical properties liquid: distilled water glycerol solutions (1) viscosity = 36 mPasec density = 1,190 kg/m^ (2) viscosity = 80 mPasec density = 1,220 kg/m^ Gas: air

221

N»4Ht

.J

I

I

I

I

t.

Power curves for the PBT at constant impeller speed.

Pg/p. o

Vtg

•

OJOOS

m/i

- ^ Vag • 0.011 m/t

A 3 ^ • U r o * Mno 8p«ro«r

mJ.

Power curves for the A315 at constant impeller speed.

t.. 1 . I

I

I

t

Power curves for the A315 at constant superficial gas velocity Q^rgeringsparger). . Pc/V|

{iH/m"9)

e v«o-aoo$m/« « VsQ • oxm M/s •

Vsg .

QLOW

m/a

100

• Laro«Mno tparftr

0

•

•

'

'

'

•

•

•

•

'

•

•

•

•

.1

v«a ("•/•) Power curves for the PBT at constant superficial gas velocity.

The minimum power consumption necessary to prevent direct loading.

Chapter 3. Pow«r draw and consumption

222 16

J h [

' »

J9^^^^

• M mPas ^ • 10 fflPM

»•

.7

'*»^«,^

fn^:* ^

y

N^

r I

H A315 • LAS • 8/0 - 0.1 - Vtg • 0.01 m/t

I [• I

0 4Hi • SRS • 7 Nz • 4 HI « 7Hx

1—1

1 1 1

1

>

» 7"^r^ \ A318 • Cn* • 0.4

t

1

-

>'''*'''^^"**>^_

^^y*^

>v,»

1

, 1 ,.A

1

1

1

1

*^^/^

J

1

•

"5^ \

'

•

y

A

1

1

1 1

A

•

•

•

'

•

1

t

1

l _ _J

—1—1

t —

.00

Power curves for the A315 with a small ring sparger and a pipe spaiger at constant impeller speed.

Power curves for the A315 at three liquid viscosities,

,Po^u L r

Vsg - 0.00$ ml% Vag - OJOIO m/t

y -11

n

•—o *

L

..v-o-1

-

T

T

\ •^

Y

Vtg « OJm m/t

«'—«

—.-i

o 4 Hx • S/O • 0.7

\ • 7Hi A31S . C/T - 0.4 I «4Hl • t/D«OJ O i M l M n f 8paro«r k • 7Hx L L i — J - J „ l - . - l . . *._L- i—X ,^L_t., i 1 1 1 i 1

P«T - M mPa* • U r o * Mifl Spwo^ 1 1

J4

Power curves for the A315, amall ring, sparger, two impeller to sparger separation distances, constant impeller speed. Notation Ab area of one impeller blade Ah, 1 projected area of one impeller blade C impeller to bottom clearance dkub impeller hub diameter dt sparger diameter D impeller swept diameter Fig gasflownumber Ub number of impeller blades N impeller rotational speed P power consumption Po impeller power number 5 impeller-spaiger separation T vessel diameter % superficial gas velocity Wi liquid v o l u m e Subscripts g gas under gassed conditions u ungassed conditions

.1 .1

.02

L. .04

M

Jl

Power curves for the PBT at 80 mPa s.

.1

3.2 Mutti phas«

223

Smith, J. M. and Tarry, K., Trans. Instn. Chem. Engrs., 72, P&rt A, 739 (1994) Impeller Power Demand in Boiling Solutions Experimental apparatus Vessel Type: dish-bottomed Diameter: 0.44 m

Impeller

Type: Rushton impeller Diameter: 0.18 m Number of impellers: 1 Number of blades on impeller: 6 Submergence: 0.3 m Working fluids 5 and 10 wt% NaCl solutions Results

A.„.76ter BJ

[vf

)

Notation g acceleration due to gravity, m/sec^ PB power under boiling conditions, W Pu power under ungassed conditions, W S impeller submergence, m Vi impeller blade tip velocity, m/sec

224

Chapter 3. Pow«r draw and eonsumptloii

Cheng, J. and Carreau, R J., Chem. Eng. Sd., 49,1965 (1994) Aerated Mixing of Viscoelasticfluidswith Helical Ribbon Impellers Experimental apparatus Vessel and impeller geometries Type: flat-bottomed Dimensions: D/d=hll w/d=0,133 p/d=0.695 /j/J=1.05 Working fluids and their physical properties Liquid: Rheological properties of test fluids n Test fluids

(-)

Glycerol 2.5% xanthan (H2O) 0.5%xanthan(H2O) 3%CMC(H20) 1%CMC(H20) 0.5% xanthan (glycerol/H2O) 800 ppm PAA (com syrup) 0.5% PIB (FB+kerosene)

1 0.183 0.250 0.299 0.409 0.199 0.94 1

m (Pas")

h (s)

lo (Pas)

7.83 0.110

469 1.57

ris

n'

(Pas)

(-)

in' (Pas")

0.19

0.782 1.67 2.00

7.85 0.15 1.29

0470 22.4 1.84

4.13 1.03 8.19

Notes: n, w, parameters in the power law model: 7;=my"; /i, rjo, parameters in Cross model: 77=770/1+(fiy)*~''; 77,, parameter in the expression: 77=mx"+77,;«', m', parameters in the expression: Ni-m'/y"', Gas: air

Results Np = P/d^N^p Laminar flow regime, 0.28 ^ Rea ^ 70 (0.028