Measurement techniques in heat transfer (AGARDograph)

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One Hundred and Thirty 1..

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Measurement Techniques in Heat Transfer \

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The Advisory Group for Aerospace Research and

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Development of NATO

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R. T

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Editors ERNST R.G. ECKERT RICHARD J. GOLDSTEIN School of Mechanical and Aerospace Engineering, University of Minnesota, Minneapolis, Minnesota, U. S.A.

Printed and published by Technivision Services Slough, England A Division of Engelhard Hanovia International Ltd

Copyright November 1970 The Advisory Group for Aerospace Research and Development. Nato

International Standard Book No. 0.85102.026.7 Library of Congress Catalog Card No. 78-82419

Contents Page

Sectiom Foreword

11

1

E r r o r Estimates in Temperature Measurement E.M. Sparrow

13

2

Precision Resistance Thermometry and Fixed Points H.F. Stimson

33

A study of stability of High Temperature Resistance Thermometers J. P. Evans and G.W. Burns

63

Thermocouple and Radiation Thermometry above 900°K H. J. Kostkowski and G. W. Burns

75

3

Temperature Measurements in Cryogenics J.A. Clark

99

4

Optical Measurement of Temperature R. J. Goldstein

5

Spectroscopic Temperature Determination in High Temperature Gases E . Pfender

229

Probe Measurements in High Temperature Gases and Dense Plasmas J e r r y Grey

269

Transient Experimental Techniques for Surface Heat Flux Rates C. J. Scott

309

6

7

17’7

a

Analogies to Heat Transfer Processes E . R. G. Eckert

329

9

Thermal Radiation Measurements D.K. Edwards

353

10

Measurement of Thermophysical Properties W. Liedenfrost

397

11

Transport Property Measurements in the Heat Transfer Laboratory, University of Minnesota W.F. Ibele

441

Fluid Velocity Measurement from the Doppler Shift of Scattered Laser Radiation R. J. Goldstein and D.K. Kreid

4 59

12

13

Operation and Application of Cooled Film Sensors for Measurements in High Temperature Gases A.M. Ahmed and L . M. Fingerson i’ Index

4 a7 505

11 Foreword Textbooks on heat transfer u'sually concentrate on the analysis of heat transfer processes and either devote only a small amount of space to the discussion of measurement techniques o r exclude this subject completely. On the other hand, special problems a r e encountered in heat transfer measurements and experience is required when accurate results a r e desired. F o r this reason, a special summer course on "Measurement Techniques in Heat Transfer" was held in June, 1968, at the University of Minnesota, organized by i t s Extension Division with lectures presented by the staff of the Thermodynamics and Heat Transfer Division of the School of Mechanical and Aerospace Engineering at the University of Minnesota, and by speakers from other organizations who are specialists in the subjects of their lectures. P a p e r s based on these lectures have been collected a t the suggestion of the Advisory Group for Aerospace Research and Development and form the content of this book. Temperature measurements in a heat transfer situation should not be considered without a check on possible systematic e r r o r s caused by conduction, radiation or, in an unsteady situation, heat capacity effects. Section 1 discusses these e r r o r s and the means to calculate them. Section 2 discusses resistance thermometers, thermocouples, and pyrometers, their calibration and use for temperature measurements. The corresponding lecture at the summer course was given by G . W. Burns of the Heat Division, Institute of Basic Standards, National Bureau of Standards. Experimentation of heat transfer processes under cryogenic conditions requires special techniques for temperature measurements which are discussed in Section 3. Optical techniques have the advantage that they do not disturb the temperature field in which the measurements a r e to be made. Optical systems based on variations At high temperatures spectroin index of refraction a r e reviewed in Section 4. scopy can be used as a diagnostic tool and this technique is discussed in Section 5 . A very useful tool for the measurement of the enthalpy in a high temperature g a s s t r e a m is the enthalpy probe discussed in Section 6. The measurement of heat flux poses special difficulties as illustrated by the techniques described in Section 7. The close analogy between heat transfer, on the one hand, and mass transfer, on the other, makes it possible to obtain information on a heat transfer process by measurements in an analagous m a s s transfer situation. This offers an advantage where m a s s transfer experiments are simpler to perform o r where clearly defined boundary conditions a r e required. The electrochemical method offers, in addition, the advantage that it requires only electrical measurements and that local and instantaneous measurements can be performed. Section 8 discusses such analogy measurements. Thermal radiation as a means of heat transfer has increased in importance in recent years because of the trend in engineering systems towards higher temperatures and because it is the only mechanism f o r heat transfer from vehicles movingthrough space outside the atnios phere. Techniques used for the investigation of thermal radiation a r e discussed in Section 9.

-

Knowledge of thermodynamic and transfer properties is required to calculate heat transfer in specific engineering problems as well as to generalize the results of heat transfer measurements with the use of dimensionless parameters. Measurements of such properties a r e often performed concurrently with heat t r a n s f e r investigations and the techniques used f o r such measurements a r e discussed in Sections 10 and 11. The measurement of fluid velocity i s often fundamental to measurements of convective heat transfer. The laser-Doppler method described in Section 12 permits

12

velocities to b e inferred from the frequency shift of a scattered l a s e r beam. The light beam, unlike a normal velocity probe, does not affect the flow field. Velocity measurements which are usually performed by hot wires a t low temperatures require special instruments when they are t o be performed a t higher temperature levels. Such instruments are discussed in Section 13. The authors wish t o acknowledge the assistance of W.T. Pennell in the preparation of the manuscript for publication and of D.R. Pedersen in the preparation of the index. I

We hope that this volume will be useful f o r those in the various branches of science and engineering who have t o perform heat transfer measurements. E. R. G. Eckert and R. J. Goldstein Minneapolis, Minnesota November, 1968

13

Error Estimates in Temperature Measurement E. M.. SPARROW Heat Transfer Laboratory, University of Minnesota, Minneapolis.

Summary Section one describes computational models f o r estimating e r r o r s in temperature measurements in fluids and in solids. Consideration is given to measurements performed with thermocouples and similar probes. The various analytical models include heat transfer by conduction, convection, radiation, and viscous dissipation effects. Both transient and steady-state e r r o r estimates are made. Introduction It is widely recognized that the output of a sensor such as a thermocouple o r a thermometer represents an approximation to the temperature at some location in a fluid o r a solid. There are a variety of factors which can cause deviations between the probe output and the actual temperature at the point of interest, in the absence of the probe. F i r s t of all, the presence of the probe itself may modify the thermal conditions at the point and in i t s surroundings, thereby altering the temperature distribution. This happens, f o r instance, when heat i s conducted to o r away from a thermocouple junction through the lead wires. A second major factor is that the sensor may communicate with other environments beside the one whose temperature is being measured. F o r example, a thermocouple whose function i s to measure the temperature in a flowing g a s may exchange heat by conduction and radiation with the duct walls. In addition, certain basic characteristics of the energy transfer and energy storage processes tend to favor the occurrence of e r r o r s in temperature measurement. One such characteristic i s that convective heat exchange cannot talte placc without a temperature difference ( i . e . , the heat transfer coefficient is not infinite). Another is that viscous dissipation (aerodynamic heating) occurs in the boundary layer adjacent to a body situated in a high speed flow. In addition, in transient processes, the heat capacity of the sensor brings about a temperature difference between sensor and fluid. The task of designing low-error temperature s e n s o r s is aggravated by the fact that near-perfect thermal insulators do not exist. This is in contrast to the situation in electrical measurements, where essentially perfect insulators a r c readily available. By careful design, it is possible to reduce the measurement e r r o r s that result from one o r more of the aforementioned causes. For instance, convectivc heat transfer coefficients can be increased by locally increasing the fluid velocity adjacent t o the sensor. Similar desirable effects can be achieved by ninnipulntinji the size and the shape of the sensor,and radiative exchange with thc surroundings

14

VISIBLE SURFACES

CONVECTION /------

-
1.3920 calibrate a t ice, steam, S-points

-

630.5 to 1063°C

660 to 1063°C Pt-Pt lO%Rh thermocouple

Pt-Pt 10%Rh thermocouple e = a + bt + ct2

e=a+bt+ct2 calibrate a t Sb, Ag, Au-points

calibrate at Sb, Ag, Au-points

above 1063°C monochromatic optical pyrometer

above 1063°C monochromatic optical pyrometer

c2 Jt - c2 log--h JAU

- 1- 1336

with c, = 1.432 cm deg

1 t + To

log

Jt

-

-JAu

c, = 1.438 cm deg

(tAu+ To)

- 1

c2 - 1 (t + To)

113 TABLE 3-3: Difference Between ITS (1927)and IPTS (1948).

Hust (6)

I

I

Platinum Thermometer Range t

"c

(Int)1948 At'C (ht) 1948

-

OC @It) 1927

0.oo*

630.5 650 700 750 800 850 900 950 1000 1050 1063

.08* .24 .35 .42 .43 .40 .32 .20 .05 .00

*

These values are uncertain since platinum thermometers are defined only up to 630.5°C on 1948 scale (see Corruccini (29)). Radiation Law Range

1

It is difficult to determine exact differences of the ITS and IPTS in this range because of the variability of X ; the wavelength of the radiation on the 1927 scale is restricted only to the visible spectrum.and is not restricted at all on the 1948 scale. The following table contains the dlfferences calculated at AI = 0.4738 x 10-4 cm and A 2 = 0.65 x 10-4 cm according to Corruccini (29). t "C (Int) 1948

At'C

(Int) 1948 A1

I

1

I

h

1063 1500 2000 2500 3000 3500 4000

'C

(Int) 1927 A2

0

0

-2 -6 -12 -19 - 28 -38

-2 -6 -12 -20 -30 - 43

114

TABLE 3-4: Relation Between the International Practical Scale and the Thermodynamic Scale (1960) International Practical Scales Celsius

Absolute

Names International Practical Temperature

International Practical Kelvin Temperature

Symbols

tint

T i n t = tint

+

TO

Designations

"C (Int. 1948) degrees Celsius inter national practical 1948

OK (Int. 1948) degrees Kelvin inter national practical 1948

Thermodynamic Scales Celsius

Absolute

Names Thermodynamic Celsius temperature

Thermodynamic Kelvin temperature

Symbols t = T - T o Designations "C (therm.) degrees Celsius thermodynamic

OK degrees Kelvin

Notes: For the international practical temperature, the subscript "int" after t may be omitted if there i s no possibility of confusion.

To = 172.15"

I

115

0.01"C as the triple point of water. Stimson (2) observes that for precision no greater than O.OOl"C, the zero on the 1948 Celsius scale (ITS 1948) may be realized with an ice bath as described in the 1948 ITS. The International Practical Temperature Scale (IPTS) specified four things: (a) the gas scale temperatures of reproducible defining fixed points and the secondary reference points at which instruments are calibrated, (b) the types of instruments to be used in realizing the scale, (c) the equations to be used for interpolating o r extrapolating from the fixed points, and (d) the experimental procedures recommended for both measurement and calibration. A summary of the IPTS and a comparison of the 1927, 1948 and the 1960 revision of the 1948 scale a r e given in Tables 3-1, 3-2 and 3-3, taken from Hust (6). The complete range of temperatures from -182.97"C to 1063°C is included for completeness. Twenty-two secondary reference points from -78.5"C to 3380°C including their vapor temperature-pressure relations are given by Stimson (3). The relationship between the International Practical Temperature Scale (1948)and the thermodynamic scale is shown in Table 3-4 (2). Because of the polynomial form of the interpolating equations used to describe the International Practical Temperature Scale (IPTS) between the defining fixed points, a n inherent difference exists between the IPTS and the thermodynamic temperature scale (TTS). This difference is determined by comparing gas thermometer readings with those from standard thermometers as prescribed by the IPTS. Hust (6)reports the data of several investigators who examined the differences between the TTS and the IPTS in the range 190°C to 0°C. These results are shown in Fig. 3-6. As may be noted, fairly large discrepancies exist between these various results probably because of differences in the gas thermometers measurements as suggested by the data in Fig. 3-5. In order to examine and define these differences systematically, Preston-Thomas .and Kirby (35)redetermined part of the TTS, in t e r m s of platinum resistance thermometer readings, by means of a constant volume helium gas thermometer of reasonably high accuracy. These authors expect to extend similar measurement to -219"C, the triple point of oxygen. Their measurements in the range -183°C to 100°C are given inF'ig. 3-7. As may be seen by the data in Fig. 3-6 and 3-7, the IPTS and the TTS differ by a maximum of about 0.04"C in the cryogenic range.

-

Temperature Scales Below 90°K Below the oxygen point (-182.97"C, 90.18"K) no International Temperature Scale presently exists. During the past few y e a r s however, a great deal of study has been devoted to this problem by the CCT and a number of proposals for extending the IPTS to 13.8"K, the triple point of equilibrium hydrogen, have been made. It now s e e m s probable that the IPTS in force since 1948 will be abandoned and replaced with a new scale (4) (5). This new scale, which may take effect as early as late 1968 o r perhaps during 1969, will conform to the best experimental values of the thermodynamic temperatures now available. If these events transpire as expected, it will m a r k a period of 20 y e a r s between the new scale and the 1948 scale which itself replaced the 1927 scale after about a similar 20 year tenure. This will, of course, leave the important range below 13.8"K undefined by an international standard and since this includes the entire region of the He4 and He3 it can only be hoped that similar efforts by the CCT will bring about a standard scale a t these very low temperatures. Because of the absence of an international standard below 90°K several 'national' o r 'laboratory' scales have been developed, each of which is different from the others and from the thermodynamic scale. They are based on the resistance characteristics of platinum calibrated against a gas thermometer and several of these scales were compared inFig. 3-2. Scott (36) compares several.other scales as

116 11s-IPTS

('C)

-180

Fig. 3-6

-160

-1LO

-120 -100 -80 -60 TEMPERATURE ("Cl

-LO

-20

0

Temperature differences between thermodynamic and internal:ionaI temperature scales

TTS - IPTS ("C)

-200

-160

Fig. 3-7

-120

-80

-

10 0 TEMPERATURE ("C)

LO

80

120

Comparison of measurements of TTS-IPTS (35)

TI'K)

Fig.

3-8

Comparison of temperature scales (36) Calif = University of California (37); NBS = National Bureau of Standards ( F 18); PSU = Pennsylvania State University (12); P T R = Physikalishe Technistlae Reichsanstalt (36)

117

indicated in Fig. 3-8. The NBS (1939) scale has been superseded by the NBS (1955) scale formed by lowering all temperatures on the NBS (1939) scale by 0.01"C and these scales have been the basis for all NBS calibrations in the interval 1 2 9 0 90°K since 1939. The agreement of the NBS (1939) scale with the thermodynamic scale was f 0.02"C in the range 1 2 9 0 90°K. It is interesting to note that the scale identified as 'Calif (1927)' in Fig. 3-8 is formulated on the basis of a copper-constantan thermocouple which was stable over a period of 3 years having an estimated accuracy of 0 . 0 5 " K in the range 12"to 90°K (37). In 1964 the CCT established a provisional temperature scale to be considered as a replacement for the IPTS below 273.15"K. This scale is referred to as CCT-64 and is in the form of a resistance-temperature table for platinum thermometers, extending from 10°K to 273.15"K. The derivation for the range 90°K to 273.15"K is given by Barber and Hayes (38). Currently, certain modifications are being considered in it prior to its recommendation as an international scale (5) but, any modification in CCT-64 will doubtless be small, and the low temperature part is assumed (6) to be the best approximation to the thermodynamic scale in this region. Calibration of thermometers below 90°K may be accomplished using a number of multi-phase equilibrium states, called fixed points and Timmerhaus (39) lists several of these states which a r e given here in Table 3-5.

TABLE 3-5: Fixed Points Below 90°K (39) Point Lambda point of helium Boiling point of helium (1 atm) Triple point of equilibrium hydrogen Triple point of normal hydrogen Boiling point of equilibrium hydrogen (1 atm) Boiling point of normal hydrogen (1 atm) Triple point of neon Boiling point of neon (1 atm) Triple point of oxygen Triple point of nitrogen Boiling point of nitrogen (1 atm)

Temp., OK 2.173 4.215 13.81 13.95 20.27 20.39 24. 57 27.17 54.36 63.14 77.35

These a r e not presently 'secondary reference points' as prescribed by an International Temperature Scale, but represent the best literature values. An equilibrium cell o r vapor pressure thermometer is employed to determine these states and would be similar to the oxygen vapor-pressure thermometer described by Timmerh a w (40) and shown in Fig. 3-9. For precise calibration of thermometers in the range 0.20"K to 5.2"K the vapor pressure scales of He4 and its light isotope He3 are available. For temperatures between 1 ° K and 5.2"K the International Committee on Weights and Measures in October 1958 recommended for international use a scale based on equilibrium between He4 liquid and its vapor now known as-the '1958 He4 scale of temperatures'. This scale is described by Brickwedde,'el al.(41) where the vapor pressure of He4 is tabulated for intervals of 0.001"K from 0. 50°K to 5.22"K. Clement (42) concludes that the He4 1958 scale is accurate within 0 . 0 0 1 to 0.002"K with a roughness less than 0.0001"K. Values of the vapor pressure of He4 in microns (10-3 mm Hg) for intervals of 0.Ol"K a r e given in Table 3-15, taken from ref. 41.

Ih'

A comparison of the 1958 He4 scale with previous scales is shown in Fig. 3-11, taken from Hust (6). The identification of the various scales is given by Brickwedde, et a1 (41). The acoustical thermometer of Plumb and Cataland (11) provides an

118

.

THERMOCOUPLE

4

THERMOMETER

/

INSULATING SHIELD

'COMMERCIAL LIQUID OXYGEN

, HEAVY

COPPER CYLINDER

--

-PURE LIQUID OXYGEN

MERCURY 1 , MANOMETER 1

Fig. 3-9

Oxygen vapor-pressure thermometer for calibrating working thermometers (40)

119 PRESSURE (mmHg)

0

1

2

3

4

s

TEMPERATURE ('K)

Fig. 3-10

Fig.

3-11

Phase diagram for helium

Deviations of earlier helium vapor-pressure scales from 1958 He4 scale ( 6 )

120

1000

100

10 PRESSURE (mm Hg)

1.0

I I

0.1

I

U 0.5 1.0 1.5 2.0 2.5 3.0 3.5

'O10

1

K

I I

I I

(A). Vapour pressure measurement. 1958 He- scale: (B). Estimated reproducibility of a Ge resistance thermometer 'wire scale'; (C). Estimated reproducibility of any of the Pt resistance thermometer 'national' scales; 0). Reproducibility of the Barber van Dijk scale (46)on the (optimistic) assumption of the fixed points being realisable to 0.2 millikelvin; (E). IPTS in the 90 (K) to 273 (K) range assuming the indeterminacy shown by Barber (32): (F). IPTS in the 90 (K) to 273 (K) range assuming the indeterminacy shown by Lovejoy (47)(F,) o r alternatively the use of an additional fixed point (CO2 point) in a modification of the IPTS (Fa); (G). IPTS in the range Reproducibility of a modification of the IFTS in the 0°C to 630°C; @I). manner suggested by McLaren (48); (J). Estimated reproducibility of a Pt resistance thermometer scale in the 630°C to 1063OC range; (K). Reproducibility of the IPTS (using P t 10 Rh/Pt thermocouples) in the 630°C to 1063OC range.

I I

1

121

interesting comparison with the results of the vapor pressure scale. The phase diagram for He4 is shown in Fig. 3-10.

Below the A-point a t 2.173"K liquid helium experiences a transition to its superfluid state. The tendency of superfluid helium to flow makes vapor pressure measurements difficult below the A- point and furthermore, below 1°K the vapor pressure of He4 is less than 120 microns adding additional problems in measurement. To overcome both of these drawbacks the vapor pressure of the light isotope He3 was determined and developed into the He3 scale. A comparison of the vapor pressures of He3 and He4 is given in Fig. 3-12, taken from Arp and Kropschot (43). F o r comparison it will be noted that the vapor pressure of He3 at 1°K is 8,842 microns and that of He4 a t the s a m e temperature is only 120 microns. The International Committee on Weights and Measures in 1962 recommended the use of the He3 vapor pressure temperature data for international use. This scale, which is known as the '1962 He3 scale of temperatures', is tabulated in intervals of 0.001"K from 0.20"K to 3.324 "K by Sherman, et nf (44). Vapor pressure data in intervals of 0.01"K for He3 a r e given in Table 3-16, taken from the summary table of Sydoriak, et 01 (45). Preston-Thomas and Bedford (5) have examined the reproducibilities of various actual and postulated temperature scales in the range 1°K to 1063°K. Their results are given in Fig. 3-13 indicating a general reproducibility of 10-2 to 10-3 over the f u l l range. Thermometers for Cryogenic Temperatures The remaining sections of this paper will consider the principle devices which a r e employed to measure cryogenic temperatures, including thermoelectric, electrical resistance and magnetic thermometers. A survey of available low temperature thermometers is illustrated in Fig. 3-14 for the temperature range 0.05"K to 300°K. This is an extension of a similar chart presented by Timmerhaus (40). A comparison of the performance of several of these devices has been prepared by Corruccini (63) in a survey of temperature measurements a t cryogenic temperatures. His results a r e given in Table 3-6. TABLE 3- 6: Comparison of Cryogenic Temperature Measuring Devices Type

Range, "K

Best Reproducibility,, "K

1 Platinum Res istance 2 Carbon 3 Germanium 4 Gold-Cobalt vs Copper Thermocouple

10-900

10-3 to 10-1

10-2

to 10-4

to 10-3 10-3 to 1 0 - 4 10-1 to 10-2

10-2

to 10-3

1-30 1-100 4-300

10-2

Best Accuracy, "K

1 0 - 2 to

10-3

0.10

Thermocouples The familiar thermo-electric circuit - the thermocouple - i i i which an E M F is produced by subjecting the junctions of dissimiliar metallic combinations to different temperatures is commonly used in the cryogenic temperature range. In circum-

122

-

I

I I

la

+ ' / // / / / / / / / / / / / / / / / / /

02 VAPOUR PRESSURE

CARBON RESISTANCE THERMOMETER

I

n

He' VAPOUR PRESSURE

I

Nz VAPOUR PRESSURE I

m

H 2 VAPOR PRESSURE

He'VAPOUR PRESSURE

I I I

I

I

P PT RESISTANCE THERMOMETER I

P / / / / / / / / / / / / / / / A / *

-////////l/l/l MAGNETIC THERMOMETER

I

THERMOCOUPLE

V / / / / / / / / / / / / / / / / / / A / d

I I

GAS THERMOMETER

0.05 I

0.10 I

LIQUIDS-

1

10

I

I

I

A=He

1

He

100 I

I

H2

N:h2

I

300 I

ROOM TEMPERATURE

TEMPERATURE SCALE ( ' K )

Fig. 3-14

Temperature ranges normally associated with various low temperature thermometers

I ~

1 1 I I

I

'

I

, l I

123 stances where measurement accuracy is from 0.25 to 0. 50'K a thermocouple may even be the preferred temperature sensing element. There are several reasons f o r this. A thermocouple is easily made, is small and can be mounted relatively simply in remote and fairly inaccessible locations, requires only standard laboratory o r industrial measuring instruments, can be made rugged and relatively insensitive to environmental disturbances, and is inexpensive. Other desirable characteristic that can be obtained using themocouples are: a large net thermal EMF, a monotonic o r linear EMF-temperature characteristic, a stable EMF-temperature characteristic, resistance to chemical corrosion, including the effects of both oxidizing and reducing atmospheres, uniformity of the wire material in large batches and high thermal response. The influence of the environment must often be reduced by the use of protection tubes. The common thermo-electric elements in use today at temperatures from 4'K to 300'K are the gold-cobalt vs copper and the constantan vs copper junctions, described below. Measurements made a t the liquid nitrogen, liquid oxygen and liquid hydrogen temperature probably have used the constantan vs copper thermocouple with greater frequency than any other single combination. As was mentioned earlier, the 'Calif (1927)' scale in Fig. 3-8 was formulated on the basis of a copper-constantan thermocouple (37) and this particular thermocouple was found to be stable for a period of 3 years in the temperature range 12'K to 90'K with an accuracy of 0.05"K. Although thermocouples are commonly used a t temperature below 300'K the International Practical Temperature Scale is not specified in t e r m s of thermo-electric systems in the cryogenic range of temperatures. The principal reasons for this a r e accuracy and reproducibility as compared with the platinum resistance thermometers. The general principles of thermo-electric thermometry and the various thermoelectric circuits and instrumentation are of course, important to design for the installation of thermocouples. In view of space limitations here and the generally wide availability of this kind of information, it will not be included in this discussion. Finch (49) has given a thorough presentation of the principles of thermoelectricity. Some improved reference tables for iron-constantan, chromel-alumel, copper-constantan and chromel-constantan thermocouples a r e presented by Benedict and Ashby (50). Caldwell (51) discusses the properties of various materials that could be used as thermocouple elements a t temperatures above 0°C and the use of thermocouples in engineering measurements and their circuits are given by Weber (52), Baker, et a1 (53) and Dike (54), among others. The behavior of a thermocouple element is usually characterized by i t s thermoelectric potential of EMF, E , and its thermoelectric power, dE/dT. Its EMF, E , is always related to an arbitrarily selected reference temperature. At cryogenic temperatures the common thermoelectric combinations a r e gold-cobalt (Au + 2.11 atomic percent CO) vs copper, copper vs constantan (60 percent Cu and 40 percent Ni), gold-cobalt vs normal silver (Ag + 0.37 atomic percent Au), Iron vs constantan and chromel-P (90 percent Ni and 10 percent Cr) vs Alumel (95 percent Ni and 5 percent (Al, Si, Mn). Themorefrequently used thermocouples, however, are the goldcobalt vs copper and the copper vs constantan combinations. These thermocouples have been used to temperatures as low as 0.2'K. Their best accuracy in the temperature range 4 to 300'K is 0. 10°K,for gold-cobalt vs copper and 0.50"K for copper vs constantan. The thermoelectric potential differences for these 5 thermocouples is given in Table 3-7, taken from Powell, et af (55). The principal advantage of the use of the gold-cobalt vs. copper combination is evident from these data as it has a significantly higher thermal EMF. However, owing to inhomogeneities in i t s chemical constituency this combination produces irregular EMF'S that are uncompensated for in i t s calibration and therefore give rise to measurement e r r o r s . In fact, this lack of homogeneity in composition is

124 TABLE 3-7: Thermoelectric Potential Differences in Microvolts for Several Thermocouple Combinations (55)

--

-

Thermocouple Combination

Temp. OK

Cons tantan vs Copper

4-20 20-76 76-273

57.8 646.9 5545.6

GoldCobalt

.

--

vs. Copper

Norma1 Silver

vs Copper

0.2 171.4 1562.5 37.9 8123.2 133.7

Iron vs Constantan

.

Chrome1 P vs . Alumel

59 805 8252

41 616 6182

TABLE 3-8: Inhomogeneity of Thermoelectric Voltages Obtained from Dip Tests (50)

-_

Samples

Bath temperatures 76-300°K 4-300'K Voltage (uv) Voltage (uv) Maximum Average Maximum Average

(a)

Cu

4. 5

2.5

2.0

0.8

(b)

cu

1.8

0.7

1.0

0.3

(c)

Constantan

0.5

0.2

0.5

0.2

(d)

Au-CO

5.0

3.0

4.0

2.5

(e)

Au-CO

5. 5

3.5

4.0

2.5

(f)

Ag-Au

2.2

1.2

1.2

0.8

.

Samples were: (a) Instrument grade copper, 32 A. W. G.; (b) Thermocouple grade copper, 36 A. W. G.; (c) Thermocouple grade constantan, 36 A. w. g. ; (d) Goldcobalt, Bar 9, 36 A. w. g. (1960); (e) Gold-cobalt, Bar 5, 36 A. w. g. (1958); (f) 'Normal' silver, 36 A. w. g. the greatest single defect in the Au-CO vs. Cu thermocouple. When the chemical metallurgy of the Au-CO wires can produce a product having a constant, controllable and stable composition this thermocouple will come into much wider use a t very low temperatures. The effects of inhomogeneity are usually greatest when the measuring and reference junctions are at widely different temperatures. In such cases the thermocouple lead wires are subjected to steep temperature gradients and a t the points of greatest temperature change in the wire chemical inhomogeneity will produce an EMF. Thus, the Au-CO vs. Cu combination is best used where temperature differences to be measured are small. A convenient and practical application is the use of the Au-CO vs. Cu combination a6 a differential thermocouple in a n installation where the temperature differences are s m a l l or zero, as i n constant temperature baths, cryostats and equilibrium cells f o r temperature calibration. The Fe vs. Con and Ch vs. A1 thermocouples are infrequently used at low temperatures principally because of voltage uncertainties resulting from inhomogeneities in the wires.

125

TABLE 3- 9: Thermoelectric Potential Differences in Microvolts f o r Gold-Cobalt and Constantan vs. Copper Thermocouples (56)

Constantan

Temp.,

Au-CO

0.00 2.09 8.22 18.20 31.83 48.93 69.30 92.75 119.1 148.1 179.6 269.1 372.5 483.0 614.2 749.9 893.9 1045.2 1202.9 1366.2 1534.5 1707.1 1883.5 2063.4

0.00 0.66 2.62 5.83 10.26 15.88 22.64 30.50 39.43 49.40 60.40 92.31 130.3 173.9 222.9 276.8 335.6 398.8 466.2 537.5 612.7 691.2 773.0 858.1

90 95 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 2 50 260 270 280 290 300

Temp.,

OK 0 2 4 6 8 10 12 14 16 18 20 25 30 35 40 45 50 55 60 65 70 75 80 85

OK

Au-CO

Constantan

2246.8 2433.3 2622.6 3008.5 3402.8 3804.1 4211.2 4623.2 5039.1 5458.4 5880.4 6304.6 6730.6 7158.0 7586.4 8015.7 8445.5 887 5.6 9305.9 9736.2 10166.3 10596.1 11025.5

946.7 1038.5 1133.7 1333.7 1546.4 1771.7 2009.5 2260.0 2522.7 2797.1 3083.1 3380.3 3688.6 4007.7 4337.4 4677.5 5027.8 5388.0 5757.9 6137.3 6526.0 6923.7 7330.2

126

THERMOELECTRIC POWER (pVl'KK)

Fig. 3-15

Thermoelectric power a s a function of temperature for various thermocouple combinations ( 6 3 )

R I R (273.15

0

Fig. 3-16

OK)

100 200 TEMPERATURE

300 (OK)

Resistance ratio of platinum as a function of temperature

I

127

An estimate of the inhomogeneity of thermoelectrical voltages obtained by placing one section of a wire sample in a cryogen while the two ends of the wire a r e attached to a potentiometer is reported by Powell, et a1 (56) and shown in Table 3-8. As is evident from this sampling, the gold-cobalt wire is subject to the greatest voltage uncertainty. Thermocouple grade copper and constantan exhibit the least voltage uncertainty owing to inhomogeneity.

1

1 1 ~

' I

Powell, et a1 (55)(56) have studied the thermoelectric characteristics of several thermocouple combinations in the temperature range 4°K to 300°K. A summary of their results for the Au-CO vs. Cu and Cu vs. Con thermocouples is given in Table 3-9 f o r a 0 ° K reference temperature. An extensive tabulation of the thermoelectric potentials and thermoelectric power in 1°K intervals for these combinations from 0°K to 300°K is found in ref (56). These results represent the best average or smoothed data f o r a family of thermocouple combinations and thus, they may be used as the standard reference data for each thermocouple. Such data a r e of great value in thermocouple calibration, as is discussed later. The thermoelectric power, dE/dT, in microvolts per degree Kelvin for the five thermocouple combinations in Table 3-17 is given in Fig.3-15 as a function of temperature. At temperatures from 4°K to about 200"K, the Au-CO vs. Cu thermocouple is clearly the superior combination from the standpoint of thermoelectric power. Below about 40°K the Fe vs. Con, Ch vs. Al and Cu vs. Con thermocouples have about the s a m e thermoelectric power. Normal silver vs. copper produces a n almost insignificant thermoelectric power a t low temperatures. The thermoelectric power, dE/dT, in Fig. 3-15 may be used to give an indication of the sensiti,vity of temperature measurement when it is related to the measurement sensitivity of the potentiometer AE* in microvolts, used to measure the thermal EMF of the thermocouple. That is, the uncertainty in temperature indication, AT*, may be written: Eq. 3-18

Thus, thermocouples having large thermoelectric power will enable a smaller measurement uncertainty for a given measuring instrument. The calibration of a thermocouple is conveniently done by establishing its deviation characteristic as compared with Standard thermocouple EMF. Standard thermocouple potentials a t cryogenic temperatures are given in Table 3-9 in summary form for Au-CO vs. Cu and Cu vs. Con and may be found in much greater detail in ref. 56. The thermocouple 'Deviation' is defined as: Eq. 3-19 where E,,, is the standard EMF corresponding to the temperature of the thermocouple for which Eo,, is its observed EMF. A deviation plot is usually constructed by obtaining several corresponding values of AE,,, and E,,, over a range of temperature and generally, when these data a r e plotted as AEDEvvs. EOBs a smooth, frequently almost linear, curve may be used to join the data points. This is a result of the fact that while each individual thermocouple wire combination will differ slightly from others of similar composition, the EMF-temperature characteristics of a 'family' of similar wires are essentially parallel. Thus, their deviations will be almost linear and exactly zero at a common reference temperature. The use of a deviation plot provides a very convenient method for making accurate temperature measurements with thermocouples. Owing to the essential linearity of a deviation curve, interpolation between a minimum number of calibration points may be done with confidence. The determination of an unknown temperature in measurement is made by computing E,,, from equation 3-19 using AE,,, taken from the deviation plot corresponding to the EOBSfor the thermocouple. The unknown temperature is found from the 'standard' table of E,,, vs. temperature.

128.

Fig. 3-17

Resistance-temperature relationships for various resistance-type temperature sensors - high range sources of data: platinum, mean of NBS calibration; tungsten; copper and nickel. (Courtesy of Rosemount Engineering Company)

.

129

The 'standard' table is usually formulated in great detail and represents the best, smoothed data for a family of thermocouple combinations. A potentiometer is probably the most satisfactory instrument for precision temperature measurement using thermocouples. These instruments are described in detail elsewhere (52) (53) (57). Instruments presently available by the Leeds and Northrup Co., the K-5 (facility) and K-3 have sensitivities 0 . 0 2 - 0 . 1 pVand 0 . 5 py respectively. The Wenner potentiometer has a sensitivity of 0 . 1 pVand a potentiometer manufactured by the Minneapolis Honeywell Co. also has a sensitivity of 0 . 1 pV. Similar potentiometers are produced by other companies. Comparing these sensitivities with the thermoelectric power of the Au-CO vs. Cu thermocouple, temperature sensitivities will range from 0.002"K to 0.01"K at a level of temperature of 10°K.

Resistance Thermometry The variation of electrical resistance with temperature provides a very convenient, accurate and practical method for temperature measurement. This method is enhanced when the material from which the thermometer is made has a stable and easily reproducible composition. Otherwise, the method becomes impractical owing to inherent instabilities in the resistance-temperature characteristic and consequent uncertainties in the temperature. The basic measurement required is that of electrical resistance and this can be done with great precision using available resistance bridges or potentiometers. Hence, with a stable material and present instrumentation a resistance thermometer can be used to measure temperature to a high degree of accuracy (52) (53) (58 - 60). F o r precision measurements the platinum resistance thermometer is the most widely used temperature measuring device in the range 1°K to 300°K. As mentioned earlier, the International Practical Temperature Scale (1948) is defined in t e r m s of the resistance characteristics of platinum from -183°C to 630.5"C. Undoubtedly, when the new International temperature scale is introduced (4) (5) (6) some time in the period 1968-69, as expected, it also will employ the resistance characteristic of platinum as the standard below 300°K, as well as above that temperature. The reason for this of course, is the unusually high degree of purity that can be achieved in the production of platinum, the reproducibility of the purity from batch to batch, its monotonic resistance-temperature curve in the strain-free, annealed state, and i t s inertness to chemical contamination. Its cost is high which may be a factor in i t s use. Other materials which are also used include copper, nickel, carbon, germanium and certain semi-conductors known as thermistors. These will be discussed later. The resistance-temperature characteristic of platinum is shown in Fig.3216. Above 50°K this relationship is essentially linear. The 1948 IPTS requires that the r e s i s tance ratio in Fig. 3-16 be equal to o r greater than 1 . 3 9 2 0 a t 373.15"K (100°C) to insure purity in the platinum wire. The resistance-temperature characteristics of platinum film on a non-conducting substrate, nickel, tungsten and copper are shown in Fig. 3-17.

i

Precision platinum-resistance thermometers are made of a fine coil of highly purified, strain-free platinum wire wound around a non-conducting frame. A typical method of construction is shown in Fig. 3-18. The ice-point resistance of these thermometers is commonly s e t a t approximately 25.5 absolute ohms. The platinum thermometer is usually manufactured as a capsule (Fig. 3-18) o r as a cane. In each case four lead wires are provided for resistance measurement. Precision resistance is best measured using a Mueller Bridge with a four lead wire thermometer as shown 3-19. The accuracy of this bridge circuit is 10-5 ohms (39) which would in correspond to approximately 0.003"K at 12'K and 0.00009"K at1OO"K. Except at very low temperatures accuracies from 0.0Ol"K to 0. 0001°K can be obtained using a platinum thermometer and Mueller Bridge. As indicated inFig. 3-19, the four lead

130

0.1 mm platinum wire

Fig. 3-18

Capsule-type, strain-free resistance thermometer (40) GALVANOMETER

z ADJUSTMENT TO MAKE RATIO EXACTLY 1:1,

NORMALOAOB CQ O D REVERSED )D( C

B ~ OA '

THERMOMETER

Fig. 3-19

Mueller bridge with a four-lead platinum resistance thermometer

131 wire circuit provides a means for reversing lead wire connections duringa measurement, this technique permitting the complete cancellation of lead wire resistance s o that the net measured resistance is that of the platinum resistance thermometer wire itself. Potentiometric methods for resistance measurement are summarized by Dauphinee (61). Calibration of a platinum thermometer can be made using a gas thermometer, another standard thermometer o r using the defining fixed-points and a polynomial equation between resistance and temperature, such as the Callendar o r CallendarVanDusen equations (28) which are equivalent to those given in Table 3-2. In the United States calibration is frequently done by the National Bureau of Standards, Institute f o r Basic Standards. Typical calibration data for a platinum thermometer is given in Table 3-10. The constants a, 6 and p were found from the CallendarVanDusen formula:

TABLE 3-10: Report of Calibration of Platinum Resistance Thermometer, L & N No. 1653433. Submitted by The University of Michigan (62) Constant

a 6

Value 0.003925780 1.49168

P P

0.11116 (t below O°C)

RCJ

25.5510 abs. ohms

0

(t above O°C)

Additional qualifying information was provided by the NBS for this calibration as follows: "The value of 6 was estimated using the assumption, based on experience with similar thermometers, that the product a * 6 is a constant. The uncertainty in the estimated value of 6 is equivalent to a n uncertainty at the sulphur point of l e s s than f 0.01 deg C. The other values given are determined from measurements a t the triple point of water, the steam point, and the oxygen point. The uncertainty of the measurements a t these points, expressed in temperature, is less than f 0.0003, f 0.0015 and f 0.005 deg C respectively. About one-half of each of these uncertainties is an allowance for systematic e r r o r s , including the differences among national laboratories, the remaining part representing the effect of random e r r o r s in the measurement process. The effects of these uncertainties on other measured temperatures are discussed in Intercomparison of Platinum Resistance Thermometers between -190 and 445OC, J. Research NBS 28, 217 (1942). During calibration the value of Ro changed by the equivalent of 5 X 10-4 deg C. These results indicate that this thermometer is satisfactory for use as a defining standard in accordance with the text of the International Practical Temperature Scale. " Resistance -temperature data on the thermometer described in Table 3-11 a r e listed in Table 3-17 f o r a small range of temperatures above 90°K. These data are computed from the following equation and represent a few of the numerical results abstracted from the original calibration:

132

5.0

4.0

RT/R 20° K

3.0

2 .o

1.0

0

Oo K

Fig. 3-20

iO°K

20° K

30°K

35OK

Resistance-temperature relationship for various resistance-type temperature sensors-low range sources of data: platinum, mean of NBS calibrations; carbon resistor; germanium thermometer; thermistor; tungsten; and indium (Courtesy of Rosemount Engineering Company)

I I

I

133

The f i r s t column is the temperature in OK (IPTS 1948), the second column is the thermometer resistance in absolute ohms and the third column gives the inverse (reciprocal) of the difference between each two successive values in the second column. These reciprocal f i r s t differences are included to facilitate interpolation. The e r r o r introduced by using linear interpolation will be l e s s than 0. 0001°C. The third column may also be expressed as dT/dFt, 'K/ohm, as the tabular difference in the f i r s t column is 1.0"K. The thermometer described in Table 3-11 was also calibrated and the results tabulated in 0.1"K intervals from 11°K to 92°K by the NBS using the "-1955 temperature scale. This temperature scale was referred to earlier and Fig. 3-2 and defines the temperature in t e r m s of the electrical r e s i s tance of platinum in the range 10°K to 90°K.

!' I

An important class of low temperature thermometers are those whose electrical resistance increases with decrease in temperature, rather than the opposite, as is the case with platinum. Below 20°K these thermometers become most practical. This class of thermometers includes carbon, germanium, and the semi-conductors (thermistors) and are the most sensitive resistance elements to temperature changes at low temperatures available. The electrical resistance characteristics of these materials is shown in Fig. 3-20 in comparison with platinum, tungsten and indium.

I I

I

The most common resistance element, which also is readily available and inexpensive, is the conventional carbon radio resistor. In addition to its high thermal sentivity a t low temperatures, the carbon resistor can be made small, is rather insensitive to magnetic fields and has a small heat capacity for rapid thermal response. It is slightly pressure sensitive, having temperature changes of 0. 31°K at 20°K and 0.02"K at 4°K for an increase in pressure of 1000 psi (64), and is subject to thermal instabilities o r ageing. This lack of reproducibility is particularly significant after the resistor has been exposed to thermal cycling. Carbon in the form of thin graphite coatings has been used as a thermometer (65), this type of thermometer being especially useful where high response is required, as in low temperature ( 0 . 1 OK) adiabatic demagnetization experiments. Lindenfeld (66) reports on the use of carbon and germanium thermometers between 0. 30°K and 20°K. One problem i n the use of carbon radio r e s i s t o r s below 1°K is the difficulty in measuring their high resistance. Maximum power dissipated in these r e s i s t o r s is about 10-8 watts for temperatures 1 "K and higher and using a Wheatstone Bridge temperature changes of 10-5 to 10-6'K can be detected. The use of the carbon resistor in measurement is greatly aided if a reasonably simple and accurate formula can be written relating resistance to temperature. Clement and Quinnell (67) found that Allen-Bradley Company cylindrical carbon radio resistors has a resistance temperature relationship below 20°K which could be expressed to within f 1/2 percent by a semi-empirical expression of the form: log,,R+-

i*

K B = A+logloR T

Eq. 3-22

The constants K, A and B are determined by a calibration of the resistor a t a minimum of three known temperatures. Typical resistance-temperature curves for two Allen-Bradley carbon r e s i s t o r s are shown in Fig. 3-21. Schulte (68) calibrated an Allen-Bradley 0 . 1 W, 270 ohm carbon r e s i s t o r between 4'K and 296°K and found his results to correlate within 7 percent of equation 3-22. For a range of temperatures from 2°K to 20°K Mikhailov and Kaganovskii (69) also found that equatioii 3-22 gave satisfactory results for carbon thermometers. In this case the constants in the equation were determined from calibrations a t 2"K, 4.2'K and 20.4"K. This permitted temperatures to be calculated with a n accuracy of a few hundredths of a degree in the range 2'K to 4.2"K. After 100 heating and cooling cycles between 300°K and 77"K, uncertainty in the temperature measurements i n the same 2. 2°K interval did not exceed 0.01"K.

134

Fig. 3-21

Resistance-temperature curve for two Allerrbradley carbon resistors (39)

MONITORING RESISTOR

-Gfl.5V

L B N TYPE K-3 UNIVERSAL

**

BINDING POSTS

L-----

Fig. 3-22

I

Schematic diagram of the L & N type K-3 universal potentiometer circuit (70)

135

1

i 1

I

Measurement of the resistance of a carbon thermometer may be made with a r e s i s tance bridge, as in Fig. 3-19, o r with a potentiometer using a n accurately calibrated monitoring resistor of known resistance,a schematic diagram of which is shown in 3-22 as used by Greene (70). He calibrated a carbon r e s i s t o r having a nominal resistance of 82 ohms with a measuring current of 10 p A. The results of this calibration are given in Fig. 3-23 which illustrates the influence of thermal cycling, the reproducibility of the calibration before and after a calibration r u n and heat conduction along the thermometer lead wires. The ordinate in Fig. 3-23 is the voltage drop a c r o s s the r e s i s t o r f o r a 10 1-1 A current. During any one calibration the accuracy amounts to f 0.022"K and is within the precision of the measurements. Although thermal cycling did produce a shift in the calibration curve, its slope remains constant and thermal conduction along the lead wires raised the calibration curve by approximately 0. 10°K in this instance. The use of carbon r e s i s t o r s for field measurement where laboratory precision is not demanded has been studied by Herr, let al (71). Allen-Bradley Co. 0.1 watt, 100 ohm (f 5 percent a t 300'K) r e s i s t o r s were found to be reproducible within f 1 percent of the absolute temperature in the range 19.5"K to 55.5'K (35"R to 100"R). The measurement of resistance ratio rather than absolute resistance was found to be a more satisfactory method owing to drift in the resistance values of the carbon resistor. The word 'thermistor' is a trade name f o r a class of semi-conducting solids having a large negative temperature coefficient of electrical resistance. It is a name derived from the word combination thermal-sensitive-resistor. In a physical description these substances are classed as electronic semi-conductors whose characteristics have been given much theoretical and experimental examination since World war 11. Semi-conductors may be classed with those substances having electronic conductivi-

ties in the range 10-5 to 103 (ohm-cm)-l, or resistivities falling between 10-3 and 10 ohm-cm (72). This can be compared with the pure metals and metallic alloys whose resistivities (73) are generally less than 10-4 ohm-cm or with the electrical insulators, as mica and quartz, having resistivities above 106 ohm-cm a t ordinary temperatures. Figure 3-24 shows these relationships. The important difference between semi-conductors and metals for thermal sensitive uses is not, however, their o r d e r s of magnitude of resitivity but the great differences in the change of resistivity with temperature as compared with the metals. This may be illustrated by a typical thermistor which will increase in resistance from 780 to 17,800 ohms for a temperature change from +30 to -30°C. This is a total change of approximately 17,000 ohms or a percentage change of about 2000 percent. Compared with standard platinum and copper resistance thermometers the corresponding change i s about 6 and 100 ohms, respectively, over the s a m e range of temperature, both changing about 20 percent. The thermistor, then, undergoes a percentage change in resistivity of about 100 times that of the metals in this range of temperature. Should a greater interval of temperature be examined, as in Fig. 3-24, the percentage change for the thermistor might be as large as 2 X l o 6 . Possibly of greater significance in the field of thermal measurements i s (dR/dT), the r a t e of change of resistance with temperature, of this thermistor as a function of temperature. At 25"C, for example, dR/dT is 44 ohms/"C and a t -30°C it i s 1120 ohms/'C, while for a standard 25-ohm platinum resistance thermometer, dR/dT is about 0.10 ohms/"C in this same range of temperature. This means Iliat if one is able to measure changes in resistance, say, to 0.01 ohm, the temperature change capable of detection with this thermistor is 0.0002"C a t 25°C and 0.000009"C a t -3O'C but some commercially available thermistors have sensitivities 100 to 1000 times greater than this. The ordinary resistance thermometer would detect n temperature change of 0. 1'C under these s a m e circumstances. It is quite generally

136 E M F MICRO-VOLTS

80

i

1

1

1

1

I

I

i

1

l

l

I

l

l

1

0 5/10/66 Therm immersed

in liquid Therm. immersed in liquid Cycle 2 0 5/25/66 Therm immersed in liquid Cycle 1 X 5/25/66 Therm in vapor above liquid A 5110166 Therm immersed in liquid ReDroducibilitv Check

A 6/7/66

-

60

-

LO

-

20 2900 -

-

80

60 -

-

LO

20 2800

-

80 -

60

-

L

o

14 0

.

l

'

l

l

l

l

1L.5

l

l

l

TEMPERATURE

Fig. 3-23

15 0 [ 'K

15.5

1

Typical calibration curves for carbon resistance thermometer (nominal resistance 82 ohms) (70) 101' 10'2 1010

10 lo6 RESISTIVITY (ohm cm)

lo4

to2 1 10-2

IO-^ -6

-100

0

100 200 300

Fig.

3-24

LOO 500

('C) Temperature-resistivity relationship of insulators, semi-conductors, and good conductors (84) TEMPERATURE

I

,

I

137 true that thermistors have greatest sensitivity a t lower temperatures. For absolute temperature measurement other considerations, naturally, a r e necessary, not least among which is the thermal stability of the thermistor element, a property possessed in the highest degree by an annealed, strain f r e e platinum resistance thermometer. Thermistors a r e available f r o m the manufacturers in a variety of shapes and sizes: discs, beads, rods, washers, and wafers. The shape selected depends on the use to be made of the element and sizes range from 0.0152" to 2.54" diameter f o r beads, 5.08" to 19.05" diameter and 1.02" to 12.7" thick for discs, wafers and washers, and from 0.0254" to 12.7" diameter, 6.35" to 50.8" long f o r rods. Lead wires of various lengths and diameters consist of platinum, platinum-iridium alloys, o r copper which can be butt-soldered, wrapped and soldered o r fired in place on the thermistor element. Silver paste contacts are available to which the u s e r can soft-solder lead wires, if desired. Washer type elements have terminals which may be mechanically clamped into place against the faces of the element. Protective coatings are frequently placed over the thermistor to prevent or retard atmospheric attack. These consist of a thin o r thick layer of glass o r enamel coating. F o r certain applications the element can be placed in an evacuated o r gas-filled bulb. The recommended maximum temperature for continuous service varies but it can be as high as 3OO0C, however some manufacturers recommend a temperature no greater than 150°C. To a large extent this will depend upon such things as the accuracy required, the atmosphere surrounding the element and the melting point of the solder, if any, used to fasten the lead wires to the element. In any event, the thermistor is used to its greatest advantage, from a thermal-sensitive consideration, at lower temperatures. Most thermal-sensitive semi-conductors (thermistors) a r e manufactured by sintering various mixtures and combinations of metallic-oxides, the common materials being the oxides of manganese, nickel, cobalt, copper, uranium, iron, zinc, titanium, and magnesium. For the commercial thermistors the oxides of manganese, nickel and cobalt, however, are the most commonly used substances for the mixtures. The result of this type of manufacturing process is a hard, dense ceramic type of material. Other materials (72) (74) which may be classed with the semi-conductors and which possess a large negative temperature coefficient of electrical resistance include chlorides such as NaC1, some sulphides like Ag,S, CuS, PbS, C a s and some iodides, bromides, and nitrides. Lead sulphide has been used as a detector of infra-red radiation in a radiation pyrometer and is marketed commercially. Its response i s high (10,000 cps) and it can detect temperatures as low as 89°K. The uses of thermistors in a radiation-type pick-up is reported (77) for measurement of sub-zero temperatures. Some pure materials such as silicon, tellurium, germanium and selenium (74) which a r e monatomic become semi-conductors in the presence of certain impurities. This effect is shown qualitatively in Fig.3-25 and 3-26 for silicon containing an unknown impurity and for cuprous oxide with varying amounts of oxygen in excess of the stoichiometric. Figure 3-25 taken from Becker, el a/ (75), shows a 107 increase in the conductivity of pure silicon by the addition of a foreign impurity. A similar large increase in conductivity is seen in the case of cuprous oxide, Fig. 3-26, also taken from (75) where the increase is due to an excess of oxygen up to 1 percent. These effects vary greatly with the type of impurity, its amount, its dispersion within the solid, and the heat treatment of the solid. Generally speaking, a thermistor can be considered for use in any application r e quiring a thermal sensitive electrical resistance element, the obvious and perhaps most widley employed application being that of temperature measurement. A s was

138

CONDUCTIVITY (ohm crn1-l

3-25 Logarithm of the conductivity of various specimens of silicon as a function of inverse absolute temperature (84)

LO0.C 100

INVERSE ABSOLUTE TEMPERATURE(+)

CONDUCTIVITY (ohm cml-'

Fig. 3-26 Lognrilhin of the conduclivity of various specimens of cuprous oxide a s a function of inverse absolute temperature.

L O O T 2b0 1 l O

6-c

(+)

INVERSE ABSOLUTE TEMPERATURE

139

(

pointed out earlier, it is possible to detect very minute changes in temperature with a thermistor owing to the large change in its electrical resistance with temperature. Brown (76) employed a Western Electric 17A thermistor to measure s m a l l changes in air temperature. The device was used in a bridge circuit, the output of which was amplified and fed into a recording oscillograph and during the initial measurement it was found that the thermistor was s o sensitive that it recorded with fidelity the fluctuation in air temperature resulting from atmospheric turbulence. A typical oscillograph is shown in Fig. 3-27. Changes in temperature could be measured to an estimated 0.0007"C.

1

Theoretical work of Wilson (78) (80) and others has lead to the following expression for the electronic conductivity of a semi-conductor:

1

I

- B/T

I

1

p

=

Ae

Eq. 3-23

Since the conductivity 6 is the reciprocal of the resistivity

we may write:

I

I

p = Ce

or :

B/T

P = p0e

B($

-

5)

Eq. 3-24

I

Also, since the electrical resistance is a geometric extension of the resistivity .equation 3-24 may be written: B

R = Roe

Eq. 3-25

Because of the form of equations 3-24 and 3-25, the logarithm of the resistivity o r resistance is frequently plotted against the reciprocal of the absolute temperature, as shown in Fig. 3-28, in o r d e r to demonstrate the electrical characteristics of a thermistor and to compare it with others. These data are experimental and are taken from Becker, et af' (75). 1

1

The experimental curves in Fig. 3-28 are almost straight, as required by Equation 3-24. However, close inspection will disclose a slight curvature which may be shown to increase linearly with increase in level of temperature (75). Hence, the equation is sometimes modified as: p = ET

-c

e,D/T

Eq. 3-26

where C is a s m a l l number compared with D or B and may be positive, negative o r zero depending on the material (75). For our present purpose we shall employ equation 3-25, since if the interval T - To is not too great this equation will adequately represent the data and it is somewhat easier to handle mathematically. t As was mentioned above the relationship of resistance to absolute temperature, given by equation 3-25, has the s a m e shape as the curve shown in Fig. 3-28, from which several important characteristics may be obtained relative to the suitability of a thermistor as a temperature sensing element. A curve of R vs. 1/T is also a convenient chart for comparing several different thermistors for use i n temperature measurement. By taking logarithms and differentiating equation 3-25 the following equations are obtained: Eq. 3-27 Eq. 3-28

140

Fig. 3-27

Thermistor response to room temperature variations (84)

SPECIFIC RESISTANCE (ohm cm)

INVERSE ABSOLUTE TEMPERATUREP~

I

I I

i

Eq. 3-29

I I

~

Equation 3-29 may be interpreted in relation to a curve similar to Fig. 3-28 o r Log R vs. 1/T. It will be noted that the slope of a curve on such a chart is written: d (Log R) = d(l/T) -dR/T

= (slope of Log R

-

I/T curve)

Eq. 3-30

Comparison of equations 3-29 and 3-30 disclosed that the right hand side of equation 3-30, the slope of a curve plotted as Log R vs 1/T, is equal to the parameter B in equation 3-25. Hence : B = (slope of Log R vs. 1/T curve).

Eq. 3-31

Equation 3-29 is then rearranged to: dR - _ dT

-

- (slope) -R

T2

Eq. 3-32

Interpretation of equation 3-32 is as follows. F o r use as a temperature sensing element it is desirable that a thermistor have as large a value of dR/dT as possible in o r d e r that it be sensitive and capable of detecting small changes in temperature for any given resistance measuring system. F r o m equation 3-32 it follows that a t any given temperature, that thermistor which has the greatest slope on a Log R vs. 1/T plot and the greatest resistance will also be the most sensitive as a temperature sensing element. In this way, therefore, a series of thermistors can be very rapidly evaluated as to their thermal sensitivity. Another method for evaluation of thermistors consists of plotting Log R, vs. B, where B is determined from experimental thermistor data in the region of To, which may be taken to be 0°C; R, is then the resistance of the thermistor a t O'C. Because most thermistors have similar characteristics it will be generally true that a thermis t o r with superior thermal sensitivity a t O°C will also have superior sensitivity at other temperatures. In any event the resistance-temperature characteristics of the thermistor can be obtainedapproximately from equation 3-25 o r from the manufacturer's published data. Equation 3-25 is approximate owing to the non-linear nature of Log R vs. 1/T, as mentioned above in connection with equation 3-26 and Fig. 3-28. The technical literature does not contain a large body of data on the stability o r ageing effects of thermistors s o what is reported here are heterogeneous results of a number of observers on a few isolatedtests. It may be generally concluded, however, that an ageing effect may be expected which usually is of the nature of an increase with time of the electrical resistance which is not linear but logarithmic, resulting in smaller percentage changes in resistance with increased time. Preageing may be accomplished by heating o r by the passage of higher than service current through the thermistor (79). These have the effect also of accelerating the ageing if the temperature is high enough.

'

The change of electrical resistance is sometimes attributed to a rearrangement in the distribution of the components of the mixture of oxides making up a semiconductor. Heat treatment is believed to play a major role in the dispersion of the components s o that ageing and pre-ageing usually involve some kind of heat treatmelit. Muller and Stolen (81) tested two Western Electric 14A thermistors a t 25°C over a period of s i x months and they report a decrease in resistance of about 50 ohms out of a total of approximately 100,000 ohms. This c o r r e s p n d s to an ageing effect of about 0.012"C.

142

PERCENT INCREASE IN RESISTANCE

1.5 1.0

0.5

0 10'

TIME

Fig. 3-29

lo3

lo2

lo4

IN HOURS AT 105'C

Effect of ageing in 105" C oven on thermistor characteristics; materials 1 and 2 (84)

TABLE 3-11: Short Range Stability of a Western Electric 14A Thermistor Time Mitis

Thermistor A

Thermistor B

0 5 10 15 20 25 30 35 40 45

96,234.0 96,234.6 96,234.2 96,23 5.0 96,234.8 96,234.8 96,234.7 96,234.8 96,234.6 96,235.0

96,234.7 96,234.6 96,234.9 96, 234.4 96,234.4 96, 234.8 96,234.2 96,234.7 96,234.0 96,234.6

.

1

143

Figure 3-29 shows ageing data (75) taken on three quarter-inch diameter discs of material No. 1 and No. 2 (No. 1 is composed of manganese, nickel oxides; No. 2 is composed of oxides of manganese, nickel and cobalt) with silver contacts and soldered leads. These discs were measured soon after production, were aged in an oven at 105°C and were periodically tested at 24°C. The percentage change in resistance over its initial value is plotted versus the logarithm of the time in the ageing oven. It is to be noted that most of the ageing takes place in the first day o r week so that if these discs were pre-aged for a week o r a month and the subsequent change in resistance referred to the resistance after pre-ageing, they would age only about 0 . 2 percent in one year. In a thermistor thermometer, this change in resistance would correspond to a temperature change of 0.05"C while thermistors mounted in an evacuated tube, o r coated with a thin layer of glass age even less than those shown in the figure. For some applications such high stability i s not essential and it is not necessary to give the thermometers special treatment. Thermistors have been used at high temperatures with satisfactory ageing characteristics. Extruded rods of material No. 1 have been tested for stability by treating them f o r two months at a temperature of 300°C and -75°C for a total of 700 temperature cycles, each lasting one-half hour. The resistance of typical units changed by less than one percent. In order to determine the life of a 1A thermistor, Pearson (82) placed it in a circuit where an off-and-on current of 1 0 mA. a. c. was repeated 30 seconds over an extended period of time. Resistance measurements were made on the units periodically in order to determine their stability with time and the general trend was a rise in resistance during the first part of its life, after which the resistance became quite constant. Over a period of 1 5 months, during which time the thermometer was put through 6 5 0 , 0 0 0 heating cycles, the cold resistance did not increase by more than 7 percent. The resistance of the thermistor when hot was found to be equally stable. The characteristics of both thermistors and thermocouples shift when exposed to high temperatures for lengthy periods of time (83). For thermistors the resistance change varies logarithmically with time with higher temperatures accelerating the change. This suggests that' if thermistors are subjected for several days o r weeks to temperatures somewhat higher than those to encountered in actual use, the major portion of the change would have occurred. For thermocouples, the change in voltage output becomes greater as the exposure time to high temperature is increased. Over a three month period in which thermistors and thermocouples were exposed to 365°K f o r about 1 5 hours, the thermistor shifted a maximum of 0. l l " K , while the thermocouple shifted 0.17"K. However, when new elements were tested and aged for 1 0 0 hours a t 530"K, the thermistors still shifted only 0.11"K while the thermocouples shifted twice as much o r 0.33"K. It was found by Muller and Stolen (81) that if the exciting potential is left impressed a c r o s s the thermistor, a steady state is reached. This implied a resistance change of less than 1 ohm on daily measurement, the cold resistance of this thermistor a t 0 ° C being 350,000 ohms. Short range stability of a Western Electric 14A thermis t o r measured a t five minute intervals a t 25°C (in ohms) is shown in the table opposite. The authors (81) used the thermistor to measure small temperature difference in a laboratory experiment. The conclusion is that no significant change in resistance was detected which could not be attributed to measurement uncertainty. To obtain a stable thermistor the following steps a r e generally thought to be necess a r y (75). By these precautions remarkably good stabilities can be attained. (a)

Select only semi-conductors which a r e pure electronic conductors.

(b)

Select those which do not change chemically when exposed to the atmosphere a t elevated temperatures.

144 RESISTANCE (ohms1

8,000

6,000

2,000

n 1

2

3

4

5

TEMPERATURE ('K 1

Fig. 3-30

Calibration curve for a germanium thermometer (79)

0 JULY 1963 0 STARTED JAN. 7. 6.4 (RESOLDEREDI

RESISTANCE (ohms1

0 STARTED JAN. 12,6L A ENDED FEB. 12. 64

A T (MILLI'K)

1

2628.61

1.0

NUMBER OF ACCUMULATED CYCLES

Fig. 3-31

Equilibrium resistance as a function of the number of accumulated cycles T = 4.2" K (87)

145 (c)

Select one which is not sensitive to impurities likely to be encountered in manufacture or in use.

(d)

Treat it SD that the degree of dispersion of the critical impurities is in equilibrium o r else that the approach to equilibrium is very slow at operating temperatures.

(e)

Make a contact which is intimate, sticks tenaciously, has an expansion coefficient compatible with the semi-conductor, and is durable in the atmosphere to which it will be exposed.

(f)

In some cases, enclose the thermistor in a thin coating of glass o r a material impervious to gases and liquids, the coating having a suitable expansion coefficient.

(g)

R e - a g e the unit for several days or weeks a t a temperature somewhat higher than that to which it will be subjected.

Clark and Kobayashi (84) (85) have studied the general characteristics of thermist o r s to be used for temperature measurement. This includes the theory of their conductance properties, the dynamic response and steady-state e r r o r of the thermistor temperature-sensing element, their stability and the resistance-temperature characteristics of approximately 300 commercially available thermistors from 8 different manufacturers. Friedberg (79) describes a semi-conducting film of ZnO used as a thermometer a t 2°K which had an electrical resistance of 5(105) ohms a t liquid helium temperatures, and a sensitivity of approximately 5(104) ohms per degree K at 2°K. Germanium, with impurities consisting variously of arsenic, gallium or indium, has become one of the most satisfactory materials for thermal resistance elements in the range 0.2'K to 20'K. This material possesses a negative temperature coefficient of resistance, a moderate level of resistance, high sensitivity of resistance change to temperature change, high reproducibility and stability to thermal cycling and is readily manufactured and fabricated. The impurities are included in the germanium in controlled quantities to influence both the resistance-temperature characteristics and the sensitivity and a typical resistance-temperature curve for germanium 'doped' with 0.001 At percent indium is shown inFig. 3-30 for the temperature range 1°K to 5°K. This particular element was found to be highly reproducible over a period of several months and the thermometer was subjected to a number of warming and cooling cycles following which its resistance-temperature characteristic could be reproduced to within f 0.001 OK. The measuring current used was 0.01 ma although the author reports an increase of current to 0.1 ma did not appreciably influence the R-T characteristic (79). Edlow and Plumb (86) (87) studied the reproducibility and temperature-resistance characteristics of a number of commercially available germanium thermometers, the germanium having either arsenic or gallium as the impurity. Their purpose was to find out if a germanium thermometer was sufficiently stable to be used as a basic secondary standard thermometer. As a consequence of their study the NBS adopted the germanium resistance thermometer as the basis for the NBS scale from 2'K to 20°K and used it for basic temperature calibration in this range. The determination of reproducibility was made by cycling the resistance element from 4.2'K to 300°K and measuring the resistance change a t 4.2"K which was then related to the corresponding temperature change. Two typical heating-cooling cycle tests are shown in Fig-3-31 and 3-32. In each case the reproducibility is within f 0.001"K. In the case of r e s i s t o r D, Fig. 3-32, the reproducibility is within 0.0005'K after 86 cycles. Because of this high degree of stability the resistor of Fig. 3-32 became one of the NBS standard thermometers. This result is auite tvoical of that found bv others.

146

I 2566.6

-

2566.2

-

2565.8

-

I

I

1

I

I

I

I

I

- 1.0 - 05 I

I

1

I

1

I

I

I

0

NUMBER OF ACCUMULATED CYCLES

Fig. 3-32

Equilibrium resistance a s a function of the number of accumulated cycles for a resistor D. T = 4 . 2 " K ( 8 7 )

15,000

I

I

I

I

i O r

10,000 9.000

or

-

-

-

6,000

1 %

-

5.000

-

-

4,000 -

-

3,000 -

-

8.000 8.000 7.000

-

CL

-

0,

0,

-

RESISTOR IDENTIFICATION 0 RESISTOR No. 1

0 RESISTOR No. 2 X RESISTOR No. 3

2,000

-

1

1,500 1.500 1.5

Fig. 3-33

1

I

I

I

-

2

3

C

5

6

A plot of the resistance-temperature calibration data for resistors 1, 2, and 3. (86) Temperatures were derived from liquid helium-4 vapour pressures

147

'

~

1 1

Kunzler, et a1 (88) for example, cycled arsenic 'doped' germanium encapsulated in helium-filled thermometers as many as 50 times and found no evidence of calibration change of as much as 0.0001"K. Furthermore, they report two such thermometers in use for 3 years on low temperature experimental apparatus with no observable change in calibration. From results such as these it s e e m s safe to conclude that germanium 'doped' with a selected impurity is a suitable material for low temperature thermometers below 20'K. The resistance-temperature calibration data for a number of encapsulated, hermetically sealed, arsenic 'doped' germanium thermometers was determined by Endlow and Plumb (86) in the range 2 . 1 " K to 5.O"K. The resistance was measured a t temperature intervals of 0.1"K in a pressure-controlled helium liquid-vapor equilibrium cell and other measurements were made in a calibration comparator apparatus. The results agreed to within O.OOl"K, the basic standard temperature reference was the NBS 1958 He4 scale, Table 3-15 and some typical data a r e given in pig. 3-33. A polynomial function was derived for each thermometer to represent its resistance-temperature calibration in the range 2.1"K to 5.O"K. The sensitivity of a germanium thermometer, dR/dT, manufactured by Cry0 Cal, Inc. (89), is shown in Wg. 3-34 for the temperature range 2°K to 28'K. At 20'K the sensitivity of this thermometer is 3 ohms per "K which be compared with a sensitivity of 0 . 0 1 8 5 ohms per "K for a platinum thermometer a t the s a m e temperature. The very large increase in sensitivity for germanium at temperatures below 20°K is characteristic of this type of resistance thermometer. The use of arsenic-doped germanium prepared from a single germanium crystal is reported by Kunzler, et a1 (88), the germanium element being cut into the form of a bridge of dimensions 0 . 0 6 X 0 . 0 5 X 0 . 5 2 cm with side a r m s near each end for electrical connections. An encapsulated thermometer design is illustrated in Fig. 3-35. When covered with a platinum case it is filled with helium gas which limits its lowest useful temperature to about 0.25"K. Bare bridges have also been used in applications such as adiabatic demagnetization experiments where a thermometer with minimum heat capacity is required to give high response and in this case a lag time between the thermometer and sample was 0 . 1 second. Higher currents are permitted with the bare bridge than with encapsulated models owing to the improved cooling permitted by the exposed germanium element. The resistancetemperature characteristics of the encapsulated model were found to be unaffected (within * 0.0001"K) by thermal cycling o r aging over a period of several years. Cycling of the bare bridge between 4.2'K and 293°K several times produced only a few thousandths of a degree change in i t s calibration. The resistance-temperature characteristics of four typical encapsulated thermometers are shown in Table 3-1 2 and Fig. 3-36. The R-T characteristics of a carbon thermometer is shown for comparison. At low temperatures the germanium thermometers have widely different electrical properties because the arsenic impurity concentration is not the same in each sample even though they were cut f r o m the s a m e germanium crystal. This is a good example of the extreme sensitivity of the electrical properties of these r e s i s t o r s to impurity concentration. However, the resistivity - temperature characteristics of an element a r e defined approximately by its resistivity at 4.2"K (88) and in the range 2°K to 35"K, the ratio (dR/R)(dT/T) is of the order of unity f o r all samples, a result found with germanium.bridges cut f r o m other crystals as well. This characteristic is r e sponsible for the tremendous temperature sensitivity of the resistance thermometers. The sensitivity dR/dT at 4 . 2 " K of several thermometers, including those in Table 3-12, is shown inFig. 3-37. An increased sensitivity may be arhievcd roiighly according to R3/2, by selecting a thermometer of higher resistance providing the instrumentation is compatible with the selected r e s i s t c r . The resistance of germanium is influenced by a magnetic field. The variation of the magnetoresistance with temperature was studied by Kunzler, et a1 (88) using a

1 48

dR

lohms/degrcc j

0

Fig. 3-34

5

10

15 20 TEMPERATURE ( * K )

25

28

Sensitivity dR/dT typical standard cryoresitor (Courtesy Gryo. Cal, Inc. ) (89)

PI-GLASS SEAL

w

Pt WIRE

.007 cm GOLD WIRE AND Au- Ge BOND

1mm

.Fig. 3-35

Encapsulated germanium thermometer-model 11, with cover removed (88)

149

R (ohms) 4000

1000

w I

DISTANCE

~

\

500

ZA-19 4,-59)

r

6: ex5

FROM DIFFERENT CRYSTAL

ss

100

50

10

5

'

0.5 1 TEMPERATURE

Fig. '3-36

dT

( O K )

Resistance-temperature characteristics of germanium thermal sensing elements.

(A

deg'

RESISTANCE, R, Ifil

Fig. 3-37

Variation of dR/dT with resistance at 4 . 2 " K

150 TABLE 3-12: Resistance-Temperature Characteristics of Germanium Thermom e t e r s Fabricated from Arsenic-Doped Crystal 8-899-N (88) ~

~~

Sample No 15- 2R

9-2R

T"K

RG -1 2.0 4.6 8.0 10.5 18.3 101 789 2300

273 77 35 20 15 10 4.2 2 1.5

dR/dT

0.16 0.5 0.8 2.8 50 1000

dR/dT

-1 1.8 3.9 5.9 7.3 10.7 29 77 120

273 77 35 20 15 10 4.2 2 1.5

dR/dT

-1

21-2R Rs1

TOK

RR

0.11 0.22 0.4 1.1 7.7 46

.

1.9 4.3 7.0 9.0 14.1 53 216 4 50 27-28 Rs1 -1 1.7 3.4 4.9 5.9 8.0 16.7 29. 5 36.5

0.13 0.3 0.6 1.8 15. 5 200

dR/dT

0.07 0.15 0.25 0.67 2.6 11.2

I

germanium bridge having a zero field resistance (R,=b) of 200 ohms at 4.2"K. The magnetoresistance (AR/RH,o) a t 18 kilogauss was found to be 0.16 a t 4.2"K and gradually increased with decreasing temperature, reaching a maximum value of 0.28 a t 1.9"K. Below 1.9"K the magnetoresistance decreased to a value of AR/R,=, equals 0.21 a t 1.2"K. At 4.2"K the corresponding change in temperature calibration as a result of the magnetic field would be approximately 0.20"K. The magnetoresistance of germanium is also slightly anisotropic, being somewhat less than 10 percent of the total magnetoresistance over 180 angular degrees a t 4.2"K and in an 1 8 kilogauss field. Other papers treating the germanium resistance thermometers have been published by Low (90) and Orlova, ef a1 (91). Antcliffe, et af (92) report the use of germanium thermometers below 1°K. Their lowest temperature was 0.40"K obtained by a He3 bath and the range of temperatures investigated was 4. 20°K to 0.40"K. Between 4. 20°K and l . 20°K the data were fitted to:

-0p

-A

R = C T

e

,

with representative values of the constants as A = 0.507 and C = 71.89 112.8 for three r e s i s t o r s calibrated.

-

Eq. 3-33

- 1.004,

- B = 1.245

- 1.399

Magnetic Thermometry The practical minimum temperature which may be produced by pumping helium is about 1'K for He4 and 0.5"K for He3 as below these temperatures the vapor pressure is too low to be maintained for most useful experimental purposes. To produce as well as measure temperatures below 0.5"K the properties of paramagnetic substances, usually paramagnetic alums, are used. The low temperatures a r e achieved

151

TABLE 3-13: Temperatures Attained by Adiabatic Demagnetization of Various Paramagnetic Salts (96)

1

i

I

Initial Initial field, temp. oersteds OK

Final magnetic temp. T* OK

Gadolinium sulfate

8,000

1.5

0.25

Cerium fluoride Dysprosium ethyl sulfate Cerium ethyl sulfate

27,600

1.35

0.13

19, 500

1.35

0.12

27,600

1.35

0,085

Chromium potassium alum Ironammonium alum Alum mixture Cesium titanium alum Gadolinium sulfate Maganese ammonium sulfate Iron ammonium alum Iron ammonium alum Iron ammonium alum

24,600

1.16

0.031

24,075

1.20

0.018

24,075 24,075

1.29 1.31

0.0044 0.0055

5,400

1.15

0.35

8,000

1.23

0.09

14,100

1.23

0.038

8,300

1.23

0.072

4,950

1.23

0.114

8,090

0.94

0.098

Iron ammonium alum

32,000

1.08

Experimenters

Date

Paramagnetic salt

Giauque and MacDougall

1933

De Haas, Wiersma,

1933

and Kramers

De Haas and Wiersma

1934 1935

Kurti and Simon

MacDougall and Giauque Kurti, Laine, Rollin, and Simon

193 5

1936

1936

Gadolinium nitrobenzene sulfonate

0.010 I

. I

Kurti, Laine, and Simon

1939

Iron ammonium alum

28,800

9.5

0.36

Ashmead

1939

Copper potassium sulfate

35,900

1.17

0.005

DeKlerk (95)

1956

Chromium potassium alum

--

0.0029

--

152

Fig. 3-38

Temperature-entropy diagram for a paramagnetic salt under the influence of different magnetic fields (40) BERKELEY SAMPLE TUBES

LEIDEN SAMPLE TUBE

(a 1 PYREX

Fig. 3-39

b) LEXIGLASS

Typical paramagnetic salt samples (94)

*

diluted chromium alum has produced a final temperature of 10-3°K with a field of 9000 gauss but to reach this temperature in a single demagnetization from 1°K a field of 25,000 gauss would be required. Temperatures of a few hundredths of a degree absolute can be achieved without exceptional difficulties and those of the order of one-thousandths of a degree can be obtained with somewhat greater effort (94)(95). Table 3-13, prepared by Zemansky (96), summarizes some results of adiabatic demagnetization experiments and identified the paramagnetic salts used. Certain properties of commonly used paramagnetic salts are given in Table 3-14

(96).

o r:

M

= XH

Eq. 3-35

154

HIGH VACUUM PUMP

HELIUM PUMP

RADIATION TRAPS LIQUID HYDROGEN LlOUlD HELIUM

PRIMARY COIL

SECONDARY COIL

THIN WALLED FOOT

Fig. 3-40

Typical leiden demagnetization cryostat, one-fifth of real size (97)

1

155

TABLE 3-14: Properties of Paramagnetic Salts (96) Gramionic weight M (gm)

Density, gm cm3

765

--

0.318

Chromium potassium alum C r (SO,) ,KzS0,24H20

499

1.83

1.86

Chromium methylammonium alum Cr, (S0,),CH3NH3S0,24H,0

492

1.645

1.87

Copper potassium sulfate CuS0,K2S046H,0

442

2.22

0.445

Iron ammonium alum Fe,(S04)3(~4),S0424H,0

482

1.71

4.35

Gadolinium sulfate Gd,(S04)38H,O

373

3.010

7.85

Manganese ammonium sulfate MnSO4(NH,),SO,6H,O

3 91

1.83

4.36

Titanium cesium alum Ti, (S04)3Cs2S0,24H20

589

-2

0.118

Paramagnetic salt

Cerium magnesium nitrate 2Ce(N03),3Mg(N03),24H,0

Curie const., cm3 deg gm ion

~~

,

156

80 I

I

I

I

I

I

I

I

I

10

20

30

LO

50

60

70

80

60 1000 K-'

T

0

40

20

0 Fig. 3-41

0

Plot of susceptibility per gm vs reciprocal temperature for powdered CuS04 K,S04' 6H20,showing the curie law temperature dependence (100)

MAGNETIC MOMENT (BOHR MAGNETONS/IONI

0

0

X 0

1.30 O K 2.00 'K 3-00'K 4-21 O K

HIT x 1 0 - ~OERSTEDIDEG

Fig. 3-42

Plot of magnetic moment H/T for spherical samples of (a) potassium chromium alum (b) ferric ammonium alum and ( c ) gadolinium sulfate octahydrate (100)

-

with:

157

x = -CT ,

Eq. 3-36

where M is the magnetization o r magnetic moment, C is Curie's constant, H i s the magnetic field strength and x is the magnetic susceptibility. The magnetic susceptibility is related to the permeability, p , and the magnetic flux intensity, B, by:

B = pH

and:

4n

x

= p

Eq. 3-37

-

Eq. 3-38

1.

Substances a r e classified according to the value of magnetic for X > 0, and ferromagnetic X >> 0.

x:

diamagnetic for x ro the index of refraction is that of the reference region

Ra

Rayleigh number, based on diameter for circular cylinder

S

source

Sc

screen

Sp

splitter plate

t T

dummy variable used in equation 4-A-7. temperature

Tref temperature in reference region

T,

free stream temperature

224 I

x

direction normal to y and z

y

direction perpendicular to z and i t i s usually the direction in which the gradient of density and temperature lies

yi

height of light ray at entrance to test section

I I

I

ySc height of light r a y at s c r e e n ysc m i l x maximum value of ysc height of light r a y at exit from test section yT

g)T

slope of light ray at exit of test section

z

z,,

direction along light beam distance f r o m test section to screen

Greek symbols ~

a

angular deflection of light r a y as measured in air outside test section and is s a m e as a’ if n =nil

a,,, maximum deflection angles that can b e measured with Schlieren system amax’

a’

angular deflections of light ray within test fluid; a’ EZ a if n test fluid i s gas)

a”

angle defined and used in Fig. 4-4

P

angle defined and used in Fig. 4-4

= na

(i.e., if

Y

angle defined and used in Fig. 4-4

6

boundary layer thickness

A

phase difference

E

interferometer fringe shift, optical path length difference in vacuum wave lengths

0

angle between interferometer beams when recombined

A

wave length of light

A”

vacuum wave len@h

Asc

wave length at screen o r when beams a r e recombined

AA

spectral width of light source

P

density

Po

density at standard condition

i’, c. 1 density in reference region U

dummy variable introduced into equation ( 4 - A - 5 )

T

dummy variable used in equation 4-A-7

Subscript w

refers to condition at the wall

225

I

I I

Appendix

i,

Interferogram Analysis of Axisymmetric Fields

1 1

'

i 1

1

Although the optical techniques described in this paper have found their widest use in two dimensional-rectangular coordinate systems they are also applicable to other geometries. In particular, interferograms of &symmetric density o r temperature distributions can b e quantitatively evaluated using the Abel transformation (63). Consider Fig. 4-28a which is a c r o s s section of a field in which the index of refraction is a function only of r, and possibly position normal t o the section (x) , but not of the angular position. We shall only consider the field in this particular section (i. e. constant x ) . A light beam from an interferometer passes through the test region in the direction z. At radial positions greater than ro the field is assumed to b e uniform with an index of refraction of n r e f . This is no real limitation as we can make ro as large as we want: Neglecting refraction [cf (64)] the fringe shift from the light ray at a particular position y is, from equation 4-55: 1 Eg)=-

I

Lo =O

[ n k ) - nref I dz

Eq. 4-A-1

where the integration is carried out at constant y. The integration limits are functions of y but could with full generality b e extended to * W. Since: z = I

I ~

p - y2

Eq. 4-A-2

and at constant y: r d r dz =

Eq. 4-A-3

-4

equation 4-A-1 can be written as: Eq. 4-A-4

!

Multiplying both sides of equation 4-A-4 by:

and integrating between

U

and r,:

Note that the integration on the right-hand side i s first over r between y and yo and then over y between U and ro. This is shown in Fig. 4-28b where the integration is carried out over the whole shaded area by first integrating to obtain the horizontal element shown and then in the second integration (over y) to sweep out the finite area. Integration of the integrand over this s a m e region can be performed as shown in Fig. 4-28c by f i r s t getting the vertical element (i.e. integrating over y between U and r ) and then over the whole area (a second integration over r between U and ro). Thus:

226

Fig.

4-28a

Light beam passing through axisymmetric field

b Region of integration for equation 4-A-5

Y

c Region of integration for equation 4-A-6

227

The significance of this change in the order of integration can be observed by considering the inner integral on the right-hand side of equation 4-A-6. Let:

and since r and

U

are constant over the inner integration:

Thus:

Eq. 4-A-7 The right-hand side of equation 4-A-7 is in the form of a Beta function and i s equal

Equation 4-A-6 thus becomes? Eq. 4-A-8 If the left hand side is integrated by parts:

Eq. 4-A-9

Eq. 4-A-10 since the first t e r m on the right-hand of equation 4-A-9 is zero at both limits. Combining equations 4-A-8 and 4-A-10:

Eq. 4-A-11 Differentiating both,sides of Equation 4-A-11 with respect to

02,

Eq. 4-A-12

o r if

U

is set equal to r,

l

I i

228

I

Eq. 4-A-13

~

I T h i s equation can b e used to evaluate interferograms of axisymmetric fields.

It relates the measured fringe shift, really its derivative, which is a function of y to the desired index of refraction which i s a function of the radial position r. In practice the measured E (y) can be represented by best-fit least-square polynomials. This representation and the required differentiation and integration can be easily done on a high speed computer to yield n(r) and from this the density o r temperature distribution. Since the original presentation of this material a convenient method for interferometric analysis of axisymmetric fields has appeared (65).

,

I '

I I

229

5

Spectroscopic Temperature Determination in High Temperature Gases E. PFENDER University of Minnesota, Minneapolis, U. S. A. Summary

In the first part of this survey the various physical laws and definitions of gaseous radiation are reviewed including the different types of radiation which a r e emitted by a high temperature gas. The second part contains a discussion of the most important direct and indirect spectrometric methods which have been developed f o r temperature measurements of emitting-absorbing high temperature gases. Introduction F o r a description of the heat transfer situation in a medium o r between adjoining media, the temperature o r enthalpy field must be known. Temperature and heat flux measurements at moderate temperature levels a r e thoroughly covered in the other review papers. In this review, techniques will be discussed which are suitable f o r temperature measurements at very high temperature levels at which ‘matter is in a gaseous, more o r less ionized state. The term plasma has been adopted to describe such gases, and this paper will survey the most important spectrometric methods which have been suggested for the determination of temperatures in plasmas. The upper limit of temperatures considered in this survey will be approximately 30 x 103°K which corresponds to the maximum temperatures experienced in present engineering applications, as for example, in plasma propulsion devices, in a r c o r high frequency gas heaters and in plasma torches for welding, cutting and spraying. The lower temperature limit is in the order of 104°K. Such temperatures a r e of importance f o r molecular radiation and spectrometric methods have been developed to determine temperatures in this range and at least one of them will be included in this report. Another limitation in this survey i s imposed by the pressure of the high temperature plasma. In general, such plasmas represent multi-component mixtures (molecules, atoms, ions, electrons) in which numerous chemical reactions may occur. A single temperature concept of this mixture i s meaningful only when thermodynamic ( T E ) o r local thermodynamic equilibrium (LTE) prevails. Otherwise the various components may have different temperatures and the possible chemical reactions can no longer be described by an equilibrium temperature. One of the decisive parameters which determines whether o r not LTE may be expected is the pressure, a s low pressure plasmas of laboratory dimensions frequently show strong deviations from LTE, whereas high temperature plasmas at atmospheric o r higher pressures approach a state of LTE. Since the majority of the spectrometric temperature measurement techniques are based on the existence of LTE, the discussion will be essentially restricted to these situations.

230 Spectrometric methods offer two important advantages compared with methods which use probes o r thermocouples for sensing the temperature. Since radiation emitted by the plasma i s used for the temperature evaluation, the diagnostic tool may be in a remote location relative to the plasma and does not have any influence on the plasma, in that it does not a l t e r the quantity to be measured and the method provides an excellent spatial resolution of the measured temperature field. In general, gaseous radiation sources do not have a uniform temperature distribution but in many cases of practical interest, however, such sources display rotational symmetry. In such cases, conversion of the observed side-on radiation intensities into local intensities i s a straight-forward procedure. The f i r s t part of this review will be devoted to a discussion of the important laws and concepts in gaseous radiation. Since most of the spectrometric methods to be discussed in this review a r e based on the existence of TE o r LTE in the plasma, the second part will review the conditions which are favorable f o r this situation. In the next part the various types of radiation which are emitted by a plasma, and which are crucial for the development of spectroscopic methods a r e considered. Finally, in the last section the most important spectroscopic methods will be discussed, those which have been adopted f o r diagnostic purposes in high temperat u r e gases. References to specific research papers will not be included in this review because they may be found in texts, proceedings of symposiums and/or special review articles (1 - 1 5 ) . This survey covers only the methods which are well known today in high temperatire spectroscopy; it does not include spectrom e t e r s and the associated hardware. Basic Concepts of Gaseous Radiation In this section the most important general definitions and laws which govern radiation in a gaseous medium will be reviewed. When electromagnetic radiation passes through a medium with varying index of refraction, the wavelength X as well a s the propagation velocity c of the wave vary with the index of refraction. A s the frequency U = c/X does not depend on the particular properties of the medium, it will be used a s a wave parameter in this review, although the index of refraction in gases is usually close to unity. Intensity and density of gaseous radiation The monochromatic radiation intensity I, is defined as the amount of radiant energy A X which passes per unit time At through an a r e a element Aa which i s perpendicul a r to the direction of a radiation pencil of solid angle Aw. This definition includes only radiation which i s emitted in a frequency interval from v to v + AV. Writing this definition as a formula yields:

;.

I

I =

AtAaAwAu "

U

(

',. T,. T, is the electron temperature and T, the temperature of the heavy species, assuming that ion and neutral g a s temperatures a r e the same.

In the two-fluid model of a plasma defined in this manner, two distinct temperatures T, and T, deviate from each other will depend on the thermal coupling between the two species. The difference between these two temperatures can be expressed by the following relation (1) : T, - T a - - ‘e

ma am,

(X,eEI2 ( 3/2kT,)

(Eq. 5-34) 2

m a is the m a s s of the heavy plasma constituents, X, the mean free path length of the electrons, and E the electric field intensity. Since the mass ratio m /am, is already about 230 f o r hydrogen, the amount of (directed) energy (X,eEJ which the electrons pick up along one mean f r e e path length has to be very small compared with the average thermal (random) energy 3/2kT, of the electrons. Low field intensities, high p r e s s u r e s (X,-l/p) and high temperature levels are favorable for a kinetic equilibrium among the plasma constituents. F o r example, a t low press u r e s , appreciable deviations from kinetic equilibrium may occur. Figure 5-2 shows in a semi-schematic diagram how electron and gas temperatures separate in an electric arc with decreasing pressure. F o r at atmospheric argon high intensity a r c with E = 13V/cm, A, = 3XlO-%m, mA/me = 7x104 and T, = 30x103K, the deviation between T, and T, is only 2% ( 1 ) .

-

Excitation Equilibrium in order to determine the excitation equilibrium, every conceivable process which may lead t o excitation o r de-excitation has to be considered. This discussion is restricted to the most prominent mechanisms which are collisional and radiative excitation and de-excitation. Excitation ( a ) electron collision ( b ) photo absorption

De-excitation ( a ) collision of the 2nd kind (b) photo emission

2 40

TEMPERATURE

( 'K

PRESSURE (mmHg1

Fig. 5-2

-

Electron and gas kinetic temperatures in

an arc-generated plasma

I

241 F o r the case of TE, micro-reversibilities have to exist f o r all processes, i. e., in the above scheme, excitation by electron collisions will be balanced by collisions of the 2nd kind, the reverse process. Also, excitation by the photo absorption process will b e balanced by photo emission processes which include spontaneous and induced emission. Furthermore, the population of excited states is given by a Boltzmann distribution ( s e e Eq. 5-31). The micro-reversibility f o r the radiative processes holds only if the radiation field in the plasma reaches the intensity B v of blackbody radiation. However, actual plasmas are frequently optically thin over most of the spectral range, s o that the situation for excitation equilibrium s e e m s to b e hopeless. Fortunately, if collisional processes dominate, photo absorption and emission processes do not have to balance. Only the sum on the left-hand side and the right-hand side of the scheme above have to b e equal. Since the contribution of the photo processes to the number of excited atoms is almost negligible when collisional processes dominate, the excitation process is still close to LTE.

-

Ionization Equilibrium f o r the ionization equilibrium again only the most prominent mechanisms which lead to ionization and recombination will be considered: Ionization

Recombination

( a ) electron collision (b) . _photo absorption

(a) (b)

three body recombination photo recombination

In a perfect thermodynamic equilibrium state with cavity radiation, a micro-reversibility among the collisional and radiative processes would exist and the particle densities would be described by the Saha-Eggert equation. Without cavity radiation, the number of photo ionizations is almost negligible requiring instead of the micro-reversibility, a total balance of all processes involved. Photo recombinations are not negligible, especially a t lower electron densities. The frequency of the three remaining elementary processes is a function only of the electron density leading, for ne = 7XlOl5cm-3, to the same order of magnitude frequency of these elementary processes. The result is a n appreciable deviation between actual and predicted values (Eq. 5-32) of the electron densities. Only for values ne > 7X1015cm-3 does the Saha-Eggert equation predict correct values. F o r smaller electron densities the Corona formula has to be used, which considers ionization by electron impact and photo recombination only: (Eq. 5-35)

rn

thenumber of valence In this equation Q is Sommerfeld’sfine structure constant, electrons, n the principal quantum number of the valence shell, x i , the ionization energy of hydrogen and g a constant with a value between 1.4 and 4. The particle concentrations in low density a r c s a t atmospheric pressure, for example, have tobe calculated with this formula. Significant deviation of the electrondensity predictedby the Saha equationfromthe trueelectrondensity may also occur inthefringes of highintensityarcs and plasma jets. In summary, it has been found that LTE exists in a steady state optically thin plasma when the following conditions are simultaneously fulfilled: (a)

The different species which form the plasma have a Maxwellian distribution.

(b)

Electric field effects are small enough, and the pressure and the temperature are high enough to make T, = T,.

(c)

Collisions are the dominating mechanism for excitation (Boltzmann distribution) and ionization (Saha-Eggert equation).

242

loi9

10lB

1O2O

lo2'

10 2 2

ELECTRON DENSITY (m-3)

-----

NON- LTE LTE'

Fig. 5 - 3

State diagram for hydrogen in LTE and non-LTE

(d) l

I

I

2 43 Spatial variations of the plasma properties are sufficiently small.

Besides the conditions for the two extreme cases, namely LTE (based on Saha ionization equilibrium) and Corona equilibrium, conditions in the regions between these two limiting cases are a l s o of interest. In this range three body recombination as well as radiative recombination and de-excitation a r e significant and a number of theories have been advanced f o r ionization equilibrium over the entire range of radiative-collisional elementary processes. In particular, detailed calculations of optically thin and optically thick hydrogen plasmas have been reported. Some results of these calculations follow f o r the optically thin case.

I

I

If CY is the combined collisional-radiative recombination coefficient and S the corresponding ionization coefficient, rate equations may be established which describe the effective rate of population and depopulation. The rate of population of the ground state is described by:

(Eq. 5-36) In this relation, no represents the number of neutral hydrogen atoms in the ground state and ne' and n1 are the electron and ion densities, respectively. The rate of depopulation of the ground state is given by:

(Eq. 5-37)

,

Under steady state conditions: (Eq. 5-38) (Eq. 5-39)

1

I 1 I

Figure 5-3 shows a state diagram f o r values of S / ( Y as a function of the electron density with pressure and electron temperatures as parameters. At high electron densities ( 31024m-3) p a i r s of LTE and non-LTE curves plotted f o r the s a m e electron temperature merge. At low electron densities ( SlOzlm-3) the non-LTE curves merge into curves valid for Corona equilibrium. The divergence of the non-LTE curves from the LTE curves a t lower p r e s s u r e s and/or lower electron temperatures and densities shows how large the deviation from LTE may become in such parameter ranges. Taking values f o r 1 atm. it can be seen that LTE is closely approached f o r electron temperatures in the interval 14,000 < Te < 28,000°(K). Deviations of this kind from LTE may b e found, f o r example, in plasma regions adjacent to walls where the electron density drops appreciably, and in all types of low density plasmas of laboratory dimensions. Well known examples of the latter are the positive column of glow discharges and the plasma generated in fluorescent lamps.

Radiation Emitted by a High Temperature Gas ,

In this section the different types of radiation which may b e emitted by a plasma will b e discussed with emphasis on the emission from plasmas which contain only atoms as the neutral component.

244

NORMALIZED LINE EMISSION )E FFICIENTS

1.0

0.9

0.8

0.7

0.6

0.5

0.L

0.3

0.2

0.1

0 0

5000

10000

15000

20000

25000

30000

TEMPERATURE ('K)

Fig. 5-4

Relative emission coefficients of two argon lines

II 1

'1 ,

'

245 The pressure in the plasma shall be sufficiently high (>. 1 atm) , to make LTE feasible.

An analysis of the total emitted radiation of a plasma reveals a number of different radiation mechanisms. Their relative importance i s a function of temperature and pressure and, in magnetized plasmas, also of the magnetic field. From a theoretical point of view, this radiation is useful for diagnostic purposes if i t s origin and temperature dependence i s known. The experiment requires, in addition, that there is sufficient intensity of the spectrally resolved radiation and that this radiation is sensitive to temperature changes. Line radiation (bound-bound transitions) Excited neutral atoms o r ions may return to the ground state in one o r several steps. Because of the discrete nature of bound energy states the emitted radiation appears as spectral lines according to equations 5-20 and 5-20a. By combining equations 5-20a and 5-21 the line emission coefficient f o r an optically thin homogeneous plasma is found to be:

EL

=

1

r,s

f i A r , t n r , s hv

(Eq. 5-40)

1

,

The factor represents the unit solid angle. Therefore, the dimension of the line emission coefficient is Watt/sterad cm3. The line emission coefficient i s already integrated over the natural width Ax of a spectral line:

cL =

IC

,dv

Ax c v is the monochromatic emission coefficient ( s e e Eq. 5-6). F o r the following considerations, it will be assumed that LTE prevails in the plasma, i. e. the number density of excited atoms o r ions may be expressed by a Boltzmann distribution ( s e e Eq. 5-31). Replacing n,, ,in equation 5-40 hy this Boltzmann distribution yields:

'

(Eq. 5-41) In this equation the temperature appears explicitly only in the exponential term, but n, a l s o depends strongly on the temperature whereas the partition function exp (-xr ,/kT) is a rather weak function of the temperature. F o r Z, = Zg, constafit dressure, E ; ( T ) assumes a maximum at a certain temperature T* because of the tendency of n, to decrease owing to the depletion of particles of species r by increasing ionization to species r+l and the effect of the perfect gas law (ne + C n, = p/kT, where p is the total p r e s s u r e ) . A s an exampl e, Figure 5-4 illustrates the emission coefficients of two argon lines (r=Oand r = l ) on a re1 ative scale and according to this figure, the neutral line will show up in the spect r u m only in the temperature interval 104"K>X immersed in a subsonic plasma flow, the electrons of which are in a Maxwellian distribution around a temperature no lower than the heavy-particle temperature. The foregoing arguments permit u s to assume that (a) the boundary-layer thickness 6 is

284

much greater than that of the sheath ( 6 >> h ) , and (b) electrons are captured by the probe when they reach the sheath boundary. Furthermore, the heavy-particle temperature in the boundary layer is assumed t o decrease from its freestream value to the cooled-probe wall temperature in accordance with usual boundarylayer behavior. Finally, we a s s u m e for the moment that although the electrons may lose energy t o the ions or atoms by elastic collisions, they do not suffer recombination, i. e. , the boundary layer is chemically frozen. The fraction of energy lost by an electron to a heavy particle in a single elastic collision may be written as:

is the average steric factor over all possible deflection angles where has the value $

.

x and

Thus, for me < < mH:

For argon:

AE/E,

1/36,600

s o that after n collisions, where n 0 .

I

'

(a) T, = constant, Ti = Ti (x) Consider an infinite slab of thickness t, with the initial temperature distribution Ti 6).The temperature of the surface T(o, 7 )is suddenly changed to Tf = const for all T M . The solution must satisfy the system:

I Eq. 7-19

316

WALL THERMOCOUPLE FLOW

r G A S TEMP

7 (SECS)

Fig. 7-5

Illustration of the measurement of the heat transfer coefficient by means of sinusoidal temperature oscillations

I

0.001

0005

0.01

005 FO=QT/L*

Fig. 7-6

01

0.5

1

2

Temperature response of a plate 0 C x C L with insulated back face x = L after sudden change in external fluid temperature from T when 7 < O T, when r a0.

317

T = Ti (x)

at

r = O ; 0 5 x 0

at

x=L; r > 0

I I

i1 I

T(o, 7 ) = T f = const ~ ( L , T =)

ax

o

Eq. 7-20

I

For the special case of a uniform initial temperature Ti (x) = Ti the general solution of the system (Eq. 7-19, 20) presented in (1) and plotted i n Figure 7-6 is presented in (1) and plotted in Figure 7-6. Figure 7-6 illustrates the use of Schneider's time-temperature charts.

1

Case C - Exact Solutions and the Time-Temperature Charts (Finite Internal and Surface Resistance)

'

The most realistic heat flux measurements require consideration of both internal and surface resistances. In this discussion we consider the ambient fluid temperature Tf to be uniform a s well as the heat transfer coefficient. Consider the convective heating of a large plate of uniform thickness L which again is initially at a uniform temperature T i . The plate is suddenly exposed to a fluid temperature T, for 7>0 while the back face a t x=L is insulated. The general solution is, (7): -Mn2F, T-Tf = T i Tf Eq. 7-22

-

!

where M, a r e the eigenvalues given by the characteristic equation:

M, tan M, = B,

1 1

1 I

Eq. 7-23

Note that the solution is a function of two parameters, Fo and Bi rather than just one as i n the case of negligible surface resistance. Schneider presents a large (120) number of time-temperature charts covering a variety of body shapes for a wide range of Fourier and Biot numbers. These charts a r e convenient for thermal engineers who need to deduce heat flux r a t e s from transient temperature response measurements while not having sufficient computational experience or direct use of a computer. Figures 7-7 and 7-0 presents the plotted results of Equations 7-22, 7-23 for the locations x/L = 0, 1.0 and these curves apply to the case of large Biot and Fourier numbers. To use the curves one can plot the experimental temperature difference ratio versus the Fourier number and examine the theoretical Biot number curve which best fits the data. One must remember that to obtain surface heat flux values in this way accurate values of the thermal conductivity, density, heat capacity and thickness must be available.

I I

The temperature difference that exists across the thickness of the surface may be obtained by a superposition of Figures 7-7 and 7-8, and in this way an estimate of the e r r o r s involved in assuming negligible internal resistance are readily made. Case D

-

Rapid Response Measurements

The development of heat transfer gauges has always been directed to some particular application. Earlier work focused on determination of cylinder wall temperature

318 (T-Til/(Tf - T i l

Fig. 7-7

-

Fo=ar/L' Temperature response of a plate 0 C x C L with insulated back face x = L after sudden exposure to a uniform convective environment at

x=o (T-Tit/[Tf-Tit

F o = aT/L2

Fig. 7-8

-

Temperature response of a plate 0 Q x 5 L with insulated back face x = L after sudden exposure to a uniform convective environment at ~

x=o 9(0.T)

I

1 kg

4 k8

SUBSTRATE

Po CP,

Fig. 7-9

Gage notation for thick and thin films

319 1

I I

1I I

~

' 1 ~

l

I

1

1

I

1

variations in reciprocating engines and the surface temperature history in gun barrels subjected to continuous firing. Later it was necessary to develop instrumentation to determine heat flux rates to aerodynamic models in shock tubes and shock tunnels with 10 microsecond test duration. An early form of a shock wave detector consisted of a thin film mounted flush i n a shock tube wall. The gauge provided a very fast electrical pulse for trigger purposes to indicate the passage of the shock wave.

Two basic techniques have evolved for such measurement techniques, (8) which are: thin film surface thermometry and thick film calorimetry. The f i r s t method records instantaneous surface temperature from which instantaneous heat flux rates a r e deduced using classical heat conduction theory. In the second method the gauge absorbs the total heat input to the surface, and the instantaneous heat flux r a t e is determined by the time rate of change of temperature of the gauge.

-

-

It is clear that most heat flux gauges a r e based on approximations. It is necessary for the experimentalist to a r m himself with a variety of exact solutions; i. e. those tabulated in (1). In dealing with the heat conduction equation, the property, sensor thermal diffusivity (ag=kg/p CpJ, is fundamental. Recall (9) that for metals the thermal diffusivity is about 4'00 times that of thermal (and electrical) insulators. The thermal diffusion depth (6 g= CY 7) is a measure of the extreme depth to which a surface heat flux has penetrated i n ' i i m e E Therefore, thermal diffusion depths of metals a r e 20 times those of insulators. Thin-Film Gauges When a film thickness t is much less than the thermal diffusion depth (tg < < 6 ), temperature gradients fn the film may be neglected (see Fig. 7-9 for notation). The film senses the instantaneous surface temperature of the substrate (subscripts) but there exists a response lag relative to zero film thickness because of the small but finite gauge heat capacity. As an example of this response lag consider a suddenly applied heat flux rate varying inversely with the square root of time. With zero gauge thickness the substrate temperature jumps to a new constant value. For a finite gauge thickness, the substrate surface temperature attains 94 percent of the

and

T,

is the characteristic time of the gauge-substrate combination.

In most applications the heat flux rate into the gauge is one-dimensional. The re-quired relation between the surface heat flux rate and the measured gauge temperature is obtained by solving the one-dimensional, constant-property, heat conduction equation in a semi-infinite slab:

Eq. 7-25 '

Where T(x, 7 )is the difference between the instantaneous and initial temperatures. The boundary conditions are q (0, T ) = - k % (0, 7);T(x, 0) = 0. The general solax ution (10): "2

Eq. 7-26

320

is obtained by use of the convolution integral of the Laplace transform. At the subs t r a t e surface SO, the relations between the wall temperature T(0, T ) and the impressed heat flux +(T) are: Eq. 7-27

Eq. 7-28 Equation 7-28 is not suited for numerical evaluation since it involves derivatives of temperature integrals. Equation 7-28 can also be written: -l

Numerical difficulties encountered in evaluating the integral as t-v are the subject of several recent papers. The integrand evaluated a t 7 takes the form O/O and application of L'H6 pital's rule yields an infinite integrand a t 7. It is necessary to evaluate the t e r m s enclosed in the square brackets by numerical procedures.

For constant heat flux q(0, T

)=

q, = Const,

Equations 7-27 and 7-28 integrate to: q (x, T ) = q,

erfc

X

Eq. 7-30

P Bcps

Eq. 7-31

For a heat flux gauge several possibilities exist for determiningthe gauge temperature. For example either a thermocouple or a resistance thermometer may be used for measuring the time-temperature trace. The greater sensitivity of the resistance thermometer gives it an advantage over the thermocouple. For example sensitivities of resistance thermometers are as great as 1 mv/"C while the sensitivities of conventional thermocouples range from 0.005-0.05 mv/OC. Evaporated thermocouples require two overlapping films and ceramic films (thermistors) are sometimes considered (vs metallic films) because their temperature coefficient of resistance (dFt/dT) is much larger, but is constant only over a narrow range. Other techniques (10) employ a variable reluctance gauge (a copper mass used to vary reluctance i n a magnetic circuit), or a dielectric material as a temperature sensor. When a dielectric material such as barium titanate is heated an electric charge is generated which is proportional to the temperature change. If the gauge is connected to a resistor the circuit is directly proportional to the time rate of change of gauge temperature. Some normal operating conditions of thin-film thermometers are listed below, (10):

- platinum evaporated or painted on pyrex substrate Film thickness - 0.025 microns Film response time - 10-7 second Film material

321

Film current

- 10-2 amp

Film resistance

-

l o w 2 5 ohms

- 6 . 3 5 X 0.635 mm 1 Film allowable temperature change - / 4 watts Film p, Cpgk, - 1520* 5% Film dimensions

to 280'K

mZ0K

If the temperature changes a r e not too large (AT<SENSOR

T

Fig. 13-1

Schematic diagram of constant temperature system

BRIDGE VOLTAGE

(VOLTS)

C.0

3.5

3.0

2.I

2.0

l.!

1.C

10

20

30

LO

50

60

70

.EO

VELOCITY (mls)

Fig.

13-2

Calibration curve for 0.0038 mm tungsten hot wire and comparison with King's law

489

I I

I 1

t

I

1

,

'

The first requirement in the system of Figure 13-1 is that the sensor resistance changes with temperature. F o r maximum sensitivity, this change of resistance with temperature (temperature coefficient of resistance) should b e high. The resistance of the bridge a r m s are set s o that the bridge is in balance with the sensor transferring heat to the environment. The high gain feedback amplifier maintains this condition ( a balanced bridge) but adjusting the current thmugh the sensor. F o r example, as the environment velocity increases, more heat wmld b e transferred between the sensor and i t s environment. To maintain the sensor temperature, the bridge system increases the current through the sensor. Therefore, the current required by the sensor is a direct measure of the heat transf e r r e d between the sensor and i t s environment. This heat transfer from the sensor ( s e t and maintained a t a constant average temperature by the bridge) is therefore the basic measurement. Heat i s transferred f r o m the sensor by convection, radiation, and conduction. Similarly, the r a t e of heat transfer is affected by any property of the environment that influences heat transfer including temperature, velocity, pressure, composition, etc. In the normal application of anemometry, convection is the dominant mode of heat t r a n s f e r and velocity is the only environment variable. Hence the t e r m anemometer. Limiting the heat transfer to convection, the heat transfer between the sensor and environment where velocity is the only variable, can be expressed approximately by what is commonly referred to as King's law (2):

I

' I

I 1 ~

I

1

1

P = 12R, = ( A

where:

+B

v)

(T,

-T

)

(Eq. 13-1)

A, B = constants V = environment velocity T

sensor temperature

T= , environment temperature Figure 13-2 shows a calibration curve of a fine hot-wire and the calculated curve using two calibration points (end points) and King's Law. Many heat transfer relations have been derived which are a significant improvement on King's Law. Still, when discussing hot-wire anemometry the simplicity of the relation in equation 13-1 makes it a useful reference. Figure 13-3 shows two types of sensors commonly used f o r work in hot wire anemometry. The fine hot wire is the original type of sensor and still is widely used. The hot film (3), ( 4 ) is more recent and has advantages in many applications. It consists of a glass substrate with a thin metallic film on the surface. The g l a s s substrate dominates the physical and thermal characteristics of the sensor while the metal film dominates the electrical characteristics. Figure 13-4 shows the physical characteristics of a typical cooled film sensor and support and a diagram showing i t s operation. The entire right hand side of equation 13-1 is simply - QE (negative since QE is shown as heat transfer to the sensor from the environment) in the Figure. Therefore, f o r an idealized hot film sensor without cooling: P=-QE

(Eq. 13-2)

and f o r an idealized hot film sensor with cooling: P = Qc -QE

(Eq. 13-3)

490

-TUNGSTEN WIRE WITH THIN PLATINUM

Y

GOLD PLATED STAINLESS STEEL SUPPORTS

PLATING TO DEFINE SENSING LENGTH

Fig. 13-3a

Tungsten hot wire sensor and support needles (0.0038 m m )

- 0. 00015wdia.

GOLD PLATING DEFINES SENSING LENGTH

S STEEL SUPWR 1s

FILM-

CnAfEn

10.051m m D l a )

b

PLATINUM ROD

S~tiSb'k-51 N GLASS

Cylindrical hot film sensor and support needles (0.051

mm)

- 0.002" dia.

I

491

SECONDARY COOLING LOOPS TUBE BUNDLE (WHEN PROBE IS COOLED)

UPP PORT

SENSOR ELEMENT LENGTH 1.5"

GOLD PLATING PLATINUM FILM GLASS TUBE 0.15mm O.D. 0.125" I.D.

NT AND ELECTRICAL CONNECTION TO SENSOR

ELECTRICAL POW PLATINUM FILM

TEMPERATURE

QC

=

UC(ts-t,,,)= %=Heat

Constant Transfer Coefficient, J / S

-OK

Q C = P *QE

QE

=

Heat Transfer From Environment to Sensor

Since P>O QC >QE For Proper Operations

Fig. 13-4

Cooled probe and fundamental heat transfer relation

492 where: P

= electrical power input to the sensor

Qc = heat transferred,from the sensor surface to the cooling fluid QE = heat transferred from the environment to the sensor surface Equation 13-3 gives the basic information on maximum environment conditions. Since P must be g r e a t e r than zero, for proper operation:

Qc

’ QE

(Eq. 13-4)

The maximum heat transfer from the environment to the sensor is then equal t o the cooling rate. On present s e n s o r s the practical upper limit f o r short t e r m t e s t s is 20 watts with 10 watts being realistic f o r continuous use in most types of environments. These figures are f o r the heat transfer rate in watts from the environment t o the sensor surface area (0.15 mm dia. by 1.5 mm long). Frequency responses of up to 50 ICHz can be attained (-3db point) using cooled film sensors. An important requirement of the cooled film sensor is that the t e r m Qc remains constant, independent of external environment conditions. The circuit operates to maintain the average sensor surface temperature constant. If the entering cooling fluid temperature and flow rate is a l s o constant, then ideally the t e r m Qc will remain constant. A number of factors affect this idealized situation but in actual operation of the cooled probe this assumption must usually be made. Some potential e r r o r s in the assumption are discussed later.

In a constant temperature, constant composition environment a calibration curve s i m i l a r to that shown in Figure 13-2 could be plotted for a cooled probe. The operation and data reduction technique under these conditions are then essentially identical to those f o r a hot wire of similar diameter operated at constant temperature. The t e r m Qc can b e handled like the free convection t e r m is f o r a hotwire. Perhaps the most important difficulty with the cooled probes is that a high temperature environment seldom, if ever, satisfies the constant temperature condition. In addition composition changes are common due t o different constituents, chemical reactions, o r even ionization. In this sense measurements with cooled probes resemble m o r e closely measurements in supersonic flows with hot wires. An important difference is that in supersonic flows the hot-wire can usually be operated very close to the environment temperature. This permits quite effective separation of velocity and temperature when two probes are used operating a t different surface temperature. In high temperature g a s e s this separation is much more difficult since the sensor cannot be operated close to the environment temperature. Other complexities in cooled probe systems are: the need to water cool the probe, increasing both cost and size; the need f o r water tight connections with no condensation that can cause electrical shorting; difficulties in inserting the probe in many high temperature environments; and higher power required from control circuitry. These are practical problems that are largely eliminated by proper design and operation of the system. At high heat fluxes, the cooling fluid in the sensor will be turbulent to maintain the desired cooling rate. This lowers the signal-to-noise ratio of the system when compared with a normal hot wire, since the low frequency signals get transmitted through the tube to the sensitive film. Finally, the cooling a l s o limits over heat ratios because f o r a given coolant temperature, the heat flux from the surface to the coolant is determined by the sensor operating temperature. Arbitrary selection of a sensor temperature can result in ( a ) this cooling rate being excessively high, so the cooling water boils o r the s e n s o r burns out o r (b) the cooling rate,

493 Q,, being l e s s than maximum heat transfer from the environment t o the sensor,

QE. Under these conditions the circuit shuts off and no data is obtained until

the inequality in equation 13-4 is again satisfied. The result is that it is the maximum expected heat flux, QE, that determines sensor operating temperature rather than a selected overheat ratio as in hot-wire anemometer operation. Heat Transfer Correlation for Cooled Probes

F o r a cooled-film sensor placed normal to a high temperature fluid s t r e a m of low Mach number, the forced convective heat transfer to the film is a function of stream temperature, stream velocity and the fluid transport properties. F o r a s t r e a m composed of a binary mixture, the transport properties of the mixture are functions of the mixture ratio. Thus, a cooled-film anemometer may b e calibrated to measure temperature, velocity and percentage composition of a binary mixture flow. Direct calibration is straightforward f o r measurements in flows where only one of the independent parameters is a variable, as discussed earlier f o r the common measurement of velocity in low-speed aerodynamics. F o r measurements in fluid s t r e a m s where more than one of the independent parameters is a variable, such as in hypersonic wakes, mixing regions of jets of dissimilar fluids and/or of dissimilar temperatures, and diffusion flames, a direct calibration over the entire range of variables is often tedious and time consuming. F o r such cases interpretation of measured heat flux data by means of a more general, nevertheless accurate, correlation of the appropriate dimensionless groups involved is more appropriate. In considering the nature of the cooled-film operation and i t s application for measurements in diffusion flames and hypersonic wakes, one may stipulate that the required heat t r a n s f e r correlation must be valid f o r the following cases: (a)

when the transfer of heat is from the environment to the sensor ( i . e . T m > T,).

(b)

when the temperature difference between the sensor and the ). environment is large (i. e. T ~ / >T 2 ~

(c)

when the environment is composed of flows of different g a s e s and g a s mixtures. when the Reynolds number (based on sensor diameter) of the flow is low, (i.e. Re < 100).

(d)

It may be noted that conditions of very low Reynolds numbers, where free and forced convection may interact, a l s o conditions of high Knudsen numbers where f r e e molecular effects may be important, have been left out of the stipulated conditions. Forced convective heat t r a n s f e r involving cylinders has been extensively investigated. However none of the investigations, individually o r all of then1 collectively, cover the entire range of conditions mentioned above ( 5 ) . It must be emphasized that such correlations a s that obtained by careful experimentation by Collis and Williams ( 6 ) f o r hot-wire work are not applicable to precise cooled-film work This is because of the different nature of dynamical dissimilarity (when T , < T,). with temperature loading between c a s e s of heating and cooling (5). On the othrr hand, data obtained for the heating of cooled cylinders such a s those by Churchill and B r i e r ( 7 ) are f o r Reynolds numbers above 300. A detailed discussion of the existing correlations has been presented in ( 5 ) .

In the present investigation the flow conditions were simulated in a plasma-jet

494 (jet orifice diameter 12 cm. ) The jet conditions were maintained such that a t the points of heat transfer measurement (i. e. a t the potential core of the jet, where the distribution of velocity, temperature and concentration are uniform) ionization was negligible and recombination was complete. By means of a cooled-film the maximum relative intensity of heat f l u x fluctuations was found to be less than 3 % . If it is considered that the heat flux fluctuations are due only to velocity fluctuations, the e r r o r in heat transfer measurement will be less than 2% due to turbulence. Constant temperature, quartz coated, cooled-films were used as the heat transfer gurface. The film is obtained by a deposition of platinum of thickness 1000 - 2000 A on a loop made on Vycor tube, 0.0152 cm 0.D. and 0.0102 cm I. D. The sensitive section of the film is isolated by a heavy gold plating (0.013 - 0.025 mm thick) on the rest of the loop. The length of tbe sensing film is 0.103 cm and the thickness of i t s quartz coating is around 5000 A Along with the heat transfer measured by the cooled film, velocity and temperature were obtained by means of a carbon tipped pitot probe of orifice diameter 0.103 cm and a Pt - Pt 10% Rh thermocouple of bead diameter .127 c m respectively. Further details of experimental set-up and procedure may be found in ( 5 ) . The variables and the variable ranges considered in the investigation are as follows:

.

a.

Temperature loading. The range of jet temperature considered was 800°K to 1600"K, and the film temperature was varied in three steps between 350°K From this a temperature loading (Tw/T s) range of 1 . 5 to 4.5 to 525'K. was obtained.

b.

Reynolds number.

c.

Flow composition. The plasma-jet was composed of He, N, and mixtures Two mixture ratios were considered f o r each of H e - N,. N, - CO,. mist u re.

The range of Re based on cylinder diameter was 4 t o 80.

The true jet temperature was obtained from the thermocouple temperature by applying correction f o r radiation and conduction e r r o r s . Transport property values of the gas species and specie mixtures f o r data analysis were calculated from the expressions collected in ( 8 ) . In the course of data analysis the following points were noted: Tw Consideration of the film temperature (Tf = -1

Ts

f o r the evaluation 2 of fluid properties in the dimensionless parameters Nusselt number and Reynolds nuniber? was not sufficient to eliminate the temperature loading effect. The residual effect caused a decrease in Nusselt number with increased temperature loading at a particular Re for the present case of heating of cylinders. +

'Replacement of the usual temperature ratio in the temperature loading factor by a kinematic viscosity ratio enabled a unique correlation to b e derived f o r flows composed of g a s species whose transport property value variations with temperature are different. This conclusion is supported by arguments presented in (9) f o r hot wires. The expected slight influence of the small variation of Prandtl number (because of the consideration of different flow species and specie mixtures and a l s o because of variation of temperature), could not be discerned.

495 d.

The Re, dependency of Nu, was found to be'different from that according to King's Law.

e.

A discontinuity in the heat transfer curve was noted between Re, = 40 and Re, = 55. Unfortunately, no data were collected between these values of Re, and no specific investigation was carried out to determine a change in the flow features, (viz. onset of eddy shedding) in this range. F o r the present, data collected in the Re, range below Re, = 40 was considered f o r correlation purpose.

In view of the above discussion, the following form of correlation was considered: Nuf ( v m / v f ) " = C + D Refm The constants n, m, C and D evaluated by the least square method were found to be

as follows: Ref

4 -40

n .15

m .45

C .2068

D '

,4966

Figure 13.5 shows the effectiveness of this relation in correlating the entire body of data below Re, = 40. The r m s deviation considering this range of data was 0924.

I

1

Finally 13-6 compares values of Nu, calculated from some of the correlations obtained f o r heat transfer from heated cylinders with values calculated from the present correlation. The evaluation is for an identical condition of heat transfer to a cooled cylinder with T, = 400"K, T m = 1200°K and the flow composed of N,. Even considering the wide discrepancies in values calculated from correlations obtained for heated cylinders only, the e r r o r involved in using them to analyse heat transfer to cooled cylinders is quite apparent. T e s t s in Severe Environments The maximum environment capabilities of the cooled film probe have been expressed in t e r m s of heat transfer rates f r o m the environment to the sensor. To convert this to temperature and velocity requires an accurate heat transfer relation o r t e s t s where the conditions are well known. Although the following data does not conipletely satisfy either criteria, it does give some indication of the capability of the cooled film sensors.

I

Figure 13-7 shows a traverse a c r o s s the tip of an acetylene torch for two distances from the tip. The inside diameter of the tip is 3.8 mm and maximum heat flux to the sensor is 16 watts. Referring to Figure 13-7, the traverse was made from left to right. The sensor did shift in resistance during each traverse, as shown by the failure of the points on the right t o approach closer to the abscissa. A single t r a v e r s e took approximately five minutes. The 16 watts represents a heat transfer rate to the 0.15 mm dia. sensor of 2.66 KW/cm2.

't I

Reference (10) is another application where the cooled film sensors were exposed t o a severe environment. The cooled sensors were used in a combustor that burned ethanol and liquid oxygen at an average chamber pressure of 178 psia. P r e s s u r e oscillations of *15 p e r cent were sustained at 1190 cps with a siren mounted directly downstream of the exhaust nozzle. Under test conditions the average environment temperature was calculated to be 1900°K and the maximum velocity (measured from streak photographs) about 110 m/second. Velocity

496

5.0

3.0

2.0

1.0 2.0

5.0

3.0

6.0

7.0

90

Ref 045

T K

Flow

Symbol

TS

Nitrogen

852 -1660

Helium

803

He 40% by vol. N2 60% by vol.

900 -1269

He 77.5% by vol. N2 22.5% by vol.

900

He 42% by vol. CO2 58% by vol.

701 -1088

He 93.5% by vol. CO2 6.5% by vol.

702

- 1090

342

- 465

N 50% by vol. Cb2 50% by vol.

703

- 1278

367

- 512

703

- 1277

367

-

- 1360 - 1270

'361 -496 387

- 532

361

- 496

387

- 532

342 -465

A 0

Q

N2 30% by vol.

bo2 70% by vol. Fig.

13-5

512

A

* 45 showing all heat transfer data f o r various species and specie Mixtures and f o r various temperature loadings uniquely correlated by the relation Nu,( u , , / v , ) ~ l5 = .2068 + .4966 Re,-45 in the Re, range of 5 to 40.

Nu, ( u o o / u , ) ~l5 vs Re,

497

I

.

(1) Kramer (18)

.

0.33 0.50 Nuf = 0.42 Pr O S 2 O + 0. 57Prf Ref f

(2) 'Van d e r Hegge

Nuf = 0.35 + 0.5Re

'i'ijnen (19) (3) Collis and Williams

Nuf = ( 0.24 + 0.56 Ref

Fig.

13-6

0.45

)

Tf

(T) .17

-

(5) Present result T

+ .OOIRef

25 .385 Nuf = .821 (Ref(Ts,/ T )' ) 0.45) ( )-. 15 Nu = (0.2068 + .496 Ref

(4) Hilpert (20)

Ts = 400 K,

f

f

=

1200 K

,

flow = Nitrogen

Comparison of present correlation for forced convective heat transfer to cooled cylinders in heated cross-flow with previous correlations f o r heat transfer from heated cylinders in ambient o r near-ambient cross-flow.

I

498

Fig. 13-7

Heat flux traverse of acetylene torch.

HEAT TRANSFER TO SENSOR

c-P

7 TIME

-

HEAT TRANSF TO SENSOR

1 WATTS I

CYCLE

Fig. 13-8

TIME

tltq

Typical heat-flux sensor output and average heat flux for one cycle of oscillation. (reprinted from (10)

I

I

I

t 1

499 (possibly temperature and/or composition included) fluctuations gave heat flux variations to the sensor of about 6 to 17 watts (10). In this case the standard sensor diameter(O.15 ")was used but it was shorter than standard length 1 . 0 mm.

The value of Q c set for the experiments of (10) was 20 watts, which went down to 18.8 watts after the one second run even for 'successful' runs. Initially, sensor breakage was a serious problem which was corrected by shielding the sensor during engine start-up. Even then, as reported in ( l o ) , sensor stability and longevity caused a serious problem f o r the experiments. The velocities cal- . culated from cooled sensor data did not agree with the streak photographs. A s pointed out in the reference, no detailed calibration was deemed practical so the heat transfer relation used could be suspect, in addition to,other sources of e r r o r . The maximum Reynolds number of 580 is well beyond the calibration data of Figure 13-5.

~

Figure 13-8 shows a typical set of data from the cooled sensor when exposed to the test chamber of (10). The lower curve is for the sensor when shielded on the inlet side. This data was taken t o identify the reverse flow point, since a cylindrical sensor cannot differentiate flow direction. The environment of (10) would seem to b e a t the upper heat flux limit for useful data from cooled sensors. Since many environments exceed these conditions (e.g. hydrogen oxygen combustors, plasmas, etc.) there is a need to extend the range of cooled s e n s o r s to higher temperatures. Some efforts have been made in this direction (11) which led to the present sensor design using.Vycor rather than the original Pyrex ( 1 ) . Although further improvement is always possible, the difficulty of cooling a small tube adequately f o r survival s e e m s t o preclude a significant improvement. Going t o l a r g e r tubes is not generally desirable since characteristics such as frequency response and spatial resolution would be compromised.

1

I I

, ~

I

Accuracies With Cooled Probes

Experimental data on the accuracy of the cooled probes is limited. Reference (11) discusses several potential sources of e r r o r and gives calculated estimates of the effects while (12) gives details on the e r r o r in the two-sensor technique. The consistency of the calibration data in this paper indicates the kind of reproducibility that can b e expected f o r mean measurements. The primary source of e r r o r is in the assumption that the heat transfer from the sensor surface t o the cooling fluid, Q,, is constant during external environment changes. One source of e r r o r i s the exposed part of the sensor tube between the protective cooling jacket and the 'sensitive' portion of the sensor. In a high temperature environment the water temperature will rise in this passage, while during the t a r e reading of Q, there would be no temperature rise. Another cause of e r r o r is the re-distribution of sensor surface temperature between the t a r e reading and the reading in the environment. Some measurements of sensor surface temperature distribution are given in (12). F o r the calculated roiiditions in ( l l ) , the e r r o r estimate f o r all the above factors was 5.2 per cent on the hcat flux reading. In measurements with hot-wire and hot-film probes, an assumption is niade that the steady-state calibration can be used directly to interpret unsteady-state dntn. This s e e m s valid f o r the very fine hot wires used near atmospheric temperature and p r e s s u r e conditions. F o r the larger cooled films at high Reynolds numbers,

500

-

.1

0

UNCERTAINTY IN TEST CONDITIONS

-

-

*

-

TYPICAL

UNCERTAINTY

IN o c o o L n N I

-

0-I

Fig.

13-9

'

I

I

I

I

I

I

I

I

I

I

Nusselt-Reynolds number calibration data. (reprinted from (14)

I

501

I

11

flow separation effects around the sensor could invalidate the assumption. In addition, the complex nature of the cooled film can cause transient e r r o r s due to changes in surface temperature distribution both longitudinally and radially under varying flow conditions. Applications of Cooled Film Sensors

1

1

l

1

Much of the data given above has been concerned with the problems associated with cooled film sensors. It is important to recognise these problems before undertaking measurements. At the same time, the unique capabilities of the cooled s e n s o r s make them not only a valuable tool, but sometimes the only tool that can give the required data in a given situation. The measurements in a rocket chamber have been discussed as an example of the upper limit of conditions where the cooled films are applicable. Other applications that data are available on are:

a.

Measurements of a hypersonic boundary layer

b.

Measurements in the wake of a hypersonic projectile

Other applications are certainly feasible and in fact have been made, but no published data is available. ~

Hypersonic boundary layer measurements were made by McCroskey, et a / (13), (14). Nominal test conditions in the nitrogen tunnel were: To, =. 2000"K, Pol. = 135 - 340 atm,Mm = 23 26, and Re/cm = 2,950 5,900. Tests in Helium were run at To, = 297'K, Pol= 15.3 atm,Mm = 16.5, and Relcni = 47,200 (15) with hot wires. Although there is some scatter, most of it is between s e n s o r s and the slope for all sensors agrees with Dewey's results.

-

I

1

-

In this work a pitot probe, a cooled film probe, and the recovery temperature of a hot wire were used to calculate the variables of interest such as velocity, density, and p r e s s u r e near the leading edge of a sharp flat plate. In the nieasurements with cooled probes, one of the problems that came up was inadequate resolution. Even though the total temperature of the environment was high, the total heat flux to the probe was 0.1 to 0.5 watts. Therefore, to increase sensitivity and lower dependence on entering coolant temperature, nitrogen was used for cooling rather than water. This increased resolution by permitting a much higher temperature difference between sensor surface and coolant,. while keeping the total power dissipation to the coolant low.

I

I

ff+

An extensive investigation of turbulence characteristics of hypersonic wakes by means of cooled-film anemometers is being carried out a t the Canadian Armament Research and Development Establishment at Val Cartier, Quebec (12), (16), (17). Owing to the high temperature encountered in the near wake region of hypersonic projectiles, the application of the cooled-film technique appears appropriate. Further, cooled-films have proved to b e sufficiently robust to survive the hypersonic range environment at least for a sufficient length of time to record a signal of several thousand body diameters in duration (15). The above experiments are performed in the CARDE Hypersonic Range No. 5 which consists of a light g a s gun with a 102 mm b a r r e l capable of launching projectiles into a depressurized tank of 122 m length at velocities in excess of 415 m/s (17). Two constant-temperature cooled-film sensors with different sensor surface temperatures, positioned several thousandths' of a centimeter

502

apart are located near the flight axis of the projectile, (16). The cooled film anemometer bridge voltage is recorded by means of oscilloscopes viewed by Wollensak Fastax cameras. The two cooled film sensors are operated at two different surface temperatures to attempt the separation of environment temperature and velocity. It is important that the temperature difference between sensors be large to optimize the accuracy using this technique (11) , (12). At the same time, it is best to have both anemometer circuits operating a t about the s a m e power level f o r nearly equivalent frequency response and sensitivity. One way t o satisfy these criteria is to use water as the coolant f o r the sensor with low surface temperature and an oil (such as Fluorolube FS o r Silicon Oil 704) f o r the sensor with high surface temperature (12). The method of reduction of recorded voltage data in t e r m s of velocity and temperature distribution in the wake, to determine their power spect r a l density functions h a s been shown in (12).

I

I I

I ~

Conclusions From the data presented, some tentative conclusions can be drawn for cooled film sensors presently available:

, I

The maximum heat fluxes from the environment to the sensor are:

a.

About 10 watts for good sensor stability and longevity

b.

Up to 20 watts maximum with decreasing stability at increasing heat fluxes.

The use of a coolant other than water is often desirable f o r a given measurement situation. Accuracies of better than * five p e r cent on heat flux are probably not possible unless the calibration covers a range that includes the test conditions exactly.

1 I

I

I

The heat transfer correlation presented indicates that the cooled sensors can be calibrated in high temperature environments. Of particular interest is the successful use of a transport property (kinematic viscosity) to correlate different compositions. The cooled film sensor greatly extends the temperature range of the hot-wire o r hot-film anemometer. It retains many of the important features such as small size, high frequency response, and high resolution which make the hot-wire anemometer a valuable tool in fluid mechanics research. Also, like the hot w i r e , it has definite limitations in both'accurac)i.'and environment conditions which must be rccognizcd before measurements are attempted. References 1.

Fingerson, L.M., 'A Heat Flux Probe f o r Measurements in High Temperature Gases, ' Ph. D. Thesis, Univ. of Minnesota, 1961.

2.

King, L.V., 'On the Convection of Heat from Small Cylinders in a Stream of Fluid: Determination of the Convective Constants of Small Platinum Wires with Applications to Hot-wire Anemometry, ' Proc. Roy. Soc. (London), Vol., 214A, No. 14, 1914, p.373.

I

I

503 3.

Ling, S.L., and Hubbard, P. G., 'The Hot-Film Anemometer A.New Device for Fluid Mechanics Research, ' Jour. Aero. Sci., Vol. 23, 1956, p. 890.

4.

Lowell, Herman H., 'Response of Two-Material Laminated Cylinders to Simple Harmonic Environment Temperature Change, ' Jour. Appl. Phys. Vol. 24, No. 12, 1953, p.1473.

5.

Ahmed, A.M., 'Forced Convective Heat Transfer to Cooled Cylinders a t Low Reynolds Numbers and With Large Temperature Difference, ' McGill MERL. T.N. 67-5.

6.

Collis, D. C., Williams, M. J., 'Two Dimensional Convection from Heated Wires a t Low Reynolds Numbers, J. of Fluid Mech. Vol. 6, 1959, p. 357.

7.

Churchill, S.W., Brier, J. C., 'Convective Heat Transfer from a Gas Stream at High Temperature t o a Circular Cylinder Normal to the Flow, ' Chem. Eng. Progr. Symposium Series, No. 17, 51, 57, 1955.

8.

Brakaw, R. S.,

9.

Davies, P. 0.A. L., and Fisher, M. J., 'Heat Transfer from Electrically Heated Cylinders, ' Proc. of the Royal Society, A, Vol. 280, 1964, pp. 486-527

10.

Povinelli, Frederick P . , and Ingebo, Robert D., 'Evaluation of a Thin-Film, Heat-Flux Probe for Measuring Gas Velocities in an Unstable Rocket Combustor, NASA Tech. Mem. TM X-1333, Feb., 1967.

11.

Fingerson, L. M., 'Research on the Development and Evaluation of a TwoSensor Enthalpy Probe, ' Aerospace Res. Lab. Rep. ARL 64-161, Oct., 1964.

12.

Ellington, D., and Trottier, G., 'Some Observations on the Application of Cooled-Film Anemometry t o the Study of the Turbulent Characteristics of Hypersonic Wakes, ' Canadian Armament Research and Development Establishment Report CARDE T. N. 1773/67, Sept. 1967.

13.

McCroskey, W.J., Bogdonoff, S. M., and McDougall, J. G., 'An Experimental Model f o r the Leading Edge of a Sharp Flat Plate in Rarefied Hypersonic Flow, ' AIAA P a p e r 66-34 1966.

14.

McCroskey, W. J., 'A new Probe f o r Hot-wire Anemometry a t High Temperature, ' Princeton Gas Dynamics Lab. Int. Mem. 7, *Aug. 1965.

15.

Dewey, C. F., 'Hot Wire Measurements 'in Low Reynolds Number Hyper sonic Flows,' J. ARS, Vol. 31, No. 12, Dec. 1961, p. 1709.

16.

Trottier, G., Ahmed, A.M., Ellington, D., 'Cooled-Film Anemometer Measurements in the Hypersonic Wake, ' CARDE TN 1720/66, May, 19GG.

17.

Staff of Aerophysics Wing - Compiled by D. Heckman, 'Re-Entry Physics Research Program on Turbulent Wakes, .CARDE TN 1741/67, Jan. 1967.

18.

Kramer, H.,

19.

Van der Hegge Zijnen, B. G., Appl. Sci. Research A, Vol. 6, 129,1956.

'Alignment Charts for Transport Properties Viscosity, Thermal Conductivity and Diffusion Coefficients f o r Nonpolar Gases and Gas Mixtures a t Low Density, ' NASA TR-RB1.

Physics, Vol. 12, no. 2-3, 61,1946.

-

504 20.

Hilpert, R , Forsch, Gebiete Ingenieurw., 4, 215, 1933.

Nomenclature constants sensor diameter

A, B, C, D d I

current in sensor

M

Mach number

m, n

constants electrical power input to sensor

P

k a t transferred from sensor surface t o cooling fluid heat transferred from environment to sensor surface

Q C

QE

Rc

Reynolds number (Vd/v)

R,

scnsor opcrating resistance

t

t ellipera t u re

T

absolute temperature

V

environment velocity

V

kinematic viscosity

Subscripts: 'i

=

S C I I S O ~ surface

=

arithmetic niean (when referring to fluid properties, signifies tl!ey a r e evaluated aP the arithmetic mean temperature (e.g.

T, =

=

T,

4.

T,

2

free s t r e a m

505

1

Index

5137 SUBJECT INDEX

A Abel inversion, 225-228, 235-237, 260 Ablation, 341 Absolute continum emission coefficient, 256 Absolute (Gas) Temperature Scale, 106-109 Absorptance, directional absorptance, 364, 371 directional absorptivity vector, 361 hemispherical absorptaoce, 364 hemispherical absorptivity, 362 total absorptivity, 362 total hemispherical absorptivity, 362 Absorption in gases band absorption, 387-389 coefficient, 383, 387 mass absorption, 231 monochromatic absorption, 231-233, 247 volume absorption, 231 narrow band absorptivity, 389 Absorptivity, see Absorptance Accuracy (See also E r r o r s , E r r o r Analysis) of cooled film anemometer, 499-501 of Int. Practical Temperature Scale, 76, 77 of Mueller bridge, 129 of optical pyrometer, 90 of Schlieren system, 185-187 of Shadowgraph, 192-193 Acoustical thermometer, 117 Adiabatic demagnetization, (See Magnetic thermometry) Advisory Committee on Thermometry, (See Comite' Consultatif de Thermom6trie) Aging of thermistors, 141-150 Air-mixture properties, 443-447 Airy disc, 467, 472 Alpha coefficient of platinum resistance thermometer, 37, 56, 131 Alumina, 81, 82, 83 Amplitude limiter, 477 Amplitude modulation, 477 Analogies, 329-351 (See a l s o Mass transfer analogy) conduction, 329 convective, 331 -351 optical, 331 radiation, 331 Analysis of cooled electrostatic probe, 281-285

Anemometer, ( s e e Cooled film anemometer) Angle factor, radiation, 284, 330-331, 372 optical analogy, 331 Angles of emergence, 354 Angles of incidence, 354 Angular-hemispherical reflectance, 364, 371-378 (See a l s o Reflectance) Angular light spread, 473 Annealing of thermocouples, 79, 81 Argon properties, 443-447, 453 Aspirated hemispherical radiometer, 367 Astigmatism in intrrfersmeters, 212 Axisymmetric fields, ( s e e Abel inversion)

B Backward scattering coefficient, 383 Band absorption, 387-389 Band-pass radiometer, 367 Bandwidth of l a s e r , 461 ' of signal of laser-Doppler system 459, 465-469 of spectrum analyzer, 469, 477 Base metal thermocouple, 75, 79, 80 (See also Thermocouple) Benzoic acid cell, 34-35 Beryllia, 85 Bidirectional reflectance, 363, 369371, 383 (See also Reflectance) Bidirectional reflectance matrix, 363 Bidirectional reflectometers, 363, 370 Bidirectional transmittance, 369-371 (See also Transmittance) Biot number, 309-311 . for radiation, 312 Black body, 75, 87, 88 energy density, 232 intensity, 232-237, 356 radiation, 28-30, 87, 232-237, 355-356 Black temperature, 233, 261 Bohr's frequency relation, 234 Boltzmann distribution, 235, 237, 245, 246 Bose-Einstein statistics, 355 Boundary layer on cooled electrostatic probe, 283, 284 thermal, 193, 199, 205, 209 transient thermal, 205, 209

508 Bremsstrahlung, 246-247 Brewster angle, 358 Bridges, developments and construction, 41 Johnson noise, 41, 42 Mueller-type, 59-61 Smith bridge, 41 Brightness, 87 Brightness temperature, 87-91, 260, 261

Chopper, 368, 369 Chrome1 P vs Alumel thermocouple, 79, 80, 84, 86, 123-126 CIE standard visibility function, 88 Coating for integrating sphere, 372 Coherence angle of laser-Doppler system, 473 cone in laser-Doppler system, 473 length of interferometer, 212 of scattered and reference beam, 472 in thermal radiation, 357-359 C Coiled capillary viscometer, 399 Cold window cell, 385 Calibration, Collimator, 293 of calorimetric probe, 275 Color temperature, (See Colour of cooled film anemometer, 493-495 temperature) of optical pyrometer, 89, 90, 112 Colour temperature, 88, 233 of platinum resistance thermometers, Comit6 Consultatif de ThermomBtrie, 59-61, 107, 112, 131-133 109, 167-168 of thin-film thermometers, 321 Compensating tank, 212 Callendar formula, 37, 56, 57 Composition indicating probe in plasma, tables 59 269-293 Callendar-VanDusen formula 131 Conducting paper, 329 Calorimeter, 25-28, 309-322, 415, Conduction-coupled radiometer, 368 425 -431 Conduction Nusselt number, 309 (See a l s o Calorimetric probe) Conductive heat transfer, 16-30, 309differential, 429 325, 406,423 drop-type, 427-429 Analogies, 329 flow, 430 Constant temperature anemometer, ice, 427 (See Cooled film anemometer) ideal slug, 311-313 Constatan vs copper thermocouple, mixing, 430 123-127 steam, 415 Construction of platinum resistance slug with internal resistance negligible, thermometers, 311-315 high temperature, 63-65 slug with surface resistance negligible, low temperature, 39, 40 315-322 Contact resistance, 415-417 Calorimetric probe, 270-281 Const r a s t (See also Cooled electrostatic probe) of Schiieren system, 184, 185 Calibration, 275 of shadowgraph system, 192 double. 278-279 Convection heat transfer probe sensitivity, 275-277 analogies, 329, 331-351 equation for, 277 Free convection from shock-swallowing double, 278-279 cylinder, 187, 188, 197, 198, "split-flow" probe, 277 205, 208 Capillary viscometer, 398, 399 flat plate, 205, 207, 209, 210 coiled, 399 propane torch, 187, 188, 193, Carbon atmosphere on thermocouples, 194 83 Forced convection from Carbon-dioxide properties, 443-447 cooled film sensor, 493-502 Carbon resistance thermometer, 122, cylinder, 343 133-135 flat plate, 338, 339, 341, 414, Ceramic films, (See Thermistors) 441-443 Characteristic length, 269 rotating disk, 339-341 Characteristic time of thin-film, 319 solid surfaces, 17-20 Chemical contamination of platinum thermocouples, 16-23 rodium thermocouples, 81 tubes, 3341338, 342, 343 Chemically frozen, 284, 287 Cooled electrostatic probe, 281-293

509 Depth of field, 467 Detailed balancing, 361, 363, 371 Detector absorptivity vector, 365 Differential calorimeter, 429 Diffuse surfaces in thermal radiation, 363-364 Diffusion coefficient, 447-449 Diffusion thermo effect, 447-449 Diffusivity of heat, (See Thermal conductivity, Thermal diffusivity) Dimensional analysis, 331-332 Directional absorptance, 361, 364, 371 (See also Absorptance) Directional absorptivity vector, 361 Directional emittance, 371 (See a l s o Emittance) Directional-hemispherical reflectance, 364, 371-378 (See a l s o Reflectance) Directional radiometer, 371 Directional reflectance, 371 -378 (See a l s o Reflectance) Directional reflectivity , 361 (See a l s o Reflectance) Directional reflectometers, 372, 374, 377 Disappearing filament pyrometer, 76 Dispersion spectrometer, 371 Doppler (See a l s o L a s e r Doppler system) current, 463 effect, 459 shift, 459 equation of 462-464 Double calorimetric probe, 278-279 platinum resistance thermometers, Double cavity reflectrometers, 372, 129-133 377 temperature scales, 105-121 Double-sonic orifice temperature probe, 271 Drop-type calorimeter, 427,429 E

I

I

D Debye length, 283 Defining fixed point, 99, 105 (See Fixed points) Density measurement by optical met hods, 177 218

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Effective circular c r o s s section, 19 Effective emittance. 93 Effective environmcnt temperature, 30 Effective heat transfer coefficient. 30 Effective temperature. 234 Eigenvalues for diatoniic molecules, 249 Einstein photoelectric law, 353 transition probabilities, 234. 235, 245, 251-252 Electrical conductivity, 421. 422 Electrical system f o r constant lcmperature anemcmeter, 488-489

I

510 calorimetric probes, 275-281 Electro-chemical analogy, 341-344 cooled film anemometer, 499-501 electrolyte used, 344 gas radiation, 389 saturation current, 342 in interferometers, 214-217 Sherwood numbers, 342 supporting electrolyte, 343 Johnson noise, 41, 42, 54 perturbation analysis, 381-383 Electro-chemiluminescence, 344, 313' Electron platinum resistance thermometers, cyclotron radiation, 249 35-40, 63-72 density in plasma, 238-263 passim, precision manometer, 47 269-293 probes, 13-32 Larmor radius, 249 quenching effect on thermocouples, temperature in plasma, 238-263 69-72 passim, 269-293 radiation measurement, 381-383 Electrostatic, probe, (See Cooled slug calorimeter, 309-322 electrostatic probe) spectroscopic methods, 253-263 Electronic excitation temperature, 260 passim Emission coefficient, 231-233, 235-238, sulpher point boiler, 51-52 temperature measurement, 13-32 245-247. 251-256 absolute continium, 256 thermal conductivity cells, 407-412, line, 245. 251-256 4 54 modified. 232. 233 thin-film therometers, 321, 322 monochromatic. 231-233. 245-247 Excitation equilibrium, 239-241 neutral line, 252-256 External total hemispherical emissivity, 363 relative line, 252-256 Emissivity. (See Emittance) (See also Emittance) Emittance. External radiation characteristic, 362 (See also Spectral emittance) correction of pyrometers. 75. 87, F 88 directional emittance. 371 effective. 93 Fabry-Perot interferometer, 477 external total hemispherical emissivity,Fnlling body viscometer, 401 363 Film sensor, (See Cooled film anemohemispherical emissivity, 362 meter, Hot-film sensor) internal total hemispherical Film temperature, 494 Filters, 367 emissivity. 363 internal total emissivity, 362 Fixed points. 43, 105, 106, 111 total emissivity. 363 below 90@K. 115, 121 total hemispherical emissivity, 362 Defining, 99. 105 total hemispherical emittance, 378, Fundamental, 99 381 gold, 63, 76, 81, 111 End effects ice, 33, 43, 111 in interferometers, 214-215 oxygen, 33, 54, 76, 111 in Schliercn system, 181 primary, 99 Enthalpy probe in plasma, 269-293 secondary reference points, 99 Environmental effect of thermocouples, silver, 63, 76, 81, 111 79. 80, 82. 83 steam, 33, 48-50, 76, 111 Equilibration length, 239 sulphur, 33, 50-52, 76, 111 Equilibration time, 239 triple point, 43, 105, 106, 111 E r r o r analysis, 381-383, 389 Fizeau effect, 459 interferometers 214-217 Flash method of thermal conductivity in probes, 13-33 measurement, 419 in radiation measurements, 28-32, Flat plate heat-mass transfer, 338, 381-383. 389 339, 341, 414, 441-443 in thermal conductivity measurement, Floating potential for electrostatic 419 probe, 283, 285, 287, 289 E r r o r s in Flow calorimeter, 430 (See also Accuracy, E r r o r Analysis) Flow visualization, 337, 338

1

511 Fluid temperature 'measurement e r r o r s , (See Temperature measurement) Fluid thermal conductivity measurement, 406-415 Forced convection, (See Convection heat transfer) Forward scattering coefficient, 383 Fourier equation of heat conduction, 406 hypothesis, 309, 406 number, 316-318 transform in interferometer, 367, 371 Fractional function of black bodv radiation, 355, 363 Fraunhofer diffraction pattern, 218 Free convection, (See Convection heat transfer) Free jet cell, 385, 387 Frequency discriminator, 477 Frequency limitations, of Doppler shift, 462 of laser-Doppler system, 474, 475 Frequency modulation, 477 Fresnel relations, 359 Fringe shift, 202-217 equation, 202 end effects, 214-215 refraction effects, 215-216 for Mach-Zehender interferometer, 201-207 Frozen electron temperature, 287 Fundamental Fixed point, 99 ,

G Gas containment systems for gas radiation, 385-387 Gas diffusion techniques, 413 Gas radiation, 229-267, 383-389 (See a l s o Spectroscopic temperature determination) emitted radiation, 243, 251 e r r o r analysis, 389 gas containment systems, 385-387 model, 389 molecular radiation, 249-251 theory of, 230-237 Gas radiation measurements, (See Gas radiation) Gas thermometers, 44, 76, 77, 106-109 corrections, 107, 110 Geminol P vs Geminol N thermocouple, 79 General Conference on Weights and Measures, 99, 109 Germanium resistance thermometer, 133, 145-150

magnetic field effecf, 147-150 Geometric constant, 407-410 Geometrical optics, 179-198 Gladstone-Dale, 178, 203 equation, 178 constant, 178 Golay cell, 365 Gold-cobalt v s copper thermocouple, 121-129 Gold fixed point, 63, 76, 81, 111 Goniospectrophotometers, 363 Gradients effect on local thermodynamic equilibrium, 243 temperature in thermometers, 35 velocity in Laser Doppler systems, 469 Grashof number, 333, 351 Grating inferometer, 217 (See also Inferometer) Grid schlieren, 190 Guard heaters, 407-430 passim

H Hagen-Ruebens reflection law, 361 Heat flux at wall, 193-198 (See also, Transient heat flux) Heat Transfer (See also Mass transfer analogy) analogies, 329 conduction analogy, 329 convective analogy, 331-351 radiative analogy, 331 Heat transfer coefficient, 28-30, 309-315 (See also Mass Transfer analogy) effective, 28-30 radiation, 28-30 optical measurement, 193-198 Heat transfer rate probe, 269, 295297 (See also, Transient heat flux) Heated cavity reflectometers, 372, 375, 377, 383 Heavy-partical temperature, s e e Ion temperature probe in plasma Helium atmosphere on thermocouples, 83 cryostat, 153, 154 properties, 117-121, 169-176, 443-338, 450 Helium -3, 120, 121 temperature scales, 121 vapor pressure, 173-176 Helium -4. 117-121 temperature scale, 117-119

512 vapor pressure, 169-173 Helmholtz reciprocity principle, 363, 364, 371 Hemispherical absorptance, 364 (See also Absorptance) Hemispherical absorptivity, 362 (See also Absorptance) Hemispherical -angular reflectance, 364 (See also Reflectance) Hemispherical-directional reflectance, 3 64 (See a l s o Reflectance) Hemispherical emissivity, 362 (See also Emittance) Hemispherical m i r r o r reflectometer, 378, 379 Hemispherical property operator, 362 Hemispherical radiation, 356, 362, 378 Hemispherical transfer operator, 356 Hemispherical transmittance, 381 (See a l s o Transmittance) Hetrodyne techniques, 459, 462, 469, 475 High temperature gas, (See Temperature) History of platinum resistance thermometers, 33 Hohlraum, (See Black body) Hot-film sensor, 489 (See a l s o Cooled film anemometer) Hot window cell, 385 Hot wire anemometer, (See Cooled film anemometer) Hot wire cell, (See Thermal conductivity cell) Hydrogen atmosphere on thermocouples, 83 Hypersonic boundary layer, 501, 502 I

Ice calorimeter, 427 Ideal calorimeter, 311-313 Ideal gas, 106-107 Ideal radiometer, 365 Imbedded thermocouple e r r o r s , 20-23 Incoherent thermal radiation, 358 Index of refraction, 177-179, 179-218 passim Inferometers axisymmetric fields, 225-228 basic principles, 198-201 design and adjustment, 207-214 e r r o r analysis, 214-217 fringe pattern, 201-207 kinds Fabry-Perot, 477

Fourier transform, 367, 371 grating, 217 laser, 217 Mach-Zehender, 198-217 polarization, 218 Schlieren, 218 Twyman-Green, 218 Infinite fringe, 203 Inhomogeneity effects in thermocouples, 124-127 Insulation for thermocouples, 79, 81-85 Integral weighting factor, 372 Integrating sphere, 372, 272, 383 Intensity (See a l s o Spectral radiant intensity, Spectral radiance) black body radiant, 232, 233, 238, 261-263 monochromatic radiation, 230-233, 261-263 radiant, 356 of thermal radiation from gases, 383-390 of thermal radiation from solids, 356-357 total radiation, 230 Inter-modal beats of laser, 474 Internal radiation characteristic, 362 Internal thermal resistance, 27, 28, 311-315 Internal total emissivity, 362 (See a l s o Emittance) Internal total hemispherical emissivity, 363 (See a l s o Emittance) International Bureau of Weights and Measures, 109 International Committee on Weights and Measures, 109 International Practical Temperature Scale, 37, 56-59, 63-72, 75-77, 80, 85, 86, 109-121, 167-168 (See also, Temperature scales) of 1948 accuracy, 76, 77 Callendar formula, 37, 56, 57 Callendar -VanDusen formula, 131 interpolation procedures, 112 ice point to 630"C, 56-59 630°C to 1063"C, 63-72 above 1063"C, 85 of 1968 109, 167, 168 International Temperature Scale, 33, 76, 100, 109-121, 167-168 (See a l s o International Practical Temperature Scale)

513 Interpolation procedures of ITS 19271948, 112 Interreflection e r r o r of 2 r -steradian m i r r o r , 378 Ion densities in plasma, 281 Ion temperature probe in plasma, 269-293 Ionization equilibrium, 241 Ionization probe, degree of, 269-293 Iridium vs iridium-404 rhodium thermocouple, 83-86 Iron vs constantan thermocouple, 123126 Irradiation, 357 Irreversible thermodynamic process, 398 J

Johnson noise, 41, 42 Joule-Thompson. coefficient measurement, 421-422, 431

K Kanthal + vs Kanthal- thermocouple, 79 Kelvin temperature, 105 temperature scale, 105-106 Kinetic equilibrium, 239 Kinetic gas temperature, 260 King's Law, 489, 495 Kirchoff's Law, 232, 260, 261, 361-362

coheience cone, 473 depth of field, 467 frequency limitations, 474, 475 optical hetrodyne, 459, 462, 475 optimization, 464 path length, 471 scattering angle, 460, 464, 467, 469 scattering centers, 479 scattering volume, 464, 467, 472474 signal bandwidth, 459, 465-469 signal to noise ratio, 469 spectrum analysis, 475-479 velocity gradients, 469 Laser-etalons, 474 L a s e r inferometer, 217 (See also Inferometer) Law of thermocouples, 77, 123 Lead in losses, s e e Lead wire model Lead wire losses, 16-30, 410, 412, 427 single wire model, 16-17 two wire model, 17 Limitations of laser, 474, 475 Line emission coefficient, 245, 251-256 Line radiation, 245 Line reversal spectroscopic methods, 259-263 Local thermodynamic equilibrium, 229-263 passim concept of, 238-243 excitation equilibrium, 239-241 ionization equilibrium, 24 1 kinetic equilibrium, 239 Lorenz-Lorentz relation, 178

M L L-surface, 357 Langmuir, 271, 281, 285 classical electron-current expression, 285 Larenz method, 253-256 L a r m o r radius, 249 Laser (See also Laser-Doppler system) applications, 464, 480 bandwidth, 461 etalons, 474 inter-modal beats, 474 resonance condition, 474 resonator length, 474 Laser-Doppler system, 459-486 airy disc, 467, 472 alignment requirements, 472 applications, 463, 4 8.0 coherence angle, 473

M-surface, 357, 368 Mach number in plasma, 269-293 Mach-Zehender interferometer, (See Inferometer) Magnetic cooling, 153 Magnetic field effect on resistance thermometers, 147-150 Magnetic temperature, 157 Magnetic thermometry, 150- 161 temperatures attained, 151 theory of, 153-159 thermodynamics of, 159-161 Manometer, precision, 44-48 e r r o r s , 44 Marangoni effect, 345 Mass absorption coefficient, 231-233, 247 Mass transfer analogy, 331 ammonia absorption, 334-335 ablation, 341

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514

electro-chemical, 341-344 electro-chemiluminescence, 344-345 naphthalene, 339 turbulence measurement, 341 variable property, 345 water evaporation, 335, 338-339 Mass transfer coefficient local, 343 rotating disk, 341 Massive solid, thermocouple in, 17-19 Maximum heat flux to cooled film sensor, 487, 492, 495, 499 Maxwell-Boltzmann distribution, 237 (See a l s o Boltzmann distribution) Mean specific heat, 423, 424 Measurement e r r o r s , (See E r r o r Analysis, E r r o r s ) Measurement of temperature below -150°C, 99-175 ice point to 630°C, 33-63 500°C to 11OO"C, 63-73, 79, 80 above 11OO"C, 75-98, 229-267, 293 Measurement of thermophysical properties, ( s e e Thermophysical properties) Membrane analogy, 329 Mercury line, 179 Misalignment angle, 472 Mixing calorimeter, 430 Models for lead wire, 16-17 Moire fringe pattern, 205 Molecular radiation, 249-25 1 Monochromatic absorption coefficient, 231-233

sulphur point boiler, 50-52 triple point cell, 34, 35, 43 National temperature scales, 102, 117-120

Natural thermal radiation, 358 Navier-Stokes equation, 331, 403, 405

Negative absolute temperature, 107-108 Neutral atmospheres effect on thermocouples, 81, 83 Neutral line emission coefficient, 252256

Neutrally bouyant particles, 479 Newton's law of cooling, 309 Nickel base thermocouples, 79, 80 Noble metal thermocouple, 75, 80-82 (See also Thermocouple) Noise from photomultiplier, 463 Noise equivalent power of detector, 365 (See also Signal to noise ratio) Non-black body, 87, 88 spectral radiance, 87 Nongray e r r o r , 363 Nozzle s e a l cell, 385, 387 Number density, 234, 235 Nusselt number 196, 332, 350, 494-501 conduction, 309 0

Off-axis peaking, spectroscopic method, 253-256

N

Operators hemispherical property, 362 hemispherical transfer, 356 total property, 362 total transfer, 356 Optical analogy, 331 Optical depth, 232, 233 1 (See a l s o Optically thin) Optical hetrodyne techniques, (See Het rodyne techniques) Optical measurement of temperature, (See Interferometers, Optical pyrometers Spectroscopic temperature determination) Optical path length in interferometer,

Naphthalene molding, 339 properties, 338, 339 Narrow band absorptivity, 387, 389 National Bureau of Standards, 33 bridge calibration, 59-61 bridge construction, 4 1 precision manometer, 44 steam point boiler, 48-50

definition, 201 Optical pyrometers, 75, 85-98, 261 accuracy, 90 brightness temperature, 87-91 calibration, 89, 90, 112 colour temperature, 88 disappearing filament, 76 emittance corrections, 75 mean effective wavelength, 88

Monochromatic extinction coefficient, 232

Monochromatic radiation density, 231, 232, 234, 235

Monochromatic radiation intensity, 230-233, 261-263

Monochromatic scattering coefficient, 232

Monte Cnrlo,technique, 331 Mueller brihge, 59-61, 129 Multiple scattdring, 464

200-217

515

photoelectric, 75, 77, 90-91 spectral bandpass, 88 spectral radiance, 87, 88, 91, 93 standard visibility function, 88 temperature determination, 87, 88 three-colour 75, 91-93 total-radiation, 75, 93, 94 two-colour, 75, 91 visibility function, 88 Optical pyrometry, (See Optical pyrometers) Optical system for Schlieren, 184-187 for shadowgraph, 191, 192 Optically thick medium, 233. 243, 247 Optically thin medium, .233-263 passim Oscillating body viscometer, 4 0 m Oxidizing atmosphere on thermocouples,

bilography, 269 If concept of local thermodynamic equilibrium, 238-243 Plasma jet, 493-494 Plasmas probes, 269-307 (See also Calorimeter probe, Cooled electrostatic probe) cyclic probe, 293-295 double-sonic orifice temperature, 271 heat transfer rate, 269, 295-297 ion densities, 281 p r e s s u r e oscillations, 295 radiation, 293 turbulent intensity, 293 Platinel thermocouple, 80, 84. 86 Platinum rodium alloy thermocouples, 81,

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82, 84, 86

Platinum resistance thermometers 79. 80. 82-85 alpha coefficient, 37, 56 Oxygen fixed point, 33, 76, 111 bird cage, 64 calibration, 59-61, 107, 112. 131-133 construction, 54 Oxygen-vapour p r e s s u r e thermometer, construction 117, 122 cryogenic temperatures, 129 high temperature, 63-65 low temperature, 39, 40 P cyrogenic atmospheres, 129-133 errors Palladium v s platinum 15%iridium, 80, at high temperature, 63-72 84, 86 conduction, 35, 40 Paraboloidal m i r r o r , 212 observations, 3 7, 40 Paraboloidal reflect romet ers , 3 78, 379 resistance, 38 Paramagnetic alums, 150-161 history of, 33 Paramagnetic salts, 150-161 high temperature stability, 63-72, 77 Participating media in thermal conductipurity, 63 vity cells, 411, 412 quenching, 69-72 (See Gas radiation) recent developments, 33 Particles in laser-Doppler system tables, 59 density, 464, 477 temperature gradients in, 35 interaction, 464 time lag. 35. 59 Platinum vs platinum - 10%r~iodiumt~ierniopolystrene, 479 couple, 63,76,80,84,86 size, 463, 477, 479 Partion function, 237, 238, 245, 247, calibration, 112 251, 252 chemical contamination, 81,. 82e Photo absorption, 239-241 preferential volatization. 81,1.tr7 . J j l , , ,:A Photo emission, 239-241 rhodium migration, 81, 82 i/i Photo recombination, 241 * Platinum vs platiiiuni 13:t rhodiuni.81, 82, Photoelectric pyrometers, 75, 77, 90-91 84, 86 Photomultiplier, 90, 364, 365, 462, 463, Platinum -5%rhodium v s plntinuni -20':( rhodium thcrmocouplc, 82. 84. 86 472, 475-479 Platinum-G? rhodium vs platiiiuni -30'( acceptance angle, 473 rhodium thcrmocouplc, 82. 84, 8G current output, 463 noise, 469 Platinum -20'A rhodiuni v s platiiiuni -4o'k rhodium thcrmocouplc, 82, 84. 86 sensitivity, 475 Physical optics, 179, 198-218 Poiseville flow, 398, 399 . Planck's constant, 355 Polarization, 357 Polarization inleronirter, 218 Planck radiation equation, 87, 238 Plasma Polarization of lheriiial radiation, 357-359, (see also Plasma probes, Spectroscopic 369 temperature determination)

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516

~

directional, 371 Polarization vector, 369 ideal, 365 Polystrene particles, 479 spectral, 366 Population density, 237 Potentiometer sensitivity, 129 total, 366 Radiometry, (See Radiometer) Power spectrum, 463, 477 Prandtl number Radiosity, 357 measurement of, 414, 415, 441-447 Raliegh-Jeffereys instability, 414 mixtures, 443 -447 Raliegh number, 187, 333, 351, 410, 413, molecular, 25, 332, 347, 350, 414, 41 4 critical value, 414 415, 441-447, 494 turbulent, 332, 334, 347, 350 Ranisauer cross-section, 284 Prefer enti a1 migration i n platinum Rankine viscometer, 399-401 Rapid scan spectrometers, 367 rhodium thermocouples, 8 1 Ratio of specific heats, measurement, 430 P r e s s u r e oscillation probe, 295 Primarv fixed uoint. 99 Ray outics. see Geometrical outics Principie of detailei balancing, 361, 363,Re&i*ocity, 361, 369 371 Recombination mechanisms in plasma, 287 Principle,of interferometery, 198-201 Recovery factor, 25, 414, 441-443 Probe e r r o r analysis, 13-32 Recovery temperature, 25, 414, 441-443, Probes in liifili-temperaturc, (See Plasma 501 I,robrs) Red shift, 459-460 Purity oI platinuni, 63 Reducing atmospheres effect 011 thermoPyrometric carbon arc. 89 couples, 81 Reflectance Pyronirtry, (Sec Optical pyrometer) angular -hemispherical reflectance, 364, 371-378 bidirectional reflectance, 363, 369-371, Q 383 Qiantuni states, 234. 235 directional-hemispherical reflectance, Qucnchin~of resistance thermometers, 364, 371-378 69-72 directional reflectance, 371 -378 directional reflectivity, 361 Helmholtz reciprocity principle, 363, R 364 h e m i s p h e r i c a l - ~ i ~ l areflectance, r 364 Radiant intensity, 356 hemispherical-directional reflectance, (See also Intensity) 364 Radian: flus, 357 specular reflectance, 361 Radiation Biot number. 312 Reflectance matrix, 3 63 Radiation density bidirectional reflectance matrix, 363 black body, 232 Reflectivity (See Reflectance) iiiotiocliroiiiatic, 231, 232, 234, 235 Reflectivity matrix, 359 total. 231 Reflectometers, 374-381 Radiation e r r o r analysis, 28-32, 381-383, directional, 370, 372, 374, 377 389 heater cavity, 372, 375 Radiation heat transfer Coefficient. 28-30 double cavitv. 372. 377 paraboloidal",' 378,' 379 Radiation intensity. (See Intensity) Radiation probe in plasma, 293 Refraction e r r o r s , 215, 216 Radiation shield. 15, 29 Refractory metal thermocouple, 75 Radiation thermometry, (See Optical Relative beam strength in laser -Doppler pyroniet e r ) system, 469 Radiative heat transfer Relative line emission coefficient, 252-256 analogies, 329-331 Reluctarice gauge, (See Variable reluctance e r r o r estimates, 28-30 gauge) Radiometer, 364-390 Reproducibilities of low temperature aspirated hemispherical, 367 scales, 121 band-pass, 367 Resistance thermometers, (See Carbon conduction-coupled, 368 resistance thermometer, German

517 resistance thermometer, Thermistors, Selection-of thermocouple, 79, 99 Platinum resistance thermometers) Sensitivity of calorimetric probe, 275-277 Resonance condition, laser, 474 equation for, 277 Resonator length, 474 Sensitivity of Schlieren system, 184-187 Reststrahlen crystals, 367 Sensitivity of thermocouples, 127 Reversal temperature, 260 Shadowgraph systems, 177, 190-198 Reynolds number, 284,332,398,399, 469, accuracy, 192-193 493-499 contrast, 192 Reynolds s t r e s s e s , 463 heat flux measurement, 193-198 Rhodium migration in platinum rhodium optical geometries, 191, 192 thermocouples, 81 Schmidt-Schlieren system, 193-198 Ronchi Schlieren, 190 Shape factor, 372 Rotating body viscometer, 401-403 (See also Angle factor) Rotating disk, 339-341 Sheath on cooled electrostatic probe, 283. 284 Sherwood number, 333, 351 S Shield, radiation, 15, 29 Shock-swallowing double calorimetric S-surface, 357, 368 probe, 278-279 Saha-Eggert equation, 238 Shock wave detector, 319 (See also Saha equation) Signal bandwidth, 459, 465-469 Saha equation, 238-263 passim, 273, 287 Signal broadening from Saturated electron current for electroangular spread, 465 turbulence, 476-477 static probe, 283 Saturated ion current for electrostatic velocity gradient, 469 Signal detection of laser-Doppler system, probe, 283, 287 Saturation current 475-480 for electro-chemical system, 342 Signal to noise ratio (See also Noise, PIoise equivalent ratio for electrostatic probe, 285, 287, 289 power) Scattered beam in laser-Doppler system, for Laser-Doppler system, 469-471 for cooled film anemometer, 492-493 462 angular spread in, 473 Silver fixed point, 63, 76, 81, 111 Single-colour pyrometers, (See Optical intensity of, 464 pyrometers) wavelength, 462 Scattering Slug calorimeter, (See Calorimeter) angle, 460, 464-467, 469 Smith bridge, 41 Snell's Law 181 center, 479 Solid thermal conductivity measurement, c r o s s section, 464 geometry, 464 415-421 Somnierfeld's fine structure canstant, mass coefficient, 383 241 volume, 464, 467, 472-474 Schlieren interferometer, 218 Specific heat mean, 423-424 (See also Interferometer) Schlieren systems, 177, 179-190 measurement of, 423-431 effect of angular deviation, 181, 182 Specific surface conductance, 309 effect of walls, 181 Specific surface thermal resistance, 309 optical system, 183-190 Spectral, (See also Specular) other schlieren systems, 191 Spectral bandpass of pyrometers. 88 Ronchi o r grid Schlieren, 190 Spectral emittance, 87, 88, 91-93 sensitivity, 184-187 (See also Line emission coefficient) Schmidt number tables of, 88 Spectral measurements, (See Radiometry. molecular, 333, 347, 350 Reflectometers, Spectrometers) turbulent, 333, 347, 351 Spectral radiance, 87, 88, 91-93 Schmidt-Schlieren'system, 193-198 (See also Intensity) Second Law of Thermodynamics, 101,105 Secondary reference point, 99 equation for black body, 87, 355 equation for non black body, 87 Seeding in plasmas, 260, 263

518 Spectral r a d i m t intensity, 355-358 T (See also intensity, bptctral r a d i m c e ) equation for black body, 355, 356 Tables of constantan vs copper thermocouple, Spect r a1 radiometer, 366 125 of gold-cobalt vs copper thermocouple, response function, 387 slit function, 366 125 of helium vapor pressure, 169, 175 Spectrometers for palladium vs platinum - 15Xiridium dispersion, 371 rapid-scan 367 thermocouple, 80 for olalinum resistance thermometers. Snectrosconic temnerature determination 59 concepts of gas'radiation, 230-237 of spectral emittance, 88 direct methods of, 251-256 emitted radiation, 243-251 T a r e measurement, 271-281, 499 indirect methods of, 256-263 Temper at ur e (See also Cooled film sensor, Cryogenic thermodynamic state of plasma, temperature measurement, Germanium 237-243 resistance thermometer , Optical Spectrum analysis, 475, 479 methods of temperature determination, Spectrum analyzers, 477 Optical pyrometers, Plasma probe, Specular, (See also Spectral) Specular reflection, 359, 363 Platinum resistance thermometers, Spccular reflectance, 361 Spectroscopic temperature determinaSpecular surfaces to thermal radiation, tion, Temperature scales, Thermistors, Thermocouple, Thermometers, Variable 359-363 reluctance gauge). Speed of light, local value of, 179 Sphere efficiency, 382 black, 233, 261 brightness, 87, 91, 260, 261 Split-flow probe, 277 Splitter plate, 205 colour, 88, 233 Square wave detector, 463 concept of, 101-105 Stability effective, 234 criteria for thermistors, 143-145 effective environment, 30 of platinum resistance thermometers, electron, 269 63-72, 77 excitation, 237, 260 of thermocouples, 86 gradient in thermocouples, 79, 81 Slandard lamps, 368 ion, 269 Standard visibility function, 88 ionization, 238 Star1 broadening, 252, 257-259 jump in thermal conductivity cell, 412, Steam calorimeter, 415 451-454 Steam fixed point, 48, 76, 111 kinetic gas, 260 hoilcr, 48-50 loading of cooled film sensors, 494 Slcfan-Boltzmann constant, 356 measurement in, 17-23 Stcradian 2n mirror, 378-381 imbedded thermocouple, 21-22 Stcrcoscopic Schlieren, 190 fluids, 23-30 Steric IacIor, 284 massive solid, 17-19 thin plate, 22-23 ' J l (See also Angle factor) Stoke's unsteady state, 23, 25-28 ' coefficicnls, 358 measurement in range flow, 401 below -150°C, 99-175 Strip lamp, (See Tungsten s t r i p lamps) ice point to 630°C, 33-63 Sulphur fixed point, 33, 76, 111 500°C to llOO°C, 63-73, 79-80 sulphur point boiler, 50-52 above llOO°C, 75-98, 229-267, 293 Surlace mounted thermocouple e r r o r s , measurement with 17-19 cooled film sensor, 487-504 other optical methods, 177-228 Surface radiation measurements, 368-383 magnetic, 157-161 Surface resistance, 309-315 platinum resistance thermometer, Sweep technique, 325 57-59, 63-73, 129-133 optical pyrometers, 87, 88

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519

Thermodynamic equilibrium, 229-263 Total hemispherical emissivity, 362 passim (See also Emittance) (See also Local thermodynamic equili-Total hemispherical emittance, 378, 381 brium) (See also Emittance) Thermodynamic Kelvin Temperature Total property opcrator, 362 Scale, 75, 76 Total radiation density, 231 Thermodynamic state of plasma, 237-243Total radiation intensity, 230 Thermoelectric force of therinocouplcs, Total radiation pyrometers, 75, 93, 94 77, 79, 84, 86, 124, 126 Total radiometer, 367 (See also Thermocouple) Total transfer operator, 356 Thermometers, (See Acoustical thernio- Transcient boundary layer, 205, 209 meter, Carbon resistance) Transcient heat flux, 309-328 thermometers, Cryogenic temperature (See also Unsteady-state temperature measurement, Gas thermometers, measurement) Magnetic thermometry, Oxygen r apid-response measurements, 322-325 vapor-pressure, Platinum resistance slug calorimeter, 25-28, 309-322 thermometers, Temperature thermithick-film calorimeter, 309. 319, 322325 stors. Thermocouples, Thin-film thermometers) thin-film thermometer, 309, 319-322 T h e r n ~ o m e t r i ccorrections for gas scale, Transient pressure probe, 295 Transition probabilities for 107 Thermophysical properties, measureabsorption, 234-235 ment of induced emission, 234-235 diffusion coefficient, 447-449 spontaneous emission, 234, 235, 245, Joule-Thompson coefficient. 421-422, 251-252 431 Transition region on cooled electrostatic Prandtl number, 414-415, 441-447 probe, 283, 284 specific heat, 423-431 Transmittance, 364, 367, 369 thermal conductivity, 406-423, bidirectional transmittance, 369-371 449-454 hemispherical transmittance, 381 thermal diffusion factor, 447-449 Transpiration-cooled probe, 281 thermal diffusivity, 419 Transport properties, (See Ther mophysical ratio of specific heats, 430 properties) viscosity, 398-406 Triple point cell, 34, 35 Thermoscopes, 101 construction, 43 Thick-film calorimeter, 309, 319, Triple point of water, 43, 105, 106, 111 322-325 Tubes, convection from Thin-film thermometer, 309, 319-322 composite, 334-337 calibration, 321 single, 187-188, 197, 198, 205, 208, characteristic time, 319 334, 338, 342 thermal diffusion depth, 319 Tungsten s t r i p lamps, 89 Thin plate temperature measurement, Tungsten vs rheium thermocouple, 82, 83, 22-23 86 Thompson heat, 421-422 Tungs ten vs tungsten -26% rheium thermocoefficient of, 421, 431 couple, 82, 83, 86 Thoria, 85 Turbulence intensity, 463, 477, 479 Three-colour pyrometer, 75, 91-93 in plasma, 293 Time constant Turbulence measurement, 269, 293, 341 f o r radiometer, 367-368 Turbulent for resistance thermometers, 35, 59 mass transfer, 334- 351 for slug calorimeter, 312, 313 Prandtl number, 332, 334 for thermocouple, 26 Schmidt number, 333 Total absorptivity, 362 Turbulent broadening, 476-477 (See also Absorptance) Turbulent diffusivity, 332 Total emissivity, 362 heat, 332 (See also Emittance) mass, 332 Total hemispherical absorptivity, 362 momentum, 332 (See also Absorptance)

5% 0

negative absolute, 107-108 Thermal resistance, 309-315 recovery, 25, 414, 441-443, 501 T.hermistor, 320,335-350, 365-367 scales (See Temperature scales) stability criteria, 143-145 scales below 90"K, 115-121, 167 aging, 141- 150 Temperature scales, 105-121 Thermocouple Absolute Thermodynamic Tempera(See also Thermocouple materials) ture scale, 105-106, 114 annealing, 79, 81 calibration of, 127-129 Absolute (Gas) Temperature scale, 106-109 cryogenic, 121-129 differential, 443 below 90"K, 102, 104, 105, 115-121, 167 e:iviroiimental effect on, 79-83, 123 heliuni, 117-120 fundameiital laws of, 77 Iiiternatioiial Temperature scales, imbedded e r r o r s , 20-23 100, 109-121, 167? 37, 56-59,63-72, inhomogeneity effects, 124-127 75-77, 80, 85, 86, 89 insulation, 79, 81-85 national scales, 102, 117-120 lead wire e r r o r s , 16-17 reproducibility, 121 in oxidizing atmosphere, 79, 80, 82-85, Tlicriiial boundary layer, 193, 199, 205. 123 209 platinum rhodium alloy, 81, 82 Tlierliial Cotii1)arator, 422-423 selection, 79, 99 Tlicrnial conductivity cell, 406-412, 449- sensitivity of, 127 454 stability, 86 errors in, 407-412, 454 surface mounted e r r o r s , 17-19 tempcrnture jump in, 412, 451-454 temperature gradients in, 79, 81 Thermal conductivity measurement, types 406-423, 449-454 base metal (less than 1200"C), 75, error analysis of, 407-412, 417 79-80 of fluids, steady-state, 406-412, noble metal (less than 18OO0C), 75, 449-454 80-82 of fluids, unsteady-state, 412-415 refractory metal (above 18OO0C), 75, of loiv conducting solids, steady-state, 82-85 415-417 Thermocouple materials of loiv conducting solids, unsteady Chrome1 P vs Alumel, 79, 80, 84, 86, state, 417-421 123-126 of metallic solids, 421-423 constantan v s copper, 123-127 in tliernial conductivity cell, 406-412, Geniinol P vs Geminol N, 79 449-454 gold-cobalt vs copper, 121-129 Thermal detectors of radiation, 364, 365, iridium vs iridium - 40%rhodium, 366 83-86 Theriiial diffusion dcpth of thin-film, 319, iron vs constantan, 123-126 323 Kanthal + vs Kanthal -, 79 Thermal diffusion effect, 447-449 ni anganin - const ant an, 443 Thermal diffusion factor, 447-449 palladium vs platinum - 15%iridium, Thermal diffusivity measurement, 419 80. 84, 86 Thermal radiation, 353-396 platinel, 80, 84, 86 (See also Gas radiation) platinum vs platinum - lo$ rhodium, 63, black body radiation, 355-356 76, 80, 84, 86, 112 'coherence and polarization, 357-359 platinum vs platinum -13%rhodium, 81, diffuse surfaces, 363-364 82, 84, 86 e r r o r analysis, 381-383 platinum -5SLr1iodium vs platinum -20% L-surface, 357 rhodium, 82, 84, 86 M-surface, 357, 367 platinum - 6%rhodium vs platinum -30% S-surface, 357, 367 rhodium, 82, 84, 86 specular surfaces, 359 -363 platinum -2O%rhodium vs platinum -40% surface radiation measurements, rhodium, 82, 84, 86 367-383 tungsten vs rheium, 82, 83, 86 radiant intensity, 356-357 tungsten vs tungsten -26%rhenium, 82, radiometry, 364-368 83, 86

Turbulence scale, 463, 477 in plasma Two-color pyrometers, 75, 91 Two-pL steradian m i r r o r reflectometer, 378, 379 Twyman-Green inferometer, 218 (see also Inferometer) Unpolarized thermal radiation, 358 Uiisteady state temperature measurement, 23, 25-28 (See also Transcient heat flux)

52 1

V Vacuum atmospheres effect on thermocouples, 81, 83 Variable reluctance gauge, 320 Velocity measurement (See also Laser-Doppler system, Plasma probes, Cooled film anemometer) by cooled film sensor, 487-504 by Doppler shift, 461-464, 477 limitations of laser-Doppler, 474, 475 in plasma, 269-293 Velocity, propagation, 230 Visibility function, 88 Viscosity measurement, 398-406 capillary viscometer, 398, 399 falling body, 401 oscillating body, 403-406 Rankine viscometer, 399-401 rotating body, 401-403 Volume absorption coefficient, 231 W

Wafer probe, 295-297 Wave analyzer, 477 Wave front, 179, 203 Wave optics, (See Physical optics) Wavelength of laser, 174, 461 mean effective of optical pyrometer, 88 mercury line, 179 of scattered radiation in laser-Doppler system, 462 Wedge fringes, 203-206 Wein radiation equation, 88 Work function of photomultiplier, 364, 365 Z

Zero-order fringe, 203, 212 Zeroth Law of Thermodynamics, 101