c F"~RCED COHY'IVE HEAT PRM.ASFER1COOLED C LINDERS AT LOW REYNOLDS NUMBERS

A11 WITH LARG'E TEMPERATURE DIFFERENCES

A.M. Ahmned

fo pu/ i cjx'*(: "'o R ib 1

DFENCE RESEARCU BOARD CONSEIL DE RECtIERCHES POUR LA VFENSF

CARDE TECHNICAL REPORT 588/68 UNCLASSIFIEDPROJECT: D46-95-51-10

FORCED CONVECTIVE HEAT TRANSFER TO COOLED CYLINDERS ATLOW REYNOLDS NUMB ERS AND WITH LARGE TEMPERATURE DIFFERENCES

by

A.M. Ahmed*

*Hypersonic Propulsion Laboratory, McGill University, Montreal

Distribution of this document is unlimited

This research was sponsored jointly by

The Canadian Armament Research and The Advanced Research ProjectsDevelopment Establishment Agency. ARPA Order 133.

P.O. Box 1427, Qu6bec, Que., Canada Monitored by the US Army MissileUnder Projects: D46-95-51-10 Conmmand,

D46-99-10-35 Redstone Arsenal, Alabama 35809Contract DA-01-021-AMC-14468(Z)

CANADIAN ARMAMENT RESEARCH AND DEVELOPMENT ESTABLISHMENT

Qu6bec, Que. Sertenbotr, 1968

I

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ABSTRACT

-For the purpose of determining a general correlation for forcedconvective heat transfer coefficients for circular cylinders in cross-flowunder conditions pertaining to cooled-film application for measurementsin flames and hypersonic wakes, heat transfer measurements were obtainedunder simulated conditions created in a plasma-jet. Measurements weremade by means of constant temperature, internally cooled, cylindricalfilm sensors in the Reynolds number range 5-75 for various temperatureloadings, the maximum being T.0 /Ts = 4, and for flows composed of He,N2 and C02 . The plasma-jet conditions were maintained sach that at thepoints of measurements, i.e. at the potential core of the jet, ionizationwas negligible, recombination was complete and the turbulence intensitywas low. By a statistical analysis, the data cbtairied for Rem 5 to 40were correlated by

.•15 •45Num(-) - .2068 - .4966 (Ren)

All the fluid property values in the dimensionless parameters were evaluatedat the arithmetic mean temperature. A kinematic viscosity ratio insteadof tho more usual temperature ratio was considered in the temperatureloading factor to account for the different dependency of the transportproperties on temperature for different gas species.

Though no previous correlations -.are obtained for conditions con-sidered here, the direction of the temperature loading effect and thedeparture from ?dg's law appear to be consistent with some of the existingcorrelations.

-

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li

TABLE OF CONTENTS

ABSTRACT ............................................................. 1

NO.. ..MC..ATUR......... ........ .... ................. iii

1.0 Introduction ................................................... 1

2.0 Review of Previous Investigations ............ ......... 4

3.0 Description of Equipment, Experimental Set-Up andMeasurement Procedure .......................................... 8

4.0 Data Analysis Procedure, Results and Discussion ............ 14

5.0 Conclusions ....................... .......................... 18

ACKNOLEDGE24ENS ........................... ..... ....... 19

REFE ENCES ............... ....................... 20

APPENDIX A ...................... ... o .... 21

RrEFEPM. CES FOR APPENDIX A ..................... .... . .... 24

• i~e9 oeet • 8 ee eeo oo ooeo ooe oes eoe e~o

-a

h

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NC',ENCLATURE

Roman Symbols

A Constant

a Surface area of the cylinder (sensor)

B Constant

C Constant

Cp Specific heat

d Diameter, sensor

G Mass velocity

h Heat transfer coeff'icient

K Thermal conductivity

M 11m, m Consta.ntsrD, n%z

Nu Nusselt number hdK

Pr Prandti. n'mber Cp04

Q Heat transferred K

R ResiZstance, electrical

Re Reynolds number V , VdV

T Tempsrature

v Fluctuating component of velocity parallel to

mean flow velocity

V Mean flow velocity no.mal to cylinder (sensor)

Greek Symbols

"0 Temperature coefficient of resistance

Absolute viscosity

Kinematic viscosity

Mass Dernsity

@_•

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NOMENCLATURE (Cont'd)

Subscripts

mn Arithmetic mean and when referring to dimensionlessgroups signifies that the fluid property values areevaluated at the arithmetic mean temperature, i.e.at Ts+To

2

s Surface, sensor

o Free stream

I

I?

iii

C-i

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1.0 INTRODUCTION

1.1 Direct measurements of dyziamic characteristics in high temperature

fields as exist in laminar and turbulent flames, hypersonic wakes, rocketnozzle flows demand a rapid response instrument able to withstand hightemperature environments. An extension of constant-temperature hot-wireanemometry to constant-temperature, internally cooled, thin-film anemom-etry towards this end is considered. (Compared to hot-wire seneors,cooling of the cylindrical film sensor not only presents melting of thesensing element but also allows interpretable measurements to be obtainedwhen the environment is at a higher temperature than the sensing film,

without sacrificing response). The principle of operation of the cooled-film sensor as compared to that of the hot-wire or hot-film sensors isshown in Fig. 1.

For cooled-film operation when the environment temperatureis greater than the sensor temperature, a heat balance applied tc thesensing film gives (See Fig. 1):

Q-.LIN QCOOLANT - SUPLIED .(i

In the above relation , Q.. is the heat equivalent of

the electrical power supplied by an iAPIkE-etwork to maintain theconstant film temperature Ts. QEWI is the heat absorbed by the film

from the environment and O01MINT is the heat removed by the coolant.From equation 1, the parameter of interest QEMV is obtained by measuring

QCOOLtan and QSUPPLIED, As long as the coolant flow r-ate and inlettemperature remain constanti heat absorbed by the coolant (QCOOLANT) fromt?.e constant-temperature film will remain constant and is independent ofthe environmental conditions. The actual value of this QCOOLANT isobtained from a measure of the QSUPPLIED in an environment where QFNV 0.QSUPI ED, at any timeis obtained by measuring the current in thenetwicr required to maintain Ts constant. In effect then, under operatingcondition s

QENV QSUPPLIED (when 0v-)O) - QSUPPLIED (IB)

The QaV measured in this way then may be interpreted in terms of theparameters if interest of the flow field by means of an accurate heat

transfer relation. The purpose of the present experimental investigationwas to obtain this heat trnsfer relation under conditions of such variablesranges that are likely to be encountered in tne applization of cooled.'filmsensors to laminar and turbulent flames and hypersoric wakes.

1.2 Since QaV is predominantly due to forced convection, thenthe forced-convectiv-e heat transfer relation for single cylinders in in-compressible cross-flow is required. Further, th- relation must be validfor the following cases:

a) W'hen t.,:e transfer of heat is from the environment to the~cY]inde':,

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b) When the temperature difference between the cylinder andthe environment is large) and

c) When the environment is composed of flows of differentgases and gas mixtures.

1.3 For forced-convective heat transfer between single cylindersand incompressible cross-flows under near-isothermal conditions (or onthe basis of the assumption that the fluid properties are independent oftemperature), a dimensional analysis of the pertinent parameters givesthe following relation-

(hd) - f(Vd , ) (2)k- k

However, for large temperature differences existing betweenthe heat transfer surface and the bulk of the fluid, when a considerablegradient of fluid properties exists in the thermal boundary layer, theabove dimensionless groups cannot be uniquely defined. For the purposeof correlation, this so-called temperature loading effect must then betaken into account by evaluating the fluid properties at suitable meantemperatures - arithmetic mean, weighted arithmetic mean, logarithmicmean, geometric mean, or even the individual fluid properties at differenttemperatures. Since the temperature loading effect is empirical, thechoice depends solely on the success axnd convenience in the evaluationand application of the correlation.

However, it is to be realized that for non-isothermal cases,a consideration of the dimensionless groups evolved for near-isothermalcases alone does not suffice for the condition of dynamic similarity.The condition of dynamic similarity is that the same ratios must existbetween the significant fluid properties at geometrically equivalentpoints. Sin,!e the gradient of properties, being dependent on thetemperature ratio, will va7 with a variation of temperature loadirg, adynamic similarity deficiency may be expected between cases of differenttemperature loadings. For complete dynamic similarity then, a temperatureratio must be included in the dimensionless relation, so that

hd = f(Vd , , (temperature ratio). (3)k V K

If it is quite possible that the nature of the similarity deficiencywith temperature loading will be different depending on the direction ofheat flow, then two relations of the above form are necessary to describethe two processes - heating and cooling. In these relations the fluidproperties may now be evaluated at ary of the temperatures Tt, Ts aor a suitable mean temperature, and the temperature ratio may be obtainedby any combination of any two of the temperatures. In line with someof the more successful previous investigations we may choose thearithmetic mean temperature for the evaluation of all the fluid properties(1, 2, 3, 4) and a ratio of T . and Tm for the temperature ratio (1),so that:

hd -f~vd. mJ _

where the subscript m refers to the azrithetic ne-an te Merature.

Hfowever, a correlation of the atove znesnimn!less gr-upsstill fails to give a unique expression for the heat transfer pr-cess.as is apparent by a consideration of the following points!

a) Considering the fact that for a .articular fluid theproperties of the fluid do not vary with temperature in the sa way atdifferent teziperature, Leve.Ls, it =ay be expected that the fashion thegro4p TOO /Tm enters in the heat trnsfer expression, i.e. the temeratureloading factor, will be different at different te=perature levels. Bythe same token it will also be dependent on the range cf tepe;raturesconsidered. Thus, a correlation may not hold for cases diffe.ri Zramthe case for which the correlation was obt ned with resect to thetemperature loading factor, and an evaluation of the correlation at theparticular te-perature level and range of interes. bec ses necessary.

b) Apart fro= a particular fluid at different te :eturelevels we may also copnsid#r a gz p cf fluIt at similar tererturelevels. if the variatiorn of the transort propertles with te=peratureof the fluids considered are not identical, then it becmes n-cessaryto evaluate the tempersture loading factor individually for each fluid.Since inclusion of the group Tac- /T. in Lhe heat transfer expressiceis to account for the shift in sivilarity #f the fluid proper-ty gradien'ts,the 'property ratios' may have to be considered directly in the c-ex-relation.,in place of the temperature ratio, to give a urique relation valid o.-era group of fluids. Since for a particular gas the significant transportproperties vary nearly identically with temperature, variations in al!the properties may be lumped together by cons-dering a ratio of valuesof any one of them. Considerir kinematic viscosity as the propert-y,we obtain the more general expr-ssions

hd f f(Vd fkm .-

. n light of the above discussion azd the conditionsstipulated in Section 1.2, ve may now fo.-malize the purposes behindthe present investigation as follows.

a) To ivestigate the nature of the temperature loadi;gfactor for heating of cylinders in cross-flow for high temoer-aturoe iOA43g-

b) To investigate, in terms of improved uniqueness of t6.hecorrelation, whether it is werthwhile to replace the ratio T.0 /T by;)c/) /Vm, whe-n different =ases aad gas mixtures are cor.sidered atightemperature lo~&tiLgs.

V c) To investigate whether the slight variaticn an ?randtlnumb-r, (due to temperature loading and due to the flow beirg ofdifferent gases and gas mix.tures), is sigrni-icamt enough to be

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considered in the heat transfer relation.

d) To obtain a general correlation for forced convectiveheat transfer for the conditions stipulated in Section 1.2.

1.5 The ranges of variables considered in the preaentinvestigation were as follows:

a) Reynolds number: The Rem (based on cylinder diameter)range considered was 5-75. However, only data from the range Rem 5 to 40were correlated.

b) Temperature loading: The maximum environment temperature(Te) considered was around 15000K, a limitation imposed by uncertaintiesin the evaluation of the fluid propertivs above that temperature. Thecylinder temperature (T.) range considered was 3500K to 5500K. Thus, thetemperature loading range achieved was To = 2 to 4

Ts

c) Flow composition: The flows were composed of N2 and Heand mixtures of N2-He, N2-CO2 and He-CO2 . For each mixture at least twomixture ratios were considered. However, only data from He and N2 flowswere considered for the statistical analysis, while the rest of the datawere checked against the result of this analysis. The Prandtl numberrange amongst data for the statistical analysis was Pr - 0.72 - 0.75.

2.0 REVIEW OF PREVIOUS INVESTIGATIONS

2.1 Considerable data are available for forced convective heattransfer from heated cylinders in air cross-flow (1,2,3,5,6,7,8,9,10).On the other hand, data are scarce for the case of heat transfer to cooledcylinders (11, 12, 13). McAdams (14) has collected and correlated resultsfrom some of these sources. However, due to misinterpretation of themore important original data, McAdamst correlation must be consideredsomewhat approximate (for elaboration on this point see Ref. 4). Douglasand Chu-chill (4) recorrelating some of the data considered by McAdamsalong with some more recent results, indicated that a unique correlationis possible for cases of heating and cooling over a wide range of temp-erature loadingsby evaluating all the fluid properties in the correlationat the arithmetic mean temperature. However, considering the remainingdiscrepancy in results between different investigations under dissimilarand even similar cases it is to be concluded that such a general cor-relation is at best an engineering approximation and may not be suitablefor accurate instrument work.

Among the data considered by Douglas and Churchill (4) onlythose of Hilpert (2) and King (6) fall in the low Reynolds number rangeof our interest, i.e. Rem -. 100. However, their data are for heattransfer from heated cylinders. On the other hand, all data for heatiligof cylinders, i.e. data of Reiher (12), Vornhem (13), and Churchilland Briar (11), are for Reynolds numbers above 300. Still, the data of

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Churchill and Briar are of special interest aince they are the onlyones obtained for any real high temperature difference existing betweenthe cylinder (100 0 F) and the gas stream (580-1800 0 F).

2.2 Consideration of temperature loading effect

Among the investigations reported by Douglas and Churchill (4),only those by Hilpert (2) for convection from cylinders and those byChurc':ill and Briar (11) for convection to cylinders consider explicitlythe temperature loading effect. However, in the former investigations theeffect was obtained over a narrow range of Reynolds numbers. A considerationof thisalong with the fact that Hilpert's power law correlation is anapproximate representation of the data, led Collis and Williams (1) toobtain a more accurate correlation for hot-wire applications. Further,Collis and Williams obtained their correlation under conditions of lowturbulence intensity in the free-stream; the significance of the effectof free-stream turbulence on heat transfer had not been realized in previousinvestigations. The data due to their carefully conducted experiment werecorrelated in the following form:

NUm TrI-O'i7 = A+ B. Remn (6)

The values of the constants in the different Rem ranges are shown inTable I.

Rem A B n

0.02-44 0.24 0.56 0.45

44-1 0 TABLE

This may be compared to Hilpert's correlation:

Num C iRe. ITS 02 (7)

Table Iicontains the values of the constants in the different Rem ranges.

Rem c m ]1-,4 0.891 0.330

4-40 0.821 0.385 I TABLE II

40-4000 0.615 0.466

The important point to note is that both investigations showed thatfor forced convective heat transfer from heated cylinders, an increase intemperature difference is associated with an increase in hd . For heat

km

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transfer in the opposite direction , i.e. heat transfer to cooled-cylinders, the opposite effect is to ue expected, i.e. hd/km will decreasewith an increase in temperature difference. This seems reasonable sincean increase in temperature difference has opposite effects on the velocityand the temperature gradients as the heat transfer direction is reversed.Consider the case of heat transfer from cylinders, i.e. T5 > TOIn this case viscosity of the fluid near the wall is greater than theviscosity in the free-stream, causing deceleration of the flow near the

wall which results in a steeper velocity profile in the aerodynamidcboundary layer as compared to the isothermal case. As the temperaturedifference is increased, the viscosity difference is increased, the de-celeration of the flow near the wall is greater and the boundary layerprofile is steeper. Since variation of thermal conductivity with temperatureis similar to that of viscosity, a similar effect occurs for the temperatureprofile. On the other hand, when TO > Ts, the viscosity near the wall isless than in the free-stream - consequently the flow near the wall acceler-ates with a flatter velocity profile. As the temperature difference isincreased the flatness of ths velocity and temperature profiles will in-crease. From this reasoring, though no conclusion can be reached as t-:whether hd/k, will either increase or decrease with an increase of temp-erature difference for a particular direction of he-tt flow, it appears

clear however, that the effect of a variation of the temperature differ-ence will be opposite if the direction of heat flow is reversed.

iowever, Churchill and Briar's (11) results from their

experiment with cooled cylinders at 1000 in heated nitrogen flow, wherethe Nitrogen temperature was varied systematically from 5800F to 18000F,show the effect on hd/km with temperature loading to be in the samedirection as obtained by Hilpert (2) and Collis and Williams (1) in theirexperiments with heated cylinders and wires in ambient air flow. Churchilland Briarts correlation is in the following form:

Num = 0.60 Prm0 33 Rem0 5 Tol 2 (8)

for a dG range of 300 to 2300.

It is this anomaly in the direction of the temperature loading effect

obtained by Churchill and Briar that focussed attention in the presentinvestigation to be placed on the determination of the correct temperatureloading factor.

2.3 Consideration of the Reynolds Number Dependencyof the Heat Transfer

Earlier investigators, notably King (6), for theoreticalreasons presupposed in their correlation the linear dependency ofNusselt number on (Rem )0-50. Kramer (5), analysing results from laterexperiments, obtained the same form of correlation as King but withmodified constants:

Nu = 0.2 .0.57 Pr 0 "33 Re0.5 (9)

tIRI CL tS ' I ED7

The exact ranfe of Re and the reference temnperature for procerty valueevaluation were not specified. On t;,e other hand, althouth tiilpertl3 (2)Dower law correlation (Fouation 7) is somewhat approximlate and itnoresthe finite heat transfer at zero Pe,,,, it never~helc~s ind-Icates tiat thedependency of Nu., on Rl,~ is itself a fitnction of Rer.. H e noted diSconti-nuities in thce slone of it.h, hr-at transfer curve at Rev, = h and Re-. = .

Later, :.-ore careful experiments with hot-wires (15) tendeato show a systempatic deviation of observed Nurn from the Num, obtained fromKing's equation with increasing Rem.

Collis and Williams (1), provoked by this deviation from Kingtslaw and also by the suspected discontinuity at Rem = 40 conducted theirexperiment very carefully and obtained a lie,~ dependency of Num different fromthat of King's law and also found a disccntinuity at Re,, - 44. This dis-continuity was confinmed by an aerodynamic investigation of the flow-fieldaround the -wire by observing the onset of eddy sheddirng a4, Hem, - "- '(I).

Now, considering Churchill and Briar's (1i.) analysis of theirdata it i~s to be noted that they presupposed the linear relation of Nui, toRe 0_50 . Further, the correlation was obtained by assuming no heattransfer at zero Re,., i.e. they presupposed the form of correlatIon -as:

=t. A 0.33 Re0,5 1 n (10)m T

and obtained the values of the constants A and n. Apart from theassuptio as o th Re dependency of Nurn, this form of correlation may

be Justifiable at h-igher 'Re,, where the heat transfer at zero Re,, is asmall percentage of the total heat transier, but an extrapolaLion of theCorrelation to low e a o eacrt nugh. it must be noted thattheir correlation was obtained for dG/1u4-m beyond 300.

Thus in-he presen investigation at low Pea., the determinationof the exact Re dt-endency of Nurn is considered as part of the analysis.

2.1; Cons ide rat ion of ?randtl Numrber E"ffect

Kramer's (5) analysis explicitly considers the effect ofPrandtl number variaticn on heat transfer. Data were obtained for air(Pr - .71), wdater (Pr - 7.1), white oil (Or - 29.6), Transformer Oil i(Pr - 35.) and Transformer Oil II (?Pr - 525.). From this correlation(see equation 9) it appears 'hat if interest is li-mited to heat transferwith gases only, the effect of the slight differences in Pr for differentspecies will be very small and may not be detectable In an eXac rihent, dueto normal data scatter. By the same token, the effect of the smallvariation of Pr with tempera'ture for a particular sp-cie-s of ras w,.ili isobe negligible.

Investigat ions with different gases have not been carriedout, all investigators having used air with the exception of Churcill1.

£and Br-iar (11) who used Nitrogen. As suc'~ it is not possible to determinothe uniqueness of any temperature 2loading factor for different gas spec ien -

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a point to be investigated in the present analysis.

3.0 DESCRIPTION OF EQUIPM.ENT, EXPERE14ENTAL SET-UPAND MEASUREMENT PROCEDURE

3.1 Heat transfer measurements were obtained by traversinginternally cooled, electrically heated, constant temperaturf, cylindricalfilm sensors across the potential core of a plasma jet. T ,e power inputto the plasma jet and the plasma gas flow rate was maintained such thatnot only would ionization be negligible at the jet exit plane butalso recombination of the dissociated species would be complete in theplenum chamber. Binary -mixture flows were obtained by mixing the secondgas speciewith the primary ionization gas in the plenum chamber. Temper-ature and velocity measurements were carried ,out by means of a Pt - Pt10% Fuh thermocouple and a pitot probe respectively, both mounted on thesame traverse as the cooled-film sensor. All measurements as functionsof the traverse distance along the diameter of the jet were recorded onan X-Y plotter. Knowing the relative position of each instrument withrespect to the jet axis, point measurements of pitot pressure, thermo-couple output and the film sensor bridge voltage were obtained from therecorded prcfiles.

3.2 Description of SDeclal Fouipment

The sensors, probes, electrical circuitry and the sensorcooling water supply system are manufactured by the Thermo Systems Inc.,Minneapolis, Minnesota, as standard equipment. The description of theequipment that follows has been obtained from private communicttion -. thDr. L. Fingerson of the Company and from their various bulletins, techniLalnotes and instruction manuals, listed as Ref 16.

3.2.1 Cooled Film Sensor and Sensor Holder

A photograph of the sensor with explanatory sketchesis shown in Fig. 2. The loop type sensor is made of vycor tube. .015cm. 0. D. aid .010 c- I.D. A thin film of platinum, iOCO - 2C 0.thick, on one limb of the loop acts as the resistance element and isisolated by heavy gold platir4g (1 - 1 mil thick) on the rest of the loop.The length of the sensing element, in the sensors used, is .103 cm andits resistance around 3 ohms. The sensing element is coated with a film(5000 2 thick) of silicon monoxide to reduce catalytic effects when thesensor is exposed to flame environia nt.

The sensor is soldered onto the tip of the sensorholder, which serves as an electrical lead and also as the sensor coolingwater connection and contains a built-in filter on the water inlet side.The fittings for the electrical connection to the power supply systemand the fittings for the coolant line connection to the water supplysystem are mounted on a fitting plate, as shown in the photograph inFig. 3A.

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3.2.2 Probe

A photograph and a diagram of the probe with thesensor holder assembly insert5a are shown in Fig. 3B and in Fig. 4respectively. A close-up of the probe tip, showing the sensor inoperating position, is shown in Fig. 5. The probe is made up of aseries of cascading cooling jackets, the cooling jackets in turn madeup of a tightly fitting bundle of stainless steel tubes, to r-rovideuniform and near optimal cooling. The probe is provided wit,..traversing sleeve and a fitting plate containing the fittings for thejacket cooling water connections. When the sensor holder is in place,its fitt.ng plate is attached to that of the probe by means of screwsin slots, allowing for a certain amount of play, so that the holder canbe pulled back and the sensor withdrawn inside the probe when it is notin operation.

3.2.3 Sensor Cooling Water SuRPly System

The sensor water supply system supplies coolant tothe sensor at constant pressure andhenceat a constant mass flow rate.It consists of a stainless steel pressure tank of 1 litre capacity whichis filled with distilled water and pressurized through a regulator froma nitrogen bottle.

3.2.4 Probe Jacket Water Supply System

Ordinary tap water, filtered through a 25 micronfilter, is used for probe cooling. The water pressure is maintainedaround 80 p.s.i.g.

3.2.5 BriLge and Control Circuit

A simplified functional schematic diagram of thecircuit is shown in Fig. 6. The platinum film on the sensor is maintainedat constant resistance and hence at a constant temperature by placingit across one arm of a bridge. The desired resistance of the censor(calculated from the desired operating temperature and the r.old resist-ance of the sensor) is obtained by adjusting the resistance deck P1.A choice of two bridges is possible, one for low energy dissipation(.005 to approximately 0.5 watts), as encountered in usual hot-wire orhot-film operatin and the other for higher energy dissipation (up to40 watts) for cooled-film operation.

Once a voltage is applied across the bridge andthe bridge is balanced, the film will be maintained at the desiredtemperature. Any change in environmental conditions (changes in temper-ature, velocity or composition) causing a variation in the rate of heattransfer to or iram the film, will tend to vary tae film temperature andhence the film :-ccistance, causing an imbalance between the two sides ofthe bridge. This imbalance is amplified by the bridge amplifier whichsignals the Dower amplifier to increase or decrease the power to thesensor acco-ding to the direction of voltage change in the bridge. Thisfeed-back loop has a frequency response of 5,00 KHz, (honal).

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The system allows measurement of both bridge voltageand actual electrical power supplied to the film. The latter is obtainedby means of a power computer which takes values of the bridge voltage andsensor resistance aid uses a squaring circuit, aplifier and a voltagedivider. The panel meter may be switched either to read the mean bridgevoltage or the mean energy dissipation in watts, when the sensor is ex-posed to a steady state environment. A photograph of the panel along withthat of the sensor water supply system is shown in Fig. 7.

A detailed description of the circuit may be foundin Ref. 16A.

3.2.6 Cooled-Film Sensor Operating Principle

Referring to Fig. 1 we note that for usual constanttemperature, cooled-film application, i.e. To. > Ts, a heat balance of thesystem gives:

QSPPLIED = OOLANT-

If the cooling water inlet temperature and flow rate(i.e. the coolant pressure) is kept constant, %(,LANT will remain constant.A measure of QcUPpLIE1, then will be a mesure of QV, i.e., the heattransferred from the environ=ent to the sensor.

For adequate operation it is then mandatory thatCO01ANT > Q pV (yAXDM). if heat transferred to the coolant is less

than that absorbed from the environment, not only does measurement becmeimpossible but the sensor te--mperature will increase beyond the .set valueand the sensor may burn out. A proper QCO jIN mby be set by exposingthe sensor to a condition of maximum heat transfer and then by adjustingeither the coolant pressure or the sensor temperature or both to cbtaina QC LT greater thar Q r (.MAX). Since a prior determinatton of Qp, (MI i)is not always possible (viz. as in the case of application in the hyper-sonic -wakes of projectiles launched in free-flight ranges), a rough estimateof the expected maximum heat transfer ray be made, aid from the calibrationchart in Fig. 8, the sensor operating temperature, and coolant pressure maybe determined. As shown in Fig. 8, at a particular coolant pressure themaximur, sensor temperature is limited because of coolant boiling insidethe sensor resulting in unstable heat transfer to the coolant.

Tne sensor is set to operate at the desired temp-erature by setting the proper resistence in the resistance deck. Theoperating resistance is obtained by measuring the sensor ',old" resist-ance and using the relation:

R= Re 1(T -cLs c(" _ Tc)J .

Of CLASS TF ED

where Rs is the sensor resistance at the selected operating temperature,T .and Pe is the "cold" resistance at temperature T. (usually room temper-a~ure). The temperatu're coefficient of resistance, c4.is obtained bya calibration of a representative nimber of sensors or fro the manufacturer'squoted figures. A typical ca! i4ration curve for c obtained for threesensors from the batch used in the present investigation is shown inFig. 9.

The value of Q,-COLIT is measured by maintaining thesensor at the onerating te= perature and coolant pressure and exposed toroom environ-ent. Since consertatively calculated heat losses frm thesensor due tc radiation, free convection and conduction together add upto be two orders of magnitude less than the heat transferred to the coolant;all the hPat transferred urer room condition =ay be considered to betransferred to the coolant, i.e.

zSW ,L='F (at ro. t-e=.) COOU.IT

may be nasured directly in electrical unitsby using the power computer or by zeasuring the bridge voltage and usingthe following relation (refer to Fig. 6):

-2

-t S(Rs -3

where Et - bridge voltage

R_ - sensor resistance

resis-ne of the top leg of the bridge

R. = probe ard cable resistance.

For the measure of QfnC mm under operation thesame two =eth-ods may be used. fieever. s-Zince thYere ws so=e doubt asto the calibratio, of the power com puter, in the present investigaticoit was the bridge voltage that was recorded.

3.3 E erimental Set-Un

A schematic and a photograph of the experim-euta. set-up areshown Lin Figs. 10 and 11 respectively. The hot jet was obtained by meansof a bench mounted plasmd-ne ps torh fitted wth a nozzle, the

nozzle exit diameter being I in. Tne gas flow rates were metered by zeznsof calibrated flow meters and pressure gauges mounted on the controlpanel of Lhe p-ia torch. The Me. uriJn instruments, i.e. the cooledfilm sensor probe, the ther-ocoupie and the pitot were mountea on a

IJNCLASS LFIED12

traversing table. A close-up photograph of the instuzruments and the plasmmtorch is shown in Fig. 12. The traverse dist~ances of the table along andacrmss the jet were monitored by a -knife-edge slider fixed toc the tableand sliding over a calibrat'ed linearly variable potentiometer. The cross-traverse Dotentiometer ctput was connected to the tX'. in put of a Mosley-X-Y plotter, whereas the axi-al travers. potentiometer reading was displayedor. a Jobm Fluke differential vacutm tube voltmeter.

APt t 10% Rh thermocouple with a bead diameter of .127 c=was used to measure temper-ature. it was thought to be taore judicious touse an uns:ielded therMOCOUple anid to correct for radiation and conductionloss rather thamn to use a shielIded ther--ocouple with uncaetain radiationeff.ectL-. Further, the mir~imum size lrtion and the valne-rability of theshielding to high temperature .dith -.onsequent geometry change precluded thl.use of shielded ther-mocouples.

or eloc;t m-easurements a, carbon-tipped pitot orobe -with anorifrice size of . 103 c= x-as used. The pitat pressure was measured byv meansof a calibrated KKS Baraton type 77 pressure =eter using a ty-pe 7771pressure head.

The thermocouple mr output, the press-ure meter out-omut andthe brdeLlaeD h film sensor were connected +.o the I-If inma-t ofthe X-Y plottter through a control box, so that during a run as each:Instr=-ent would traverse across the jet their outputs could be successivelys-iitched onto the ?Tt input of the recoxrder for recorilng. Thie re-ordinrgstation arrangement is sahcw4n in ri-g. 13.

7ne cross traverse distance -*as recor-ded atL dour11e scale for.better positional resolution, uwhereas the out-ts of each instrum-entE were

rorded or. a scale to -ive the maximrm deflection on thme recorder. 1typical recording of a run is shown in Fig. 11-

3.4 Meas'are±.ent Procedure

3 .1 inst.raent A.llrinzent

B-efore each set of rinns (usual-1-1 consi L-xg o' 4 .o5r-ans) the sensing eie:-ents az e measur-"ig instr-,=enAts were aligned tobe in ths same horizontal and ve.-tical planes, the horizonm-tal planebent;hat, of the j:et axis ard tine vwertlical nlane that of the cross-tra~arsr-i.e. nmral to thaPt of the Jet as. - --ne cooled4-fii2-- sens-or w?-s a2ignedto be accurately normal to the Jet axis. The aligm-ent of the instr-zmentswas achieved by a macrosccpe -,epl* irz the ila=--a-jet C1, its- bracke-,sruch that the axis of tine .iet would coicide with that of the- microscopt-.as shown in Fig. 15, and bya t-hodolite tDLaced at a slipaht ang"e to t-hevertical plane of the instruments. Alignm=ent wras ensur-ed by traversingthe itrenssuccessively to the r=icroscc-oe6 ais amdv adjsting theirpositicns such that they coizmcidel -dth the cross-hairs of both the Mco

scooe~ ~ an tethodlte 4tr i went the uositEions of th.2eintu nswith respect to t4.1e jet axis and each o-ter Werle nOted by tray'ersingthem to the m&icroscoze axis and recording I.he crs-rvreOctenti0-

meter out-ma oni the X--Y ploitter.

UNCLASSIFIED13

During alignment the physical condition of thesenzing elements as to deposition of contaminannt on the cooled film,flaking of the film and thermocouple geomiet!-y alteration was checked.

3.4~.2 Plasma Jet Conitions

? owoer Setting

The plasmra jet was run at very low power inputs sothat the temperature at the nozzle exit never exceetded WW00K. This weasto ensure that no part or the gas flow was ionized. Further, the gas :lowrates were such that. the residence time in the plenu.m char~ber was sil-fficientfor the recombination of the products of disscociation. (The latter con-diti3n -aas vierified by the addition of CO zin the plenum chamber and notingthe absence of any CO fl'a--e at the JetL exit..J

jet Stabi-ity-

The stabilit;-y of the jet after a 5 ran. war=-up periodwas checked by placing t-he sooled-film sensor ir. the jet wid recordig thebridge voltage on a time scale. Sir.ce tLhe fill will sense any change inboth the velocibty and the te=oerat-ure of the Jet, this ensured a check

o~avy drift of both properties. Over a reoddpezic cf 15 mirnites(aierage time for a run) no drift was noted. However, fr;= time to tin-ethe jet would tend to beccre unstable due to electrode erosion. Radingsobtained during these periods were either disc-arded or retaken.

Jet i'urbulence

Mhe tu.-bulence level in the core of the jet wasestimated by monitoring the cooled-fi-lm brid1ge voltage by an oscilloscope.7he =aid==ooe-fl frequency response is around 50 5.C.S. Since thefilm wifl ser-se not o.-ly the vel*ezity fluctuatiew, but the temeratureaTISa concentration fluct nations as well, decoupig of the sial to cbtain-ouanta,4 ive measarement of the intensityv of'L each parazieter beccomes cam-DUJ cated. F. --- the osciilloscope tracin, a tracing of the 3UPe.-=moosedeffects of the fIh.ation of all the three oara=etezz in the core of thej4,et, the max!:_-- relative intensity was fo~un.d to Ie less than 1'D9 0a)Tf it is considered ta-the film- is sensing cnly' velocity A

fluc-tuations5,, the =ost acute sittnation, 2-then the error in heat transfer=-easurement will be less than ZX. (See Ref. 1? for wi claboration, =ntheeft of Jax-ge turbulence flact aicns on -heat transfer.) h

eroreu to temperature fluctuation will arise bemcause of con~siderationof the fluid properties evaluated at the average temperature rather thana consideration of the average of: the Mdid prc-perties -the diffiezrebetwfean th.m being due to t~ennlna aito ffluid propertieswit-h temperatu-e Similarl the error becaus of cocenzt-atio lctuaLioM AMl be due to the 'di- ference etm- the evaluated D'roierties

at he eanconcentration, rather thn h -vrg of the prc-toerties - ad~feeiebeeauseofn..1ea -ritn of flui-3 d properte. Wt

percentage concentr-ation. 1novever, these effects wAc-i small cpav__ !-cse diueto l~arge velocity fluctuatins i.e. due totelateral tr

boen-ce-velocity e xmon-nt perpe~dicular to t-!h.e cylin-der.

214

3.4.3 Run Conditions

During stable operation of the jet, the pitot, thethermocouple and the cooled-filn sensor were traversed across the jet, thelast traversing thrice for three different sensor reei slEarces and hencethree different temperature settings. Due to the variation of the sensor"cold" resistance from one sensor to another and somet:.mes from one nrn toanother it was not always possible to set the same three sensor temperatLuresfor all runs. The distances of the section of traverse from the -Jet exitwere such that the major portion of' the traverse would be through thepotential core of the jet. A typical recording of a single run is shown inFig. 14. To obtain measurements over a range of Rem and temperature loadingthe flow rmte of the cas and the p'lasma power input were variJed. For each gassnecies or species mixture, usually three power settings and for eachpower setting three flow rates -were employe4. With 3L particular powersetting and flow rate usually three or four traverses at different distances

fromthejetexit plane were made. For zixture runs, three difern--xue -N H, 1-0 2 , He -CO2 were considered. 51iring these runs,

usually the major species interms of mol fraction wazs used as the arc-gas,the second speciesbeing mixed with this in the plenuzm chamber. Hovever,C2was never used as the are-gas. For each. mixture , two mixture ratios

,were considered. Due to t~he volime-fliow rate im-itation of the plasma--jet,judicious set tings for the mixtutre ratio were not always possible.

4.0 DATA IMIALYSIS PROCEDURES, RESULTS A01D DISCUSSION

I. he values of t-hermocouple ezaf, pitot pressure and the cooled-film bridge voltage at any particular point in the traverse -were obtainedby taking values equidistant from the jet axis from their respective proflies,the posiltion of the jet-axis with respect', to each traverse having been pre-recorded as mentioned in Section 3.4.1. Such point values were ocbtainedfroM only the potential core of the jet.

L..2 The amcorm! ted temperatdre was obtained from th;.e mi'llivoltreading ofl the thtrmocouple using the callibration tables of Omega Erg. inc.This temperature iras cori-ected for the error due ;to, radiatfon from a heat-balance of the thenmoournle bead. "See any standard; text for elaboration).tr=- an independent approxiinate calculation the conduction error was foundto be negligible. For the heat balance, the theim-c-ouple bead was consideredto be a sphere and the forced convective heat transfer coefficient wasobtained from ?KI-arerts (.5) corrzelation for spteresand the erdssivity factorfor the platinum bead as a function oil tezperature was obtained from Ref. IS.Since- evalusation of" the forcec convection coefficient de7man.ds a detemmaiiationof flow velocity and the flu tanj! propereties at the true temperatureand since tn'e velocity interpretation fram the pitot pressure is againdepiendent on the knowledge of fluid density at the true tEemperature, aniteration process was used to solve for the true termperature.

The transport property values of the vas species and specfes=ixtures for the above-rmentioned luemmerature correction process and forth-e subsequent data analysis were calcilated from the expressions collectedin Ref. 17. Details of" the expressions used may ;-,e f-ound in Appendix A

U.NCLASSUED

15

rO r the coo:ed-film bridge voltage outside the jet and ".the bridge voltage when t- iJm was at the point of measure.ent in thejet, the heat transferred from the envirorzent was obtained according tothe method discussed in section 3.2.p. The heat transfer coefficient wasthen detersined frc-

h=

4.3 As a pre-liminary step to data correlation the dimensiorless

heat transfer coefficient hd/k was plotted as ; t-. nction of e. to determirethe general trends and the data scatter. The follow ing points were noted.(Fig. 26 =ay be consulted for this discussion.)

(i) Because of the narrw range of volze-flou rates possiblein the plasa-jet, the Re range obtained for a partic.uar species or speciesnixture by a variation of the plabxa-gas flow rate was rather 1Lted.Eoweveer, because of the widely differing ineatic viscosities of the speciesand species -!ixt;res considered the overall R. r-nge obtained extendedfrom 5 to 75-

(ii) 14, data for Rem =ore than 55 were above the trend lineof the rest of the points (i.e. those below ?e.- - 40)when extrapolated tothat range. No data were obtained for ?.e between 40 and 55. From prei ousinvestigations (1, 2) with heated cylinders a change in slope in the heattransfer curve was noted around Be = O - 40 due to the onset of eddyshed.-. Vowever there is no reason to expect the onset of eddy sheddingat exactly the same Re. for the case of cooling of cylinders since theboundary layer characteristics in the two cases are different, atdiscussed in section 2.1. No aerodynamic investigation specifical1- aimedat the determination of the onset of eddy shedding was carried out in thepresent investigation and, hence, any conclusion as to the exmct Pe, ofdiscontinuity in the h-at transfer cur-e and as tc. the reason for thehigher Nua for Re- greater than 55 will. be deferred until further ex-perimentation. For the present analysis the range of Fe considered was5 to C.

(iii) The scatter of data i r=m the gas mixture wasnoted to be slightly more than that f:.m the p-e_ gas runs. Possibithis is due to impe-rfect midng of the gases in the plenumm c-ha=ber ofthe jet. For this reason and also because of less certainty in theproperty value evaluation of ix1tures at high te.peratures, the s-bsequentstatistical analysis was confined to data fro= .7ire He and is flows only

(iv) :Die to the narrow ran e ref R. obta--ned for a particulargas specie.F or species mixtixre and due to the d-i- sca~tter, the expectedslight influence of the very szmll variation of Prandtl number on he&ttransfer could not be properly detected. in any case, since thestatistical analysis was to be confined L-o data -fr= Fe and H2 1i!o4, thePrandtl .numbers being very. nearly identical for the two gases, con-sideration of .-. andti nu-ber as a variable was zot considered inportzrnt.

6NCLASSIFIED16

4.4 In the light of the above discussion, it was decided tocorrelate the data from pure Ile and N2 flows, between Rem - 5 and Rem = 40,by a relation of the following form:

Num (To) nl 14 B 1 Rem 1Nu (. A1 +B- Re

Tm m

the values or the constants n!, A1 , B1 and mI to be determined by a leastsquare fit. The values of the constants were evaluated separately forN2 P-Ld He flows to determLne whether the temperature loading effect wasdifferent for th, two cases. Further, the values were evaluated individuallyfor the two cases of temperture loading, onie when the loading was appliedby a variatioa of Ts while To was constant and again when TOD was variedwhile T. was kept constant. This was done to determine whether a weightedman temperature rather than the arithmetic mean temperature was moresuitable for the evaluation of fluid property. however, since for theindividual cases the Rem ranges were limited, the value of the constant mlwaQ evalnated b,- considering all data together, and using this value of m1

the values of r, , A1, B1 were calculated for each case. The result ofthis analysis is shown in the table of Fig. 16. The n1 values were foundto be somewhat dIfferent for the two cases, though for a particular gasthe values were close for the two types ef temperature loading.

4.5 The next step was '.o replice the temperature ratio by akinematic viscosity ratio in the analysis, so that the correlation formnow became:

Num( - j A - B. Rem

The values of the constants evaluated fo." each case and when all He andN2 data were considered together are shown in the table of Fig. 17 Com-pared to nI valuestthe values of n were found to be close for the differentcases. It remained now to consider whether a unique relatio wa possible.The fits of the data from each case were checked with the overall relationwhose constants were evaluated by considering all He and N2 data togethe"and as shown in the table of Fig. 17. The worst increase in r.m.s. errorwas less than 2.5%.

The results of this analysisare shown graphically in Figs.18 to 26. Figs 18A and 19A are Hum vs. Rem plots (' the data from N2 andHe flows respectively for the temperature loading obtained by c variationof T., while Ts was kept constant.

In Figs. 18B an, 19B are shown the same data but with thetemperature loading factor included. Fig. 20A and 21Aand 20B and 21Bare similar plots but for data obtained when the temperature loading wasapplied by keeping T 00 constant while T. was varied.

UNCLASSIFIED27

The next step was to consider the temperature loading effecton data from the mixture flows. Considering the lower accuracy in theevaluation of mixture transport properties, it was felt that the signif-icance of the T.L.F. obtained for the mixture flows individually wouldbe ambiguous and in any case not more significant than the value alreadyobtained for He and N flows. As such the data from the mixture runswere checked for th" ilimination of the temperature loading effectby using the T.L.F. obtained for He and N2 flows. Figs. 22A, 23A and24A show Num data from He-N2 , N2-CO2 and He-C02 mixture flows respectively(two mixture ratios considered for each mixture) plotted as a function ofRem. Figs 22B, 2313 and 24B are replots of the cvrresponding data butconsidering the T.L.F. A considerable improvement in data scatter may benoted, though no claim to the complete elimination of the temperature loadingeffect can be made.

All data corrected for the temperature loading effect plottedtogether are shown in Fig. 25. it is eviden that except for C02-N2 datawhich were for Rem greater than 55, data below Rem - 40 overlap and followthe same heat transfer curve and, as such, show that along with a uniqueT.L.F. a unique correlation is also possible. Finally, the obtained Remdependancy of the Num was checked for the different species mixture flowsby plotting the data on Num(-)o/,)-.15 vs. Rem.4 5 grid, as shown in Fig.

26. The r.m.s. deviation of Num from the correlation line was found tobe .0924 when all data below Rem = 40 were considered together.

4.6 Comparing the correlation obtained in the present in-vestigition, i.e.:

Num (0.2068 + .4966 Rem045)

with previous correlations (see section 2.0), the following points maybe noted.

(i) It is found that for the case of heat transfer tocooled cylinders, as the temperature loading is increased, the hd/kM isdecreased. This is consistent with the previously observed (1, 2)increase in hd/km with increasing temperature loading for the case ofheat tfansfer from heated cylinders, as has been elaborated in section 2.2.However, from Churchill and Briar's (11) result for similar direction ofheat flowas in the present investigation the opposite effect is noted.

(ii) In the Rem range of 5 to 40, the Num was found to varylinearly with Rem -45. ThLit deviation from Kirg's law is similar to thatobserved by Collis and Williams (1) in their experiment with heated wires.However, there is no reason to expect the same law to hold for the twocases of cooling and heating sinceas previously discussed, the aero-dynamic features in the two cases are different. A valid comparisonexists only with correlations obtained for similar direction of heatflow. However, Churchill and Briar's analysis presupposed a linearNu variation with Rem-5 and as such can not be properly compared to the

m~present result.

UNCLASSIFIED18

(iii) Finally Fig. 27 compares values of Nu. calculated from

some of the correlations obtained for heat transfer from heated cylindersSwith values calculated from the present correlation, the evaluation beingfor an identi.cal condition of heating of cylinder with T. - 400OK, To =12000K -!.e flow composed of N2 . Even considering the wide discrepanciesin vau.4es -a-culated from correlations obtained for cooling of cylindersonly, the error involved in using them to predict heat transfer for heatingof cylinders is quite apparent.

5.0 CONCLUSIONS

5.1 For forced convective heat transfer to circular cylindersplaced normal to a heated flow, a correlation was obtained statisticallyfrom data measured in the Reynolds number range of 5 to 40, temperatureloading range of T o /Ts - 2 to 4 and for flows of N2 and He. Over theentire range the following correlation was determined;

.15 45Num ( ;- ) = .2068 + .4966 Rem.

where all the fluid properties in the dimensionless parameters areevaluated at the arithmetic mea temperature.

5.2 Because of increased data scatter and also because of someuncertainty in the property value evaluation of mixtures at elevated temp-eratures, data from the binary dxture flows composed of any two gasesfrom the gas species He, N2 aid CO2 were not included in the statisticalanalysis. However, these data were checked for fitness with the cor-relation. The r.m.s. deviation of Num from the correlation line was foundto be .0924 when all data below Rem - 40 were considered together.

5.3 Due to the narrow range of Rem investigated for a particularspecies -spedes mixture and, also due to the data scatter, the e.gpectedslight influence of the small variation of Prandtl number (because of theconsideration of different species and speciesmixtures and also because ofvariation of temperature) could not be discei, ed.

5.4 Replacement of the usual temperature ratio in the temperatureloading factor iy a viscosity ratio enabled a unique correlation to bederived for flows composed of gas species whose transport property valuevariations with temperature are different.

5.5 The direction of the temperature loading effect, i.e. inthe present investigation for heating of cylinders a decrease in hd/kmwith an increase in temperature loading, is consistent with previouslyobserved increase in hd/km with an increase in temperature loading forthe case of cooling of cylinders.

5.6 The Rem dependency of Num was found t3 be different fromthat according to King's lawas also o'servcd in previous investigationswith hot wires. However, due to absence of previous data for the caseof heating of cylinders, no direct comparison could be made.

UNCLASSIFIED19

5.7 A discontinuity in the heat transfer curve was noted betweenRe- 40 and Re. - 55. Unfortunately, no data were collected between thesevalues of Rei, and since no specific aerodynamic investigation was carriedout to determine a change in the flow features in this range, no firmconclusion as to the exact Rem and nature of the discontinuity can at presentbe made.

5.8 Finally, a comparison of the Num values calculated for thecase of heating of cylinders from correlations obtained specifically forcooling of cylinders w-ith Num obtained in the present experiment (forheating of cylinders) clearly shows the need for two separate correlationsfor the two directions of heat transfer. The error Involved in predictingheat transfer in one direction from a correlation obtained for heat transferin the opposite direction may not be negligible, especially when significanttemperature loading is involved.

I ACKNOWLEDGEM!FNTS

Thanks are due to the following staff members and personnel ofMcGill University: Professor S. Mblder for his overall supervision, Messrs.L. Vroomen and J. Kelly for assistance with the instruments and to Mr. J.M.Ford for reading the manuscript.

Thanks are also due to the following members of CARDE staff:Mr. G.H. Tidy, Director Aerophysics Division, for his cooperation, andMessrs. D. Ellington, F. Christie, G. Trottier, G. Gu6rin, P. Desjardinsand N. Verreault for their assistance.

UNCLASSIFIED20

RPFEPYECES

1. Collis, D.C. and Williams, M.J., Journal of Fluid Mechanics6, 357 (1959).

2. Hilpert, R., Forsch. Gebiete ingenieur', L, 215 (1933)

3. Van der HF-gge Zijnen B.U., Appl. Sci. Research A, 6, 129 (1956)

4. Douglas, W.J.M. and Churchill, S.W., Chem, Eng. Przogr. SymposiumNo. 18, 52, 23 (1956)

5. Kramer, H., Physica, 12 No. 2-3, 61 (1946)

6. King, L.V., Trans. Royal Soc. (London) A214, 373 (191)

7. Benke, R., Arch. WIrmewirtsch, _, 287 (1938)

8. Hughes, J.A., London Phil, I-lag., 31, 118 (1916)

9. Griffiths, E. and Awberry, J.H., Proc. Inst. Mech. Engrs. (London)25, 319 (1933)

10. Small, J., London Phil. Mag. 19, 251 (1935)

11. C.-rchill, S.W.. and Briar, J.C., Chem. Eng. Progr. Syrup. No. 17,51, 57 (1955)

12. keiher, H., Forsch. Gebiete ingenieurw, No. 269, 1 (1925)

13. Vornehem, L., reported by J. Ulsamer, ibid, 3, 94 (1932)

14. McAdams, W.H., "Heat Transmission", 3 ed., McGraw-Hill, New York (1954)

15. Newman, B.G., Australian Council of Aeronautics, Report ACA-53,

16. Thermo Systems Inc.. a) Instruction ManualMinneapolis, Inesota b) Tech. Bulletin Nos. 2,3,4.

c) Brochuresd) Private Communication

17. Hinze, J.0., "Turbulente", McGaw-Hill, New York (1959)

18. Caidwell, F.R., "Temperature - Its Measurement and Control inScience and industry" - Ed. Herzfeld, C.M., Vol. 3 Part 2, Page 81,Reinhold, New York (1962)

19. Brokaw, R.S., NACA T.R. R-81 (1960)

IUNCLASSIFIED

21

APPEN DIX A

Expressions for the Calculation of Transport Propertiesfor Pure Gases and Gas Mixtures

MENCLATURE UNIT

Dimensionless heat capacity

K Thermal conductivity calci. Sec -7,(

Monatomic thermal conductivity -

K" internal thermal conductivity H

k Boltzman constant erg/°K

M Molecular weight g/g - mole

R Universal gas constant cal/mole °K

T Absolute temperature K

Molz fraction

£ Madmum energy of attraction erg.

Absolute viscosity g/cm. see.

Zero energy collision diameter A

- SReduced collision integral

SUBSCRITS

i,j Components i and j of a mixture

Entire mixture

n Number of components in the -mixture

1.2 Componentsl and 2 of a mixture

The following expressions were used to calculate transportproperty Yalues for non-polar pure gases and gas -ixures.

I i) Viscosity (Refs, 1.2,3)

1.T

JA- 26. 9xl10 4 M

I _-

_

UCLSSiE D22

APPk2DDk( A (Con'd)

or ,/ = 24.693 x 10 LF- i-ii) Ther-al conductivity (RPefs 1,3)

K ,K- 4 K"

K1 = 198.91 x lr-6 __/__

6 1

W = K x .5 R

iii) Viscosity of gas mixtures (Refs 3, 4 )

"# 4 J-' 'i+ 2."

-: iv) Theral conductivity of gas mixetures (R~efs 3,4,5)-+ I

-J-

U 141

where f+ ( 4it1

URCLASSIFIED23

APP ?D( A- (Con d

- V.t

XA-

-_he es:one- heat capvc-ty i.e. Cp/R values as functions of

te-perazure were cbtained fram Ref. 6. The reduced collison integral{'or viscositv 3n: thera. ccruct;vity, va "es a- functions of reducedterata .. were obtained fro= a table of Ref. 7. Values of therest of the consta.-s were ta-kei: fri Table _ of Ref. 3.

oF

3<

24~

aREFPICES APPE10M AIA

1. Hirschfelder, J.O., Curtiss, C.F. and Bird, R.B., "MolecularTheory of Gases and Liquids", John Wiley (1954)

2. Bromley, L.A. and Wilike, C.R. "Yiscosity Behaviour of Gases"Ind and Eng. Chem. !J, No. 7, 1641 (July, 1951)

3. Brokaw, R.S. "Aiigrent Charts for Transport Properties"N.A.C.A. M. R-S1 (1960)

4. Brokau, R.S. "Approidzate ForLlas for the Viscosity and Therm-alConductivity of Gas Ylixturms. J. Chem Phys. 2, No. 2, 391 (August1958)

5. Hirschfelder, J.O., "Proc. of the Joint Co:-. on The.--cmd.ic andTransport Properties of Fluidsl Th-e inst. of Mech. ng. (London)p 133 (1958) .1

6. Hilsenrath, J., Tables of Tne'.-al Properties of Gases. Cir 564,IMS (1955)

?. Bird, R.B., Stewart, W.E. and Lightfoot, E.N. "TransportPhencmeral John Wiley, N.Y. (1963)

WNCASSFMW

25

z

zww

a.i D

is;' 0z

z z

0 +l0 I- Lz S z

z uvi

-~I w

8D

UW CI--I w u

IILI

(t;

00I-w

vi

UNCLASSIMI]26

-"ENSING ELEMENT

IM. rUARTZ F;LM

SENSING FILM D FILM

NSULATING GLASS TUBE NSULATINGGLASS TUBE

COOLANT (waier) "--COOLANT (WaW)

SECTION A-A SECTION 9-0

FIG ,E 2 - Cooled Filu Sensor

(fot, ogaph - Magnification x 5, Sketch.s - Not to Scale)

OrCLASSIYIM~27

'irI3

FIGMR 3 -A) Stnwor Holder; B) Heat ?bzz Frobv; c) Aspirating pob.(Scale in Centiers)

UNCLASSIFIED

,140 DIA. .230 DIA..65D.

r.-.

' 625 DIA.

SENSOR PROBE TRAVERSINGdiACKET SLEEVE

FITTINGPLATE

MODEL HF-21

FIGURE 4 - Diagram of Probe with Sensor Holder Inserted

---... zU---- SENSOR

TRAVERSING PROBE COOLINGSLEEVE TUBE BUNDLES

FIGURE 5 - Probe Tip With Sensor in Operating Position

UNCLASSIFIED29

BRIDGE VOLTAGE POWERPOWER V OUTPUTOUT

AI ;j

° I° ' -r 1 tL-TE'CIlRCUIT

V_1

R DGE - AM PAMP

RD" R, " VKI2Rs

FIGURE 6 - Functional Schematic of Circuit

'- 1

FIGURE ? - Cooled-Film Circuit and SensorWater Supply Control Panels

110

700.

650 ........ . .. .....

W 6.0 i

,Q (IN WATT

4000 30 0 00 60t

SENSOR COOLtING WATER PRESSURE (PsIG)

FIG.8 CALIBRATION CHART FOR THE DETERMINATION OF SENSOROPERATiNG TEMPERATURE AND COOUNG WATER PRESSURE

FROM ESTIMATED OCOOLANT

UNCLASSIFIED

31

2.4__i~T~ T T [~~~

ZO I I

I _ I

F-T-

.~~~ .~.-. ...... £.... .... 1

INTS-TY)G

FI. SENSOR~ RESISTANC Vs TEPRTR IAoCUV OBAE FO 3 ESOS

UNCLASIFIED

32

a- -

ww

00Q z

ow 08

0z0

w 61

0 (n 0

w .a u.. I AtD

0r 0z-

bfld-G1OO

in a

UNCLASIFIED

33

7 W

Z44

14

it I

Ii-Ic

IF-

UNCLASSIFIED314

0 ;0

F.

UNCLASIFlPE335

w14

I' U

L3L

UNCJA.SST -I F,-,3b

. . - 6. ..

t.-,j-' . ...-.-0=- . : :

z; CC

I -- I -- -

i

A

....... .-

........-- ..--

. . .. .......

:"" " ' "-_ __:. . . I --- I; .t

": - -I - I . .- , . . .I

_ .. . .. .. * - C! I.*. .. . -

• :' .... 'I I i. ,

""1 : I" - I- - --' .I z

-. . -, ... i! " I

-! !I! :. .. - "" -

.. ... . . ..... . 1. . . _ II .... . .. I .... I.. .. . . ... !I -,-..' ,. ",

__ _'. -_." .? ' " . ' :1 . . .l I _ _ • "_ _ t .

iawLeHt~j

UWCLASSIFI~

371

4)

IA

C

0aS05q(I

IU''-4

1-4

UNCLASSI FIE

18

T,,, . ' 1 AmNum (T-)j "A' B Rem

CONDITION A BA* n" t VIAT:OIN C

FLOW - NZFLON 2 .1880 .5092 .45 .26 .O601

T - VARi-BLE I

FLOW- He1690

2 Ts - CONST . .5086 .45 .21

T. - VARIABLE

FLOW- N2 I!I13 T - VAR;ASLE 9

TM - CONST _

FLOW -He I4 T - VARIABLE .2003 .4936 .45 23 025?5

Tm.- CONST .

FIG.16 TABLE SHOWING VALUES OF CONSTANTS EVALUATED BY

A LEAST SQUARE FIT OF THE DATA FOR DIFFERENT

CONDITIONS WHEN A TEMPERATUE RATIO IS CONSIDERED

IN THE CORRELATION.

ULss I M-39

-U A +8Rel*rnit; m

COITO A 8 IN

FLOW___- 1142______ 0~N~

FLOW -t Me-2Ts CONST .7090155 A5 1.6 02Z4 1.0609 232-

I ~FLOW-HeI.I

.2T,; -'CNSI 18.04 .45 -15 D224 j1.0 2202%j

FLW-J - -' _

43, T- XVAME 1 -20 .42 .45 -14 1.06-0M0 2331

Tft

WHC USM OS ______ E C---- SZ ALL__ 4__-- I "2DAT TOEHR I h-%KUSV C-TFiJ TABL IOWVGYU OF5 C*IT EAIA3 f5Y. A

LEAST96 __AS __T __F THEE DAAFRr-

* WEN AS4 CCD4S1~4T ViSZM RJATE ~S EESMz OfL 1423

CORRELATION-

UNCLASSIFlED

40

0.5t 7 ' -7-.

. ... ... ..... .. .i...... I. . . " .. ................... .

. 4 .. . . . ..... . . . ......

'i .O .45 i i ' , 'I " ; ' . , i - C i . I .

I ... ........ .

, -........ ".."." ........ ...... .... .

/ ' I "; ;- I ': : I I " I " : " I i . I t • I • ' - ! - ,I. , ; ,I i . - , I ! i i i I

0-I----- --' "-...... .. .... I

# I i ' a ' I I I_I 1 .. ...1 , " a ," • ; ...I I . II I , ,l I I I I I

0.25 ,, .. .. -- -

' .i ; .....L .._ .. ..-.... .• . .. -- -

r--,'"- .......t-- ---.-..-...-.. .02I _, . ' I I . . . i " ' '

[30 135 140 145 [.50 .. .160 165 170 175 W.,

LOGIRem

FIG.I8AHUm V, Re. FOR A CrCULAR CYLINDER IN NITROGEN CROSSFLOW ,.R VARIO,STEMPERATURE LOADIGS. TEMPERATURE LOADING EFFECT OBTrAINED BY VARYINGTHE FLOW TEMPERATURE AND KEEPING THE CYLINDER TEMPERATURE CONSTANT.

CYUNDER DIA. .0,152 cm.

T.0OK TsOK L- V6.. MG

1627- 42 15831- 21'75- x

428 1-990 2.193

1435- 42 [1540- 2.073- .14615 [548 2.090

1244- 42 (488- 1947ri- 0

1263 1.494 V.973

0350- 42 1421- (.79.0- *428 [425 [.810

852A4- 1,331- WSOO-428

058 1.334 [SOT

UNCIASSIFIED

i41

0.60 .:I T j 7.rrr .

... .2 . .." ' '. i .I. . . . .

051- ------- I*1

... ..... --.. .

........ . .... ... . ... .I

1 I ,. .. ! .I! I.. ..... ...... . -J... J ...:. , _

010

-. ..... l . .. .

0 .5 . , ; ... ..

........ CI..E .IA .0.. .

0.25 ' f ' itl id

FLO Re ,I

:3-; 428 FIG.1 2B,

N% (y./&" 15 43R.5O ITOE 1.540 7- HVN ELMATN

CYLNDE 428 .15 2 2.09

428 4' .1

845- 140 2.073558

o~ ~~ 16 L548 2 -- =bi -- ''-., ,i.090-r -- 24-- "I-8t ' 19 ...

I. -T '" I - 3 IA 94'"' 19....i .1..,..t..... 0=..

"~ ~ ~ ~ ~ ~00 428.. ,A1 ' 1......7..90... :., "ICA' 1'" 1"-i5 ":--r -.... ,l- - :'i- i 8- A-, 42 1331 t 1600- I! -"d

0.55~85 1334F- .:I , - 1 - :.......

UNC:LASSI T 142

.305

I I . ... . . .I ....

.. . .. .. . .. ..

x.. . .....

.15-.. .. ... ......

.10 _ _ _ -.. . I

.. .. .....

.7 75 .0 85 .90 .95 1000 LOS 110 15 1.20

1LOG toRe

FIG.19A

NUm Vs Re rnFOR A CIRCULAR CYLINDER IN HELIUM CROSS -FL0vi FOR VARIOUS

TEMPERATURE LOADINGS. TEMPERATURE LOADING EFFECT C'3TAINED BY VARYINGT AND KEEPING Ts CONSTANT.

CYLINDER DIA 0152 cm.

FLOW - HELIU-M

T-9~K Ts 3K Tim SYMBOL

1356- 46 493- 1.910-1360 460 .I94 1.920

1173 460 1.438- 1800 0831.440 1.820

99- 46C 1.367- I.Z-0- 0197 369 1678

802.7-

803 460 1.271 1500OO

UNCLASSIFIED43

'.... .......... .....

I 30 1 11

... . .... .1 .. 1..1.

L .......... ...... .............._ _ _ _--- -------

.5 . I

.10.1 I II Gj' .8

CYINE DIA015 1.20

LOW-RELK

15 IG 1,93-LB O

RESIOUM0 460EATR L494iN EF9ECT

46

994E- 12673- ISMO-97460L39 m

8024- 137 50

460 L271 L.500 .

UNCLASSTIFIED44

---- --- ...- *~*~ . . ...... ....

. .. .. .. ....

.- ~ .I .. .. ..

E-.-- 1 ... ...ii

0.401 , 1 4 .

...5: . .... ..--- I---

..... WW....15 .0 AQ---

LOG ReK0 m

FiG.20A

N vr Vs Re mFOR A CIRCULAR CYLINDER IN NITROGEN

CROSS -FLOW FOR VARIOUS TEMPERATURE LOADINGS.

i'EMPERAT'JRE LOADING EFFECT OBTAINED BY VARYING

THE CYUNDER TEMPERATURE WHILE KEEPING THE

FLOW TEMPERATURE CONSTANT

CYLINDER DIA. .0652 cm.

FLOW - NITROGEN

Too K Ts OK T4 Ila* SYMBOLTm Vrtn

1435- 36. 598- 2.204-

1465 1.604 12-221

1455- 1540- 2073

1465 48 1.548 2.090 0

1435- 1.486-1-953-495.9

1465 1.494 1.972

UNCr.LASSIFIED

45

0.50I, ,INI

A ........-J. 0. ........

... ... .. ....

I m

.3.~ ~ ~~FG t 20B______1

LOW. -rem GE

1435- FI W 2-204

-LOW - ITROGE

1435- 49598- L9503-

1465 i.494 L972

NrLA3SjFT'-

-~~I --------

I ~ '4V.ji

1'..- ---- ----- -- --------

E O... .I ......

.. . .....

B5 .90 .95 to100011 11 1.20

LOG1Q Rem

FIG. 21 A

Nu Vs Re FOR A CIRCULAR CYLINDER IN HELIUM CROSS-FLOWmi I i

FOR VAR!OUS TEM.PERATURE LOADINGS. TEMPERATURE LOADING

EFFECT OBTAINED BY VARYING Ts WHILE KEEPING T.. CONSTANr

CYLINDER DIA .0152 cm.

FLOW -HELIUM

To K TsOK f cc-- 2i- SYMBOLTm 1/r

056.0- 370 1556- 2.044-t3387.0 1557 2.045

M356- 4600 493- 1.910- 01360D 6. 1494 1!920

1356.0- 532-0 L436- L792-136.0 l.437 1802

UNCLASSIFIED47

... ...1....

0.30 4<1l-IM U*It i-1

. ... ... .

E ;.N ;: _: :: _ 10.25 ~~~ ........

... . ... .

OaO~ t::.:±: ;:....I:-:.85 .90 .95 .00 505 110 1.15 1.20

LOG 10 Re

FIG. 21B

Nu '.Ilm Ws Rem FOR HELIUM CROSS -LOW SHOWING

ELJtMWJ4TN OF RESIDUAL TEMPERArURE WOADING EFFECr

CYLINDER DLA M12cm.

FLOW - HELIIUM

'6 0 K Ts*K ya SYMBOLTm V mn

1356.0- L556- 2.044-3 36701360D1557' 2.045

1360D L494 L920

13560o- 532.4I36- 1792-1360.0 1437 18902

UNCLASIFI ED48

L Lz-A ...... -10.. ..... --- ......

0.45

YF~ A ......

_______A

lu .....

_._0

I j I [ -tT...........- E:

La .5 13 .5 .0 14 .0 1.5 IO 16 7LOV J e

FWW~~~~ --- --0 ------ (Y O

T-451 I~O -702565 .. 4.6.....

L20 L L30 L35 4 7 1.456L 155.0 W 7

FL G* Rem75 ;N-2.%(B O

1267.3-ASturn~ Re FO A RCUA43YL.DE INHE.493TGt L #XTUR

CR0SS-FLW ~ 30. FDR3 VA1I TEPRTR OAIG.TMERTR ODN

EFFET OTAWE ByVARYtO. AND3 KEPW s4OSTN

CYINER0. O52in

UNCLASSIFIED49

0.5

G 0[ - -----------

E

3.1 I -T

0

0.25 I

Nu m61VYI' A R. FO HEfUM NITOGE MITR CRS-FO 1

I.hW~ %O I.O EMEAURE#£G FET

CYLVDER DI DW c

2- 427 t43 IS

4300 r-6 149 1940

ImI025J1.3, ti

109__.4

s mi-r- 430. L353 16490071e

UNCIASSIFIIT50

0.65 _ _

OALOS, 1- 1 --.-

- .- 2- . S

win% emFO A RUARC,-*0ERtmPa~o~m CAe,*: o:()F j-TtjS

z R)S -FLO FO *1 ESAWLAO-. ~VZ*UELA~GOF

0~T- :ft ,--

IM70.45 43Z L4 5a

7037 4379 .1233IA

r -Lw--230% rD -50(L- VO)

127c4. 79 k 489 t-%32787D

0-a -4379 t426 L756

9032-

7M37 4379 i2-33 13806

51

-4

-1. j 1

I ~~FD + 3K - -

-oj) 4i7 37 !f

-~a 43912i Z

9m4 _________ uz904-- - -- - --

UNClASSIFIED

.70

-j I- i i i......* I I 0I

II 50IP

*j A.I

.0 Im .. AOL912 B 4 5 j i617 i LII T f T i Femh '

FIG.2ti

NUV O O ICLRCLNE N~~ WL~iIUM W IOXD IXTR

Nu V Re OR ACIRCLARCYLINDER I5 cEJmCR IXD ITR

FLOW-He -42% aC0 2 -58%(BY VOL)

Tm"K TBOK LT. V_.0 BOTm s"n SAO

1082 368.13 1.4943 3.899 0

899.85-9023 368.13 L4194 1.743

701112-36813 13456 13

FLOW -No. -93 5%; C02 -6.5 %1088.5-1089A4 36813 1.928

900.6-900.94 36833 L773

702.06-702.4 368.13 1555

UNCLASSI FIED53

7- .. -.

f I

z .40 .-.--.- 2Ji I _ __ _ _

8 --- A: J i2 I 121I.J

20.S A .

.T. . ... ..L I.. ...:: j

0-9 Lo0 L. 2 1.3 1.4 15 Is 1.7 1.0 Is

LOG ORg

FIG248

Nuf (140vmY5 Vs Ref FOR HELIUM -CARBON DICAJDIE MIXTIJWC CRMS-F12ff S!$C7.VNG

ELIMI4iTION OF RESIDUAL TEMDERUURE LOADING EFFECT

CYLINDER DIA .0W5 cm.FLOWfH-4% 02 58 %(By Vol.)

Tm K rS*K Too V~. SYMBOL.

108Th 368.13 L4943 IS"910882

899J85 36813 19404 LT43900.28

70OW8 368J3 1.3456 1.533 9702.14

FLWh-3% 0.65

1088b5 368.13 1928M09.4

90QL6 368.13 1.773

702.06 368.13 1.555702.47

UNCL SSIFIE

*4 a

54

oe

il

-.. " - * {

4nJdoN

d~ ~ ~~l a -.....4, i

• , A i I -

InI

* " -, iI. - - . * i..

PF

-w 0i !

n ga

r, i 4

![ I i

. ,

o" UO 9

1W;CLSTEDI

55

- -T~-

. . . -.

ID4 - I

* 1'

at~

A J F

t I*I- - -~ -

56

4. .-. s-

0j L

-jj

0. 1l o 01 3 14 1 .

LOGI-S.!

KRME N. -0.2S 5 rR

0.6 0E7,- 3 0.85 . R.-5 013 p,LO Re M

C)~em KResm * Nu (0.268 +OSP Re6 ,-4xf 1in m I'M

(5)* F OAGN.T-0-KT-WFL-W 0.5 RGE