TEMPERATURE RECOVERY FACTORS

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NAVORD REPORT 2742

TEMPERATURE RECOVERY FACTORS IN THE TRANSITIONALAND TURBULENT BOUNDARY LAYER ON A 40-DEGREE CONE

CYLINDER AT MACH NUMBER 2.9

t-

I JULY 1953

Us S. NAVAL ORDNANCE LABORATORYWHITE OAK, MARYLAND

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NAVORD Report 2742

Aeroballistic Research Report 168

TEMPERATURE RECOVERY FACTORS IN THE TRANSITIONALAND TURBULENT BOUNDARY LAYER ON A 40-DEGREE CONS

CYLINDER AT MACH NUMBER 2.9

Prepared by:

K. H. Gruenewald

ABSTRACT: Temperature recovery factors have beendetermined on the cylindrical surface of a numberof 400 cone cylinder models at zero angle of attackand at a Mach number of 2.86. The investigation wasperformed in the intermittent NOL 40 x 40 cm Aero-ballistics Wind Tunnel No. 2 and the continuous NOL18 x 18 cm Aerophysics Wind Tunnel No. 3. Withatmospheric tunnel-supply conditions the turbulentrecovery factor was found to be 0.890 ± 0.5% andindependent of Reynolds number in the range of 200,000to 800,000 with Reynolds number based on wall conditions.The turbulent recovery factor can be represented by thecube root of the Prandtl number for a Prandtl numbercalculated at wall conditions. In the transitionalregion of the boundary layer a maximum recovery factor0.5 to 1 higher than the turbulent value was obtained.Furthermore, it was found that boundary-layer historyhas a marked effect on the value of the recovery factor.The results of the investigation are compared with thetheoretical and experimental findings of other investigators.

U. S. NAVAL ORDNANCE LABORATORYWHITE OAK, MARYLAND

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UNCLASSIFIEDNAVORD Report 2742

NAVORD Report 2742 3 July 1953

The results presented in this report representadditional information on aerodynamic heating ofbodies in supersonic flow. The investigation re-ported was carried out during the period of 1950to 1952 in the 40 x 40 ca Aeroballistics TunnelNo. 2 and the 18 x 18 cm Aerophysics Tunnel No. 3of the U. S. Naval Ordnance Laboratory under thejoint sponsorship of the U. S. Navy Bureau ofOrdnance under Task No. Re9a-108-1 and the U. S.Air Force Flight Research Laboratory.

The author wishes to express his gratitude toDr. G. R. Eber for his stimulating discussions con-cerning the investigation and to Mrs. Z. C. Brooke,Miss M. Jennison and Messrs. S. M. Dwohoski, H. McGraw,H. J. Honecker, and I. Korobkin for assistance givenin the course of the investigation.

EDWARD L. WOODYARDCaptain, USNCommander

H. H. KURZWEGAeroballistic Research DepartmentBy direction

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UNCLASS IFIEDNAVORD Report 2742

CONTENTS

PageI. Introduction 1

II. Review of status on temperature recovery 3factors

III. Test arrangement 5IV. Test procedure 7V. Method of data reduction 10

VI. Measurement accuracy 11VII. Results 13

VIII. Comparison of the results with those of 19other investigators

IX. Conclusions 21X. References 23

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LIST OF FIGURES

1. Temperature recovery factors from boundary layeranalysis for Prandtl number Pr = 0.715.

2. The assembly of the models used.3. Parts of the bakelite and copper wall model.4. Configurations of the 400 cone cylinder model.5. Test arrangement in the NOL 40 x 40 cm intermittent

tunnel No. 2.6. Test arrangement in the NOL 18 x 18 cm continuous

tunnel No. 3.7. Distribution of static pressures and local Mach

numbers along a 400 cone cylinder at Mach number2.87.

8. Distribution of static pressures and local Machnumbers along a 200 cone cylinder at Mach number2.87.

9. Local recovery factors on a 400 metal cone bakelitecylinder at Mach number 2.87 (40 x 40 cm intermittenttunnel).

10. Local recovery factors on a 400 metal cone bakelitecylinder at Mach number 2.87 (40 x 40 cm intermittenttunnel).

11. 400 cone cylinder at Mach number 2.87.12. 400 cone cylinder at Mach numbsr 2.87.13. Local recovery factors on a 40 cone cylinder of

bakelite with and without a metal cone at Mach number2.87 (40 x 40 cm intermittent tunnel).

14. Local recovery factors on bakelite cone cylinders ofdifferent head shapes at Mach number 2.87. (40 x 40cm intermittent tunnel).

15. Recovery factor measurements on cone cylinders at Machnumber 2.87 in the intermittent tunnel.

16. Typical time-temperature curves for a 400 cone cylindermade of bakelite at Mach number 2.86 (18 x 18 cmcontinuous tunnel).

17. Typical time-temperature curves for a 40 cone cylindermade of lucite at Mach number 2.86 (18 x 18 cm continuoustunnel).

18. Temperature recovery on a 400 cone cylinder made of luciteat Mach number 2.86 in the 18 x 18 cm continuous tunnel.

19. Local recovery factors on 400 cone cylinders at Machnumber 2.86.

20. Local recovery factors on a 40 oversize cone cylindersat Mach number 2.86.

21. Local recovery factors on a 400 rough cone cylinder atMach number 2.86 (18 x 18 cm continuous tunnel).

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22. Temperature recovery on 400 cone cylinders atMach number 2.86 in the continuous wind tunnel.

23. Recovery-factor measurements on 400 cone cylinderat Mach number 2.86 in the continuous wind tunnel.

24. Recovery factor measurements on 400 cone cylindersat Mach number 2.86 in the continuous wind tunnel.

TABLES

I. Temperature recovery factors for laminar boundarylayer.

II. Temperature recovery factors for turbulent boundarylayer.

III. Conditions of the tunnel supply air during the tests.IV. Experimentally determined turbulent temperature

recovery factor and some theoretical solutions.

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SYMBOLS

T = Temperature (degree C, degree K)

p = Static pressure (kg/cm2 )

r : Temperature recovery factor

I a Length (i)

v Velocity (&/sec)

C = Specific heat at constant pressure (kcal/kg-deg C)

k = Thermal conductivity (kcal/m sec. dog C)

g : Acceleration due to gravity (9.81 a/sec2 )

Density of air (kg. sec2/m4 )

Absolute viscosity (kg. sec/m2)

u Component of velocity parallel to surface

y Cartesian coordinate normal to surface

: Dynamic boundary-layer thickness

N = Velocity-profile parameter, u/u1 . (y/ )/N

M Mach number

Pr Prandtl number =- OLtgk

Re = Reynolds number - v.l.

Subscripts

o Stagnation condition of the air corresponding tothe supply conditions of air at the state of rest,ahead of the intake of the wind tunnel.

a Free-stream conditions in the test chamber in theundisturbed flow.

1 Local conditions in the flow along the surface ofthe body at the outer edge of the boundary layer.

e * Local conditions at the surface of the body in thestate of thermal equilibrium.

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TEMPERATURE RECOVERY FACTORS IN THE TRANSITIONALAND TURBULENT BOUNDARY LAYER ON A 40-DEGREE CONE

CYLINDER AT MACH NUNBER 2.9

I. INTRODUCTION

1. A body flying through air at supersonic speed isheated by friction and compression of the surroundingair resulting in elevated temperatures. The effect ofthese high temperatures on construction, material, andcargo of the body increases with increasing speed andis an important factor in modern aircraft and missiledevelopment. To determine the quantity of heat enteringthe body per unit of time, one must know the surfacetemperature of the body, its surface area, the heat-transfer coefficient,and the recovery temperature. Bydefinition, the recovery temperature is the temperaturein the boundary layer immediately adjacent to thesurface of a perfect heat insulator. It is,therefore,the temperature of a body surface which is in thermalequilibrium with the boundary layer,i.e., zero heattransfer between air and body. For this reason therecovery temperature is also called equilibrium temp-erature. In practice,a body in free flight will notattain the equilibrium conditions because of heatconduction and radiation effects but will approachequilibrium temperature as a limit.

2. The experimental determination of the equilibriumtemperature in the supersonic wind tunnel in terms ofa dimensionless parameter is the subject of this report.

3. The numerical value of the equilibrium temperatureis intermediate between the stagnation and ambient airtemperatures and depends on two effects:

a. Generation of heat by compression and frictionof air on the body.

b. Diffusion of heat by conduction and convectionthroughout the boundary layer.

The interaction of these effects creates an energydistribution in the boundary layer which leads us toexpect different surface temperatures depending onwhether the boundary layer is laminar, transitional, orturbulent.

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UNCLASS IF lEDNAVORD Report 2742

4. The equilibrium or recovery temperature isusually expressed in terms of the recovery factor,r, which is defined as the ratio of the actualtemperature rise across the boundary layer to thetemperature rise resulting when the ambient airis adiabatically brought to rest relative to thebody. Therefore

r z

where

Te = the equilibrium or recovery temperature,

T = the static air temperature at the outeredge of the boundary layer, i.e., ambientair temperature,

To =the stagnation temperature, e.g., thetemperature reached when the flow at theouter edge of the boundary layer (T)is adiabatically brought to rest relativeto the body.

This factor, r, is generally a function of thesimilarity parameters, Reynolds number, Re, Prandtlnumber, Pr, and Mach number, M. If r is known, theequilibrium temperature T can easily be calculated.This temperature is important for two reasons:

a. It determines the possible maximum thermalstress to which a body flying at high ppeedis subjected since the equilibrium temperatureis the limiting temperature a body may reachduring its flight at a certain velocity andaltitude.

b. It is the temperature upon which thedetermination of the coefficient governingthe heat transfer from air to body is based.

5. When the investigation presented in this report wasstarted, the theoretical solution for the recovery factorin the laminar region had been well verified by experiments.However, experimental results for recovery factors in theturbulent region were inconsistent and approximatetheoretical solutions were inconclusive.

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For transitional boundary-layer flow no results eithertheoretical or experimental were known at all. Theprincipal purpose of this investigation was, therefore,the experimental determination of temperature recoveryfactors in the transitional and turbulent regions ofthe boundary layer. The investigation was actuallyconducted on cone cylinder models in the wind tunnelat a Mach number of 2.9 and at zero angle of attack.

II. REVIEW OF STATUS ON TEMPERATURE RECOVERY FACTORS

6. For laminar flow along a flat plate the recoveryfactor has been theoretically determined by severalinvestigators (reference a) and may be representedby the square root of the Prandtl number (r a Pr) forMach numbers up to 5. In the analyses the Prandtl numberis assumed to be constant. For the real case, however,the Prandtl number is dependent on temperature andtherefore varies considerably across the boundary layer.For instance, in a wind tunnel having a supply temperatureof 3000 K the Prandtl number varies from 0.660 to 0.757 forall possible boundary-layer temperatures within the Machnumber range of 1 to 5. Accordingly, the recovery factorvaries from 0.812 to 0.870. The analytical result doesnot specify at which reference temperature the Prandtlnumber has to be evaluated. Therefore a comparison withthe experiment can be made on a basis of an approximationonly.

7. Experimental results on laminar temperature recoveryfactor are presented in Table I. The table shows thatthe theoretical prediction of the recovery factor forthe laminar boundary layer is well verified by theexperimental results. It may be noted that all recoveryfactor values obtained on flat plates are higher thanthose attained from other models. These high recovery-factor values, however, can be attributed to heat conductioneffects in the leading edge of the flat-plate model(reference k).

8. For the turbulent boundary layer there are severaltheoretical treatments in existence. The results ofthese treatments do not agree with each other. Solutionsfor incompressible flow, where the variation of fluidproperties in the turbulent boundary layer is not considercJ,have been obtained by Ackermann (reference 1), Seban(reference a, m), Shirokow (reference a), and Squire(reference n).

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UNCLASS IFlEDNAVORD Report 2742

9. Ackermann determined the recovery factor to be

Seban found an expression for the recovery factordependent on Reynolds number,

r (4.71 - 4i B-.601Pr)Re2

where

1 - P_ (5IP, 7)2 (5Pr +1)

A similar expression was obtained by Shirokow in hisformula

r- 1-4.55 (1 -Pe)- Re-° - .

The analysis of Squire results in

rPr/*

where N is the reciprocal of the exponent of thevelocity distribution within the turbulent boundary layer:

II

U1 d

In this formula u is the velocity component parallel tothe surface at the distance y normal to the surface,ul is the corresponding velocity component at the outereage of the boundary layer, and 6 is the boundary-layerthickness. A solution which includes the Mach numbereffect has been obtained by Tucker and Maslen (reference o)by extending Squire's analysis. Tucker and Maslen givethe following approximation formula for the calculationof the recovery factor:

?- Pr"/

with N a 2.6 .Re

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10. The results of the above theoretical solutions forturbulent boundary layers are shown in Figure 1, calculatedwith a Prandtl number of 0.715, which corresponds to 0°C,the approximate surface temperature obtained in wind-tunnel tests with atmospheric supply conditions. ForSquire's analysis the value for N was chosen to be 7, thefactor commonly accepted for the turbulent boundary-layerprofile. For the Tucker-Maslen analysis the Mach numbertaken was 2.84 corresponding to the local Mach numberemployed in the investigations to be discussed in thisreport. It can be seen that the recovery factor forthe turbulent boundary layer obtained from the varioustheoretical solutions ranges from 0.87 to values closeto 1.

11. The experimental results of the recovery factor forthe turbulent boundary layer are given in Table II andalso show considerable variation. The present investigationwas initiated because the need of additional informationwas evident.

III. TEST ARRANGEMENT

12. The measurements were performed in the NOL SupersonicWind Tunnels Nos. 2 and 3 described in reference s. Forboth tunnels the air is taken from the atmosphere, passedthrough a dryer which dries to a dew point of approximately-300 C, expanded in the Laval nozzle, and discharged througha supersonic diffuser into a vacuum vessel of 2000 m3

volume. Tunnel No. 2 is of the intermittent type with40 to 60 seconds blowing time and has a nozzle exit crosssection of 40 x 40 cm . Tunnel No. 3 operates continuouslywith a nozzle of 18 x 18 cm cross sectional area at the exit.The investigations were conducted at a free-stream Machnumber of 2.87 ± 0.01 in Tunnel No. 2 and of 2.86 ± 0.03in Tunnel No. 3. The deviations given for the Mach numbersare average values along the centerline of the workingsection of the nozzle.

13. A rotationally-symmetric body was chosen as a model,making it possible to mount a model of considerable lengthin the wind tunnel without the flow contaminations en-countered with two-dimensional models. The models werecone cylinders which had the advantage of simplicity inconstruction and instrumentation. Furthermore, a conecylinder eliminated the choking condition in the tunnelencountered with cones of comparable length. Allmeasurements were made on models with zero angle of attack.

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The models employed had a conical head of 400 totalangle with one exception where a 200 cone was employed.They are described as follows: (see Figures 2 - 4)

a. The "bakelite model" consisted of a conefollowed by cylindrical sections. The sections were2 inches in diameter each, 1 to 2 inches long and madeof linen-base bakelite. The cylindrical sections weremounted on a sting at the rear of a cone so that thecylinder could be expanded to 24 inches total length.The model was held in place on the sting by means ofa screw in the base section. One or more sections wereused for surface-temperature measurements and anothersection for static-pressure measurements. Since thewires and tubes of these measuring sections could beconducted through a slit along the sting, the sectionscould be placed at any desired location along thecylinder. The section for surface-temperature measure-ments contained four copper-constantan thermocouplesof low heat capacity hich were inserted flush withthe surface and at 90 intervals around the circumference.The junction of each thermocouple (wire size GE 36 AVG,wire thickness 0.005 inches) was soldered into a copperdisk 0.016 inches thick and 0.125 inches in diameterwhich was inserted into the surface of the measuringelement. For the determination of local-flow conditionsalong the model 2 static-pressure sections made of steelwere used. One section had a slit around its circum-ference (0.030 inches wide), the other one, 6 orifices(0.050 inches in diameter) equally distributed around itscircumference. Measurements of pressure and temperatureon the models were frequently made simultaneously. Athermocouple inserted flush into the base of the lastmodel section 0.750 inches from the model axis allowedtemperature measurements to be made on the model base.

b. The "coppr wall model" was of the samedimensions and built the same way as the bakelite modeljust described except that it contained copper rings of0.125 inches wall thickness, mounted on bakelite sections.However, adjacent copper sections were insulated fromeach other by bakelite sections,0.06 inches long andpermanently attached to one side of the main sections.As in the case of the bakelite model one or moresections served as temperature-measuring elements andeach element contained one copper-constantan thermocouple.

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c. The "lucite model" consisted of a cylinder1.125 inches in diameter and 10 or 15 inches in length,and a cone which was screwed onto the cylinder. Itwas made of lucite, had a wall thickness of 0.125 inches,and was held by a sting mounted in the thickened end ofthe cylinder. Thermocouples of the same kind asdescribed for the bakelite model were inserted in thesurface. In order to avoid mutual influence thethermocouples disks were mounted in a spiral curvealong the model 1 inch apart axially and 150 apart inangulary~sition. At the base, 0.406 inches from themodel axis and 900 apart, two thermocouples were insertedfor base-temperature measurements. Another thermocouplewas inserted in the surface of the cone.

14. For the promotion of turbulence in the boundary layeron the cylindrical portion of the model, oversize cones anda rough surfaced cone were used. The oversize cones with abase diameter 12.5% larger than the cylinder diameter wereused in the case of the bakelite and lucite models. For thecopper wall model the cone and a small part of the adjacentcylindrical section (0.125 inches) were covered with sandglued to the surface by a hardening-plastic solution. Themaximum peak-to-peak roughness of the sanded part of the modelwas 1 m.

15. The thermocouples of the measuring sectionsof thebakelite and copper wall models or of the lucite modelwere connected to four General Electric photo-electricpotentiometer recorders. The supply temperature of theair was measured in front of the Intake funnel behindthe dryer by a copper-constantan thermocouple (wiresize GE 36 AWG) and was recorded simultaneously with thetemperature of the model surface either by a Brownrecorder or a General Electric potentiometer recorder.The temperatures were measured against the temperatureof melting ice. Figures 5 and 6 show the test arrangementof the temperature-recording instruments. Static pressureswere measured with a butyl-phthalate manometer against anair pressure less than 0.1 mm Hg. This pressure wasmaintained by a vacuum pump and measured with a McLeodgauge or an Alphatron pressure gauge.

IV. TEST PROCEDURE

A. 40 x 40 cm intermittent tunnel

16. The investigation in the 40 x 40 cm intermittenttunnel was performed with the bakelite model. Sincebakelite is a material of low heat conductivity, it wasassumed that heat conduction in and along the model issufficiently small to allow the measurement of insulated

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surface temperatures. The blow duration of the tunnelof 40 to 60 seconds was too short for the thermocouplesto indicate thermal equilibrium between surface tempera-ture and boundary-layer temperature. The temperature-measuring section was therefore cooled to approximatelythe expected equilibrium temperature by means of a copperring previously cooled with dry ice. During the blow theindicated surface temperature decreased or increased,depending on whether the surface temperature at themeasuring point at the start of the blow was above or be-low the equilibrium temperature. After thermal equili-brium had been reached the surface temperature stayedconstant for the remainder of the blow.

17. In particular a cone cylinder was tested consistingof a bakelite cylinder and the following cones:

a. 400 steel cone,b. 40 bakelite cone,c. 400 bakelite oversize cone,d. 200 bakelite cone.

kll configurations were tested using 3 different testarrangements:

a. The model length was varied up to 24 inchescylinder length. A combination of thermo-section, non-measuring section and pressure section was used withthe pressure section placed next to the base section ofthe model in all tests. On models shorter than the lengthof the above combination, static pressure and equilibriumtemperature were measured separately.

b. The model was kept at a constant length of 15 or20 inches. A combination of thermo-section, non-measuringsection, and pressure section was used with the pressuresection in the down-stream position. This combination waskept unchanged but was varied in its position along the model.

c. The model was kept at a constant length of 15or 20 inches and the position of the thermo-section wasvaried along the model. No pressure section was usedin this arrangement.

B. 18 x 18 cm continuous tunnel

18. In the 18 x 18 cm continuous tunnel all 3 types ofmodels, the bakelite , copper wall, and lucite models wereused. The continuous blow permitted the attainment ofthermal equilibrium between surface and boundary layer

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without any precooling procedure, as applied in theintermittent tunnel. Since heat-insulating materialsuch as lucite and bakelite minimizes axial heatconduction, it was assumed that a non-isothermalboundary-layet temperature distribution could bemeasured along the model if existing. The 2-inch dia-meter bakelite and copper wall models had a cylinderlength of 8 to 19 inches*). Because of the relativelylarge model diameter the reflected head-shock wavestruck the model at about 8 inches from the beginningof the cylinder. Therefore tests were also performedwith the lucite model, with a diameter of only 1.125inches. Temperature equilibrium was reached from twodirections. The initial temperature of the model atthe start of the blow was either room temperature ora low temperature attained by precooling the model withdry ice. The change of the model surface temperatureat 4 measuring points and the supply temperature wererecorded simultaneously by 5 GE recorders operatingat low recorder chart speed. A timing device automati-cally short-circuited the GE recorders at regular timeintervals, thus producing time marks on the recordedtemperature curves. When the temperature change withtime had become zero, i.e., the thermal equilibriumhad been reached, the distribution of the equilibriumtemperatures along the entire model was determined.Since only 4 GE recorders were available, the thermo-couples on the model were connected 4 at a time bymeans of multiple switches to these recorders. Duringthe measurement of the equilibrium temperature therecorders were switched to fast recorder chart speedand the temperature at each point of the model wasmeasured for a short period of time.

19. The model configurations tested were:

a. A bakelite cylinder with

1. 400 bakelite cone,2. 400 bakelite oversize cone,

b. A copper-wall cylinder with

1. 400 steel cone,2. 40 sanded steel cone including a sanded-

cylinder portion 0.25 inches long,

*) The copper wall model was the same as used by Eber(reference g) for heat-transfer measurements in theintermittent Tunnel No. 2.

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c. A lucite cylinder with

1. 400 lucite cone2. 400 lucite oversize cone.

V. METHOD OF DATA REDUCTION

20. The measured data are presented in the form ofthe temperature ratio Te/To, the "local free-stream"recovery factor

r T e - Ta

and the "local" recovery factor

r 1 = Te - T1

To 1

Te and T are the measured equilibrium and supplytemperat8 res, Ta is the temperature of the flowat the test-section Mach number as taken from flowtables (reference t), and T1 is the local temperatureat the outer edge of the boundary layer as obtainedfrom the local flow conditions.

21. The local flow conditions were taken from compu-tations of R. F. Clippinger and J. H. Giese (referenceu) and from static-pressure measurements. The compu-tations give the local-flow conditions only in the flowfield between conical shock and reflected shock wave,which is formed at the intersection of the conicalshock and the expansion waves from the cone cylindershoulder. For Mach number 2.87 this portion of theflow extends to 3.6 cylinder calibers only*). Sincemodels of a length up to 12 cylinder calibers had beenused, the computed data were extrapolated by means ofstatic pressure-distribution measurements along themodel assuming no pressure gradient across the boundarylayer. From these measurements the local-flow conditionswere obtained by computing the ratio of the stagnationpressures before and behind the shock wave, the ratiobeing constant along a stream line and then using NACAtables (reference t). The static-pressure distributionsalong the models were measured in the intermittent tunnelonly. For the data reduction of measurements made in the

*) For the 200 cone cylinder this portion extends beyond12 cylinder calibers.

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continuous tunnel the local-flow conditions obtained forMach number 2.87 were transferred to Mach number 2.86.The distribution of the static pressure and the localMach number obtained in this manner for the 400 conecylinder are shown in Figure 7 and for the 200 conecylinder in Figure 8. Since recovery factor measurementson oversize cone cylinders are considered as supportinginvestigations only, no attempt has been made to determinelocal-flow conditions for this model configuration. Thedata measured have been referred to local-flow conditionsprevailing along the usual cone cylinder model.

22. The results of the present investigations are plottedversus Reynolds numbers expressed in three different ways.They are the free-stream Reynolds number Rea with allphysical properties of the air referred to the conditionof the undisturbed flow ahead of the model

Rea _

the local Reynolds number Re 1 with all properties referredto the outer edge of the boundary layer at the locationof the measuring point

1Re1: v.1r

and the local Reynolds number with the kinematic viscosityevaluated for the equilibrium temperature Te at the measuringpoint, and with the velocity, againtaken at the outer edgeof the boundary layer,

Ree : V.e

The characteristic length is, in all cases, the wettedlength of the model along the surface from the tip of thecone to the corresponding measuring point. For modelswith oversize cones the difference between maximum conediameter and cylinder diameter was not considered incalculating the characteristic length.

VI. MEASUREMENT ACCURACY

23. The accuracy of the measurements in the tunnel isdetermined by the following factors: The sensitivity ofthe measuring instruments, the distribution of the Machnumber in the working section of the nozzle and thedistribution of the supply-air temperature in the centralportion of the tunnel intake. Since it cannot be expectedthat the flow characteristics in both of the tunnels usedare identical, different measuring accuracies must result.

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A. 40 x 40 intermittent tunnel:

Within the temperature range used the equilibriumtemperature T could be measured with an accuracy of± 0.20 C and the supply-air temperature T with ± 0.30 C.

The Mach number along the centerline of tRe nozzle workingsection was constant within about ± 0.01 ( t 0.4%). Pressurereadings could be made with an accuracy of ± 0.05 mm Hgfor the butyl-phthalate manometer and of ± 0.1 mm Hgfor the mercury barometer. The accuracies in pressurereadings yielded a maximum error of ± 0.3% for themeasured local static-pressure ratios pl/Po. Theactual scatter of the static-pressure values about theaverage static-pressure curve was ± 1.5% (see Figure,7).This high value is probably caused by the discontinuitiesalong the bakelite model and the variation of the free-stream Mach number in the working section of the testrhombus. The inaccuracy of the free-stream Mach numberalready gives a scatter of ; 1.7% in the static-pressureratio pl/Po. Since this error is somewhat higher thanthe scatter of the experimentally determined static-pressureratios, the value of T 1.7% was used for the determinationof the maximum errors in local recovery factors and localReynolds numbers. Based on these values, the accuracyof the recovery factor was determined to ± 0.3%. Theaccuracies computed for the Reynolds numbers were * 0.8% forthe free stream and local Reynolds numbers Re and Re1and :; 1.8% for the local Reynolds number Ree cased on wallconditions. The reproducibility of the local recoveryfactor in the measurements was found to be ± 0.5%.

B. 18 x 18 cm continuous tunnel:

The equilibrium temperature Te could be determined to0.20 C and the supply-air temperature to t 0.60 C. The

average variation of the free-stream Mach number was ± 0.03(±1%) and was used for the determination of the scatter inthe local flow values, as was done for the tests in theintermittent tunnel. This procedure was justified sinceno pressure-distribution measurements on models had beenmade in the continuous tunnel. Thus the followingaccuracies were determined: ±0.5% for the recovery factor,Z 1.9% for the free stream and local Reynolds numbers Rea

and Rel, and ; 4.2% for the local Reynolds number based onwall conditions. In the measurements the local recoveryfactor was found to be reproducible on the average to ± 0.4%.

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VII. RESULTS

A. Measurements in the 40 x 40 cm intermittent tunnel

24. The arrangement of the temperature and pressure-measuringsections on the model was found to have no influence on themeasured data. The same result was found on the other modelstested in this tunnel. Therefore no distinction betweentest results obtained with these three model configurationsis made for the results to be discussed later in this report.

25. The model first tested was a 40 cone cylinder con-sisting of a metal cone and a bakelite cylinder. Figures9 and 10 show the measured local recovery factors plottedversus cylinder length and local Reynolds number Rerespectively. The recovery factor increases along thecylinder to a maximum, then drops to a constant valuetoward the rear part of the model. Schlieren pictures takenwith about 1 microsecond exposure time show that thedistinct and smooth boundary layer attached to the modelsurface assumes a blurred appearance at a certain locationon the model,thus indicating the beginning of the turbulentboundary layer (Figure 11). It was again found that thestart of turbulence does not occur at a fixed point butrather oscillates back and forth along the model. Theevaluation of numerous schlieren pictures located thiseffect in a Reynolds number range where the recoveryfactor curve drops from its maximum to its constant value.It is therefore concluded that the recovery factor has amaximum in the rear portion of the transition region andbecomes constant when the turbulent boundary layer is fullydeveloped. Then the Reynolds number at the start of theconstant recovery factor values can be considered representingthe end of the transitional boundary-layer region. Theexperiments in this tunnel show that the transitional regionstarts at the shoulder of the cylinder, because at thispoint the recovery factor already exceeds the value of 0.85found for laminar flow along cones. On schlieren photosit could also be observed that small disturbances appearin front of the fully-developed turbulent region but dieout again without disturbing the image of a clearly distinctlayer along the model (see Figure 12).

26. An interesting result of this test is the fact thatthe recovery factors of the transitional region do notrepresent a simple transition from the values of thelaminar to the turbulent boundary layer as was generallyassumed at the outset of this investigation (1950).Ratherthey reach values which are higher than those of the

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turbulent boundary layer. A similar observation wasmade on a flat plate at Mach number 1.8 by Eckert in1949 (reference r) and at Mach number 2.4 by Stalder,Rubesin, and Tendeland in 1950 (reference e). Eckertfound a maximum of 0.915 and a minimum of 0.898 forthe recovery factor. In the discussion of Eckert'sresults Seban (reference r) considers all values betweenthese extremes as being connected with the turbulentboundary layer. Stalder, Rubesin, and Tendeland alsoconsider the recovery factor maximum, which they ob-tained as a turbulent value. The constant value of0.92 of the turbulent boundary-layer recovery factoris higher than the values found by other investigatorswith the exception of the value Kraus obtained on acylinder extending from the subsonic region into thesupersonic region of the nozzle. He found a recoveryfactor of 0.94 at the same Mach number of 2.87(reference p). The results of the NOL test werepublished by Eber in January 1952 (see reference g).

27. The model next tested was a 400 cone cylinderwith cone and cylinder both made of bakelite. Thecone material was changed because of the followingconsiderations:

28. Cone and sting of the model first tested werescrewed together and made of steel. This combinationrepresented a mass of large heat capacity made frommetal of high heat conductivity. Since the conicalportion of the model could not reach equilibriumtemperature during the short tunnel blow and waspartly warned up again in the time between blows, someheat transfer from the cone to the air had to takeplace during the experiment. It can be assumed, there-fore, that the recovery factor values near the shoulderof the cylinder had been affected by this process Inorder to investigate the significance of this probableheat transfer, the test was repeated with the same modelwhere the metal cone was replaced by a cone made of linen-bakelite. Figure 13 shows the results in comparison withthe data previously obtained on the metal-cone model. Therecovery factor curves obtained with the two models arealmost identical in shape, but actual values are lower forthe linen-bakelite model. Since the only difference betweenthese two tests was in the material of the cone, theheat transferred from the relatively warm metal cone intothe boundary layer must be responsible for the high re-covery factor values obtained previously. The thermalinfluence of the cone on the boundary layer is not confinedto the neighborhood of the cone but prevails along the

14UNCLASSIFIED


entire model, thus indicating an influence of theboundary-layer history on the recovery factor. Itmay be recalled that each recovery factor valuewas measured at a point of the model where no heattransfer occured between model and air due to theprecooling procedure applied at each test.

29. The turbulent recovery factor of 0.905 foundwith the bakelite-cone model could be confirmed ontwo other models of the same bakelite material. Onemodel was a 200 cone cylinder, the other one a 400oversize cone cylinder (see Figure 14). The 200cone cylinder shows qualitatively the same recoveryfactor curve as obtained on the 400 cone cylinderbut gives a fully turbulent boundary-layer flow ata higher Reynolds number. This latter result iscaused by the fact that a 200 cone generates lessdisturbance of the flow at the shoulder of thecylinder than the steeper 400 cone. With the 400oversize cone used as a turbulence promoter, themaximum of the recovery factor curve is moved towardthe front part of the model. Turbulence is reachedat a shorter cylinder length or lower Reynolds numbercompared with the other models. The recovery factorfor the turbulent boundary-layer flow was found tobe 0.905 for all models. It is, therefore, unaffectedby the shape of the model head. Schlieren picturestaken of all models supported the result that thestart of turbulent boundary-layer flow occurs betweenrecovery factor maximum and the constant recoveryfactor beyond.

30. All results obtained during this investigationare presented in graphical form in Figure 15. Theconditions of the tunnel supply air during the testsare given in table III. Every point in the graph,T /T vs. cylinder length, is the average of about28 measured single values. Several average valuespertaining to one location on the model cylinder andto the same Reynolds number are averaged again inorder to simplify the presentation in the remaininggraphs of Figure 15. A few recovery factor valueshave also been determined on a 600 cone cylinder.The above findings were confirmed by the followingexperimental results on this model:

a. Turbulent recovery factor z 0.905,b. The optically-determined start of turbulence

is affected by the strong disturbance at the shoulderof the cylinder. The turbulence starva closer to thecylinder shoulder than in the case of the 400 cone cylinder.

15UNCLASSIFIED


31. Since the influence of the boundary-layer historyon the recovery factor was found to be of significance,the question arose whether heat transfer would alsooccur with the bakelite material, even with its heatconductivity 1/70th of that of steel. This questionwas justified because the measuring point had to beprecooled to reach equilibrium within the short tunnelblow, and it was unknown to what extent a small amountof heat trawfsr from the uncooled bakelite ahead ofthe measuring point affected the recovery factor values.Therefore these tests were repeated at practically thesame Mach number in the continuous tunnel where equili-brium temperature along the entire model could bereached due to the long blowing time.

B. Measurements in the 18 x 18 cm continuous tunnel:

32. In the 18 x 18 cm tunnel short test rhombus and shockreflection from the tunnel wall limited the length of the2 inch diameter models and necessitated the use of 1.125inch diameter models made of lucite. The initial modeltemperaturs at the start of the blow was either +20 0 C orabout -20 C, the latter attained by dry-ice cooling.The time needed to reach equilibrium temperatures alongthe entire model was 35-45 minutes for the bakelite andcopper wall models, 15-20 minutes for the lucite models(see Figures 16 and 17).

33. A typical graph in the form of the ratio of thecharacteristic temperatures Te/To vs. model length isshown in Figure 18 for a lucite model. Each circle onthe plot represents the mean value of 1 to 4 singlemeasurements within one test. Each shaded circle isthe value determined from two time-temperature curvesobtained by using the model precooled and at roomtemperature. The recovery factors calculated from suchratios and plotted vs. Reynolds numbers on Te-basis areshown in Figures 19 - 21. In addition, these figuresshow the results of some measurements on the same modelsin the intermittent tunnel. The dashed part of therecovery factor curve indicates recovery factor valuesmeasured downstream from where the reflected shockwave strikes the model surface.

34. The absolute values of the recovery factors asobtained in this tunnel were all found to be lower thanthose obtained in the intermittent tunnel on the samemodel. In the continuous tunnel the blowing time wassufficient for the modelID attain equilibrium temperature

16UNCLASSIFIED

I-I---- --

UNCLASS IF lEDNAVURD Report 2742

along its entire length, i.e., no heat transfer occurredat any point of the model. The result of these measure-ments indicates therefore that, in fact, heat transferfrom model to air produced apparent higher recoveryfactors in the intermittent tunnel, even for modelsmade entirely of so-called heat-insulating material(bakelite). In this tunnel the influence of theboundary-layer history on the measurements with themetal-cone model was noticeable over the entire modellength, because not only the metal cone but also thepart of the bakelite model ahead of the momentarymeasuring point transferred heat to the boundary layer.

35. Within measuring accuracy the recovery factor valuesobtained on the lucite models agree well with those ofthe bakelite models. On any lucite model radial heatconduction can be considered as negligible since thelucite model was held at its end only by a sting andthe model interior was filled with stagnant air oflow pressure. Furthermore, a recovery factor valuedetermined on the inside of the model wall at 5.0inches cylinder length (see Figure 18) was in fullagreement with the outside wall value. Axial heatconduction due to the non-isothermal equilibrium temp-erature is likewise negligible, if one considess thelow heat conductivity of lucite (0.2 kcal/m-h" C) andthe 0.125 inch wall thickness of the model. It can beconcluded, therefore, that the recovery factor valuesobtained with such a model give the true boundary-layertemperatures along an insulated surface. This is alsotrue for the bakelite model since both models gaverecovery factor values which agreed well with each other.The slightly lower values obtained on the partitionedcopper wall model may be caused by heat transfer fromthe air to the metal cone, due to heat conduction withinthe cone-sting system. It is improbable that the lowervalues could be caused by different surface roughness ofthe models since roughness determinations with a pro-filometer (Brush Development Co., Cleveland, Ohio) gavethe largest differences between the lucite and t~ebakelite models. (RIS values fgr lucite, 310 -610-6

inches, for coppeg-wall: _.10- -10.10- inches, forbakelite: 50.10 - -90-10 " inches.) Furthermore, thediscontinuities on the bakelite and copper wall modelscaused by the individual cylindrical sections are largerthan the roughness values but equal for both models(see Figure 4). The lucite model does not have thosediscontinuities.

17UNCLASSIFIED

UNCLASSIF IEDNAVORD Report 2742

36. In order to promote turbulence models withoversize cones have again been used. The resultsof these measurements are shown in Figure 20. Thetrend of the recovery factor has been found to bequalitatively the same in both tunnels. The absolutevalues of the recovery factor, however, are differentand again were found to be lower in the continuoustunnel. In this tunnel recovery factors determinedon the lucite model are in good agreement with thoseof the bakelite model.

37. The recovery factor value of the turbulentboundary layer was found to be 0.890 ± 0.5% whetherturbulence is promoted or not and remained practicallyunchanged after the reflection of the shock wave ontothe model. The maximum is 0.897 for models withand without an oversize cone, a value only 0.5 to 1%larger than that for the turbulent flow. As foundby schlieren pictures, the turbulence starts againclose to the recovery factor maximum. Only in caseswhere the recovery factor maximum could not bereached on the model, because of premature shockreflection, the start of turbulence was found tooccur at the location of the shock reflection. TheopticaLly-determined Reynolds number ranges ofboundary-layer transition are shown on Figures 19and 20 corresponding to the various models. Thestart of turbulence on the. oversize lucite modelfrom schlieren pictures was found to occur a littleahead of the recovery factor maximum.

38. A definite explanation of the recovery factormaximum cannot yet be given. However, it is knownthat the transition from laminar to turbulent flowis characterized by the generation of growingturbulent motion, which increases friction andequilibrium temperatures as well. This motiondevelops an energy distribution in the boundarylayer, which may be in a state of non-equilibriumjust before attaining the fully-developed turbulentboundary layer and thus may cause high temperaturesat the inner edge of the boundary layer at the endof the transition region.

39. Besides oversize cones a cone covered with sandparticles up to 1 mm high was used to promote atwbulent

18UNCLASSIFIED

UNCLASS IF IEDNAVORD Report 2742

boundary layer. Although schlieren pictures showturbulence right at the end of the rough part ofthe model, the recovery factor does not remainconstant (see Figure 21). It passes a minimum of0.87 and increases without reaching the value of thefully developed turbulent boundary layer before thereflected head shock wave hits the model.

40. Recovery factors determined on the cones ofthe lucite models were found to be substantiallythe same as those Eber obtained for laminar flowon cones in the intermittent tunnel (reference f).

41. For the sake of completeness in the datapresentation, the ratios of equilibrium temperatureto supply temperature, the free-stream recoveryfactors, and the local recovery factors are plottedas functions of cylinder length and the threeReynolds numbers Rea, Re,, Re (Figures 22 - 24).Furthermore, the conditions of the tunnel supply airduring the tests are given in Table III. The inter-pretation of the data presented in Figure 22 is thesame as given for Figure 18. In Figures 23 and 24each point represents the mean value of the resultsof several tests. Note that the difference betweenthe local recovery factor and the free-streamrecovery factor becomes smaller, the more thelocal Mach number appraoches the free-stream Machnumber with increasing cylinder length (see Figure 7b).

42. Furthermore, some equilibrium temperature ratiosTe/To at the model base have been determined. Ingeneral, they were found to be 1% higher than theT /To values at the corresponding model length(Figure 22).

VIII. COMPARISON OF THE RESULTS WITH THOSEOF OTHER INVESTIGATORS

A. Experimental results

43. In the course of this investigation some resultsconcerning recovery factors in turbulent boundary-layerflow have been published by other investigators (seeTable II). They are in agreement with the results

19UNCLASSIFIED

- -,-MEW . ...


presented here within measurement accuracy. In somecases this is also true for the recovery factor maximum.In one case the maximum could not be detected (referenceh); in another case its absolute value was subject towide scatter (reference i) probably due to the specialtest conditions in both cases. Eckert's maximum recoveryfactor of 0.915 is within the measurement accuracy of theturbulent recovery factor of 0.90 t 2% given in referencer. Kraus (reference p) performed his test in the same40 x 40 cm intermittent tunnel but with a blowing timeof 15 to 20 seconds. He approached temperature equili-brium by a local cooling method as was done in thecorresponding tests of the present investigation. Itis apparent, therefore, that the turbulent recovery factorKraus found on a cylinder in axial flow is subject to thesame boundary-layer history influence as found in thecourse of this investigation. Eber's recovery factorvalues, obtained on relatively short thin copperwallcones with a boundary layer tripped by a wire, areprobably related to transitional boundary-layer flowor influenced by axial heat conduction. Eber, himself,does not assign these values to the turbulent boundarylayer (reference f).

B. Theoretical solutions

44. The theoretical solutions of Ackermann (reference 1),Squire (reference n), and Tucker-Maslen (reference o)evaluated on the basis of the present investigation givethe numerical values on turbulent recovery factors pre-sented in Table IV. The Prandtl number was calculatedfor the equilibrium temperature and local temperature atthe outer edge of the turbulent boundary layer. The valuesof N, the reciprocal of the exponent of the velocity dis-tribution of the turbulent boundary layer, were based onthe range of local Reynolds numbers Re and Rj actuallyinvestigated in the experiments. The bounda y layerbeyond the point of the reflection of the head shockwave on the model was not considered. As the tableshows, the experimentally determined turbulent recoveryfactor found to be 0.890 ± 0.5% in this investigatitqcan be approximated by Ackermann's solution, r a Prwith a Prandtl number taken at equilibrium temperature.Since Squire's expression r = Pr (r1")/(3N*1) does not differ

20UNCLASS IF IED


much from Prl/3 with an N-value of about 7, theexperimental result also agrees with this solutionwithin measurement accuracy. However, the experi-mental value is found to be slightly higher thanthat given by the approximation formula of Tuckerand Maslen. Agreement with this formula is foundif the Prandtl number is based on the temperatureat the outer edge of the boundary layer. Since,in the Reynolds number range investigated theexperimentally obtained value of the turbulentrecovery factor does not show any variation withthe Reynolds number as predicted by Shirokow(reference a) and Seban (referencesa, m), thetheoretical solutions of these investigators havenot been evaluated.

45. It may be recalled that the Prandtl number isa function of temperature and it remains to be seenif the given comparison between theory and experimentholds true if the supply temperature is greatlydifferent from that of the present investigation.A verification of the results at other operatingconditions therefore will be necessary.

IX. CONCLUSIONS

46. The experimental investigation of temperaturerecovery in transitional and turbulent boundary-layer flow on cone cylinders at Mach number 2.86in two NOL supersonic wind tunnels with atmosphericsupply conditions has shown the following:

a. With zero heat transfer along the entiremodel the recovery factor for turbulent boundary-layer flow at Mach number 2.86 was found to be0.890 t 0.5%. The method of turbulence promotiondid not affect this value. Furthermore, this valuewas found to be independent of Reynolds number in aReynolds number range between 200,000 and 800,000for a Reynolds number based on wall conditions andwetted model length. In addition, agreement wasfound between the experimentally obtained turbulentrecovery factor and the theoretical solutions ofAckermann and Squire, when the Prandtl number wasbased on wall conditions. For a Prandtl number

21UNCLASSIFIED


based on the flow conditions at the outer edge ofthe boundary layer the experimentally determinedrecovery factor agrees also with the Tucker-Maslensolution,

b. With zero heat transfer along the entiremodel the recovery factor for transitional boundary-layer flow increases with increasing Reynolds numbersto a maximum value which is 0.5 - 1% larger than theturbulent recovery factor value,

c. The temperature recovery is affected bythe history of the boundary layer along the surfaceof the model. The recovery factor at a point withzero heat transfer is not a fixed value as long as aheat source of heat sink exists anywhere ahead of thepoint under consideration.

22UNCLASSIFIED


X. REFERENCES

a. Johnson, H. A. and Rubesin, M. w., "AerodynamicHeating and Convective Heat Transfer Summary ofLiterature Survey", Trans. ASME 71, p. 447 (1949)

b. Eber, G. R., "Experimentelle Untersuchung derBremstemperatur und des Waermeueberganges aneinfachen Koerpern bei Ueberschallgeschwindigkeit",Peenemuende Archiv No. 66/57 (1941)

c. Wimbrow, I. R., "Experimental Investigation ofTemperature Recovery Factors on Bodies ofRevolution at Supersonic Speeds", NACA TN 1975,(1949)

d. Blue, R. E., "Interferometer Corrections andMeasurements of Laminar Boundary Layers inSupersonic Stream", NACA TN 2110 (1950)

e. Stalder, J. R., Rubesin, M. W., Tendeland, T.,"A Determination of the Laminar-, Transitional-and Turbulent-Boundary-Layer Temperature-RecoveryFactors on a Flat Plate in Supersonic Flow",NACA TN 2077 (1950)

f. Eber, G. R., "Determination of TemperatureRecovery Factors on Cones in the NOL 40 x 40 cmSupersonic Wind Tunnel No. 2", NOL Memorandum10107 (1950)

g. Eber, G. R., "Recent Investigation of TemperatureRecovery and Heat Transmission on Cones and Cylindersin Axial Flow in the NOL Aeroballistics Wind Tunnel",Journal of Aeronautical Sciences 19, p. 1 (1952)

h. Stine, H. A., Scherrer, R., "Experimental Investi-gation of the Turbulent-Boundary-Layer Temperature-Recovery Factor on Bodies of Revolution at MachNumbers from 2.0 to 3. 8", NACA TN 2664 (1952)

i. Slack, E. G., "Experimental Investigation of HeatTransfer through Laminar and Turbulent BoundaryLayers on a Cooled Flat Plate at a Mach Number of2.4", NACA TN 2686 (1952)

j. des Clers, B., Sternberg, J., "On Boundary-LayerTemperature Recovery Factors", Journal of Aero-nautical Sciences 19, p. 645 (1952)

23UNCLASSIF lED.

. ........

UNCLASS IF IEDNAVORD Report 2742

k. Korobkin, I., "Apparent Recovery Factors on theLeading Edge of a Flat Plate in SupersonicLaminar Flow", (Unpublished)

1. Ackermann, G., "Plattenthermometer in Stroemungmit grosser Geschwindigkeit und turbulenterGrenzschicht", Forschung a.d. Gebiet d.Ingenieurwesens 13, p. 226 (1942)

m. Seban, R. A., "Analysis for the Heat Transfer toTurbulent Boundary Layers in High Velocity Flow",Ph.D. Thesis, University of California, Berkeley,California, 1948

n. Squire, H. B., "Heat-Transfer Calculations forAerofoils", British Air Ministry, Rep. and MemoNo. 1986 (1942)

o. Tucker, M. and Maslen, S. H., "TurbulentBoundary-Layer Temperature Recovery Factors inTwo-Dimensional Supersonic Flow", NACA TN 2296,(1951)

p. Kraus, W., "Braking Temperature Measurements ona Tubular Probe Paralleling the Air Flow at Sub-and Supersonic Velocities", Kochel Archive No.66/170 (1945)

q. Hilton, W. F., "Wind-Tunnel Tests for TemperatureRecovery Factors at Supersonic Velocities",Bulletin of Bumblebee Aerodynamics SymposiumAPL/JHU TG 10-4 (1948)

r. Seban, R. A., and others, "Adiabatic WallTemperatures for Turbulent Boundary-Layer Flowover Flat Plates", Contract W33-038-AC-15229,Dept. of Eng., University of California, April 1949

s. Lightfoot, J. R., "The Naval Ordnance LaboratoryAeroballistic Research Facility", Naval OrdnanceLaboratory Report (NOLR) No. 1079, (1950)

t. Notes and Tables for use in the Analysis ofSupersonic Flow. NACA Technical Note 1428 (1947)

u. Personal communication with R. F. Clippinger andJ. H. Giese of the Ballistic Research Laboratories,Aberdeen, Md., 1950

24UNCLASS IF IED

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NAVORD REPORT 2742

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Mmemenwt at 13.5 in.cylinder length.

(Runs 140,141)

0 10 20 30 40 50 G0O 7TUNNEL BLW TIME IN MINUTES

NAVORD REPORT 2742

1.00

FIGG17 TYPICAL TIME- TEMPERATURECURVES FOR A 40* CONE-CYUNDERMADE OF LUCITE AT MACH 2.86

(18 X 18 CM CONTINUOUS TUNNEL)

,0.96-

COOLJNG OF WARM MODEL

0

0.9

.9

Measurement at 9.5 in.cylinder length.

(Runs 16,17)

o 6 6_ I I0 10 20 30 40 50 60 70

TUNNEL S3LOW TIME IN MINUTES

NAVORD REPORT 2742

w Z~

00D

w :gno zoLJ

w x

O~D

cI

N L~

cs 0 d

*dw3J AideAs / dnUL wrflin9fo3 oI±va

NAVORD REPORT 2742

co

0 1!0 l

00Ez*~E 0 0 -

o~ o

0 0q

0 c

0 0

c > w

0 _ __ I

0 -0

N

_ _ _ _ _ 0

oc C

NAVORD REPORT 2742

0(

V 0 u

4- 0 900

44

00 v 0o(

w

0

0 0crJ

4 N 0 CD 400 0 0 D C D

CS C CS S CSCS C~c

NAVORD REPORT 2742

cc

4-o V 0________ _______ _______

I z

rcZ Zr

z 0 win mD

00) Cf)_ _ _ _ - _ _ _ _ _ _ _

D

w>J

0

10

vdow MMD3 wo

NAVORD REPORT 2742

IBAKE LITE BAKELITE

4, 146 4'

IC K)54) "20

096r 7.-' C--* -4

0944

08 90' '' "A

AT242 4'E20 A. 19 25,2.29,

086. W J8b[l05 ICIob C4 20

L

096 04(l

TO04 094

A5----092- ~ 092

09 !090. 1' 25

0OW 088!086 ow. 1 34

0 0 0 5 I)) 15 20

Te/T, fATj f)111 -FT f M INAJIA TI, jip T[MfI FATORI VA~lS MfAII~tWP AT !)CfIN R L ENGTH AT r4~ HtfRN L.x* MILL

L CCLNP 1141$ FT.TII IN IN(CHF' B ASF VALlk5

L(ATIC;N (A 'IO(A' FFL( TI,4. 0 V.AtiLAS TAKEN FF4Of. TINF TEMFIFFATL*?E CURVES'Hi' 11CL 'iI RH W~l FN[,(HE 1A'I14(, (AW C04t IGC* O DI L )

U.7 k4IIF (A ()'TI(AI ly [A 7FIHMINf[I TIJF*FAtI NXI ' AFT I EP' (1*N1 2061 I.01,8. AL C06* VA4L8 W, R T Tf AT L -0

FIG 22 TEMPERATURE RECOVERY ON 40' CONE CYLINDERS

AT MACH NUJMBER 286 IN THE CONTINUOUS WIND TUNNEL

NAVORD REPORT 2742

092 09a .

0 9 0 Q902!

086 0L

084! -- 8 -C- - " - "096 . OE

&vOEMD LUCITE MODE L

082 ° Q t ]82L Re

ow- (192

0. 08 L --

088'

Q816 096

0~~~~~~~ LNUN8AEJh (iI MZE BAKELJTE MODELQtA YAR51L LUCITE MDL 084 Ov '~ksiZE LuCITE MODL

0 5 ,o 0 2121' s( 4082L R

o

092r- -OW[09

OSCI *090'

086

08 Dl '.ANDEDCOPPENR ACN"DEE 08E4 *0 SANDED COPPER WALL MODEL

ra,qr FREE STREAM AND LOCAL RECOVTFRY FACTOR W RANGE OF TLILEE START FR(M SCHLIEREN PICTURES

L CYLINDER LENGTH IN INCHES L. XATKFI OF 594CK REFLECTION

Re, REYNOLDS NMWR BASED ON FRI E STREAM CONDITIONS A VALUES MEASURED ON CONE

A VALUE MEASUIRED ON INNER MODL WALL

FIG 23 RECOVERY FACTOR MEASUREMENTS ON 40" CONE CYLINERSAT MACH NUMBER 2.86 IN THE CONTNJOUS WI TUNNEL

NAVORD REPORT 2742

0Q92

,090 9

086 06 -

Q&4 5 0 8ESQ u2T -

2o O 0 2 '413 b

092j - - 092

Q 90. Q0 0~-.

086 Q_ - _ __ _ __

00VWBAET I OE o8 socUESOM W

082 -Q- 8223~t 0 40, 4' R e

098-~~~ It-' H- s

LOCAL RECOVERY FACTR RAWE OF TLRBLLENCE START FROM SCIEREN

FiREYNOLDS NLWIBER BASED ON LOCAL CONDITKWS WYTLRES

AT OUTER EDGE OF BOUNDARY LAYER A VALL(ES MEASUED 0ON CONE

Re, REYNOLDS WOOER BASED ON WALL CO(IiONS A VALLE MEASURED ON INNER MODEL WALL

FIG 24 RECOVERY FACTOR MEASUREME]NTS ON W0 CONE CYLt()ERS

AT MACH NMBER 2.86 IN THE CONTIIVOS WINO TUNNEL

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TEMPERATURE RECOVERY FACTORS