Heat transfer and pressure distribution on sharp and finite bluntness bionic and hemispherical geometries at various angles of attack in a mach 15-20 flow

von

KARMAN INSTITUTE

FOR

FLUID

DYNAMICS

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HEAT TRANSFER AND PRESSURE DISTRIBUTION ON SHARP AND FINITE BLUNTNESS BICONIC AND HEMISPHERICAL GEOMETRIES AT VARIOUS ANGLES

OF ATTACK IN A MACH 15-20 FLOW

by

B.E. RICHARDS. V. DICRISTINA. M.L. MINGES

RHODE-SAINT-GENESE, BELGIUM

HEAT TRANSFER AND PRESSURE DISTRIBUTION ON SHARP AND FINITE BLUNTNESS BICONIC AND HEMISPHERICAL GEOMETRIES

AT VARIOUS ANGLES OF ATTACK IN A MACH 15-20 FLOW

by

B E . . l.C ar s, R· h d " V . D'C' l. rl.stl.na, h . . l.nges . t ' L M' V

•

von Karman Institute for Fluid Dynamics, Rhode-Saint-Genase, Belgium

t AVCO Corporation, Wilmington, Mass., U.S.A.

v

U.S. Air Force Materials Laboratory, Dayton, Ohio, U.S.A.

Presented at the 22nd International Astronautical Federation Congress, Brussels, Belgium, 20-25 September 1971.

This research has been sponsored in part by the Air Force Materials Laboratory through the European Office of Aerospace Research, OAR, United States Air Force, under

SUMMARY

1. INTRODUCTION

2. MODEL INSTRUMENTATION AND CALIBRATION

4

3. TEST FACILITY AND RAW DATA CHARACTERISTICS

6

4. MEASUREMENT RESULTS

8

Hemisphere models

8

Smooth sharp-nosed model

8

Smooth blunt-nosed biconic model

9

Macro-roughness biconic model 10

5.

DISCUSSION OF RESULTS

11

Pressure distribution and shock shapes

11

Heat transfer on smooth and rough biconic

model 12 Heat transfer on smooth and rough hemisphere

models 13

6.

CONCLUDING REMARKS AND FUTURE PLANS

14

ACKNOWLEDGEMENTS

16

SUMMARY

Heat transfer and pressure measurements and sc~lieren flow visualisation photographs have been made on five vehicle nose shapes tested in the V.K.I. Longshot free piston wind tunnel at flow Mach numbers of 15 and 20. The models tested were two hemisphere configurations with a smooth and a chemi-cally etched rough surface, and three 50° - 8° half-angle

biconic configurations with sharp-and blunt-nosed smooth surfaced versions ahd a sharp-nosed version with a heavily machined

roughness. These configurations resembled the stable shapes of nose cones which have undergone laminar and turbulent ablation. High Reynolds number test conditions which closely simulate aerodynamic re-entry values were selected. Comparisons have been made of the measurements of heat transfer rate with currently used engineering predictions of heat transfer rate. Measured pressure distributions and shock shapes agreed well with proven inviscid theories. The boundary layer measurements on the smooth models at M ~ 20 conformed to laminar behaviour. Model surface roughness appeared to promote turbulent flow. The shock-wave on the 50° half-angle cone at 10° incidence

remained unexpectedly attached to the nose even though subsonic flow was formed on the windward side.

In the design of thermal protection components

for re-entry vehicles, i t is critical to have dependable heat transfer coefficient correlations available over the range of conditions encountered. Before tackling the problem of under-standing the processes in for instance a highly blown boundary layer with ablative thermal protection, it is necessary to correlate basic pressure and heat transfer results under non-blown hypersonic flow conditions. However, there is a lack of dependable pressure distribution and heat transfer measurements on entry vehicle front al sections under hypersonic freestream conditions with which to test analyses. Data is required

particularly within the most critical regions of sub-orbital or orbital re-entry which are defined by maximum vehicle

deceleration and maximum surface heating. These regions occur at aerodynamic conditions of high Reynolds number between Mach numbers of 15 and 20. The Longshot Facility of the von Karman Institute for Fluid Dynamics was specifically designed to provide such testing conditions by operating at reservoir pressures up to 4,000 atmospheres. At the above-mentioned Mach numbers, the wind tunnel can provide simulation of both the Reynolds number and the convective. heating experienced by full-scale lifting re-entry vehicles such as NASA space

shuttle and components (e.g. nose sections) of re-entry

vehicles which have a high ballistic coefficient. This paucity of experimental data on simple nose shapes tested in this flow regime motivated the series of tests described in the following sections.

A tests series, in ~hich were taken pressure distri-bution, heat transfer rate distribution and Schlieren photograph

flow visualisation measurements on several axisymmetric bodies, was conducted in the nitrogen test flow of Longshot. The

2

-and surface textures developed on ablating nose sections entering the earth's atmosphere. The models included (1)

two metallic hemisphere bodies with nose radius RN

=

3.5 inches, one model having a smooth surface. the other having a uniform surface roughness typical of an ablated graphite material;

(2) two sharp-nosed metallic 50° - 8° biconic models of 7.0 inch base diameter, one with a smooth surface, the other with a

uniform surface roughnes5 typical of an ablated plastic composite material; and (3) a blunt-nosed metallic 50° - 8° biconic

model with RN

=

0.75 inches and a smooth surface. In Fig.1, the degree of roughness of each model surface is compared to the typical roughness heights of various materials used on nose sections af ter having undergone ablation. Photographs of the two models with roughened surfaces are shown in Fig.2.

The experimental data recorded in this study is compared with current engineering theories suggested in a review of ablation phenomenology by Minges (Ref.l). Laminar heat transfer rates are compared with the reference enthalpy method of Eckert (Ref.2) and the local similarity solution of Lees (Ref.3) using the stagnation point correlation of Fay and Riddell(Ref.4). The heat transfer measurements are also compared against two turbulent theories, the Sommer and Short reference enthalpy method (Ref.5) and the semi-empirical

method of Spalding and ehi (Ref.6). All these theories have proven useful in many compressible flow applications and the interest here is to examine their validity under more severe conditions. For instance the boundary layer on a 50° half-angle cone tested in the M

=

20 flow of Longshot develops in an M

=

1.5 flow-field with a stream temperature of the order of 2,3000 _{K and a wall temperature of 300}0

K. These conditions are outside the range in which these empirical theories were originally correlated or verified.

This paper has a two-fold purpose in firstly outlining the ability of the Longshot facility combined with its

instrumentation in achieving good quality measurements in a unique ground-simulated re-entry environment and secondly in discussing the new aerodynamic data obtained to date.

4

-11. MODEL INSTRUMENTATION AND CALIBRATION

The five models supplied by AVCO Corporation vere fitted with heat flux gauges and pressure taps. Ten heat

gauges were mounted axially along the model surface beginning at or near the geometrie stagnation point. Seven pressure taps on each model vere similarly spaeed along the surface but at 1800 around .the model from the rov of heat transfer gauges.

The heat flux gauges constructed by Bolt, Beranek and Newman, U.S. were of the calorimeter variety. The heat sensor was a 0.004 inch copper disc on the back face of vhich a chromel-alumel thermocouple junction approximately 0.0015 inch diameter had been welded using 0.001 inch vires. The discs

had diameters of both 0.125 inch and 0.110 inch and vere bonded to an insulating hol der as shown in Fig.3. All gauges were contoured to the local body configuration. Output signals

fr om the calorimeters were recorded on Tektronix oscilloscopes af ter pre-amplification. Typical heat flux assemblies vere calibrated in the AEDC (U.S.A.) radiant heat flux calibration facility. The purpose was to obtain for a given set of standard material properties, the ave rage gauge assembly effective

thickness to be used in the reduction analysis of the heat flux data. Of six gauges tested, this average thickness was found to be 5% below the actual disc thickness. The maximum deviation, hovever, varied from + 4.8% to - 12.6% in actual thickness.

The transducers used for sens~ng pressures fr om the models and from a Pitot probe situated near the models vere

Hidyne types Wand HR variable reluctance diaphragm differential pressure gauges. The reference side of the transducer was kept at about 1 micron of mercury during a test. CEC and Vibrometer carrier amplifiers of 20 kHZ and 100 kHz carrier frequency respectively were used to process the signals vhich vere

recorded on a multiple channel CEC oscillograph with a paper speed of 100 inches/sec. using CEC galvanometers with a 5 kHz response. The lengths of the pipes to the pressure taps on the models were kept to a minimum such that the internal volume of the complete pressure system was small enough to

g~ve a pneumatic response which matched the electronic response time of less than a milliseconde Each complete measuring system was calibrated befo're each test against a mercury or a Betz-type water manometer with the reference side of the gauge at atmospheric pressure. The calibration pressure was applied to the transducers such that the diagram deflected in the same direct ion as in the test. The electronic amplification of each system was adjusted in each test such that the predicted pressure would deflect the oscillograph trace by 20 to 30 mmo The calibration plots were generally so linear that errors incurred in using a constant calibration factor were smalle

6

-111. TEST FACILITY AND RAW DATA CHARACTERISTICS

A schematic of the Longshot wind tunnel is shown in Fig.4. Longshot differ~ from a conventional gun tunnel in that a heavy piston is used to compress the nitrogen test gas to very high pressures and temperatures (Ref.7). The test gas 18 th en trapped ln a reservoir at peak conditions by the

closing of a system of check valves. The flow conditions decay mo· notonically during 10 to 20 mmlliseconds running times as the nitrogen trapped in the reservoir flows through the

6°

half-angle conical nozzle into the pre-ev~uated open jet test chamber.

The maximum supply conditions used in these tests are approximateJ 4000 atmospheres at 2,4000_{K. These provide unit Reynolds}

numbers of

6

x 10 6 and 3 x 10 6 per ft at nominal Mach numbers of 15 and 20. Tests at M • 20 with a lower Reynolds number of 2 x 10 6 per ft were also employed in this series. The two Mach numbers were obtained at the 14 inch diameter nozzle exit plane by using throat inserts with different diameters.

The reservoir pressure was measured uSlng a Kistler piezo electric gauge. A typical trace shown in Fig.5 i~lustrates

the pressure decay during a run. The reservoir temperature was estimated from the output of a tungsten-rhenium thermocouple mounted in the wall. The slow response of the gauge is

illustrated in Fig.5. It is seen t~at the thermocouple bead did not reach equilibrium with its surroundings until approxi-mately 20 milliseconds from the peak conditions. A simple thermodynamic relation between the pressure and temperature of a gas escaping through an orifice from a constant volume reservoir was combined with the information ot the measured temperature at 20 milliseconds to calculate the temperature

vari&ti~n ~rougn~~t the run. Experimentally determined

corrections for conduction and radiation losses were also made. The method is described more fully in Ref.8. The accuracy of the temperature and pressure measurements is estimated to be 4% and 5% respectively.

The model wal 1 pressure variation is also shown in Fig.5 to be qualitatively similar to that of the reservoir pressure. In the same figure the heat gauge signal illustrates the gradual temperature rise of the calorimeter as i t sensed the heat transfer. Normally the time dependent heat transfer was determined fr om this trace by measuring the signal slope at the selected time and multiplying i t by the instrumentation calibration factor. Because of the computational inaccuracies of numerical ditferentiation, a more satisfactory method was devised in which an equation for the expected qualitative heat transfer variation (estimated fr om tunnel calibrations) was integrated to generate a set of transient temperature readings which were compared to the experimental output of the heat gauge. Excellent re-construction of the thermocouple output could be achieved af ter several selections of the peak heat transfer rate had been made. The method is described in full in Ref.8. The accuracy of the pressure and heat transfer measurements are within ± 5% and ± 10% respectively. The accuracy of the heat transfer measurements is conditioned primarily by the difficulties in welding the thermocouples to the calorimeter discs, and was estimated from calibrations of sample gauges as described in Section 11.

A typical schlieren picture recorded with the Longshot's 18 inch single pass Toepier schlieren system illuminated by a one microsecond spark is shown in Fig.6.

a

-IV.MEASUREMENT RESULTS

Typical pressure and heat transfer distributions measured on each of the five models are presented in Figs.7 to 10. A more complete record of the test results is given in Ref.a. The results are compared to appropriate theories more fully explained in the following section. Such comparisons have been made to assess the quality of the measurements and to illustrate the effects of conicity on them. Each model configuration is examined in turn.

Hemisphere models

Fig.7a shows the pressure distribution for all the five test runs on the smooth and rough hemispheres, non-dimensionalised by a Fay and Riddell stagnation point value. The results vere compared with the theory of Belotserkovskii (Ref.9) with and without a correction for flow conicity.

From examination of the theoretical curves, the correction for conicity can be seen to be important away from the nose of the model. The experimental spread of the non-dimensionalised data lay within a region of 3% of the stagnation point pressure and was in excellent agreement with the conicity-corrected

theory. Typical heat transfer rates measured on the smooth hemisphere are shown in Fig.7b compared with the laminaa

similarity theory of Lees (Ref.3) corrected both for conicity and for a Belotserkovskii instead of a Nevtonian pressure distribution. Within the first 30 degrees from the stagnation point, the measured values were higher than the theoretical value. This discrepancy, as yet unexplained, is contrary to tests on the blunt biconic model and in other reported tests (Ref.7). At angles larger than 30°, the measured values were smooth and agreed well with laminar theory, as expected.

Smooth sharp-nosed model

at zero inc idence, non -dimens ionali sed wi th. respect to the freestream dynamic pressure in the plane of the nose and

compared to Newtonian and tangent cone theories. These theories were corrected for source floweffects by including both

changes of flow angularity at locations away fr om the nozzle centre-line and changes in streamwise flow parameters, as

was done in theories used for hemispheres.. Numerical extrapolations of the tables of Jones (Ref.10) from cone half-angles of 40°

were used for calculating the tangent cone theory. The conicity correction was as high as 10% at the end of the 50° cone

surface. The measurements were smooth and agreed to vithin a few per cent with the corrected tangent cone theory which itself predicted pressures roughly 5% above Nevtonian theory. The heat transfer measurements for the same run is shown in Fig.Bb. Laminar Eckert reference enthalpy theory (Ref.2)

was chosen to provide a qualitative comparison to the measurements. The measurements, if smoothed, gave the correct trend with

theory; however, humps existed which occurred consistently at the same position on the model for all the tests on this model. These humps were not expected to be caused by freestream flow irregularities in view of the regularity of the pressure data, and vere thought to be caused mainly by the neglect of individual heat gauge calibration.

Smooth blunt-nosed biconic model

A typical pressure distribution is shovn in Fig.9a to agree well with Belotserkovskii theory (for the spherical nose surface) and tangent cone theory (fer the cone) both being corrected for conicity. The flow appeared to ree over from the over-expansion on the spherical surface before reaching the first gauge on the conic surface. The data scatter was smalle Heat transfer rates shown in Fig.9b were reasonably smooth and consistent with Eckert theory.

Stagnation point heat transfer rates agreed to within 5% of the theory of Fay and Riddell (Ref.4).

- 10

-Macro-roughness biconic model

The pressure measurements on this model are compared with smooth-model data in Fig.l0a. The large data scatter

was probably due to viscous-inviscid interaction of the large roughness elements with the flow since the pressure taps were located in arbitrary positions with respect to the roughness elements. The heat transfer data shown in Fig.lOb exhibits similar scatter. These latter results illustrated that extreme care must be taken in select ion and location of instrumentation in order to gain illuminating data from rough-surfaced modeIs.

From these assessments of data, it is concluded that the pressure measuring technique used produces results which show l i t t l e data scatter and are consistent with well-proven prediction methods. It is likely that the larger data scatter observed with the heat transfer measurements can be reduced by individual calibration of the gauges. Conicity

corrections of up to 10% of mea~ured quantities were found

necessary; however the simplified correction procedures

employed appear to adequately describe the flow behaviour. It can be interpreted from this conclusion that conicity does not measurably affect the flow features under examination.

V. DISCUSSION OF RESULTS

The measurements that are the most accurate and

that would be expected to agree with well-proven and insensitive predictions are those of pressure and shock shape. A simplifi-cation in applisimplifi-cation of theory lay in the boundary layer thickness being so insignificant under these test conditions that the flow was considered inviscid. Success in such

comparisons provided the ground work for the more interesting but less well understood viscous phenomena of convective

heat transfer. It was shown in the last section and in further tests on cone models at ± 100 _{incidence (Ref.8) that pressure} measurements agreed satisfactorily well with theory. Also in Ref.8, it was shown that the shock angles to all the sharp and blunt cone surfaces . (in the latter case, far downstream from the blunt nose) at angles of attack 00 _{and ± 10}0 _examined agreed with cone tables of Ref.10 to within 1/2 degree.

The measured shock stand-off distance for each test on the blunt models (biconic and hemisphere) is shown to compare well with the theory of Van Dyke and other experiments

(Ref.11) in Fig.11.

An interesting flow feature brought out from the flow visualisation over the 500 _{half-angle biconic surfaces} at a positive angle of attack to the stream (i.e. surface at

600 _{to the flow)was that the shock remained attached to the nose,} despite the fact that a 600 _{half-angled cone in a Mach 20}

flow would have a detached shock. The flow behind the attached shock on the windward side was subsonic, whilst flow on tne "leeward side" was supersonic. This implies that there

occurred a sonic line (or surface) similar to that around a cylinder (at right angles to the flow) or sphere as the flow expanded around the cone. At even higher angles of attack, the shock would undoubtedly detach from the nose forming a

- 1 2

-third flow phase. This is illustrated schematically in Fig.12. As yet, no measurements (and it is believed no calculations) have been made to locate the boundaries of these flow phases.

In Fig.13 three heat transfer theories are compared with experimental results on the smooth sharp-n08ed biconic model at zero incidence in a Mach 20 flow. These are the laminar Eckert theory, and the turbulent Sommer and Short

reference enthalpy and Spalding and Chi semi-empirical theories. It was assumed for the turbulent theories that the virtual

origin of the turbulent boundary layer occurred at the nose of the body. The measurements were generally in agreement with the laminar theory, although many of the data points also agreed well with the Spalding-Chi theory. The proximity of the laminar and turbulent predictions was a reflection of

•

•

the fact that the Reynolds number on the surface 18 so low that turbulent flow was unlikely to be naturally achieved. The same conclusion was made in Ref.8 for all the tests on both the pointed and blunt smooth surfaced models at M • 20 at

all incidences examined. Data from the rough model was plotted on the same figure. Ignoring the two very low data points

(sinee these could have been caused by a separated flow) the measurements lay above the smooth model results. The spread of the two turbulent heat transfer predictions encompassed portions of the data as well as portions of the laminar

curve thus making it difficult to assess whether the boundary

• The surface Reynolds number was low despite the high value of the freestream Reynolds number because of the high statie temperature (~20000K) of the flow outside the boundary

layer caused by the high incidence of the surface to the freestream.

layer was laminar or turbulent. One interpretation is that the boundary layer on the rough model was turbulent, however it is not unknown that high values of heat transfer can be caused by roughness elements whilst the flow remains laminar. Richards (Ref.12) has put forward the explanation that roughness elements can transfer,by mixing processes, high energy flow fr om the outer part of the laminar boundary to the layers immediately adjacent to the surface thus causing higher heat transfer rates but without causing turbulent flow. A test carried out in the higher Reynolds number flow of

Longshot at M

=

15 however showed more convincing evidence

that the macro-roughness elements caused turbulent flow (Fig.14). The heat transfer results were more easily discernible to

be in agreement with the turbulent Spalding-Chi theory. It is intended to carry out additional tests at an even higher

Reynolds number at M = 15 on the smooth model when it is expected that measurements of naturally occurring turbulent boundary layers will help to confirm this conclusion.

Measurements of heat transfer on the chemically etched rough hemisphere body at M

=

15 are illustrated in Fig.15. These rough body results again showed considerable scatter (as in similar tests at M

=

20) and illustrated once more that viscous-inviscid behaviour is important.

Higher non-dimensional heat transfer rates than on the smooth model have been measured which may be attributed to turbulent boundary layer behaviour. As yet a theory has not been

developed in this programme to predict the turbulent heat transfer on a hemisphere.

- 1 4

-VI. CONCLUDING REMARKS AND FUTURE PLANS

The combination of the Longshot facility and its instrumentation has generated good quality pressure, heat transfer and shock shape data on models resembling entry vehicle frontal sections at the high Reynolds number, high Mach number conditions necessary to simulate the critical region of atmospheric re-entry. The freestream conditions used vere Reynolds numbers of 2 to

6

million per foot at Mach numbers from 15 to 20. More accurate heat transfer rates were expected to be achieved by individual calibration of the heat flux gauges mounted in the modeIs. Source floweffects due to the use of a

6°

half-angle conical nozzle vere not negligible; hovever, for these model configurations, they appeared not to be large enough to obs~ure the main features of the flow

under examination. Simple corrections to the theories adequately compensated for the observed discrepancies.

Pressures and shock shapes we re in good agreement vith veIl proven inviscid theories. This was in accord with the information that the boundary layer thickness on these surfaces at high incidences to the flow was negligibly small. The shock shapes on biconic models at incidence indicated that the flow on the vindward side of the model was subsonic even though the shock remained attached at the nose. This suggests a flov phase unknown to the authors which deserves further study.

The heat transfer measurements on the smooth bodies at M

=

20 were representative of those expected of a laminar boundary layer. Roughness could have caused turbulent flov at the M

=

20 cases; however, the turbulent predictions of

heat transfer vere too close to laminar theory to differentiate the behaviour of the data ~n this flow region. The turbulent theories differed as much between themselves as between the

laminar theory. At M ~ 15, when the Reynolds number was higher, the heat transfer results on the roughened model suggested

that a turbulent boundary layer was present. Further investi-gations will be carried out at M

=

15 and Reynolds number of

9

x 10 6 per root when i t is expected that naturally occurring boundary layers will be formed. Further tests with more

careful consideration of the roughness effects on heat flux measurements will also be carried out. One such consideration is to continue the roughness onto the gauge itself. As

additional experimental results become available, detailed intercomparisons of analytical inviscid flow transport

coefficient theories will be made applying more sophisticated techniques along with the engineering correlations described and used above.

- 16

-ACKNOWLEDGEMENTS

The authors vish to thank Mr. Jos Slechten of VKI andDott. Salvatore Culotta of the University of Palermo for their inputs into this programme. The earlier vork of

Professor Kurt Enkenhus (nov of NOL, Maryland, U.S.A.) on the Longshot contributed greatly to the success of the testing capabilities. Mr. Jean Hugé and Mr. Fernand Vandenbroeck of VKI ensured the smooth running of th Longshot. Finally thanks are due to Mademoiselle Lysiane Abbott, vho typed the manuscript.

1. Minges, M.L. : "Ablation phenomenology" (A review) High Temperatures - High Pressures, 1969, VOl.l, pp.607-649.

2. Eckert, E.R.G. : "Survey on heat transfer at high speeda" University of Minnesota, ARL 189, Dec.1961.

3. Lees, L. : "Laminar heat transfer over blunt-nosed bodies at hypersonic flight speeds", Jet Propulsion

April 1956, pp. 259-269.

4.

Fay, J. A., Riddell, F. R. : "Theory of stagnation point heat transfer in dissociated air", Journalof Aerospace Sciences, Vol. 25, 1958, pp. 73-85. 5. Sommer , S. C ., Short, B. J. : "Free fl i ght measurement s

of turbulent boundary layer skin friction in the

presence of severe aerodynamic heating at Mach numbers fr om 2.8 to 7.0", NACA TN 3391,1955.

6. Spalding, D.B., Chi, S.W. : "The drag of a compressible turbulent boundary layer on a smooth flat plate with and without heat transfer", Journalof Fluid Mechanics, Vol.18, part 1, pp. 117-143, 1964. 7. Richards, B.E., Enkenhus, K.R. : "Hypersonic testing 1n

V.K.l. Longshot piston tunnel", AlAA Journal, Vol.8, No.6, June 1970, pp. 1020-1025.

8. Richards, B.E. Culotta, S. Slechten, J. : "Heat transfer and pressure distributions on re-entry nose shapes in the VKI Longshot hypersonic tunnel"

A.F.M.L. Report No.71200, June 1971.

9. Hayes, W.D., Probstein, R.F. : "Hypersonic flow theory" 2nd edition, Vol.1, Academic Press, 1966, p. 423. 10. Jones, D.J. : "Tables of inviscid supersonic flow about

circular cones at incidence y

=

1.4", AGARDograph 137, November 1969.

11. Truitt, R.W. : "Hypersonic Aerodynamics", The Ronald Press Company, 1959, p.269.

12. Richards, B.E. : "Transitional and turbulent boundary layers on a cold flat plate in hypersonic flow" Aeronautical Quarterly, Vol.18, Pt.3, August 1967, pp 237-258.

SILICAI PHENOLIC

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o

AND O~

__

~~

______

~

____

~

______ _

0 1 2 3 4

DISTANCE FROM STAG. Pl./ NOSE RADIUS

o

Fig.9a - PRESSURE

DISTRIBUTION ON

BLUNT

"

NOSED

MODEL AT

ZERO

1.0

M=20

J

RE/FT= 3Xl0

\

\

- - -

LEES

SIMILARITY THEORY

\

0.8

\

0\

ECKERT

q

qSTAG

.

\

0

EXPERIMENT

0.6

\

,

,

0.4

,

"-"

_""

0::

'

...

...

w

0.2

0 ..J :::J 0

:r

(J')

0

1

2

3

4

5

DISTANCE

FROM

STAG. PT. / NOSE

RADIUS

Fig.9b-HEAT TRANSFER DISTRIBUTION ON

BLUNT NOSED MODEL AT

ZERO

I Nel DENC E

-

.c

=

6

UJ

cr

:::> V') V')

~

4

a..

o

UJ

cr

2

:::> cJ') <{ UJ ~

o

• •

o

_o

•

• SMOOTH MODEL

•

_o

o

ROUGHENED MODEL o~~_

... _...-_____ ...

o

2 3

4

DISTANCE MEASURE FROM TIP (IN.)

Fig.l0

a -

PRESSURE

DISTRIBUTION ON

ROUGH

SURFACED

BICONIC

200

u

~100

N ~

u..

80

-

::;

.c.

~.

60

al

w

~

40

cr

cr

30

w

u..

(/)

z

<{ ~

20

~ <{

w

:r

ECKERT

o

EXPERIMENT 10~

__

~

____________

~

__

~

____

~

__

~

OS

10

DISTANCE

Fig.l0b-HEAT TRANSFER DISTRIBUTION ON

ROUGH SURFACED BICONIC MODEL

0

.

8

0.6

-

I

0.4

--

_0.2

- - VAN DYKE { EXPERIMENTS

o

REVIEWE 0 IN TRUITT (REF. 11 ) b ll. PRESENT RESULTS ON

BLUNT CONE & HEMISPHERE MODELS

0.1 ~ ______ ~~ ______ ~ ____ ~ __ ~~ ________ ~

2

4

6

8 10

20

MACH NUMBER

SHOCK ATTACHED SUPERSONIC FLOW BEHfND SHOCK a) ____ ~

+

-b)

c)

---SHOCK ATTACHED SUPERSONIC FLOW ON "LEEWARO" SURFACE SUBSONIC FLOW ON WINDWARD SURFACE SHOCK DETACHED

FIG.12. THREE FLOW PHASES OF A 50°

CONE AT VARYING ANGLES OF

:H

--

_::::>

.

100 CD

80

UJ

60

~ <{

cr

cr

UJ U. IJ') Z <{

cr

~ ~

40

30

<{ 20 UJ I

-

....

----

--....

-

---

-

....

-

_....

--

_.

_-

_""-

_....

- - - _ _ 0

----.

-~

• •

•

SOMMER - SHORT SPALDING - CHI ECKERT

o

EXPERIMENT I SMOOTH MODEL

• EXPERIMENT I ROUGH MODEL

REYNOLOS NUMBER

Fig.13 - HEAT TRANSFER ON

SHARP- NOSED

BICONIC MODEL - COMPARISON WITH

THEORY

500

_M

₌

₁₅

_{RE / FT}

₌

₆

_x

_{10 6}

400

~

300

In

--

=!

200

---

...

.

---

----

---

...

-

-...

---

...

---

_o

_---..

_{- 0 -}

o

w

0

0

...

₁₀₀

<t

a::

- - - 5CH-AMER - SHORT

a::

80

_{_ _ _}

_{SPALDING - CHI}

w U-V')

60

z

ECKERT

<t

a::

...

0

EXPERIMENT

...

₄₀

ct W I

30

4

₂

₃

₄

₆

NUMBER

Fig. 14 - HEAT TRANSFER ON ROUGH -SURFACED

-

CORRECTED LEES

0

TH EORY

:x:

1.5

....

-

c.!)

0

<(

....

c./)

0

0

~

-

1.0

...

~

O.S

o

0

o

o

o~

______

~

________

~

______

~

o

30

60

90

ANGLE SUBTENDEO

BY

GAUGE

TO

AXIS (DEG.)

Fig. 15 - HEAT

TRANSFER

DISTRI BUTION ON