Hypersonic heat transfer measurements on reentry vehicle surfaces at high Reynolds number

-1

t El

t.

van KARMAN

INSTITUTE

FOR FLUID DYNAMICS

TECHNICAL NOTE 91

HYPERSONIC HEAT TRANSFER MEASUREMENTS ON REENTRY VEHICLE SURFACES

AT HIGH REYNOLDS NUMBER

B.E. RICHARDS

JUNE 1973

K!:.!}'VC-''/ê:;) 1 - O:::"FT

~!~

-~O~-

RHODE SAINT GENESE BELGIUM

von KARMAN INSTITUTE FOR FLUID DYNAMICS

TECHNICAL NOTE 91

HYPERSON IC HEAT TRANSFER MEASUREMENTS ON REEN TRY VEHICLE SURFACES

AT HIGH REYNOLDS NUMBER

B.E. RICHARDS

JUNE 1973

Bibliotheek TU Delft

Fac. Lucht- en Ruimtevaart

FOREWORD

The activities and results documented in this report were supported under Project 7381, "Materials Applications

Useful in USAF Weapon Systems", Task 738102 "Space, Missile and Propulsion System Materials and Component Evaluation" with

Mr. Gary L. Denman, Technical Manager for Thermal Protective Systems, Systems Support Division, Air Force Materials Labora-tory, acting as project engineer. The report covers work

conducted during the period June 1971 through July 1972.

The technical advice and guidance of Mr. Victor

DiCristina, Manager, Thermodynamics and Material Test Department, AVCO Systems Division, AVCO Corporation, Wilmington, Massachusetts

in the areas of model design and instrumentation was particularly valuable. The author would like to acknowledge the help of

Mr. Jos Slechten and Mr. Cyriel Appels for their contribution to the data reduction of the data, Mr. Jean Huge and Mr. Fernand Van de Broek who operate the Longshot facility, and other members of the technical staff of the Institute. Miss D. Sandford

type d the manuscript.

-ABSTRACT

Heat transfer rates, using calorimeter sensors, and pressures, using variabIe reluctance diaphragm transducers, have been measured on five model shapes in the VKI Longshot facility at Mach numbers of 15 and 20 and over a unit Reynolds number range of 2 x 10 6 to 7 x 10 6 per foot. Two basic shapes, a hemisphere and a 50° - 8° half angle biconic configuration with and without nose bluntness, were tested with different surface roughnesses. Pressures were weIl predicted by the theory of Belotse:rkovskii.fur spherical surfaces, and tangent cone theory, using the tables of Jones for conical surfaces. Laminar heat transfer rates, slightly underpredicted _by

Eckert Reference Enthalpy ·method on cones and reasonably weIl predicted by Lees similarity theory on hemispheres, were gene-rally achieved for the tests at M

=

20 which used low Reynolds numbers. Turbulent heat transfer rates, overpredicted by

Sommer and Short Reference Enthalpy method on a smooth wall by 10

%

and underpredicted by the same method for walls with

0.004 in roughness by 15

%,

were measured on the 50° half angle forebodies of the biconic models tested at M

=

15 high Reynolds number. Transition was completed by the first gauge on the rough model and by the fourth gauge on the smooth model.

-FORE'~ARD ABSTRACT LIST OF LIST OF TABLE OF CONTENTS

...

...

ILLUSTRATIONS . . . . TABLES . . . . • • . . . • . . . • . . . I. INTRODUCTION . . . • .

11. MODEL INSTRUMENTATION AND CALIBRATION . . . . 111. TEST FACILITY . . . • . . . .

IV. MEASUREMENT RESULTS . . . . 1. Hemisphere models (D and E)

...

2. Smooth sharp-nosed biconic model A . . . . • • . . .

3.

Rough biconic models (F and G)

...

V. CONCLUSIONS . . . • REFERENCES APPENDIX TABLES

...

i i i i i i iv v 1 3

4

5

5

6 9 1 1 13 1

5

17

LIST OF ILLUSTRATIONS

,. Details of models . . . 24

2. Pressure distributions on smooth hemisphere, M=20 . . . . 25

3. Pressure distribution on rough hemisphere, M=20

...

4.

Pressure distribution on rough hemisphere, M=15

...

5 • Heat transfer distribution on smooth hemisphere, M=20

6.

Heat transfer distribution on rough hemisphere, M=20

.

7.

Heat transfer distribution on rough hemisphere, M=15

.

8.

Pressure distribution on sharp smooth biconic model

25

26

27

27

28

M= 1 5 an d 20 • . . . . • • • . • • . • . • • • . • • • . . • • • • • ~ . • • • • ••

28

9. Heat transfer rate on smooth biconic model (Raw data) 10. Heat transfer rate on rough biconic models (Raw data) 1,. Heat transfer rate on smooth sharp biconic model

( Smoothed data)

...

12. Comparison of heat transfer data on smooth and rough

sharp biconic models (Smoothed data) . . • . . . • . 13. Heat transfer on rougt sharp biconic model at a=10

(Srnoothed da.ta) .. : . . . .

14. Heat transfer rate on rough blunt biconic model

(Smoothed data) . . . .

15. Pressure distribution on sharp rough biconic model, M= 1

5 . . . .

16. Pressure distribution on blunt rough biconic model,

M= 1

5 . . .

.

- J.V

-29

30 31 32 33 34 35 35

LIST OF TABLES

1. Heat transfer sensor calibration constants

17

2. Estimated test conditions at nose of model at time,

t=O msecs from peak . . . • . . . 18

3. Typical test section conditions . . . • . . . • . . . • • • . . 19

4.

Pressure measurements on hemisphere models D and E . 20

5.

Pressure measurements on biconic models A, F and G 21

6.

Heat transfer measurements on hemisphere models D .

an dE • . . . • . . • • . . . • 22

7.

Heat transfer measurements on biconic models A,

23

F and G, time t=o msecs • . . . • . . . .

-I. INTRODUCTION

In the design of thermal protection components for

re-entry vehicles, it is critical to have dependable heat transfer coefficient correlations available over the range of conditions encountered. Before tackling the problem of understanding 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 frontal sections under hypersonic freestream conditions with which to test analyses. Data is required particularly within the most citical regions of sub-orbital or orbital re-entry which are defined by maximum surface heating. These regions occur at aerodynamic conditions of high Reynolds number betwéen Mach numbers of 15 and 20.

Following a first test series, reported in Ref. 1, more tests, in which were taken pressure and heat transfer rate distributions and schlieren flow visualisation photographs on several axisymmetric bodies, were conducted in the nitrogen test flow of Longshot. The models included

1. Two metallic hemisphere bodies with nose radius R

N

=

3.5.

in., one model having a smooth surface (designated model D), the other

(model E) having a uniform surface roughness (0.001 in. to 0.004 in.) created by a chem-etching process.

2. Two sharp nosed metallic 50° - 8° half angle biconic ~odels~

one model (model A) having a smooth surface, and the other having a uniform rurface roughness (0.004 in. to 0.005 in.) on the 50° co ne forebody created by flame-spraying with copper (model F). The sharp tip of the rough biconic model could be replaced by a rough spherical nose of 0.75 in. nose radius (model G) providing five configurations whicp were tested in this test series.

The experimental data recorded in this study is

compared with current engineering theories, suggested in a review of ablation phenomenology by Ming~ (Ref. 2), to assess transition~

point from laminar to turbulent flow. Laminar heat transfer rates are compared with the reference enthalpy method of Eckert (Ref. 3) and the local similarity solution of Lees (Ref.

4)

using the

stagnation point correlation of Fay and Riddell(Ref.

5).

The

heat transfer measurements are also compared against twà turbulent theories, the Sommer and Short reference enthalpy method (Ref.

6)

and the semi-empirical method of Spalding and ehi (Ref.

7).

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 500 _{half-angle cone tested in the M}

=

_{20 flow of Longshot}

develops in a 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. The comparison will also be used to assess the position of transition.

11. MODEL INSTRUMENTATION AND CALIBRATION

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

transfer gauges were mounted axi&lly along and flush with the model surface beginning at or ne ar the geometrie stagnation point. Seven pressure taps were similarly spaeed along the surface but at 1800 _{around the model from the row of heat}

transfer gauges. The models are illustrated schematically in Fig. 1. Details of the heat and pressure sensors used, their

calibration and associated recording equipment is given in Ref. 1.

The heat sensors mounted in the rough models differed from those mounted in the smooth models as described in Ref. 1 by the

calorimeter disc being 0.008 in. thick and roughened to

approximately the same extent as the model surface. The exposed surface of the insulating holder was also roughened. Most of the heat gauges were calibrated in the AEDC radiant heat flow

calibration facility before mounting. The gauges were calibrated over a heat flux range from 20 to 80 B.T.U/ft2sec. The

111. TEST FACILITY

The VKI Longshot test facility was used for this program. Longshot differs 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.

8).

The test gas is then trapped

in a reservoir at peak conditions by the closing of a system of check valves. The flow conditions decay monotonically during 10 to 20 milliseconds running times as the nitrogen trapped in the

reservoir flows through the

6°

half-angle conical nozzle into

the pre-evacuated open jet test chamber. The maximum supply

conditions used in these tests are approximately 4000 atmospheres

at 20000 _{K to 2,400}0

K.

_{These provide unit Reynolds numbers of}

7

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 1n. diameter nozzle exit plane by using throat inserts with different diameters.

IV. MEASUREMENT RESULTS

The testscarried out on the five models are summarised in Table 2 listed in order of testing. Measured reservoir con-ditions and Pitot pressures at peak concon-ditions are given. Also tabulated are the calculated conditions of Mach number, Reynolds number, dynamic pressure and stagnation point heat

transfer on a 7 in. diameter hemisph~re.Three basic test section conditions vere used throughout. These were a high and a low Reynolds number case at M

=

20, and a low Reynolds number case at M

=

15. The peak condit i ons are revi ewëd i-n ~able ' 3 •

Pressure and heat transfer distribution measur~on each of the five models are presented in ~ables

4-7

and in

figures following Fig. 2. The results are compared to appropriate theories more fully explained in the ~ollowing section. Such

comparisons have been made to assess the quality of the measure-ments and to illustrate the effects of conicity on them. Each model configuration is examined in turn.

1. Hemisphere models (D and E)

Figs. 2-4 show the pressure distribution for all the three test runs on the smooth and rough hemispheres. The results were compared with the theory of Belotserkovskii (Ref. 9) includ-ing a correct ion for flow conicity. Generally the experiment al spread of the nondimensionalised data lay within a region of 3

%

of the stagnation point pressure and in excellent agreement with the conicity-corrected theory. This is in agreement with the earlier results of Ref. 1. Some scatter in the data from the rough model can be explained by the viscous-inviscid inter-action of the roughness elements with the flow.

The heat transfer rate on the smooth hemisphere are shown in Fig. 5 and on the rough hemisphere are shown in

Figs. 6 and 7 compared with the laminar similarity theory of Lees (Ref.

4)

corrected both for conicity and for a

Belotserkovskii (Ref.

9)

instead of a Newtonian pressure dis-tribution. Also shown in Fig.

5

are results of a test under similar conditions carried out in a previous test (Run

288

of Ref. 1) but with different gauges. Within approximately the first 30° fr om the stagnation point in all tests, the same trend was evident as fuund in Ref. 1 in that the measured values were higher than the theoretical values. This effect, as yet unexplained, is contrary to tests on the blunt biconic model and in other reported tests (Ref. 10). The Mach 20 flow case (Run 350) shows this effect

extended, inexplicably, further than its earlier counterpart

(Run

288)

up to 50°. For the Mach 15 high Reynolds number test on the rough body considerable higher values than laminar theory suggests (particularly in the region within 40° from the nose) were measured which indicates that turbulent flow on the model was achieved (Fig.

7).

2. Smooth sharp-nosed biconic model (A)

The wall pressure, nondimensionalised with respect to the tangent cone theory, for the three tests (Runs 354 to 356) are presented in Fig.

8.

Close agreement of the experiments with tangent cone theory is obtained for the cross-flow case

(Run 355) as weIl as the zero angle of attack cases, confirming and extending the findings of Ref. 1.

The heat transfer results of the three tests on model A are shown in Fig.

9

plotted against distance from the tip. Also shown are the laminar predictions using Eckert reference enthalpy theory (Ref. 3) for all three tests and the Sommer and Short

(Ref.

6)

and Spalding and Chi (Ref.

7)

theories for turbulent

flow for the M

=

15 test. The method of application of these

theories is described in Ref. 1 Appendix C. The M

=

20 tests

(Runs

354

and

355)

agree closely with the trends given by the

laminar theories, indicating (as in the previous tests at

similar conditions reported in Ref. 1) that the flow is indeed laminar.

On examination of the experimental points obtained in these two runs, one sees that the data scatter is similar from run to run. If one assumes that the heat transfer rate variation on a smooth body in a near uniform flow is without seatter then comparison of the data with theory shows that a particular gauge gives values which are consistently high, similar or low values compared to theory in consecutive runs. The same result is found on the rough biconic model, only the pattern of scatter along the model is different (see Fig. 10). Although most of the gauges were calibrated, this calibration was carried out before mounting them in the model, and one might conceive that the calibrations have changed slightly during mounting, or the gauges are very sensitive to mounting. This latter remark may be reasonable because of the extremely small dimensions of the boundary layer on the modelsurfaces. To examine this finding, correction

factors obtained by fitting the data from a selected test (Run

355)

to a best fit curve with the same slope as the theory, were applied to the data of the other tests and the results plotted in Figs. 11 and 12 (Figs. 12 and 13 for the rough sharp-nosed biconic model) against local Reynolds number are seen to be somewhat smoother. The correct ion factors applied to the data extended from

0.89 to 1.11 for the smooth model and 0.87 to 1.21 for the rough model.

For both Runs

354

and

355

(M

=

20 tests, plotted in

Fig. 1) the experiment al results are, on average, 10 per cent

above Eckert reference enthalpy theory. Run

354

is a repeat

test of Runs 209 and 210. The latter experiment al data reported in Ref. 1 are found, however, to agree weIl with theory. One reason for the difference in obse~vation is that the earlier runs used uncalibrated gauges and the calibration constant, obtained fr om calibrations of spare gauges, used was 0.715 (BTU/ft 2sec)/(mv/sec) whilst the average calibration constant for the latter tests was 0.77 (BTU/ft 2 sec)/{mv/sec), a differen-ce of

8

per cent. The specification of the gauges used in each series was similar. It was considered that the latter calibration constant was correct for both series of tests. Thus i t is

considered that repeatability was obtained and that the laminar Eckert theory underpredicts experiment by

8

to 10 per cent.

The assumption made to simplify the calculation of the inviscid flow over the cross-flow surface (i.e. 900 _{from the}

windward or "leeward" surfaces) of the 500 _{cone at 10}0 _angle

of attack as in Run 355 was that it was the same as that on a

500 _{cone at zero angle of attack. The smoothed results of Fig. 11,}

again show that the Eckert theory discrepancy as found in the ealier test (Run 354), and thus one can conclude that the above assumption can lead to a good assessment of the cross-flow heat transfer ratel

At M

=

15 and high Reynolds numbers, the test conditions of Run 356, the heat transfer variation near the tip plotted in Fig. 12 can be seen to be close to the laminar theory, but near the end of the cone forebody close to turbulent theory of Sommer and Short (Ref.

6)

and several times higher than the laminar prediction. This test shows that transition occurred in a region between one and ~wo in. from the tip.

It is also observed that the measured turbulent heating rate near the end of the cone is overpredicted by Sommer-Short by 10

%.

The measurements are also underpredicted by

Spalding-ehi by 30

%.

It 1S pointed out here that the range of conditions of Mach number, wall to recovery ratio, and Reynolds number

are out of the range of the correlations used in these empirical theories.

3. Rough biconic models (F and G)

The wall pressure, nondimensionalised with respect to the tangent cone theory, for the two tests (Runs 351 and 352) on the pointed model F are presented in Fig. 15. General agreement of experiment al data with tangent cone thoery is obtained,

although considerable data scatter is found which is again due to the layer of roughness sprayed onto the model in some cases distorting the geometry around the pressure ~aps. The

non-dimensionalised wall pressures on the blunt model G for the Run 353 are presented in Fig. 16 and again general agreement with Belotserkovskii (Ref.

9)

theory on the hemisphere part and tangent cone theory on the conical part of the model is obtained with similar scatter as on the sharp-nosed model.

The heat transfer results of the two tests on model F and the tests on model Gare shown in Fig. 11 plotted against distance fr om the tip. Also shown are the laminar and turbulent predictions as used for the smooth sharp-nosed model, zero

angle of attack case. On comparison of theory and experiment, i t is strikingly obvious that the data is turbulent over the

whole 500 _{half-angle cone forebody. As noted in the last}

sub-section a regular pattern of data scatter is seen. A similar

correction procedure is thus made (but this time the data of Runs 351-353 is smoothed to vary as the Sommer and Short theory

using Run 351) and illustrated in Figs. 12 and 13. It is seen from Fig. 12 that the measured heat transfer rate of Run 351 on the rough model is 15 per cent higher than the Sommer-Short prediction, and hence at least 25 per cent higher than the

smooth body result of Run 356 also shown on Fig. 12. Fig. 13, illustrating the results of heat transfer rate on the "leeward" side of the rough sharp-nosed biconic model at. 10° angle of attack similarly show that the experiment is 30 per cent over Sommer and Short theory. It is shown in the Appendix that the simple strip theory used for this angle of attack case may be in error.

The "smoothed" measurements from Fig. 10 of the heat transfer rate on the rough blunt-nosed biconic model Gare replotted in Fig. 14 against distance from the nose, non-dimensionalised with nose radius R

N. The results are compared with the sharp-nosed cone Sommer and Short turbulent theory, and Eckert and Lees laminar theory. It is seen that the laminar theory undergoes transition, from its laminar state on the

spherical nose, very gradually between gauges 2 and 5 achieving the heating ~ate as obtained on the sharp-nosed model at the end of the forebody.

V. CONCLUSIONS

Tests have been cariied out on 3 biconic and 2

hemisphere models in a M

=

15 and 20 flow in the VKI Longshot tunnel at unit Reynolds numbers from 2 x 10 6 to

7

x 10 6 . The data has been compared with simple engineering theories. The following conclusions can be made from the comparisons.

1. Pressure data on the biconic forebodies and the hemispheres agree very weIl with tangent-cone and

Belotser-kovskii theories where appropriate. More scatter was found on rough models than on the smooth due to interactions of the roughness

elements with the pressure holes.

2. The stagnation point heating on the blunt cone model agreed fairly weIl with the theory of Fay and Riddell, but some inexplicable high heating rates are found in the

7

in. hemisphere results. similar sized unexplained deviations fr om Lees' laminar similarity heat transfer theory within 30° fr om the stagnation point are found. At Mach 20 these data agree weIl with this latter theory further from the stagnation point. At a Mach 15, high Reynolds number ease higher heat transfer

rates than laminar theory over the whole surfaee, partieularly within 40° fr om the stagnation point ~uggest the presence of a turbulent boundary layer.

3. For M

=

,20, and hence low Reynolds number, tests laminar flow was maintained over the whole of the bieonic forebodies. The heat transfer rates measured for the cases of symmetrie flow and cross-flow on the forebody at 10° incidence were underpredieted by laminar Eekert reference enthalpy theory by about 10%.

4.

At M

=

15 and high Reynolds number, transition to turbulent flow occurred between one to two in. from the tip for the smooth-surfaced sharp-nosed biconic forebody model and

before half an inch from the tip on the equivalent rough surfaced

model. Sommer and Short reference enthalpy method overpredicted

the turbulent heating on the former case by 10

%

and

under-predicted the latter by 15%. Hence 25% more turbulent heating was caused by the presence of roughness which has a height from

0.004 ~n. to 0.0005 in. The transition point on the blunt-nosed rough-surfaced model was delayed over that found on the sharp-nosed equivalent model, but its turbulent heating rate was similar. The turbulent heating on the "l ees ide" of the sharp-nosed rough-surfaced model at 10° incidence was underpredicted by Sommer and Short theory by 30%. Some of this discrepancy may be due to the deficiency of the application of the theory in the lack of explanation of the boundary layer thinning due to cross-flow.

REFERENCES

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

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

2. Minges , M. L.: "Ablation phenomenology", (A review) High temperatures - High Pressures,

1969, vol. 1, pp. 607-649

3. Eckert, E.R.G.: "Survey on heat transfer at high speeds", University of Minnesota, ARL 189, December 1961

4.

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

April 1956, pp. 259-269

5.

Fay, J.A., Riddell, F.R.: "Theory of stap;nation point heat transfer in dissociated air", Journalof Aerospace Sciences,

vol. 25, 1958, pp. 73-85

6.

Sommer, S.C., Short, B.J.: "Free flight rneasurements of

turbulent boundary layer skin friction in the presence of severe aerodynamic heating at Mach numbers from 2.8 to 7.0",

NACA TN 3391, 1955

7.

Spalding, D.B., Chi, S.\.J.: "The drag of a compressible turbulent boundary layer on a smooth flat plate with and without heat transfer", Journalof Fluid Machanics, vol. 18, part 1, pp. 117-143, 1964

8.

Richards, B.E., Enkenhus, K.R.: "Hypersonic testing in VKI Longshot piston tunnel", AIAA Journal,

vol. 8, No 6, June 1970, pp. 1020-1025

9. Belotserkovskii, O.M. "The calculation of flow over axisymmetric bodies with a decaying shock wave", Translation from Academy of Sciences USSR, Compu-tation Center Monograph, 1961,

AVCO-RAD-TM-62-64, 1962

10. Richards, B.E., Enkenhus, K.R. "Stagnation point heat transfer and pressure distribution on a hemisphere at M = 15",

VKI TR 39, 1970

11. Jones, D.J. "Tables of inviscid supersonic flow about circular cones at incidence, y

=

1.4",

AGARDograph 137, part II, November 1969

12. Jones, D.J. "Tables of inviscid supersonic flow about circular cones at incidence, y

=

1.4",

APPENDIX

Further notes on the prediction of heat transfer rate on a sharp 50° half-angle cone

J. Slechten and B.E. Richards

Appendix C of Ref.1 describes a computer program to estimate the laminar and turbulent flow over a 50° half-angle cone 1n a hypersonic flow. The program calculates the inviscid flow over the cone by curve fitting tabulated data from Jones (Ref.11). At the time of Ref.1, the tables of Jones extended only to cone half-angles up to 40° and th us it was necessary to use extrapolations to the data. Since this work was reported, Jones has published another report (Ref.12) which extends the tables up to cone angles of 57 1/2° enabling interpolation to be used. Extrapolation was s t i l l necessary for the case of the 50° half-angle cone at 10° angle of attack, since subsonic flow would be produced on the "windward" side which case is beyond

the scope of the method used to generate the tables. Comparison ,

of the "extrapolated" calculations of the cone flow parameters with "interpolated" calculations of the cone flow parameters with "interpolated" calculations showed very little changes. In both calculations, however, some anomalies, occur, indicating that the simple approach used to predict heat transfer rates on cones at angle of attack is in error. These anomalies are illustrated

in the following table concerning the Longshot flow of M

=

20

with reservoir pressure of 60,000 psi and a temperature of

2,4000_K.

a

-10

0

0°

+10°

p (ps i)

3.1

,

6

5.24

6.61

e T e (OK) 2~340

2,203

2.749

u (ft/sec) e

4,138

4,495

2,838

M _e

1.279

1 .432

0.809

qlaminar ' (BTU/ft 2 sec)

94.7

1 1 7 • 0

104.8

qturbulent(BTU/ft 2 sec)

93. 1

129.2

101 .4

Re ( ft -1 )

2.23Xl0

s

3.69 x10

5

2.09xl0

s

Some of the results shown in this table look intuitively

wrong. For example: T (too high), M (too low) at a

= -

10

0 _;

e . e

heat transfer rates too low at a

=+ 10°.

The former anomalies are probably associated with the cross-flow effects. _{The 10'"} heat transfer rates at a

=

+ 10°

is probably associated with the application of a Man~ler transformation used in the program not being adequate to cope with the th inning of the boundary

layer due to the cross-flow. The conclusion of this appended note is that the simple approach used here for predicting heat

transfer rates on a

50

half-angle cone at

10°

angle of attack is not adequate. The solution of this problem will be

particularly complex because of the combination of

GAUGE TABLE 1 MODEL No

0

2

3

4

5

6

7

8

9

10

12

HEAT TRANSFER SENSOR CALIBRATION CONSTANTS (BTU/FT 2 SEC)/(MV/SEC)

-_

..

__

._._

-

-

_

..

_-

..

'

-_._----

- - -

-

- -

--_

.

_

._-

-

- .

A D E F G

1 .86*

0.77*'

0.77*

1 .6*

1 .86*

1 .91

0.78

0.64

1 .6·

1

.86*

1

.86*

0.735

0.83

1.

519

1 .857

1

.857

0.60

0.77

1 .796

1

.86*'

1 .86·

0.80

0.88

2.044

1 .826

1

.826

x

0.77 (0.89) 0.74

1 .6*

1

.747

1 .747

0.73

x

(0.90) 0.77*

1

.871

1 .950

1 .950

0.81

0.77

•

1 .757

1 .836

1

.836

0.77*

1 .609

1 .778

1 .778

0.77-

0.77"

1 .924

2. 196

2.196

o .

9 1

~--, ...

_--

-,..-

•.... -..

_-.---

- -

--.

-

-_

.. __ .-. .. -._---, ...

• uncalibrated gauges, average value used,

0.77

for model A,

1.86

for models F and G,

1.6

for model E

x gauge broke in test

354,

replaced with another gauge for

TABLE

g

: ESTIMATED TEST CONDITIONS AT NOSE OF MODELS AT TIME T

=

0 ms~cs FROM PEAK

RUN MODEL AVCO nrCIDENCE P T_o Pitot M ReX_10-6 _{qD q}

RUN 0 No. 350 D 2

+~o(cros.

]

355 A 4 58,900 2400 8.2 19.7 3.03 630 69.0 357 E ( 1 ) 3 -9 flow) 354 A 0 37,600 2250 5.0 19.5 2. 16 383 47.0 351 F 6 0

}

352 F 8 -10 353 G 7 0 55,000 2100 24.5 1 5.8 6.8 1893 82.3 356 A 0 358 E ( 1 ) ₅ 0

Units Pand pitot (1b/in

2 );

dynamic pressure, qD (1b/ft

2 );

T

(OK);

o 0

TABLE 3 TYPICAL TEST SECTION CONDITIONS

T(MS) _{PO (PS I ) TO (K)}

PI TOT (PS, )

MACH

NO POP (PS I ) TO P (K) _RE/FT p (PS I ) T(K)

_ruw

_{V( FT /S EC)} Q!H Lt3/FT **2) Q(BTU) TT2fl(K) _COW1ENSATION

CASE 1 _O.

_O

_.

_CO

_O.5.39000E

_OS

_{O. 2.40 00 0 E 0 4}

O.7G:J9g9E

Ol

_ 19.965 O.6.99723E

OS

O~ 3.09583E 04 O.2:l3812E 07 O.14302aE-OI _{C.383497E 02 O.173874E-04 0.8.2716 SE}

₀₄

U. 5.~ 4 815 E u3 _{0-6.71600 E} 02 0.2.7035 SE 04 O.3GG777E 02

CASE 2 o ~ 0.00 0.3.76000 E 05 0.2.2S000E 04 O.4699~9E

Ol

1~.6;8 _{O.3:J7990E 05 0.2.7 74 53 E 04 O.203557E 07}

o •

9.3086 1 E - 0 2 O.3.53(j90E

₀₂

_{O.118SS2E-04 C. 7 329171: 04}

O.3.63j40E

03 C ,I.G 1570 E 02 O.2.44:J4:JE 04 0.349571E ₀₂

CASE

3

0.000 0.5.50000 E CS _{O. 2.1C 00 OE} 04 _{0.245000E ·02}

15,360 0,7.% 3038E 05 O. 2.G J g 3 G E 04 0.6.39077 E 0 7 o,74710JE-01 _{0.5.26163E 02 C. 6. 39 G 0 6 E - 0 4 O.7G96ti!jE 04}

G.18~443E ('4 _{û.lC2047E 03 O. 2,3 S~ 2 OE C4}

0.4237tilE 02

Case 1 . Runs 350, 355, 357. Pitot a.t 1t$ cm from nozzle exit Case 2. Runs 354. Pitot at 19.5 cm from nozzle exit

Case 3. Runs 351 , 35;2, 353, 356, 358. Pitot at 18.3 cm from nozzle exit

RUN No INCIDENCE TEST CASE MODEL PITOT

2

3

4

5

6

7

8

9

TABLE

4

PRESSURE MEASUREMENTS ON MODELS D

&

E (1b/in 2 ) HEMISPHERE MODELS

M

=

20

High Re D

7.97

7.86

7 • 1 1

3.71

3.60

2.41

1.

50

0.89

0.73

20

357

9°

M

=

20

High Re E

7.88

8. 18

7.08

6.86

6.33

4.61

3.24

2.35

1 .80

M

=

15

High Re E

26.0

26.8

23.3

20. 1

14.5

1 1 .3

7.3

4.3

2.9

...

TABLE

5

PRESSURE MEASUREMENTS ON MODELS F. G AND

A

(1b/in

2 )

BICONIC MODELS

RUN No

351

352

353

354

355

356

INCIDENCE

0

10°

0°

0°

10°

0°

TES'l' CASE

M

= 1

5

M

=

1 5

M =

1 5

H = 20

M

=

20

M =

15

High Re

Hi

g

h Re

High Re

Low Re

High Re

High Re

Cross flow

MODEL

F F G

A

A

A

PITOT

24.9

24.0

24.2

4 .71

7.66

24.5

11 .3*

10.4·

15.6

3.48

5 .16

17.9

2

22.6

13.6

3 . 0 1

4.94

16 • 1

3

16.4

20.9

1 5.7

3.19

4.67

16.3

4

18.6

22.6

17.3

3 . 1 8

4.56

_15.9

5

18.8

22.6

3.30

4.84

15.8

6

17.4

21.9

17.7

3 • 14

4.66

15.6

7

14.0

18.7

13.5

3.32

4.96

1 6. 1

8.

0.82

2.0

0.79

o.

195

0.30

0.97

TABLE

6

HEAT TRANSFER MEASUREMENTS ON HEMISPHERE

MODELS D

&

E TIME T

=

OMSEC (BTU/ft2sec)

RUN No

350

358

MODEL D E E GAUGE

1

.

88.7*

88. 1

*"

209

ll-2

87.6

66.4~

164*'

3

99.0

59.5

186

4

63.8·

50.0

168

5

68.7

47.5

172.5

6

50.7

22.5

Jt

93.6"

7

29.9*

13.9

60. 1

8 24.9~

1 1 . 7

5 1 . 1

9

1 1 .

5

*

8.05

35

. 1

10.

6. 1 .-

4.8

.

_17.9

*

uncalibrated gauge

22

"

IU lAl TABLE 7 RUN No MODEL GAUGE 0

2

3

4

5

6

7

8

9

10

12

HEAT TRANSFER MEASUREMENTS ON MODELS A. F AND G TIME T

=

OMSEC

(BTU/ft2sec)

351

352

353

354

355

356

F F G A A A

239-423·

324'

111. 5

71 .5*

120*

141.5"

248*

224'

189--

65.3

97.7

150

286

232

222

52.7

76.5

182

216

~

183*

189*

50. 1

73.7

218

172

220

39.8

58.7

182

226

179

226

49.6

171

218

172

243

43. 1

52.0

169

13.8

7.7

13. 9

4.5

8.55

15.6

7.43

4.7

12.6

3.8

10. 3

3.15*

5.24*

7.5~

3.37

5:78

10.65

~ uncalibrated gauge

"\) ç=-Heat flux gauges Pressure gauges

MOOELS

A, F, G

7.00

EO. SP

go

APART

EQ ~SP

go

APART

Pressure gauges

~

7.00

MOOELS

D, E

lOL

pit.ot~

.

B~

0.

6

4

2

.

~(]

RUN 350

CORRECTED

o

« /

BELOTSERKOVSKII

~

THEORY

~~

o

10

20 30 40 50 60

70

80

e

_o 90

Fig.2 PRESSURE DISTRIBUTION ON SMOOTH HEMISPHERE

M =20

8

N Z

... 6

m

- l

2

RUN 357

o

10 20 30 40 50 60

70

Ba

90

eO

Fig.3 PRESSURE DISTRIBUTION

ON ROUGH HEMISPHERE

N

z

--

al - l

w

a::::

:::> U') U")

w

ct: Cl.

22

20

18

16

1l.

12

tO

8

6

4

2

RUN 358

-o

CORREC1ED

\ , /

BEL01SERKOVSKII

~

lHECRY

\

o

\

0~

o

tO 20 30 40 50 60 70 80 • 90

e

FIG. 4

PRESSURE DISTRIBUTION ON ROUGH

0

0

_{RUN 350}

1.4

<>

RUN

288

1.2

iJ

q

1.0

(qst )th O~

0

.

8

corrected lees

0

0.6

similarity theory

0.4

Experiment

o

calibrated gauges

0

.

2

Cf

un-calibrated gauges o~~--~--~~~~--~--~~~~

10

20

30

40

80

Er

90

Fig.5 HEAT TRANSFER

DISTRIBUTION ON SMOOTH

HEMISPHERE,

M= 20

1.4

1.2

q

1.0

(qst )th

0.8

cf

_{RUN 357}

Experiment

o

calibrated gauges

o.

aun-calibrated gauges

o

o--~~~~~~~~~~--~~~~

80

e

o

90

Fig.6

HEAT TRANSFER

HEMISPHERE,

DISTRIBUTION

.

ON ROUGH

RUN

358

o

1.2

d

06 corrected Lees . similarity theory

o

o

0.4 Experiment

o

calibrated gauges

d

un-calibrated gauges

o

o

o

Fig. 7 HEAT

TRANSFER DISTRIBUTION

ON

ROUGH

HEMISPHERE, M=15

Pmeas·a Ptheor. 0.6 0.4 0.2

o

RUN

354.

M=20

o

RUN

355,

M = 20, cross-flow

o

RU N

356,

M

=

15

O~----~----~--~~----1·0

2·0 .

3

·

0

.4·0.

dlstance from tip, 5 In.

Fig.8 PRESSURE

DISTRIBUTION ON SHARP

u C» U) N_

...

-

;::) ~

cri

1000 300 200 100 80 60

1.0

30 20 MODEL

A

o

RUN

351.

[] RUN 355

o

RUN 356

....

_..

_..

--

... M=20 Re Ift=2xl0 ó oL = O·

M = 20 Re Ift=3x lOG d =10·(cross-flow) M = 15 Re/H=7xl06 C( =0·

o

--:::--

-...

_...

---

---356

o

0 0

...

_...

0

"'s..

..

...

,

_...

...

_...

...

,

...

..

_...

... 0

- - - _____ 356

...

...

_...

---...

_...

...

... ,...

_...

8

...

.

...

...

..

...

.. ... El

....

_{... ...}

...

... <2>

' . .. ... f";1 ....

...

~

"

... ~ ~

'"

~ ... :::' "V' ... ....

L:J

&.:J

...

'~fSS

... <2>

....

_...

Sommer- Short

_

_

_

Spalding-Chi

____ Eckert 10----~~~~--~---~----~--~~ 1-0 2-0 3-0

1.-0 5-0

Sin

Fig.9 HEAT TRANSFER

BICONIC

MODEL

RATE ON

SMOOTH

SHARP

1000

800

600

400

200

u al 11)

100

""

t -(Ij

60

40

M :15

Re/ft: 7xl01)

o

Sommer - 5 hor t

o

...

,

...

--.~­

...

-::---....

-.

...

---....

...

,

---

---... ... Spalding-

a;r-

--....

,

... Eckert ' ... _... ... ... ...

_....

...

...

... _... ... _...

o

RUN

351

Model F C(:

0°

El

RUN

352

Model

F

Q(

:-10°

30

0

RUN

353

Model G ~ :

0°

20--~~--~~~---~---~

0

·

4

0·6

0

.

8

1

·

0

2·0

3·0

4·0

5

·

0

5

in.

Fig.l0 HEAT

TRANSFER

RATE ON

ROUGH BICONIC

u ~ 11) N

....

...

-

::::>

400

300

200

100

80

60

40

30

20

MODEL A El RUN 3S4 M=

20

Re/ft=2xl06 «=00

Re

I

ft= 3 )( 106

c(

=

10·

Cross-flow test

o

RUN 3SS

M =20

" 0

....

_....

"

....

_....

...

_....

-<IJ

... 0

....

...

0

... ....

' ...

0

' ... ,... <:)

...

... 0

_..

...

...

...

_..

-- - - - Eckert I aminar theory

10~~~---~----~--~~~~~~~

104

2

3

4

S

6

8

105

local Reynolds number

Fig

.

l1 HEAT TRANSFER RATES ON SMOOTH SHARP

BICONIC MODEL

(SMOOTHED

DATA)

40~

__

~~~~~~~---~--~--~~ 4xlO' 6 8 lOS 2 3 4 S

local Reynolds number

Fig.12 COMPARISON OF HEAT TRANSFER DATA ON

SMOOTH AND ROUGH SHARP BICONIC MODELS

1000

800

o

RUN 352 M

=

15 Re Ift :: 7x

10

6 0(

:-10-600

_{Model F} 400 300

f[J

u

0

~ IJ)

0

N 200

'

--

=>

o

0

0

0 0

.c ~

m

0-100

80 - Sommer- Short turbulent theory 60

~O~

__

~~~

__

~~~~

__

~

________

~

__

~

2 3 4 6 8 10 ·2 3

local Reynolds number

Fig.13 HEAT TRANSFER ON

ROUGH SHARP BICONIC

MODEL

AT

0.=10

0

(SMOOTHED

DATA)

MODEL

G

1·2

0

RUN 352 M =15 Re/ft: 7

x

10'

0·6

o

0·4

0·2

0:: W

o

...J ::::>

~

(J')

,

_,

, ,

_,

,

'" '"

'"

..

...

...

_...

... Lees ---- Eckert

...

....

--

... --0.. -_ .... _ .. - Sommer- Short

O ____

~I---~----~---1.0

2

·

0

3

·

0

4·0

5·0

5/RN

Fig.1l. HEAT TRANSFER

RATE ON ROUGH

BLUNT

'·2

.

0

0

'

.

0 -

----O--"A--

o --

Q -

iL

--Pme~. ~

C

Ptheor. 0.8

o

RUN 351 M =15

Fig.15

o

RUN 352 M= 15

0

·

4

0·2

o~--~~--~~--~~--~

'·0

2

·

0

3

·

0

[.·0

distance from tip I 5 in

PRESSURE

DISTRIBUTION ON SHARP

BICONIC MODEL

_J

M=15

'

·

5

1-0

~ w 0·5 0 -J :::>

o

J: IJ)

o

-ru

theory

o

o

/

tangent co ne theory o~~--~---L----~~----~

'

·

0

2·0

3._{0 51 RN}

4

·

0

ROUGH

o

Fig.16

PRESSURE DISTRIBUTION ON BLUNT

UnclassifieJi

-!;toc-urity CI ••• lhcotlon

DOCUMENT CONTROL DÁ T Á • R &. D

(~/y c1 ••• lflc.,I<oft ol t"'., boet, ol .b."."t .rtd Irtd •• "., _ot.,lon

w>u.,

t># .",erH-wh .. " Ilu. 0"""" ,.,..", I. cI ••• tlledJ

'OR'G'N"T'NG "CTIVITY (Corpor.' • • ulI".),

Fluid Dynamics

ze, REPORT 5ECURITV CLA5SIFICATION

von Karman Institute of _Unclassified 1640 Rhode-Saint-Genèse ,Zb. GROVP

:Belgium REPORT TlTLE

HYPERSONIC HEAT TRANSFER MEASUREMENTS ON RE-ENTRY VEHICLE SURFACES AT HIGH REYNOLDS NUMBER

OESCRIPTIVE NOTES (Type ol report _ d I"c:I_' ... • , • • )

Scientific. Final.

AU THOR"I (Flr./ ... ",., ",Iddl. ,,,,,,.,. , • • , _ _ )

Bryan E. Richards

REPORT DATE 7 •• TOT4L NO. OF PAGE5

17b.

_{NO. OF REFS}

P ugust 1973 40 12

•• CONTRACT OR GRANT .. O . . . ORIGINATOJII'S REPORT NUM.ERtS,

USAF contract

F-61052-70-C-b. PROJEC T HO. 0031 N.A.

7381-02

62102F leb. OTH!:"~~POAT NO(S, (A",. oth., " ... ;..,. ",.,_,. ba ••• 'F.d

687381 _{AFML-TR-73-187} thl.

~. _VKI-TN-91

10 OI~TRIBUTION STATEMENT

This document l.S approved for pUblic release and sale; its distribution 1.S unlimited

,

SVPPLE"ENTARV NOTES IZ ... ONSO.UNG MILITARV ACTlYITV

Tech. Other Air Force Materials Laboratory(LAS)

Wright-Patterson AFB Ohio 45433

ABSTRACT

Heat transfer rates, using calorimeter sensors, and pressures, USl.ng variabIe reluctance diaphragm transducers, have been measured on five model shapes in the VKI Longshot facility at Mach numbers of 1 5 and 20 and over a unit Reynolds number range of 2 x 10 6 _{to 7x 10}6 _{per foot.} Two basic shapes, a hemisphere and a 500

-8°

half-angle biconic configu-ration with and without nose bluntness, were tested with different sur-face roughness. Pressures were weIl predicted by the theory of

Belotserkovskii for spherical surfaces, and tangent cone theory, USl.ng the tables of Jones for conical surfaces. Laminar heat transfer rates, slightly underpredicted by Eckert Reference Enthalpy method on cones and reasonably well predicted by Lees similarity theory on hemispheres, were generally achieved for the tests at M

₌

20 whieh used low Reynolds

numbers. Turbulent heat transfer rates, overpredicted by Sommer and Short Referenee Enthalpy method on a smooth wall by 10

% and

underpre-di ct ed by the same emthod for walls with 0.004 l.n. roughness by 1 5

% ,

were measured on the 500 _{half-angle forebodies of the bieonic roodels}

tested at M

₌

1 5 high Reynolds number. Transition was eoropleted by the first gauge on the rough model and by the fourth on the smooth model.

Unclassified Secunty Clasllllcatlon

I. LINK A LINK e - LINK C

K EY WOROI

.. RpLE WT ROI..E WT ROL..E WT

I I HYPERSONIC RE-ENTRY ABLATION NOSE SHAPES HEAT TRANSFER PRESSURE

LAMINAR BOUNDARY LAYER TURBULENT BOUNDARY LAYER

BOUNDARY LAYER TRANSIT ION CRITERIA

I

i

I

I

I

I

I

I

I

i

I

I

I

i

I

,

!

I

I

I

1 , ,

1

I

I