Correlation of supersonic convective heat-transfer coefficients from measurements of the skin temperature of a parabolic...

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Material Information

Title:
Correlation of supersonic convective heat-transfer coefficients from measurements of the skin temperature of a parabolic body of revolution (NACA RM-10)
Series Title:
NACA RM
Physical Description:
39 p. : ill. ; 28 cm.
Language:
English
Creator:
Chauvin, Leo T
Moraes, Carlos A. de
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Publisher:
NACA
Place of Publication:
Washington, D.C
Publication Date:

Subjects

Subjects / Keywords:
Body of revolution   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
Abstract: Free-flight tests at supersonic speeds have been made to determine the local convective heat-transfer coefficients, evaluated from measured skin temperatures along the body of a rocket-propelled fin-stabilized parabolic body of revolution. The Mach number range covered was 1.02 to 2.48 and the Reynolds number range was 3.18 x 10⁶ to 163.85 x 10⁶. The experimental values are compared with the results obtained from the V-2 research missile and also with several equations for heat transfer in a turbulent boundary layer.
Bibliography:
Includes bibliographic references (p. 12-13).
Statement of Responsibility:
by Leo T. Chauvin and Carlos A. deMoraes.
General Note:
"Report date March 7, 1951."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003810614
oclc - 133703632
sobekcm - AA00006206_00001
System ID:
AA00006206:00001

Full Text


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VII ... .,


RESEARCH MEMORANDUh



CORRELATION OF SUPERSONIC CONVECTIVE HEAT-TRANSFER

COEFFICIENTS FROM MEASUREMENTS OF THE SKIN

S.. TEMPERATURE OF A PARABOLIC BODY

SOF REVOLUTION (NACA RM-10)

By Leo T. Chauvin and Carlos A. deMoraes
Langley Aeronautical Laboratory
Langley Field, Va.

UNIVERSITY OF FLORIDA
DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE UBRARY
P.O. BOX 117011
GAINESVILLE, FL 32611-7011 USA
.:.. .

it NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
WASH INGTON
March 7, 1951


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NACA RM L51A18

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS


RESEARCH MEMORANDUM


CORRELATION OF SUPERSONIC CONVECTIVE HEAT-TRANSFER

COEFFICIENTS FROM MEASUREMENTS OF THE SKIN

TEMPERATURE OF A PARABOLIC BODY

OF REVOLUTION (NACA RM-1O)

By Leo T. Chauvin and Carlos A. deMoraes


SUMMARY


Local coefficients of convective heat transfer have been evaluated
from skin temperatures measured along the body of an NACA research
missile designated the RM-1O. The general shape of the body was a
parabola of revolution of fineness ratio 12.2.

Heat-transfer data are presented for a Mach number range of 1.02
to 2.48 and for a Reynolds number range of 3.18 x 106 to 163.85 X 106
based on the axial distance from the nose to the point at which temper-
ature measurements were made.

Results from the data obtained are presented as the product of
Nusselts number and the -1/3 power of Prandtl number against Reynolds
number based on axial distance to the station where the measurements
were made. The equation for heat transfer for a turbulent boundary layer
on a flat plate in subsonic flow (NNuNpr-1/3 = 0.0296 RO.8) is shown
to be in good agreement with the test results when the heat-transfer
parameters are based on the temperature just outside the boundary layer.

Basing the correlation of heat-transfer parameters on air properties
calculated at the wall temperature gave results that agreed well with
the equation for convective heat transfer for cones in a supersonic
flow NNuNPr-1/3 = 0.034 R08.

Heat-transfer coefficients from the V-2 tests correlated on a
Nusselts, Prandtl, and Reynolds number relation gave values that were
approximately 15 percent lower than the results obtained on the RM-10
research missile, for conditions where the parameters were based on the
temperature just outside the boundary layer, or on the wall temperature.







NACA RM L51A18


Values of recovery factor were obtained for the stations at which
temperature measurements were made and are in agreement with theoretical
values of recovery factors for a flat plate.


INTRODUCTION


Aerodynamic heating in supersonic flight has long been recognized
as a major problem in the design of supersonic aircraft, and experimental
heat-transfer data for high Mach numbers and Reynolds numbers are in
great demand. Except for some work done on the V-2, all of the con-
vective heat-transfer work has been done in wind tunnels utilizing
steady-state conditions; however, the results presented herein are for
the transient conditions encountered along the trajectory.

As the problem of aerodynamic heating is closely related with that
of skin-friction drag, investigations of these two phenomena are being
carried out simultaneously by the Langley Pilotless Aircraft Research
Division as a part of an NACA program on supersonic aerodynamics. Models
of a specific configuration, designated NACA RM-10, were flight-tested
at the Pilotless Aircraft Research Station at Wallops Island, Va.

Heat-transfer coefficients obtained from data measured on two
RM-10 test vehicles are presented herein. The transient conditions
encountered during the flight of a rocket-propelled test vehicle are
particularly suited for obtaining aerodynamic heating and heat-transfer
data. The skin temperature measured along the body by resistance
type thermometers cemented to the inner surface of the skin, was con-
tinuously telemetered to a ground receiving station during the time of
flight. From these data the skin temperature, time rate of change of
skin temperature, adiabatic wall temperature, and convective heat-transfer
coefficient were determined.

The Mach number range covered in these tests was approximately 1.0
to 2.5. The Reynolds number range, based on free-stream conditions
and distance along the axis of the missile from the nose to the test
station, was approximately 3.18 x 10l to 163.85 x 10.


SYMBOLS


M Mach number

V velocity, feet per second

he local effective convective heat-transfer coefficient,
Btu per second, square foot, OF







NACA RM L51A18


t time, seconds from start of flight

Cp specific heat of air, Btu per slug per OF

p density of air, slugs per cubic foot

k thermal conductivity of air, Btu per second, square foot,
OF per foot

T thickness, feet

P viscosity of air, slugs per foot-seconds

I distance from the nose along the axis of the body, feet

T temperature, OF

NNu Nusselt number, dimensionless (heZ/k)

Npr Prandtl number, dimensionless (Cpl/k)

R Reynolds number, dimensionless (pVZ/i)

RF recovery factor

Q quantity of heat, Btu

A area, square feet

Cw specific heat of wall, Btu per pound per OF

7w specific weight of wall, pounds per cubic foot

Subscripts:

0 undisturbed free stream ahead of model

v just outside boundary layer

s isentropic stagnation

aw adiabatic wall

w conditions of material pertaining to wall







NACA RM L51A18


TEST VEHICLES


The general configuration and body equation of the RM-10 are shown
in figure 1. Figure 2 is a photograph of the test vehicle on the launcher.
The bodies were basically parabolas of revolution having a maximum
diameter of 12 inches and a fineness ratio of 15; however, the stern was
cut off at 81.3 percent of full length to allow for the installation of
the rocket motor. This resulted in an actual fineness ratio of 12.2.
Four untapered stabilizing fins were equally spaced around the afterbody.
They were swept back 600 with a total aspect ratio of 2.04 and had a
10-percent-thick circular-arc cross section normal to the leading edge.
The design was chosen to attain a high degree of stability which insured
testing at zero angle of attack.

The RM-10 test vehicles were designed for heat-transfer investi-
gations covering large Mach number and Reynolds number ranges. A minimum
of internal structure was accomplished by internally pressurizing the
models. Figure 3 shows the internal construction of the models.

The test vehicles were all metal in construction, utilizing spun
magnesium alloy skins and cast magnesium alloy tail sections to which
the fins were welded. The skin thickness used for each station is
tabulated in table I. All of the surfaces were smooth and highly polished
at the time of flight.

Both models were propelled by a 6.25-inch ABL Deacon rocket motor
carried internally. These motors are designated 3.5ES 5700, 204A3 and
are described in reference 1. The case of the rocket motor has a tem-
perature rise of 500 F; this was not sufficient to affect the accuracy
of the tests. This small rise in temperature is due to the internal
burning of a Deacon rocket motor; that is, the burning starts in the
center and works outward towards the case so that the powder and the
inhibitor act as insulators between the flame and the rocket case.


INSTRUMENTATION AND TESTS


Skin temperatures were measured by means of resistance-type
thermometers cemented to the inner surface of the skin. These ther-
mometers were made of fine platinum wire 0.0002 inch in diameter. Refer-
ence 2 describes the thermometers more completely.

Thermometers were located at stations 8.9, 17.8, 36.3, 49.9, 86.1,
and 123.5 on one test vehicle (model A) and at stations 14.3, 18.3,
and 85.3 on the other test vehicle (model B). Reference 2 shows that
these thermometers had a time lag of 3 milliseconds, corresponding to







NACA RM L51A18


a maximum temperature error of 0.3o F for the test conditions where the
heat transfer is the greatest. This error was considered to be negli-
gible compared to the 3.20 F error due to the thickness of the skin.
Continuous temperature readings were telemetered to ground receiving
stations.

The models were launched from a zero-length launcher at an elevation
angle of 550. Data were obtained during the decelerating portion of the
flight trajectory. Trajectory and atmospheric data were obtained from
the NACA modified SCR-584 radar theodolite and by radiosonde observations.
The time history of the flight velocity was obtained from the continuous-
wave Doppler theodolite radar unit (as described in reference 3). Thermo-
dynamic properties of the air shown in figure 4 were obtained from refer-
ence 4. The specific heat of the magnesium wall presented in figure 5
was obtained from reference 5.

Time histories of the measured skin temperature presented in fig-
ure 6 were obtained as the vehicles coasted from a Mach number of approxi-
mately 2.5 to 1.0. At the time of rocket motor burnout, which was
approximately 3.2 seconds after the start of flight, the test vehicles
were at their maximum velocity and Mach number. No skin temperature
measurements were obtained throughout the initial 3.2 seconds, the period
of powered flight, during which time the telemeter signal was unsatis-
factory. Properties of the air in the undisturbed free stream ahead of
the models and Mach number for models A and B are shown in figure 7
plotted against time. Reynolds number per foot, based on free-stream
conditions, is shown in figure 8 plotted against Mach number. The
difference of Reynolds number between the two models is attributed to
difference in atmospheric conditions and performance of the rocket motors.


METHODS AND PROCEDURES


The transient conditions encountered during the flight of the rocket-
powered test vehicle result in the skin being heated by the boundary layer
during the first part of the flight and cooled by the boundary layer during
the latter part of the flight. Thus, the skin temperature increases during
the heating period, passes through a maximum, and decreases during the
remainder of the flight.

Considering radiation and conduction as negligible, the heat lost
by the boundary layer is equal to the heat absorbed by the skin of the
model. The time rate of heat exchange between the boundary layer and
the skin .is

he V (Taw- ) (1)
dt







NACA RM L51A18


and the time rate of change of the heat contained in the skin is



d= 7,TACw d (2)
dt dt

Equating equations (1) and (2) and solving for the effective heat-transfer
coefficient results in

dTw
TwCZw at
he (3)
Taw Tw


The properties of the wall material are known and the rate of change of
wall temperature is the slope of the measured time history of the skin
temperature. To obtain the temperature difference (Taw Tw) it is first
necessary to define the recovery factor.


RECOVERY FACTOR


Recovery factor defined here has been discussed in references 6
and 7 and is briefly defined as the fraction of stagnation temperature
rise, above the temperature just outside the boundary layer, attained by
an insulated wall. As the stagnation temperature is constant throughout
the flow, the recovery factor may be written as

T -T
RF = aw v (4)
so T

In the absence of radiation and conduction at the peak of the skin-
temperature curve, no heat is being transferred and the skin temperature
and adiabatic wall temperature coincide. It is from this point that the
recovery factor is determined. Trajectory and radiosonde data yield the
free-stream static and stagnation temperatures. The temperature outside
the boundary layer is obtained from the free-stream static temperature
by correcting for the local pressure on the body.

Assuming this recovery factor to be constant during the decelerating
portion of the flight, equation (4) may be re-solved to yield the time
history of the adiabatic wall temperature

Taw = T + RF(Tso T (5)







NACA RM L51A18


This adiabatic wall temperature is the temperature that the skin
would have throughout the test range if it had no heat capacity.


ACCURACY


The error introduced in evaluating the local convective heat-transfer
coefficients is caused either by inaccurate measurement of the data or
by the assumptions made in the analysis. Listed in table II are the
maximum values expected of these errors. As the maximums do not occur
at the same time, these errors combine to give a probable maximum error
in evaluating convective heat-transfer coefficients of +6 percent for
the time during which the data were used.

During the time of flight, as the skin temperature approaches its
peak, the rate of change of skin temperature approaches zero, as does
the temperature difference (Ta T). Thus, he becomes indeterminate.
As the rate of change of skin temperature and the temperature difference
(Taw T.) approach zero, any error in either quantity causes an
increasing error in he, and the scatter in the curve of he against
time becomes large (as can be seen in fig. 9). Therefore, only the
data on the smooth portion of the curve where the probable maximum error
was written 6 percent were used.

It can be noticed from figures 12 and 13 that the scatter between
results obtained from similar stations on two different models is 3 per-
cent, or the scatter of *11 percent from the mean values. It therefore
2
appears that the actual errors are substantially less than the maximum
shown by the preceding analysis.


RESULTS AND DISCUSSION


Recovery factors shown in figure 10 were obtained for all the test
stations on models A and B. Stations 8.9 on model A and 18.3 on model B
had recovery factors of 0.835, while station 14.3 of model B had a
recovery factor of 0.841. These agree well with the recovery factor
of 0.846 predicted by the theory of reference 6 (RF = Npr1/2) for laminar
boundary layers. Recovery factors obtained for the other test stations
agree with the value of 0.894 predicted by theory in reference 8
(RF = Nprl/3) for turbulent boundary layers. To evaluate these theoretical
recovery factors, the thermodynamic properties of air in the Prandtl num-
ber were based on the temperature just outside the boundary layer.







NACA RM L51Al8


Although the recovery factors obtained at three of the stations agree
with\the theoretical value for a laminar boundary layer, only station 8.9
on model A has a Reynolds number range that is likely to accompany a
laminar boundary layer. All of the heat-transfer coefficients were of the
same 9rder of magnitude and were of a magnitude expected for a turbulent
boundary layer. This suggests that these three stations were in a transi-
tion region where it may have been possible to obtain laminar recovery
factors in conjunction with turbulent heat transfer. This view is sup-
ported by Eber's tests on cones, at Mach numbers from 1.2 to 3.1 (refer-
ence 9), in which the heat-transfer data indicated that transition occur-
red on the cones, but the measured recovery factors along the cones were
equal to the values predicted by the theory for laminar flow.

Time histories of the measured skin temperatures and the calculated
adiabatic wall temperatures are shown in figure 11 for stations 8.9 and
123.5 of model A. The skin-temperature curves show the variation in the
magnitude and time of occurrence of the maximum skin temperature measured
at the extreme test stations on the body; that is, a maximum skin temper-
ature of 3980 F at 5.35 seconds for station 8.9 and a maximum skin temper-
aire of 2790 F at 7.94 seconds for station 123.5. The greater rate of
hiat transfer and thinner skin at the forward station causes the skin
temperature there to rise faster and reach a higher peak than at the aft
station, even though the adiabatic wall temperature at the forward station
is less than that at the aft station. During the cooling part of the
flight, when the adiabatic wall temperature is lower than the skin temper-
ature at a given station, the greater rate of heat transfer and thinner
skin at station 8.9 results in the skin cooling faster there than at
station 123.5.

The heat-transfer data obtained in the present test are presented
in figure 12 in terms of Nusselts, Prandtl, and Reynolds numbers. The
temperature used to evaluate the viscosity, conductivity, density,
velocity, and specific heat of the air in the aforementioned parameters
is the temperature just outside of the boundary layer TV. The flow con-
ditions just outside the boundary layer were determined by correcting
the free-stream conditions for the theoretical pressure distribution,
which was obtained from reference 10. (Although theoretical, the pres-
sure distributions thus obtained have been substantiated by the wind-
tunnel test of reference 11.)

It can be seen from figure 12 that the heat-transfer parameter,
NNuNpr-1/3, is primarily a function of Reynolds number rather than body
station; that is, results obtained at different body stations were the
same where the Reynolds numbers were equal. Although it is expected that
the body contour would have some effect on the heat transfer, there was no
apparent effect on the high-fineness-ratio body used for this investigation.

It would be more convenient in reducing the heat-transfer data for
engineering purposes to base the heat-transfer parameters, Nusselts,
Prandtl, and Reynolds numbers, on conditions of the air in the undisturbed







NACA RM L51A18 9


free stream ahead of the model. The results thus obtained are shown in
figure 13. This correlation agrees well with the correlation based on
local conditions, probably because the free-stream conditions are not
very different from local conditions for this high-fineness-ratio body.
The equation for thermal conductance for turbulent flow over a.flat
plate at subsonic speeds is given as NNu = 0.0296 RO-8Nprl/3 in refer-
ence 12. This equation results from frictional drag measurements on a
flat plate in parallel turbulent flow as correlated by Colburn (refer-
ence 13) using a momentum heat-transfer analogy. The dashed line shown
in figures 12 and 13 represents the preceding equation. This line
falls remarkably close to the test data obtained on the parabolic body
of revolution at supersonic speeds and is in agreement with the test
results correlated either on flow conditions just outside the boundary
layer or on free-stream conditions. While the agreement is better at the
higher Reynolds number, this equation could be used to evaluate the heat-
transfer coefficient with fair accuracy over the entire range of Reynolds
numbers shown.

Investigations similar to those described in this paper were con-
ducted on two V-2 research missiles. Figure 4 of reference 14 shows the
results from the heat-transfer tests on the V-2 research missiles compared
with Eber's correlation (reference 9), that is, as a plot of Nusselts
number against Reynolds number. The thermal conductivity and viscosity
of the air were based on the adiabatic wall temperature and the density
and velocity on conditions just outside the boundary layer. These results
are reproduced in figure 14. The line faired through the points is
40 percent above the Eber line. For further comparison the RM-10 heat-
transfer data, based on the same flow properties, are also shown. A
line faired through the RM-10 test results is approximately 60 percent
above Eber or 20 percent above the V-2 line.

Results from the V-2 tests shown in figure 14 are expressed in fig-
ure 15 as NNuNpr-1/3 plotted against Reynolds number based on conditions
of the air just outside the boundary layer. Reference 14 states that
the decrease at lower Reynolds number in the points M and K for the
V-2 No. 27 and for the point of V-2 No. 19 is attributed to partial
transition. Neglecting these points at the low Reynolds number, the
V-2 heat-transfer data are approximately 15 percent lower than the
RM-10 data represented by the solid curve. The correlation
NNuNpr-1/3 = 0.0296 RO.8 is shown as a dashed line and falls approxi-
mately 20 percent higher than the V-2 points.
I-
In figure 16, the heat-transfer parameters NNuNpr-1/3 from the
RM-10 data are plotted against Reynolds number. The thermal conductivity,
viscosity, and specific heat of air are based on adiabatic wall temper-
ature, and the density is based on conditions just outside the boundary
layer. For this temperature basis, somewhat greater scatter can be seen







NACA RM L51A18


in the test points. The faired line through the test points falls
approximately 20 percent lower than the flat-plate correlation
NNuNpr-1/3 = 0.0296 RO.8.

The V-2 data are expressed to the same basis as in figure 16 and
are shown in figure 17. For comparison, the RM-10 faired curve and the
flat-plate correlation NNuNpr-1/3 = 0.0296 RO.8 are also shown in this
figure. The V-2 points fall roughly about 15 percent lower than the
RM-10 faired curve and approximately 35 percent lower than the flat-plate
equation.

Heat-transfer parameters NNuNpr-1/3 for the RM-10 data are plotted
(fig. 18) against Reynolds number. The thermal conductivity, viscosity,
and density of the air are based on the wall temperature. The solid
line in the figure is the faired curve of the RM-10 points. Refer-
ence 15 gives a theory for heat transfer on cones in a supersonic
turbulent boundary layer (NNuNpr1/3 = 0.034 RO'8) and is approxi-
mately 7 percent lower than the curve line representing the RM-10 points.
The flat-plate equation NNuNp-1/3 = 0.0296 RO-8 is shown in the fig-
ure as a dashed line and is approximately 20 percent lower than the
RM-10 faired curve.

In figure 19, the V-2 heat-transfer parameters are plotted against
Reynolds number. The thermal conductivity, viscosity, and density are
based on wall temperature. Disregarding again for low Reynolds number
the points K and M and V-2 No. 19 shows the V-2 heat-transfer data to
be roughly 15 percent lower than the RM-10 faired curve reproduced from
figure 18. A line representing the cone theory (NNuNpr-1/3 = 0.034 RO.8)
falls approximately 8 percent above the V-2 data. The flat-plate
correlation NNuNPr-1/3 = 0.0296 R0.8 is shown by a dashed line approxi-
mately 6 percent lower than the V-2 points.

The agreement between the same approximate stations on models A
and B is well within the estimated accuracy. From the various methods
of correlation it appears that by basing the properties of the air on
the temperature just outside the boundary and on wall temperature gave
results that were approximately 15 percent above the V-2 heat-transfer
data and also agreed well with the referenced equations.


CONCLUSIONS


Supersonic convective heat transfer has been measured in flight on
a parabolic body of revolution. The Mach numbers covered by the tests







NACA RM L51A18


were from 1.02 to 2.48 and the Reynolds numbers were from 3.18 x 106
to 163.85 x 100 based on the axial distance from the nose to the stations
where the skin-temperature measurements were made.

Results of the test indicate that:

1. Heat-transfer parameters from the RM-10 data when correlated on a
Nusselts, Prandtl, and Reynolds number relation, based on conditions just
outside the boundary layer, showed that the equation for convective heat
transfer on a flat plate in a subsonic flow (NNuNpr-1/3 = 0.0296 RO8)
was in good agreement with the test results, and the results from the
V-2 tests were approximately 15 percent lower than the RM-10 data.

2. Correlation of the heat-transfer parameters for the RM-10 on wall
temperature showed that the equation for cones for convective heat transfer
in a supersonic turbulent boundary layer (NNuNpr-/3 = 0.034 R0O8) was in
good agreement with the test results and the results from the V-2 tests
were approximately 15 percent lower than the RM-10 data.

3. The RIM-l0 heat-transfer data are approximately 60 percent higher
than Eber's empirical equation.

4. Good agreement was obtained in the heat-transfer coefficients
between models A and B and the scatter is within the estimated accuracy
of 6 percent.

5. Recovery factors measured along the body are in agreement with
the flat-plate theory.

6. No evidence of boundary-layer transition was apparent in the
heat-transfer data.


Langley Aeronautical Laboratory
National Advisory Committee for Aeronautics
Langley Field, Va.







NACA RM L51A18


REFERENCES


1. Anon.: Jato Manual. SPIA/MI, The Johns Hopkins Univ., Appl. Phys.
Lab., March 1949.

2. Fricke, Clifford L., and Smith, Francis B.: Skin-Temperature
Telemeter for Determining Boundary-Layer Heat-Transfer Coefficients.
NACA RM L50J17, 1951.

3. Morrow, John D., and Katz, Ellis: Flight Investigation at Mach
Numbers from 0.6 to 1.7 to Determine Drag and Base Pressures on a
Blunt-Trailing-Edge Airfoil and Drag of Diamond and Circular-Arc
Airfoils at Zero Lift. NACA RM L5OE19a, 1950.

4. Keenan, Joseph H., and Kaye, Joseph: Thermodynamic Properties of
Air Including Polytropic Functions. John Wiley & Sons, Inc., 1945.

5. Kelley, K. K.: Contributions to the Data on Theoretical Metallurgy.
II. High-Temperature Specific-Heat Equations for Inorganic Substances.
Bulletin 371, Bur. Mines, 1934, p. 32.

6. Wimbrow, William R.: Experimental Investigation of Temperature
Recovery Factors on Bodies of Revolution at Supersonic Speeds.
NACA TN 1975, 1949.

7. Stalder, Jackson R., Rubesin, Morris W., and Tendeland, Thorval: A
Determination of the Laminar-, Transitional-, and Turbulent-Boundary-
Layer Temperature-Recovery Factors on a Flat Plate in Supersonic
Flow. NACA TN 2077, 1950.

8. Squire, H. B.: Heat Transfer Calculation for Airfoils. R & M No. 1986,
British A.R.C., 1946.

9. Eber, G.: Experimental Research on Friction Temperature and Heat
Transfer for Simple Bodies at Supersonic Velocities. Rep. GTR 22,
Chance Vought Aircraft Translation, May 20, 1946.

10. Jones, Robert T., and Margolis, Kenneth: Flow over a Slender Body
of Revolution at Supersonic Velocities. NACA TN 1081, 1946.

11. Esenwein, Fred T., Obery, Leonard J., and Schueller, Carl F.: Aero-
dynamic Characteristics of NACA RM-10 Missile in 8- by 6-Foot
Supersonic Wind Tunnel at Mach Numbers from 1.49 to 1.98. II -
Presentation and Analysis of Force Measurements. NACA RM E50D28,
1950.







NACA RM L51A18 13


12. Anon.: A Design Manual for Determining the Thermal Characteristics
of High Speed Aircraft (Reprint). AAF TR No. 5632, Air Materiel
Command, U. S. Air Force, Sept. 10, 1947.

13. Colburn, Allan P.: A Method of Correlating Forced Convection Heat
Transfer Data and a Comparison with Fluid Friction. Trans. Am.
Inst. Chem. Eng., vol. XXIX, 1933, pp. 174-210.

14. Fischer, W. W.: Supersonic Convective Heat Transfer Correlations
from Skin-Temperature Measurements during Flights of V-2 Rockets
No. 27 and No. 19. Rep. No. 55258, Gen. Elec. Co., July 1949.

15. Gazley, C., Jr.: Theoretical Evaluation of the Turbulent Skin-
Friction and Heat Transfer on a Cone in Supersonic Flight. Rep.
No. R49A0524, Gen. Elec. Co., Nov. 1949.







NACA RM L51A18


TABLE I


'Station
distance from


,- .NACA, /
number denotes axial -
nose measured in inches.


TABLE II


Sources of error


Maximum error in
convective heat-
transfer coefficient
(percent)


A possible error in measured
skin temperatures of
2 percent of maximum skin
temperature at that station 4

Summation of temperature lag
through the skin and of the
thermometer 1

Possible 2 percent error in
skin thickness 12

Neglected heat flows in making
heat balances 4-1
2


Modl Station Skin thickness
Model
(1) (in.)
A 8.9 0.0587
17.8 .0587
36.2 .0927
49.9 .o816
86.1 .0933
123.5 .0863

B 14.3 0.0591
18.3 .0591
85.3 .0935







NACA RM L51A18 15






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Figure 8.- Reynolds number per foot (based on the condition of the air
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NACA RM L5LA18


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