Experimental convective heat transfer to a 4-inch and 6-inch hemisphere at Mach numbers from 1.62 to 3.04

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Material Information

Title:
Experimental convective heat transfer to a 4-inch and 6-inch hemisphere at Mach numbers from 1.62 to 3.04
Series Title:
NACA RM
Physical Description:
18 p. : ill. ; 28 cm.
Language:
English
Creator:
Chauvin, Leo T
Maloney, Joseph P
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Publisher:
NACA
Place of Publication:
Washington, D.C
Publication Date:

Subjects

Subjects / Keywords:
Heat -- Transmission   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Turbulent boundary layer   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
Abstract: Equilibrium temperatures and heat-transfer coefficients for a hemispherical nose have been measured for Mach numbers from 1.62 to 3.04. Heat transfer to the surface of the hemisphere was presented as Stanton number against Reynolds number for various surface heating conditions. Heat transfer at the stagnation point has been measured and correlated with theory. Transition from a laminar to a turbulent boundary layer was obtained at Reynolds numbers of approximately 1 x 10⁶ corresponding to a region on the body located between 45° and 60° from the stagnation point.
Bibliography:
Includes bibliographic references (p. 11-12).
Statement of Responsibility:
by Leo T. Chauvin and Joseph P. Maloney.
General Note:
"Report date November 24, 1953."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003808467
oclc - 129383217
sobekcm - AA00006151_00001
System ID:
AA00006151:00001

Full Text


RM L53L08a


RESEARCH MEMORANDUM





EXPERIMENTAL CONVECTIVE HEAT TRANSFER TO A 4-INCH

AND 6-INCH HEMISPHERE AT MACH NUMBERS FROM

1.62 TO 3.04

By Leo T. Chauvin and Joseph P. Maloney

Langley Aeronautical Laboratory
Langley Field, Va.


UNIVERSITY OF FLORIDA
DOCUMENTS DEPARTMENT
1'20 MARSTON SCIENCE LIBRARY
0.O. BOX 117011
GAINESVILLE, FL 32611-7011 USA


NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
WASH I NGTON
February 3, 1954


'S




I.

*-I': .










NACA RM L55L08a

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

RESEARCH MEMORANDUM


EXPERIMENTAL CONVECTIVE HEAT TRANSFER TO A 4-INCH

AND 6-INCH HEMISPHERE AT MACH NUMBERS FROM

1.62 TO 5.04

By Leo T. Chauvin and Joseph P. Maloney


SUMMARY


Experimental investigation of supersonic aerodynamic heat transfer
has been conducted on hemispheres. The manner in which heat-transfer
coefficient varies along a spherical surface has been determined for a
Mach number range from 1.62 to 3.04. The variation of equilibrium tem-
peratures along the surface was also determined. Although heat-transfer
coefficients and equilibrium temperatures were found to be independent
of Mach number over the range tested, heat-transfer coefficients were
found to vary 14 percent for a change in the ratio of surface temperature
to adiabatic wall temperature from 0.70 to 0.96. Transition from a lami-
nar to a turbulent boundary layer was obtained at a Reynolds number (based
on length along the surface from the stagnation point) of approximately
1 X 106, corresponding to a region on the body located between the 450
and 600 stations. Comparison of the heat transfer at the stagnation
point with theory is presented and shows good agreement.


INTRODUCTION


From the standpoint of minimum drag, high fineness ratio and nearly
pointed noses are desirable in the design of supersonic missiles and air-
planes. However, it is necessary for some supersonic vehicles to have
hemispherical noses to house guidance equipment. The use of this nose
shape may result in severe drag penalties and high skin temperatures.
Reference 1 presents the results of a previous investigation on aerody-
namic heat transfer to a hemisphere at M = 2.8. However, the model used
was influenced by large magnitude of heat conduction. The National
Advisory Committee for Aeronautics has made tests in the preflight jet of
the Langley Pilotless Aircraft Research Station at Wallops Island, Va. to
determine the pressure drag, pressure distribution, and aerodynamic heating
of hemispherical noses. The pressure distribution and pressure drag for a







2 NACA RM L55L08a


hemispherical nose at M = 2.05, 2.54, and 5.04 have been reported in
reference 2. The test results presented herein are for the aerodynamic
heating on a hemispherical nose 4 inches in diameter at Mach numbers of
1.62 to 3.04 and for a Reynolds number of approximately 4.5 x 106 based
on nose diameter. Additional tests were made at M = 1.99 on a hemi-
spherical nose 6 inches in diameter. Reynolds number for this test was
approximately 6.4 x 106, and tests were made for two different degrees
of surface smoothness. These Reynolds numbers for both models were based
on properties of the air in the undisturbed free stream.


SYMBOLS


M Mach number

V velocity, ft/sec

h local heat-',ransfer coefficient, Btu/(sec)(sq ft)(OF)

TW skin temperature, OR

Te equilibrium skin temperature, OR

Ts stream stagnation temperature, OR

Taw adiabatic wall temperature, OR

T skin thickness, ft

c specific heat of skin, Btu/lb OF

d mass density of wall, lb/cu ft

t time, sec

1 length along the surface from the stagnation point on the
model, ft

p density of air, slugs/cu ft

p. absolute viscosity of air, lb-sec/sq ft

Cp specific heat of air at constant pressure, Btu/slug OF


thermal conductivity of air, Btu/(sec)(ft)(oF)






NACA RM L53LO8a


Nu Nusselt number, hl/k

Pr Prandtl number, cpni/k

R Reynolds number, pVZI/

CH Stanton number, h = Nu
cH pV Pr R


APPARATUS, MODELS, AND TESTS

The 4-Inch Model


The preflight jet test facility is a blowdown-type tunnel, supplying
air from storage spheres to an 8-inch auxiliary jet and a 12-inch main
jet. The 4-inch model was tested in the 8-inch auxiliary jet which
utilized interchangeable nozzles to obtain different Mach numbers. Refer-
ence 2 showed that the flow properties along the hemisphere was not influ-
enced by the relatively large ratio of model diameter to jet diameter.
Elaboration on the details of the preflight jet test facility can be
secured from reference 3.

Steady flow conditions are obtained approximately 5 to 8 seconds
after initial opening of the jet exhaust valve. In order to prevent the
model from being subjected to any jet starting transients, the model was
inserted into the air stream after steady flow was established. Inserting
the model was accomplished by mounting the model support on a pivoted
strut which was swung into the flow by a quick-operating hydraulic sys-
tem. Prior to each test the model was clear of the air stream and then
was injected into test position in 0.5 second. A position indicator
recorded the model location as it moved into the flow. All the test
results are for the model alined with the center line of the jet. A
photograph of the model and strut in the test position is shown in
figure 1.

The 4-inch-diameter model was a hemispherical nose, made of K-monel,
0.037-inch thick, and having a smooth and highly polished surface.

Eight no. 36 iron-constantan thermocouples were fused to the inner
surface of the hemispherical nose. Stagnation temperatures were meas-
ured ahead of the nozzle throat and at the model support.

All measurements were recorded on recording galvanometers, synchro-
nized by means of a timer having a frequency of 10 cycles per second.
The instruments were accurate to 1 percent of their full-scale deflections
which corresponds to *50 F.







NACA RM L55LO8a


The Reynolds number for the test Mach numbers of 1.62, 2.05, 2.54,
and 5.04 were 5.80 X 106, 4.54 x 106, 4.86 x 106, and 3.93 x 106,
respectively, based on body diameter and free-stream conditions. The
small change in Reynolds number with Mach number was due to the varia-
tion in static pressure and temperature. The tests at M = 1.62 and 2.05
were for approximately sea-level conditions, whereas the tests at
M = 2.54 and 3.04 were for a static pressure corresponding to an alti-
tude of approximately 13,000 and 28,000 feet, respectively. Testing at
steady flow conditions was maintained until several seconds after equi-
librium conditions had been established. The air supply was sufficient
to enable testing at the desired flow conditions for approximately
55 seconds.


The 6-Inch Model

The 6-inch-diameter model was tested in the 12-inch main jet of the
preflight test facility. The tests were made in a two-dimensional nozzle.
A photograph of the model mounted in the jet is shown in figure 2.

The model was made of 0.057-inch-thick K-monel. Two tests were con-
ducted on this model, the first with a smooth and highly polished surface
and the second with a roughened surface. The roughened surface corre-
sponded to a light sand blast.

Nine iron-constantan thermocouples were installed on the inner sur-
face of the model. Thermocouple locations for both hemispheres can be
obtained from figure 3. The model was mounted on a fixed support and
unlike the 4-inch model was subjected to heating during the starting of
the jet. The stagnation temperature measured in the heat exchanger,
total pressure, and skin temperature measurements were recorded on
recording galvanometers.

The Mach number for both the smooth and roughened models was 1.99
and the Reynolds number based on body diameter was 6.4 x 106 which corre-
sponds to sea-level conditions. Steady flow was maintained for 50 seconds,
at which time the skin temperatures were essentially in equilibrium.


RESULTS AND DISCUSSION

Equilibrium Temperatures


The measured equilibrium temperatures for the 4-inch and 6-inch noses
are shown in figure 3. The values were obtained at approximately 50 sec-
onds after the start of the test when it was observed that the skin had
reached a thermal equilibrium. The equilibrium skin temperature expressed






NACA RM L55LO8a


as a ratio to stagnation temperature is plotted on a radial scale which
indicates the location at which the measurements were made. The meas-
urements from the 4-inch nose show a temperature ratio of 1 corresponding
to stagnation temperature occurring at the front of the nose. The equi-
librium temperature decreases gradually along the surface and at the
900 station the skin temperature is about 95 percent of the stagnation
temperature.

Equilibrium temperatures are not shown for the stagnation point and
the 120 station on the 6-inch nose because of thermocouple failure.
Thermocouples at the stagnation point and at the 700 station on the rough
nose also malfunctioned.

Data for the test at M = 5.04 on the 4-inch nose were confined to
the stations from 300 forward because the low static pressures in the
nozzle caused a normal shock whose influence was felt beyond the 45 sta-
tion, as shown in reference 2.


Heat-Transfer Coefficient

The aerodynamic heat-transfer coefficient was measured during the
transient heating of the model after the establishment of steady air flow
from the nozzle. Radiation from the model and conduction along-the sur-
face were calculated and found to be negligible. By neglecting these
terms, the convective heat transferred to the model can be equated to the
heat absorbed by the model skin per unit of time.


h(Taw Tw) = Tcd dTw/dt


The heat-transfer coefficient h can then be obtained from this equation.

For conditions where radiation and conduction are negligible, the
measured equilibrium skin temperature Te is equal to the adiabatic wall
temperature Taw.

The aerodynamic heat-transfer coefficients were evaluated by this
equation, taking the mass density of the K monel skin as 555 lb/cu ft
and its specific heat as 0.127 Btu/lb/oF. The skin temperature and its
time rate of change were obtained from the measured time histories of the
skin temperature. The adiabatic wall temperatures were computed from the
experimentally determined temperature ratio Te/Ts. A typical skin tem-
perature and stagnation temperature variation with time is shown in
figure 4.






NACA RM L55L08a


Measured aerodynamic heat-transfer data are presented in figure 5
as Etsntori number plotted against Reynolds number for various heating
conditions. The heating condition, expressed as a ratio of wall tem-
perature to adiabatic wall temperature, varied from 0.70 to 0.96 during
the experimental investigation. The air properties in the Stanton
and Reynolds numbers obtained from reference 4 are based on conditions
just outside the boundary layer, and the length term in Reynolds number
is taken as the distance along the surface from the stagnation point to
the measurement station. Local conditions outside the boundary layer
were calculated by assuming isentropic flow behind the nose shock and by
utilizing reference 2 for the static pressures on the body. Heat-transfer
data are shown for the 4-inch- and 6-inch-diameter hemispheres having
smooth and highly polished surfaces for Mach numbers from 1.62 to 3.04,
and for the 6-inch-diameter hemisphere having a rough surface at a Mach
number of 1.99.

Data points for the 4-inch nose are shown in figures 5(a), (b), (c),
and (d) for temperature ratios Twy/aw equal to 0.70, 0.80, 0.90,
and 0.96, respectively. The 6-inch-nose data points were confined to a
temperature ratio of 0.96 only (fig. 5(d)) since the data at lower tem-
perature ratios were obtained during the period of unsteady flow associ-
ated with starting the jet.

Laminar flow prevailed on the 4-inch nose for Reynolds numbers to
approximately 1 x 106, corresponding to approximately the 450 station.
Beyond the 450 station the data dispersed from the trend established
during the laminar region; this dispersion indicates the flow was under-
going transition to turbulence. During this transition, a large increase
in heat transfer is effected by small changes in ReTolds number. Conse-
quently, the equilibrium temperatures for stations beyond 450 in figure 3
are characteristic of transitional and turbulent flow. Heat transfer for
fully developed turbulent flow is shown in figure 5(d) for the roughened
6-inch hemisphere having a temperature ratio of 0.96.

The heating-condition effect on the laminar heat transfer is demon-
strated by plotting the lines representing the faired data from each of
the four heating conditions on a composite curve (fig. 5(e)). As the
heating condition Tw/Taw increased, the Stanton number, which contains
the heat-transfer coefficient, decreases proportionately. These faired
curves yielded the following empirical equation for the laminar heat
transfer on a hemispherical surface.
-0.5
CH = 1.46 R-0-556 (Tw


For an increase in Tw/Taw from 0.70 to 0.96 a decrease of 14 percent
occurred in CH.






IHACA RM L55LO8a


Since the data presented in each of the heating conditions investi-
gated covered a range of Mach numbers from 1.62 to 3.04, the lack of any
systematic scatter of the data points indicated that no Mach number effect
was present in this range. This laminar heat transfer was not unexpected,
however, as the stations in the laminar flow region were also in the
region of subsonic flow behind the bow wave.

Figure 6(a) presents the heat-transfer data measured at the stag-
nation point on the 4-inch hemispherical nose. The data are plotted
according to a theory presented in reference 5 which correlates the
stagnation-point heat transfer as Nu Pr-04 = 1.32R0O5. The flow con-
ditions are based on the air properties just behind the center of the
bow wave, and the length parameter is the diameter of the body. The dis-
crepancy between theory and experiment is partially due to the fact that
heating effect is not accounted for in the equation, whereas the data
show a trend with heating condition. The experimental data are for a
range of heating Tw/Taw from 0.7 to 0.9. Figure 6(b) gives the com-
parison between the calculated time histories of skin temperature using
the theory of reference 5 for the heat-transfer coefficient and the meas-
ured skin temperature to M = 2.05. The maximum deviation of the theo-
retical skin temperature from the measured skin temperature was approxi-
mately 200 F. Similar agreement was obtained for other Mach numbers
investigated.


CONCLUDING REMARKS


Equilibrium skin temperatures and convective heat transfer have been
measured on a 4-inch- and 6-inch-diameter hemispherical nose. The Mach
number for the 4-inch nose ranged from 1.62 to 3.04 for a Reynolds number
based on body diameter of approximately 4.5 x 106. The 6-inch nose was
tested at M = 1.99 at a Reynolds number based on body diameter of
6.4 x 106 and for two surface conditions.

The measured equilibrium skin temperature for these tests was equal
to the stagnation temperature at the 00 station (stagnation point) and
decreased gradually along the surface to 95 percent of the stagnation
temperature at the 900 station.

Transition from a laminar to a turbulent boundary layer occurred on
the hemisphere at a Reynolds number of about 1 X 106 corresponding to a
region between the 45 and 600 station.

The heat-transfer data indicated the influence of the heating con-
dition expressed as the ratio of the wall temperature to the adiabatic
wall temperature Tw/Taw from 0.70 to 0.96. An increase in heat transfer







NACA RM L53LO8a


was noted at the onset of transition on the smooth nose, approaching the
turbulent values measured on a roughened nose.

Heat transfer was measured at the stagnation point which when com-
pared with theory yielded good agreement.


Langley Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va., November 24, 1955.







REFERENCES


1. Korobkin, Irving: Local Flow Conditions, Recovery Factors and Heat-
Transfer Coefficients on the Nose of a Hemisphere-Cylinder at a
Mach Number of 2.8. NAVORD Rep. 2865 (Aeroballistic Res. Rep. 175),
U. S. Ellial Ord. Lab. (White Oak, Md.), May 5, 1953.

2. Chauvin, Leo T.: Pressure Distribution and Pressure Drag for a Hemi-
spherical Nose at Mach Numbers 2.05, 2.54 and 3.04. NACA RM L52K06,
1952.


5. O'Sullivan, William J., Chauvin, Leo T., and Rumsey,
Exploratory Investigation of Transpiration Cooling
Aerodynamic Heating on an 80 Cone in a Free Jet at
2.05. NACA RM L53H06, 1955.


Charles B.:
To Alleviate
a Mach Number of


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

5. Sibulkin, M.: Heat Transfer Near the Forward Stagnation Point of a
Body of Revolution. Jour. Aero. Sci. (Readers' Forum), vol. 19,
no. 8, Aug. 1952, pp. 570-571.





NACA RM L55LO8a


..... .,
III*YT --

--' ...iii .... .


L-78137.1
Figure 1.- Photograph of 4-inch-diameter hemispherical nose mounted in
the 8-inch auxiliary jet.


~""


I







NACA RM L55LO8a


- si -,^ ... ... I 1J




L-70981.1

Figure 2.- Photojr.i-p of the 6-inch-diameter hemispherical nose mounted
in the main jet.





NACA RM L53LO8a


Symbol Dlam. il ach
number


0 4 in /2


820 R


Surface
cond/ fon

Smrootr


2.05 997
2.54 /10/2
3.04 980
/.99 386 Roughened
/.99 96 7 Smnooth


-/00
-t/.OO


/00 .90 .80

TS


Figure 3.- Equilibrium


skin temperature for the 4- and 6-incl-diian-eter
hemispherical nose.


Stperaubor






NACA RM L55LO8a


50


Figure 4.- Typical temperature-time histories.


Stagna t/or fempe a Lure




SKin temperature
/5 0 sta/o0n, M 2.os5


Soo00




400




S300




200




/00


20 30
77m/n, Sec


UL.'






NACA RM L55LO8a


(a) = 0.70.
Taw


Figure 5.- Correlation of heat transfer for hemispheres with Reynolds
number for various heating conditions.


4-/n. nose
Mach
number
o /.62
o 2.05
-- o 2.54 -------
A 3.04











o


/0-4
I(


R/0s 6e
Reynold ,'i/rn z


04






NACA RM L55LO8a


/O-











/O-4


(b) Tw = 0.80.
aw

Figure 5.- Continued.


4-/n. /'nose
Mach
number
o /.62
o 2. 5O
0 2.54
A 3. 04










0U
------
", ... ~


/06
nutn-beRz


/05
Rey r)/Q






IACA RM L55LO8a


4 -n. nose
/ach

o /.62
o 2.05
0 2.54
A 3.04










Ro



0







/O4 105 106 /o
Reynolds number


(c) Tw = 0.9.
Taw


Figure 5.- Continued.






NACA RM L55LO8a


/06


(d) Tw = 0.96.
Taw

Figure 5.- Continued.


Symbo/ Dioam Moch Surface
number cond/ ihon

o 4 /7. /.;2 Srnooth
o 4 2.05
0 4 2.54
A 4 3.04
S & /.99 Roughened
S 6 /..99 Smoolh








La minar-
S.


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tz


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/0-3


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o4


/05
Rcynoiods nunmlber






NACA RM L55LO8a


/0s /06
Reyno/ds number


(e) Summary of the faired laminar heat-transfer
data on hemispherical surfaces.


Figure 5.- Concluded.


C, = 1.46 R -056 (55/6w)-&5




-0.70
/0.8 0
/-0.90
0.96


(II)
/0-3











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IC


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NACA RM L55LO8a


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0 M=2.54





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/ 4 6 8 lOx/C'


(a) Heat transfer.


0 /0 20 30
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40 J0


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Figure 6.- Comparison of measured and theoretical heat transfer at the
st grT.it ion point.


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UNIVERSITY OF FLORIDA

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UNIVERSITY OF FLORIDA
DOC L'M.,TS DqOSEPARTMENTr
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