Convective aerodynamic heating estimates for air- carbon dioxide gas mixture

Laumann, E. A.

English

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Copyright 0 1965 
Jet Propulsion Laboratory 
California Institute of Technology 
Prepared Under Contract N 
National Aeronautics 8, 
Technical Report No. 32- 715 . 
Comparisons of Experimental and Theoretical 
Aerodynamic Heating Results in 
Air-Carbon Dioxide Mixtures 
E. A. Laumann 
Bain Dayrnhn, Jr.; ,Ehiq+ 
Aerodynamic Facik$es . . ' 
J E T  P R O P U L S I O N  L A B O R A T O R Y  
PASADENA, CALIFORNIA 
C A L I F O R N I A  INSTITUTE OF TECHNOLOGY 
January 15, 1965 
~ ~ ~ ~~ 
JPL TECHNICAL REPORT NO . 32-715 
CONTENTS . 
1 . Introduction . . . . . . . . . . . . . . . . . . . . .  1 
II . Experimental Data . . . . . . . . . .  . .  . . . . .  4 
111 . Theoretical Calculations . . . . . . . . . . . . . . . .  4 
IV . Comparison of Results . . . . . . . . . . . . . . . . .  7 
V . Conclusions . . . . . . . . . . . . . . . . . . . . .  9 
Nomenclature . . . . . . . . . . . . . . . . . . . . . .  9 
References . . . . . . . . . . . . . . . . . . . . . . .  11 
FIGURES 
1 . Models used in the experiment: (a) Model I; (b) Model II; 
(cl Model 111 . . . . . . . . . . . . . . . . . . . . . .  2 
2 . Typical model installation . . . . . . . . . . . . . . . . .  3 
3 . Specific heat vs % CO, . . . . . . . . . . . . . . . . . .  5 
4 . Viscosityvs % CO. . . . . . . . . . . . . . . . . . . .  5 
5 . Thermal conductivity vs % CO, . . . . . . . . . . . . . . .  6 
6 . Prandtlnumbervs % CO. . . . . . . . . . . . . . . . . .  6 
7 . Enthalpy difference vs % CO, . . . . . . . . . . . . . . .  6 
8 . Mach number vs % CO. . . . . . . . . . . . . . . . . .  6 
9 . ~ V S  % CO. . . . . . . . . . . . . . . . . . . . . . .  6 
10 . Stagnation point heat transfer vs % CO, . . . . . . . . . . . .  7 
8 
8 
8 
11 . Heat transfer distributions for Models I and 111 at a = O  deg . . .  
12 . Heat transfer distributions for Model I1 at a = 0 deg . . . . . .  
13 . Heat transfer distributions for Model 111 at a = 180 deg . . . . .  
111 
JPL TECHNICAL REPORT NO. 32-715 
ABSTRACT 
Convective heat transfer experiments were conducted in the Jet 
Propulsion Laboratory hypersonic wind tunnel in air-carbon dioxide 
mixtures. The mixtures were in chemical equilibrium, and the amounts 
of carbon dioxide in air were vaned from 0% to 72% by volume. The 
convective heating of three different model shapes was measured, 
using calorimetric techniques. 
The results of these experiments are compared with the stagnation 
point heating theory of Fay and Riddell, using the Lennard-Jones 
potential theory to evaluate the transport properties of the gas mix- 
tures. The heat transfer distributions are compared to the theory of Lees. 
1. INTRODUCTION 
The design of planetary entry capsules is highly de- 
pendent upon the type and severity of the aerodynamic 
induced heat to which the capsule will be subjected dur- 
ing its high-velocity entry. Considerable effort is being 
expended to investigate that portion of the trajectory 
where both radiative and convective heating are present, 
and both theoretical and experimental information are 
becoming available concerning stagnation point aerody- 
namic heating at superorbital velocities. 
The purpose of this Report is to describe the results 
of an investigation to determine the validity of making 
convective aerodynamic heating estimates for air-carbon 
dioxide gas mixtures using the theories developed and 
verified in air. The experimental convective heat transfer 
data described here were obtained at a nominal Mach 
number of 6 in air, with carbon dioxide added (up to 
72% by volume). The stagnation enthalpy was approxi- 
mately 7.8 X lo6 ft2/secz, and the unit free-stream 
Reynolds number was approximately 0.15 X 106/in. for 
all tests. Because the enthalpy levels were relatively low, 
the flow was in chemical equilibrium at all times. The 
theories that are compared with experimental results are 
the stagnation point theory of Fay and Riddell and the 
heat transfer distribution theory of Lees. 
The experimental portion of this work was conducted 
in the Jet Propulsion Laboratory 21-in. hypersonic wind 
tunnel. This facility is a flexible-nozzle, continuous-flow 
facility capable of operating at Mach numbers from 4 
to 11. Stagnation pressures of 650 psi and stagnation 
temperatures of 1300OF are possible. A detailed descrip- 
tion of the tunnel is given in Ref. 1. 
The experimental test data were obtained using the 
so-called transient heat transfer technique. This tech- 
nique consisted of measuring the time rate of tempera- 
ture change of a thin-skin metallic model. Prior to each 
test run, the model was cooled to a temperature below 
the recovery temperature. Details of the test technique 
are contained in Ref. 2. 
1 
JPL TECHNICAL REPORT NO. 32-715 
1.635 
-1.255 4 
ta- 2.021 '+ 1.350 1 
T 
2.000 
ALL DIMENSIONS IN INCHES 
RADIUS I \ 2.225 / 
Fig. 1. Models used in the experiment: (a) Model I; (b) Model II; ( c )  Model 111 
2 
- ~~ 
J P L  TECHNICAL REPORT NO. 32-715 
The procedures followed for introducing significant 
amounts of carbon dioxide into the wind tunnel circuit, 
and the effects produced by doing so, are described in 
Ref. 3. Briefly, the procedure is to introduce liquid CO, 
downstream of the test section and to allow gaseous mix- 
ing to occur through the compression stages of the tunnel 
circuit. The nozzle shape is not adjusted to compensate 
for the changing 7.l This causes a reduction in the test 
rhombus Mach number, but flow calibrations show that 
the Mach number variation through the test rhombus 
remains very small. 
. 
Three model shapes (Fig. 1) were used for the experi- 
mental work. The models were constructed of electro- 
lytic nickel with a uniform wall thickness of approximately 
0.025 in. Local model wall temperatures were measured 
using 0,010-in. dia chromel-constantan thermocouples 
spot welded to the inner surface of the model wall. The 
thermocouples were located on several meridians of 
the axisymmetric models. The models were mounted 
in the wind tunnel on a vertical strut as shown in Fig. 2. 
This arrangement permitted angular rotation of any 
model from 0 deg to 180 deg. 
'See Nomenclature for definitions of terms. 
Fig. 2. Typical model 
installation 
3 
JPL TECHNICAL REPORT NO. 32-715 
II. EXPERIMENTAL DATA 
The thermocouple data, recorded every 0.05 sec during 
each run, were reduced and used to determine the rate 
of change of model surface temperature with time and 
subsequently to determine the calorimetric heat rates. 
Details of this procedure are described in Ref. 2. Model 
temperatures ranged between 500°R and 600OR for the 
data presented here. 
Heat transfer data were obtained for each of the models 
at various angles of attack from 0 deg through 180 deg. 
Because the model support created a flow disturbance 
that was atypical of a model in free flight, all model 
temperatures measured at locations that lay in the vicinity 
of or behind the support bow shock were considered 
invalid. The same reasoning was used to invalidate all 
heating measurements in separated flow regions lying 
behind the support strut, because of the possibility of 
subsonic pressure disturbances. 
The experimental data for Models I and 11, obtained 
when the flat base was facing the oncoming stream, ex- 
hibited excessive scatter and are invalid. The flat base 
was not sufficiently strong to prevent physical deflection 
(oil canning) of the surface; the concave deflection wag 
noticeable but not measurable. The experimental results 
showed enough scatter to indicate that unsteady flow 
existed over the concave surface under these conditions. 
4 
The worst-case inaccuracy of the experimental results 
is estimated to be &6%, based upon the following factors: 
uncertainties of material thermal properties 1.0% 
uncertainty of model wall thickness 2.5% 
uncertainty of temperature change rate 1.5% 
conduction losses caused by non-zero 
model wall temperature gradients 1 .O% 
Other uncertainties are considered negligible compared 
to these. 
111. THEORETICAL CALCULATIONS 
The stagnation point convective heat transfer theory 
of Fay and Riddell (Ref. 4) was used as the basis of 
evaluation of the stagnation point heat transfer data pre- 
sented in this Report. Because of the low test enthalpy, 
no dissociation was considered. The expression of stag- 
nation point heat transfer was written as 
by assuming that a Bernoulli-Newtonian velocity gradi- 
ent exists at the stagnation point. 
The theoretical variation of heat transfer with CO, 
content was determined by calculating the thermal and 
transport properties of several air-CO, mixtures and by 
introducing these calculations into the above equation. 
The thermal properties were based on molecular ratios, 
and the transport properties were obtained using the 
Lennard-Jones potential theory as outlined in Ref. 5. 
In making the calculations, a binary mixture of air and 
CO, was assumed, rather than a multicomponent mixture 
of the several molecular elements involved. Reference 6 
was used as a source for the properties of pure gases. For 
simplicity, the wall temperature was assumed to be M O R  
for all wall-property calculations. 
The specific heat, enthalpy, and Prandtl number were 
calculated as follows: 
k%, 
k w  
Pr, = -
4 
~ ~ ~~ 
~ 
JPL TECHNICAL REPORT NO. 32-715 
The enthalpy difference integration was carried out by 
assuming a linear variation of C, over intervals of M O R .  
The results of all of the above calculations are shown 
in Fig. 3 through 7. 
4 
The wind tunnel nozzle flow was assumed to be best 
represented by the isentropic expansion of a perfect gas. 
The values of specific heat at constant pressure were ob- 
TEMPERATURE, OR 
Fig. 3. Specific heat VI YO CO, 
tained from Ref. 6 by assuming a reference pressure and 
temperature of 0.4 atm and 360OR respectively, and the 
ratios of specific heats for the various air-CO, mixtures 
were calculated as 
C,/R 
= C,/R - 1 
The Mach number, static pressure, stagnation point 
density, and wall stagnation point density were deter- 
mined from measured values of total pressure, pitot pres- 
sure, and total temperature. The calculated variations of 
Mach number and y in the test section are shown in Fig. 8 
N 
c02. % 
Fig. 4. Viscosity vs YO CO, 
5 
JPL TECHNICAL REPORT NO. 32-715 
3.4 
3.2 
3.0 
2.8 
2.6 
2.4 
2.2 
2 .a 
0.80 
0.78 
0.16 
0.74 
0.72 
0.7c 
con , O/4 
Fig. 5. Thermal conductivity vs % CO, 
- 
P-0.4 otm 
T =  540 OR 
20 40 60 60 IC 
c02, % 
Fig. 6. Prandtl number vs YO CO, 
P z O . 4  atm 
T, = 1260 OR 
7,= 540 OR 
420 
0 20 40 
L 
I 80 IO0  
cop , x 
Fig. 7. Enthalpy difference vs % C 0 2  
cop,% 
Fig. 8. Mach number vs % CO, 
c02, % 
Fig. 9. y vs % C 0 2  
6 
JPL TECHNICAL REPORT NO. 32-715 
0.0060 
0.0058 
0.0056 
and 9. All experimental data were obtained under the 
following constant tunnel conditions: 
Newtonian pressure distribution. The heat transfer dis- 
tribution was written as 
I I I I 
0 MODEL I , a = O d e g  
A MODEL IIi,a=o dag 
0 MODEL I I , a = O  deg 
- 0 MODELlU,o=l0Odeg - 
- FAY-RIDDELL THEORY 
-- FAY-RIDDELL THEORY WITH BOISON 
-CURTISS VELOCITY GRADIENT FOR 
. MODELS I AND IE AT a = O  deg - 
stagnation pressure 174 psi 
pitot pressure 5.01 psi 
0 stagnation temperature 1260OR 
The integration was carried out numericallyy with the 
actual body coordinates of the conical sections adjusted 
to conform to the virtual apex geometry. 
The heat transfer distribution calculations were based 
upon the theory of Lees (Ref. 7), assuming a modified 
IV. COMPARISON OF RESULTS 
The experimental convective heat transfer results are 
presented in Fig. 10. Superimposed on these results 
are the theoretical curves calculated for the noted test 
conditions. The experimental data for Model I1 at 0 deg 
and for Model I11 at 180 deg show excellent agreement 
with theory. The data for Models I and I11 at 0 deg show 
only good agreement with theory; this is due to the in- 
accuracy in Bernoulli-Newtonian velocity gradients for 
very blunt noses, as was pointed out in Ref. 8, where the 
gradient becomes no longer inversely proportional to 
the square root of the nose radius. By assuming a New- 
tonian sonic line position, a Boison and Curtiss effective 
nose radius can be determined for Models I and 111. Sub- 
stituting this dimension for the geometric stagnation point 
radius in the Fay and Riddell theory, the dashed curve in 
Fig. 10 is obtained. Thus the experiment shows excellent 
agreement with theory when the stagnation point velocity 
gradient is more accurately determined. 
The windward heat transfer distributions obtained for 
Models I and I11 (geometrically similar) at 0 deg are 
presented in Fig. 11, together with the calculated theo- 
retical distributions. Excellent agreement exists between 
experiment and theory, with two notable exceptions. The 
theory consistently overestimates heating in the region 
of l /D  values of 0.25 to 0.40 and underestimates heatjng 
in the region of the torus-cone intersection (I/D = 0.55). 
Other data (not presented), obtained with intermediate 
amounts of CO,, fall within the scatter band of the data 
presented here. The presence of CO, in the gas flow 
has a neghgible effect on the aerodynamic heating dis- 
tribution. 
0 2 0  40 60 80 1 0 0  
cop, % 
Fig. 10. Stagnation point heat transfer VI % CO, 
7 
JPL TECHNICAL REPORT N O .  32-715 
5.62 1.35 72 THEORY 
6% OF THEOR 
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 
Fig. 11. Heat transfer distributions for 
Models I and 111 at (Y = 0 deg 
The windward heat transfer distributions obtained for 
Model 11, together with the theoretical distributions, are 
presented in Fig. 12. Again, agreement between experi- 
ment and theory is very good. The theory, however, 
consistently overestimates heating in the region of I/D 
values of 0.1 to 0.2 and underestimates heating in the 
region of the hemisphere-cone intersection. The rather 
wide variations in experimental heating data between 
l /D values of 0.6 and 1.3 are of unknown origin, but 
they can probably be attributed to warping of the model 
shape due to an improper fit between the model and the 
support fitting. All of the data that show higher heating 
rates in this region lie along the meridian closest to the 
model support. The addition of CO, to the gas flow pro- 
duces a negligible effect on the heating at all measuring 
stations, not only for the data presented here but also 
for several other intermediate values of CO, content 
under which heating data were measured. 
Figure 13 presents the experimental data and the theo- 
retical calculations for Model I11 at 180 deg. Again the 
experimental results verify the theory extremely well. 
The theory slightly overestimates heating at I/D values 
of 0.4 to 0.6. 
6.06 1.40 0 THEORY 
0.0 I 6 5.65 1.35 64 THEORY 
0 6.06 1.40 0 EXPERIMENT 
5.65 1.35 64 EXPERIMENT 
Fig. 12. Heat transfer distributions for 
Model II at a = 0 deg 
I I M y cop, % 0.0 I 2 
$ & I  - 6.06 1.40 0 THEORY 
o.o,~ '\.k - - 5.77 1.37 38 THEORY , 
0 6.06 140 0 EXPERIMENT 
I ly A 5.77 1.37 38 EXPERIMENT 
m I I I \. I 
c' 0.004 
0.002 
l/O 
Fig. 13. Heat transfer distributions for 
Model 111 at (Y = 180 deg 
Additional experimental data were obtained at angles of 
attack in increments of 20 deg between 0 deg and 180 deg. 
All of these data show a negligible effect on heating when 
any amount of CO, is added to the flowing gas. 
8 
JPL TECHNICAL REPORT NO. 32-715 
V. CONCLUSIONS 
The convective heat t r ade r  to blunt entry bodies can 
be predicted for any air-CO, mixture with an accuracy 
of approximately 5%, using the theories of Fay and Ridden 
and Lees at moderate enthalpy levels. The Lennard-Jones 
potential theory adequately predicts the transport prop 
erties of the mixtures at these enthalpy levels. 
The total variation of stagnation point heat transfer 
and the heat transfer distribution are shown to be neg- 
ligibly affected by the presence of large amounts of CO,. 
The C0,-induced Mach number effect is ais0 very small 
and is reflected primarily in the minor variations of the 
Newtonian pressure gradient. 
The data presented by Collins and Horton (Ref. 9) ais0 
show that the addition of CO, to the flowing fluid has 
a negligible effect on convective heat transfer at the stag- 
nation point. These data were obtained in a shock tube 
under stagnation enthalpy conditions 25 to 50 times 
greater (or flight velocities 5 to 7 times greater) than 
those of the tests reported here. 
It must be concluded, therefore, that the presence of 
unknown amounts of carbon dioxide in a planetary atmos- 
phere need not be of concern to a planetary capsule heat- 
shield designer for entry velocities below 30,OOO ft/sec. 
NOMENCLATURE 
C, specific heat (ft2/sec2 OR) 
D 
H enthalpy (ftZ/s&) 
h 
i indicates a specific gas 
k thermal conductivity (lb/sec OR) 
1 surface distance from stagnation point (ft) 
major diameter of model (ft) 
heat transfer coefficient (BTU/ft3sec O R )  
M Machnumber 
P pressure (lb/ft2) 
Pr Prandtlnumber 
(i 
R gas constant (ftz/sec' OR) 
heat transfer rate (BTU/fP sec) 
S 
T 
W 
X 
Y 
a 
Y 
P 
a 
e 
conditions immediately behind the normal shock 
temperature (OR) 
conditions at the model wall 
mass fraction of a gas 
radial distance from model axis of symmetry to 
model surface, measured normal to axis of sym- 
metry (ft) 
angle of attack of axis of symmetry 
ratio of specific heats 
density (lb sec2/ft4) 
viscosity (lb sec/ft2) 
angle between the body surface and the normal 
to the free-stream wind vector (rad) 
9 
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JPL TECHNICAL REPORT NO. 32-715 
REFERENCES 
1. "Wind Tunnel Facilities at the Jet Propulsion laboratory," Technical Release 
No. 34-257, Jet Propulsion laboratory, Pasadena, California, April 18, 1961. 
2. Laumann, E. A., "Determining Aerodynamic Heating Rates Using Calorimetric Models 
in the Jet Propulsion laboratory Hypersonic Wind Tunnel," Technical Memorandum 
No. 33-7 27, Jet Propulsion laboratory, Pasadena, California, March 7, 1963. 
3. Hanks, D., Herrera, G., and Koester, H., "The Use of a Conventional Wind Tunnel 
as a Multigas Facility," Technical Memorandum No. 33-7 45, Jet Propulsion labora- 
tory, Pasadena, California, April 8, 1963. 
4. Fay, J. A. and Riddell, F. R., "Theory of Stagnation Point Heat Transfer in Dissociated 
Air," Journal of the Aerospace Sciences, Vol. 25, No. 2, p. 73, February, 1958. 
5. Hirschfelder, J. O., Curtiss, C. F., and Byrd, R. B., Molecular Theory of Gases and 
Liquids, John Wiley and Sons, Inc., New York, 1954. 
6. Hilsenrath, J. et al., "Tables of Thermal Properties of Gases," Circular No. 564, 
U. S. Bureau of Standards, 1955. 
7. lees, l., "laminar Heat Transfer Over Blunt Nosed Bodies at Hypersonic Flight 
Speeds," Jet Propulsion, Vol. 26, pp. 259-269, 1956. 
8. bison, J. C. and Curtiss, H. A., "An Experimental Investigation of Blunt Body 
Stagnation Point Velocity Gradient," ARS Journal, Vol 29, No. 1, pp. 130-1 35, 
February, 1959. 
9. Collins, D. J. and Horton, T. E., "Experimental Convective Heat Transfer Measure- 
ments,'' AlAA Journal, Vol. 2, No. 11, pp. 2046-2047, November, 1964. 
11 


Comparisons of experimental and theoretical aerodynamic heating results in air-carbon dioxide mixtures

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