NASA Technical Memorandum 102652

EQUILIBRIUM

FOR EARTH

RADIATIVE

ENTRY

HEATING TABLES

Kenneth Sutton

Lin C. Hartung

+,._',:J- _ 3 6 7 5

Unc I _._3s

G 3 / 3 ++ 0 _..<:: o,,.,"' n 7 6 _-_

May 1990

N/ A

National Aeronautics and

Space Administration

Langley Research Center

Hampton, Virginia 23665
EQUILIBRIUM RADIATIVE HEATING TABLES FOR EARTH

ENTRY

Kenneth Sutton

Lin C. Hartung

NASA Langley Research Center

Hampton, VA 23665

Introduction

The recent resurgence of interest in blunt-body atmospheric entry for applications

such as aeroassisted orbital transfer and planetary return has engendered a corresponding revival of interest in radiative heating. Radiative heating may be of importance in

these blunt-body flows because of the highly energetic shock layer around the blunt

nose. Sutton 1 developed an inviscid, stagnation point, radiation-coupled flow-field

code for investigating blunt-body atmospheric entry. The method has been compared

with ground-based and flight data, 2 and reasonable agreement has been found. To provide information for entry body studies in support of lunar and Mars return scenarios

of interest in the 1970's, the code was exercised over a matrix of Earth entry conditions. These results were never published. Recently, this matrix was extended slightly

to reflect entry vehicle designs of current interest. The complete results are presented

in this report.

Method

The method used is the Radiating, Inviscid Flow, Stagnation Point (RIFSP) code.

Details of the method, which is essentially a solution of the radiation-coupled inviscid

flow equations at a hemispherical stagnation point, can be found in Sutton. 1 The radiation portion is the equilibrium radiation line group method developed by Nicolet, 3

which includes atomic line and continuum mechanisms, as well as molecular bands.
-2-

The RIFSPcodewas recentlyupdatedto FORTRAN V, and its overlay structurewas

removedin the process. It runs easilyon currentcomputers,requiring about1 second

of computertime per iteration on a mainframeand generallyabout700 to 5000iterations per casedependingon the magnitudeof theradiativeflux. Flow fields with very

heavyradiation requiremore iterations. Memory size is no longer a concernfor this

codewith currentcomputers.

Entry Matrix

The matrix of altitude and velocity conditions for which solutions have been

obtained was generated by attempting to bracket the flight conditions of most Earth

entry bodies and some aeroassist bodies that are currently envisioned. A matrix of

these conditions is given in Fig. 1. The range of conditions is limited by the code's

ability to solve flows with very heavy radiation. A series of body sizes was also considered at each flight condition to bracket the vehicle designs under consideration.

These range from a slender body with a nose radius of 5 cm to a blunt-body with a

10-m nose radius.

Results

The equilibrium radiative heating results obtained for the Earth entry matrix are

given in Tables 1-10 for altitudes ranging from 30 to 84 km. For interpolation, the

freestream density 9= (kg/m3), not the altitude, should be used as the independent variable. The density at each altitude is given in the tables. Each table also includes the

entry velocity V in kin/s, the nose radius R, in meters, the radiative, heating rate Qr in

MW[m z, and the shock standoff distance _ in centimeters. The results are plotted in

Figures 2-11, showing the variation of the logarithm of radiative heating with the logarithm of the nose radius for various velocities at each altitude (density).
-3-

Discussion

The resultsgenerallydisplay the expectedtrendsof increasingradiativeheating

with increasingnoseradius or entry velocity. For caseswith relatively heavyradiation, an increasein the numberof grid points acrossthe shock layer is required to

properly resolve the radiation. Thesecases,at the highestfreestrcamvelocitiesand

body noseradii, have beenrun with 20 grid points insteadof the 11 grid points used

in all other cases.Using morethan20 grid points causesonly a further 1 to 2 percent

increasein the radiative heating, and thus does not significantly alter the results.

Using morethan 11 grid points hasa negligible effect (less than 5 percent)at lower

velocitiesandnoseradii.

In addition,the high velocity cases(16 and 18 km/s) at the highestaltitude (84

km) wererun with only five speciesin the chemistry:N, O, N+, O+, ande-. For the

ratherextremeconditionsof theseflow fields, the calculationon the largerspeciesset

was found to breakdown. This is believedto becausedby a breakdownin thechemistry curve fits at the very high temperaturesencounteredin theseflow fields. The

curve fits were generatedfor temperaturesof at most 10000K, whereastemperatures

in theseflow fields areof the orderof 12000K, anddensitiesarevery low. Thecombination of thesetwo extremesis believedto be beyondthe capacityof the chemistry

solution as it exists. However, basedon a radiationlesssolutionfor thesecases,the

largest mole fraction of the ignored speciesis 6x 10-7. Therefore,ignoring these

speciesshouldhavea negligibleeffect.

Note that this is strictly an equilibrium method. Nonequilibrium effects,which

may be important particularly for the higher altitude cases,have been completely

ignored. Also, since the method is for inviscid flows, the influe_ce of the viscous

boundarylayer,which might beexpectedto absorbsomefraction of the radiation,has

beenneglected.
4

Conclusion

A matrix of equilibrium radiative heating results has been generated for Earth

entry. These results have been presented in tabular and graphical form for use in

design and parametric studies.

References

1. Sutton, Kenneth, "Characteristics of Coupled Nongray Radiating Gas Flows with

Ablation Products Effects About Blunt Bodies During Planetary Entries," Phi)

Thesis, North Carolina State University, Raleigh, North Carolim_, 1973.

2. Sutton, Kenneth, "Air Radiation Revisited," in Progress in Astronautics and

Aeronautics: Thermal Design of Aeroassisted Orbital Transfer Vehicles, ed. H.F.

Nelson, vol. 96, pp. 419-441, AIAA, New York, 1985.

3. Nicolet, W. E., "Advanced Methods for Calculating Radiation Transport in

Ablation-Product Contaminated Boundary Layers," NASA CR-1656, Sept. 1970.
Table 1. Radiative Heating Prediction at 30 km Altitude. (p.= 1.8410E-2 kg/m 3)

V, R,, Qr, 8,

km/sm MW/m2 cm

8.0 0.05 1.332 2.655E-01

0.10 2.410 5.310E-01

0.23 4.884 1.221

0.50 9.482 2.655

1.00 1.664E+01 5.290

2.30 3.074E+01 1.210E+01

5.00 5.155E+01 2.610E+01

10.00 7.685E+01 5.150E+01

8.5

9.0

9.5

0.05 2.208 2.620E-01

0.10 3.815 5.240E-01

0.23 7.609 1.205

0.50 1.460E+01 2.620

1.00 2.531E+01 5.220

2.30 4.682E+01 1.189E+01

5.00 7.750E+01 2.560E+0t

10.00 1.123E+02 5.040E+01

0.05 4.006 2.625E-01

0.10 6.676 5.250E-01

0.23 1.283E+01 1.205

0.50 2.389E+01 2.610

1.00 4.093E+01 5.190

2.30 7.386E+01 1.180E+01

5.00 1.184E+02 2.525E+01

10.00 1.649E+02 4.950E+01

0.05 9.316 2.675E-01

0.10 1.442E+01 5.350E-01

0.23 2.578E+01 1.224

0.50 4.517E+01 2.645

1.00 7.376E+01 5.240

2.30 1.259E+02 1.184E+01

5.00 1.911E+02 2.515E+01

10.00 2.514E+02 4.910E+01

V, Rn, Qr, 8,

km/sm MWhn2 cm

10.0 0.05 2.668E+01 2.740E-01

0.10 3.868E+01 5.460E-01

0.23 6.305E+01 1.247

0.50 1.011E+02 2.675

1.00 1.508E+02 5.270

2.30 2.325E+02 1.180E+01

5.00 3.201E+02 2.490E+01

10.00 3.861E+02 4.830E+01

11.0

12.0

0.05 1.269E+02 2.765E-01

0.10 1.703E+02 5.480E-01

0.23 2.468E+02 1.240

0.50 3.460E+02 2.635

1.00 4.550E+02 5.140

2.30 5.962E+02 1.138E+01

5.00 7.013E+02 2.385E+01

10.00 7.709E+02 4.590E+01

0.05 3.097E+02 2.700E-01

0.10 3.961E+02 5.330E-01

0.23 5.421E+02 1.196

0.50 7.171E+02 2.525 t .00 8.923E+02 4.890

2.30 1.077E+03 1.079E+01

5.00 1.215E+03 2.230E+01

10.00 1.171 E+03 4.360E+01
-6-

Table 2. RadiativeHeatingPredictionat 36km Altitude. (p..=7.2579E-3kg/m B)

V, Rn, Qr, 15,

km/s m MW/m 2 cm

8.0 0.05 2.493E-01 2.550E-01

0.10 4.548E-01 5.100E-01

0.23 9.506E-01 1.173

0.50 1.871 2.550

1.00 3.482 5.100

2.30 7.120 1.168E+01

5.00 1.317E+01 2.525E+01

10.00 2.194E+01 4.990E+01

8.5

9.0

9.5

0.05 4.345E-01 2.520E-01

0.10 7.658E_01 5.040E-01

0.23 1.517 1.159

0.50 2.931 2.520

1.00 5.358 5.030

2.30 1.084E+01 1.152E+01

5.00 1.994E+01 2.485E+01

10.00 3.286E+01 4.900E+01

0.05 9.116E-01 2.530E-01

0.10 1.476 5.060E-01

0.23 2.711 1.164

0.50 5.032 2.525

1.00 8.889 5.040

2.30 1.749E+01 1.150E+01

5.00 3.151E+01 2.470E+01

10.00 5.016E+01 4.850E+01

0.05 2.659 2.600E-01

0.10 3.963 5.190E-01

0.23 6.640 1.191

0.50 1.115E+01 2.580

1.00 1.824E+01 5.130

2.30 3.312E+01 1.166E+01

5.00 5.572E+01 2.480E+01

10.00 8.326E+01 4.820E+01

V, R,,, Q,, 8,

km/s m MW/m 2 cm

10.0 0.05 9.384 2.670E-01

0.10 1.296E+01 5.330E-01

0.23 1.963E+01 1.219

0.50 3.010E+01 2.625

1.00 4.492E+01 5.190

2.30 7.213E+01 1.168E+01

5.00 1.082E+02 2.460E+01

10.00 1.470E+02 4.750E+01

tl.0

12.0

14.0

0.05 4.716E+01 2.680E-01

0.10 6.065E+01 51320E-01

0.23 8.480E+01 1.207

0.50 K188E+02 2.575

1.00 1.604E+02 5,030

2.30 2.232E+02 1.115E+01

5.00 2.887E+02 2.315E+01

10.00 3.574E+02 4.370E+01

0.05 1.178E+02 2.605E-01

0.10 1.459E+02 5.150E-01

0.23 1.951E+02 1.159

0.50 2.611E+02 2.450

1.00 3.361E+02 4.720

2.30 4.368E+02 1.042E+01

5.00 5.264E+02 2.150E+01

10.00 6.196E+02 4.020E+01

0.05 3.569E+02 2.435E-01

0.10 4.168E+02 4.770E-01

0.23 5.242E+02 1.060

0.50 6.666E+02 2.210

1.00 8.209E+02 4.230

2.30 1.001E+03 9.108

5.00 1.189E+03 1.820E+01

10.00 1.234E+03 3.480E+01
-7-

Table 3. RadiativeHeatingPredictionat,42km Altitude. (9_=2.9948E-3kglm 3)

V, R,, Qr, &

km/s m MW/m 2 ¢m

8.0 0.05 5.083E-02 2.455E-01

0.10 9.289E-02 4.910E-01

0.23 1.946E-01 1.129

0.50 3.918E-01 2.455

1.00 7.251E-01 4.910

2.30 1.550 1.129E+01

5.00 3.090 2.450E+01

10,00 5.603 4.850E+01

8.5

9.0

9.5

0.05 9.308E-02 2.430E-01

0.10 1.633E-01 4.860E-0!

0.23 3.268E-01 1.118

0.50 6.296E-01 2.430

1.00 1.136 4.860

2.30 2.380 1.113E+01

5.00 4.701 2.410E+01

10.00 8.361 4.780E+01

0.05 2.124E-01 2.450E-01

0.10 3.515E-01 4.900E-01

0.23 6.467E-01 1.125

0.50 1.153 2.445

1.00 2.008 4.890

2.30 4.008 1.120E+01

5.00 7.657 2.415E+01

10.00 1.313E+01 4.770E+01

0.05 8.145E-01 2.535E-01

0.10 1.231 5.060E-01

0.23 2.002 1.164

0.50 3.212 2.525

1.00 5.012 5.020

2.30 8.851 1.145E+01

5.00 1.528E+01 2.450E+01

10.00 2.415E+01 4.790E+01

V, R,, Qr, 8,

km/s m MW/m 2 c m

10.0 0.05 3.336 2.610E-01

0.10 4.720 5.200E-01

0.23 7.026 1.191

0.50 1.018E+01 2.570

1.00 1.446E+01 5.100

2.30 2.266E+01 1.152E+01

5.00 3.471E+01 2.450E+01

10.00 4.914E+01 4.740E+01

11.0

12.0

14.0

0.05 1.767E+01 2.600E-01

0.10 2.315E+01 5.160E-01

0.23 3.135E+01 1.175

0.50 4.201E+01 2.520

1.00 5.557E+01 4.940

2.30 7.849E+01 1.102E+01

5.00 1.056E+02 2.300E+01

10.00 1.316E+02 4.400E+01

0.05 4.535E+01 2.525E-01

0.10 5.667E+01 4.990E-01

0.23 7.286E+01 1.127

0.50 9.429E+01 2.395

1.00 1.208E+02 4.660

2.30 1.618E+02 1.026E+01

5.00 2.047E+02 2.120E+01

10.00 2.553E+02 3.950E+01

0.05 1.437E+02 2.355E-01

0.10 1.689E+02 4.600E-01

0.23 2.044E+02 1.028

0.50 2.518E+02 2.150

1.00 3.090E+02 4.120

2.30 4.105E+02 8.740

5.00 4.945E+02 1.765E+01

10.00 5.560E+02 3.330E+01
-8-

Table4. RadiativeHeatingPredictionat 48 km Altitude. (p.: 1.3167E-3kg/m 3)

V, R,z, Qr, 8,

km/s m MW/m 2 cm

9.0 0.05 5.477E-02 2.380E-01

0.10 9.356E-02 4.750E-01

0.23 1.741E-01 1.093

0.50 3.077E-01 2.375

1.00 5.193E-01 4.750

2.30 1.012 1.090E+01

5.00 1.936 2.360E+01

10.00 3.435 4.660E+01

9.5

10.0

11,0

0.05 2.660E-01 2.480E-01

0.10 4.080E-01 4.960E-01

0.23 6.803E-01 1.139

0.50 1.084 2.470

1.00 1.644 4.930

2.30 2.758 1.127E+01

5.00 4.588 2.425E+01

10.00 7.275 4.770E+01

0.05 1.174 2.550E-01

0.10 1.734 5.080E-01

0.23 2.674 1.166

0.50 3.882 2.520

1.00 5.377 5.010

2.30 8.017 1.207E+01

5.00 1.185E+01 2,425E+01

10.00 1.688E+01 4.740E+01

0.05 6.404 2.535E-01

0.10 8.824 5.030E-01

0.23 1.239E+01 1.145

0.50 1.650E+01 2.460

1.00 2.119E+01 4.840

2.30 2.897E+01 1.088E+01

5.00 3.905E+01 2.290E+01

10.00 4.996E+01 4.400E+01

V, Rn, Qr, 8,

km/s m MW/m 2 cm

12.0 0.05 1.684E+01 2.455E-01

0.10 2.227E+01 4.860E-01

0.23 2.958E+01 1.099

0.50 3.745E+01 2.340

1.00 4.639E+01 4.580

2.30 6.098E+01 1.017E+01

5.00 7.856E+01 2.115E+01

10.00 1.015E+02 3.950E+01

14.0

16.0

0.05 5.597E+01 2.300E-01

0.10 7.013E+01 4.490E-01

0.23 8.603E+01 1.003

0.50 1.025E+02 2.110

1.00 1.278E+02 4.010

2.30 t.617E+02 8.671

5.00 1.992E+02 1.755E+01

10.00 2.324E+02 3.280E+01

0.05 1.229E+02 2.175E-01

0.10 1.486E+02 4.190E-01

0.23 1.726E+02 9.223E-01

0.50 1.960E+02 1.915

1.00 2.400E+02 3.570

2.30 2.953E+02 7.544

5.00, 3.522E+02 1.505E+01

10.00 3.973E+02 2.760E+01
-9-

Table 5. RadiativeHeatingPredictionat 54 km Altitude. (p_=6.3137E-4kg/m 3)

V, R_, Q,, 8,

km/s m MW/m 2 cm

9.0 0.05 1.526E-02 2.325E-01

0.10 2.710E-02 4.650E-01

0.23 5.316E-02 1.067

0.50 9.716E-02 2.320

1.00 1.632E-01 4.640

2.30 3.062E-01 1.065E+01

5.00 5.744E-01 2.310E+01

10.00 1.021 4.590E+01

9.5

10.0

11.0

0.05 9.657E-02 2.435E-01

0.10 1.521E-01 4.870E-01

0.23 2.582E-01 1.118

0.50 4.147E-01 2.425

1.00 6.268E-01 4.840

2.30 1.029 1.109E+01

5.00 1.651 2.390E+01

10.00 2.549 4.730E+01

0.05 4.329E-01 2.495E-01

0.10 6.610E-01 4.980E-01

0.23 1.064 1.143

0.50 1.598 2.470

1.00 2.239 4.910

2.30 3.293 1.118E+01

5.00 4.707 2.400E+01

10.00 6.547 4.720E+01

0.05 2.355 2.475E-01

0.10 3.438 4.920E-01

0.23 5.090 1.122

0.50 7.006 2.410

1.00 9.059 4.760

2.30 1.215E+01 1.072E+01

5.00 1.598E+01 2.270E+01

10.00 2.045E+01 4.410E+01

V, R,, Q,, 8,

km/s m MW/m 2 c m

12.0 0.05 6.297 2.400E-01

0.10 8.886 4.750E-01

0.23 1.250E+01 1.074

0.50 1.635E+01 2.295

1.00 2.024E+01 4.500

2.30 2.592E+01 1.003E+01

5.00 3.270E+01 2.105E+01

10.00 4.253E+01 3.970E+01

14.0

16.0

18.0

0.05 2.148E+01 2.255E-01

0.10 2.923E+01 4.410E-01

0.23 3.839E+01 9.844E-01

0.50 4.669E+01 2.070

1.00 5.447E+01 4.010

2.30 6.961E+01 8.625

5.00 8.532E+01 1.760E+01

10.00 1.015E+02 3.290E+01

0.05 4.784E+01 2.155E-01

0.10 6.393E+01 4.150E-01

0.23 8.004E+01 9.085E-01

0.50 9.217E+01 1.885

1.00 1.083E+02 3.540

2.30 1.291E+02 7.567

5.00 1.541E+02 1.515E+01

10.00 1.774E+02 2.790E+01

0.05 8.421E+01 2.115E-01

0.10 1.127E+02 4.000E-01

0.23 1.370E+02 8.556E-01

0.50 1.509E+02 1.740

1.00 1.646E+02 3.250

2.30 2.000E+02 6.670

5.00 2.344E+02 1.310E+01

10.00 2.575E+02 2.420E+01
- 10-

Table 6.

V,

km/s

9.0

9.5

10.0

11.0

Radiative Heating Prediction at 60 km Altitude. (p_.=3.0592E-4 kg/m 3)

R,,, Qr, 8,

m MW/m 2 cm

0.05 4.066E-03 2.275E-01

0.10 7.402E-03 4.550E-01

0.23 1.518E-02 1.006

0.50 2.926E-02 2.270

1.00 5.156E-02 4.540

2.30 9.884E-02 1.042E+01

5.00 1.822E-01 2.265E+01

10.00 3.223E-01 4.500E+01

0.05 3.462E-02 2.395E-01

0.10 5.639E-02 4.790E-01

0.23 9.802E-02 1.099

0.50 1.618E-01 2.385

1.00 2.470E-01 4.770

2.30 4.021E-01 1.092E+01

5.00 6.324E-01 2.360E+01

10.00 9.508E-01 4.680E+01

0.05 1.539E-01 2.445E-01

0.10 2.391E-01 4.880E-01

0.23 4.020E-01 1.120

0.50 6.277E-01 2.425

1.00 9.077E-01 4.830

2.30 1.360 1.102E+01

5.00 1.940 2.365E+01

10.00 2.644 4.660E+01

0.05 8.078E-01 2.415E-01

0.10 1.246 4.810E-01

0.23 1.974 1.097

0.50 2.860 2.360

1.00 3.822 4.670

2.30 5.196 1.056E+01

5.00 6.784 2.250E+01

10.00 8.543 4.370E+01

V, R,,, Qr, 8,

km/s m MW/tcl 2 cm

12.0 0.05 2.174 2.345E-01

0.10 3.281 4.650E-01

0.23 4.996 1.053

0.50 6.872 2.250

1.00 8.765 4.430

2.30 1.13013+01 9.913

5.00 1.411E+01 2.085E+01

10.00 1.70113+01 4.010E+01

14.0

16.0

18.0

0.05 7.540 2.215E-01

0.10 1.112E+01 4.340E-01

0.23 1.607E+01 9.706E-01

0.50 2.065E+01 2.000

1.00 2.472E+01 3,960

2.30 2,969E+01 8.694

5.00 3.720E+01 1.765E+01

10.00 4.383E+01 3.330E+01

0.05 1.688E+01 2.135E-01

0.10 2.480E+01 4.130E-01

0.23 3.478E+01 9.039E-01

0.50 4.258E+01 1.870

1.00 4.854E+01 3.570

2.30 5.510E+01 7.774

5.00 6.810E+01 1.525E+01

10.00 7.83013+01 2.830E+01

0.05 2,92413+01 2.130E-01

0.10 4.35513+01 4.040E-01

0.23 6.087E+01 8.625E-01

0.50 7.203E+01 1.740

1.00 7.927E+01 3.250

2.30 9.170E+01 6.693

5.00 1.005E+02 1.325E+01

10.00 1.174E+02 2.430E+01
-11-

Table 7.

V,

kngs

9.0

9.5

10.0

11.0

Radiative Heating Prediction at 66 km Altitude. (p.= 1.4713E-4 kg/m 3)

Rn, Qr, 8,

m MW/m 2 cm

0.05 1.066E-03 2.225E-01

0.10 1.954E-03 4.450E-01

0.23 4.083E-03 1.023

0.50 8.107E-03 2.225

1.00 1.484E-02 4.440

2.30 3.010E-02 1.021E+01

5.00 5.611E-02 2.215E+01

10.00 9.815E-02 4.430E+01

0.05 1.192E-02 2.350E-01

0.10 1.980E-02 4.700E-01

0.23 3.567E-02 1.081

0.50 6.070E-02 2.345

1.00 9.651E-02 4.690

2.30 1.612E-01 1.074E+01

5.00 2.503E-01 2.325E+01

10.00 3.696E-01 4.620E+01

0.05 5.211E-02 2.390E-01

0.10 8.288E-02 4.780E-01

0.23 1.442E-01 1.097

0.50 2.347E-01 2.380

1.00 3.497E-01 4.740

2.30 5.428E-01 1.081E+01

5.00 7.805E-01 2.325E+01

10.00 1.069 4.600E+01

0.05 2.591E-01 2.355E-01

0.10 4.116E-01 4.700E-01

0.23 6.968E-01 1.074

0.50 1.074 2.315

1.00 1.511 4,590

2.30 2.148 1.037E+01

5.00 2.845 2.215E+01

10.00 3.590 4.320E+01

14.0

16.0

18.0

Rn, Q_, 5,

m MW/m 2 cm

0.05

0.10

0.23

0.50

1.00

2.30

5.00

10.00

6.892E-01 2.285E-01

1.089 4.550E-01

1.800 1.035

2.672 2.215

3.585 4.360

4.810 9.775

6.056 2.065E+01

7.340 4.000E+01

0.05 2.405 2.170E-01

0.10 3.773 4.280E-01

0.23 6.020 9.591E-01

0.50 8.454 2.020

1.00 1.065E+01 3.920

2.30 1.323E+01 8.648

5.00 1.560E+01 1.800E+01

10.00 1.907E+01 3.360E+01

0.05 5.401 2.105E-01

0.10 8.473 4.110E-01

0.23 1.335E+01 9.062E-01

0.50 1.814E+01 1.870

1.00 2.181E+01 3.570

2.30 2.559E+01 7.728

5.00 3.050E+01 1.540E+01

10.00 3.470E+01 2.870E+01

0.05 9.138 2.135E-0t

0.10 1.465E÷01 4.100E-01

0.23 2.343E+01 8.809E-01

0.50 3.145E+01 1.775

1.00 3.667Ea-01 3.300

2.30 4.125E+01 6.946

5.00 4.760E+01 1.350E+01

10.00 5.260E+01 2.460E+01
- 12-

Table 8. RadiativeHeatingPredictionat 72 km Altitude. (p.=6.6593E-5kg/m 3)

V, R,_, Qr, 8,

km/s m MW/m 2 cm

9.0 0.05 2,619E-04 2.180E-01

0.10 4.789E-04 4.360E-01

0.23 1.004E-03 1.003

0.50 2.016E-03 2.180

1.00 3.759E-03 4.360

2.30 7.889E-03 1.003E+01

5.00 1.550E-02 2.175E+01

10.00 2.731E-02 4.340E+01

9.5

10.0

11.0

0.05 3.420E-03 2.305E-01

0.10 5.749E-03 4.610E-01

0.23 1.076E-02 1.060

0.50 1.891E-02 2.300

1.00 3.176E-02 4.600

2.30 5.744E-02 1.056E+01

5.00 9.484E-02 2.285E+01

10.00 1.424E-01 4.540E+01

0.05 1.576E-02 2.330E-01

0.10 2.512E-02 4.660E-01

0.23 4.497E-02 1.072

0.50 7.685E-02 2.325

1.00 1.207E-01 4.630

2.30 1.965E-01 1.060E+01

5.00 2.939E-01 2.285E+01

10.00 4.052E-01 4.530E+01

0.05 7.573E-02 2.290E-01

0.10 1.204E-01 4.580E-01

0.23 2.109E-01 1.049

0.50 3.463E-01 2.260

1.00 5.131E-01 4.490

2.30 7.794E-01 1.019E+01

5.00 1.082 2.180E+01

10.00 1.389 4.270E+01

V, R_, Qr, 8,

km/s m MW/m 2 cm

12.0 0.05 1.995E-01 2.220E-01

0.10 3,145E-01 4.430E-01

0.23 5.414E-01 1.010

0.50 8.674E-01 2.175

1.00 1.252 4.290

2.30 1.804 9.637

5.00 2.382 2.040E+01

10.00 2.918 3.960E+01

14.0

16.0

18.0

0.05 6.750E-01 2.115E-01

0.10 1.079 4.190E-01

0.23 1.847 9.476E-01

0.50 2.867 2.005

1.00 3.947 3.900

2.30 5.270 8.602

5.00 6.465 1.790E+01

10.00 7.443 3.410E+01

0.05 1.491 2.065E-01

0.10 2.418 4.060E-01

0.23 4.146 9.039E-01

0.50 6.342 1.885

1.00 8.453 3.600

2.30 1.066E+01 7.751

5.00 1.239E+01 1.590E+01

10.00 1.452E+01 2.920E+01

0.05 2.501 2.110E-01

0.10 4.074 4.110E-01

0.23 7.169 8.993E-01

0.50 1.107E+01 1.830

1.00 1.459E+01 3.400

2.30 1.773E+01 7.130

5.00 2.048E+01 1.415E+01

10.00 2.234E+01 2.560E+01
- 13-

Table9.

V,

km/s

9.0

9.5

10.0

11.0

RadiativeHeatingPredictionat 78 km Altitude. (p_=2.5239E-5kg/m 3)

Rn , Qr , 8,

m MW/m 2 cm

0.05 4.728E-05 2.130E-01

0.10 8.719E-05 4.260E-01

0.23 1.833E-04 9.820E-01

0.50 3.698E-04 2.130

1.00 6.922E-04 4,260

2.30 1.476E-03 9.798

5.00 2.983E-03 2.125E+01

10.00 5.630E-03 4.250E+01

0.05 6.853E-04 2.250E-01

0.10 1.154E-03 4.500E-01

0.23 2.193E-03 1.033

0.50 4.055E-03 2.245

1.00 6.975E-03 4.480

2.30 1.317E-02 1.033E+01

5.00 2.356E-02 2.240E+01

10.00 3.891E-02 4.460E+01

0.05 3.168E-03 2.265E-01

0.10 5.248E-03 4.530E-01

0.23 9.373E-03 1.040

0.50 1.667E-02 2.260

1.00 2.793E-02 4.510

2.30 5.058E-02 1.033E+01

5.00 8.350E-02 2.230E+01

10.00 1.251E-01 4.430E+01

0.05 1.640E-02 2.215E-01

0.10 2.590E-02 4.420E-01

0.23 4.585E-02 1.012

0.50 7.863E-02 2.195

1.00 1.250E-01 4.370

2.30 2.068E-01 9.959

5.00 3.096E-01 2.140E+01

10.00 4.250E-01 4.190E+01

V, R,,, Qr, 8,

km/s m MW/m 2 cm

12.0 0.05 4.333E-02 2.140E-01

0.10 6.752E-02 4.280E-01

0.23 1.168E-01 9.798E-01

0.50 1.95!E-01 2.110

1.00 3.027E-01 4.190

2.30 4.817E-01 9.453

5.00 6.938E-01 2.015E+01

10.00 9.172E-01 3.930E+01

14.0

16.0

18.0

0.05 1.435E-01 2.035E-01

0.10 2.247E-01 4.060E-01

0.23 3.873E-01 9.223E-01

0.50 6.393E-01 1.975

1.00 9.707E-01 3.870

2.30 1.478 8.579

5.00 2.009 1.790E+01

10.00 2.493 3.430E+01

0.05 3.153E-01 1.990E-01

0.10 4.969E-01 3.950E-01

0.23 8.626E-01 8.924E-01

0.50 1.419 1.890

1.00 2.120 3.650

2.30 3.245 7.889

5.00 4.141 1.610E+01

10.00 4.840 3.030E+01

0.05 .5798 .2055

0.10 .9102 .404

0.23 1.529 .9039

0.50 2.558 1.880

1.00 3.773 3.550

2.30 5.593 7.406

5.00 6.986 1.465E+01

10.00 7.984 2.660E+01
- 14-

Table 10. RadiativeHeatingPredictionat 84km Altitude. (9_=9.6940E-6kglm 3)

V, Rn, Qr, 5,

km/s m MW/m 2 cm

9.0 0.05 9.285E-06 2,090E-01

0.10 1.749E-05 4.180E-01

0,23 3.748E-05 9.614E-01

0.50 7.665E-05 2.090

1.00 1.455E-04 4.180

2.30 3.138E-04 9.614

5.00 6.390E-04 2.090E+01

10.00 1.199E-03 4.170E+01

9.5

10.0

11.0

0.05 1.423E-04 2.195E-01

0.10 2A42E-04 4.390E-01

0.23 4.653E-04 1.010

0.50 8.583E-04 2.190

1.00 1.497E-03 4.380

2.30 2.927E-03 1.007E+01

5.00 5.296E-03 2.180E+01

10.00 8.960E-03 4.350E+01

0.05 6.142E-04 2.195E-01

0.10 1.032E-03 4.390E-01

0.23 1.929E-03 1.010

0.50 3.406E-03 2.195

1.00 5.746E-03 4.390

2.30 1.090E-02 1.007E+01

5.00 1.945E-02 2.180E+01

10.00 3.146E-02 4.340E+01

0.05 3.181E-03 2.135E-01

0.10 5.120E-03 4.270E-01

0.23 9.155E-03 9.821E-01

0.50 1.611E-02 2.130

1.00 2.704E-02 4.250

2.30 4.958E-02 9.706

5.00 8.296E-02 2.090E+01

10.00 1.233E-01 4.130E+01

V, Rn, Qr, _,

km/s m MW/m 2 cm

12.0 0.05 8.620E-03 2.065E-01

0.10 1.385E-02 4.130E-01

0.23 2.462E-02 9.476E-01

0.50 4.281E-02 2.055

1.00 7.00 I E-02 4.080

2.30 1.230E-01 9.269

5.00 1.943E-01 2.075E+01

10.00 2.724E-01 3.870E+01

14.0

16.0

18.0

0.05 3.181E-02 1.965E-01

0.10 5.057E-02 3.910E-01

0.23 8.757E-02 8.947E-01

0.50 1.464E-01 1.930

1.00 2.310E-01 3.800

2.30 3.682E-01 8.533

5.00 5.810E-01 1.795E+01

10.00 7.695E-01 3.450E+01

0.05 7.707E-02 .1915

0.10 1.164E-01 3.820E-01

0.23 .2049 .8671

0.50 .3306 1.855

1.00 0.5035 3.630

2.30 .8223 8.004

5.00 1.214 1.65el

10.00 1.572 3.120E+01

0.05 .1245 .201

0.10 .2062 .397

0.23 .3536 .8924

0.50 .585 1.885

1.00 .8757 3.630

2.30 1.434 7.797

5.00 2.096 15.55

10.00 2.649 28.4
H, km

30

36

42

48

54

60

66

72

78

84

_Voo,

Poo'_,,,_m/s

kg/m3

1.8410E-2

7.2579E-3

2.9948E-3

1.3167E-3

6.3137E-4

3.0592E-4

1.4713E-4

6.6593E-5

2.5239E-5

9.6940E-6

8.0

ti

ii

v'

8.5

v'

v'

v'

9.0

v'

ii

ii

v'

v'

v'

v'

ii

v'

v'

9.5

v'

v'

v'

v'

v'

v'

v'

v'

ii

ii

10.0

ii

v'

it

v'

v'

v'

II

v'

ii

v'

11.0

v'

v'

v'

v'

v'

v'

v'

1I

v'

ii

12.0

v'

v'

v'

II

v'

v'

v'

ii

v'

14.0

v'

ii

v'

v'

v'

ii

i1

v'

v'

16.0

v'

v'

v'

v'

v'

v'

v'

18.0

v'

ii

v'

v'

v'

i1

O1

I

Figure 1. Flight Conditions Selected for Radiation Calculations.
10 4 -

10 3

Qr, MW/m2

10 2 -

101 -

10 0

1 0 -2

V, km/s

---E}-- 8

8.5

9

--0-- 9.5

10

11

--l--- 12

Rn, m

Figure 2. Radiative Heating Prediction at H=30 kin. (p=1.8410E-2 kg/m s)

i

..,,,&

i
10 4 -

103

10 2 -

Qr, MW/m2 -

101 -

10 ° -

V, km/s

---[3--- 8

8.5

9

---0--- 9.5

---0-- 10

11

----II-.-- 12

14

1 0 2 10 -1 1 0 ° 1 01

an, m

!

""4

Figure 3. Radiative Heating Prediction at H=36 km. (p=7.2579E-3 kg/m 3)
(_LU/6_t E:-:lg1766" g= d) "LU>!gl;'=H _,_ uo!;o!peJct 6u!].BeH eA!]._!psM 1' ejn6!-I

i

,,i,,--

i

z_Oi-

__0 L

- __01.

oOL

_OL

zO I.

cOL
103 -

10 2

101

Qr, MW/m2

10 o

1 0 "1 -

10 -2

10 -2

V, km/s

---0--9

9.5

10

---0.-- 11

---0-- 12

14

16

.,..._...-.--4l--.._-

II-----

10-1 10 ° 101

Rn, m

!

(,o

I

Figure 5. Radiative Heating Prediction at H=48 km. (p=1.3167E-3 kg/m 3)
10 3 -

10 =

101

Qr, MW/m2

100

10_

V, km/s

9

9.5

+ 10

_ 11

12

14

-----II--- 16

18

I i I

x

10 -1 10° 101

Rn, m

!

O

i

Figure 6. Radiative Heating Prediction at H=54 km. (p=6.3137E-4 kg/m 3)
1 0 3 -

10 2

101

Qr, MW/m2

10 o

10 -1

1 0 -2

V, km/s

---EF-- 9

9.5

10

11

12

14

16

18

Rn, m

!

!

Figure 7. Radiative Heating Prediction at H=60 km. (p=3.0592E-4 kg/m 3)
102 --

101

10 0

Qr, MW/m2

_0 -1

1 0 2 -

10-3!

10 .2

V, km/s

9

9.5

10

11

12

14

16

18

I I I

10 -1 10 0 101

Rn, m

i

r_

|

Figure 8. Radiative Heating Prediction at H=66 km. (p=1.4713E-4 kg/m 3)
10 2 -

101

10 o

er, MW/m2

10 "1

1 0 2

10 .3

V, km/s

----tD_ 9

9.5

_ 10

--'0--11

12

14

16

18

10-4 _ , , , , _,,I _ _ , , , ,,,I , , , _ l

1 0 -2 1 0 "1 1 0° 101

Rn, m

i

ro

r,.,o

|

Figure 9. Radiative Heating Prediction at H=72 kin. (p=6.6593E-5 kg/m 3)
10 _ _

100

10 _

1 0 -3 --

10-4

10s

10 .2

V, km/s

---{3-- V=9

V=9.5

V=lO

----O-- V=11

V=12

V=14

V=16

V=18

10 1 10°

Rn, m

I 1 I I I ]

10_

a

b_

4_

I

Figure 10. Radiative Heating Prediction at H=78 kin. (p=2.5239E-5 kg/m 3)
(sLUI6>I 9,B0#69"6=d) "LU>t17'8=H _._ uo!_,o!peJcl 6u!_._eH eA!]._!peEt 1. I. eJn6!-.I

I

I.,O

i

_0I. oO i. _.0L

gl.

9_

lzl.

I.I. ---<_

Ol.

E6

6 ---c--

sAu)l 'A

__OL

9.0L

s.OL

._0_

__OL

_W/AAIAi "0

- z-OL

__Ot

oOL

_OL
NAS6

Nat K)n,al Aeronaut_:s ark-I

Space A(_rnlnistraDon

1. Report No.

NASA TM-102652

4. Title and Subtitle

Report Documentation Page

2. Government Accession No.

Equilibrium Radiative Heating Tables for Earth Entry

3. Recipient's Catalog No.

5. Report Date

7. Author(s)

Kenneth Sutton and Lin C. Hartung

9. Pedorming Organization Name and Address

NASA Langley Research Center

Hampton, VA 23665-5225

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, DC 20546-0001

May 1990

6. Performing Organization Code

8. Performing Organization Report No.

10. Work Unit No.

506-40-91-01

11. Contract or Grant No.

13. Type of Report and Period Covered

Technical Memorandum

14. Sponsoring Agency Code

15. Supplementary Notes

16. Abstract

The recent resurgence of interest in blunt-body atmospheric entry for

applications such as aeroassisted orbital transfer and planetary return has

engendered a corresponding revival of interest in radiative heating.

Radiative heating may be of importance in these blunt-body flows because of

the highly energetic shock layer around the blunt nose. Sutton developed an

inviscid, stagnation point, radiation-coupled flow-field code for

investigating blunt-body atmospheric entry. The method has been compared

with ground-based and flight data, and reasonable agreement has been found.

To provide information for entry body studies in support of lunar and Mars

return scenarios of interest in the 1970's, the code was exercised over a

matrix of Earth entry conditions. These results were never published.

Recently, this matrix was extended slightly to reflect entry vehicle designs

of current interest.

17. Key Words (Suggested by Author(s))

Radiative heating

Equilibrium

Aerobraking

18. Distribution Statement

Unclassified-Unlimited

Subject Category 34

19. SecuriW Cla_if. (of this report)

Unclassified

20. SecuriW Cla_if. (of this page)

Unclassified

21. No. of pages _. Price

26 A03

NASA FORM 1626 OCT 86