Total radiative intensity calculations for 100% CO2 and 90% CO2-10% N2

J. Quant. Specmsc.

Radiat.

TOTAL

Transfer. Vol.

IO. pp. 249-270.

Pergamon

Press 1970. Printed in Great

Britain

RADIATIVE INTENSITY CALCULATIONS 100 % CO2 AND 90 % C02-10 % N2*

FOR

G. H. STICKFORD, JR. Aerophysics Section, Jet Propulsion Laboratory, Pasadena, California 91103 (Received 10 July 1969)

Abstract-Radiative intensity calculations have been performed for plasmas of 100 % CO, and 90 % C02-10 % N, for temperatures of from 10 000 to 20 000X, densities from 0.0001 to 1.0 earth standard density, and path lengths from 1.0 to 30.0 cm. The actual spectral detail of the continuum absorption coefficient was computed from 240 to 30 000 A. The ultraviolet atomic lines were computed by adding the individual line absorption coefficients to the continuum at f A intervals, thus accounting for reabsorption due to lineline overlap. The visible and infrared lines are individually integrated and added to the total intensity. The total radiation is found to consist primarily of ultraviolet radiation, the lines being generally more important than the continuum. The addition of small amounts of N, to CO2 seems to have only a small effect on the total radiant intensity.

INTRODUCTION

A VEHICLE entering the atmosphere of Venus at a speed greater than the parabolic speed (10.42 km/set) will develop a shock layer plasma with temperatures in excess of 10 000°K. Characteristically, at these temperatures plasma radiation becomes very strong and may be the dominant source of heating experienced by the vehicle. Furthermore, in this temperature regime, and at normal densities, the plasma radiation is generated primarily by atomic reactions, i.e., free-free, free-bound, and bound-bound (line) processes. Molecular radiation is important at and below 10 000X, however, convective heating will normally dominate in this temperature regime. The first step in computing the radiative flux transmitted to a vehicle by the shock layer plasma is to determine the emissive intensity associated with the particular plasma. Having calculated the intensity, one may then proceed to the flux calculation for a particular vehicle geometry. In the case of extremely high temperatures when radiative energy losses become comparable to the kinetic energy of the fluid, the flux calculation becomes coupled with the fluid dynamics equations. The intensity calculations must then include the varying temperature and density field within the shock layer. The purpose of this paper is to present the results of a study in which the emissive intensity generated by plasmas consisting of 100% COz and 90% C02-10% N2 were computed for temperatures ranging from 10 000 to 20 000°K. The plasma was assumed to be isothermal and in local thermodynamic equilibrium. The following includes a discussion on the calculation procedure used and a method by which these results can be * Research sponsored by NASA under Contract NAS-7-100. 249

G. H. STICKFORD.JR.

250

applied to predict the stagnation point radiative heating to be expected from the shock layer of an entry vehicle. COMPUTATIONAL

METHODS

Radiative intensity The equation of radiative transfer within a gas, for steady state conditions, is”’ dZl = K;(l -e-hcl”kT)(B1-ZI). dx

-

The total absorption coefficient, K;, is defined as ic;. = 11 j

Njc+)j i

where N$ is the number density of the ith energy level of thejth specie, and u(1): is the crosssection of the same energy level and specie. The exponential in equation (1) is the induced emission term; IA is the spectral radiative emission or specific intensity, and BA is the Planck or black body function. For a completely isothermal gas, which is treated in this study, equation (1) reduces to the familiar form IA = B,(l -eeKlx)

(2)

where KI includes the induced emission term, 1 -e-hc”kT. The determination of the spectral emissivity by a numerical evaluation of equation (2) would be very tedious since one must sum over hundreds of microscopic processes at each wavelength to obtain K,. This must be repeated at very small wavelength intervals such that the spectral details of the discrete emission of atomic lines is accounted for. The total calculation may require lo* or lo9 computations, depending of course on the accuracy desired. The final result would not be general but would depend on the gas or gas mixture as well as temperature, density and path length. Alternatively, one may simplify the problem by writing the total absorption coefficient as the sum of a continuum absorption coefficient and a line absorption coefficient, K1 = Kf+K:.

(3)

Substituting into equation (2) and rearranging the terms one obtains@) Z, = B,(l-e-K~x)+B,(I-e-K~“)e-K~x.

(4)

The first term in equation (4) is the contribution of the continuum processes. This contribution can be accurately predicted by evaluating K: at only a few hundred spectral points. The second term is the line contribution and it is in evaluating this term that it becomes necessary to make some simplifying approximations. Most generally it is assumed that all the lines have a similar shape defined by the line shape parameter, LJbJ, where bi is the half-width of the line, and that the lines are completely isolated from one another. It is then possible to analytically integrate each line independently and simply add the line contribution to the integrated continuum contribution.

Total radiative intensity calculations for 100 % CO2 and 90 % CO,-10 % N,

251

The total integrated intensity in this case is given by m

I(x) =

i 0

I,dl

=

s

B~(l-e-KF)d~+CBliW,(x)e-K~x

(5)

I

0

where Izi is the line center wavelength, and Wi(X)is defined as the equivalent width of the line, 00 W’(x) =

s

(I- e-sL+(bi)X)dR.

(6)

0

The line strength parameter, S, is defined as S = 2xZrocN,.f,,.[l For lines that can be characterized the equivalent width ist3’

-e-hc’akT],

by a dispersion profile an approximate

w(x) = [46$x( 1 - e - Sx/4bi)]II2

(7) expression for (8)

where bi is the line (half) half-width in frequency units. By applying this technique, the total number of computations required is less than 103, a reduction of 106. The resultant accuracy of such a simplified calculation is very poor for most of the plasma conditions of interest. For plasmas composed of several atomic species the lines are not completely isolated and reabsorption due to line-line overlap is important, especially in the ultraviolet region of the spectrum. These lines contribute greatly to the total intensity and errors of 100 per cent or more would not be uncommon if overlapping were neglected. In the present work an attempt has been made to include the effects of reabsorption due to line-line overlap while retaining some of the simplifying assumptions described above. Consider first the ultraviolet portion of the spectrum. A detailed calculation of the continuum absorption coefficient was performed by summing over all the various continuum sources at 4 A intervals from 240 A to 2000 A. Added to this at each wavelength interval was the spectral contribution of the lines assuming a dispersion profile for each line. However, since the Stark broadened lines vary in half width from lo3 to 10d3 A (Ne N 1Ol6 to 10” part./cm3), a significant portion of many narrow lines would be excluded using a mesh size of f A. To properly account for this contribution the lines with (half) half-width less than the mesh size were treated as isolated lines and their contribution was determined by analytical integration. The radiative intensity was thus computed using equation (5) where K: is now the continuum contribution plus the contribution of the wide lines (A1,,2 > 1 A), and the narrow lines are accounted for by the second term of this equation. An illustrative example of this computational method for 100 % CO2 is presented graphically in Fig. 1. In Fig. l(a) is shown the results of the simplest calculation where all the lines are treated analytically. The line contribution is illustrated schematically as a rectangular region of width Ali = W~X&-~%

(9)

G. H.

252

STICKFORD,

JR.

Overlapping of the rectangular regions indicates an over estimation of the line contribution and is indicated here by extending the overlapped portion above the black body limit. Figure l(b) shows the results of choosing a step size of 4 A. In this particular example, the overlapping is reduced a great deal. Figures l(c) and (d) are the result of decreasing the step size to i and &A respectively. Shown in Table 1 is the integrated intensity for this wavelength interval (800 + 1000 A) for the four mesh sizes used. Choosing the &A case as the norm, the method of treating all lines analytically is 23 per cent high, using a mesh size of :A reduces the error by 3, to 7 per cent. The a A mesh size case was only 2.6 per cent higher than the & A case. The conclusion to be drawn from this analysis is that the method of including the wide lines into the continuum absorption coefficient reduces significantly the error due to

CONTINUUM

01

+ LI

13.0

12.0 0.m

I o.w5

FIG. l(a, b). Detailed spectral emittance

/ 14.0 PHoTONENERGY / O.opo w*vEtENGTHX.

I

/ 15.0

16.0

hv, w I 0.085

0.080

microns

of CO2 from 800 to 1000 A for various wavelength

step sizes.

Total radiative

intensity

.zo-

calculations

for 100% CO, and 90 % CO,-10%

I

I

I

253

N,

(cl A)r - l/4 i I.15 -

.I0 -

1.05 -

CONTINUUM

+ LINE 1

O_

I

I

I

0-

I

I

I

(dJ Ax - 1116 A 5-

0-

CONITINUUM

+ LINE 1

16.0

15.0

140

13.0

I

I

I

I

I, 12I.0

PHOTON ENERGY hv, ev I 0.100

FIG. l(c, d). Detailed

I

0.095 spectral emittance

I

0.090 WAVE LENGTH &, microns

I

I

0.085

of CO, from 800 to 1000 k~for various wavelength

0.080

step sizes.

254

G. H. STICKFORD,JR. TABLE 1. INTEGRATED INTENSITY FROM FIG. 1 Step size

Intensity

Error (%I

1493 1301 1248 1216

22.8 7.0 2.6 norm

(‘Q t t A-

reabsorption of overlapping lines. A mesh size of & A would of course be the most accurate but due to computational limitations it was necessary to limit the mesh size to f A. The 7 percent error indicated for this particular condition is not necessarily typical. The actual error may be more or less depending on the plasma conditions. The important point is that this method leads to a significant reduction of the line overlap error. The visible and infrared regions (,I > 2000 A) of the spectrum were treated in a more approximate manner. The continuum absorption coefficient was determined at 25A intervals and all the lines were individually integrated. Since the line contribution is nearly always less than 10 per cent of the total intensity, the error due to neglecting overlapping line reabsorption in the visible and infrared will be small. Radiative jlux

The spectral radiative flux is defined by the expression FA =

5 R

Z,(x) cos 0 dR

(10)

where FAis the incident energy per unit area dA. Figure 2 defines 0, do, dA, and the distance x. For a plane-parallel, isothermal slab of thickness 6 the flux becomes n/2 FL = 2nBA

s

(l-e-

Kld/cos“) cos 0 sin 8 de.

0

FIG. 2. Description of coordinates used in equation 10.

(11)

Total radiative intensity calculations for 100 % CO, and 90 % CO,-10 % N,

Performing the integration one arrives at FL = nB,[l -e-K”dE(K&J

_

d)3

(K

2.

A very good approximation

+

wa4

---

VW5

2.2 !

3.31 + *...

to equation (12) is given by Fn = ~rB~[l-e-KAc2a)].

(13)

Note that the right side of equation (13) is simply 71times the intensity evaluated at 26, FA = 7X1,(26).

(14)

The total isothermal flux is al

F =

s

Fi dl = x1(26).

(15)

0

Similarly, one may integrate equation (10) for various geometries and arrive at an approximation comparable to that given by equation (15). In the present study, this has been done for the spherical cap and cylindrical cap geometries and the results can be summarized by the expression F = nl(A6).

(16)

The value of A is presented in Table 2 as a function of 6/R, the ratio of shock layer thickness to body nose radius. Equation (16) gives the total flux incident at the stagnation point. Equations (15) and (16) are exact in the limits of optically thin and optically thick plasmas. However, for the range of optical thicknesses 0.1 < K,6 < 1.0 these results will be on the order of 10 per cent too high. Radiative lossks from the shock layer can have a large effect on the shock layer flow field. PAGE et CX~.,‘~’ have made extensive calculations of the nonadiabatic, nonisothermal TABLE 2. VALUE OF A FOR EQUATION (16) Body type Spherical Spherical Spherical Cylindrical Cylindrical Cylindrical

W

A*

0.05 0.10 0.15 0.05 0.10 0.15

1.67 1.56 1.50 1.77 1.73 1.66

*These results compare quite favorably with the calculations of BOBBIIT.(~’

256

G.

H. STICKFORRJR.

flux for a strongly absorbing air shock layer. Their results differ from the transparent treatments of this problem, nevertheless they still correlate quite well with the radiative cooling parameter, r, defined as I-=

2Fisothermal

t&Y”, .

For T’s ranging from 0.04 to 1.0, the nonisothermal

flux can be expressed simply as(@

F = (O-2-0.295 lOg,oIJFisothemai.

(17)

input data

The input data used in preparing the present calculations have come from various sources. The atomic line data have come exclusively from the tabulation of WILSONand NICOLET.(‘)They have presented nearly 300 atomic and ionic lines for the three species carbon, nitrogen, and oxygen, giving the f number, line width, and line shift. Some grouping of upper energy levels was done, however for the dense plasmas of interest, Stark broadening tends to smear these levels together, making this a good approximation. To obtain the free-free continuum contribution, the hydrogenic f-f cross-section of KARZASand LATTER@)was used. In the visible and infrared, the free-bound cross-sections computed by ANDERSONand GRIEM(9) for carbon, nitrogen, and oxygen have been used. These cross-sections were computed using the quantum defect technique. In the ultraviolet, the free-bound cross-sections used were those recently calculated by THOMAS.(“)The selfconsistent field method was used including a correction for the effects of exchange. The resultant continuum cross-section, summed over all energy levels, is presented for T = 15 000°K in Figs. 3(a), (b),(c). As a comparison, the results of WILSONand NICOLET(‘) as well as AVILOVAet al.‘“’ are shown. The final input data required is the high temperature thermochemistry of the plasma. For this data, the calculations of MENARDand HORTON were used. COMPARISONS WITH OTHER CALCULATIONS AND EXPERIMENTS A comparison with the calculations of WILSONand GREIF(‘~)for air is shown in Fig. 4. The isothermal, radiative flux was computed using equation (15). The negative ion continuum source was neglected in both calculations, and the positive ion continuum source was neglected in the present calculations. The positive ion continuum is important at the highest temperatures and shorter path lengths which may explain the lack of agreement at these conditions. In all but this small region, the disagreement is no greater than 20 per cent. In Figs. 5 and 6 are shown comparisons of the present calculations with shock tube radiation measurements for air in the visible and infrared. The nitrogen negative ion contribution was determined by assuming a constant, effective cross-section, f$

=

= 0.25 x lo-l6 cm2

Total radiative intensity calculations for 100% CO, and 90 % CO,-10 % N,

‘Ol6 !U

257

00

1015

10’4

0

-

0

WILSON

0

AVILOVA.

AND NICOLET,

REF 01

d al REF IllI

PRESEti? ESTIMATE

101* lb) % 2

lo”-

NITROGEN 7. xc _.I

I

5.0

I

I

10.0 PHOTON ENERGY, hv,

15.0

a.0

ev

FIG. 3. A comparison of continuum cross-section calculation with other calculations.

summed

contributing

ASINOVSKII et al. ; (16) however and MENARD.~’‘)

negative ion this approximation one with N- measurements and it is a factor of 2 or 3 below the measurements of THOMAS

* These results may be subject to error from 5 eV to the ground state threshold.“4)

258

G.

H. STICKFORD.

JR.

PATH

AIR

P = 1 .o atm

0.024< A < 3.0 microns

-

-

-

WILSON

AND GREIF,

PRESENT

ESTIMATE

I 1

REF 13

N- NOT INCLUDED Of, N+ CONTlNULlh4 NOT INCLUDED IN PRESENT ESTIMATE I

IO

12

18

14 EQUILIBRIUM

TEMPERATURE,

22 1000 ‘K

FIG.4. A comparison of the present estimate with the isothermal flux calculation of WILSNand C&E&“)in air.

The calculations agree quite well with the data of NEREMand STICKFORD, as shown in Fig. 5, but are lower than the data of THOMASand MENARD, in Fig. 6. Shown in Fig. 7 is a comparison with the data of GRUSZCZYNSKI,(‘~) also in air, and the calculations of AVILOVAet al. GO) The present results are lower than the data; for the visible and infrared region the difference is approximately S-60 per cent, whereas the total intensity difference is only 30 per cent. Finally in Figs. 8(a), (b) are presented the shock tube data of LIVINGSTON and WILLIARD@’ in air and 90 % C02-10 % N2. These measurements are the sum of convective and total radiative heating, thus a convective heat transfer contribution was added to the radiative contribution. For this purpose the convective heat transfer theory of VAN TASSELL(*‘)

Total radiative intensity calculations for 100% CO, and 90 % CO,-10 % N, I

I

I

I

I

I

/PI

259

=l.OmmHg

/ / / /

/

O/

AIR 0.17 < AC 2.7 microns OL*O.l8sm NEREM AND STICKFORD, OL=O.36cm

(DARK SYMBOLS

-

P, = 0.20 mm tis)

L = 0. I8 cm PRESENT

----_=0.36sm

8

ESTIMATE

I

0

IO’

REF 17

1

I 10

1

1

1

I

I

I2

I4

16

18

20

EQUILIBRIUM

TEMPERATURE.

22

1000 *K

FIG. 5. A comparison of the present estimate with the data of NEREMand

STICKFORD

in air.

was used for 90 % C02-10% N2, and that of DE RIENZO and PALLONE@‘) for air. The total radiative flux was determined using equations (15) and (17). In both cases the comparison is quite good. RADIANT

INTENSITY

CALCULATIONS

The results of the calculations for the two gases, 100 % CO2 and 90% C02--10% N2, are presented in Figs. 9-13. The calculations were performed for temperatures ranging from 10 000 to ZGOOO”K,for 5 densities between 0.0001 and 1.0 po, and for path lengths of 1, 3, 10, and 30 cm. The limiting black body intensity is included in Figs. 11-13 and is

G. H. STICKFORD,JR.

260

IO’

f AIR 0.2<

A < 3.0 miCrO”l

P, =0.25mmHg;.5=0.7cm

0 IO9

I IO

I

FIG. 6. A comparison

of the present

I

11 EQUILIBRIUM

estimate

THOMAS AND MENARD, PRESENT

12 TEMPERATURE,

REF 16

ESTIMATE I

13

I 14

15

1000 OK

with the data of THOMASand MENARD(‘~’ in air.

defined as

s

Bndll =

aT4. 7l

(18)

It can be seen from the figures that the presence of 10% Nz has a very small influence on the total radiative intensity of COz, the largest effect being a 10 per cent increase at some conditions. At the lowest temperatures and at the higher densities the presence of small amounts of Nz has negligible effect on the radiant intensity. In order to represent the relative importance of the individual radiative processes and to show the contribution of the different spectral regions, the total intensity was divided into six components. These components are: 1. the continuum above 2OOOA,

Total radiative

intensity

calculations

for 100 “/, CO, and 90 % CO,-10

P, = 0.33 rnnl~ ; Oh > 0.088 Oh>0.170 -

--

11

IO

SIMULATED FIG.

7. A comparison

I2 FLIGHT

GRUSZCZYNSKI,

PRESENT

REF 1s

CI .I REF 19 CALCULATION

13 VELOCITY,

261

6 = 1.0 cm

AVILOVA,

-

9

I

% N,

14

Km,.&

of the present estimate with the data of GRUS2CZYNSK1(‘*‘and the calculations of AVILOVA et ~1.“~’

2. the lines above 2000 A, 3. the continuum below 2000 A, 4. the lines below 2000 8, 5. the CO(4 +) molecular contribution,* and 6. the ion lines. The results are presented for two densities and for two path lengths at each density in Figs. 14 and 15. The results are for 100% coz. The ultraviolet region was found to be the dominant radiator for most of the conditions treated. However, at large mass path lengths (pL large) the visible and infrared continuum becomes very strong. In almost all cases the visible and infrared lines contribute less than 10 per cent to the total intensity. The molecular contribution becomes important at the very lowest temperatures and the higher densities, whereas the ion lines are important at the highest temperatures and lower densities. * The CO(4f)

contribution

was estimated

using the

results

of

GRUSZCZYNSKI@~)

for an f number

of 0.15.

262

G. H. STICKFORD, JR.

I

10.0

I

I

90%

8.0 -

4.0

AND WILLlARD

DATA6

0

3.17 ctn DIATRUNCATED

A

12.7 cm DIA HEMISPHERE

-

-

PRESENT

--

I mmHg

N2

LIVINGSTON 6.0 -

I P, = 0.25

C02-10%

1

CYLINDER

ESTIMATE

I CONTRIBUTION

I

PLUS CONVECTIVE 21

OF VAN T&SELL

4

0.4

-

0.2

-

0.11 6.0

I 6.5

I 7.0

I 7.5

I 8.0

SHOCK VELOCITY,

FIG. 8(a). A comparison

of the present estimate 90 % CO,-10

I 8.5

1 9.0

A

5I.5

bn/,.c

with the data of LIVINGSTON and WILL~ARD’~’for % N, and air.

Computation of flux The results of the intensity calculations can be used to estimate the stagnation point flux of a particular body using the simplified approach given by equations (15) or (16), along with equation (17) to account for radiative losses. * In order to determine the intensity at the path length of interest, one may construct cross-plots of the data. To facilitate crossplotting a tabulation of the results is presented in Table 3. The probable error of this

*The results of OLSTAD@~~agree qualitatively with this method of accounting for radiative losses, however, his results show a dependence on vehicle velocity. Nevertheless, equation (17) never differs more than 30 per cent from his results or the data presented in Ref. (24).

Total radiative intensity calculations for 100 % 1.0’

I

I

CO, and 90 % CO,-10 % N, I

I

1

263

I

I.0 AIR

P, = 0.25mmHg

.oLIVINGSTON

AND WILLIARD

3.17 cm DIA TRUNCATED 12.7 cm DIA HEMISPHERE

:

DATA6

CYLINDER

.o PRESENT -

-

ESTIMATE

I CONTRIBUTION

PLUS CONVECTIVE

OF DeRlENZO

AND PALLONE”

.o -

.o -

.a .6-

.4-

.2-

.I6.C)

I 6.5

I 7.0

I 7.5 SHOCK VELOCITY,

FIG.8(b). A comparison

I 8.0

1 8.5

I 9.0

9.5

k&c

of the present estimate with the data of LIVINGSTON and WILLLARD@) for 90 % CO,-10 % N, and air.

approach is estimated to be approximately 47 per cent, allowing 25 per cent error for the input data, 25 per cent for the intensity calculation, 10 per cent for the flux calculation, and 30 per cent for the radiative loss correction. This is very good when compared with the much longer “exact” solution which would have a probable error of at least 25 per cent just due to the uncertainty of the input data. SUMMARY

A method of computing the atomic radiative intensity from an isothermal plasma has been described which account for reabsorption due to line-line overlap. A simplified approach to the flux calculation was proposed which describes the flux to the stagnation

264

G.H.STICKFORD,

10-l

8

I 10

JR.

I

I

I

12

14

16

I 18

I 20

22

EQUlLlRlUhl TEMPERATURE, 1WO'K

FIG. 9. Isothermal

intensity

results for p/p,, = 0.0001.

region of a cylindrical, spherical, or plane parallel shock layer as an algebraic function of the intensity. A correction for nonadiabatic flow is also included. Several comparisons are made between the present method of computing radiation and other theories and several experiments. The agreement was good in most cases, however, in two instances, the present results were low. Calculations of radiant intensity were performed for gas mixtures of 100% COz and 90% COz-10% Nz between 10000 and 20 000°K. The addition of 10 % N2 to pure CO* has a small effect on the radiant intensity, causing at most a 10 per cent increase at some conditions. The ultraviolet region of the spectrum was found to contribute the majority of the radiation, the lines being generally stronger than the continuum.

Total radiative intensity calculations for 100 % CO, and 90 % CO,-10 % N,

265

R

1 0

G. H. STICKFORD, JR.

266 ’

’

II s

5

‘90 -’

=_

I

III

’

III

I

III

I

I

I

I

III

‘“z”=/M

I

Ill

I

III -0

‘0

3

I

I

‘AllSN31NI

I

I

I

I

Total radiative

intensity

calculations

OllV11 AUSN~INI

for 100 % CO, and 90 % CO,-10%

N,

G. H. STICKFORD.JR

268

TABLE 3. TABULATION

OF RAD~.~T~VEINTENSITYCALCULATIONS,IN

W/cm*-ster.

L = l.Ocm PIP0

1o-4

10-r

10-j

T 1000°K

10

0.695(O)* 0.681(O)

0.105(2) 0.107(2)

0.890(2) 0.902(2)

0.62q3) 0.666(3)

0.190(4)

12

0.240(l) 0.216(l)

0.546(2) 0.525(2)

0.661(3) 0.653(3)

0.378(4) 0.376(4)

0.108(S)

14

0.394(l) 0.355(l)

0.141(3) 0.130(3)

0.248(4) 0.238(4)

0.148(5) 0.142(5)

0.327(5)

16

0.517(l) 0.490(l)

0.220(3) 0.202(3)

0.596(4) 0.506(4)

0.379(5) 0.361(5)

0.743(5)

18

0.737(l) 0.731(l)

0.255(3) 0.261(3)

0.104(5) 0.971(4)

0.752(5) 0.714(5)

0.143(6)

20

0.114(2) 0.116(2)

0.261(3) 0.321(3)

0.141(5) 0.132(5)

0.133(6) 0.127(6)

0.245(6)

L = 3.0cm

PIP,

lo-*

10-l

lo-‘+

1o-3

loo

0.160(l) 0.159(l)

0.239(2) 0.245(2)

0.168(3) 0.169(3)

0.115(4) 0.149(4)

0.276(4)

0.558(l) 0.509( 1)

0.128(3) 0.124(3)

0.11944) 0.121(4)

0.671(4) 0.728(4)

0.163(5)

0.920(l) 0.832(l)

0.338(3) 0.314(3)

0.458(4) 0.442(4)

0.228(5) 0.228(5)

O&1(5)

0.119(2) 0.111(2)

0.537(3) 0.495(3)

0.115(5) 0.109(5)

0.536(5) 0.534(5)

0.965(5)

18

0.158(2) 0.154(2)

0.633(3) 0.628(3)

0.215(5) 0.203(5)

0.105(6) 0.104(6)

0.172(6)

20

0.228(2) 0.228(2)

0.662(3) 0.749(3)

0.314(5) 0.295(5)

0.183(6) 0.183(6)

0.275(6)

T 1000°K

10

* Number in parentheses indicates power of 10. Upper number for 90 ok Co,-10 oY N,, lower number lOO%CO,.

Total radiative intensity calculations for 100% CO, and 90% COz-10%

N,

269

TABLE3 (contd.) L = 10.0 cm PIP0

1o-4

10-a

1o-2

10-l

IO0

T 1000°K

10

0.412(l)* 0.412(l)

0.536(2) 0.544(2)

0.332(3) 0.342(3)

0.193(4)

0.473(4)

12

0.143(2) 0.133(2)

0.309(3) 0.302(3)

0.220(4) 0.216(4)

0.100(S)

0.230(5)

14

0.238(2) 0.217(2)

0.856(3) 0.804(3)

0.830(4) 0.795(4)

0.303(5)

0.602(5)

16

0.285(2) 0.265(2)

0.142(4) 0.132(4)

0.209(5) 0.199(5)

0.689(5)

0.113(6)

18

0.378(2) 0.364(2)

0.172(4) 0.166(4)

0.402(5) 0.380(5)

0.131(6)

0.184(6)

20

0.506(2) 0.499(2)

0.184(4) 0.194(4)

0.630(5) 0.597(5)

0.222(6)

0.282(6)

L = 30.0 cm PIP0

1o-4

10-J

1o-2

10-l

loo

10

0.975(l) 0.984(l)

0.985(2) 0.992(2)

0.667(3) 0.678(3)

0.291(4)

0.765(4)

12

0.346(2) 0.324(2)

0.607(3) 0.593(3)

O&3(4) 0.393(4)

0.145(5)

0.318(5)

14

0.574(2) 0.530(2)

0.183(4) 0.174(4)

0.144(5) 0.138(5)

0.420(5)

0.671(5)

16

0.707(2) 0.663(2)

0.330(4) 0.310(4)

0.399(5) 0.330(5)

0.907(5)

0.118(6)

0.859(2)

18

0.820(2)

0.423(4) 0.397(4)

0.607(5) 0.620(5)

0.162(6)

0.189(6)

20

0.107(3) 0.106(3)

0.464(4) 0.469(4)

0.103(6) 0.976(5)

0.267(6)

0.29q6)

T 1000°K

* Number in parenthesis indicates power of 10. Upper number for 90% CO,-lOO/O N,, lower number 100% coz.

REFERENCES

1, V. V. SOBOLEV,A Treatise on Radiariue Transfer, Van Nostrand, Princeton, New Jersey (1963) 2. L. E. LASHER,K. H. WILXIN and R. GREIF,JQSRT7,305 (1967). 3. C. L. TIEN, .fQSRT6,893 (1966).

270

G. H. STICKFORD.JR.

4. P. J. BOBBITT,Effects of shape on total radiative and convective heat inputs at hyperbolic entry speeds. Presented at the 9th Annual American Astronautical Society Meeting of the Interplanetary Missions Conference, Los Angeles, California (1963). 5. W. A. PAGE, D. L. COMPTON,W. J. BORUCKI,D. L. CIFFONEand D. M. COOPER, Radiative transport in inviscid nonadiabatic stagnation-region shock layers, AIAA 3rd Thermophysics Conference, Paper No. 68-784 (1968). 6. F. LIVINGSTON and J. WILLIARD,Planetary entry body heating rate measurements in air and Venus atmospheric gas up to T = 15 OOO”K, AIAA 4th Thermophysics Conference, Paper No. 69-635 (1969). 7. K. H. WILSON and W. E. NICOLET, JQSRT 7,891 (1967). 8. W. J. KARZAS and R. LATTER,Astrophys. J. Suppl. Ser. 6, No. 55 (1961). 9. A. D. ANDERKJN and H. R. GRIEM, Proceedingsof the Sixth International Conference on Ionization Phenomena in Gases, Vol. 3, p. 293. North Holland, Amsterdam (1963). See also H. R. GRIEM, Plasma Spectroscopy, McGraw-Hill, New York (1964). 10. G. THOMAS,Jet Propulsion Laboratory, Pasadena, California, Private Communication. Article to be submitted to JQSRT. 11. I. V. AVILOVA,L. M. BIBERMAN, V. S. VOROBJEV, V. M. ZAMALIN,G. A. KOBZEV,A. N. LAGAR’KOV,A. CH. MNATSAKANIAN and G. E. NORMAN,JQSRT 9,89 (1969). 12. W. MENARDand T. HORTON,“Shock Tube Thermochemistry Tables for High Temperature Gases, Vol. IAir, Vol. II-90% CO,-10% N,,” JPL TR 32-1408 (1969). 13. K. H. WUON and R. GRIEF,JQSRT8, 1061 (1968). 14. K. H. WILSON,Lockheed Palo Alto Research Laboratory, Palo Alto, California, Private Communication. 15. J. C. MORRIS, R. U. KREY and R. L. GARRISON, “Radiation Studies of Arc Heated Nitrogen, Oxygen, and Argon Plasmas,” Aerospace Research Laboratories, ARL 68-0103 (1968). 16. E. I. ASINOVSKII, A. V. KIRILLIN and G. A. KOBZEV, “Continuous Radiation of Nitrogen Plasma,” Translated from TeploJizika Vysokikh Temperatur 6,146 (1968). 17. G. M. THOMASand W. A. MENARD,AIAA J. 5,2214 (1967). 18. R. M. NEREMand G. H. STICKFORD,AIAA J. 3, 1011 (1965). 19. J. S. GRUSZCZYNSKI and W. R. WARREN,AIAA J. 5,517 (1967). 20. I. V. AVILOVA,L. M. BIBERMAN, V. S. VOROBJEV, V. M. ZAMALIN,G. A. KOBZEV,A. N. LAGAR’KOV,A. CH. MNATSAKANIAN and G. E. NORMAN,JQSRT9, 113 (1969). 21. W. VAN TASSELL, Convective heating in planetary atmospheres, AVCO/RAD-TM-63-72, Oct. 1963. 22. P. DE RIENZOand A. J. PALLONE,AIAA J. 5, 193 (1967). 23. J. S. GRUSZCZYNSKI,Hypervelocity heat transfer studies in simulated planetary atmospheres, General Electric Co., Final Report, JPL P. 0. 950297 (1967). 24. W. B. OLSTAD,AIAA J. 7, 170 (1969).