-

AIAA-87-1576 Navier-Stokes and Viscous Shock-Layer Solutions for Radiating Hypersonic Flows Roop N. Gupta, Vigyan Research Associates, Inc., Hampton, VA

AIM 22nd Thermophysics Conference June 8-10, 1987/Honolulu, Hawaii

For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 1633 Broadway, New York, NY 10019

IUVIER-STOKES AND VISCOUS StlOCK-LAYER SOLUTIONS FOR RADIATING BYPERSONIC FLOWS

Roop N. Gupta Vigyan Research Associates. Inc.

Hampton. VA 23666-1325

Abstract

Results are presented from the Navier-Stokes and viscous shock-layer (VSL) calculations with nonequillbrim and equilibrium chemistry, respec- tively. These calculations eontain coupling to the Aerotherm radiation code RAD. A simplified form of the electron energy equation is used to obtain an electron temperature in the Navier- Stokes calculations. The radiation in the flow- field is calculated using this temperature. The Navier-Stokes code Is used at high altitudes only. whereas the VSL code is employed for the entire entry period to make estimates of the radiative and convective heating to the Fire I1 vehicle. Results from the Navier-Stokes code have also been compared with the predictions of Lee and Kawamura. who used gray-gas radiation model and thin-layer Navier-Stokes equations.

quite good agreement is obtained between the measured and computed values of radiative and con- vective heating from the VSL code in the medium- to-low altitude flight regime of the Flre I1 vehicle. At high altitudes, the Nsvier-Stokes calculations considerably overpredict the Fire I1 flight data far radiative intensity. This is attributed to the deficiencies in the Aerotherm radiation model when used for low-density flight conditions. This model contains the thermal equi- librium assumption and precludes accounting for the collision-limiting phenomenon at high alti- tudes. Present Navier-Stokes calculations high- light the effect of these assumptions on radiative heating calculations for such conditions.

uomene1ature

freestream specific heat at constant premure concentration of electrons in moles/volume radiation intensity backward reaction rate for species J

forward reaction rate for species j concentration of N in moles/volume

concentration of N+ in moles/volume coordinate measured normal to the body,

concentration of 0 in mles/volume

concentration of O+ in moles/volume divergencg of the net radiant flux, Q*Rfi/p3J: convective heat flux, qt/p:UU*_ net radiant heat flux normal t4 the

surface, q*/p*u*

n*/R;

3

3 r - -

1

(+)*

(-)*

component of radiant f lux away from wall

component of radiant flux towards the wall spectral radiative flux

9,

9,

R* universal gas eonstant q:,"

R i nose radius T temperature T*/T:ef

2 reference temperature U*_/C*

electron temperature freestream velocity

T:.f P" 2 u: 0. absorptance E surface emissivity r J Stefan Boltzmann constant

freestream density ionization energy per mole of species J

0:

5 superscripts

* dimensional quantities

Subscripts

wall value w e electron

Abbreviations

NS Navier-Stokes VSL viscous shock layer

3

I . 1ntroductioo

Intensive the r tical efforts have been made in the recent pastP-' to obtain the convective and radiative heating rates needed for the design of a reusable and relaible heat protection system for space-based aeroassisted orbial transfer vehicles (AOTV). Since it is very difficult, if not Impos- sibile, to simulate high-enthalpy low-density flow with chemical as well as thermal nanequi- librium and strong viscous-interaction effects in ground-based facilities, much reliance will be placed upon the theoretical methods for the design of an AOTV. A flight experiment9 is currently being planned by NASA to gather the required data for verification of the computational methods.

One of the important problems to be addressed in the design of an AOTV is the role played by nonequilibrium radiation. Only Refs. 1, 4 , 6, 7, and 8 have included radiati n in their analysis. Park has presented resul sp*' with a continuum formulation, whereas Bird' has provided calcula- tions with a particle approach to describe the nonequilibrium radiation. References 7 and 8 have analyzed equilibrium radiation with inviscid and viscous shock-layer codes, respectlvely. Even though Park*$ nonequilibrim radiation code is the most detailed, it is difficult to couple to a - flowfield code.

In the present study an attempt has been made to develop a computationally tractable and effi- cient method for coupling B radiative transport code to a flowfield solution with nonequilibrium chemistry. The Navier-Stokes code of Ref. 10 has been coupled to the Aerother - s radiative transfer code developed by Nieolet. The radiation is computed by using an electron temperature obtain from an approximate electron energy equation. The calculations are limited to the stagnation region of a blunt body. The Aerotherm code employed for radiation flux calculations is based on the assumption of thermal equilibrium. This code is easy to couple to a flowfield code and is known to g i v e good results for flow conditions where thermal equilibrium can be assumed. This is not, however, strictly applicable under the low- density conditions where both thermal and chemical nonequilibrium conditions prevail. Under these conditions, there might a180 be a deficiency in the excited state populations because of the lack of particle collisions. This phenomenon known as collision limiting, is not accounted for in the Aerotherm radiation code. With these limitations, thie code clearly does not model all the physics of thermal nonequilibrium phenomenon. However. the coupled results obtained by using this code can provide information about the importance of the interaction between the radiative and convec- tive heating under the chemical nonequilibrium flow conditions. These results may also be help- ful in developing a more realistic radiation code which could be coupled to a flowfield solution with nonequilibrium chemistry.

Chemical equilibrium results have also been obtained here for the coupled radiative heating by employtqg the viscous shock-layer ( E L ) equa- - tions. These results are comqared with those of Ref. 8 and the Fire I1 data. Chemical (and thermal) equilibrium is considered to prevail at lower altitudes for the Fire I1 vehicle

v

?$

trajectory.

XI. Analysis

Governing Equations and Method of Solution The Steady Navier-Stokes equations employed

for a reacting gas mixture are taken from Ref. 10. A radiative cooling term, -Q (which repres- ents the radiative flux divergence V.q ) is added to the right-hand side of the energy Eq. ( 4 ) of Ref. 10. The viscous shock-layer (VSL) equations used with equilibrium chemistry and radiation are those of Ref. 13. In Ref. 10, the governing Navier-Stokes equations are first reduced to a Set of coupled nonlinear ordinary differential equa- tions with the help of local similarity assump- tion. A successive relaxation method is then used to solve the nonlinear algebraic equations resul- ting from a finite-difference approximation of differential equations. The viscous shock-layer equations of Ref. 13 are solved as a parabolic Set of equations using an implicit finite-difference, numerical procedure. Similar to the Navier-Stokes results, the VSL analysis also provides a direct means of accounting for interactions between the inviscid and viscous flow regions due to radiative transfer.

Radiative Transport

represented as the difference of two components: v The net radiative flux, q,, can be

At the wall

~

2

where E is the surface emissivity.

The precursor effects are neglected in the VSL analysis, whereas these are automatically included i n the Navier-Stokes calculations since the governing equations are integrated from the body surface to freestream. The energy reradiated from the surface is included in the radiation transport calculations. The radiative flux, q,, and the divergence of the radiative flux, Q, are calculated with the radiative transport code RAD, as presented in Refs. 11 and 15. The RAD computer code has been incorporated in the present Navier- Stokes code. The VSL code (HYVIS) of Ref. 13 is already coupled to the RAD code.

The RAD code accounts for the effects of "on- gray self-absorption and radiative cooling. Molecular band, continuum, and atomic line transi- tions are included. A detailed frequency depen- dence of the absorption coefficients is used for integrating over the radiation frequency spectrum and the tangent slab approximation is used for integrating over physical space. The chemical species considered in the present study for determining the radiative transport are: N. N2. N+, N;, 0, 0 2 , 0+, 0:. NO, NO+, and e-.

Chemical Composition (a) Equilibrium: The equilibrium chemical

composition is determined (for a given tempera- ture, pressure, and elemental composition using a free-energy minimization analysis. since the criterion for equilibrium at constant temperature and pressure is that the change in free energy be zero, the equiltbrium composition is determined when the total free energy of the mixture is made a minimum with respect to any possible change in composition.

1 6 , 3

(b) Nonequilibrium: When the finite rate of the chemical reactions is considered, the rate of production terms, + are required. The produc- tion terms appear ii'n the energy equations when formulated in terms of temperature and in the species continuity equations. These terms are obtained from the various chemical reactions among the individual species. The number of equations to be included in a chemlcal reaction model depends an the particular problem being con- sidered. For most re-entry applications, the temperature in the shock layer is less than 15000 K. For such a case, a seven-species reaction model (02, N2, 0, N, NO, NO', ltd e ' ) represents the chemistry reasonably well. For the high- energy flows such as those encountered by the AOTVs, the temperatures in the shock layer can be greater than 20,000 K. For such applications, the ionization of atoms and molecules of oxygen and nitrogen must be mnsider$d a%d an eleven-species (02. N 0, N, NO, 0;. N2, 0 , N+, NO+, and e-) chemica? model represents the reactions in the flowfield more appropriately.

The present study included a comparison of the seven- and eleven-species chemical models f o r a given application. The reaction-rate coeffi-

cients for the lyen-species model have been taken from Blottner, whereas the reaction-rate coef- ficients for the eleve species model were adopted from Kang and Dunn. '' The values of these reaction-rate coefficients as obtained from Blottner and Kang and Dun" are given in Table l(a) along with the chemical reactions employed i n the computations. The corresponding third-body efficiencies relative to argon are given in Table l(b).

Electron Energy Equation The electron temperature used in the radia-

tive flux calculations is obtained from an apprp- 2 ximate form of the electron energy equation. This equation is similar to the one obtained from the steady-state form of Eq. ( 5 ) of Ref. 22 by neglecting the advection and vibrational-electron coupling terms but keeping the electron energy loss term. T$r following form of the electron energy equation has been employed to obtain the electron temperature.

where the reactions considered are the electron impact ionization reactions (given as reactions 8 and 9 in Table l ( a ) . In Eq. ( 3 ) , * is a mass- averaged elastic collision frequency and is obtained from

- "e k . * - I k m k

( 4 )

In Eq. ( 4 ) . Y is the collision frequency between the electron end the species k. The collision frequency for electron-atom or electron-molecule collisions is related t o the elastic collision cross-sections by

ek

where 9 is the number density of species k, v*[-(8k T:/n m:)1'2] is the average electron velocity (k is the Boltzmaon constant), and Q* is the elastic collision cross-section. The cross- sections used are those given in Ref. 23. For electron-ion collisions. the collision frequency is obtained from

ek

-10

-28 where e ( - 4.8~10 esu) is the electron charge

and m*(- 9.11~10 gm) is the mass of an electeon.

** It should be mentioned here that the simplified form, Eq. ( 3 ) . of the electron energy equation nay result in unrealistic electron temperatures (such 8s negative values) without the radiative cooling in the flawfield. For such cases, the complete electron energy equation given in Refs. 12 or 22 may be more desirable to use.

Thermodynamic and Transport Properties Thermodynamic properties for specific heat,

enthalpy. and free energy and transport properties for viscosity and thermal conductivity are 'd required for each species considered. Values for the thermodynamic and transport ropertjes are obtained by using curve fits. lo*'' The mixture viscosity is obtai ed by the method suggested by Armaly and Sutton. 'O For the ionized species, ambipolar type of diffusion is assumed. For such a diffusion model the binary diffusion coeffi- cients must be doubled in the calculations for the multicomponent diffusion coefficients. In this study, the Prandtl number and Lewis number for the "on-ionized species are set equal to 0.72 and 1.4, respectively.

111. Results and Discussion

Two sets of calculations have been performed in this study. The first set corresponds to the case analyzed by Lee and Kawamura in Ref. 21. This set of calculations was carried out to check the Navier-Stokes computer code" with and without coupling to the radiative transfer code" for the eleven-species chemical model. The second set of calculation corresponds to the Fire I1 flight experiment. 54 For this case, the Navier-Stokes calculations with finite-rare chemistry and radia- tive transfer coupling were done for the high- altitude trajectory points (time - 1631 sec. and 1632 sec.) , whereas full viscous shock-layer calculations with equilibrium chemistry and radiative transfer coupling were carried Out for 19 points covering the entire trajectory of Fire 11.

Lee and Kawamura Case (Ref. 21)

Lee and Kawamura analyzed the nonequilibrium flow in the stagnation region of a blunt body with thermal radiation under the low density condi- tions. They used a gray-gas radiation model without absorption of the radiation energy and employed the thin-layer Navier-Stokes equations. Both of these approximations limit the applicabil- ity of their results. Further. they considered only a seven-species chemical model. One of the attractive features of their results, however, is that, similar to the present calculations, also employed the polynomial curve fit formulas for the thermodynamic and transport properties as a function of temperature. Therefore, a direct comparison of the present full-layer Navier-Stokes code with that of Ref. 2 1 could be made. Table 2 gives the freestream conditions for Case B analyzed in Ref. 21 and used here for obtaining results for the purpose of comparison.

Figure 1 shows the predicted temperature profiles along the stagnation streamline. The profiles with gray-gas radiation and no radiation are very close to those obtained in Ref. 21. The small differences are due to the eleven-species chemical model and full Navier-Stokes equations employed in the present computations. Figure 1 also contains the temperature profilfa with non- gray radiation model of Aerotherm and with finite-rate and equilibrium flowfield chemistry. There is a strong coupling. for the reasons explained later, between the flowfield and nongray radiative transport as compared to the gray-gas radiation with nonequilibrium chemistry. This results in substantial lowering (or cooling) of

W

'$f

the flowfield temperatures. In fact, the maximum temperature obtained with nongray radiation model and finite-rate chemistry Navier-Stokes calcula- tions is almost the same as the one obtained with the same radiation model and equilibrium viscous

i shock-layer (VSL) calculations. The maximum electron temperature (used for the radiative heat transfer computations) is about 4% lower than the heavy particle temperature as shown in Fig. 1. The electron temperature is found from the steady- state approximate form of the electron energy equations given earlier.

Figure 2 gives the radiative flux components corresponding to the cases considered in Fig. 1. The flux component towards the wall is almost negligible with the equilibrium chemistry, whereas it is very large with the nonequilibrium chemistry when obtsi ed from the nongray radiation model of Aerotherm. '' With gray-gas assumption the radiative flux approaches towards the equilibrium chemistry value and the radiative cooling in the flowfield is substantially less ( s e e Fig. 1) as compared to the nongray model (with finite-rate chemistry).

The net radiative flux, q:, and its diver- gence. Q*. are shown in Fig. 3 . Profiles for the divergence of the radiative flux show that there is a Strong emission (indicated by positive Q*) from the shock transition zone and negligible absorption (reflected by negative Q*) in the viscous region with nonequilibrium chemistry as compared to the equilibrium chemistry predic- tions. The gray-gas model considered neglects absorption.

Figure 4 depicts the effect of doubling the nose radiua on radiative flux toward the body. Tvo things are tQ be noticed from this figure. - First, with the increase in nose radius, there is still negligible absorption in the viscous region. Second. the radiation reaching the surface does not increase linearly with nose radius as given in Ref. 8 . Also noted from Figs. 2 and 3 , most of the viscous region appears to be tranparent to the radiation and there ie negligible abeorption in this region. As will be explained later with the help of spectral flux distribution, most of the radiation reaching the surface comes from the 0- 6.2 eV range with nonequilibrium chemistry calculations wder the low-density. finite-ehock- thickness condition. Unpr these conditions, absorption is most likely for the ultraviolet radiation (in the 6.2 - 16.5 eV range) to a low energy or ground state, because m s t of the gas molecules and atom near B cooled surface will be in these stetee.

Fire I1 Data

The present predictions will now be compared with the flight data obtained from Fire I1 (Refs. 14 and 24). The forebody configuration for Fire I1 vehicle was a truncated hemispherical shape with B mall Corner radius 8s shown in Fig. 5. It had a layered heatshield composed of three beryl- lium layers, each backed by phenolic asbestos. Heatshields 1 and 2 were ejected during the entry to expose a clean surface for thO next data period. The dimensions of the heatehielda were smaller from heatshield 1 to 3. FOK the study, equivalent hemispherical nose radii 0.75, 0.66, and 0.60 m wre used for heatshields

I 1, 2 and 3 , respectively. The freestream eondi- tians considered are given in Table 3 .

?:Re:;

The Fire I1 vehicle was instrumented to measure incident radiation intensity using spectral and total radiometers and total heating rates (convective plus absorbed radiation fluxes) using calorimeters during re-entry. Radiometers were located at several locations, but the present analysis considers only the centerline location. The vehicle entered at zero angle of attack. Therefore. the centerline location was the flow stagnation point. Two types of radiometers were used. A total radiometer measured the intensity in the 0.2 - 6.2 eY range (limited by the quartz window). A spectral radiometer measured the spectral radiation, which was then integrated to provide total intensity in the 2 - 4 eV interval.

( a ) Navier-Stokes Results With Nonequilibrium Chemistry and Without Radiative Transport:

As pointed out in the introduction, for high energy flaws similar to those encountered in the Fire I1 flight experiment, temperatures in the shock layer would be greater than l50OO0 K . For such flows a seven-species chemical model may not be adequate. Therefore, a study was first made of the differences in the flowfield structure resul- ting from the seven- and eleven-species chemical models. Figure 6(a) shows the differences in the temperature profiles obtained from the two chemical reaction models. Two things are to be noted from this figure. First, the extent of the flowfield disturbance zone is larger with the seven-species model than it is with the eleven- species model. Second. the maximum temperature in the shock layer is greater with the seven-species model. The temperature distribution also shows that the shock-transition-zone thickness is about 50% of the shock-layer thickness and, therefore, considerable low density effects are noticeable at an altitude of 84.6 km in the Fire I1 trajectory. For viscous shock-layer calculations, a shock-slip boundary condition will. therefore, be required. However, the temperature obtained behind the shock (even with e shack-slip boundary condition) will be the sameb2 with both seven- and eleven-species chemical model due to the frozen-flow appronima- tion required in obtaining the flow properties behind the shock. The differences in temperatures shown in Fig. 6(a) m y not be important from con- vective heating point of view, but could be quite important in obtaining the radiative heat flux reaching the surface. Since the present calcula- tions integrate through the shock, the -precursor zone. (which would exist in front of a thick shock) is automatically accounted for. The electron number density distribution for the two chemical models is shown in Fig. 6(b). The electron number density is smaller with the eleven-species model.

The lower temperatures and electron number density obtained with the eleven-species model can be explained if the results of Figs. 6 ( c ) and 6(d) are analyzed. More energy is taken out of the flow to ionize the four additional species in an eleven-species model than in a seven-species model. This results in lower overall temperature levels in the merged viscous layer obtained with an eleven-species model. Because of the lower tempertures, the gas is denser through most of the shock layer and, therefore, the extent of the flowfield disturbance zone is smaller with the eleven-species model. Also, greater dissociation of N2 and O2 is obtained (see Fig. 6 ( c ) ) with the seven-species model due to the larger temperature

levels in the shock layer in this ease. The electrons are produced (for the case considered in present calculations) mostly through the ioni- zation of NO in an eleven-species model because of the trace quantities of other ionized species (Fig. 6(d)). However, these trace species do tie up energy and prevent a higher ionization level for NO'. In case of seven-species model with only one species to ionize, the larger temperature levels give greater amount of NO'. From the local charge neutrality condition employed here, a larger electron number density is, therefore, obtained with the seven-species model. Figure 6(e) shows the density proflles obtained with the two chemical models. These are consistent with the temperature dietribution given in Fig. 6(a).

Figure 7 shows the effect of change in altitude on the flowfield structure. With the decrease in altitude the extent of the flowfield disturbance zone as well as the thickness of the shock transition zone are reduced as expected. The results of Fig. 7 as well as those which follow have been obtained with an eleven-species model.

Figure 8 contains the temperature profiles with nonequilibrium and equillbrium chemistry. Due to the frozen-flow approximation, the inviscid ehock-layer analysis with nonequillbrim chemistry gives temperatures behind the shock almost twice of those obtained in the shock transition zone by the Navier-Stokes calculation. This would affect the radiation calculations considerably. Also, shown in this figure are the temperature profiles obtained with inviscid and viscous shock-layer calculations incorporating the equilibrium chemistry. When compared to the Nauier-Stokes calculations with finite-rate chemistry, these calculations show that the flow is far removed from equilibrium.

absorption noticeable with the nonequilibrium chemistry predictions in Fig. 9. Further, the equilibrium chemistry gives larger mass fractions as compared to nonequilibrium calculations of N2, 02, and NO, which act as absorbers near a cooled surface.

One of the weak links in the present Navier- Stokes results rithlfonequllibrium chemistry is the radiation model. This model was primarily developed under the assumption of thermal equlli- brium and also does not account for the deficiency in the excited state populations because of the lack of atomic and molecular collisions in the low density regime. Further, the radiation model of Ref. 11 gives large radiative flux when coupled to the nonequilibrium flowfield code. Even the use of electron temperature (which is not too different from the heavy particle temperature with radiative cooling) does not give radiative heat transfer comparable to the Fire I1 data as shown in Figs. 11 and 12. There is an encouraging trend, however. resulting from the Navier-Stokes results with nonequilibrium chemistry given in these fizures at times of 1631 seconds and 1632

v

- seconds. These times correspond to the altitudes of 84.60 km and 81.86 km, respectively. With the decrease in altitude. the radiative intensity appears to approach the data. Since the Navier- Stokes code could not be run at lower altitudes due to the sharpening of the shock (which in- creases the gradients of the flowfield quantities considerably in the shock transition zone), these results could not be continued to a point where the thermal equilibrium may be more appropriate in the radiation model. This difficulty could be overcome by fitting a shock and carrying out the viscous shock-layer (VSL) analysis with nonequi- librium chemistry. Some problems associated with the frozen-flow approximation (which gives rise to tremendouslv lame temoeratures behind the shock)

Y~ ~~~ r~~~~~ ~~ ~~

(b) Radiatively coupled Results F~~~ ~ ~ ~ i ~ ~ - are to be analyzed first, however, to make the VSL Stokes Equations With Nonequilibrim Chemistry and Viscous Shock-Layer Equations with Equilibrium Due to the oroblems associated with the

code for the high energy

Chemietry: The radiatively coupled solutions with

nonequilibrium and equilibrium chemistry are given in Fig. 9. This figure gives radiative flux for the Fire I1 case (analyzed earlier without the radiative transport). Similar to the Lee and Kavamura case of Ref. 21 considered earlier, there is negligible absorption in the viscous region near the wall for nonequillbrim chemistry. The viscous shock-layer (VSL) calculations with equilibrium chemistry do show absorption in the viscous region near the surface. Figure 10 presents the spectral flux distribution incident at the wall for bath continuum and line radiation. Following the usage of R e f . 11, continuum radia- tion includes band system radiation of the diatomic species as well as free-bound and free- free transitions. For the nonequilibrium chemistry case, line radiation is negligible and most of the continuum radiation is from 0 - 6.2 eV energy range. For the equilibrium chemistry calculations, the continuum radiation is still dominant. However, it is mostly from the ultra- violet (6.2 - 16.5 ev) energy range. In general, the ultraviolet radiation is more likely to be absorbed i n the cool wall region (where most of the molecules are in the ground state) because the ground state connected .transitions usually require higher photon energy. Therefore, there is no

W

radiation model at higher altitudes and with the Navier-Stokes and VSL codes with nonequillbrium chemistry at lower altitudes, it was decided to use the VSL code with equilibrium chemistry for obtaining results for comparison with the Fire I1 data throughout the entry. The solid curve in Fig. 11 represents the Fire I1 data taken during the prime data periods for each heatshield. The dashed curve is the data taken outside the prime period. The prime data periods far heatshields 2 and 3 were less than 0.5 seconds. The error band for the experimental data were estimated to be f201 (Ref. 14). An explanation of the anomalies seen in the data is given in Ref. 14.

The VSL results with equilibrim chemlstry were also obtained in Ref. 8 . They used an inverse predictive procedure. wherein a body shape is computed from the given shock shape. The present VSL predictions, from this point of vie are based on a direct predictive procedure, i.e., a shock shape is computed for the given body shape. In an inverse method, in place of computing the stagnation point, an effective stagnation point slightly off-centered f m n the body centerline is used.

The present predictions are i n good agreement with the Fire I1 data throughout the entry for the 0.2 - 6 . 2 eV interval a8 shorn in Fig. 11. The agreement is, in particular, quite good during the I

Yl

5

later part of the first prime data period and the entire third prime data period and fairly good during the second prime data period. For the early entry times, the equilibrium VSL results are not expected to be good due to considerable chemical (and thermal) nonequilibrium as Shown earlier. The presently predicted spectral inten- sities also give a similar trend in the 2 - 4 eV range as shown in Fig. 12. However, the agreement is not so good during the second prime data period. The present predictions compare very well with he inviscid shock-layer calculations of Sutton' during the third prime data period and afterwards. This result is physically expected because most of the shock-layer under the high density (low altitude) condition behaves like inviscid flow except for a narrow region (less than 10% of shock layer thickness) near the sur- face. The results of Ref. 8 are somewhat lower even at lower altitudes. They are considerable lower both from the experimental data and predic- tione during the first and second prime data periods. The reduction in radiation intensity is explained due to the self-absorption of the radia- tion by the cold gas in the viscous layer near the surface. The present VSL results, however, show that the net reduction in intensity due to self- absorption takes place at higher altitudes (see Fig. 13) because the viscous effects are spread throughout the shock layer. At lower altitudes (see Fig. 14). the reduction in the ultraviolet range is somewhat compensated by the increase of intensity i n 0 - 6.2 eV range. Further, at these altitudes (Fig. 14), the radiation intensity predicted by VSL becomes closer to the inviscid shock-layer predictions if the molecules are not included in VSL calculations. This may be because the inviscid shock-layer calculations will not - show large molecular mass-fractions near the surface due to high temperatures. The radiative heat flux and intensity for the total (0 - 16.5 ev), partial (0.2 - 6.2 ev) and short ( 2 - 4 eV) ranges are given in Table 4 along with the radiative flux absorbed at the wall.

The total heating rate calculations are compared with the Fire I1 data in Fig. 15. A time of 1617.75 seconds must be added to Fig. 15 to equal to the flight time presented in Figs. 11 and 12. The VSL calculations with equilibrium chemistry for the convective heating and the total (convective plus absorbed radiative) heating are presented throughout the entry. The total heating calculations employed the measured values for the beryllium absorptance. Also, shown are the Navier-Stokes calculations for total heating and convective heating with nonequilibrim chemistry. The present results are i n excellent agreement with the data for heatshield 3. This period is dominated by convective heating, which is con- trolled by the equilibrim chemistry. The present results are also in very good agreemen with the inviscid shock-layer result8 of Sutto2 in this period as expected. The various heating results are tabulated in Table 5 . The agreement be the present predictions and those of Sutton good and only fair with the data for heatehielde 1 and 2, respectively. The convective heating values by Sutton have been obtained from an engineering correlati~n.~~ For the peak heating period, heatshield 2, the present maximum value occurs at an earlier time and then decreases

-2 earlier than shown by the flight data. This trend is similar to the one predicted in Ref. 7. At

" 2

peak heating, the present calculations indicate that about one-third of the total heating is due to absorbed radiation. A l s o , the absorbed radiation is about two-thirds of the total radiative flux reaching the surface.

It is not surprising that the present equilibrium VSL and the engineering correlation results of Ref. 7 give values for the convective heating higher than the total experimental value during the earlier phase of heatshield 1 as seen from Fig . 15. This is because no allowance is made in both of these calculations for the low density effects. The convective heating predicted even by the Navier-Stokes calculations is higher than the total flight data at the earlier times because no surface slip boundary conditions are employed in these predictions. With Navier-Stokes predictions, the shock-slip effects are auto- matically accounted for. The validity of the total heating results may also be called into question at the earlier times for heatshield 1 due to the thermal equilibrim assumption contained In the radiation model employed in all the calcula- tions of Fig. 15. It should be mentioned here that a better agreement for total heating is seen in Fig. 15 between the experimentally measured date and Navier-Stokes predictions even though the predicted radiative intensities are large. This is due to the strong radiative cooling contained in the Navier-Stokes results. As a result of this cooling, the convective heat transfer (as compared to the no radiative cooling ea e) is reduced from 81.64 w/cm2 to about 16.75 w/cm at time = 1631 S,

for example. The absorbed radi tive flux at this trajectory point is 82.80 wlcm , giving a total heating of 99.55 wlcm'.

3 .?

IV. Conclusions This study presents results from the Navier-

Stokes and viscous shock-Iayer (VSL) calculations with nonequilibrium and equilibrium chemistry, respectively. These calculations contain coupling to a radiative transfer code RAD (referred to as the AerotheB radiation code here) developed by W. E. Nicalet. A simplified form o€ the electron energy equation is used to obtain an electron temperature in the Navier-Stokes calculations. The radiation in the flowfield is calculated using this temperature. The Navier-Stokes code is used at high altitudes and the VSL code is employed for the entire entry period to make estimates of the radiative and convective heating to the Fire I1 vehicle. The VSL code with equilibrium chemistry and radiative coupling is known to produce results of good accuracy.13 The Navier-Stokes code with nonequilibrium chemistry and radiative transport has been developed recently. The code checkout has been accomplished by analyzing a case con- sidered by Lee and Kawamura. They have used a simplified gray-gas radiation model with thin Navier-Stokes equations. The present full Navier- Stokes code gives comparable results under the similar aasumptions.

Quite goad agreement is obtained between the measured and computed values of radiative and con- vection heating from the VSL code in the medium- to-low altitude flight regime of the Fire I1 vehicle. At high altitudes, the measured and predicted values for the total heating and, in particular, that of radiative intensity differ considerably.

6

The large radiative intensity values obtained f r m the Navier-Stokes predictions are considered to be due to the assUmptions contained in the Aerotherm radiation model. This model was developed under the assumption of thermal &ut- librium and is not expected to be valid for the low-density flow conditions. Further, it also does not account for the collision-limiting phenomenon under these conditions .9 The present Navier-Stokes results. however, do provide an estimate of the effect of chemical nonequilibrium on radiation under the assumption Of local thermal equilibrium. These results also point to the need of obtaining a better continuum radiative trans- port model under the thermal nonequilibrium condi- tions. Recently developed jonequilibriwn radia- tion code NEQAIR by Park, even though most detailed. is difficult to couple to a flowfield solution. Hence, efforts should be made to improve the Aerotherm code for its deficiencies in the low-density flow regime. The chemical kinetics as well as the radiative transport calculations based on a two-temperature model is thought to be necessary under these conditions. The present Navier-Stokes results highlight the need for work in this direction.

Acknowledgments

This work was supported through NASA Contract NAS1-17919.

The author is thankful to Drs. K. Sutton and 3. N. Moss of NASA Langley Research Center for frequent discussion during the course of this work. Comments made by Mr. J. J. Jones during the preparation of this ramscript are also gratefully acknowledged.

1.

2.

3.

4.

5.

6.

7.

References

Park, C. , '"Calculation of Nonequilibrium Radiation i n the Flight Regimes of Aero- assisted Orbital Transfer Vehicles," - Design of Aeroassisted Oribtal Transfer Vehicles. Progress in Astronautics and Aeronautics, Vol. 96, 1985, pp. 395-418.

Gnoffo, P. A. and Greene. F. A., "A Computational Study of the Flowfield Surrounding the Aeroaesist Flight Experiment Vehicle," AIAA Paper 87-1575, June 1987.

Li, C. P, "Implicit Computation of Chemically Reactive Flow About Hypersonic Vehicles," AIAA Paper 87-0282, January 1987.

Bird, G. A., "Nonequilibrimn Radiation During Reentry at 10 kmla ." AIAA Paper 87-1543, June 1987.

Dogra, V. K.. Moss, J. N.. and Simmonds, A. L.. "Direct Simulation of Aerothermal Loads for an Aeroassist Flight Experiment Vehicle," AIAA Paper 87-1546, June 1987.

Park, C., "Radiation Enhancement by Nonequi- librium in Earth's Atmosphere," Spacecraft and Rockets, Vol. 22, No. 1, January-February, 1985, pp. 27-36.

Sutton, K., "Air Radiation Revisited," AIAA Paper 84-1733, 1984.

~

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

Balakrishnan, A., Park, C., and Green, M. J., "Radiative Viscous Shock Layer Analysis of Fire, Apollo, and PAET Flight Data," AIAA Paper 85-1064, 1985.

Jones. J . 3.. "The Rationale for an Aero- b'

assist Flight Experiment," A I M Paper 87- 1508, June 1987.

Gupta, R. N. and Simmonds, A. L., "Hypersonic Low-Deneity Solutions of the Navier-Stokes Equations with Chemical Nonequilibrium and Multicomponent Surface Slip," A I M Paper 86- 1349, June 1986.

Nicolet, W. E., "User-s Manual for the Generalized Radiation Transfer Code (RAD/ E Q U I L ) , " NASA CR-116353. October 1969.

Aooleton. J. P. and Brav. K. N. C.. "The .. _ I

Conservaiion Equations for an Equiiibrium Plasma." J. Fluid Mech., Vo1. 20, Part 4, 1964, pp. 659-672.

Moss, J. N., Anderson, E C., and Bolz, C . W.. "Viscous-Shock-L.ayer Solutions with Radiation end Ablation Injection for Jovian Entry," A I M Paper 75-671, May 1975.

Cauchon, D. L.. "Radiative Heating Results from the Fire I1 Flight Experiment at a Reentry Velocity of 11.4 Kilometers per second," NASA RI X-1402, 1966.

Nicolet. W. E., "Advanced Methods for Calculatine Radiation Transoort in Ablation- - Produce Contaminated Boundary layer," NASA CR-1656, 1970.

L' Stroud, C. W. and Brinkley, K. L., "Chemical Equilibrium of Ablation Materials Including Condensed Species," NASA TN 0-5391, 1969.

Moss, J. N., "Reacting Viscous-Shock-Layer Solutions with Multicomponent Diffusion and Mass Injection,'' NASA TR R-411, 1974.

Blottner. F. G.. "Viseous Shock-Layer at Stagntion Point with Nonequilibrium Air Chemistry,"*.. Vol. 7 , No. 12, December 1969, pp. 2281-2288.

Kane. S. W. and D u m . M. G.. "Theoretical and -. Experimental Studies of Reentry Plasmas," NASA CR-2232, 1973.

Acmaly. B. F. and Sutton, K., '"Viscosity of Multicomponent Partially Ionized Gas Mix- tures,*' A I M Paper 80-1495, 1980.

Lee, J.-H. and Kawamura, R., '"Nonequilibrium Flow Around Blunt Body with Thermal Rndia- tion." Institute of Space and Aeronautical Science, University of Tokyo, Report No. 546, January 1977.

Park. C.. "Problems of Aeroassisted Orbital . . Transfer Vehicles;' Thermal Design of Aeroassisted Orbital Transfer Vehicles, Progress in A6tronautic8 and Aeronautics. Vol. 96, 1985, pp. 511-537.

Yos, 3. M., "Transport Properties of Nitro- gen, Hydrogen, Oxygen. and Air to 30,000 K,"

7

AVCO corp., Tech. Men. RAD-TM-63-7, March 1963.

24. Cornette, E. 5.. "Forebody Temperatures and v Calorimeter Heating Rates Measured During

Projecr F i r e I1 Re-entry at 11.35 Kilometers per Second," NASA ?M X-1305, November 1966.

25. Zoby, E. V. and Sullivan, E. M . , "Effects of Corner Radius on Stagnation-Point Velocity Gradients on Blunt hisymmetric B o d i e s , " NASA ?M X-1067. March 1965.

26. Swaminathan. S., Song, D. J., and Lewis, C. H., "Effects of Slip and Chemical Reaction Models on Three-Dimensional Nonequilibrium Viscous Shock-Layer Flows," J. Spacecraft and Rockets. November-December 1984, pp. 521-527.

27. Sutton, K. and Graves, R. A., Jr., "A General Stagnation-Point Convective-Heating Equation for Arbitrary Gas Mixtures," NASA TR R-376, November 1971.

__

Table l(a) Chemical Reactions and Rate Coefficients Used in Nonequilibrium Navier-Stokes Calculations (after Kang and Dunn)

NO. Reaction Forward rate coeff., kf Backward rate coeff., $ Third body, M 3 cm /mole sec OR cm6/mole2 sec 3 cm /mole see

15T-0.5 1* O M :2DtMl 3. 6 1 ~ 1 0 ~ ~ T - ~ "exp( -5.94x10 IT) 3.OlXlO 0,N,0Z,N2,N0

4 2 1

16 -0.5

21 -1.5

20 -1.5

1.09~10 T 0,02,N2,N0

2.32~10 T

1.01~10 T 0,N.0Z,N2,N0

2' N2M2 ; 2N+M2 1.92~~~~T-~'~exp(-1. 131x10 5 IT)

4* NDcn3;N+O+M3 3.97x1020T-1'5exp(-7.56x10 4 IT)

5* NO+O z 02+N 3.18~10~ T1.0exp(-1.97x10 4 IT) 9.63~1O'~T~'~exp(-3.6xlO 3 IT)

6* N Z W : N W N 6.75~1O~~exp(-3.75~10 4 IT)

7* N + 0 z NO++e- 9.03~1O~T~~~exp(-3.24~10 4 IT)

22 -1.5 5 3* N2ffl ; 2N+N 4.15~10 T exp(-1.131xlO IT)

13 1.5~10

1.80~10 T

- 19 -1.0

5 40 -4.5

- + - - 3ZT-3. 14 5 40 -4.5 8 Ot e- z O++e-+e- (3.6*1.2)~10~~~-~'~~ exp(-1.58~10 IT) (2.2M.7)xlO T

exp(-1.69~10 IT) ( 2 . 2 M . 7 ) x l O T 9 W e z N +e +e (1.1M.4)xlO (1.6+0.4)x10'7T-0~98exp(-8.08x10 4 IT) (8.0k2.0) x1021T-1.5 10 0 + 0 o++.- 2

11 0 . 5

11 0.5 7.8~10 T

7.8~10 T

(1.5+0.5)~10 T

1.0~10 T

2 . 2 ~ 1 0 T

1 . 5 ~ 1 0

2.48~10 T

4.8~10

1.8~10

1.ox10

4 2 . 9 2 ~ 1 0 ~ ~ T - ~ "lexp( -2.8~10 IT) + 11 @to; z a**

+ + 2 . 02x1011T0'81exp(-1. 3x10 4 IT)

+ - (1.4M.3)~1O'~exp(-6.78X10 4 IT)

14 0 +N + NWNO + - +e 1.38x1020T-1'84exp(-1.41~10 5 IT)

ND+M4 z NO++e-+M4 2.2x1015T~0~35~xp(-1.08x10 5 IT) + 3 . 6 3 ~ 1 0 ~ ~ T ~ ~ ~ e x p ( - 5 . 0 8 ~ 1 0 4 IT)

12 N2+N z N+N2 13 N+N z N2+e

2 2 t

22 -1.5

24 -2.5

26 -2.5

13 O2 "2 15

16 WNO+ z NOIO 19 -2 .2 17 N2+0 + z W N Z + 3 . 4 ~ 1 O ~ ~ T - ~ ~ ~ e x p ( - 2 . 3 ~ 1 0 4 IT)

1.0x1019T~0.9!xp(-6.1x10 4 IT)

19 02+N0 + z NOM2 + 1.8x1015T0'17exp(-3.3x10 4 IT)

14

UTO. 5

14

18 N+NO+ z NWN+

+ 1 . 3 4 ~ 1 O ~ ~ T ~ ~ ~ ~ e x p ( - 7 . 7 2 7 ~ 1 0 4 IT) 20 WNO' 02+N

*These seven reactions and reaction rate coefficients are from the 8lottner.s seven-species chemical model.

-

8

Table l(b). Third Body Efficiences Relative to Argon

~ ~

Efficiencies relative to argon of Catalytic

02 N2 0 N NO NO' 0: o+ Nf W - Bodies

- e 0 0 0 0 0 1 1 1 1 1

M1 9 2 25 1 1 0 0 0 0 0

M2 M3 1 1 20 20 20 0 0 0 0 0

M4

1 2.5 1 0 1 0 0 0 0 0

4 1 0 0 0 0 0 0 0 0 -

Table 2. Freestream Conditions (Lee and Kawamura)i

Mole Fractions R; 3

52 u*. T* 9 T; 9 a* Condition Altitude Density

- km/ 6 K K km/s m xo2 3 km k d m

B 70 km .~.8~10-5 10.0 196.7 1500.0 0.297 0.03 0.233 0.767

+Wall treated as fully catalytic

** Table 3 . Freestream Conditions (Fire 11)

Heat Time Altitude Density U* I

km/e Shield eec km 3 kg/m

1631 1632 1634 1636 1637.5 1639

1640.5 1642

1642.7 1643 1644 1645 1646.5 1648

1648.3 1649.5 1651

1652

1653

84.60 81.86 76.42 71.04 67.05 63.11 59.26 55.48

53.77 53.04

50.67 48.37 45.14

42.14

41.60 39.50 37.19

35.86

34.68

9.15~10'~ 1.43~10-~ 3.72~10-~ 8. 5 7 x N 5 1 .47x1r4 2.41~10-~

3 . 8 6 x W 4 5.98x10-4

7.20~10-~ 7.80x10-4 1.02~10-~ 1.32~10-~ 1 . 9 9 x W 3 3. oox

3.25~10-~ 4.41 x

6.05~

7.28~10-~

8. ~ O X ~ O - ~

11.37 11.37 11.36 11.31 11.25 11.14 10.97 10.71

10.55 10.48 10.19 9.83 9.16 8.30

8.10 7.27 6.19

5.49

4.85

a:. Effective Nose km,s Radius, RG, m

P* 3 T: * T:, , N/m2 K K

0.56 0.86 2.09 5.20 9.55 16.70 28.20

45.90

57.60 62.00

82.50 108.00 159.00 230.00

245.00 325.00 440.00

526.00

617.00

212 460 210 500 195 615 210 810 228 1030 242 1325

254 1560i 266 1560t

274 475 276 640 282 1100

285 1520 280 1560t 267 1560t

263 460 255 790 253 1060

252 1160

248 1225

0.292 0.291 0.280 0.291 0.302 0.311

0.319 0.328

0.332 0.333

0.336 0.338

0.336 0.338

0.324 0.320

0.319

0.317

0.315

- 0.747 0.747 0.747 0.747 0.747 0.747 0.747 0.747

0.656 0.656 0.656 0.656 0.656 0.656

0.600 0.600 0.600

0.600 0.600

** Mole fractions: X - 0.763. X - 0.237; Wall treated as fully catalytic.

N2 02 +Melting temperature for the beryllium heat shield.

9

Table 4 . Equi l ibr ium Viscous Shock Layer Resul ts (Fire 11)

Radia t ive Heat F l u i a t Wall, q:, Rad ia t ive Heat Rad ia t ion I n t e n s i t y a t Wall, 2 Heat Time. wlcm Flux Abeorbed I?. wlcm 2

r - Shield sec A t t he Wap

v Tota l P a r t i a l Short a+ v/cm Tota l Pa r t i a l Short (0-16.5 eV) (0.2-6.2 eV) (2-4 ev) (0-16.5 eV) (0.2-6.2 eV) (2-4 eV)

1 1631 1.05 1632 3.01 1634 19.60 1636 70.50

0.34 1.03 6.50

23.80

0.05 0.13 1.00

0.82 2.34

15.20 53.60

0.20 0.57 3.71

13.36

0.06 0.20 1.23

0.01 0.03 0.19 0.90 4.16

12.00 25.70 49.90 78.60

79.40 82.60 80.80 57.70

4.51 10.17 19.89

1637.5 143.00 1639 248.40 1640.5 390.10 1642 502.00

2 1642.7 487.00 1643 486.00 1644 401.00 1645 221.20 1646.5 63.50 1648 42.20

53.70 105.00

105.00 176.00 265.00 327.00

316.00 313.00 250.00 132.00

27.09 47.06 73.91 95.11

92.27 92.08 75.98 41.91

2.27 4.87 9.45

14.89

15.04 15.65 15.30 10.93

188.00 271.00

35.62 51.35

267.00 272 .OO 244.00 150.00

48.70 31.80

50.59 51.54 46.23 28.42

9.23 6.03

~~

27.90 18.70

37.30 25.00

12.03 7.99

5.29 3.54

3 1648.3 46.05 33.10 19.20 27.70 8.73 6.27 3.64 1649.5 36.41 25.40 11.90 21.80 6.90 4.81 2.25 1651 23.35 16.20 5.00 13.70 4.42 3.07 0.95 1652 14.94 10.90 2.49 8.57 2.83 2.07 0.47 1653 7.40 5.91 1.18 4.11 1.40 1.12 0.22

Table 5. Convective and To ta l Heating Rates (Fire 11)

Convective Heating Rate To ta l Heating Rate 2 Time, q;, u/cm2 q: + q:, v/cm Heat

Sh ie ld sec Present s u t t o n Present S"tt0" (VSL) (Cor re l a t ion )

89.9 112.0 180.0

106.7 136.9 223.7

92.2 117.0 202.0

269.0 346.0 427.0

341.4 455.1

337.0 478.0 1637.5 350.1

lh39 442.0 ~~ ~

618.0 808.0 937.5

648.0 835.0 984.0

~ . . . . 1640.5 543.0 1642 610.5

. . 513.0 593.0

2 1642.7 684.1 1643 705.3 1644 741.9 1645 757.1

679.0 690.0 718.0 724.0 714.0 647.0

679.0 562.0 385.0 294.0 215.0

1000.7 1018.3 991.9

1056.0 1065.0 1038.0 930.0 778.0 688.0

715.0 591.0

889.1 792.9 694.2

1646.5 755.6 1648 669.2

3 1618.3 696.6 1649.5 566.1

724.3 587.9 447.2 1651 433.5

1652 327.5 1653 238.8

404.0 306.0 221.0

336.i 242.9

10

20 Nonesulllbrlwn cnemlstry I N S ) : NOngrQY roamion lwlth obsorPtlon): Aerotherm mael Gray-gas rodlotlon Iultnout ODSOrPtlOnl NO rndlotlon

Nongroy rodlotlon tWLfn absorption): Aerotherm mdel

tno rodlotton curve sow

-__- 12

1: 'K

q, cm

Fig. 1. Predicted cemperature profiles (Condition B, Lee 6 Kawamura).

NWe4ulllOrlm tl\e"lStW 1NSI: - N w g w roaiotion lwltn oDsorptlo"1: oerotnern maei Gray-Qos radiotion iwitnwt o~rerptioni

m g m y roaiotian ' Y l l n aOsorPtlanl: oerotnern mael

1Mo

E C I I IQrlm CnmlStrY IVSLI :

- .(I5 .10 .15 .20 .25 .30 .35

11: m

Fig. 2. Predicted radiative f lux components (Condition B, Lee h Kawamura).

1500r R;( = 6 cm

5w

.05 .10 .15 .20 .25 ", M

Fig. 4. Predicted radiative flux toward Lhe body for different nose radii (Condition B. Lee 6 Kavamura, non-gray radiation).

1 1 6 7 . 2 1.0 91.5 71.7 2 I 63,O 3 .6 80.5 66.0 3 I 58.7 0.6 70.2 60.0

k 5 2 . 5 7 8 m d

Fig. 5. Fire I1 reentry package dimensions.

TI, O K

(a) Temperature profiles

Fig. 6 . Effect of 7- and 11-species chemical model on flowfield structure (Fire 11, time - 1631 eec', fully catalytic wall, no radiation).

v

L'

11

1013

Freest ream 1O't I , 1/ 1 oca t 1 on

109 0 .05 .10

n'/Ri

11 species ---- ? species -

- ,'--, , Freestreom number

(b) Electron number density

Fig. 6. (continued)

Freestrean - 11 svecles ' l o p Iocotlon ---- 7 species '!2

CI

( c ) Mass fraction of chemical species

Fig. 6. (continued)

lo-*[

11 species 7 specles

- -_--

10-6 0 I 05 I10

17*/Ri

(e) Density profiles

Fig. 6. Concluded.

T H O . K

(d) Ma88 fraction of chemical species .-- Fig. 6. (continued)

8U.6 Lm I t - 1631 secl 81.9 km I t = 1632 secl 7

T:'K

Fig. 7. Effect of change in altitude on flowfield structure (Fire 11).

Cnemlstry (11 s~eclesi:

0 .os 1.0 "IRr;

-c- lnvlscla ShocK-layer Full NOVler-Stokes

SnOcK-layer

Shock-layer

- * InVlSCld -u- VlSCOUS

Fig. 8. Comparison of predicted temperatures along the stagnation streamline (Fire 11, time - 1631 sec).

12

N o n e q u l l l b r l u m N a v l e r - S t o k e s E q u l l l b r l u m VlSCOUS ShOCk l a y e r ". P,R~ = 6,84 x

q;(-',

w/cm2

. '1 .cm

Fig. 9. Predicted radiative flux toward the body (Fire 11. time - 1631 see) .

103

102

101

10-1

lo-:

10.'

- Nonequll lbrlum Navler-Stokes Equl 1 1 br lum viscous shock layer

\

4 8 1 2 16 Photon energy, eV

(a) Continurn radiation

Fig. 10. Comparison of predicted spectral radiative flux to the wall.

_--- f q u l l l b r l m VISCOUS S ~ O C K layer - Nonequl I 1 b r l m Navler-Stokes

. I 2

resul ts ore on tne m e r of l a - 8

Photon energy. ev

(b) Line radiation

u 1651 1655

Fig. 11. Comparison of predicted intensities with Fire I1 data (0.2 - 6 . 2 e v ) .

I , v , 0"OlYIlf 1631 1615 1639 16UJ 16") 1651 1651

TI*. s

Fig. 12. Comparison of predicted spectral intent itiea with Fire I1 data ( 2 - 4 eV).

lnvlscla snack

4 8 12 16 PnOtOn energy. ev ( a ) Continuum radiation

Fig. 13. Comparison of equilibrium vi6cous and inviscid spectral flux to the wall (Fire 11, time - 1631 sec) .

Euulllbrlum VISC0"S SIlOCk l w e r - Holec~les lncluilea

HOleCUleS noi ~ n c I uaed

....

j , i- i .- .>.

2 4 6 8 1 0 1 2 l U ~noton energy. ev

(b) Line radiation

Fig. 13. Concluded. Fig. 10. Concluded.

13

E u u l l l b r l m r Vlscous shock lover: Molecules Included MOleCuleS not "L 40 L r b r I m included InvlSCld . Shock

20 \.;.

'x.

4 8 12 16 0

Photon energy. ev

(a) Continuum radiation

Fig. 14. Comparison of equilibrium viscous and inviscid spectral flux to the wall (Fire 11, time - 1640.5 sec) .

40 35 30 25 20

M l e c u l e s Included HOleCuleS not Included

. 15 lnvlscld mock l o w Ur,v w m - e v 10

5 0 -5 -10 -15

0 2 4 6 8 1 0 1 2 1 9 Photon energy. ev

(b) Line radiation

Fig. 14. Concluded.

Fig. 15. Comparison of the predicted heating rate v

with total heating data from Fire 11.

14