AIAA-89-03 12 On the Compumtion o Shock Shapes in Nonequilibrium Hypersonic Flows G , Candler NASA Ames Research Center Moffett Field, CA 94035

27th Aerospace Sciences Meeting January 9-1 2, 1989/Reno, Nevada

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ON THE COMPUTATION OF SHOCK SHAPES IN NONEQUILIBRIUM HYPERSONIC FLOWS

Graham Candler * NASA Ames Research Center

Moffett Field, CA 94035

Abstract Several models using different descriptions of high tem-

perature air are used to compute the bow shock shapes on experimental model configurations. The test conditions re- sult in nonequilibnum chemical reaction and thermal ex- citation of the gas which has a first-order affect on the shock shapes. The computed results are compared to exper- iment and demonstrate that the model using seven chemi- cal species and six temperatures predicts the experimental shock shapes very well. The other gas models, including perfect gas, equilibrium gas and one-temperature chemical nonequilibrium models are less accurate. The results illus- trate the necessity of including both thermal and chemical nonequilibrium in the description of the gas. The use of these experimental data makes it possible to verify aspects of current and future chemically reacting flow algorithms.

Nomenclature v

c. = mass fraction of species s Q~ = translational specific heat &s =rotational specific heat G~ = translational specific heat of electrons E = total energy per unit volume E,. = vibrational energy per unit volume Elk = electronic energy per unit volume F =fringenumber h; = heat of formation of species s kf = forward reaction rate e = geometrid path length (see(l1)) L = reference length (nose radius or body length) M, =atomic mass of species s M =Machnumber Re = Reynolds number T, = uanslational temperature T, = rotational temperature T.. = vibrational temperature of species s

Copyright 01989 by the American Institute of Aeronau- tics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, US. Code. The U.S. Govern- ment has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental purposes. All other rights are reserved by the copyright owner. * Research Scientist, Member, AIAA

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T. = elecmn ~anslational temperature Td =electronic temperature u, = i direction velocity wb =chemical source term of species s 7 =ratio of s p i f i c heats q =normal distance from wall X =wavelength used in interferogram p =viscosity { = distance from nose p. = density of species s $ =reactivity of gas (see (2))

Introduction The computation of hypersonic chemically reacting

flowfields has been reporled by a number of authors'-7. These researchers have developed different physical mod- els to describe essentially the same flow physics. Thus the question arises as to which model or models are adequate to describe these hypersonic flows. Little attempt has been made to validate these numerical methods by comparing them to experimental results. This paper is designed to il- lustrate that numerical methods can be verified using exist- ing experimental evidence and that in certain regimes sim- plified gas models are inaccurate.

The experimental data that have been used for compar- ison are bow shock shapes on a wedge, a sphere, a cylin- der, two cones, a sphere-cone, and an axisymmevic Aeroas- sisted Orbital Transfer Vehicle (AOTV) model measured in ground-based testing facilities. The shock detachment is essentially inversely proportional to the density rise across the bow shock wave, which is dependent on the degree of chemical reaction and thermal excitation of the gas. Thus a model of the gas that predicts the correct degree of reac- tion and thermal excitation will yield the correct standoff distance.

The models used by researchers in this field generally al- low the flowfield to react at finite rates; however, the gas is assumed to be in thermal equilibrium. The reaction rates are assumed to be governed by the one temperature that characterizes the thermal state of the gas. In this paper these assumptions are tested by comparing the results ob- tained with one-temperature models to experiment and to a

2 AIM89-0312

thermoshemical nonequilibrium model. The limitations of the different gas models will be made evident.

The Deeree of Noneauilibrium All high-speed gas flows are out of thermo-chemical

equilibrium to a certain extenL However, for the cases where the chemical and thermal relaxation time scales are much smaller than the fluid time scales we can assume that the gas is in equilibrium. And for conditions where the re- laxation rates are much greater than the fluid time scales, a frozen-flow assumption is applicable. Between these two limits thcre is a continuum of degrees of thermo-chemical nonequilibrium which may be quantified in the following manner.

If we consider the species s mass convection equation for a steady-slate condition. we have

where w. is the mass source term due to chemical reac- tions. We may non-dimensionalize this equation with the free-stream (00) conditions and the reference length, L , as

L we (psuaj) = -2

P m U m azj PmUm

~a -_

The non-dimensional quantity, $, which is a form of the Damkohler number, may be thought of as the ratio of the fluid time scale to the chemical time scale, or as the ratio of the chemical reaction rate to the fluid motion rate. For the case of chemical equilibrium, the chemical rates are in- finitely fast, or $ -+ 00. and for frozen-flow case where the fluid rates are much larger than the chemical rates, $ --t 0. For conditions between these two limits the flow is, to some degree, in chemical nonequilibrium.

A more useful form of the parameter $ may be derived by considering the primary reaction that occurs in high- temperature air flows, which is the dissociation of diatomic oxygen by collisions with diatomic oxygen and nitrogen. In this case we have

If we substitute expression the Arrhenius form for the for- ward reaction rate, kJ = CT" exp( -O,/T), and use the hypersonic limit for the density change aaoss the shock, we have

Ko, = cu, ( e)z $ N 3.4 x ( m 3 K/kg s ) , 7- 1

( 4 )

where we have substituted the values of the constants that were used in the computations. The post-shock tempera- ture,T.~, can be approximated using the hypersonic shock relation

v'

We have assumed that the peak mction rate occurs imme- diately behind the normal shock wave. and for simplicity that the reaction is governed by the translational tempera- ture only. Alternatively, we can write $o, in terms of the Reynolds number @ased on the reference length) as

Re pm

urn $a = K q T L e ~ p ( - 5 9 5 I X l / T & ) ~ . (6)

For cases where air or oxygen is not the reacting gas, this expression must be modified slightly. If the gas is nitrogen, thenthe+&

For the case where the shock wave is oblique, such as a cone orwedge, the expression for computing the post-shock tem- perature must be m d e d by using the Mach number nor- mal to the shock wave. We will see that the relative value of the reactivity of the gas, $, gives a direct indication of the degree of nonequilibrium of the flow.

v

Models of High TemDerature Air When air passes through a hypersonic shock wave, its

translational modes are excited to a high temperature. This energy is rapidly transfered to rotational modes and then more slowly to vibrational and elecuonic modes through intermolecular collisions. Some of these collisions result in chemical reactions and ionization of the gas. Because, on average, these processes take between several and thou- sands of collisions, they occur over finite times and in what may be an appreciable distance. These physical phenom- ena must be modeled accurately to predict the shock shape about a hypersonic vehicle or wind-tunnel model.

In this paper, we will discuss results for two sets of experiments in which Ihermc-chemical nonequilibrium is present. The models used to describe the gas flowing over the experimental models will range in complexity from the perfect gas equation of stare, to thermo-chemical equilibrium, to thermal equilibrium and chemical noncqui- librium, and finally lo lhermo-chemical nonequilibrium.

v

AIM894312 3

The total energy per unit volume, E, is composed of the translational energy, paheTt, the rotational energy, C P & ~ ~ T , , the freeelectron translational energy, ~.G.T,. the vibrational energy, Eve( Tva), the electronic energy,

E d T C r ) , thechemicalenergy, Cp,h;. and thekinetic energy, $puiu.. i.e.

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where the summations are over all of the chemical species except electrons. A perfect gas analysis assumes that the internal energy modes are not excited and no chemical re- action occurs. Then we have

An equlibrium approach uses the energy and density to determine the chemical composition that minimizes the Gibb's free energy, assuming that one temperature, T , de- scribes the excitation of each internal mode6.

This is the same equation of state usedwith a chemical non- equilibrium analysis, but the chemical composition is de- termined by solving the chemical kinetics equations along with the fluid equations. Thus the chemical state evolves according to finite-rate chemical kinetics as a function of the thermodynamic state of the gas along each stream- line. A fully thermo-chemical nonequilibrium method uses equation of state (8). however this requires a large number of separate energy equations to be solved. The thermo-chemical nonequilibrium method used in this study makes the approximation that the translational and rota- tional modes are characterized by the same temperature, T, because of rapid equilibration between these modes. Sec- ondly, it is assumed that the electron translational and elec- tronic modes are characterized by the same temperature, T.. This assumption res& on the fact that the barrier to ex- change between free electrons and b u n d excited electrons is small. The resulting equation of state is

where all summations are over heavy particles. The chem- ical reaction rates are assumed u) be a function of the trans- lational and vibrational temperature. where applicable. The reaction rate model used is the. TT. model of Parkz,', which tends to suppress the reaction rates to physically correct lev- els. This thermo-chemical nonequilibrium method has been discussed previously',2.

Test Case Conditions The six-temperature, seven-species, thenno-chemical

nonequilibrium method has been compared to the RAM- C experiments for elecmn number density', and was shown to yield excellent results. However, the new one- temperature chemical nonequilibium method has not been compared to experiment or to other calculations that use a similar chemical model. Thus, the first test case is de- signed to compare this technique with an existing one- temperature numerical method and to the six-temperature algorithm. (These numerical methods allow seven species to be present Nz, a, NO, NO+, N , 0, and e-.) The case chosen is a 10" wedge with a free-stream speed of 8.lOkm/s at an altitudeof61km. This case has been cal- culated by Prabhu, Tannehill, and Marvin' and shows a small degree of nonequilibrium in the boundary layer of the wedge. The second test problem is an experimental case of a sphere ked in air at a speed of 5.28krn/s. A shadowgraph of a one-half inch diameter sphere at a pres- sure of lOtorr is given by Lobb*: the shape of the com- puted bow shock wave is compared to this figure. The third and founh test cases are experimental shock standoff dis- tances along 45" and 34.9 O cones in hot oxygen9. The next two cases replicate experiments performed by Homung" for 1 and 2 inch diameter cylinders in dissociating nitro- gen at 5.59km/s. The seventh test case is an axisymmet- ric AOTV-like geometry fired in the NASA Ames ballistic rangeat 4.02km/s andapressureof75torr". A shadow- graph exists for this case so that the bow shock &d other features may be compared to the computational results. Fi- nally, the Planetary Atmosphere Experiments Test (FAET) vehicle geometry was tested extensively'*, and the heat transfer for a nonequilibrium case is compared to computa- tion. The quality of the bow shock shape results from this test are inadequate for comparison to the computed results. The other parameters that characterize these flows are givcn below in Table 1.

CnmDutational Results for IO' Wedge

model to a one temperature, chemical nonequilibrium model. This is done to validate the new computational tech-

The first test case is a comparison of the multi-temperature

4 MAA 89-0312

nique and to demonstrate the difference in the results be- tween the two models. Figure l is a plot of the translalional- rotational temperature and the nimgen vibrational temper- ature versus the normal distance from the wall at a point 3.5m from the tip of the cone. The temperature from the Panbolized Navier Stokes (F"S) calculations of Prabhu, Tannehill, and Marvin5 is also ploued here. We see that there is a difference of about lOOOK in the inviscid region (between the shock wave and the thermal boundary layer) between the two temperatures from the multi-temperature model. The temperature from Ref. 5 falls between them, as expected. The two different methods predict a very simi- lar behavior of the temperature near the cooled wall (wall temperature of 1200K). The next plot shows the temper- ature derived from the new one-temperature model com- pared with the PNS calculations at the same point on the body. We see essentially identical results within the shock layer,butthelccationoftheshcckwaveandtheamountthat it is smeared are different. However, a comparison with the first figure shows the same behavior, which is in part due to the use of a dissipative central difference method in the PNS calculation. Figure 3 plots the mass fraction of atomic oxy- gen normal to the body surface at the 3.5m point for the three different methods. We see that there is some differ- ence in the amount of atomic oxygen produced by the dif- ferent methods; however, the general shape of the distribu- tions is very similar. We would expect there to be less reac- tant produced in the multi-temperature case because of the use of the TT, model for reaction rates, which suppresses reaction. The difference in the results between the one tem- perature models is likely due to different reaction rates and equilibrium constants. These results show that the multi- temperature and one temperature models agree well with the PNS calculations, however there is a small disparity in the peak value of atomic oxygen. Also we see for this case (which is relatively unreactive, as compared to the remain- ing cases), there is a significant degree of thermal nonequi- librium predicted by the multi-temperature model.

Comoutational Results for Sohere The shock standoff distance for test case 2. the ;inch

diameter sphere at 5 .ZSkm/s is plotted versus the distance along the body surface in Figure 4. The experimental points are From the shadowgraph of Lobb'. This plot shows that the multi-temperature model accurately predicts the shock location, whereas the perfect gas (7 = 1.4) solution over- predicts the shock detachment by about 20%. The one- temperature model is better. but under-predicts the shock location by about 10%. These results are as expected, be- cause the perfect gas model under-predicts the density rise

across the shock wave and the one-temperature model ovcr- predicts it. This is seen in Figure 5. which is a plot of the dcnsity along the stagnation sucamline denved from the three models of air. For cases where 11, is of the magnitude in this case (11 = 58.7). we wuold expect a one-temperature model to be inadequate.

Figure 6 is a plot of the temperatures along the stagnation sueamline for the two nonquilibrium models used. We see that the peak translational-rotational temperature is more than 3OOOK greater than the temperature from the one tem- perature model. The vibrational temperature of Nz does not equilibrate with the translational-rotational tempcrature un- til just before the gas gets to the body surface. Thus much of the stagnation region is characterized by vibrational non- equilibrium. The next plot (Fig. 7) shows the mass fraction of two of the chemical species for each of the nonequilib- rium models. We see an interesting feature of this flow, namely that ihe point where appreciable reaction begins oc- curs at the same point for both models. This is a result of using mto govern the dissociation rate; the dissociation of 0 2 does not begin until the vibrational temperature has reached a fairly high level, and once it does begin, it pro- ceeds more slowly than with the one-temperature model. The six-temperature model also predicts more NO forma- tion than the one-temperature model. This is because NO is primarily formed through exchange reactions which are governed by the uanslational temperature, which is higher in the six-temperature solution.

i/

~

Comoutational Results for Cones Theresults forthetwoconecasesaresummarizedinFig-

ures8and9,whichareplotsofshockdetachmentversusax- iallocationonthecone. Thefirstplotis forthe45" caseand shows very good agreement between the experiment and the six-temperature model. However, the one-temperature model underpredicts the shock standoff, as before. The per- fect gas (7 = 1.4) solution overpredicts the shock detach- ment by about 100%. The equilibrium calculation from Spurkg is about 50% tco low for this case. Also ploued are the results of Spak for a one-temperature gas model (using different reaction rates). These results fall considerably be- low those of the current one-temperature model. However this maybecausedby Spurk'suseofashock-fitting method, while the shock is captured in the present calculations. In either case it is clear that the onetemperature model under- predicts the shock standoff distance. Clearly this flow is nonequilibrium, which strongly affects the shock standoff distance. This test case serves as an example of the limita- tions of neglecting the effects of thermo-chemical noncqui- librium.

LY

AlA.4894312 5

The 34.9 e cone case shows rather poor agreement be- tween computation and experiment, this is likely a prob- lem with incorrect free-stream conditions. The computa- tion was performed with the free-stream conditions sug- gested by Spurk (cq = 0.885, Q = 0.115). however he expresses uncertainty that these are correct

between the shoulder geome@y used in the calculation and that used in the experiment. Small changes in the shoul- der shape affect greatly the shear-layer shape'l. The wake shock that appears in the experiment is not seen in the cal- culation, which is likely due to inadequate mesh spacing in the wake region. (The entire computation was performed

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Computational Results for Cylinders The flow about twocylinders in hot, partially dissociated

nitrogen (a, = 0.927, CN = 0.073) was computed us- ing the thermochemical nonequlibrium algorithm. These cases replicate an experiment of Hornung", in which in- terferograms were made of these flowfields. To compare the computed results with experiment, we relate the density change, Ap, to the fringe pattern using an expression from Ref. 10

where F is the fringe number, X is the wavelength, and 1 is the experiment's geometrical path. Contours of constant fringe number are plotted in Figure 10 for the lin diameter case and in Figure 11 for the 2 in diameter case. The shapes of the computed contours are very similar to the experi- mental fringe patterns and the location of the experimen- tal and computed shock waves coincide. Thus, the multi- temperature model predicts the correct dismibution of den- sity within these reacting flows. The flow about the 2in diameter cylinder was computed using the one-temperature model; the fringes for this case are plotted in Figure 12. We see very poor agreement tetween the experiment and this calculation. The shock standoff distance is 50% of what it should be and the shape of the fringes is erroneous. This case provides graphic evidence of the limitations of using a one-temperature model for a case where the reactivity is fairlylow($= 5 . 5 ) .

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Computational Results for AOTV Model The next test case is the axisymmetric AOTV model fly-

ing at 4.02 km /s . The comparison of the computed shock shape to that taken from the shadowgraph" shows a good agreement, as seen in Figure 13. A more qualitative com- parison of the computation and the experiment is given in the next figure (Fig. 14). which is a side-by-side plot of computed stranlines and the experimental shadowgraph. We clearly see the bow shock wave and the region of sep- arated flow in the aftcrbody region. The extent of the sep- arated region is similar in each case. However, the com- putation predicts that the shear-layer formed between the recirculating flow and that passing over the shoulder of the body is tm far inboard. This may be a result of a disparity

Y

on a 90 x 49 mesh.) Figures 15 to 17 are contour plots of aanslational-rotational temperature, N2 vibrational tem- perature, and mass fraction of 0 , respectively. An exami- nation of Figures 15 and 16 shows that there is significant thermal nonequilibrium in the wake region of this body. This is a result of the vibrational energy being frozen in the molecules as the gas expands rapidly around the shoul- der of the body. This results in much of the wake being at about 4000K. whereas the translational-rotational drops rapidly due to the expansion. We can also see a rise in the temperature in the recompression region on the centerline just behind the afterbcdy. Figure 17 shows extensive freez- ing of the chemical state of the gas as it expands around the shoulder. As a result a tongue of reacted gas extends well into the wake region, which is further evidence of non- equilibrium affecting the fluid dynamics. This case demon- strates that even with a fairly high reactivity ($ = 182), there are obvious thermo-chemical nonequilibrium effects that a simplilied approach would neglect

Computational Results for PAET Vehicle The final test case is for the spherecone PAET shock-

tunnel model. The experimental shock shape results are inadequate to compare to experiment; however, the con- vective heat transfer was measuredt2. This is compared to the computed heat transfer using the six-temperature model in Figure 18. We see very good agreement The peak in the heat transfer distribution that occurs at 1.1 nose radii around the body is a result of the sharp comer geometq of the PAET vehicle; this causes a localized heating. This ef- fect is captured by the numerical solution, but the peak is spread out due to poor mesh resolution in this region.

Conclusions The correct prediction of hypsonic flowfields is im-

portant for the development of future aerospace vehi- cles. Many authors have reported solution procedures for such flowfields, but little attempt has been made to ver- ify these methods. In this paper existing experimental evi- dence, primarily in the form of shock shapes, is compared with results computed using a previously reponed thermo- chemical nonequilibrium technique and with several dif- ferent gas models. The seven-species and six-temperature model yields very good agreement for all seven experimcn-

6 AIM89-0312

tal cases. which span a wide range of 11. the reactivity of the gas. However, the other gas models, including perfect gas. thermo-chemical equilibrium, and chemical nonequi- librium give inadequate results. Two therm-chemical non- equilibrium cases were compared with experimental inter- ferograms, and excellent agreement with shock shapes and fringe locations was obtained. The method also yields good agreement with convective heat transfer on a sphere-cone.

The paper demonstrates that there are sufficient exper- imental data to validate severai aspects of an algorithm for computing chemically reacting flows. Also the impor- tance of using a thermo-chemical nonequilibrium method for some regimes (through which many hypersonic vehi- cles would fly) is shown.

References Candler, G.V. and MacCormack, R.W., “The Compu-

tation of Hypersonic Flows in Chemical and Thermal Non- equilibrium,” Presented at the Third National Aero-Space Plane Technology Symposium, NASA Ames, Moffen Field, Mountain q e w CA, 1987.

* Candler, G.V. and MacComack, R.W., ‘The Compu- tation of Hypersonic Ionized Flows in Chemical and Ther- mal Nonequilibrium,” AIAA Paper No. 884511,1988,

Gnoffo, P.A. and McCandless, R.S., ‘Three Dimen- sional AOTV Flowfields in Chemical Nonequilibrium,” AIAA Paper No. 8647230,1986.

~

Table 1. Conditions for Test Cases.

Li, CP., “Implicit Methods for Computing Chemically Reacting Row.” NASA TM58274, 1986. ’ Pnbhu, D.K.. Tannehill. J.C. and Marvin, J.G., “A New PNS Code for Chemical Nonequilibrium Flows,” AIAA Paper No. 874284,1987.

Palmer, G.. “An Improved Flux-Split Algorithm Ap- plied to Hypersonic Flows in Chemical Equilibrium,’’ NM

Paper No. 88-2693.1988. ’ Park, C., “Assessment of Two-Temperature Kinctic

Model for Ionizing Air,” AlAA Paper No. 87-1574, 1987. * Lobb, R.K., “Experimental Measurement of Shock

Detachment Distance on Spheres Fired in Air at Hyperve- locities,” in The High Temperature Aspects of flypersonic Flow, ed. W.C. Nelson, Pergammon Press, MacMillan Co., New York, 1964.

Spurk, J.H., “Experimental and Numerical Nonequi- librium Flow Studies,” AlAA J., Vol. 8. pp. 1039-1045, 1970.

lo Hornung, H.G., ‘Won-equilibrium Dissociating Ni- bogen Flow Over Spheres and Circular Cylinders,’’ J. Fluid Mechanics, 53, pp. 149-176.1972.

l1 Inhieri, PY. and D.B. Kirk,“High-Speed Aerodynam- ics of Several Blunt-Cone Configurations,” J. Spacecraft, 24,1987.

l2 Stewart, D.A., “Convective Heat-Transfer Rates on a Blunted 110’ Cone with Hemispherical A f t e M y at Hy- personic Speeds,” NASA TND-6433.1971.

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LJ

Re I 49oooo I 14600 I 49600 I 61400 I 6000 I 12ooo I 343000 I 7550 rl, I 10-1” 1 58.7 I 1550’ I 94.5’ I 2.74 I 5.48 I 182 I 3.85

‘ (rl, for the wedge and cones was computed using M , normal to the bow shock.)

AlM89-0312 7

0.4

0.3

0.2

0.1

0.0

Figure 1. Temperatures normal to surface of 10" wedge at 5 = 3 .Sm for 6 temperature model and Ref. 5.

0.4

0.0

+I .a 0.w 0.0 0.5 1.0 1.5 2.0

5 tr, Nmmalkd Distance Imm Nose

Figure 4. Shock detachment on fr inch diameter sphere.

1

30 II --c BTemperatureModel - 1 Temperature Model - Perf& Gae Model

Tempratwe 0

Figure 2. Temperatures normal to surface of 10" wedge at 5 = 3.5m for 1 temperame model and Ref. 5.

- : 0.00 0.65 0.io C

q ir, Normalized Distance from Wall

5 0.03 ib i 0.W

0.W 0.02 0.M 0.C6 0.08 Atamic Oxygen Msaa Fraction

- 6TemperatweMdel - ITemperatweMdel _c Ret6

0.W 0.02 0.M 0.C6 0.08 Atamic Oxygen Msaa Fraction - Figure 3. Atomic oxygen mass fraction normal to surface

of 10' wedge at z = 3 .Sm for 6 and 1 temperature models and Ref. 5.

Figure 5. Density ratio on sphere stagnation streamline for three different air models.

,-" - Trans-RotTempmtuTe - NpVibTem eratare -c TransW.&b Tempratwe

lw00 !2 4 E e 8 mo

n 0.02 0.04 0.06 0.08 0.10 0.12

qlr, Normaliwd Distance From Wall

Figure 6. Temperatures on sphere stagnation strerunline Cor six and one-temperature models.

8 NM 89-0312 0.25

0.20

s 0.15 '5 2 2 0.10

E

0.05

0.M

-+- Dietomic Oxy n, 6 Temp. Model Nittic Oride.rTe;hm Model Diatomic Oxy n, l%mp. Model - Niltie Oxide. $Temp Model

B

0.02 0.M o m 0.08 0.10 0 11 k, Normalized Diritance fmm Wall

Figure 7. Diatomic oxygen and ninic oxide mass frictions on sphere stagnation sueanline for six and one-temperalure models.

I 0 5 10 15 20 25

Axial Location (m)

Figure 8. Shock detachment on 45" cone in pure oxygen for different gas models.

3

/ /

m LowerSuliace Experiment U per Sudace Experiment

- 6 ?emperaturn Model ....... . Perfect Cas Model . " . 0 5 10 15 20

Axial Loention (mm)

Figure 9. Shock detachment on 34.9" cone in pure oxygen for two gas modcls

model

Fieure 10. Frinee Daltem on lin diameter cvlinder.

model

W Figure 11. Fringc patterns on 2 in diameter cylindcr.

NM890312 9

Figure 12. Fringe patterns on 2 in diameter cylinder.

Figure 14. Comparison between computed streamlines and experimental shadowgraph on axisymmetric AOTV model

0.04 1 inair.

J I I I - 0 0 1 0.00 0.01 0.02 0.03 0.04 0.05 0.W

x (rn)

Figure 13. Shock detachment on axisymrnetric AOTV model in air.

Figure 15. Translational-rotational temperature contours for axisymmetric AOTV (K).

AIM 89-0312

Figure 16. NZ vibrational temperature contours for ax- isymmetric AOTV (K).

Figure 17. 0 mass fraction contom for axisymmeaic AOTV (percent).

'- I

; s 6

.- - 0.4- u

0.2-

E eriment 1.0" --G%mperature Model

.- e

3 0.8- n

i . 2 0.6-

; s 6

.- - 0.4- u

0.2- .. 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Normalized Distance from Noae

Figure 18. Convective heat transfer ratio on PAET model.