Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.

AIAA Meeting Papers on Disc, June 1996A9636349, AIAA Paper 96-1861

A new technique for the computation of severe reentry environments

Bilal A. BhuttaAeroTechnologies, Inc., Yorktown, VA

James E. DaywittLockheed Martin Missiles & Space, King of Prussia, PA

John J. RahaimLockheed Martin Missiles & Space, King of Prussia, PA

Darius N. BrantLockheed Martin Missiles & Space, King of Prussia, PA

AIAA, Thermophysics Conference, 31st, New Orleans, LA, June 17-20, 1996

A novel multi-discipline approach has been developed to compute recession and transient heating in the event of anaccidental reentry of the Cassini spacecraft during its Earth gravity-assist (EGA) maneuver. The technique is perhapsthe most rigorous attempted to date, yet computational times are relatively modest. A new Reacting, Ablating,Chemical Equilibrium/nonequilibrium with Radiation (RACER) full Navier-Stokes code is applied, along with anin-depth transient-heating code, to compute the thermal response of a General Purpose Heat Source (GPHS) module.The GPHS reentry velocities (20 km/sec) are higher than any previously analyzed. (Author)

Page 1

A New Technique for the Computation of Severe Reentry Environments

Bilal A. Bhutta*AeroTechnologies, Inc. Yorktown, Virginia 23692

andJames E. Daywitt*, John J. Rahaim , and Darius N. Brant

Lockheed Martin Missiles & Space, King of Prussia, Pennsylvania 19406

A novel multi-discipline approach has been developed to compute recession and transient heating in theevent of an accidental reentry of the Cassini spacecraft during its Earth gravity-assist (EGA) maneuver. Thetechnique is perhaps the most rigorous attempted to date, yet computational times are relatively modest. Anew Reacting, Ablating, Chemical Equilibrium/ nonequilibrium with Radiation (RACER) full Navier-Stokescode is applied, along with an in-depth transient-heating code, to compute the thermal response of a G_eneralPurpose Heat Source (GPHS) module. The GPHS reentry velocities (20 km/sec) are higher than anypreviously analyzed.

Nomenclature

Ae = atomic weight of the e-th element, Ibm/lbm-molea = characteristic speed of sound, scaled by a«,floo = freestream speed of sound, ft/seca« = mass of element 'e1 per unit mass of species Tan,Xk= grid metric term, £n,xk/JQ = mass fraction of the s-th speciesCp = specific-heat of the mixture, scaled by yooR»c = species mass-fraction vectorD, = effective diffusion coefficient of the s-th species,

scaled by n«,/P°°E, = mass-fraction of the e-th elementfj = inviscid flux vectorshs = static enthalpy of the s-th species, scaled by a2*,h = static enthalpy of the mixture, scaled by a2»ho = total enthalpy of the mixture, scaled by a2

xJ = determinant of the transformation JacobianJMAX = number of grid points in the streamwise (£i)

directionk = mixture thermal conductivity, scaled by k«,k» = freestream thermal conductivity of the mixtureZA = equivalent Lewis number for s-th chemical

species, (pD, Pr)/nLef = equivalent Lewis number for mass diffusion of

e-th element, where

LMAX=number of grid points in the £2 directionM = Mach number, also the number of grid points

between the body and the captured bow shockm, = molecular weight of s-th species, slug/slug-mole

* President, Senior Member AIAAt Senior Staff Design Engineer, Associate Fellow AIAAt Staff Design Engineer, Currently at GE Aircraft

Engines, Member AIAAS Manager, Thermo & Aero/Propulsion Systems,

Member AIAA

m = mixture molecular weight, slug/slug-mole>»w = surface ablation rate, scaled by pooa«ws = total surface mass-transfer rate of s-th species

due to sublimation and heterogeneous surfaceoxidation, scaled by pooflco

MS* = surface mass-transfer rate of s-th species due tosurface oxidation, scaled by p<»a<»

m? = surface mass-transfer rate of s-th species due tosublimation, scaled by pxa«,

mnjk = a grid-metric term, ^n,Xj<fn,xk

N = global (flowfield/radiation) iteration numbern = flowfield iteration numberNS = total number of chemical speciesNE = total number of elementsP,p = static pressure, scaled by y<»pooPw = wall pressure, scaled by y«>p»p,v = vapor pressure of s-th species, scaled by y<»poopw, = partial pressure of s-th species at the wall, scaled

by y,»pa,POO = freestream static pressure, Ibf/ft2

Pr = Prandtl number, (yoo-l)Pr,x,[nCp /k]Qdiff = energy term due to mass-diffusion effects, scaled

by poofl3*,Qr = energy term due to gas-radiation effects, scaled

by pooff'ooqw = total wall heat-transfer rate, Btu/fV-sec

= conduction component of surface heat flux,scaled by p«,cf«,

• = diffusion component of surface heat flux, scaledby pooO3*,

qrad = radiative component of surface heat flux, scaled

RRGRb

Ro

= base radius of the body, ft= local gas constant, scaled by y»R»= local body radius, scaled by R= distance between surface and outer boundary,

scaled by R

RL = distance between the surface and grid point L,scaled by R

R5 = distance between the surface and bow shock,scaled by R

Roo = freestream gas constant, fV/sec2-^r = axis-normal radial distance from the body axis,

scaled by RRe™ = freestream Reynolds number, (p<»Va,R)/Hoos, = viscous flux vectorsT = static temperature, scaled by T»TK = dimensional static temperature, °KTw = wall temperature, scaled by T»T,o = freestream static temperature, °RAt = time stepu = x-component of local velocity, scaled by axun = u, v and w for n=l,2 and 3, scaled by a«,Un = contravariant velocities, £j,XkUkv = y-component of local velocity, scaled by fl»V = total velocity, scaled by a<»Vw =freestream total velocity, ft/secw = z-component of local velocity, scaled by a»X,x = coordinate along body axis, scaled by Rxb = axial location of a point on the body, scaled by Ry = out-of-plane coordinate, scaled by RZ,z = coordinate normal to the body axis, scaled by RZ* = a thermodynamic state variable, Y»p/ pTxn = x, y and z for n=l, 2 and 3, scaled by RP = ballistic coefficiente = M<x,/Rea>, also surface emissivity4> = circumferential angle measured from the

windward streamline, deg0 = parameter controlling fourth-order dissipation

effects in £2 direction, and also a relaxation factorin the corrector step

#es = mass of element 'e' per unit mass of species 's'0G = inclination angle of the ̂ constant grid line, deg9, = grid metric term, J^l* + ££zy = pa2/p, also flight-path angler| = nondimensional grid stretching function in the £2

direction, ri(£2)=0 at the body and r|(£2)=l at theouter boundary

(0. = mixture viscosity, scaled by u»oHoc = freestream viscosity of the mixture, slug/ft-secp = static density of the mixture, scaled by p™poo = freestream static density of the mixture, slug/ft3

CT = Stefan-Boltzmann constantco = solution under-relaxation parameter, 0<co<lcor = under-relaxation parameter used in coupling the

flowfield and radiation solutions, 0<cor<lo>s

= mass rate of production of s-th species by chemi-cal reactions, scaled by p«,a«,/R

(ot = pseudo time-relaxation parameter, 0<cot<l

^i = marching or streamwise coordinate measuredalong windward streamline, scaled by R

E,2 = nondimensional coordinate measured from thebody to the outer boundary such that A£2=lbetween successive points

£3 = nondimensional crossflow coordinate measuredfrom the windward streamline

C, = a first-order differentiable scaling function suchthat <;--£! when £i-0

SuperscriptEQ = chemical equilbriumN = global (flowfield/radiation) iterationn = flowfield iteration indexT = matrix transpose

= scaled (nonsingular) quantitySubscripte = e-th element, where e=l,2,..,NEj,k,l = indices representing grid points in the £1, £3 and

£2 directions.S = represents a constant-entropy surfaces = s-th species, where s=l,2,..,NSsc = solid carbon surfacew = wall quantity, = represents partial derivativeoo = freestream quantityVector and Matrix NotationMatrix = bold upper-case characterVector = bold lower-case character• = vector dot product

I. Introduction

The Cassini spacecraft is scheduled for launch inOctober 1997. The spacecraft's electrical power isprovided by three Radioisotope ThermoelectricGenerators (RTGs), each containing eighteen GeneralPurpose Heat Source (GPHS) modules. Its journey toSaturn is aided by an Earth gravity-assist (EGA)maneuver. In the unlikely event of accidental reentryduring the EGA maneuver, the spacecraft will breakupand release the individual GPHS modules. Missionsafety considerations require analyses to assess theaerothermal and thermostructural response of themodules when suddenly exposed to the severe reentryenvironment. Release scenarios initially place themodules at over 80 km altitude traveling at nearly 20km/sec. Flight-path angles can range from just aboveskip-out, y = -7° (shallow), to vertical, y = -90° (steep).

Reentry velocity of the GPHS module exceeds thatof the ESA/Rosetta1 vehicle, which was probably thehighest ever analyzed. At these conditions, theflowfield is in thermochemical nonequilibrium withsignificant radiative heating. The GPHS aeroshell isprotected by a thin Fine Weave Pierced Fabric (FWPF)

carbon-carbon heatshield. Ablation of the heatshieldintroduces carbon products into the flowfield andgreatly complicates the analysis.

This analysis differs from conventional approachesthat either neglect the transient-heating phase, by using"steady-state" ablation, or treat transients withsimplified flowfield predictions and one-dimensionalin-depth conduction techniques. Instead, a rigorous fullNavier-Stokes code, coupled to a nonequilibriumradiation code, is used in conjunction with athree-dimensional, in-depth transient thermal-responsecode. In addition, three-dimensional thermostructuralanalyses are subsequently performed at selectedtrajectory points. This approach is made possible bysignificant improvements in the convergence rate of theNavier-Stokes flow solver (at least an order ofmagnitude faster than existing Navier-Stokes codes)and by the geometry of the GPHS module which can bereasonably treated using an axisymmetric model.Furthermore, multiple, networked workstations areemployed and found to yield faster turnaround than a(shared) supercomputer.

This paper describes the flowfield code and itscoupling to the nonequilibrium-radiation techniqueand predictions of the aerothermal environment. Thein-depth transient heating analyses code SINRAP2,based on SINDA3, and the elastic/plasticthermostructural analyses4 using the ABAQUS5 code,are presented in the Cassini RadioisotopeThermoelectric Generator Program, Safety AnalysisReport.6

II. Problem Overview

The GPHS aeroshell configuration is shown in Fig.1. The bounding shallow and steep trajectories for thelow-p GPHS module are contrasted with a typicalhigh-p ballistic-reentry vehicle trajectory in Fig. 2. Thefilled symbols in Fig. 2 mark the points on thetrajectories that have been selected for detailedflowfield analyses. These points encompass thesignificant portion of the heat pulse.

Coupling of CFD/Radiation and Transient-HeatingTechniques : As shown in Fig. 3, the flowfield analysisbegins in the slip-flow regime (using the Knudsennumber based on the length of the broad face).Flowfield and transient-heating computations areadvanced together down the trajectory. The flowfieldcomputations are performed for specified broad-faceand side-face temperatures. These temperatures arebased on the transient-heating solution at the previoustrajectory point. Three temperature estimates, labeled

"low", "nominal", and "high", are supplied asboundary conditions for the flowfield and radiationanalyses. This solution procedure, shown schematicallyin Fig. 4, provides surface distributions of heat flux,enthalpy, and ablation rate as a function of altitude andwall temperature. These tables are then used by thetransient-heating code to advance to the next trajectorypoint. The heating code iterates on temperature at eachnodal point and satisfies the surface-energy balance(SEE) equation.

Enabling Assumptions : Each flowfield case requiresglobal convergence of the RACER Navier-Stokes codeand the radiation code (generally four-to-fiveiterations). Over one-hundred cases are needed toadequately address the three trajectories examined inthis study, hi order to accomplish this extensive casematrix, without risk of underpredicting theaerothermal environment, it is assumed that:

(1) The module is oriented (aerodynamicallytrimmed) broad face-on-stable (FOS). This is themost likely orientation, based on motion studies,7and results in significantly higher temperaturesthan a random-tumbling motion.

(2) The three-dimensional GPHS module isrepresented by an axisymmetric, flat-face, cylinderwith a small-radius corner blending the front facewith the side of the cylinder. The diameter of thecylinder face (100mm) is an average of themodule's height and width. The notches, Fig.l,have been neglected based on arc-jet tests8 thatshow this feature quickly ablates, hi addition, thesharp edges ablate to form smooth, small-radiuscorners. This axisymmetric model greatly reducescomputational requirements.

(3) Recession (shape change) is computed. However,because the heatshield is thin (4.75 mm),burnthrough or structural failure would occurbefore shape change can appreciably perturb theflow.

(4) Radiation is computed using the tangent-slabapproach. The tangent-slab approximation is wellsuited for the flat-face geometry. Tangent-slab hasalso been shown9 to yield slightly higher heatingthan more complex three-dimensional schemes.

(5) The wall is treated as an equilibrium-catalyticsurface. The surface catalytic behavior of FWPF athigh temperatures is not known. However, theequih'brium-catalytic model should produce thehighest heating rate.

(6) The flow is assumed to be in thermal equilibrium.Numerical tests for peak-heating GPHS reentryconditions showed that thermal nonequilibriumhad negligible effect on the predicted wall

pressureassumed

and wall heat fluxes. Thus, it wasthat thermal equilibrium (a

single-temperature model) was sufficient foraccurately modeling the surface-ablation response.

III. Axisymmetric Flowfiel<VRadiationSolution Scheme

The overall nonequilibrium aerothermochemicaland radiation problem includes

(i) Aerothermal (Flowfield) Prediction (p,pu,pw,T,p)(ii) Chemical (Species) Prediction (Q and E,,, where

s=l,...,NS and e=l,...,NE)(iii) Mixture Properties/ Ablation-Rate (u, k, Pr, Le,, Cp,

h, Z*, mw ) Prediction(iv) Radiation (Qr) Prediction

To make the problem manageable, theflowfield/ radiation coupling is treated in an iterativemanner. The flowfield solution is predicted using theRACER code described herein, and radiationpredictions are performed using a version of theLORAN10 code named LORAN-C to denote theaddition of the carbon species. For most cases, 3-4flowfield/ radiation iterations were adequate on a35x35 grid.

Aerothermochemical Solution Scheme (RACERCode) : Even after separating the overall problem into asequence of flowfield solution and radiationcomputations, the number of flowfield unknowns (p,pu, pw, T, p, Cs, Ee, u, k, Pr, Leit h, Cp, Z*, mw ) is stillquite large. Thus, each flowfield iteration (n) isseparated into four parts

(1) A flowfield (pn+1, pun+1, pwn+1, T"+1/2, pn+1) predictionusing a previous estimate of the chemistry (Q", £,"),mixture properties (un, kn, Prn, Le,n, hn, Cpn, Z*n),and radiation field (Qr

N).(2) A chemical solution (Qn+1, E^1, Tn+1) using the

updated flowfield from (1) and the previousestimate of the mixture properties.

(3) Determination of the updated mixture properties(Hn+1, kn+1, Prn+1, Ler\ hn+1, Cpn+1, Z*"*1) using theupdated flowfield and chemistry [steps (1) and (2)].

(4) Determination of the surface ablation rate (ntw )using the specified Tw and the updated wallpressure (pw

n+1) and wall species composition

convergence (typically, less than 0.01% - 0.001% changein p, T and p). This updated flowfield solution is thenused to do the next radiation solution (Qr

N+1).

Governing Scaled Axisymmetric Full Navier-Stokes(FNS) Equations : A general axisymmetric coordinatesystem

(1)

is used where ̂ is the streamwise coordinate measuredalong the body surface, and T| and £2 are coordinatesmeasured from the body surface to the outer boundary.Along the stagnation streamline |i=0, at the bodysurface £2= TI =0, and r\ =1 at the outer freestreamboundary (see Fig. 5).

In this curvilinear coordinate system, thegoverning axisymmetric Full Navier-Stokes (FNS)equations for a reacting gas can be written as11'12

fnfnfis

00

-F/Jr

f21

f22

f23

0

+ £

0

522

523

524

0

Conservation of massConservation of x-momentumConservation of z-momentum (2a)Conservation of energyEquation of State

or l) + gfl (2b)

Briefly, for a specified radiation field (QrN),

these sequential steps (1) through (4) are iterated to

where fi is the streamwise inviscid flux vector, f2 is the"body-normal" inviscid flux vector, Si is the streamwiseviscous flux vector, s2 is the "body-normal" viscous fluxvector, go is a source-like vector, r is the radial distancefrom the body axis, and E=M0o/Re00.

These governing equations are singular along thestagnation streamline.13 To remove this geometricsingularity, a scaling function £(£,) is chosen such that C,is always differentiable to the first degree and ^—-^i as

§i-*0. Using this function, all the singular coordinateterms are scaled such that the governing equationsbecome finite in the limit £1— 0; i.e.,

a ] 2=(3a)

; and J = JC (3b)

where a^. = ̂ „ /J and J is the determinant of thetransformation Jacobian.

With this scaling the governing Full Navier-Stokes(FNS) equations become

(i)

(pU,w + Tlzp)C'+p/ J T

-Ui

(4)

where C = ~d£. In simpler notation these scaledgoverning equations can be written as

(5)

Flux Splitting of Scaled Inviscid Fluxes : The £2inviscid fluxes are split using an extension of thestandard van Leer flux-splitting approach14 to includereal-gas effects.15 The ^ inviscid fluxes ( f i) are splitusing the characteristic Mach number in the £1direction (Mi) which vanishes along the stagnationstreamline.

1

(6)

0

where a is the characteristic speed of sound y = pa2/p,~0i = Mx+aiz) /^ ' and Mi-Urf/Tm. Theseexpressions for Mi and the split fluxes clearly showthat although MI vanishes along the stagnationstreamline, the resulting streamwise split fluxes remainnonsingular.

Outer Boundary, Grid and Shock AlignmentProcedure : The RACER flowfield solution schemeinvolves an automatic grid-adaptation procedure inwhich the outer boundary is slowly redefined such thatthe final computational grid is properly aligned withthe evolving bow shock. This adaptation procedureconsists of:

Only move the outer boundary such that thecaptured bow shock becomes a ^constant gridline (see Fig. 6),Use the same £2 grid stretching function (TI) beforeand after the movement of the outer boundary,where

TIL = 1+1 (7)a prescribed constant

(iii) Keep a fixed number of grid points (M) betweenthe evolving bow shock and the outer freestreamboundary, which means forcing the bow shocklocation to be the T|=T]M grid line.

If the captured bow shock is located at r|=[T|s]n, theouter boundary location that will (a) not change thelocal shock-layer thickness [Rs(^i)], (b) relocate the bowshock at T|=T)M, and (c) give the desired number of gridpoints (M) between the body and the shock can bedetermined as

= «Tis]B/tiM}[Ro(Si)]B(8)

Predictor-Corrector Solution Scheme : Usingappropriate numerical differencing of the split fluxvectors and the viscous fluxes, the linearized form ofthe differenced equations can be written in thefollowing pentadiagonal form

l+Bji-Aq"*1.(9)

This differenced form of the governing equationsassumes that all remaining off-diagonal contributionson the implicit (left-hand) side of the equations havebeen appropriately lumped on the diagonal. Simplyignoring them will make the differencing inconsistent,and can cause numerical divergence. Thisblock-pentadiagonal set of equations is solved using anextension of the Predictor-Corrector solution scheme ofBhutta and Lewis16 described below.

(a) Predictor Step : In the predictor step (see Fig. 7), theimplicit streamwise coupling effects are neglected andit is assumed that

Aqjf (10)

Using boundary conditions at the wall (/=!) and at theouter boundary (/=LMAX), solution changes (Aq*j,;) arethen predicted at each grid point and recursiverelations are developed in the form

Aq*j; = - a" • Aq*. /+1 + /?£, where / =1,2,...,LMAXand j = 1,2,...,JMAX (11)

(b) Corrector Step : The subsequent corrector step (seeFig. 7) starts from the grid point adjacent to the outerboundary (/=LMAX-1) and moves toward the body(/=!). This solution step uses the recursive relationsfrom the predictor step at 1-1 and averaging thesolution at 1+1 from the predictor and corrector steps;i.e.,

r ( q )=r(q) +6(6 f 0/0q>( q -q)=r(q) + (17)

and<> * 0.5 (13)

This information is then used to reduce the originalpentadiagonal set of differenced equations to thefollowing tridiagonal system of equations

(14)

This tridiagonal system of equations is then solvedusing symmetry boundary conditions at j=l foraxisymmetric flows and parabolized Navier-Stokes(PNS) boundary conditions at j=JMAX.

Implicit Fourth-Order Pressure-Smoothing Effects :The numerical discretization procedure used in RACERinvolves higher-order finite-differenced approxima-tions of the split-flux vectors and the viscous fluxes.Typically, such higher-order approximations have littlenumerical dissipation and, thus, can not adequatelysuppress the growth of potential numerical oscillations.The RACER scheme uses a fourth-order pressure-dissipation formulation12-13 to suppress the growth ofthese potential oscillations. A brief derivation of thisfourth-order pressure-dissipation approach is givenbelow.

The governing full Navier-Stokes equations can bewritten in the residual form (for £1 > 0)

r(q)= f o + C f 1,6 + C f M, - « Cfs~U,+~s~2,6)=0 (15)

These numerical diffusion terms are needed in onlythose flowfield regions where higher-order differenc-ing approximations are used for the body-normal (£2)fluxes (i.e., the near-wall region where M{2 < 1). In thefreestream region, and across the embedded shocks,these additional smoothing terms are set to zero. This issimply done by giving appropriate values to theparameter 0; i.e.,

• when M{2 < 1•whenM{2 £ 1 (18)

Pseudo-Unsteady Approach using Unsteady Terms :Typically, when iterative steady-flow solutions arestarted from a poor flowfield approximation (such asfreestream conditions), severe numerical difficultiesmay be encountered because

(i) the initial residuals can be very large,(ii) the steady-state Jacobian matrices may not

provide an adequate or appropriate mechanismfor distributing these residuals, and

(iii) the resulting flowfield changes may not be physi-cally correct (such as negative pressure, density ortemperature).

For such cases, it is more efficient to view the problemas the time evolution of an unsteady problem. Since thedesired solution is the steady-state limit and not itsunsteady evolution, it is appropriate to adopt a'pseudo-unsteady' approach. Solution convergence canbe accelerated, and nonphysical solutions can beprevented, by including the actual unsteady flowfieldterms and by using a variable time step.

In this pseudo-unsteady approach, an additionalunsteady Jacobian matrix (At) is included on the left-hand-side of the governing differenced equations asfollows

+D • (19)

The flowfield vector is defined as q = [/?,/ni,/w,T,p]T. where At is the time step andA smoothed flowfield vector q is defined such that

-q = [0, 0, 0, 0, -p T = O(A^) (16)

To fourth-order accuracy, the governing equations canbe rewritten as

At = (At/ J ) ±\

P,t

(y,p-ZVT)/At

<20a)

or

At=0/T)

100

(h-V2)-Z*T

u w0 0

000

/?h,T-Z*p

000

(/>h,P-l) (20b)

The time step (At) is a difficult quantity to monitorbecause it can be theoretically unbounded betweenzero and infinity (0^ At< oo) . Instead, a time-relaxationparameter cat = At/(l+At) is used such that o>(-»0 whenAt— 0 and <»,— 1 when At->oo; Le., Q<, <wt £l. The govern-ing equations thus become

Aqjf

(21)

Treatment of the Geometric Axis of Singularity : Thegeometric axis of singularity corresponds to £i=C=0grid line (see Fig. 8). The grid metric terms aregenerally a function of the radial distance from thebody axis, which vanishes along the axis of singularityand, thus, the grid metric and transformation terms aresingular along this axis. After scaling the singularmetric terms with the scale factor £, the streamwise fluxvectors become finite along £i=£=0; however, theoverall equations still remain singular along £,i=£=0. Inthe present axisymmetric approach, the flowfield alongthis axis is obtained using appropriate boundaryconditions. However, this geometric singularity stillneeds to be removed because the split-flux vectors aredifferenced along grid lines which pass through thisaxis.

As shown in Fig. 9, 'pseudo grid points' (i.e., pointQ') are defined along the extension of the <f>=cc=constant(same as ^constant) surface grid line. These pseudogrid points also correspond to actual grid point alongthe surface grid line <j>=7i+a (point Q ). The grid pointQ and Q' represent the same physical location;however, some of the scaled quantities at theselocations do not have the same sign.

The contravariant streamwise velocity (Ui), thecharacteristic Mach number (Mi), and the metric termappearing in the streamwise flux vector are related asfollows:

Mi"01-MI

and ]Q (22)

Element Conservation Equations : This is one of themost important features of the RACER solution schemebecause

(i) Determination of element composition across theshock layer is essential for equilibrium ornear-equilibrium ablation computations underlow-altitude GPHS entry conditions.

(ii) Ablation boundary conditions (to determine theelement composition at the wall) can be directlyimposed on the element conservation equations.

The unsealed element conservation equations arewritten as

where e=M,»/Re,», #es = mass of element 'e' per unitmass of species 's1, and mjkk is a metric term. Tests showthat it is adequate to assume binary species diffusionwith a constant Lewis number (i.e., Le^lA) in only theelement conservation equations; i.e.,

(24)

These element conservation equations are solved usingconvection/ diffusion boundary conditions applied atthe ablating wall.17 These convection/ diffusionboundary conditions represent a mass balance of theelements at the wall (see Fig. 10) and include thecontributions due to injection at the wall, convectionaway from the wall and diffusion to the wall; i.e.,

(25)

Chemical Nonequilibrium Modeling : In addition tothe governing flowfield equations described earlier, aset of species conservation equations is also needed fornonequilibrium flows. These equations represent theconservation of mass of each individual speciesincluded in the chemical system and have the form

d(pCs) (26)

Q

where s=l,...,NS, NS is the total number of species, cosis the rate of production of the species 's', and mjkk is ametric term.

The species mass fractions at any location in theflowfield are also intrinsically related to thecorresponding element mass fractions at that locationdetermined using the element conservation equations.

These mutual relationships are governed by thefollowing atomic mass-balance constraints for 'ME'elements; i.e.,

e=l,...,NE (27)

where 'a,,' is the number of atoms of element 'e' inspecies 's', Ae is the atomic weight and Eg is themass-fraction of element 'e', and ms is the molecularweight of species 's'. Furthermore, when ions arepresent in a chemical mixture, the charge-balanceequation for ions and electrons also needs to besatisfied; i.e.,

= 0

where ^s is the charge of species 's'

(28)

This leads to the conclusion that only 'NS-NE-1'species conservation equations are truly linearlyindependent in the infinite-rate limit. Consequently,the nonequilibrium RACER scheme only uses NS-NE-1number of species conservation equations representingthe neutral molecules. The remaining NE+1 equationsare supplied by the NE atomic-mass constraints andthe single charge-balance equation which are alwaysvalid.

An adequate description of the speed of sound '<£is needed to accurately determine the various split-fluxvectors. For a reacting gas mixture, the speed of sounddefined as a= J\~g^)s is not unique. One possibleapproach is to assume that dQ=0, which is true forfrozen flow, hi RACER, it is assumed that thecharacteristic speed of sound (a) of multicomponentreacting gas mixture can be reasonably represented bythis frozen speed of sound (a/).

The gas mixture is assumed to be a reactingmixture of perfect gases. For such a reacting gasmixture, the equation of state is

where m = I/TNSLs=i ms

and Z* = m (29)

and the 'frozen speed of sound1 is

where RG -rif =Cp/(Cp -RG)

> m and(30)

Thermal Coupling of the Species Production Terms :For some reactions the rate of production of a speciescan be a very strong function of the local temperature;i.e., the electron-impact reactions such as N + e' = N*+ 2e; O + e = O* + 2e-, and C + e" = C + 2e'. Forthese electron-impact reactions, -gf- » -get" "* P~B/%~ >and must not be ignored. If it is assumed that flowfieldpressure distribution is a relatively 'weak' function ofthe local species composition, then the equation of statecan provide a reasonably accurate relationship betweenspecies density variations and the local temperaturechange; i.e.,

NS

(31)

Once the changes in the species densities areknown, the corresponding change in temperature canbe determined from the above expression. Using thisexpression for the temperature change, the speciesproduction can be linearized in terms of species densityvariations as follows:

o>r!-# »{^"Xai/vr'-f^

Nonequilibrium Solution Scheme : In each solutioniteration, the flowfield variables (p, u, v, w, p, T) arefirst solved in a coupled-matrix form using theconservation equations for mass, momentum andenergy. The molecular species conservation equationsand the constraint equations for the conservation ofatomic mass and charge are then solved in a coupledblock-matrix form by linearizing these equationsaround the previous iteration.

With the species mass-fraction vector defined as

c = [d, C2, C3, ..., CNS]T (33)

the solution of the chemistry step can be written in thefollowing block-matrix form

(34)Bn

+[(D2 -

where Acn+1 = cn+1- cn .

All matrices, except B, are diagonal in form, and themutual coupling of the species equations is solely dueto this matrix. The overall coupled-species solution isdone using the storage equivalent of one NSxNS matrix

8

and three NSxl vectors per grid point, rather than theconventional requirement of three NSxNS matrices andone NSxl vector at each grid point. Thus, by simplyusing the sparseness of these matrices, the coupledspecies solution is computed using two-to-three timesless storage and floating-point operations.

To further simplify the numerical solution of thesenonlinear species equations, it is assumed that

(i) the spatial coupling of a species at a grid point ispredominantly dictated by only the concentrationof that species at the neighboring grid points, and

(ii) the mutual coupling of the species at a grid point ispredominantly dictated by the speciesconcentrations at that grid point.

With these assumptions, a two-step procedure14 isdeveloped (see Fig. 11) in which the first step accountsfor the local mutual coupling of the species, and thesecond step accounts for the spatial coupling of eachspecies. The first step reduces to a highly vectorizablepoint-matrix solution. Using this intermediate solutionin the second step, the off-diagonal terms (representinglocal species-coupling effects) are estimated, and theresulting system of equations reduces to a diagonalizedsolution scheme. Under the equilibrium limit the firststep of this two-step procedure is dominant andsufficient, whereas in the nonequuibrium limit thesecond step of this two-step procedure is dominant.

Figure 12 shows sample flowfield predictions overthe GPHS module under low-altitude (50 kft) andhigh-velocity (25.3 kft/sec) reentry conditions with a7-species nonequilibrium-air model and fully-catalyticwall boundary conditions. In this case the shock layer isin thermochemical equilibrium as shown by thestagnation streamline plots of temperature andpressure in Fig. 12a. Figure 12b shows thecorresponding surface distributions of pressure andheat-transfer rate. The predicted stagnation pressure isin excellent agreement with the corresponding estimateobtained using the real-gas tables of Lewis andBurgess.18 The predicted stagnation-point heat-transferrate is also in excellent agreement with the estimatesbased on the real-gas tables of Lewis and Burgess18 foran 'equivalenf sphere with a nose radius of w

Following the approach of Scala20 and Scala andGilbert,21 we assume thermochemical equilibrium at thewall. Thus, in our ablation computations

The boundary conditions used consist ofthird-order interpolation along the geometric axis ofsingularity, parabolized Navier-Stokes (PNS) exit-flowconditions, and freestream (Cs=CSoo) at the outerboundary. Determination of the species mass fractionsat the wall (CjW) requires an assumption about thenature of chemical reactions occurring at the wall.

/ *1EQ (35)

where E^ are the element mass fractions at the wall, Twis the wall temperature, and pw is the wall pressure.

Thermochemical Modeling : The carbon-air chemicalmodel consists of 19 gas-phase species (N, O, Na, Oz,NO, Q, Cz, C3, CO, COi, CN, N*, O+, N2

+, O2+, NO*, CT,CO+, and e") and 44 reactions. These 44 reactionsinclude the most reliable reactions and reactions-ratedata available in the literature.22"28 The variousgas-phase reactions considered, the correspondingreaction rates and related references are summarized inTable 1. The third-body efficiency data for thesereactions are based on the data used by Blottner22 andGupta et al.26 The species thermodynamic data areprovided in the form of enthalpy curvefits,28"30 and thespecies transport properties are obtained from thecorresponding collision cross-section information.28 Thenecessary species collision cross sections weredetermined using the approach of Gupta et al.,28 andthe mixture properties were obtained using the mixtureformulae used by Gnoffo et al.26

Figure 13 shows a comparison of RACER andLAURA26 predictions of flow over the GPHS module atan altitude of 192 kft and M»=50.63. As can be seenfrom this figure, the predicted surface pressure is ingood agreement. The predicted heat-transfer rate isalso in good agreement everywhere except in thestagnation region where the LAURA predictions showa nonphysical rise. In this case, the overprediction ofstagnation heat-transfer rate by LAURA is largelyattributable to the flux-Umiters26 used in the stagnationregion where the velocities approach zero and theeigenvalues become singular.26 The RACER techniquedoes not involve such limiters and, thus, does notsuffer from such a numerical degradation of thepredicted near-wall flowfield. Figure 13 also showsthat the assumption of constant binary Lewis number isquite inadequate for these conditions.

Carbon Surface-Ablation Modeling : Thenonequilibrium carbon surface-ablation model used isbased on a combination of heterogeneoussurface-oxidation effects and nonequilibrium graphitesublimation effects; i.e.,

(36)

Based on the work of Scala20 and Scala andGilbert21, it is expected that heterogeneoussurface-oxidation effects will be dominant at lower walltemperatures («1500-3000 °K) and nonequilibriumsublimation effects will be dominant at higher walltemperatures (^3000-4500 °K).

For the case of heterogeneous surface oxidation,we extended the approach of Blottner22 to includeoxidation of graphite into CO and CO2 based on theoxidation-probability data of Rosner and Allendorf.30

Similar to the assumptions of Scala20 and Scala andGilbert,21 the relative amounts of CO and CO2produced at the wall were established usingthermochemical equilibrium.

The nonequilibrium graphite sublimation modelused is based on the Knudsen-Langmuir relations22-32

shown below

(37)

The coefficients °s are zero except for f lCi=0.24 /ac2 = 0.50 1 ̂ d etc, = 0.024 »

Radiation Code Selection : Several gas-radiationcodes were assessed to establish their ability to addressthe complex chemically reacting flow surrounding theablating GPHS module. The two most promising werethe RAD/EQUIL33 code, developed by Nicolet, and theLangley Optimized RAdiative Nonequilibrium(LORAN10) code, developed by Hartung.RAD/EQUIL's advantage is that it contains all of therelevant chemical species needed for C-N-O gasradiation. However, the code makes equilibriumassumptions to calculate species and electron-levelpopulations that are not applicable to the high-altitudeand high-velocity peak-heating conditions of the GPHSmodule. LORAN is similar to Park's NEQAIR34 code,and was developed for high-altitude aerobrakingapplications. It's formulation of the gas-radiationproblem includes all important nonequilibrium effects,but only treats air chemistry. Given the significance ofnonequilibrium for GPHS reentry, LORAN was chosenas a starting point. Extensions of LORAN developed totreat GPHS ablation, and coupling to the RACERflowfield code, are described below.

LORAN-C Code Development: LORAN contains allrequired radiative mechanisms for GPHS reentry,provided scattering (particle erosion) is not a concern.The code computes radiative transport using thetangent-slab approximation, with temperature andchemical species distributions supplied by a separateflowfield code. Electron population within the specific

atomic or molecular energy level is calculated usingPark's Quasi-Steady-State34 (QSS) model. Quantumrotational and vibrational transitions for molecularspecies are treated using a smeared-band approach.LORAN computes the radiant heat flux from the gasphase to the wall boundary, and radiation couplingterms for the flowfield code. LORAN has beensuccessfully applied on the Aero-assisted FlightExperiment (AFE),35 Project Fire,36 and other NASAstudies, usually in conjunction with the LAURA26

flowfield code.

The main drawback of the LORAN code is that itdoes not treat ablation products. The originalapplication was for nonablating aerobrakes, so only O,N, N2, Oi, NO, their ions and e" were included. Toaccount for the presence of ablation products, thecode's capability was extended to calculate emissionand absorption for the 19-species carbon-air gas modeldeveloped for the RACER code. The excitation andspectral data (excitation and ionization cross-sections,energy levels, etc.) were collected for C, Cz, C3, CN, CO,COi, C, and CO+ from Refs. 33, 37, and 38. TheLORAN version developed under this effort has beendesignated LORAN-C, to indicate the addition ofcarbon chemistry.

RACER/LORAN-C Coupling : Coupling between theflowfield and gas radiation occurs by two means. First,the flowfield is directly affected by energy transportthrough the gas, radiantly heating or cooling the shocklayer. This energy transport appears as a source termin the Navier-Stokes equations. The source term is thedivergence of the radiant flux, Qr. For the tangent-slabapproximation, this term reduces to dq,^ /d , where nis the outward normal to the surface. The source termis calculated in the LORAN-C code for use by RACER.Second, radiation is a significant component of thesurface heat transfer to the GPHS module, especiallynear the peak-heating altitudes. Radiant wall heatingaffects the boundary-layer structure and carbon-speciesdistribution by its influence on wall ablation in thesurface energy balance. Radiant flux to the wall iscalculated by LORAN-C for use by the SINRAP codewhich performs the surface-energy balance asdescribed in the following section.

Coupling between the flowfield and radiation fieldis treated by converging the flowfield solution, usingprevious gas radiation results, and then updating theradiation calculation using this new flowfield. Globalconvergence between the codes is accelerated byunder-relaxation of the source term for use in theflowfield iterations. The updated source term is givenby

10

[0, (l-C»r)[Qr] (38)

Experience shows that a variable cor (0.8 for N=l, 0.5 forN>1) yields convergence in about four-to-five globaliterations.

Quasi Steady-State Surface Energy Balance : Usingqsc ^sc^-af-) w to represent the net heat conducted intothe solid surface, it can be shown39 that the overallenergy balance for the ablating graphite surface can bewritten as

)w =(39)

The in-depth transient heating analyses code SINRAP2

was modified to use this energy balance. RACER'spredictions of the various surface heat fluxes, speciesablation rates, and species wall enthalpies wereprovided in a tabular form for three different walltemperature distributions which bounded the finalconverged wall temperature.

IV. GPHS Aeroshell Sample Results andDiscussion

The new RACER code, coupled to LORAN-C, hasbeen validated to the extent possible throughcomparisons with shock-tunnel data and with solutionsobtained using the LAURA26 Navier-Stokes code aswell as a viscous-shock layer (VSL)40 code. In all cases,excellent agreement was obtained. In addition,grid-refinement studies were performed at selectedtrajectory points to insure that predicted surface valueswere being adequately resolved. It was found that35-points from the body to the outer boundary (highlyclustered near the body), and 35-points along the body(clustered about the rounded corner), was sufficient formost cases.

SINRAP in-depth heating and recessionpredictions, based on coupled RACER/LORAN-Cresults, and ABAQUS structural analyses, show thatthe aeroshell survives the shallow (y = -7°) trajectorywith ample margin. For the steep (y = -90°) trajectory,RACER/LORAN-C and SINRAP solutions have beenadvanced to the 6th point (2.0 sec). Additionaltrajectory points were not computed because ABAQUSsolutions show aeroshell structural failure between the5th (1.6 sec) and 6th trajectory points. Failure of theaeroshell releases cylindrical Graphite Impact Shells(CIS) contained within the GPHS module. Each CIS isthermally protected by a FWPF heatshield. Work is

now in progress to assess the aerothermostructuralperformance of the GIS using the tools developed forthe GPHS aeroshell.

Flowfield Results: On the shallow trajectory, globallyconverged RACER/LORAN-C solutions were obtainedat eleven altitudes (see Fig. 2), each with threeprescribed surface-temperature distributions. On thesteep trajectory, globally converged results wereobtained for six altitudes (Fig. 2). In total, abouttwo-hundred and fifty RACER and two-hundredLORAN-C solutions were obtained for the shallow andsteep trajectories.

Surface Distributions: RACER/LORAN-C predictionsfor conditions at the surface of the GPHS module drivethe transient-thermal response. The converged SINRAPtemperature solution at the 6th (and last) point on thesteep trajectory was close to the RACER/LORAN-Ccase with a specified front-face temperature of 8260°R(4589°K). Peak heating on the shallow trajectory wasalso close to a point in the flowfield matrix. Figures 14through 17 contrast surface distributions for this steepcase with the less severe shallow-trajectory solutionclosest to peak heating.

The freestream conditions (from three-degree-of-freedom trajectory analyses), and wall temperatures(estimates from SINRAP), for these steep and shallowcases are shown in Table 2.

Figure 14 shows the specified surface-temperaturedistributions for the steep and shallow cases. In just 2seconds on the steep trajectory, SINRAP predicts thatthe front face has reached 8260°R (4589°K) while theshallow trajectory takes 21 sec to reach a peaktemperature that is 1000° less. The front-facetemperature distribution (a boundary condition forRACER computations) is chosen, based on SINRAPsolution trends, to be constant across the front facefrom the stagnation point to the vicinity of the corner.The temperature then drops linearly over the roundedcorner to a constant side-wall value. As shown in Fig.14, the side wall for the steep, at 6460°R (3589°K) is1200° hotter than the side wall for the shallow.

The computed surface-pressure distributions,shown in Fig. 15, primarily reflect the difference inaltitude. The pressure load on the GPHS aeroshell forthe steep case is 10 times larger than the shallow case.

The ablation rate, shown in Fig. 16, is nearly 26times larger for the steep compared to the shallow.However, the ablation rate, nondimensionalized by thefreestream mass-flux, gives a better measure of ablation

11

effects on the flowfield. This nondimensional ablationrate is 2.6 times larger for the steep case compared tothe shallow.

The surface distributions of the total heat flux andits components are shown in Fig. 17. Across the frontface, the heat flux due to gas-conduction plusspecies-diffusion is over 5,000 BTU/(ft2sec) (56.75MW/m2) for the steep case. Near the rounded cornerthis jumps to 20,000 BTU/^sec) (227 MW/m2). Thedistribution is similar for the shallow trajectory casebut the flux levels are less by an order of magnitude.

On both trajectories, the radiation heat flux farexceeds the gas-conduction plus diffusion component.At the stagnation point for the shallow trajectory, theradiation flux is 3.9 times the sum of the conductionand diffusion flux. Radiation is even more dominantfor the steep trajectory where radiation is 5.9 times thesum of the conduction and diffusion effects. On thesteep trajectory, the radiation component exceeds32,000 BTU/(ft2sec) (363.2 MW/m2).

The total heating for the steep case is severe. Thetotal flux in the stagnation region, and near therounded corner, approaches 38,000 BTU/(ft2sec) (431.3MW/m2). This level of heating is unequaled for Earthreentry and is comparable to that predicted for theGalileo probe41 on its plunge into Jupiter's atmosphere.The heat flux to the surface for the steep case is over 14times that encountered at peak heating on the shallowtrajectory.

Field Distributions: Isobars, shown in Fig. 18, revealthat pressure is nearly uniform across the shock layerover the front face, followed by a rapid expansion ontothe shoulder region. The pressure across the shocklayer for the steep case is about 9 atm and only 0.8 atmfor the higher altitude shallow case.

The shock-layer temperatures along the stagnationstreamline are shown in Fig. 19. The peak temperaturefor the steep case reaches 21,000°K (37,800°R) while theshallow case peaks at 17,000°K (30,600°R).

Air-species mass fractions along the stagnation linefor the steep case are shown in Fig. 20. Thedistributions for the shallow case are similar. The O2and N2 molecules dissociate and ionize so that, N, 1ST,O+, and O dominant the shock layer. Oxygen does notreach the surface because of high ablation rates.

The dominant carbon-species mass fractions alongthe stagnation streamline for the steep case are shownin Fig. 21. The mass-fraction distributions for the

shallow case are similar. In both cases, C3 is thedominant species at the wall but diminishes so rapidlyaway from the wall that it does not appear on the scaleof Fig. 21. Contours of C+ for the shallow and steepcases are shown in Fig. 22. Because C+ extends furtheraway from the wall than other ablation product it is agood indicator of the extent of the ablation layer.

Transient-Heating Results: SINRAP, modified toaccept surface-energy balance terms and recession-ratepredictions from tables of RACER/LORAN-Csolutions, successfully converged along both theshallow and steep trajectories. The computed in-depthnodal temperatures and surface recession historieswere then employed in thermostructural analyses.

Comparison of Shallow and Steep Trajectories: Thethree prescribed front-face wall temperatures forRACER/LORAN-C at the selected trajectory pointsalong the shallow and steep trajectories are shown inFig. 23, along with the converged SINRAPstagnation-point temperature history for bothtrajectories. In Figs. 21 through 23, the time scale of thesteep trajectory is 10 times faster than the shallow.Along the shallow trajectory, the temperature peaks at7260 °R (4033 °K) in about 21 sec. At the 6th point onthe steep trajectory, wall temperatures have surpassed8000°R (4444°K) in only 2 sec.

The predicted surface heat-flux from SINRAP isshown in Fig. 24. At the 6th point on the steeptrajectory radiative heating is severe, making the totalflux levels remarkably high (approaching 34,000BTU/(ft2sec) (385.9 MW/m2) at the stagnation point).This heating rate is more than 13 times the shallowpeak-heating level. The radiation heat flux exceeds thegas-conduction + diffusion component by more than afactor of seven. Radiative heating on the shallowtrajectory also exceeds the convective component.However, the steep trajectory is so severe that itsconvective component at 2 sec is almost twice the peakradiative flux on the shallow.

Wall temperature has a strong effect on theradiative component of the total heat flux becauseincreasing wall temperature leads to higher ablationrates. The increase in the amount of carbon in theshock layer, at high ablation rates, serves to blockradiation from reaching the surface. In addition, withhigh ablation rates, the boundary layer is "blown off"which reduces the convective heating component. Theablation rates for the steep trajectory at the 6th point,shown in Fig. 25, are a factor of 26 times larger than themaximum rate along the shallow trajectory.

12

SINRAP integrates the ablation rate along thetrajectory. Ablation rates, from the CFD solutions, areinterpolated in SINRAP as a function of altitude andconverged wall temperature. The resulting surfacerecession for the shallow and steep trajectories isshown in Fig. 26. The shallow trajectory continues outbeyond 100 sec with recession asymptoting at 0.125inches (3.175 mm). The minimum FWPF thickness is0.185 inches (4.7 mm), so sufficient margin remains forthe shallow trajectory (ABAQUS thermostructuralanalyses verify structural integrity for the shallowtrajectory). On the steep trajectory, recession isprogressing rapidly and burn-through would probablyoccur. However, thermostructural analyses predictfailure prior to 2 sec. The time of aeroshell failureprovides initial conditions for subsequentaerothermostructural analyses of the GIS cylinderscontained within the GPHS aeroshell.

Acknowledgments

This work was performed as part of the SafetyAnalysis Task for the Cassini RTG Program undercontract to the U.S. Department of Energy, Office ofNuclear Energy, Science and Technology, Office ofEngineering and Technology Development (NE-50).The RTG Program is under the overall direction ofRichard Hemler, Manager, Space Power Programs,Lockheed Martin Missiles & Space (LMMS). LarryDeFillipo (and previously Jim Braun) manages theSafety Analysis Task for LMMS. Wayne Tobery andPaul Klee of LMMS modified SINRAP to employRACER/LORAN-C tables and performed thetransient-heating analyses. Dan Vacek (LMMS) led thethermostructural analysis task. Dr. Clark Lewis,President, VRA, Inc., provided valuable technicalcontributions. We also gratefully acknowledge Drs.Ken Sutton, Peter Gnoffo, and Lin Hartung of NASALangley Research Center for providing the LAURAand LORAN codes.

References1 Henline, W.D., and Tauber, M.E., "Trajectory-Based

Heating Analysis for the European SpaceAgency/Rosetta Earth Return Vehicle," Journal ofSpacecraft and Rockets, Vol. 31, May-June 1994, pp.421-428.

2 Klee, P., "Background and Use of SINRAP Code,Rev. C," Lockheed Martin Missiles & Space, PIRU-Cassini-018, King of Prussia, PA, May 1994.

3 Gaski, J., "SINDA 1987 User's Manual," AerospaceCorporation version, Oct. 1987.

4 Vacek, D., "Nonlinear Constitutive Material Modelfor Fine Weave Pierced Fabric Carbon-Carbon,"

Lockheed Martin Missiles & Space, PIRU-l VC4-Cassini-103, King of Prussia, PA, Sept. 1995.

5 Anon., "ABAQUS/Standard User's Manual, Version5.4," Hibbitt, Karlsson & Sorensen, Inc., 1994.

6 Anon., "Draft Final Safety Analysis Report (DFSAR)for the Cassini Mission, Volume n, Book 2 of 2,Appendices for Accident Model Document,"Lockheed Martin Missiles & Space, CDRL C.2, Kingof Prussia, PA, June 1996.

7 Sharbaugh, R.C., "Follow-up Investigation of GPHSMotion Studies for Heat Pulse Inetrvals of Reentriesfrom Gravity-Assist Trajectories," Johns HopkinsUniversity Applied Physics Laboratory, JHU/APLANSP-M-22, Laurel, MD, March 1992.

8 Lutz, S.A., "GPHS/GIS Module Ablation ResponseTesting at the NASA Ames 20 MW AerodynamicHeating Faculty: Final Test Report," Johns HopkinsUniversity Applied Physics Laboratory, JHU/APLEM-5514/BFD-2-88-030, Laurel, MD, Dec. 1988.

9 Elbert, G. J., and Cirtnella, P., "AxisymmetricRadiative Heat Transfer Calculations for Flows inChemical Non-Equilibrium," AIAA Paper 93-0139,Jan. 1993.

10 Hartung, L.C., "Development of a NonequilibriumRadiation Heating Prediction Method for CoupledFlowfield Solutions," AIAA Paper 91-1406, June1991.

11 Peyert, R. and Viviand, H., "Computations ofViscous Compressible Flows Based on theNavier-Stokes Equations," AGARD-AG-212,1975.

12 Viviand, H., "Conservative Forms of Gas DynamicsEquations," La Recherche Aerospatiale, No. 1,Jan.-Feb. 1974, pp. 65-68.

13 Bhutta, B.A., and Lewis, C.H., "PNS Predictions ofAxisymmetric Blunt-Body and AfterbodyFlowfields," AIAA Paper 93-2725, July 1993.

14 van Leer, B., "Flux-Vector Splitting for the EulerEquations," Report No. 82-30, ICASE, NASA LangleyResearch Center, Hampton, VA, Sept. 1982.

15 Bhutta, B.A., and Lewis, C.H., "Supersonic/Hypersonic Flowfield Predictions Over TypicalFinned Missile Configurations," Journal ofSpacecraft and Rockets, Vol. 30, Nov.-Dec. 1993, pp.674-681; see also AIAA Paper 92-0753.

16 Bhutta, B.A., and Lewis, C.H., "Three-DimensionalHypersonic Nonequilibrium Flows at Large Anglesof Attack," Journal of Spacecraft and Rockets, Vol.26, May-June 1989, pp. 158-166. See also AIAA Paper88-2568, June 1988.

17 Bhutta, B.A., and Lewis, C.H., "New Technique forLow-to-High Altitude Predictions of AblativeHypersonic Flowfields," Journal of Spacecraft andRockets, Vol. 29, Jan.-Feb. 1992, pp. 35-50; see alsoAIAA Paper 91-1392, June 1991.

13

18 Lewis, C.H., and Burgess, ffl, E.G., "Altitude-VelocityTable and Charts for Imperfect Air,"AEDC-TDR-64-214, AEDC, Arnold Air Force Station,TN, Jan. 1965.

19 Zoby, E.V., and Sullivan, E.M., "Effects of CornerRadius on Stagnation-Point Velocity Gradients onBlunt Axisymmetric Bodies," NASA TM X-1067,March 1965.

20Scala, S.M., "A Study of Hypersonic Ablation,"Report No. R59SD438, General Electric Company,Philadelphia, PA, Sept. 1959.

21 Scala, S.M., and Gilbert, L.M., "Sublimation ofGraphite at Hypersonic Speeds," AIAA Journal, Vol.3., No. 9, Sept. 1965, pp. 1635-1644.

22 Blottner, F.G., "Prediction of Electron Density in theBoundary Layer on Entry Vehicles With Ablation,"The Entry Plasma Sheath and Its Effects on SpaceVehicle Electromagnetic Systems, Volume I, NASASP-252, Oct. 1970, pp. 219-240.

^Dunn, M.G., and Kang, S.W., "Theoretical andExperimental Studies of Reentry Plasmas," NASACR-2232, April 1973.

24 Park, C, Howe, J.T., Jaffe, R.L., and Candler, G.V.,"Review of Chemical-Kinetic Problems of FutureMars Missions, II: Mars Entries," Journal ofThermophysics and Heat Transfer, Vol. 8, No.l,Jan.-March 1994, pp. 9-23.

25 Lewis, C.H., Private Communications, May 1994.26Gnoffo, P.A., Gupta, R.N., and Shinn, J.L.,

"Conservation Equations and Physical Models forHypersonic Air Flow in Thermal and ChemicalNonequilibrium," NASA Technical Paper 2867, Feb.1989.

27 Park, C., Nonequilibrium Hypersonic Aerothermody-namics, John Wiley & Sons, New York, NY, 1990.

28 Gupta, R.N., Yos, J.M., Thompson, R.A., and Lee,K.P., "A Review of Reaction Rates andThermodynamic and Transport Properties of an11-Species Air Model for Chemical and ThermalNonequilibrium Calculations at 30,000 K," NASAReference Publication 1232, Aug. 1990.

29 Gupta, R.N., Lee, K.P., Moss, J.N., and Sutton, K., "AViscous-Shock-Layer Analysis of the MartianAerothermal Environment," AIAA Paper 91-1345,June 1991.

30 Gupta, R.N., Lee, K.P., Moss, J.N., and Sutton, K.,"Viscous-Shock-layer Solutions With CoupledAblation and Ablation Injection for Earth Entry,"AIAA Paper 90-1697, June 1990.

31Rosner, D.E., and Allendorf, H.D., "HighTemperature Kinetics of Graphite Oxidation byDissociated Oxygen," AIAA Journal, Vol. 3, No. 5,Aug. 1965, pp. 1522-1523.

32 Baker, R.L., "Graphite Sublimation ChemistryNonequilibrium Effects," AIAA Journal, Vol. 15,No.10, Oct. 1977, pp. 1391-1397.

33 Nicolet, W.E., "User's Manual for Rad/Equil/1973, AGeneral Purpose Radiation Transport Program,"NASA CR-13470, Nov. 1973.

34 Park, C., "Nonequilibrium Air Radiation (NEQAIR)Program: Users Manual," NASA TechnicalMemorandum 86707, July 1985.

35Hartung, L., Mitcheltree, R., and Gnoffo, P.,"Coupled Radiation Effects in ThermochemicalNonequilibrium Shock-Capturing FlowfieldCalculations," AIAA Paper 92-2868, July 1992.

36 Greendyke, R., and Hartung, L., "Convective andRadiative Heat Transfer Analysis for the Fire IIForebody," Journal of Spacecraft and Rockets, Vol.31, Nov.-Dec. 1994.

37 Whiting, E:E., Arnold, J.O., Lyle, G.C., "A ComputerProgram for a Line-by-Line Calculation of Spectrafrom Diatomic Molecules and Atoms Assuming aVoigt Line Profile," NASA Technical Note D-5088,July 1969.

38 Lotz, W., "Electron Impact lonization Cross-Sectionsand lonization Rate Coefficients for Atoms and Ionsfrom Hydrogen to Calcium," Zeitschrift fur Physiks,Vol. 216, Oct. 1969, pp. 241-247.

^Bhutta, B.A., Daywitt, J.E., and Brant, D.N.,"Interpretation of Enthalpies in the Energy Balance ofan Ablating Graphite, Surface," AT-TN-96-02,AeroTechnologies, Inc., Yorktown, VA, May 1996 (tobe submitted to Journal of Spacecraft and Rockets).

40 Song, D.J., and Lewis, C.H., "Hypersonic Finite-RateChemically Reacting Viscous Flows over an AblatingCarbon Surface," AIAA Paper 84-1731, June 1984.

41 Givens, J.J., Nolte, L.J., and Pochettino, L.R., "GalileoAtmospheric Entry Probe System: Design,Development and Test," AIAA Paper 83-0098, Jan.1983.

14

Table 1. Gas-phase reactions and reaction-rate datar

1234567891011121314151617181920212223242526272829303132333435363738394041424344

Reaction

O2 +mi <=> 2O +miN2 +m2 <=> 2N +m2

N2+N <=>3NNO +m3 <=> N +O+m3

O+NO <=>N +O2

O +N2 <=> N +NOO+N <=>NO*+e"O +02* <=> 02 +0*N2 +N* <=> N +N2*O +NO* <=> NO +O*N2 +O* <=> O +N2*O2 +NO* <=> NO +O2*N +NO* <=> NO +N*2O <=> O/ +e"2N <=> N2* +eO +&- <=> O* +2e-

N +e" <=> N* +2eN2 +o2* <=> NO +NO+

NO +ixn <=> NO* +e'+m4O +NO* <=> O2 +N*CO2 +D15 <=> CO +O+msCO +m6 <-> C +O +m«C2 +m7 <=> 2C +m7

C3 +m8 <=> C +C2 +mjCN +m9 <=> C +N +m9

N2 +C <-> CN +NCO +N <-> CN +OCO2 +N <=> CN +O2

N2 +CO <=> CN +NOCO +NO <=> CO2 +NCO2 +O <=> CO +O2

2CO <=> CO2 +CCO +O <=> O2 +CCO +N <»=> C +NOCN +O <=> C +NO2CO <=>C2+O2

CO +C <=> C2 +OC2 +CO <=> C3 +OC3 +C <=> 2C2

O2 +C+ <=> O2+ +C

CO +C* <=> CO* +CNO +C+ <=> NO* +CC +O <=> CO* +e"C +e- <=> C* +2e'

Forward Rate, kf=«Tki'exp(-</rk)

a3.61E+0181.92E+0174.15E+0223.97E+0203.18E+0096.75E+0139.03E+0092.92E+0182.02E+0113.63E+0153.40E+0191.80E+015l.OOE+0191.60E+0171.40E+0133.60E+0311.10E+0321.38E+0202.20E+0151.34E+0131.20E+0118.50E+0194.50E+0181.60E+0162.50E+0141.11E+014l.OOE+0143.00E+008l.OOE+003l.OOE+0033.00E+008l.OOE+0032.00E+0109.00E+0161.60E+0139.20E+0114.10E+0101.20E+0131.70E+009l.OOE+013l.OOE+0137.86E+0108.80E+0083.90E+033

b59000113100113100756001970037500324002800013000508002300033000610008080067800158500168200141000108000727003685012900070930874807100023200386004956092010209801821072390695005320014600163300597904324019580940031400-116433100130700

c-1.00-0.50-1.50-1.501.000.000.50-1.110.81-0.60-2.000.170.93-0.980.00-2.91-3.14-1.84-0.350.310.50-1.00-1.001.000.00-0.110.001.002.002.001.002.001.00-1.000.100.750.500.001.500.000.000.381.00-3.78

Ref.22222222222222

2S&2823&2S2S&282S&2823&2S2S&2823&2S23&2S2S&282S&282S&282S&2823&2S

222222222424242222222222222222222222222424

25&2T*2424

Backward Rate, kb=«frk'exp(:/7rk)d

3.01E+0151.09E+0162.32E+0211.01E+0209.63E+0111.50E+0131.80E+0197.80E+0117.80E+0111.50E+0132.48E+0191.80E+0134.80E+0148.00E+0211.50E+0222.20E+0402.20E+040l.OOE+0242.20E+026l.OOE+0141.50E+0062.40E+018l.OOE+0165.83E+0157.40E+0187.70E+0092.70E+0106.70E+0053.10E+0021.80E+0075.20E+0052.00E+006l.OOE+010l.OOE+0166.00E+0113.80E+0135.00E+0115.00E+0115.00E+0111.20E+0157.80E+014l.OOE+0134.09E+0228.95E+040

e0.00.00.00.0

36000.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0

-264300.00.0

-66.741208330710069601559087501430069700.00.00.0

3620020102010302018821481232002911-453.1

/-0.50-0.50-1.50-1.50-0.500.00-1.000.500.500.00-2.200.500.00-1.50-1.50-4.50-4.50-2.50-Z500.001.25-1.00-0.500.54-1.001.000.751.251.751.251.501.251.00-1.000.000.000.500.500.500.54-0.610.00-1.57-5.04

Ref.22222222222222

2S&2823&2S2S&2823&2S2S&2823&2S23&2S2S&2823&2S2S&282S&2623&2S23&28

222222

25&2T*222222222222222222222222222222

25&2T*25&2T*

2425&2T*25&2T*

Note: superscript * represents a reference used to obtain equilibrium-constant information

15

Table 2 Comparison of Freestream Environments for the ShallowPeak-Heating Case and Point 6 on the Steep Trajectory.

STEEPSHALLOW

Alt(Kft)

134192

Vel(Kft/sec)

55.253.8

Mach

55.950.7

Pressure(lb/ft2)

5.330.57

Density(slugs/ft?)

68xlO-7

7xlO-7

Temp.(-R)

456468

WallTemp.

(°R)82607260

= 0.03 in

0.71(twoplaces)

1,

= 3.826 in.

\0.28 in.(typ. frontface)

h = 3.668 in.

Fig. 1 Sketch of the General Purpose Heat Source (GPHS) module.

16

80 _

60 .

300

250 -

200 —

40. j

20 .

0 _

CFD ANALYSIS POINTS

1 -SECOND TIME INTERVALS

150 -

100

40 60VELOCITY, V_ (kft/s)

10 15 20 25

100

30

Fig,

VELOCITY, V. (km/a)

2 Comparison of GPHS and ballistic reentry vehicle trajectories.

1010

10'

• CFD ANALYSIS POINTS

- + 1-SECOND TIME INTERVALS

~ BALLISTICRV CONTINUUM

7. = -90-

7. = -10

10* -

Kn=0.01

Kn=1

SUP

TRANSITION

ID'-100

MACH NUMBER, M_

Fig. 3 Flow regimes for GPHS reentry analyses.

17

'WALL

high

nominal i

low 41 2 3TRAJECTORYPOINT

GLOBALITERATION

O ~ CFD/RADIATION SOLUTION

->-TIME

Fig. 4 Schematic of flowfield/radiation computational matrix.

Fig. 5 Coordinate system.

18

BeforeAdaptation

Aftern Adaptation

^

(Shock),n

r)=0

HR

%

Q__———— TUl"(Shock)

T\=t\M

11=0

Fig. 6 Schematic description of the shock adaptation procedure.

uy-2,/ y+i,z

B

Sz

<————>

'^/v/

01 L-V:(a) Predictor Step

[AMDf ̂ 2 >.___Ej JD_ y,w

(b) Corrector Step

Fig. 7 Schematic description of the Predictor-Corrector solution scheme.

19

Geometric Axisof Singularity

Fig. 8 Side view of the geometric axis of singularity, pitch plane, and the surface

,<p=7i-Kx ,<p=7t-a

B

Fig. 9 Front view of the geometric axis of singularity and the surface grid.

20

GasmE

f-v BJL'~

•1,1

Fig. 10 Schematic description ofthe convection-diffusion boundarycondition at the wall.

103

102

10'

10°

10-'

Lewis and Burgess (1965)nV.W43.68

\T/T.

—- X/R —

Fig. 11 Schematic description of theTwo-Step solution scheme for thespecies conservation equations.

AIt.=50 kftV =25.3 kft/secR=5 cm, Tw=4400 °K7-Species Nonequilibrium AirFully-Catalytic Wall

0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2Normal Distance from the Surface (X/R)

0.3 0.4 0.5

(a) Stagnation-streamline profiles of temperature and pressure

Fig. 12 GPHS predictions at low-altitude nonequilibrium conditions.

21

104

10"

10'

10'

10°

Surface Pressure,

M..

— — 3rd Order FVS.5I(S,)x65(y._._ 3rd Order FVS.———— 3rd Order FVS,5K5,)xlOI(4,)-D—— 3rd Order FVS,51£,)xlOKiy, Perfect-Gas• Using reaJ-gas tables of Lewis and Burgess (1965)

andZoby and Sullivan'$(1965) blunt-body correction

10=

103

102

Surface Heat-Transfer Rate, qw(Btu/ft2-sec)

Altitude=50 kftV =25.3 kft/sccR=5 cm, Tw=4400 °K7-Species AirFully-Catalytic Wall

0.0 0.5 1.0 1.5 0.0 0.5Surface Distance (S/R)

1.0

(b) Surface pressure and heat transfer

Fig. 12 (concluded).

6000

1.5

A1L=192 kitM =50.63T,~=4400 °KR=50 mm qw(Btu/rr-s)

11-Species AirNo AblationNo RadiationFully-Catalytic Wall

cVtnn.n.n n n n Q

_.._.._ RACER (Perfect-Gas, 51x45)_ — _ RACER (Le,-l. 4, 51x51)

RACER (Variable Le,, 51x51)O LAURA (Variable Us,, 51x51)

0.0Surface Distance (S/R)

Fig. 13 Comparison of fiowfield prediction techniques and effects of multi-component diffusion and variable Lewis number.

22

9000 C

8500

8000

2 7500

7000

6500

6000

5500

5000

TR

i

TRAJECTORYSTEEP

- - SHALLOW

0.0 0.5 1.0STREAMWISE DISTANCE, S/R

1.5

Fig. 14 Comparison of specified surface-temperature distributions for the steep(point 6) and shallow (peak-heating) cases.

20000

0.0 0.5 1.0STREAMWISE DISTANCE, S/R

Fig. 15 Comparison of surface-pressure distributions for the steep (point 6) andshallow (peak-heating) cases.

23

4.0:

0.5 1.0STREAMWISE DISTANCE, S/R

Fig. 16 Comparison of ablation-rate distributions for the steep (point 6) and shallow(peak-heating) cases.

.0 - - - -T- - - . - - -7 - - - - . - - - r - -7 - - - , - -~ r0.0 0.5 1.0

STREAMWISE DISTANCE, S/R1.5

Fig. 17 Comparison of heat-flux components for the steep (point 6) and shallow(peak-heating) cases.

24

19-SPECIES CARBON-AIRISOBARS (ATM)

SHALLOW STFFP

Fig. 18 Isobars. Comparison of steep (point 6) and shallow (peak-heating) cases.

25000

0.40 0.30 0.20 0.10BODY-NORMAL DISTANCE, (X/R)

0.00

Fig. 19 Stagnation-streamline temperature distribution. Comparison of steep (point6) and shallow (peak- heating) cases.

25

1.00

0.010.40

L0.30 0.20 0.10

BODY-NORMAL DISTANCE, (X/R)

Fig. 20 Air-species mass fractions along the stagnation streamline. Steep (point 6)case.

1.000F

0.100

oo<o;

0.010

0.001

R

1

J_ J_ JL0.40 0.30 0.20 0.10

BODY-NORMAL DISTANCE, (X/R)0.00

Fig. 21 Carbon-species mass fractions along the stagnation streamline. Steep (point6) case.

26

19-SPECIES CARBON-AIR(T SPECIES CONCENTRATION

SHALLOW STFFP

Fig. 22 C* mass-fraction contours. Comparison of steep (point 6) and shallow (peak-heating) cases.

9000

8000

7000

6000

4000

3000

2000

r.i IALLOW, crn ANM YGIC roiti i rSTEEP, CFD ANALYSIS POINT S

TRAJECTORYSHALLOW.SINRAP/CFDSTEEP,SINRAP/CFD

10 15 20 25 30SHALLOW TRAJECTORY - TIME FROM RELEASE (SEC)

1 2 3

STEEP TRAJECTORY - TIME FROM RELEASE (SEC)

40

Fig. 23 RACER/LORAN-C computational matrix and comparison of steep andshallow stagnation-point temperature histories.

27

40000

35000

£ 30000

5"tov" 25000x"— j

i 200002UJ

< 15000u.

V}

£ 100000

5000

n . . . . . . . .

. l i l l l

TRAJE

' _ _ _ . STEEF

- /

f/

/— /

//

/

~~ //

I /

— /

I /

| . . . ,

:TORY

.SINRAP/CFD ".

—-.

. —

"

-

_

_

-

_

-

_

-

—

0 5 10 15 20 25 30 35 4(SHALLOW TRAJECTORY - TIME FROM RELEASE (SEC)

1 2 3STEEP TRAJECTORY - TIME FROM RELEASE (SEC)

Fig. 24 Comparison of the total heat-flux (gas-conduction+diffusion+radiation) atthe stagnation point along the steep and shallow trajectories.

2.50

2.00

1.50

1.00

5m

0.50

0.00

TRAJECTORYSHAU.OW.SINRAP/CFD

_ - - - STEEP.SINRAP/CFD

10 15 20 25 30SHALLOW TRAJECTORY - TIME FROM RELEASE (SEC)

35 40

t 2 3

STEEP TRAJECTORY - TIME FROM RELEASE (SEC)

Fig. 25 Comparison of the ablation rate at the stagnation point along the steep andshallow trajectories.

28

0.12

0.10

-— °-08

Ioz

0.06

0.04

0.02

0.00

TRAJECTORYSHALLOW.SINRAP/CFDSTEEP,SINRAP/CFD

10 15 20 25 30SHALLOW TRAJECTORY - TIME FROM RELEASE (SEC)

35

1 2 3

STEEP TRAJECTORY - TIME FROM RELEASE (SEC)

40

Fig. 26 Comparison of the stagnation-point recession along the steep and shallowtrajectories.

29

Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.

Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.