Advanced Radiation Calculations of Hypersonic Reentry Flows Using Efficient Databasing Schemes

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1 JURAL F THERMPHYSICS AD HEAT TRASFER Vol. 4, o. 3, July Sptmbr Advancd Radiation Calculations of Hyprsonic Rntry Flows Using Efficint Databasing Schms I. Sohn, A. Bansal, and D. A. Lvin Pnnsylvania Stat Univrsity, Univrsity Park, Pnnsylvania 68 and M. F. Modst Univrsity of California, Mrcd, California DI:.54/.4585 Efficint schms for databasing mission and absorption cofficints ar dvlopd to modl radiation from hyprsonic nonquilibrium flows. For bound bound transitions, spctral information including th lin-cntr wavlngth and mission and absorption cofficints is stord for typical air plasma spcis. Sinc th flow is nonquilibrium, a rat quation approach including both collisional and radiativly inducd transitions is usd to calculat th lctronic stat populations, assuming quasi stady stat. Th gnral Voigt lin-shap function is assumd for modling th lin-broadning. Th accuracy and fficincy of th databasing schm was xamind by comparing rsults of th databasing schm with thos of EQAIR for th Stardust flowfild. An accuracy of approximatly % was achivd with an fficincy about thr tims fastr than th EQAIR cod. omnclatur A = Einstin cofficint for spontanous mission, s Ac; i = Einstin cofficint for spontanous mission from continuum stat to stat i, cm 3 s Ai; c = Einstin cofficint for photoionization from stat i to continuum stat, s Ai; j = Einstin cofficint for spontanous mission from stat i to stat j, s a = Bohr radius, 5:967 9 cm B = Einstin cofficint for stimulatd mission and absorption, cm 3 -m=j-s B VU = rotational constant, cm b = xponnt C, D = vctor assmbld by xcitation rat cofficints C m, D m of atom = vctor assmbld by xcitation and dissociation rat cofficints of molcul c = spd of light, :9979 cm s D w = Dopplr lin half-width, cm d = paramtr in th Voigt width [Eq. (34)] d ff = corrction factor for fr fr radiation E i = lctronic trm nrgy for atomic lvl i, cm E k = kintic nrgy of fr lctron, cm E mis = total mission nrgy, W=cm 3 E = ionization nrgy of an atom, cm = lctron charg, 4:83 statc F = rotational trm nrgy for a molcul, cm Prsntd as Papr 8-49 at th 4th Thrmophysics Confrnc, Sattl, WA, 3 6 Jun 8; rcivd April 9; rvision rcivd March ; accptd for publication March. Copyright by th Amrican Institut of Aronautics and Astronautics, Inc. All rights rsrvd. Copis of this papr may b mad for prsonal or intrnal us, on condition that th copir pay th $. pr-copy f to th Copyright Claranc Cntr, Inc., Roswood Driv, Danvrs, MA 93; includ th cod / and $. in corrspondnc with th CCC. Graduat Studnt, Dpartmnt of Arospac Enginring. Studnt Mmbr AIAA. Profssor Dpartmnt of Arospac Enginring. Associat Fllow AIAA. Shaffr and Gorg Profssor of Enginring, Dpartmnt of Mchanical Enginring. Associat Fllow AIAA. 63 F i = assmbld collisional and radiativ cofficint of lctronic stat i G = vibrational trm nrgy for a molcul, cm GF = Gaunt factor for bound fr radiation G i = assmbld collisional and radiativ cofficint of lctronic stat i g = dgnracy H = data points of lctron numbr dnsity and lctron tmpratur h = Planck s constant, 6:66 34 Js J = rotational quantum numbr j = data point indx Kc; i = rcombination rat cofficint of collisional transition from continuum stat to stat i, cm 6 s Ki; c = xcitation rat cofficint of collisional transition from stat i to continuum stat, cm 3 s K Wi = havy-particl-inducd rcombination rat cofficint, cm 3 s K W i; j = havy-particl-inducd molcular xcitation rat cofficint from stat i to stat j, cm 3 s K i; j = xcitation rat cofficint of collisional transition from stat i to stat j by lctron impact, cm 3 s Kci = lctron-inducd rcombination rat cofficint, cm 3 s k = Boltzmann s constant, :386 3 JK l = numbr of lctronic stats for bound fr transition l m = numbr of lctronic stat nrgy lvls for diatomic quasi stady stat M = matrix assmbld xcitation rat cofficints of atom M m = matrix assmbld xcitation and dissociation rat cofficints of molcul m = mass, kg max = maximum valu of vibrational or rotational lin = numbr dnsity, cm 3 n = principal quantum numbr P = numbr of data points Q = partition function q = Franck Condon factor q R = radiativ hat flux, W=cm R = transition momnt, statc-cm R = lctronic transition momnt for a vibrational band (V U, V L ) normalizd by a

2 64 SH ET AL. r = intrnuclar distanc, units of lngth, not xplicitly valuatd S = rotational lin-strngth factor T = lctron tmpratur, K T L = lowr stat lctronic nrgy of th trm symbol for molcular radiation, cm T U = uppr stat lctronic nrgy of th trm symbol for molcular radiation, cm = rotational tmpratur, K = translational tmpratur, K = vibrational tmpratur, K V = vibrational quantum numbr w g = Gaussian width, Å w l = Lorntzian width, Å w s = Stark width, Å w s; = rfrnc Stark width, Å w v = Voigt width, Å X = horizontal coordinat of dirct simulation Mont Carlo computational domain for th Stardust gomtry, m X i;data = mission or absorption cofficints from th databas at th ith wavlngth data point X i;eq = mission or absorption cofficints from EQAIR at th ith wavlngth data point Y = vrtical coordinat of DSMC computational domain for th Stardust gomtry, m E = nt kintic nrgy of a fr lctron, cm H = data point intrval = distanc from lin cntr, Å " = mission cofficint, W=cm 3 -m-sr " c = assmbld paramtr for mission cofficint, W=sr = absorption cofficint, cm c = assmbld paramtr for absorption cofficint, cm 3 = wavlngth, Å ~ = wav numbr, cm = ratio of nonquilibrium lctronic stat population to quilibrium stat H = ionization cross sction of hydrogn atom, cm bf = bound fr absorption cross sction, cm H ff = hydrognic fr fr cross sction, cm 5 = lin-broadning function, m = ratio of summation of nonquilibrium lctronic stat populations to that of quilibrium stat = vibrational wav function, units of lngth =, not xplicitly valuatd Subscripts a = atom c = cntr E = quilibrium stat = lctron mis = mission nd = nding data H = hydrognic i, j = indx of lctronic stat init = initial data k = kintic L = lowr stat LU = lowr to uppr stat m = molcul min = cutoff limit EQ = EQAIR n = principal quantum numbr R = rotational stat U = uppr stat UL = uppr to lowr stat V = vibrational stat W = havy particl = wavlngth = ion = ionization Suprscripts bf = bound fr c = constant = lctronic stat ff = fr fr = normalizd quantity I. Introduction HYPERSIC vhicls rntring into Earth s atmosphr gnrat nonquilibrium flows consisting of dissociatd and wakly ionizd air spcis. Ths typical conditions xist bhind a high Mach numbr shock wav lading to high tmpraturs that affct oprational flight issus rlatd to thrmal protction systm matrials and radar communications. In addition, du to th high Mach numbr, radiation has an important rol in gnrating hat loads to th vhicl surfac, with contributions somtims as high as 8% of th convctiv hat []. Modling th radiativ sourcs in hyprsonic shock layrs and fluxs to a spaccraft is a complx task and w mntion hr only som of th important work in this fild. Th Langly LRA cod [] and th EQAIR cod [3] hav bn usd xtnsivly in many atmosphric ntry radiativ simulations. EQAIR includs atomic bound bound, bound fr, fr fr transition, and lin-by-lin modls for molcular bands. Th LRA modl is similar to EQAIR, and was dvlopd to lowr th computational cost of EQAIR by using a smard rotational band modl for th molcular spcis. Both EQAIR and LRA us th quasi-stady-stat (QSS) assumption to dtrmin th lctronic stat population. Mor rcntly, Johnston [4] dvlopd a radiation modl that applid up-to-dat atomic and molcular data for both th non-boltzmann modling of th radiating stat and spctral distributions. In his modl, an approximat atomic collisional radiativ modl was dvlopd to calculat th lctronic stat populations of atomic spcis. For molcular radiation a simplifid non-boltzmann modl for th molcular lctronic stat populations was dvlopd by assuming that th contribution of lctron-impact dissociation and havy-particl-inducd xcitation procsss may b nglctd. Th smard rotational band modl was chosn to rduc th computational cost for molcular radiation. In nonquilibrium flows, th radiation fild may also affct th population of lctronic stats to th xtnt that a coupld radiativ transport solution is rquird for an xact solution. Thrfor, it bcoms imprativ to dtrmin mission and absorption cofficints in an fficint mannr such that a larg numbr of solutions of th radiativ transport quation (RTE) may b prformd. In this work, w dvlop an fficint databasing schm for gnrating spctral cofficints using th EQAIR cod. In contrast to th modls mntiond abov, w us assmbld paramtrs, xtractd dirctly from EQAIR, to calculat spctral lin strngths. n of th main challngs in dvloping th databasing schm was to incorporat th QSS procdur, which includs th calculation of about 4 lctronically xcitd stats for atomic oxygn and nitrogn. Also, bcaus th rntry flows ar optically thick to maintain accuracy in computing th radiativ hat loads, th databasing procdur has to incorporat th Voigt lin shap. Th accuracy and fficincy of atomic and diatomic mission and absorption cofficints obtaind from th nw databas ar xamind for a flow condition clos to pak hating along th Stardust rntry trajctory. Sinc atomic radiation is dominant for th hyprsonic rntry flow conditions undr considration hr, only th accuracy of th atomic spctral cofficints gnratd from th databas ar invstigatd in this papr. In th final sction, th accuracy of th databasing schm ar xamind by comparing th radiativ hat fluxs using th databas with thos obtaind dirctly from EQAIR. Th fficincy of th databasing schm is quantifid and th radiativ hat gnration using th nw databas ar calculatd for a Stardust rntry flowfild.

3 SH ET AL. 65 II. Databasing Schms for Atomic Spcis In this sction, th basic spctral rlationships for th mission and absorption cofficints ar introducd. Th databasing stratgy is xamind and th variabls that ar databasd ar dfind in trms of th spctral quantitis. A. Basic Rlations of Radiation by Atomic Spcis Thr ar thr radiativ mchanisms in a radiating nonscattring mdium: spontanous mission, stimulatd mission and absorption. Th spontanous spctral mission cofficint is dfind as [3] " g U U A UL hc () 4 Stimulatd mission and absorption, unlik spontanous mission, ar causd by th prsnc of photons in th vicinity of th mitting or absorbing spcis. Th ffctiv volumtric absorption cofficint is obtaind in trms of th stimulatd mission and absorption cofficints, as givn by [3] g L L B LU g U U B UL h () Using dtaild balanc [3,5], g L B LU g U B UL, th absorption cofficint xprssion can b rducd to h L U g U B UL (3) ormalizd mission and absorption cofficints can b dfind by dividing Eqs. () and (3) by th numbr dnsity of th radiating spcis, a, giving " " a " c U a (4) c L U a a (5) a whr " c and c ar dfind as " c g UA UL h c (6) 4 and c g UB UL h B UL 8hc A UL (8) for all bound bound transitions at th spcific lin-cntr wavlngth [3,5,6]. This lads to an important rsult for organizing th databas; i.., " c and c ar indpndnt of paramtrs, such as ion and lctron numbr dnsitis and tmpraturs. Thr ar two othr transition mchanisms that lad to a chang of nrgy lvl by mission or absorption of a photon. Transitions from a bound to a dissociatd stat, known as bound fr transitions and th rvrs transitions, calld fr-bound transitions ar two such mchanisms. Also transitions btwn two continuum stats, calld fr fr transitions, ar possibl mchanisms causd by photonatom intractions. For atomic radiation, th bound bound transitions ar th largst contributions to th radiation compard with bound fr and fr fr transitions. Th bound fr radiation occurs whn th uppr stat is in th ionizd, or continuum stat. In that cas, th wavlngth of th transition is dtrmind by th kintic nrgy of th fr lctron, E k,or E (9) E E i E k whr E is th ionization potntial of th atom and E i is th nrgy of th ith bound lvl. Sinc th lctron kintic nrgy E k is 5 (7) continuously distributd according to a Maxwllian distribution, radiation from bound fr transitions is spctrally continuous. Th bound fr absorption cross sction bf is dfind in trms of th ionization cross sction of th hydrogn atom H multiplid by a corrction factor known as th Gaunt factor [7]. Th hydrognic cross sctions ar dfind by Kramr s formula [8] as 3 H 7:9 8 n () whr th valu of n is givn as n n 8 =I H, I H is th ionization potntial of atomic hydrogn, 9; 679 cm, and n is th principal quantum numbr. Th Gaunt factor GF is dfind as GF ;i bf ;i () H Th Gaunt factor is dtrmind by comparing th cross sctions with thos of Pach [7]. ot that for a spcific lctronic stat bf is only a function of wavlngth. Finally, th bound fr absorption cofficint for ach nrgy lvl is obtaind by th bound fr cross sction multiplid by th lctronic stat population as bf Xl ;i bf i () i whr l stands for th numbr of lctronic stats modld in th EQAIR databas. For atomic and, thr ar l 5 out of th total 9 stats and 4 out of, rspctivly. Th rmaining lvls do not contribut to th sum bcaus thy ar assumd to b quasi-nonbound or xisting in th continuum. Th bound fr mission is calculatd from Eq. () using rlations givn by [3] " bf Xl ;i bf hc i (3) 5 i i = U whr U is chosn as th population at th ionization limit givn by n U :7 6 xp Q T :5 hc k E T (4) Th valu of :7 6 is calculatd from th xprssion of h =m k 3= = givn by [3]. Fr-fr transition occurs whn an lctron in th vicinity of an ion or an atom is dclratd and mits radiation to consrv nrgy. Th fr fr absorption cofficint dividd by th atomic numbr dnsity, mploying th hydrognic fr fr cross sction, H ff, is calculatd as [3] ff a a ff H d ff (5) whr d ff is a corrction factor for th fr fr cross sction of nonhydrognic atomic spcis [7]. Th fr fr mission is calculatd using th blackbody function givn by [3] " ff ff hc 5 xphc=kt (6) B. Calculation of Excitd Stat Populations: Quasi-Stady-Stat Assumption Undr nonquilibrium flow conditions, th atomic lctronic stats ar xcitd and dxcitd by collisional and radiativ procsss. Whn an atom collids with othr atoms, molculs, or lctrons, th lctronic stats potntially bcom xcitd. Collision inducd lctronic transitions in an atomic or molcular systm ar particularly ffctiv whn th collidr is an lctron. Spcifically, whn a fr lctron with larg nrgy collids with an atom in a bound stat, th nrgy of th fr lctron can b transfrrd to th atom in th form of lctronic stat xcitation. In this cas, th xcitation rat from th initial stat i to th final stat j is K i; j i.in

4 66 SH ET AL. nonquilibrium flow conditions, radiativ transitions also hav an important rol in dtrmining th lctronic stat of nutral spcis. A summary of th xcitation/dxcitation procsss of atoms may b writtn as i $ K i;j j (7) i $ Ki;c (8) i$ Ai;j jh (9) ih$ Ai;c () whr i and rprsnt an atomic spcis of lctronic nrgy lvl i and its ion, rspctivly. Undr nonquilibrium flow conditions, thr ar not nough collisions to dscrib th lctronic stats by a Boltzmann distribution; thrfor, a rat quation approach must b ndd to calculat th lctronic stat populations [5]. Th tim rat of chang of numbr dnsity i is givn by th diffrnc btwn th sum of th rats of all collisional and radiativ transitions that populat and dpopulat stat i formation rmoval whr th population and th dpopulation of th ith stat may b xprssd for formation as X l j K j; i j Kc; i Xl and for rmoval as X l j j K i; j i Ki; c i Xl j Aj; i j Ac; i Ai; j i Ai; c i () (3) Whn th rat of chang of i on th lft-hand sid is much smallr than both th sum of all population rats and all dpopulation rats on th right-hand sid, th QSS condition holds. For this condition, th lft-hand sid is st to zro and th systm of diffrntial quations can b rwrittn as a st of algbraic quations as follows: P X l lj Ai; jai; c K i; jki; c i j Xl whr j K i; j je Aj; i ie j Ki; cac; i (4) ie K i; j ie K j; i je Ki; c ie Kc; i (5) i i = ie (6) and ie is th numbr dnsity of th ith stat in quilibrium. Th symbols,, a, and T ar th ion, lctron, atom numbr dnsitis, and lctron tmpratur, rspctivly. Sinc th sum ovr all i must b qual to th total numbr dnsity of th atomic spcis, or X l i ie i ae (7) Eqs. (4) and (7) can b rwrittn in th matrix form of M C D a (8) ae whr a = ae and ae Xl ie i and th matrix M and vctors C and D ar functions of only T and [5]. Finally, th normalizd population can b xprssd as whr i a F i T ; a G i T ; (9) F i T ; M C ie G i T ; M D ie ae (3) Th two functions F i and G i contain th ffcts of both collisional and radiativ transitions for th xcitation of atoms in th ith lctronic nrgy stat. C. Stratgy for Gnrating Databass of Atomic Spctral Quantitis For th bound bound transitions, th lin-strngth factors " c and c for th mission and absorption cofficints givn by Eqs. (6) and (7), rspctivly, ar obtaind from EQAIR [3]. Th lin-cntr wavlngths at which th bound bound transitions occur and th potntial uppr and lowr lctronic stats for ach bound bound transition ar also obtaind from EQAIR. Tabls and show th first fiv lin-strngth factors " c and c, th lin-cntr wavlngth, and th uppr and lowr lctronic nrgy lvls for ach bound bound transition for atomic and, rspctivly. Th normalizd lctronic stat populations calculatd using th QSS assumption ar givn by Eq. (9). In this quation, sinc th ion and atomic numbr dnsitis will b obtaind from th flowfild solution dirctly, on nds to databas valus of F i T ; and G i T ; at various valus of T and to calculat th normalizd lctronic stat populations for ach lctronic stat i. Cubic splin intrpolation of F i and G i at arbitrary T and valus may thn b usd. Th data st for F i T ; and G i T ; ar dfind at 5 valus and 7 T valus, with varying from 3 to 4 6 cm 3 and T ranging from to 8, K, with a qually spacing givn by H j H : init j H: (3) whr H : Hnd : H: init=p. Hr, P is th numbr of data points, 5 for and 7 for T, and j dnots th data point Tabl Data sts for " c and c of atomic Elctronic lvls Wavlngth, Å " c, W=sr c, cm3 Uppr Lowr :374 3: :7 3: :56 9: :74 : :5 : Tabl Data sts for " c and c of atomic Elctronic lvls Wavlngth, Å " c, W=sr c, cm3 Uppr Lowr.76 :84 3: :96 : :39 : :837 : :65 3 4:68 5

5 SH ET AL. 67 indx, j P. Th form of Eq. (3) rducs th computation tim for intrpolation of F i and G i at any and T conditions bcaus sarching for a dsird point is fastr using qually spacd rathr than non-qually-spacd data points. Th total siz of th databas of F i T ; and G i T ; of ach atomic spcis and is about 6. MB. This approach allows us to incorporat all of th modls dvlopd ovr many yars in EQAIR for th QSS modl as wll as prmit th fficint rcalculation of th databas as th QSS modl volvs. To complt th databas formulation, w nd to spcify th lin shap. Th Voigt lin-shap function is slctd bcaus it is th most gnral form of lin-broadning. It considrs both thrmal and collisional broadning ffcts, as rquird to proprly simulat linbroadning undr nonquilibrium flow conditions. Th approximat formula of Whiting [9] is givn as w l =w v xp:77=w v w l =w v =f 4=w v g:6w l =w v w l =w v xpf:4=w v :5 g =f =w v :5 g=w v f:65 :447w l =w v :58w l =w v g (3) whr w l and w v dnot th Lorntzian and Voigt widths, rspctivly, and is givn by c (33) Th Voigt width is calculatd from th following approximation []: w v :8 d :3665 xp:6d :48 xp:9dsindw l w g (34) whr d w l w g =w l w g and w g is Gaussian or Dopplr width. Th main contribution to th Lorntzian width for hyprsonic flow conditions is du to Stark broadning causd by high nrgy lctron collisions with atoms. Th Stark lin-broadning widths, w s, at half-lin-cntr pak hight ar calculatd for ach individual lin by th following quation [,]: T b w s w s; (35) ; K 6 cm 3 whr th rfrnc Stark width w s; and th xponnt b ar stord in th databas for ach atomic lin. Th Dopplr lin half-width D w for th Gaussian broadning is givn by [6] D w r c k c m ln (36) whr is th translational tmpratur, and m is th mass of th radiating spcis. Th Voigt lin-shap function of Eq. (3) is a function of two paramtrs, w l =w v and =w v. Thrfor to calculat th spctral mission and absorption cofficints broadnd by th Voigt profil at any wavlngth or flow condition, valus of w l =w v from to and =w v from to ar prstord at incrmnts for w l =w v and =w v of. and.5, rspctivly. During th RTE calculation th lin shap can b calculatd using a bilinar intrpolation of ths stord databas paramtrs. Figur shows th rquird cutoff rang =w v for th half-width of th full lin shap that satisfis 99.9% of th intgratd mission as a function of th ratio of th Lorntzian to Voigt width for all possibl and T valus. It can b sn that th cutoff rang rapidly incrass as th ratio of w l =w v incrass to :4 and thn rmains constant. In othr words, whn th ratio of th Lorntzian to Voigt width is gratr than :4, th minimum cutoff limit for a singl lin such that it will captur 99.9% mission is.. In a thrmochmical nonquilibrium flowfild th widths of diffrnt atomic lins can b vary by ordrs of magnitud bcaus th chang in lctron numbr dnsity and lctron tmpratur in th λ / w v w l / w v Fig. Cutoff rang of th Voigt lin shap to satisfy 99.9% intgratd lin for atomic lin with rspct to th ratio of Lorntzian to Voigt width. hyprsonic shock layr is larg. Sinc this larg variation in th lin width can lad to diffrnt lin-broadning shaps for individual atomic lins, an fficint approach to dtrmin th propr cutoff wavlngth for ach atomic lin is ndd to accuratly modl mission and absorption of radiativ nrgy in th radiativ hat transport calculation. This approach is particularly important in radiativ transport for th optically thick hyprsonic flows considrd hr bcaus transport through th lin wings cannot b nglctd. In th prsnt work, th cutoff wavlngth that guarants that th mission intgratd ovr th lin shap givs 99.9% of th total lin mission is stord for ach lin as a function of th ratio of th Lorntzian to Voigt width. With th atomic lin shap dfind, th normalizd mission and absorption cofficints givn by Eqs. (4) and (5) ar calculatd for any givn dnsity, tmpratur, and wavlngth. For th bound fr cas, th normalizd bound fr absorption cofficints ar calculatd using th bound fr cross sctions, Eq. (), and th normalizd lctronic stat populations, i = a, which ar alrady calculatd for th bound bound radiation. Finally, th normalizd fr fr absorption cofficints ar obtaind by Eq. (5) and computd using th dnsity valus from th flowfild solution and physical paramtr data sts availabl from EQAIR. III. Basic Formulas for Radiation of Diatomic Spcis Modling of molcular radiation is mor complx than for atomic spcis bcaus in addition to lctronic transitions, rotational and vibrational transitions must also b considrd. Th larg numbr of rotational lins in a diatomic band systm maks th task of dtrmining th Einstin A cofficint for ach lin from th EQAIR databas complicatd. In EQAIR, th transition probabilitis ar calculatd from a numbr of paramtrs. Th xprssion for th Einstin A cofficint, A UL, is givn by [3] whr A UL 64 4 ~ 3 UL a 3h R q VU V L S JU J L =J U (37) ~ UL c T U T L GV U GV L FJ U FJ L (38) By using Eqs. () and (37), th spontanous mission cofficint can b writtn as [3]

6 68 SH ET AL. " 63 ~ 4 ULc 3J U a U g U R q VU V L S JU J L (39) whr is again th lin-shap function and U is th uppr stat population in a givn vibrational rotational stat. Th normalizd mission and absorption cofficints can b dfind in a mannr similar to th atomic cass givn in Eqs. (4) and (5). Hr, " c and c for molculs ar dfind as " c 63 ~ 4 ULc 3J U a g U R q VU V L S JU J L (4) c "c hc (4) To databas " c and c w nd to dtrmin th dpndncy of th quantitis in Eqs. (4) and (4) on th flowfild variabls. Sinc an lctronic transition in a molcul taks plac much mor rapidly than a vibrational transition, in a vibronic transition, th nucli hav vry narly th sam position and vlocity bfor and aftr th transition [4]. A transition momnt btwn two vibrational quantum numbrs, V U and V L of diffrnt lctronic stats can thrfor b approximatd by [4] Z R VU V L R VU VL dr (4) whr R is an avragd valu of th lctronic transition momnt. Th transition probability is dirctly proportional to R V U V L or j R VU VL drj, whr th vibrational ovrlap intgral, q VU V L j R VU VL drj, is calld th Franck Condon factor and dos not dpnd on spcis concntrations or tmpraturs [4]. Th linstrngth factor S JU J L, dpnds on th typ of lctronic transition and th spin multiplicity as wll as rotational quantum numbr. Using standard spctroscopic rlationships it can b shown that th uppr stat population, U, is givn by U U J Q VR U xp hc GVU FJ U (43) U k T V T R whr U and Q VR U ar th lctronic uppr stat population and uppr stat total partition function, rspctivly. Using th abov rlationships, th population ratio, L = U, is givn by L L Q VR U JL hc GVU GV U U xp L Q VR L J U k T V FJ UFJ L (44) T R whr th uppr stat total partition function Q VR is givn as [3] V Umax Q VR U X J UX max J U xp B VU J U J U hc kt R xp V U GV U hc kt V J U 5 c (45) A. Calculation of Excitd Elctronic Stat Population for Diatomic Spcis In this sction, drivation of th xcitd lctronic stat populations U for diatomic spcis using th QSS assumption is discussd. Th baslin xcitation/dxcitation procsss for diatomic spcis ar modld as Z U W$ K Wi ZUiW (46) ZU $ K ci ZUi (47) ZUiW$ KW i;j ZUjW (48) ZUi$ K i;j ZUj (49) ZUi Ai;j $ ZUjh (5) whr Z and U rprsnt atomic spcis, and W and rprsnt a havy particl and an lctron, rspctivly. Equations (46 5) rprsnt havy-particl- and lctron-inducd rcombination, havy-particl- and lctron-inducd xcitation, and spontanous mission, rspctivly [5]. Th tim rat of chang of normalizd numbr dnsity, i i = ie, is givn by th diffrnc btwn th incoming rats and outgoing rats Xl m K i; jk W i; j W j i Xl m K ic K iw W Aj; i je ie j j Ai; j K i; jk W i; j W K ic K iw W (5) whr K i; j is th lctron-impact xcitation rat cofficint btwn two lctronic stats of a molcul, K W i; j is th xcitation rat cofficint by nutral impact btwn two lctronic stats, and K iw and K ic rprsnt dissociation rat cofficints du to havyparticl collision and lctron impact, rspctivly. ot that th rvrsal of indics such as iw to Wichangs th rat cofficint from collisionally inducd dissociation to a rcombination mchanism. Undr th QSS condition, th lft-hand sid is st to zro and th systm of diffrntial quations bcoms a matrix quation of th form whr M m C m D m m Z (5) m Xl m i i and th matrix M m and vctors C m and D m ar assmbld by xcitation and dissociation rat cofficints. Th final form of th diatomic QSS rlation is givn as i Mm ie C m D m m Z (53) Th uppr and lowr lctronic stat populations, L and U, ar solvd by a 4 4 matrix invrsion. B. Stratgy for Crating Databass of Spctral Quantitis for Diatomic Emittrs In this sction, databasing schms for diatomic gas spcis will b introducd. First, th diatomic lin-strngth factors " c givn by Eq. (4) ar xtractd from EQAIR and stord with lin-cntr wavlngths. Sinc th vibrational trm nrgy GV and rotational trm nrgy FJ ar not dpndnt on gas concntration or tmpratur, ths nrgy trms, which ar ndd to calculat th uppr and lowr stat populations, will also b stord with th corrsponding lin-cntr wavlngth. In this work, th assmbld linstrngth-factor lin-cntr wavlngth and vibrational rotational trm nrgy of,,, and ar xtractd from EQAIR and stord in th databas. Tabl 3 shows th typs of lctronic transitions for,,, and considrd in EQAIR, and Tabl 4 prsnts th first fiv rows of th first ngativ transition data st. Th lctronic stat populations will b obtaind from th QSS assumption and thn th final forms of mission and absorption cofficints will b constructd combining th lin-cntr data st with th lctronic stat populations. Similar to th atomic cas, a

7 SH ET AL. 69 Tabl 3 Elctronic transitions of diatomic spcis in EQAIR Molcul am Spctral rang, Å (first ngativ) 547 5,759 Minl 749,645,45,798 (first positiv) 45 3,69,64 (scond positiv) 6 79 Birg Hopfild Birg Hopfild Carrol Yoshino Schumann Rung Bta 68 9 Gamma Dlta Epsilon Bta prim Gamma prim (C-A) 57,6,38 (D-A) ,484 B -B ,779 E-C 586 7,955 F-C(3) 687 9, H-C 5689,3 H -C ,55 E-D(5) ,754 F-D(3) ,63 H-D 79 4,737 H -D(5) 694 4,439 IR ,78 Voigt lin-shap function is assumd for ach vibrational and rotational lin cntr. IV. Application of Radiation Databass to Rntry Flow Cass A. Invstigation of th Accuracy of Spctral Cofficints Gnratd Using th Databas Bfor considring th radiation from spcific rntry flows, w discuss th accuracy of th nw databasing schms by comparing th mission and absorption cofficints with thos obtaind from EQAIR. Figurs and 3 show comparisons btwn th databas and EQAIR of th mission and absorption cofficints of atomic for th wavlngth rang from 5 to Å with a wavlngth incrmnt of.3 Å and from to 7 Å with.5 Å stps. For this comparison th databas and EQAIR us th Voigt linshap function. Th dnsity and tmpratur conditions wr obtaind from th flowfild solution of th Stardust vhicl with a spd of km=s at 8 km altitud, calculatd using th dirct simulation Mont Carlo (DSMC) mthod. Th conditions rprsnt th location in th flow whr high radiation occurs du to th high lctron tmpratur. Th rror in th mission and absorption cofficints is dfind as jxi;data X i;eq j rror % (54) jx i;eq j whr X i;data and X i;eq ar th mission or absorption cofficints from th databas and EQAIR at th ith wavlngth data point, rspctivly. In this comparison, most of th rrors btwn th databas and EQAIR ar obsrvd to b smallr than %, xcpt for th continuum radiation blow 8 Å and th bound bound transitions at 533 and 658 Å. Th rror at 533 Å is du to th ovrlap of th lin-shap functions in th wings of ach of th thr atomic oxygn transitions, all closly locatd at , 533.7, and Å. Th rror obsrvd at 658 Å is du to a similar problm. Th continuum spctral cofficints for both bound fr and fr fr transitions ar linarly intrpolatd using th prcalculatd valus stord in incrmnts of Å. As discussd in th prvious sction, bound fr transitions occur in spctral rgions with sharp wavlngth start and stop intrvals. Bcaus thr is a dlta-function-lik cutoff, th linar intrpolation rror can b largr, du to larg gradints in th mission and absorption lins with rspct to wavlngth. Figurs 4 and 5 show th comparisons of th mission and absorption cofficints for atomic btwn th databas and EQAIR for th rang from 5 to 7 Å. Again, th rror in th mission and absorption cofficints of atomic ar blow.%. ow w compar th bound bound lin strngths and continuum spctral cofficints of atomic spcis gnratd from th databas with thos from EQAIR for th ntir rang of and T conditions. Th bound bound mission lin strngths and continuum spctral cofficints at thr intrior points btwn two succssiv data points of and T wr gnratd and compard with EQAIR. Th maximum rror in th bound bound mission lin strngth of atomic and was found to b within.% for th ntir rang of and T conditions. Sinc th mission lin strngth is proportional to th uppr stat lctronic population, th comparison shows that th lctronic stat populations of atomic and ar wll prdictd by th databas and intrpolation schms. For th absorption bound bound lin strngth, it was obsrvd that blow, K thr ar som absorption lin-strngth rrors gratr than 3%, but this was th largst discrpancy obsrvd. Sinc th absorption lin strngth is proportional to th diffrnc of th lowr and uppr lctronic stat populations, th rror in th diffrnc may b largr than th rror in th uppr lctronic stat population. Howvr, thr ar only 7 absorption lin strngths that hav rrors of ovr 3% out of a total of 5,94, cass ( for points 8 for T points 84 for lins for and ). Sinc th ratio of absorption lin strngths with rror gratr than 3% to th maximum absorption lin strngth is within 4, this largr rror of 3% dos not affct th radiation calculation. Th avrag rror in th continuum mission and absorption cofficints was also invstigatd. Sinc th absorption and mission cofficints of th bound fr transition ar rlatd to th lctronic stat population as givn by Eqs. () and (3), rspctivly, th accuracy of th bound fr spctral cofficints dpnds on th rror of th lctronic stat populations. As discussd arlir in th bound bound lin-strngth comparisons, th lctronic stat populations calculatd from th databas agr wll thos from EQAIR, and thus th bound fr spctral cofficints obtaind from th databas ar xpctd to b in a good agrmnt with thos of EQAIR. Th fr fr absorption and mission cofficints ar calculatd dirctly in trms of numbr dnsity and lctron tmpratur, as givn by Eqs. (5) and (6), rspctivly. Thrfor th only diffrnc btwn th continuum spctral cofficints obtaind from th databas and EQAIR can occur from th bound fr transitions. Th rror in th continuum spctral cofficint was invstigatd for a rang of 5 to,5 Å with a. Å wavlngth incrmnt. Th sam numbr of and T conditions usd in th bound bound linstrngth comparisons ( for points 8 for T points) wr considrd, again, to covr all possibl flow conditions. Finally, th Tabl 4 Data st xampl for first ngativ transition Wavlngth, Å " c hc, W=sr GV k U, K hc FJ k U, K hc GV k LGV U, K hc FJ k LFJ U, K :49 5 3:486 4 :65 : : : :488 : :49 5 3:486 4 :65 : : : :487 : :33 5 3:486 4 :66 :

8 63 SH ET AL. 7 EQAIR 3 EQAIR 3 ε (W/cm 3 -µm-sr) -3 κ (cm - ) Fig. Comparison of mission and absorption cofficints of atomic from 5 to Å btwn th databas and EQAIR for a :53 5 cm 3, 3:84 cm 3, :667 4 cm 3, 4; 87 K, and T 7; 485 K. EQAIR 3 - EQAIR ε (W/cm 3 -µm-sr) κ (cm - ) Fig. 3 Comparison of mission and absorption cofficints of atomic from to 7 Å btwn th databas and EQAIR for a :53 5 cm 3, 3:84 cm 3, :667 4 cm 3, 4; 87 K, and T 7; 485 K. avrag rror in th continuum mission and absorption cofficints was found to b lss than.5 and.3%, rspctivly. With rspct to radiation from molcular spcis, Figs. 6 9 show th mission and absorption cofficints from EQAIR and th absolut diffrnc of cofficints btwn th databas and EQAIR for th,, and molcular systms, rspctivly. Thr ar small diffrncs btwn th databasing schm and EQAIR mainly du to th diffrnc in th implmntation of th Voigt lin shap. EQAIR uss an approximat approach to dfin th Voigt lin shap for ach rotational lin. In our databasing schm w us a mor accurat procdur to apply th Voigt lin shap with no additional computational cost. A summary of th diffrncs in th ε (W/cm 3 -µm-sr) EQAIR 3 κ (cm - ) EQAIR Fig. 4 Comparison of mission and absorption cofficints of atomic from 5 to Å btwn th databas and EQAIR for a 3:69 5 cm 3, 5:547 cm 3, :667 4 cm 3, 4; 87 K, and T 7; 485 K.

9 SH ET AL. 63 EQAIR 3 - EQAIR - ε (W/cm 3 -µm-sr) - -4 κ (cm - ) Fig. 5 Comparison of mission and absorption cofficints of atomic from to 7 Å btwn th databas and EQAIR for a 3:69 5 cm 3, 5:547 cm 3, :667 4 cm 3, 4; 87 K, and T 7; 485 K. Fig. 6 Comparison of mission and absorption cofficints of from 3, to 6, Å btwn th databas and EQAIR for 6:459 3 cm 3, 3: cm 3, :67 4 cm 3, 34; 469 K, and T 6; 5 K. procdurs is as follows. In EQAIR, th Voigt width is assumd to b constant for a givn vibrational band, whras in th prsnt databasing schm, th Voigt lin width is calculatd at th lin-cntr wavlngth of ach vibrational rotational lin. EQAIR prpars a tmplat for th Voigt lin shap for a singl rotational lin in th vibrational rotational transition. Th sam tmplat is thn copid to all th lins in that particular vibrational band. In th databasing schm, diffrnt lin shaps ar usd for ach vibrational rotational lin cntr. Th valu of lin-shap function is not calculatd xactly at th dsird spctral point in EQAIR. Rathr, it is assumd that som of th spctral points coincid with th lin-cntr wavlngth. Th lin-shap function is thus approximatd by th valu at a wavlngth fixd a distanc away from th lin-cntr wavlngth. In th databasing schm, th lin-shap function is calculatd at th xact wavlngth position. In EQAIR, whthr th contribution from a lin is important or not is dtrmind by a cutoff limit basd on Fig. 7 Comparison of mission and absorption cofficints of from to 7 Å btwn th databas and EQAIR for :564 3 cm 3, 3: cm 3, :89 5 cm 3, :67 4 cm 3, 34; 469 K, and T 6; 5 K.

10 63 SH ET AL. Fig. 8 Comparison of mission and absorption cofficints of from to 6, Å btwn th databas and EQAIR for :564 3 cm 3, 3: cm 3, :67 4 cm 3, 34; 469 K, and T 6; 5 K. Fig. 9 Comparison of mission and absorption cofficints of from to 3,5 Å btwn th databas and EQAIR for 6:8349 cm 3, :89 5 cm 3, :67 4 cm 3, 34; 469 K, and T 6; 5 K. th mission lin strngth, whras in th databas, w spcify two sparat cutoff limits on mission and absorption lin strngth. Th absorption limit is spcifid as a fixd valu and th mission cutoff limit is rlatd to th absorption cutoff limit according to th following rlation: " min min hc 5 cxphc= c kt (55) Th mission cutoff limit changs ach lin diffrntly. In th databas schm w ar intrstd in rtaining som of th lins which ar not important from th mission point of viw but ar important from th absorption point of viw and vic vrsa. To vrify th accuracy of th nw databasing schms for diatomic spcis, th mission and absorption cofficints from th databas and EQAIR ar compard using th sam Voigt lin distribution mthod for both th databas and EQAIR. Th accuracy of th databasing schm is tmporarily dgradd in ordr to compar as closly as possibl with th EQAIR approach. In this comparison th four mthods for th distribution of Voigt lin-shap function ar applid to th databas and EQAIR. Voigt widths ar dtrmind at th vibrational band cntr. Th lin-cntr wavlngth in Eq. (33) is dfind for ach diffrnt vibrational rotational transition. Emission and absorption cofficints at a givn wavlngth ar approximatd using th narst spctral data point in EQAIR. Th mission and absorption cofficints ar also dirctly calculatd in th databas using th sam approach. Th mission cutoff limit is usd as a singl valu, givn by EQAIR, for th ntir spctral rgion. Figurs 6 9 also show th absolut diffrnc of spctral cofficints btwn th databas and EQAIR calculatd undr th sam Voigt lin distribution mthod. It can b sn that thr is xcllnt agrmnt btwn th mission and absorption cofficints prdictd by th tmporarily dgradd databas and EQAIR. B. Invstigation of Databasing Schm Efficincis Th objctiv of this work is to crat a databas that can b usd in calculating th spctral cofficints fficintly. This is ssntial for th coupld study of radiation hat transfr in hyprsonic nonquilibrium flowfilds. Ths databasing schms provid an fficint way for calculating th spctral cofficints for full as wll as narrow wavlngth rangs. For molcular band calculation, all th rotation vibration lins that contribut to th spctral cofficints at ach givn wavlngth, ar stord in th databas. Th spctral cofficints for a givn narrowband can b fficintly gnratd using this information. ot that th basic databas, xampl shown in Tabl 4, is rad only onc and th actual computational tim of th databas is much lss than that of EQAIR bcaus it is not ndd to rpat many arithmtical oprations to calculat th basic radiation paramtrs. Th CPU tims of th dual.4 GHz AMD ptron procssors shown in Tabls 5 and 6 clarly dmonstrat that by using our nw databas schm spctral cofficints can b gnratd mor fficintly both for a larg wavlngth rang and for small narrowbands than by th prsnt procdur in EQAIR. In this CPU tim study, th wavlngth incrmnt is.5 Å, and gas clls wr considrd from th stagnation lin flow condition of Stardust at th 68.9 km altitud calculatd by DSMC. In ths gas clls, th lctron

11 SH ET AL. 633 Tabl 5 Comparison of computation tim for narrow spctral rgion from 5 to Å Spcis EQAIR Databas Atomic spcis 5.33 s.36 s Diatomic spcis.5 s 3.86 s All spcis 7.7 s 3.55 s Tabl 7 Fr stram conditions of Stardust rntry flow CFD DSMC DSMC Altitud, km Vlocity, m=s.87,9,8 Tmpratur, K umbr dnsity, m 3 4:47 :63 :639 Tabl 6 Comparison of computation tim for wid spctral rgion from 5 to, Å Spcis EQAIR Databas Atomic Spcis s.3 s Diatomic Spcis 3.33 s 75.4 s All Spcis 79.9 s 79.5 s tmpratur varis from 55 to 9,846 K. Atomic and bound bound, bound fr, and fr fr transitions and six molcular bands (first ngativ for, first and scond positiv for and, and for and Schumann Rung for ) wr considrd in this xampl. Bcaus w us an fficint intrpolation schm for gnrating atomic spctral cofficints, thr is larg savings of computational tim for th atomic calculations. Th data intrpolation schm provids an fficint and accurat mans for gnrating spctral cofficints for atomic bound bound, bound fr, and fr fr transitions. Th fficincy of applying a variabl cutoff rang in th atomic radiation calculation was also xamind. Atomic and bound bound radiation was considrd, and 4 gas layrs wr usd from th stagnation lin flow of a Stardust flowfild at th 68.9 km altitud simulatd by DSMC mthod. Th wavlngth rang from to, Å was assumd to captur mission far from th lin cntr for all th lins and th spctral rsolution was.5 Å. Th rror in th total mission nrgy, Z E mis 4 " d btwn th intgratd mission obtaind using a variabl and a fixd cutoff rang compard with th summation of th lin strngths of all atomic lins is shown in Fig. for ach cll along th stagnation stramlin. A valu of. was chosn as th fixd valu for all atomic bound bound transitions bcaus, as shown arlir, it capturs 99.9% of th total mission nrgy for all ratios of Lorntzian to Voigt widths. From th figur it can b sn that th E mis Fixd Rang (.) Variabl Rang variabl cutoff rang satisfis 99.9% total mission nrgy. Th variabl cutoff rang schm lads to a rduction of computational tim bcaus th unncssarily larg cutoff rang is not applid to all atomic lins. Th CPU tim for th calculation using th variabl rang is 6.4 s, whras using th fixd cutoff rang it was found to b.7 s. Most of th atomic lins in th spctral rgion blow Å nd to us a valu of. as th cutoff rang to satisfy th 99.9% total mission nrgy critria, undr th high lctron numbr dnsity and lctron tmpratur gas conditions. Thrfor, only a rduction of about % in computational tim was achivd. Howvr, whn itrativ calculations ar usd, such as in th photon Mont Carlo RTE, and in highly optically thick conditions [6,7], this rduction of th computational tim without loss of accuracy will b important. C. Application of Databasing Schms to Radiation Calculations In th prvious sction, w hav shown that th databas procdur calculats mission and absorption cofficints accuratly for a singl flowfild condition. As th final vrification of our databasing schm, w hav usd it to dmonstrat th calculation for radiativ hat gnration rat along th stagnation lin and a flowfild condition clos to th shouldr lin of th Stardust vhicl. For nonquilibrium gas conditions, calculations of radiativ hat gnration rquir data for both th mission and absorption cofficints. Thus, th objctiv of this work is to vrify th rliability of th mission and absorption cofficints through th radiativ hat gnration computation for all possibl flow conditions. In this work, flowfild solutions for thr fr stram conditions wr usd to provid spcis concntrations and tmpraturs in ach cll. Th radiation computation was prformd using th tangnt-slab approximation and radiativ rsults obtaind from th nw databasing schms wr compard with thos of EQAIR. Bcaus of th fact that diatomic spcis contribut much lss to th radiativ hat flux compard with atomic mittrs, it is not ncssary to us a fin wavlngth rsolution for th ntir wavlngth rang. Hnc, a variabl wavlngth incrmnt in this calculation was usd as follows: :5 A for 5 to 5 Å and : A for 5 to 4, Å. Radiativ transfr calculations wr prformd along two lins: th stagnation stramlin and on of th lins normal to th vhicl shouldr body. Th flowfild solutions ar obtaind from th dataparalll lin rlaxation (DPLR) computational fluid dynamics (CFD) cod [8] and dirct simulation Mont Carlo (DSMC) mthod [9]. Th fr stram conditions of ach flow solvr ar listd in Tabl 7. 8 E mis (W/cm 3 ) Y(m) () () Stagnation Lin () Shouldr Lin Distanc from th wall (m) Fig. Comparison of total mission nrgy rror using fixd and variabl cutoff rangs for atomic bound bound radiation along th stagnation lin of Stardust at 68.9 km altitud.. () X(m) Fig. Gomtry of th Stardust vhicl.

12 634 SH ET AL. Ths flow solvrs includ chmical raction procsss of spcis such as,,,,,,,,,, and. Figur shows th locations of th stagnation stram lin and shouldr lin for th Stardust vhicl. For th two locations, th radiativ hat gnration pr unit volum was calculatd using th databas and compard with th rsults of EQAIR. Th spatial distribution of numbr dnsitis of th six radiating spcis such as,,,,,, and and th tmpratur along th stagnation lin and th shouldr lin of DPLR flowfild ar shown in Figs. and 3, rspctivly. It can b sn that atomic spcis such as and ar (cm -3 ) Tmpratur (K) 5 5 (=T ) 3 5 Fig Distanc from th wall (cm) Distanc from th wall (cm) umbr dnsity (lft) and tmpratur (right) profil along th stagnation stramlin of DPLR flowfild. (cm -3 ) Tmpratur (K) 5 5 (=T ) 3 3 Fig. 3 3 Distanc from th wall (cm) Distanc from th wall (cm) umbr dnsity (lft) and tmpratur (right) profil along th shouldr lin of DPLR flowfild. 5 EQAIR (Stagnation lin) DB (Stagnation lin) EQAIR (Shouldr lin) DB (Shouldr lin) 7 EQAIR (Stagnation lin) DB (Stagnation lin) EQAIR (Shouldr lin) 6 DB (Shouldr lin) q R (W/cm 3 ) 5 E mis (W/cm 3 ) Distanc from th wall (cm) Distanc from th wall (cm) Fig. 4 Comparison of rq R (lft) and total mission (right) of 6 radiating spcis btwn th databas and EQAIR along th stagnation lin and shouldr lin of Stardust DPLR flowfild.

13 SH ET AL. 635 dominant in th shock layr, du to th strong dissociation of th molcular spcis. Th figur also shows that th lctron numbr dnsity is high in th shock layr, du to ionization procsss in th shock. Figur 4 shows comparison of th total mission and radiativ hat gnration pr unit volum from th aformntiond six radiating spcis calculatd using th databas and EQAIR. Th horizontal axis in Fig. 4 indicats th distanc from th vhicl wall. In ths calculations, all thr typs of transitions for th two atomic spcis and 6 lctronic band systms of th four diatomic spcis wr considrd. Sinc lctron tmpratur is not calculatd dirctly in th DPLR CFD flow solvr, it is assumd to b qual to Tmpratur (cm -3 ) (K) T Tmpratur (K) umbr dnsity (cm -3 ) T 3 3 Distanc from th th wall wall (cm) 3 3 Distanc from th wall (cm) (cm) Fig. 5 umbr dnsity (lft) and tmpratur (right) profil along th stagnation stramlin of DSMC flowfild at 68.9 km altitud T Tmpratur (cm -3 ) (K) T trn T Tmpratur (K) umbr dnsity (cm -3 ) Distanc from th wall (cm) Distanc from th wall (cm) (cm) Fig. 6 umbr dnsity (lft) and tmpratur (right) profil along th shouldr lin of DSMC flowfild at 68.9 km altitud. EQAIR (Stagnation lin) DB (Stagnation lin) EQAIR (Shouldr lin) 8 DB (Shouldr lin) 6 8 EQAIR (Stagnation lin) DB (Stagnation lin) EQAIR (Shouldr lin) DB (Stagnation lin) q R (W/cm 3 ) 4 E mis (W/cm 3 ) Distanc from th wall (cm) Distanc from th wall (cm) Fig. 7 Comparison of rq R (lft) and total mission (right) of 6 radiating spcis btwn th databas and EQAIR along th stagnation lin and shouldr lin of Stardust DSMC flowfild at 68.9 km altitud.

14 636 SH ET AL. translational tmpratur for radiation calculation using th databas and EQAIR. To confirm th accuracy of th mission cofficints from th databas, total mission along th two lins was compard with EQAIR rsults. Bcaus of th fact that radiation from atomic spcis is dpndnt on lctron tmpratur, location of th maximum pak hat gnration coincids with that of th maximum lctron tmpratur. Good agrmnt of radiativ hat gnration and total mission btwn th nw databas and EQAIR is obtaind with rrors blow.5% in th pak hating rgion. Figurs 5 9 show numbr dnsitis and tmpratur profils along th stagnation lin and shouldr lin obtaind from th DSMC flowfild at 68.9 and 8 km altituds, rspctivly. Figurs 7 + Tmpratur (cm -3 ) (K) T Tmpratur (K) umbr dnsity (cm -3 ) T Fig Distanc from th wall (cm) Distanc from th wall (cm) (cm) umbr dnsity (lft) and tmpratur (right) profil along th stagnation stramlin of DSMC flowfild at 8 km altitud. Tmpratur (cm -3 ) (K) T Tmpratur (K) umbr dns (cm -3 ) T Distanc from th wall (cm) Distanc from th wall (cm) Fig. 9 umbr dnsity (lft) and tmpratur (right) profil along th shouldr lin of DSMC flowfild at 8 km altitud. 3 EQAIR (Stagnation lin) DB (Stagnation lin) EQAIR (Shouldr lin) DB (Shouldr lin) 5 4 EQAIR (Stagnation lin) DB (Stagnation lin) EQAIR (Shouldr lin) DB (Stagnation lin) q R (W/cm 3 ) E mis (W/cm 3 ) Distanc from th wall (cm) Distanc from th wall (cm) Fig. Comparison of rq R (lft) and total mission (right) of 6 radiating spcis btwn th databas and EQAIR along th stagnation lin and shouldr lin of Stardust DSMC flowfild at 8 km altitud.

15 SH ET AL. 637 show that th nw databas and EQAIR prdict th sam amount and spatial dpndncy for radiativ hat gnration and total mission along th stagnation lin and shouldr lin of th Stardust blunt body at 68.9 and 8 km altituds, rspctivly. In th DSMC mthod, th lctron tmpratur can b dirctly calculatd and is prdictd to b lowr than th total avragd translational tmpratur in th shock layr for both 68.9 and 8 km altituds. From th figurs, it can b sn that th databas and EQAIR prdict that thr is significant hat gnration and total mission cratd in th high lctron numbr dnsity and lctron tmpratur rgion. This rsult is rasonabl bcaus radiation from atomic spcis is strongly dpndnt on lctron numbr dnsity and tmpratur. For th stagnation stramlin and shouldr lin, it is found that th radiativ hat gnration calculatd using th spctral data from th databas is in good agrmnt with EQAIR with an rror blow % in th high radiativ hating rgion. V. Conclusions w databasing schms hav bn dvlopd for advancd radiation calculations of hyprsonic nonquilibrium rntry flows. Bcaus of th nonquilibrium flow conditions, th quasi-stadystat assumption was usd for gnrating th lctronic stat populations of atomic and diatomic gas spcis. A Voigt linbroadning function was usd to dscrib th lin shap of bound bound spctral lins. Th mission and absorption cofficints for any givn flow condition and wavlngth rang wr accuratly and fficintly calculatd using th databas and its associatd intrpolation schms. Comparisons of th mission and absorption cofficints for atomic and btwn th databas and EQAIR wr prformd to validat th accuracy of th databass and good agrmnt within % rror was obsrvd. For diatomic spcis,,, and, thr ar som diffrncs of rsults btwn th databas and EQAIR. This is bcaus th broadning mthod as implmntd in EQAIR is diffrnt from that usd in th databas. It is also found that thr is xcllnt agrmnt for spctral cofficints whn th sam broadning mthod was applid to both th databas and EQAIR. Radiativ hat gnration for th Stardust rntry for two diffrnt flowfilds computd using CFD and DSMC mthods, was calculatd using th databas. Th radiativ hat production from th databasing schms prdicts th sam magnitud and spatial distribution as EQAIR mor fficintly. Th improvd computational mthod will hav a significant impact for coupld radiation/gas-dynamic calculations. Acknowldgmnt Th rsarch prformd at th Pnnsylvania Stat Univrsity was supportd through th ASA grant no. X7AC47A. Rfrncs [] zawa, T., Improvd Chmistry Modls for DSMC Simulations of Ionizd Rarfid Hyprsonic Flows, Ph.D. Thsis, Dpartmnt of Arospac Enginring, Pnnsylvania Stat Univ., Univrsity Park, PA, 7. [] Hartung, L. C., Dvlopmnt of a onquilibrium Radiativ Hating Prdiction Mthod for Coupld Flowfild Solutions, Journal of Thrmophysics and Hat Transfr, Vol. 6, o. 4, 99, pp doi:.54/3.54 [3] Whiting, E. E., Park, C., Liu, Y., Arnold, J.., and Patrson, J. A., EQAIR 96 Usr Manual, ASA Ams Rsarch Cntr, Mofftt Fild, CA, 996. [4] Johnston, C.., onquilibrium Shock-Layr Radiativ Hating for Earth and Titan Entry, Ph.D. Thsis, Dpartmnt of Arospac Enginring, Virginia Polytchnic Inst. and Stat Univ., Blacksburg, VA, 6. [5] Park, C., onquilibrium Hyprsonic Arothrmodynamics, Wily, w York, 99. [6] Modst, M. F., Radiativ Hat Transfr, nd d., Acadmic Prss, w York, 3. [7] Pach, G., Continuous Absorption Cofficint for on-hydrognic Atoms, Mmoirs of th Royal Astronomical Socity, Vol. 73, 97, pp. 3. [8] Zl dovich, Y. B., and Raizr, Y. P., Physics of Shock Wavs and High- Tmpratur Hydrodynamic Phnomna, Acadmic Prss, London, 966. [9] Whiting, E. 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