Estimation of Atomic Oxygen Concentration by Semi-emipirical Collisional-Radiative Model in High Enthalpy Flow

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1 7th AIAA Thrmophyscs Confrnc 8 Jun -1 July 00, Portland, Orgon AIAA 00-7 Estmaton of Atomc Oxygn Concntraton by Sm-mprcal Collsonal-Radatv Modl n Hgh Enthalpy Flow Makoto Matsu 1, Hrok Takayanag, Yasuhsa Oda, Kmya Komurasak, and Yoshhro Arakawa 5 1,, Dpartmnt of Advancd Enrgy, Th Unvrsty of Tokyo, Kashwanoha 5-1-5, Kashwa, Chba , Japan,5 Dpartmnt of Aronautcs and Astronautcs, Th Unvrsty of Tokyo, Hongo 7--1, Bunkyo, Tokyo 11-00, Japan Kywords: collsonal-radatv modl, hgh nthalpy flow, lasr absorpton spctroscopy Abstracton Collsonal-radatv modl for atomc oxygn was appld to arc-hatr plums to clarfy a mchansm of populaton dnsty. Th modl wth nput paramtrs obtand by lasr absorpton spctroscopy and a sngl prob masurmnt shows consstnt rsults wth that of msson spctroscopy. As a rsult, th populaton dnsty was found not to oby th Boltzmann dstrbuton. Th numbr dnsty of ground lvl was stmatd 0% lowr than that n Boltzmann dstrbuton. 1. Introducton In dvlopng thrmal protcton systms for rntry vhcls, arc-hatrs ar oftn usd to smulat rntry condtons. Howvr, thr xact plum condtons ar mostly unknown bcaus thy ar usually n strong thrmo-chmcal non-qulbrum. 1-) Although varous ntrusv and non-ntrusv masurmnts such as prob and spctroscopc mthods hav bn actvly appld to th charactrzaton of such hgh nthalpy plums, and th lctron dnsty, tmpratur and vbraton, and rotatonal tmpraturs of atoms and molculs n th plums ar gradually clarfd, t s stll dffcult to masur th chmcal compostons by ths spctroscopc mthods. In our prvous rsarch -6), numbr dnsty of mta-stabl atomc oxygn n th Unvrsty of Tokyo arc-hatr plum was masurd by lasr absorpton spctroscopy as shown n Fg.1. As a rsult, th numbr dnsty was found n th ordr of m -. Howvr, numbr dnsty of total 1- Graduat studnts, Studnt Mmbr AIAA Assocat Profssor, Snor Mmbr AIAA 5 Profssor, Snor Mmbr AIAA Copyrght 00 Th Amrcan Insttut of Aronautcs and Astronautcs Inc. All rght rsrvd. atomc oxygn, most of whch s n ground lvl, s dffcult to b dducd from th mta-stabl on bcaus ts lctronc xctaton would not b n thrmal qulbrum. Thn, n ths study, rlatonshp btwn masurd mta-stabl oxygn and ground lvl oxygn was nvstgatd dvlopng a collsonal-radatv modl. Numbr Dnsty, m Radal Poston r, mm Fg.1 Numbr dnsty dstrbutons of mta-stabl atomc oxygn n th Unvrsty of Tokyo arc-hatr plum Axal Poston z, mm 1 Insttut of Aronautcs and Astronautcs Copyrght 00 by th Amrcan Insttut of Aronautcs and Astronautcs, Inc. All rghts rsrvd.

2 . Collsonal-Radatv Modl Although collsonal-radatv modls for varous gass hav bn dscussd, most of thm ar dvlopd to stmat lctron tmpratur or lctron dnsty combnd wth msson spctroscopy. 7-1) Modls for numbr dnsty stmaton hav not bn dvlopd. In ths study, th collsonal-radatv modl for atomc oxygn dvlopd by Kunc was basd. 7-10) Snc ths modl s amd for onzng plasma, only lctron-mpact xctaton and spontanous msson n low xctd lvls ar consdrd as transton procsss. On th othr hand, hgh nthalpy flows for TPS tsts ar usually rcombnng plasma. Thn, ffcts of hghr lvls and on ar addd to th modl..1 Lvls Park s modl was usd. 15) In ths modl, ntrnal lvls ar catgorzd to 19 lvls as tabulatd n Tabl 1. Hr, s th lvl numbr, g s th statstcal wght and E s th xctaton nrgy, rspctvly. Thn, accordng to th Kunc modl, ths 19 lvls ar dvdd nto thr zons: Boltzmann, Actv and Saha zons. Boltzmann zon Th lvls wth =1, and almost always hav Boltzmann dstrbuton 9) : n g E = xp( ) (1) n1 g1 kbt Hr, n s th numbr dnsty, k B s th Boltzmann constant and T s th lctron tmpratur, rspctvly. Thn, n and n ar rprsntd by th functon of n 1 and T. Actv zon Snc Grm boundary p G and Byron boundary p B dfnd blow ar.8 and.6 at T of 8000K and n of m -, rspctvly, lvls whos prncpal quantum numbr p s ar catgorzd to Actv zon. Rat quatons for 10, 16-0) ths lvls wth = ~7 ar consdrd. 17 / p = 95n () G p B = R kbt () Hr, n s lctron dnsty and R s Rydbrg constant. Saha zon Snc prncpal quantum numbr of lvls wth p>8 s nough largr than p G and p B, ths lvls ar almost n Saha qulbrum. Thn, n s rlatd to numbr dnsty of atomc oxygn on n O+ and n as, Z n n n = O+ / g h Z = xp( ) g k BT. () + kbt Hr, Z s Saha-Boltzmann constant and s th onzaton nrgy, rspctvly. Th Grotran dagram s shown n Fg... Rat quatons Assumng th quas stady stat condton, rat quatons for = ~7 ar xprssd as, Cqpnnq Fpq C pq S p n + Apq n q p + + < q< p q> p q< p + [ F qpn + Aqp ] n + [ pn + p ] no+ n. (5) q> p Hr, C, F, S, A,, ar th rat coffcnts of lctron-mpact xctaton, lctron-mpact d-xctaton, lctron-mpact onzaton, spontanous msson, thr-body rcombnaton and radatv rcombnaton, rspctvly. Tabl 1 lvl No Confguraton g E, V 1 p P p 1 D p 1 S s 5 S s S p 5 P p P s 5 S, s S d 5 D, d D p 5 P, p P s 5 S, 5s S d 5 D, f 5 F, d D, f F 1 5p 5 P, 5p P d 5 D, 5f 5 F, 5g 5 G, d D, 5f F, 5g F 15 n= n= n= n= n= Ion p S Insttut of Aronautcs and Astronautcs

3 E,V 1.6 Saha zon 10 snglts trplts quntts p s p d f s p d 5 p 1 S 0 p 1 D 15 6s S 5p P 5d D 5f F 6s 5 S 5p 5 P 5d 5 D 5f 5 F s 1 S d p P D 1 f F s 5 S d 5 D 1 10 f 5 F s S d D 8 p s 5 S 5 P 9 d 5 D 7 p P 6 p 5 P 5 s Actv zon S s 5 S 1 p P Boltzmann zon Fg. Grotran dagram of OI. Rat coffcnts Elctron-mpact xctaton/d-xctaton Rat coffcnts of lctron-mpact xctaton C ar rfrrd to Park s data. 15) Rvrs rat F wr stmatd by th prncpl of dtald balanc xprssd as, g q E pq Fp, q = Cq, p xp( ). (6) g k T p Spontanous msson All data of A s rfrrd to NIST. 1) Although atomc oxygn has 910 msson lns, for smplcty, thos from lvls wth p>5 ar nglctd. Morovr th rst 60 lns ar rducd to 1 lns consdrng th statstcal wght as tabulatd n Tabl. Tabl Enstn coffcnt, 10 8 s -1 A A A A A A A A A A A A A A Elctron-mpact onzaton Rat coffcnt of lctron-mpact onzaton from ground lvl S 1 s rfrrd to L ), whch s a ft to th rat coffcnt gvn by Elasson and Koglshatz. ) S1 = 9 10 T xp( 1 / kbt ) (7) Th coffcnts from th othr lvls ar stmatd by th Thomson formula ) and S 1. 1/ 8 8 S = K (1 + )xp( ) 1/ / ( m ) ( kbt ) kbt kbt kbt (8) Hr, m s th mass of lctron, s th lctron charg and K s th fttng paramtr, rspctvly. B f s stmatd by th prncpl of dtald balanc wth S and Z. = Z S. (9) Radatv rcombnaton Rat coffcnt of radatv rcombnaton to th ground lvl 1 for T =100K, 1000K, 10000K s takn from Nahar. Dpndncy on tmpratur of 1 s stmatd by lnar 5) ntrpolaton. For th othr lvls, s stmatd by th scalng rul of Fujmoto. 17) 6 = m c 1 R ( ) p k T B / xp( k T " # t ) B t kbt dt (10). Calculaton procss For paramtrs ( n (=1~19), n, n + and T ), thr ar 8 unknown paramtrs ( n (=1,~7), n, n + and T ) and 18 quatons (Eqs.(,5,9)). Thn, four paramtrs ar ncssary to solv th rat quatons. In ths study, n, n, n O+ and T ar chosn as nput paramtrs. Hr, n s obtand from lasr absorpton spctroscopy, n and T ar obtand from a sngl prob mthod or msson spctroscopy and n O+ s a tunng paramtr.. Input Condtons Dtals of th arc-hatr and lasr absorpton spctroscopy masurmnt ar dscrbd n th rfrnc [-6]. In addton, msson spctroscopy and a sngl prob masurmnt hav bn appld to obtan lctron dnsty and tmpratur. Hr, lctron tmpratur was stmatd by OI and ArI msson lns, rspctvly. Obsrvd msson lns and thr transton data ar shown n Fg. and Tabl. Snc obsrvd ArI lns ar mssons from hghr lvls than th Byron boundary, ths lvls ar consdrd clos to LTE. Thn, stmatd T by ArI lns was adoptd as an nput paramtr. Snc n O+ s not qual to n for th prsnc of argon on and molcular oxygn on, n O+ s also ncssary to b dtrmnd. Hr, th raton of n O+ to n s st to b 0.1, whch corrsponds to thrmo-chmcal qulbrum. Thn, th rato s changd from 1 to All xprmntal rsults ar summarzd n Tabl. Thr-body rcombnaton Rat coffcnt of thr-body rcombnaton Insttut of Aronautcs and Astronautcs

4 shows T stmatd by Boltzmann plot of calculatd n 6 ~n 1, whos lvls wr dtctd n th msson spctroscopy. Th rsult shows th modl s consstnt wth th rsult of msson spctroscopy. Tabl 5 shows calculatd n 1 and that stmatd from Boltzmann plot. As sn n ths tabl, stmatd n 1 by CR modl s 0% lss than that stmatd by Boltzmann plot n O+ /n Wavlngth $, nm Fg. Emsson lns Tabl Obsrvd msson lns Spcs $[nm] j OI p 5 P d 5 D OI p 5 P 5s 5 S OI s 5 S p 5 P OI 8.6 s S p P ArI p [5/] 7s [/] ArI p [1/] d [/] ArI 60.1 p [5/] 5d [7/] ArI 61.6 p [1/] 6s [/] ArI 79.8 s [1/] p [/] ArI s [/] p [/] ArI s [/] p [5/] ArI s [/] p [/] ArI s [/] p [5/] ArI 80.8 p [1/] p [/] ArI 8.6 p [/] p [5/] Masurd Exctaton nrgy, V Fg. Calculatd numbr dnsty for varous n O+ /n Tabl Estmatd T n O+ /n T, K ES, OI 00 Tabl Input paramtrs n, m - (LAS) n, m - (Prob) T, K (ES, ArI) T, K (ES, OI) T tr, K (LAS) 1x x K. Rsults and Dscusson.1 Rsults Fgur shows calculatd rsults wth varous n O+ /n. As shown n ths fgur, numbr dnsty n lowr lvls s almost ndpndnt of n O+ /n. Ths mans that thr-body and radatv rcombnaton dosn t contrbut to ncras of numbr dnsty n thos lvls. On th othr hand, numbr dnsty n hghr lvls has strong dpndnc on n O+ /n. Tabl Tabl 5 Estmatd n 1 CR modl Boltzmann plot 8.00x10, m- 1.0x10, m-. Dscusson To valdat ths modl, snstvty analyss was appld. n dpndncy Dpndncy of n on n s shown n Fg.5. Numbr dnsty n lowr lvls (n 1, n 5 ) s almost constant wth n <10 1 m - and thn, rapdly dcrass. Ths suddn dcras s du to th onzaton. On th othr hand, numbr dnsty n hghr lvls (n 6, n 7 ) ncrass wth n. Thrfor, n arc-hatr plums (10 17 m - < n <10 0 m - ), n s not so mportant for n 1 stmaton. Insttut of Aronautcs and Astronautcs

5 n1 n n5 n6 n n1 n5 n6 n Elctron dnsty n, m - Fg.5 n dpndncy (n =10 16 m -, T=8000K, n O+ /n =0.01) T dpndncy Dpndncy of T on n s shown n Fg.6. Although numbr dnsty n hghr lvls (n 5, n 6, n 7 ) s almost constant, n 1 ncrass wth T. Thrfor, T s most carfully masurd for n 1 stmaton n1 n n5 n6 n Elctron tmpratur T, m - Fg.6 T dpndncy (n =10 19 m -, n =10 16 m -, n O+ /n =0.01) n dpndncy Dpndncy of n on n s shown n Fg.7. Numbr dnsty n all lvls almost lnarly ncrass wth n Mta-stabl numbr dnsty n, m - Fg.7 n dpndncy (n =10 19 m -, T =8000K, n O+ /n =0.01) 5. Concluson Collsonal radatv modl for atomc oxygn was dvlopd. Calculatd numbr dnsty of hghr lvls s consstnt wth th rsult of msson spctroscopy. OI xctd lvls wth p= ar n non-qulbrum and cannot b usd for th dtrmnaton of lctron tmpratur. Numbr dnsty of ground lvl was stmatd to 0% lowr than that n Boltzmann dstrbuton. Rfrnc 1) Salnas, I. T., Park, C., Strawa, A.W., Gopaul N. and Taunk, A.W.: Spctral Masurmnts n th Arc Column of an Arc-Jt Wnd Tunnl, AIAA Papr 9-595, 199 ) Wntr, M. W. and Auwtr-Kurtz, M.: Boundary layr nvstgaton n front of a blunt body n a subsonc ar plasma flow by msson spctroscopc mans, AIAA papr 98-60, ) Laux, T., Fgl, M., Auwtr-Kurtz, M. and Stockl, T.: Estmaton of th Surfac Catalycty of PVD-Coatngs by Smultanous Hat Flux and LIF Masurmnts n Hgh Enthalpy Ar Flows, AIAA Papr 00-6, 000 ) Matsu, M. Komurasak, K. and Arakawa, Y.: Lasr Dagnostcs of Atomc Oxygn n Arc-hatr Plums, AIAA Papr 0-079, 00 5) Matsu, M. Komurasak, K. and Arakawa, Y.: 5 Insttut of Aronautcs and Astronautcs

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