Ttl Autor(s) Two-Tmpratur Plasma Modlng of Argon Gas Tungstn Arcs Tasro, Snc; Tanaa, Manabu Ctaton Transactons of JWRI. 37(1) P.7-P.11 Issu Dat 2008-07 Txt Vrson publsr URL ttp://dl.andl.nt/11094/8887 DOI rgts
Transactons of JWRI, Vol. 37 (2008), No. 1 Two-Tmpratur Plasma Modlng of Argon Gas Tungstn Arcs TASHIRO Snc * and TANAKA Manabu ** Abstract Gas Tungstn Arc (GTA) s sutabl as a at sourc dvc for many applcatons bcaus t can stablz g tmpratur arc plasma asly by mployng a sldng gas. In many cass, t MHD smulaton modl assumng a local trmodynamc qulbrum (LTE) s utlzd for analyzng t proprty of t GTA. Altoug t LTE assumpton s ffctv for valuatng t g tmpratur rgon n t arc column, t s dffcult to apply t to t low tmpratur rgon suc as t frng of t arc column or t sat rgons clos to t lctrods du to t dcras of nrgy xcang. In ordr to consdr t ffct of cmcal racton btwn t arc plasma and t matral surfac, w av dvlopd a smulaton modl of t GTA assumng cmcal and trmal non-qulbrum. In ts papr, as a frst stp n t study, t at sourc proprty of argon GTA mployng a watr-coold coppr anod was smulatd. KEY WORDS: (Numrcal smulaton) (Gas tungstn arc) (Non-qulbrum) 1. Introducton T Gas Tungstn Arc (GTA) s sutabl as a at sourc dvc for many applcatons bcaus t can stablz g tmpratur arc plasma asly by mployng a sldng gas. T arc plasma s producd btwn a tungstn catod and an anod matral. GTA as many advantags as a at sourc dvc suc as g atng ffcncy, gly controllabl caractrstcs and low cost of qupmnt nvstmnt. Trfor, t s wdly utlzd, for xampl, for producton of nano-partcls, matral procssng suc as mltng, cuttng and wldng 1), or dcomposton, volum rducton and dtoxfcaton of toxc wast 2) and so on. In many cass, t MHD smulaton modl assumng a local trmodynamc qulbrum (LTE) s utlzd for analyzng t proprty of t GTA bcaus of sort calculaton tm and sutablnss to coupl wt otr complx procsss 3). Undr t LTE assumpton, all spcs n t plasma av t sam tmpratur and t s cmcal composton s dtrmnd dpndng only on t tmpratur. Ts assumpton s applcabl f t arc plasma as g collson frquncy btwn avy spcs (nutral gas and ons) and lctrons suffcnt to xcang tr trmal nrgy. Trfor t s consdrd to b vald only for g tmpratur plasma wt g lctron dnsty. Altoug t LTE assumpton s ffctv for valuatng t g tmpratur rgon n t arc column, t s dffcult to apply t to t low tmpratur rgon Rcvd on July 11, 2008 * Assstant Profssor ** Profssor suc as t frng of t arc column or t sat rgons clos to t lctrods du to a dcras of nrgy xcang. Espcally, n ordr to consdr t ffct of cmcal racton btwn t arc plasma and t matral surfac suc as oxdaton, non-qulbrum proprts of t arc plasma sould b consdrd wtout t LTE assumpton, snc t s rqurd to undrstand prcs proprts of t arc plasma clos to t matral surfac. A numbr of numrcal modls of RF plasma consdrng non-qulbrum ffcts av bn rportd 4, 5). On t otr and, n cas of DC GTA, a trmal non-qulbrum modl assumng cmcal qulbrum was dvlopd 6). Furtrmor, a trmal non-qulbrum modl ncludng t nrgy balanc btwn t arc and t lctrods was also rportd 7). Howvr, t surfac ara of t catod spot was assumd n ts modl. Altoug a numrcal modl assumng cmcal and trmal non-qulbrum was dvlopd, t nrgy balanc btwn t arc and t lctrods was gnord 8). Trfor, w av dvlopd a numrcal modl of GTA assumng cmcal and trmal non-qulbrum and ncludng t nrgy balanc btwn t arc and t lctrods. In ts papr, as a frst stp of t study, t at sourc proprty of argon GTA mployng a watr-coold coppr anod was smulatd. 2. Smulaton Modl T tungstn catod, t arc plasma and t Transactons of JWRI s publsd by Jonng and Wldng Rsarc Insttut, Osaa Unvrsty, Ibara, Osaa 567-0047, Japan 7
Two-Tmpratur Plasma Modlng of Argon Gas Tungstn Arcs watr-coold coppr anod ar dscrbd n a fram of cylndrcal coordnats wt axal symmtry around t arc axs. T calculaton doman s sown n Fgur 1. T damtr and t concal angl of t catod ar 3.2mm and 60dgrs, rspctvly. T lctrod gap s 5mm. T arc currnt s 100A. Ar s ntroducd at t flow rat of 10L/mn. from t outsd of t catod on t uppr boundary. T flow s assumd to b lamnar. T plasma s optcally tn. tr componnt (atoms, ons, lctrons), two-tmpratur argon arc plasma s consdrd n wc atoms and ons av t sam translatonal tmpratur wc s dffrnt from tat of t lctrons. T plasma s assumd to b n cmcal (onzaton) non-qulbrum and ts composton s calculatd assumng onzaton ractons and dffuson. T otr numrcal modlng mtods ar gvn n dtal n our prvous paprs 9,10). MHD quatons and supplmntary quatons (1)-(9) ar solvd tratvly by t SIMPLER numrcal procdur 11). On t boundars A-F, C-D and D-F, t tmpraturs s st to b 300K. T lctrcal potntal s 0V on t boundary C-D and t arc currnt s gvn nsd t catod on t boundary A-F. T lctron dnsty s 1010/m 3 on t boundars A-F and E-F. Snc w nglct t transport of t lctrons from t arc plasma to t catod surfac troug a catod sat, trmal conducton btwn t lctrons and t catod surfac s nglctd. On t anod surfac -E, t lctron tmpratur and t lctron dnsty can b dtrmnd by solvng on-dmnsonal quatons of t lctron nrgy consrvaton and t dffuson along t surfac, rspctvly. In addton, t gradnt of ac pyscal quantty n a radal drcton s zro on t arc axs A-C bcaus of t axal symmtry. T mass consrvaton quaton (1) s ( ρ u r ) = 0 T momntum consrvaton quaton (2) s r r r r ( ρu u) = p j τ, u τ αβ = η x α β u x T lctron nrgy consrvaton quaton (3) s r 5 5 φ u n T ε = ( T ) ε T n& 2 2 σ 5 φ r r r 3m j T j E n n T T R& ( υ υ ) ( ) 2 σ m T avy spcs nrgy consrvaton quaton (4) s r u 3m m {( n n ) T } = ( T ) n ( υ υ ) ( T T ) n n β α T dffuson quaton (5) s r ndn u n T r 1 E p = n& n T currnt contnuty quaton (6) s j = 0 T gnralzd Om s law (7) s r r 1 j = σ E p T n φ T lctrc fld (8) s E r = Φ T Maxwll s quaton (9) s r r = μ 0 j wr x s poston, ρ s mass dnsty, u s vlocty, n s numbr dnsty, T s tmpratur, p s prssur, j s currnt dnsty, s slf-nducd magntc fld, τ s strss tnsor, E s lctrc fld, Φ s lctrcal potntal, n& onzaton rat, D n s dffuson coffcnt of ons among nutrals, υ : avrag collson frquncy, s oltzmann constant, μ 0 s prmablty of vacuum, s lmntary carg, m s mass, s translatonal trmal conductvty, η s dynamc vscosty, φ s lctron trmodffuson factor, σ s lctrcal conductvty, ε s onzaton potntal, R & s radaton loss, subscrpt :,, n and ar lctrons, ons, nutrals, and avy spcs (ons and nutrals), z and r ar axal and radal componnts, α and β ar z or r. T transport coffcnts ar calculatd as functons of numbr dnsty and collson frquncy as follows: n T 2 = a ( T ) 3.203 (10) mυ n φ 389 D ( T ) = a 1. (11) mυ 15 = C 8 C ( n λ n λ ) ( n n) Q n n n (12) n = (13) 2 8
Transactons of JWRI, Vol. 37 (2008), No. 1 σ n 2 = a ( T ) 1.975 (14) mυ -30-25 A z r F wr C s avrag trmal spd, Q s collson cross scton and a, a and a ar factors to xprss nflunc of lctron-nutral collson. T nrgy transport du to t onzaton racton s xprssd n t scond trm on t rgt and sd of quaton (4). In addton, t nrgy transport du to t dffuson was gnord as t prvous study 10). In t soluton of quatons (1)-(9), spcal account nds to b tan at t lctrod surfac for ffcts of nrgy tat only occur at t surfac. At t catod surfac, addtonal nrgy flux trms nd to b consdrd for radaton coolng, trmonc coolng du to t msson of lctrons and on atng. T addtonal nrgy flux for t catod H s: H = εαt 4 j φ j V (15) K wc Axal dstanc (mm) -20-15 -10-5 0 5 10 Tungstn catod (1.6 mm) Arc plasma Anod C D 15 0 5 10 15 20 25 Radal dstanc (mm) E wr ε s t surfac mssvty, α s t Stfan-oltzmann constant, φ wc s t wor functon of t tungstn catod, V s t onzaton potntal of argon, j s t lctron currnt dnsty, and j s t on currnt dnsty. At t catod surfac, for trmonc msson of lctrons, j cannot xcd t Rcardson currnt dnsty J R 12) gvn by: j R = 2 φ AT xp (16) T wr A s t trmonc msson constant for t catod surfac, φ s t ffctv wor functon for trmonc msson of t lctrod surfac at t local surfac tmpratur, and s t oltzmann s constant. T on-currnt dnsty j s tn assumd to b j - j R f j s gratr tan j R ; wr j = j j s t total currnt dnsty at t catod surfac obtand from quaton (6) Smlarly, for t anod surfac, addtonal nrgy flux trms nd to b consdrd for radaton coolng, lctron ntalpy transport, lctron condnsaton, on rcombnaton and. t addtonal nrgy flux for t anod H A s: T 4 5 φ = φ j V (17) H A εαt wa j 2 σ wr φ wa s t wor functon of t coppr and j s t currnt dnsty at t anod surfac obtand from quaton (6). Fg. 1 Scmatc llustraton of smulaton doman. 3. Rsults and Dscusson Fgur 2 and 3 sow two-dmnsonal tmpratur dstrbutons of lctron and avy spcs n addton to t lctrods, rspctvly. It s sn tat t lctron tmpratur agrs wt t avy spcs tmpratur nar t arc axs and t LTE approxmaton s vald n ts rgon. ot tmpraturs nar t catod tp rac 15000K. Ts rsult approxmatly agrs wt xprmntal rsults 13). On t otr and, t s obvous tat n t rgon clos to bot lctrods and outsd t frng of t arc column t lctron tmpratur xcds t avy spcs tmpratur and non-qulbrum caractrstcs appars. T radus of t arc column sn n t lctron tmpratur dstrbuton s obvously largr tan tat of avy spcs. In addton, t max. surfac tmpraturs of t catod and anod rac 3600K and 700K, rspctvly. Fgur 4 sows dpndnc of tmpratur of lctron and avy spcs nar t anod surfac on axal dstanc from t catod tp. T axal poston of 5mm ndcats t anod surfac. It was found tat non-qulbrum proprty appars n t rgon wr t tmpratur dcrass blow 10000K and ts rgon as a tcnss of 0.7mm. T tmpratur dffrnc btwn lctron and avy spcs occurs du to t dcras of collson frquncy. Fgur 5 sows t dpndnc of lctron dnsty and collson frquncy btwn lctron and avy spcs nar t anod surfac on axal dstanc from t catod tp. It can b sn tat t lctron dnsty and t collson frquncy dcras wt approac to t anod surfac. T lctron dnsty bcoms 2*10 22 wr t plasma tmpratur dcrass to 10000K. Consquntly t was found tat non-qulbrum proprty 9
Two-Tmpratur Plasma Modlng of Argon Gas Tungstn Arcs appars blow t collson frquncy of 2*10 11 corrspondng to ts lctron dnsty. Fgur 6 sows t dpndnc of at ntnsty onto t anod on radal dstanc from t arc axs. Eac componnt of at ntnsty calculatd by quaton (17), tat du to trmal conducton and total at ntnsty wc s sum of ac componnt ar prsntd. It was found tat t at ntnsty du to lctron absorpton onto t anod (lctron condnsaton and lctron ntalpy) s sgnfcant compard wt tat of trmal conducton and tat of on rcombnaton s nglgbly small. Fg. 4 Dpndnc of tmpratur of lctron and avy spcs on axal dstanc from t catod tp. Fg. 2 Two-dmnsonal tmpratur dstrbuton of avy spcs and lctrods. Fg. 5 Dpndnc lctron dnsty and collson frquncy on axal dstanc from t catod tp. Fg. 6 Dpndnc of at ntnsty at t anod surfac on radal dstanc from t arc axs. Fg. 3 Two-dmnsonal tmpratur dstrbuton of lctron and lctrods. 10
Transactons of JWRI, Vol. 37 (2008), No. 1 4. Conclusons T man conclusons ar summarzd as follows: (1) T smulaton rsult of t max. plasma tmpratur of 15000K approxmatly agrs wt t xprmntal rsult. (2) T LTE assumpton s vald nar t arc axs xcpt for t rgon nar t lctrods. (3) T non-qulbrum proprty appars blow t collson frquncy of 2*10 11 corrspondng to t plasma tmpratur of 10000K. T tcnss of ts rgon bcoms approxmatly 0.7mm nar t anod surfac. (4) T at ntnsty onto t anod surfac du to lctron absorpton onto t anod (lctron condnsaton and lctron ntalpy) s sgnfcant compard wt tat of trmal conducton and tat of on rcombnaton s nglgbly small. Rfrncs 1) Uso M, t.al.; IEEE Trans. P. S., 2004; 32: p 108-117. 2) Inaba T, t.al.; IEEE Trans. D. E. I., 2000; 7: p 684-692. 3) Tanaa M t al.; Vacuum, 2004; 73: p381-389. 4) Tanaa Y; J. Pys. D: Appl. Pys,2004; 37: p1190-1205. 5) Watanab T and Sugmoto N; Tn Sold Flms, 2004; 20: p201-208. 6) Hsu KC and Pfndr E : J. Appl. Pys, 1983; 54: p 4359-4366. 7) Hadar J; J. Pys. D: Appl. Pys., 1999; 32: p 263-272. 8) Jnsta J and Hbrln JVR; IEEE Trans. P. S., 1997; 25: p883-890. 9) Tasro S, t.al.; ISPC17, 2005; 74: p205-206. 10) Tanaa M, t.al.; Plasma Cm. Plasma Procss, 2003; 23: p585-606. 11) Patanr SV ; Numrcal Hat Transfr and Flud Flow, Hmspr Publsng Corporaton, 1980. 12) Pfndr E; Gasous Elctroncs, Acadmc Prss, 1978. 13) Hsu KC, t.al.; J. Appl. Pys., 1983; 54: p 1293-1301. 11