行政院國家科學委員會補助專題研究計畫簡易報告

行政院國家科學委員會補助專題研究計畫簡易報告 噴射式大氣電漿源之模擬研究 -2D 與 -3D 平行化流體模型 ( 一年 ) Dvlopmnt and Applications of Parallllizd 2D and 3D Fluid Modling Cods for Atmosphric Prssur Plasma Jt (1 Yars) 計畫類別 : 個別型計畫 整合型計畫計畫編號 :96-NU-7-9-1- 執行期間 :96 年 1 月 1 日至 96 年 12 月 31 日 計畫主持人 : 吳宗信 共同主持人 : 黃楓南國立中央大學數學系 計畫參與人員 : 周欣芸胡孟樺國立交通大學機械工程學系 本成果報告包括以下應繳交之附件 : 赴國外出差或研習心得報告一份 赴大陸地區出差或研習心得報告一份 出席國際學術會議心得報告及發表之論文各一份 國際合作研究計畫國外研究報告書一份 執行單位 : 國立交通大學機械工程學系 中華民國 96 年 1 月 1

行政院國家科學委員會專題研究計畫期末報告噴射式大氣電漿源之模擬研究 -2D 與 -3D 平行化流體模型 ( 一年 ) Dvlopmnt and Applications of Parallllizd 2D and 3D Fluid Modling Cods for Atmosphric Prssur Plasma Jt (1 Yars) 計畫編號 :96-NU-7-9-1- 執行期限 :96 年 1 月 1 日至 96 年 12 月 31 日主持人 : 吳宗信國立交通大學機械工程學系共同主持人 : 黃楓南國立中央大學數學系計畫參與人員 : 周欣芸胡孟樺國立交通大學機械工程學系 中文摘要 噴射式大氣電漿源的特色為電漿可以從電極噴出, 電漿面極小, 能量集中, 處理效率高, 沒有 arcing 問題, 應用效果是大氣電漿中最好的, 在工業的應用包括局部清潔及處理用途 因此, 對噴射式大氣電漿源 (APPJ) 有基礎的認識, 在發展設備上是很重要的 在本研究計畫中我門計劃使用流體模式模擬噴射式大氣電漿, 我門使用適於處理複雜幾何與計算平行化的有限元素法 (FEM) 離散求解 APPJ 的物理方程式 在提出的三年計畫中, 在第一階段中我們首先使用 Stabilizd FEM 在 Fluid Modling 的架構下發展一套程式用以模擬二維 / 軸對稱座標系統, Fluid Modling 考慮帶電粒子的漂移 - 擴散傳輸, 使用 Stabilizd FEM 處理如鞘層區電漿參數變化較劇烈的地方 程式中重要假設包含利用 driftdiffusion approximation 求解帶電粒子的動量通量 所有的模擬程式將被平行化在 PETSc 的 AO 資料結構下 此後, 程式可以再任何平行化的機器上執行例如 PC clustrs 關鍵字 : 二維, 噴射式大氣電漿 (APPJ),Stabilizd FEM, 流體模型 Abstract Atmosphric Prssur Plasma Jt (APPJ) rprsnts on of th futur important lowtmpratur plasmas usd in modrn matrials procssing. Its importanc stms from its wid applications, such as surfac claning, dry tching, sputtring and photorsistor stripping, in addition to its low cost as compard to low-prssur plasmas. Thus, fundamntal undrstanding of th plasma physics within APPJ is important in dvloping this kind of procssing quipmnt. In this proposd rsarch projct, w intnd to apply th fluid modling tchniqu to simulat th atmosphric prssur plasma jt (APPJ), in which th INER is currntly intrstd. W shall mploy th finit lmnt mthod (FEM) for all th PDEs involvd in dscribing th APPJ sinc it is mor flxibl both in trating complicatd gomtry and paralll implmntation. Stabilizd FEM shall b usd to discrtiz th continuity quation for all chargd spcis considring th larg drift trm in th shath, Considring th flat or round APPJ, in which INER is intrstd, w will first dvlop a simulation cod for 2D/axisymmtric coordinat systm in th first phas and thn xtnd it into a 3D vrsion in latr phass to dal with mor ralistic oprating conditions. All simulation cods will b paralllizd undr th AO (Application Ordring) framwork of PETSc. In this proposd on-yar projct, w hav dvlopd and vrifid a paralllizd 1D and 2D/axisymmtric fluid modling cod using stabilizd FEM. Not stabilizd FEM is usd to trat plasma proprtis with larg gradint, such as in th shath. Important assumptions includ drift-diffusion approximation for th momntum fluxs of chargs spcis and cross sctions for valuating transport cofficints. Kywords: two-dimnisional, Atmosphric Prssur Plasma Jt, Stabilizd FEM, Fluid Modling. I. INTRODUCTION For th past two dcads, studis in lowtmpratur (non-thrmal) atmosphricprssur (AP) non-quilibrium plasmas hav attractd trmndous attntion du to thir numrous mrging applications, including lctrostatic prcipitation, ozon production, lctromagntic rflction, absorption, and phas shifts, plasma mitigation of th shock wavs in suprsonic/hyprsonic flows, 2

surfac tratmnt, thin-film dposition, chmical dcontamination, biological dcontamination and mdical applications, to nam a fw[bckr t al., 24]. Ths xcitd applications would not hav bn possibl wr it not basd on th xtnsiv basic rsarch on th gnration and sustainmnt of rlativ larg volums of non-thrmal ( cold ) plasmas at atmosphric prssur and rlativly small input powr. Thus, fundamntal undrstanding of th AP plasmas using various kinds of gass mixturs undr diffrnt typs of powr sourcs bcoms vry important in optimizing th gnration of cold plasma at lowr cost. Svral distinct faturs hav mad th non-thrmal AP plasmas vry appaling in practical applications. First, bing thrmally non-quilibrium in ths plasmas, scond, th us of atmosphric prssur incrass th opportunity of gnrating chmically activ spcis (radicals) du to thr-body procsss, such as xcitd dimmrs and trimrs. Third, th us of atmosphric prssur gratly rducs th oprational cost without th nd of using sald chambr, vacuum pumps, which is vry xpnsiv in procurmnt and maintnanc. Howvr, gnrating plasma at atmosphric prssur oftn rquirs vry larg applid voltag which is vry powr-consuming. Thus, how to ffctivly rduc th lvl of powr input bcoms a critical issu. In gnral thr ar svral typs of AP plasma sourcs. Thy includ DC and lowfrquncy plasmas, and high-frquncy AP plasmas using radio frquncy, microwav or rspctivly pulsd powr sourcs [Bckr t al., 24]. Optimal us of various kinds of AP plasmas rquirs th fundamntal undrstanding of fluid mchanics, hat transfr, plasma chmistry, plasma kintics and intraction btwn chargd particls and lctromagntic fild. Du to its intrinsic complxity, most rsarchs ar still basd on xprimntal obsrvations, xpct Kushnrs s group, which is ncssary in fficintly optimizing th prformanc in practical applications. In Kushnr s group, both finit diffrnc and finit lmnt mthods hav bn usd to solv fluid modling quations [http://uiglz.c.iastat.du/groupmmbrs /KushnrMJ.html]. Howvr, thr ar thr important numrical issus that rmain unsolvd in plasma fluid modling tchniqu. First, th modl can b solvd by Nwton-Krylov-Schwarz typ schm using th inxact Nwton itrativ schm [Hwang, 25]. Scond, no thrdimnsional vrsion of plasma fluid modling cod is availabl. Third, thr is no scalabl paralllizd vrsion of plasma fluid modling cod. Basd on th abov obsrvations, thr is a nd to dvlop a plasma fluid modling cod which includs th following faturs: paralll procssing, fully coupld axisymmtric/thrdimnsional quation solvr and flxibility in trating complx gomtry of objcts. II. BASIC GOVERNING EQUATIONS In this sction, w will dscrib th govrning quations, prliminary FEM discrtization, Nwton-Krylov-Swartz (NKS) schm in turn. In addition, PETSc library which is th backbon of th proposd numrical solvr will also b introducd brifly for compltnss. Govrning Equations W considr an atmosphric plasma systm consisting of lctron and ions. In th following, variabls with subscript, p rprsnt proprtis for lctron and ion rspctivly. Not ths cofficints for chargd spcis ar all functions of E/P alon, which is th wll known local-fild approximation (LFA). In addition, all momntum fluxs in th continuity quations of chargd spcis ar modld basd on drift-diffusion approximation. W assum that thrmal stat of th lctrons can b dscribd by a singl lctron tmpratur T, whil th havy particls, including ions ar in thrmal quilibrium with a singl tmpratur T. In what follows, w will dscrib all consrvation quations for chargd and nutral spcis along with th fild quation (Poisson s quation) dscribing th variation of lctric fild. 3

Continuity quations Continuity quation for ion spcis p, ithr positiv or ngativ charg, can b writtn as, p + Γ p = S p (1 ) whr Γ = µ ne D n (1a) p p p p p Sp = Sp( n, ni, αiz) (1b) Not th form of sourc trm as shown in q. (1b) can b modifid or addd according to th modld ractions dscribing how ion spcis p is gnratd or dstroyd. Boundary conditions at walls ar applid considring thrmal diffusion flux and drift diffusion flux. Continuity quation for lctron spcis can b writtn as, + Γ = S (2 ) whr Γ = µ ne D n (2a) S = S ( n, n, α ) (2b) i iz Similar to S p, th form of S can also b modifid or addd according to th modld ractions which gnrat or dstroy th lctron. Boundary conditions at walls ar applid considring thrmal diffusion flux and drift diffusion flux. Elctron nrgy dnsity quation In this proposd rsarch lctron nrgy dnsity quation is solvd. Elctron kintic nrgy, dfind as 3 ε = K T, can b writtn as B 3 5 5 ( K nt) + ( K T K nd T) = E Γ S I 2 2 2 2 B B B iz (3) Not I iz is th ionization nrgy of th nutral spcis. On th right-hand sid of th nrgy quation, th trms in turn rprsnt th Ohmic hating, th loss of lctron nrgy du to ionization and nrgy transfr to havy particls du to lastic collisions, rspctivly. Of cours, nrgy loss du to xcitation can b modld by adding a sourc trm to th right-hand sid of nrgy quation. Howvr, it can b absorbd into th first trm of th right-hand sid of nrgy quation for simplicity as dmonstratd in Liau t al., [23] for argon AP plasma. Boundary conditions for lctron nrgy at walls ar applid considring drift and thrmal inducd nrgy transport. Fild quation Thr ar two fild quations that ar rquird th proposd AP plasma fluid modling cod, including Poisson s quation and Maxwll s quation. In th prsnt projct, at last th Poisson s quation for lctrostatics is solvd. Poisson s quation for lctrostatics du to boundary conditions and distribution of chargd dnsity can b writtn as, ( ε E) = ( np n) (4) ε pos. ions ng. ions E = ϕ (5) Not ϕ is th instantanous lctrostatic potntial. III. NUMBERICAL METHOD Continuity quations Sinc all continuity quations for chargd particls ar similar in format, only FEM formulation for th lctron spcis is dmonstratd hr for brvity. In this proposd rsarch, w mploy Galrkin- Last Squar (or stabilizd) FEM [Dona and Hurta, 23] for discrtizing all unstady convction-diffusion quations. Considr q. (2) with th mass flux rplacd by q. (2a) as, µ E n D n = S (6) W dfin th rsidual of th continuity quation as, R µ E n D n S (7) Th form of Galrkin is, 4

ω R G = whr ω G = (8) u Th form of last-squar is, ω R R Ls = whr ω Ls = (9) ui Finally, w combin th abov two trms by adding thm togthr with a stability paramtr τ multiplying last-squar q. as th following form. ( ωg ω G µ En + D ωg n ωgs) + τω Ls ( µ E n D n ) = ω S + τω S ( ω µ En ω D n ) G Ls Γ G G i (1) Not how th stability paramtr τ dpnds on mobility, diffusity, convctiv spd and grid siz is dscribd in dtail in [Franca and Valntin, 2]. IV. RESULTS AND DISCUSSIONS Initially, w hav conductd a CCP tst cas [Passchir and Godhr, 1993] using Galrkin FEM. Unfortunatly, W find running a cas with 12,5 clls using 32 cpu in INER clustr nds mor than 2 days. It is too tim-consuming to b practical. So w ar currntly including stabilizd FEM to rduc grid siz that will gratly dcras computational tim. W turnd back to simulat a quasi-1d RF (P =.5 torr, V pp = 2 V, f = 13.56MHz, L = 2 cm) cas using Galrkin/last-squar FEM and conductd diffrnt grid tsts to gain th suitabl paramtr. Th tst grids show in Fig. (1) Gap lngth is 2 cm. It is dividd in turn by 4 to 8 grids. Fig. (2) - (4) shows th distribution of lctron numbr dnsity using τ Codina, τ Shakib and τ Franca. Among τ Codina and τ Shakib can b found in [Dona and Hurta, 23]. From th thr figurs, w can find τ Codina prforms bttr in coars grids than τ Franca and τ Shakib. Compltd cod was tstd on a PC-clustr systm with procssors up to 32. Rsults ar summarizd in Tabl 1, which shows that paralll fficincy of ~6% can b obtaind for 32 procssors for th prsnt problm siz. V. CONCLUSIONS AND FUTURE WORKS In th currnt rport, w hav slctd suitablτ for our stabilizd FEM. Important conclusions ar summarizd as follows: 1. Th cas using Galrkin mthod for vry dns msh can convrg proprly, but it taks too much tim to b practical. 2. Tsts including stabilizd trm show that th us of τ Codina in stabilizd FEM prforms th bst.. 3. Paralll fficincy can rach up to ~6% with 32 procssors. W ar now continuing to sarch a propr stabilizd paramtr in 2D axisymmtric cas to incras computational fficincy. VI. REFERENCES 1. Bckr, K. H., Nonquilibrium air plasmas at atmosphric prssur,24. 2. Hwang, F.-N. and Cai.-C., A Paralll nonlinar Additiv Schwarz Prconditiond Inxact Nwton Algorithm for Incomprssibl Navior- Stok Equations, Journal of Computational Physics, Vol. 25, pp. 666-691, 25. 3. Dona, J. and Hutra, Finit Elmnt Mthods for Flow Problms, 23. 4. Kushnr s wbpag, Iowa stat U,http://uiglz.c.iastat.du/GroupM nbrs/kushnrmj.html. 5. Franca, L. P. and Valntin, F., On an improvd usual stabilizd finit lmnt mthod for th advctivractiv-diffusiv quation, Computr mthods in applid mchanics and nginring, pp. 1785-18, 2. 6. Passchir, J. D. P. and Godhr, W. J., A two-dimnsional fluid modl for an argon rf discharg, Journal of applid 5

physics, Vol. 74, pp. 3744-3751, 1993. 2 / 4.5 1 1.5 2 2 / 5 3 2 16 / 2 2 / 2 1 / 2 5 / 2 4 / 2.5 1 1.5 2 2 / 1 N.5 1 1.5 2 2 / 2 1.5 1 1.5 2 Fig. 1 Sktch of grid tsts. N 2 / 8.5 1 1.5 2 2 15 1 16 /2 2 / 2 1 / 2 5 / 2 4 / 2.5 1 1.5 2 Fig. 4 Distribution of N for τ Franca Eff. (ILU(2) / Gmrss) 1 2 4 16 32 1 87.32 92.6 69.93 58.28 % % % % % Tabl 1. Paralll fficincy of th paralllizd FEM cod. (Tst grid siz: 16 x 8 quadrilatral lmnts) 5.5 1 1.5 2 Fig. 2 Distribution of N for τ Codina. 2 15 16 / 2 2 / 2 1 / 2 5 / 2 4 / 2 N 1 5.5 1 1.5 2 Fig. 3 Distribution of N for τ Shakib. 6