Development of G-Equation Combustion Model for Direct Injection SI Engine Simulations

Transcription

1 Deveopmen of G-Eqaon Comon Mode for Drec Injecon SI Engne Smaon Zhchao Tan and Rof D. Rez Engne Reearch Cener, Unvery of Wconn-Madon 5 Engneerng Drve, Madon, WI 5376, USA Arac An mproved par gnon mode ha een deveoped and mpemened no he KIVA-3V code. In h mode, he par gnon erne growh raced y Lagrangan parce marer. The effec of ren fow and par dcharge energy on he erne growh are condered. Afer he gnon erne ze exceed a crca ze reaed o he negra ren engh cae of he fow, he ren fame condered o e fy deveoped. A G-eqaon mode ed o rac he mean ren fame evoon. By gnorng he deaed ren fame rh rcre, fne nmerca reoon no reqred, h mang he mode ae for e n mdmenona maon of SI engne. Comned wh a characerc me cae comon mode, he mode were ed o mae he gnon and comon procee of a ma marne DISI wo-roe engne ha feare wo-par pg, where he rpe fame rcre m e condered. The evoon of he wo par erne and ren fame arng from he wo par pg are modeed. Good agreemen wh meared cynder prere wa ao oaned Inrodcon The comon n par gnon engne naed y an eecrc dcharge from he par pg. The gnon proce can e decred y hree cceve phae readown, arc and gow dcharge [Heywood, 988]. The readown phae away precede he arc and gow dcharge. Drng h phae, an eecrcay condcve comn creaed eween he par pg eecrode, where he emperare and prere hgh. Then a hoc wave creaed ha propagae away from he pg. The draon of he na readown phae very hor (~n) wh hgh-energy ranfer effcency eween he eecrca energy pped and he pama (ao 94%). Drng he eary age ( o 5µ afer he readown) of he gnon proce, he pama erne expand voeny and he ma and energy ranfer procee are mch domnaed y he prere wave and he chemca reacon conre e o he erne growh. Seqeny, he conron of chemca reacon ecome gnfcan [Kravch e a., 995]. Ahogh he gnon proce mporan, no pracca o reove he proce n dea n engne CFD maon, ecae he ypca grd-ze and me ep ed arger han ha needed o decre h eary age of gnon precey. Th, a reavey mpe -grd cae mode needed o predc he gnon proce n 3-D engne cacaon. The comon n DISI engne can ae pace n premxed mxre condon (eary njecon operang mode) or n paray premxed (rafed) mxre condon (ae njecon operang mode). In he ae njecon mode, y conrong he pray and ar-fe mxng proce, a rafed mxre can e oaned wh a derae mxre ocaed near he par pg. A h operang condon, he eqvaence rao of he rafed ar-mxre range from rch o ean. The fame propagae wh a hgher peed aong a rface of ochomerc mxre and wh ower peed on he ean and rch de. When he nrned nermedae pece ch a H, H, CO dffe from he rch premxed ranch and mee and mx wh he O and O rvvng from he ean mxre ranch, a dffon fame deveoped. Th, a rcre caed a rpe fame formed, a chemacay hown n Fg.. In he preen dy, h premxed comon modeed ng he G-eqaon mode, whch a nd of famee comon mode, and he Sochomerc premxed fame Lean premxed fame ranch Drope Rch premxed fame ranch Dffon fame O,O,CO,HO,ec Dffon fame CO,H,OH,ec Fgre Srcre of a rpe fame n DISI engne dffon comon ehnd, conroed y rence mxng, modeed y a characerc me cae comon mode. The pray reap maed y LISA [Lnearzed Inay Shee Aomzaon] mode [Schm e a, 999]. The gnon and comon mode are mpemened no he KIVA-3V code, whch ed n h dy. Ignon Mode Deveopmen In he preen wor, he gnon mode ed he ame approach a ha ed n he DPIK mode of Fan e a. [999]. The erne rface poon mared y he parce, and he fame rface deny oaned from he nmer deny of parce n each compaona ce, a hown n Fg.. The gnon erne amed o e pherca drng he na gnon proce. When he erne grow, he parce move oward raday from he par pg eecrode. The gnon parce peed,.e., he erne growh rae, nfenced y he fow rence and ar-

2 fe mxre ochomery. When he erne ecome arge, dfferen gnon erne parce occpy dfferen compaona ce, where he fow ren neny and ar-fe mxre ochomery may e dfferen. Th, he gnon erne can grow a dfferen peed n dfferen drecon. Th, he hape of he gnon erne no pherca any more. Fame Kerne Q h Q p Fgre 3 Thermodynamc yem for he fame erne Fgre Dcree parce gnon erne A hermodynamc yem of an gnon erne ed o anayze he fame erne growh rae. The yem chemacay hown n Fg. 3. The foowng ampon are made n he cacaon:. The cacaon ar a µ afer he readown perod. The gnon erne amed o e pherca. I rad amed o e.5mm a h me, whch oaned from expermen [May e a., 978].. The gnon erne fame very hn and eparae he rned and nrned ga. The erne fame rcre no reoved here. The emperare and a reacve caar jmp from her vae n nrned mxre o he correpondng eqrm vae n he rned ga 3. The gnon erne rface (defned y marer parce poon) ocaed j n fron of he fame, and h, here no hea ranfer eween he erne and nrned ga. 4. The prere nform nde he erne and ode he erne 5. The emperare nde he erne nform. The gnon erne ma-rnng rae m, whch ao he ncreae n he fame erne ma, wren a dm m = = Aeff = A( + p ) (). ama where nrned ga deny, A he fame erne rface area, and he effecve erne growh eff Eecrode where Eecrode peed. The aer he m of ren fame peed hm dv p and he o-caed pama veocy pama, whch re from he par dcharge energy. In addon, ng m = V, he ma-rnng rae can e rewren a dm d( V) dvk d = = + VK = A( + pa ) () ma and V are ga deny and erne vome repecvey, and crp ndcae he erne. Uzng he dea ga aw, d dp dt = (3) p T he foowng eqaon oaned: dvk dt dp = AK ( + pama) + VK ( T p ) (4) Normazng he vome ncreae o he fame erne rface area A, he mean expanon veocy of he fame erne can e oaned a dr V dt dp = ( + pama ) + ( A T p ) (5) Drng he gnon proce, he prere ncreae de o he comon negge. We ao ame he emperare nde he erne paay nform and eqa o he adaac fame emperare of he ar-fe mxre. Th ampon feae ecae he rea down phae, whch characerzed y hgh emperare whn he pama channe, a ony few nanoecond. The majory of he par energy ranferred drng arc and gow dcharge phae. The arc and gow dcharge phae a onger (of he order of mecond) and he emperare whn he erne doe no dffer mch from he adaac fame emperare. Wh hee wo ampon, he erne growh rae mpfed a dr = ( + pam a ) (6) Th eqaon ed o cacae he movemen of he erne parce. The pama veocy pama can e oaned from he energy aance eqaon a foow. Drng he gnon proce, he energy aance for he conro vome rronded y gnon erne rface gven y de dv Q = ( h + Vnrned ) m + p( ) (7) where Q he ne hea ranfer rae o he erne, whch he m of he eecrca energy ranfer rae o he erne, he hea o rae o he eecrode Q and he Q p reacon hea reeae rae Q. Therefore chem Q = Q p + Q chem Q. The V he veocy of h nnred nrned ga whch on he fame erne rface. Compared wh he nrned ga enhapy, h nrned ga veocy can e negeced. Th, Eq. (7) can e rewren a h

3 de dv Q p + Q chem Q h = hm + p( ) (8) de The change n fame erne nerna energy Drng he gnon erne formaon and na deveopmen proce, he rence negra engh cae ypcay mch arger han he erne ze o ha he erne can ony ene he hgh freqency fracon of he rence pecrm. The nfence of erne ze on he rence fame veocy, gven y Herweg e a. de dm = m + U = m + U m (9) [99]: where U he pecfc nerna energy of he rned ga / / r / = I + I ( ) ( exp( )) whn he fame erne. + (8) If he gnon erne hape pherca, he change n / 5/6 vome wor [ exp( / T og )] ( ) dv dr p = 4π r p = 4πr p ( + ) (). pama where he rence neny, he amnar Comnng Eq. (9) and (), Eq. (8) rewren a rnng veocy, he rence negra engh cae (ee Eq. 4). T G a characerc me cae : Q p + Q chem Q h = m + U m hm + () T G = (9) 4 π r p[ ( + pama )] + To accon for he effec of ran on he erne If no par dcharge energy p no he erne and deveopmen, I oaned from no hea o o he eecrode, he energy conervaon / eqaon () ecome F 3/ F I = ( ) () ad 5 rk Q chem = m + Uad m fame hm fame + 4π r p () where F hcne of amnar fame (ee Eq. 9). The where U ad he rned ga pecfc nerna energy a amnar peed emaed y ng he correaon of adaac fame emperare. Meghach and Kec [98], The ma-rnng rae ony reaed o he ren T α α ( φ ) fame veocy, and can e wren a = [ ( φ 3 ) ]( ) 98 () m fame = A (3) p β + β ( φ ) Sracng Eq. () from Eq. (), he eqaon ( ) (. R ).3 ad Q p Q h = m ( ) + U m U ad m where fame φ eqvaence rao, R he reda ga (4) fracon, p he rn ga prere and T he h ( m m fame ) + 4π r p pama emaed oca nrned ga emperare. The oher oaned. parameer are mode conan, whch can e fond n Accordng o he ampon ha he ga emperare Meghach and Kec [98]. whn he erne eqa he adaac fame emperare, U = U. And ao ng ad m m fame Eq. (4) wren a = 4π r pama p Q h = 4 πr ( U h ) pama + 4πr p pama (5) Q Q p Q he ne eecrca energy ranfer rae, whch h aored y he erne and can e emaed y Q Q = Q η (6) p h p eff where η eecrca energy ranfer effcency, whch eff affeced y he pg geomery. Mo of he gnon proce occr n he gow dcharge phae and η eff reavey ow ( 3% ) [Heywood, 988]. Fnay, he pama veocy oaned a pama = 4 π r ( U oa pama Q η (7) eff h ) + p 3 The pama veocy nverey proporona o, and h decreae rapdy a he gnon erne grow. I ar o from a very arge vae ecae of he pama effec, and hen nfence decreae rapdy a he erne ecome arge, whch chemacay dpayed n Fgre 4. I ao can e een ha he ren fame peed,, ncreae wh me, whe he amnar fame peed doe no change mch wh me. The crve ndcae ha he range of rence freqence ened y he erne fame ecome enarged a he erne grow. In he dervaon of Eq. (7), we amed he hape of fame erne pherca. When he erne ecome arge, hape may e changed ecae he ren fame peed for dfferen erne parce may e dfferen. B Eq. (7) can e apped n h aon. The erne amed o grow arng from a phere wh rad of.5 mm. Ony when he erne ze gger han he compaona meh ze (ay -4mm), can r

4 he erne change o oher hape. A h me, he peed very ma compared o he ren fame pama peed any more. veocy (cm/). In h cae, he pama effec no mporan 4 3 The pece deny change are cacaed y d = C w ( Y Y ) () where he fame rface deny whn a parcar ce, N p, ce 4 r π (3) = N p, o Vce Here he nmer of gnon parce n he N p, ce pama + pama Cran Ange (ATDC) Fgre 4 Hory of pama veocy and ren fame peed n a premxed SI engne wh engne peed 6 rev/mn and gnon mng 3 ATDC compaona ce, V he ce vome, he ce oa nmer of gnon parce and Cw a conan choen eqa o o are compee comon nde he gnon erne. and are he ma fracon of Y Y N p, o pece,, n he nrned and rn ga, repecvey, and he nrned ga deny. Seven pece, fe, O, H O, CO, CO, N and H are condered n he cacaon. amed o e he oca and Y nananeo hermodynamc eqrm vae of he ma fracon of pece. Once he gnon erne exceed a crca rad ha reaed o he negra ren engh cae,, of he fow fed,.e.,.5 r C m = Cm. 6 (4) ε he gnon mode wche o he comon mode. Here and ε he rence nec energy and dpaon rae, repecvey, and C a mode conan m e eqa o.. Comon Mode Deveopmen In par gnon engne, he premxed fame, where he chemca reacon ae pace, reavey hn. Th hn fame eparae he nrned and rn ga. In par gnon engne, he ren edde can wrne and ran he fame rface, he nner fame ayer, where he fe conmed and radca are depeed y chanreang reacon, no perred [Sehadr and Peer, 99]. The ren fame can e vewed a eneme of hn reacon-dffon ayer, caed fame, emedded whn a non-reacng ren fow. The advanage of he famee concep ha he cacaon of chemca reacon and ren fow can e decoped. To rac he premxed fame fron evoon, a fed eqaon of he caar Gx (, ) ed, where he fame fron repreened y eve rface Gx (, ) =. Th nerface dvde he fow fed no an nrned regon, G<., and a rn ga regon, G>. [Wam, 985, Peer, ]. In KIVA-3V cacaon, he poon of verce where he veoce are defned are ae o move o facae he appcaon of movng ondary condon (ch a he pon and he vave). Conderng h feare, he eqaon for he mean ocaon of he ren fame fron can e wren a G + ( v f vverex) G = G D M G (5) Here G he Favre mean vae of G, and he mean ocaon of he ren fame fron defned y Gx (, ) =. he nrned ga deny and he ga deny a he mean ocaon of he ren fame. M he mean fame crvare ha can e expreed n erm of he eve e fncon G a (6) M G = ( ) G v f he Favre mean fow veocy a he fame fron and v he veocy of movng verce. D he verex ren dffvy. The ren rnng veocy can e can e evaaed from [Peer, 999] a Da a v Da (7) = a43 Da / where v he rence neny, eqa o ( /3) and a 4 =.78, =. and =. 3 are conan derved from he rence mode. Da = (8) v ' F where he rence negra engh cae and ( λ / c p ) F = (9) ( ) he fame hcne. The hea condcvy, λ, and hea capacy, c p, are evaaed a he nner ayer emperare. 4

5 The amnar rnng veocy,, and he deny evaaed n he nrn ga, a hown n Eq. (). In a ypca mdmenona compaona meh, he average engh of he compaona ce ay o 4mm (f he ze redced frher, he compaon ecome mpraccay expenve). In ome engne, he fame rh hcne of he ame order a he ce ze. Th, he deaed ren fame rh rcre hard o capre ng a reavey coare meh. A new mehod propoed here o cacae he pece deny change n he ce conanng he mean fame fron, vz., d area f ( 4) = ( Y Y ) V ( 4) (3) where and are he ma fracon of pece,, n Y Y he nrned and rn ga, repecvey, and he nrned ga deny. area f (4) he mean fame rface area n a ce 4. Here 4 he KIVA-3V ce ndex nmer [Amden, 997]. A n he gnon mode, even pece, fe, O, H O,CO, CO, N and H are condered n he cacaon. Y amed o e he oca and nananeo hermodynamc eqrm vae of he ma fracon of pece. The nmerca cheme o ove he G eqaon ncde nazaon,g vae pdae, and renazaon. The narrow and oon mehodoogy ao empoyed n he mode [Tan and Rez, 3a]. In h mehod, he mean fame rface area cacaed ng he percng pon of he fame fron wh he ce edge [Tan and Rez, 3a]. Behnd he premxed fame ranche, a dffon fame deveop o conme he exce fe and oxdzer rvvng from he rch and ean premxed fame ranche eparaey. A amnar and ren characerc me cae comon mode [Araham, 985] apped o cacae he converon rae of each pece ehnd he premxed fame ranche. The converon rae of each pece amed o e * d = (3) τ c where he deny of pece, and * he oca and nananeo hermodynamc eqrm vae of he deny of pece. τ he characerc me o acheve c ch eqrm and amed o e he ame for he 7 dfferen pece. Becae he emperare of he ga ehnd he premxed fame ranche aready hgh, he pece converon rae conroed y he ren mxng me τ ony, and τ c can e amed o e eqa o τ, ha τ = τ = ε (3) c cm / where c m =.8. Re and Dcon A ma DISI wo-roe engne, whch ed wdey n marne appcaon, wa nvegaed nce expermena daa avaae [Hda, 998]. The engne ha a fa-op pon and a Chryer-degned hghprere wr-ype njecor ha cenray moned n he domehaped cynder head. The engne pecfcaon and operang condon are ed n Tae. The compng meh hown n Fg. 5. I compred of ao, compaona ce. Two par pg Fgre 5 Compaona meh are ocaed on he oo of he DISI wo-roe engne por and exha por de eparaey (ee Fg. 7). The pg reach no he dome ao mm. Each par pg repreened y ao, parce. De o exence, he ga veocy near he pg redced [Fan, e a. 999.] Tae Engne Specfcaon and Operang Condon Bore (mm) 85.8 Sroe (mm) 67.3 Tre Compreon Rao 7.4 Exha Por Tmng (ºATDC) 95 Boo Por Tmng (ºATDC) 7 Tranfer Por Tmng (ºATDC) 7 Speed (rpm) Injecon Tmng (ºATDC) 8 Ignon Tmng (ºATDC) 334 Fgre 7 how he growh of gnon erne and he fame fron evoon. A dced aove, he gnon erne repreened y marer parce. The fame fron, defned y Gx (, ) =, repreened y gh (yeow) rface n h fgre. Inde he gnon erne, he fe rned and he ga emperare Fgre 6 The ar-fe rao n he engne ymmery pane a cran ange 335 ncreaed. Snce he ar-mxre ochomery on he exha por de (rgh hand de n Fg. 6) more ae o rn, he gnon erne on h de grow faer han he ef gnon erne, a hown n Fg. 7. When he rad of gnon erne ecome arger han a crca ze, he G- eqaon comon mode ar o wor. In h engne 5

6 maon, he mode conan C n Eq. 4 e o.. A ao can e een n Fg. 7, afer he rgh hand de gnon erne wched o he comon mode, he ef de gnon erne growng. The wo eparae fame fron merge o one fame afer hey mee. m e of very fne nmerca meh o predc he gnon proce no needed. The evoon of fy deveoped premxed ren fame raced ng he eve e mehod (G-eqaon). The dffon comon ehnd he premxed fame ranche modeed ng a modfed characerc me cae mode. In pracca engne cacaon, he ze of he compaona ce of he ame order a he hcne of he ren fame rh. I hown ha he deaed ren fame rh rcre can e gnored n he preen dy. The mode wa apped o predc he comon proce n a DISI engne and he re agree we wh avaae expermena cynder prere daa. Acnowedgemen The ahor acnowedge he fnanca ppor of Ford Moor Company. Fgre 7 Evoon of he gnon erne and fame fron (defned y G ( x, ) = repreened y he gh (yeow) rface). Prere (MPa) Meared Predced Cran ange ( o ATDC) Fgre 8 Comparon eween predced and meared cynder prere The predced cynder prere race hown n Fg. 8. The agreemen eween he predced and meared re afyng. Thee mode have ao een apped o he premxed comon maon and rafed comon maon n anoher DISI engne. Thoe re are ao very encoragng [Tan and Rez, 3a, Tan and Rez, 3]. Concon An eqaon o cacae gnon erne growh rae derved n h dy. The erne growh rae hghy nfenced y he par dcharge energy n he eary age of he gnon proce. Afer he erne ecome gger, he effec of fow rence on he erne growh rae ecome apparen. To mae he mode ae o 3-D engne maon, he erne fame rface poon are mared y Lagrangan Maer parce. Even when he gnon erne ze maer han he compaona grd ze, he erne growh can e raced we. Th he Reference. Araham, J., Bracco, F. V. and Rez, R.D, Comon and Fame, Vo.6, 39-3, 985. Amden, A. A.,Lo Aamo Naona La Repor, LA-333-MS, Fan, L., L, G., Han, Z. and Rez, R.D., SAE Paper , Herweg, R. and May, R. R., SAE Paper No Heywood, J. B., Inerna Comon Engne Fndamena; McGraw-H, Hda, Erc, Maer The, Unvery of Wconn- Madon, Kravch, T., Sher, E. and Heywood, J. B., Com. Sc. and Tech., Vo. 8, -3, May, R. and Voge, M.,7 h Sympom (nernaona) on Comon, p.8, he Comon Ine, Prgh, Meghach M., and Kec, J.: Com. Fame Vo. 38: 43-54, 98. Peer, N., Tren Comon, Camrdge Unvery Pre,. Schm,D.P, Noar, I.,Seneca, P.K e a. SAE Paper Sehadr K. and Peer N. Comon and Fame, Vo ,99 3. Wam, F.A, Tren Comon, SIAM, Phadepha, Tan, Z. and Rez R.D., SAE paper 3--7, 3a 5. Tan, Z. and Rez R.D., JSAE paper 3-6, 3 6