Comparison of LES and RANS in numerical simulation of turbulent non-premixed flame under MILD combustion condition

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1 MCS 7 Cha Laguna, Caglar, Sardna, Ialy, Sepember 11-15, 2011 Comparson of LES and RANS n numercal smulaon of urbulen non-premed flame under MILD combuson condon M. Halla and K. Mazaher umars@modares.ac.r Deparmen of Mechancal Engneerng, Tarba Modares Unversy, Tehran, Iran Absrac MILD combuson s a recen developmen n he combuson of hydrocarbon fuels whch promses hgh effcences and low NO emssons. In hs numercal sudy, a urbulen nonpremed CH4+H2 e flame ssung no a ho and dlued co-flow ar s consdered o smulae a moderae and nense low oygen dluon (MILD) combuson regme. Ths flame s relaed o he epermenal seup of Dally e al. [1]. The numercal smulaon s carred ou usng he Parally Srred Reacor (PaSR) combuson model, o descrbe urbulencechemsry neracon, and a smple mechansm o represen he chemcal reacons of Hydrogen/Mehane e flame. In hs arcle he Large Eddy Smulaon mehod (LES) compared wh Reynolds Averaged Naver Socs (RANS) approach n he predcon of flame characerscs. We sudy he effecs of wo urbulence models, Smagornsy and modfed sandard -ε model, as basc models n LES and RANS for smulaon of MILD combuson. Smagornsy model has shown a beer performance, and s able o predc more accurae flame characerscs han modfed sandard -ε model. Inroducon The Moderae or Inense Low-oygen Dluon (MILD) echnology, also called flameless combuson, offers grea advanages n erms of large energy savngs wh very low polluan emssons. From a hsorcal pon of vew, he echnology was frs named Ecess Enhalpy Combuson [2], whle oday s called Hgh Temperaure Ar combuson (HTAC), Flameless Odaon (FLOX) and MILD combuson. In general, he MILD combuson aes place when he emperaure of he reacan mure s hgher han he mure self-gnon emperaure (T nle > Ts) and when he mamum emperaure dfference wh respec o he nle emperaure s lower han he mure self-gnon emperaure [3]. In he MILD regme fuel s med wh a dlued and hghly pre-heaed ar o creae a dsrbued reacon zone wh a reduced pea emperaure. These feaures produce a unform emperaure feld and lower emsson of polluans han convenonal non-premed flame [4]. The condons of elevaed and unform emperaure dsrbuon and low oygen concenraon, lead o slower reacon raes (Damohler number of he order of uny) and enhances he nfluence of molecular dffuson on flame characerscs [4]. The epermenal sudes of MILD combuson provde mporan daa ha can also be used for calbrang numercal smulaons [e.g., 1-3]. Dally [1] epermenally nvesgaed he effec of oygen concenraon n ho coflow n H 2 -CH 4 urbulen non-premed flame under MILD condon. Hs resuls showed ha reducng he oygen mass fracon from 9% o 3% n he ho odan sream resuls n consderable changes o he flame srucure. These changes

2 nclude a pea emperaure drop of up o 400 K and a hreefold drop n OH and CO levels. Chrso and Dally [4, 5] used Reynolds-Averagng Naver-Soes approach o model he flow, composons and emperaure felds. Ther resuls ndcaed he mporance of dffuson effecs n he numercal predcon of MILD combuson. The weaness of he sandard -ε model n predcng round e flames was also repored by Dally e al. [4, 5]. They concluded ha adusng he value of he C ε1 consan n he dsspaon rae equaon (from 1.44 o 1.6) led o a noceable mprovemen n predcon accuracy. They [5] also demonsraed he lmaons of conserved scalar based models (e.g. he ξ/pdf and flamele) under MILD condons and showed ha he eddy dsspaon concep (EDC) performs beer. The EDC model performed reasonably well for flames wh 9% and 6% O2. However he numercal model predcon for 3% O2 was poor. Moreover, her resuls showed ha a 120-mm aal locaon, he model dd no perform well. They suggesed ha he occurrence of nermen localzed flame encon, whch was no predced reasonably by her model, could be he reason of hs poor predcon [4, 5]. I has been shown ha hea release n MILD combuson s conrolled by boh flud moon and chemcal necs [6]. Hence, seems ha he parally srred reacor (PaSR) model can be a good canddae o assess he een of urbulencenecs neracon n MILD combuson. The PaSR combuson model was developed by Golovchev [7] n 2000 o smulae he Desel engnes reacng flow feld. Ths model s an eenson of he Eddy Dsspaon Concep (EDC) ha s capable of usng a dealed necs. Golovchev e al. [8] appled dealed necs and he Parally Srred Reacor concep (PaSR) o descrbe he urbulence/chemsry neracon n Flameless combuson. Hs Smulaon resuls clearly llusraed ha he flame srucure s sgnfcanly affeced by oygen concenraon [8]. Hgh-fdely smulaons of non-premed urbulen combuson regmes requres an accurae descrpon of he fuel and odzer mng ha canno be acheved under seady assumpons (RANS). Large-eddy smulaon (LES) of urbulen combuson has araced more and more aenon. There are dfferen sub-grd-scale (SGS) sress models [9-12] for closurng of flered equaons. The mos popular SGS model s he Smagornsy eddyvscosy model. The am of hs sudy s he evaluaon of LES wh respec o RANS approach n he predcon of flame characerscs n MILD combuson. The Numercal Se-up The numercal model consruced for hs sudy s based on he geomery and dmensons of he epermenal JHC burner used by Dally e al. [1]. The epermenal burner consss of an nsulaed and cooled cenral e (.d. = 4.25 mm) and an annulus (.d. = 82 mm) wh a secondary burner mouned upsream of he e plane. The secondary burner provdes ho combuson producs whch are med wh ar and nrogen va wo sde nles a he boom of he annulus o conrol he O2 levels n he mure. The cold mure of ar and nrogen also assss n coolng he secondary burner. The cold mure of ar and nrogen s composed of 23% O2 and 77% N2 (mass bass). Mean nle veloces of ho co-flow and wnd unnel ar are fed on 3.2 m/s and mean nle velocy n fuel e s 58 m/s. Table 1 lss he epermenal condons ha are modelled n hs sudy. The fuel e mure consss of 80% mehane and 20% hydrogen (mass bass). The compuaonal doman sared a he e plane of he burner. I eended 400 mm downsream n he aal drecon and 170 mm n radal drecon. An unsrucured mesh was generaed o dscreze he compuaonal doman. The mesh ha s used n our smulaons nvolved cells. Fg. 1 shows he 3-demensonal geomery of he combuson chamber.

3 Table 1. Operang condons for cases suded n [1]. Odan coflow T fuel T ho co-flow T shroud ar Y O2 % Y CO2 % Y N2 % Y H2O % Fgure 1. 3D vew of he compuaonal doman and boundary condons. The numercal smulaon of he flow feld ncludes he soluon of he governng equaons whch consss of connuy, momenum, energy, and speces conservaon whch are averaged and flered by wo mehods (RANS and LES approaches). For hs sudy, C++ lbrary Open Foam was ulzed for numercal soluon. Ths man flow solver n OpenFoam s based on he PISO algorhm [13]. Boundary condons a upsream are se as velocy profles, nle emperaure, speces, and mass fracons. The velocy profles a he nles are assumed o be unform. In hs paper, a smple reacon mechansm, one sep for CH 4 and one sep for H 2, s used for mure of CH 4 /H 2 whch s shown as follows [14, 15], CH 4 + 2O 2 => CO 2 H O 2 => H 2 O The LES Governng Equaons and SGS Model The flered connuy, momenum, speces and energy equaons for LES are epressed as [16, 17], ρ + ( ρu ) = 0. (1) ρy ( Y u Y ) ( u Y u (2) + ρ = Y ) + = 1,..., N. µ ρ ω ρu ( p u u ) ( ( u u u u (3) + ρ + = τ ρ ) + ρg. ρh ( Dp µ h ) ( (4) + ρu = + u h u h ). Pr h ρ D In Eq. 2, he hermal dffuson (Sore effec) and he pressure dffuson are negleced. In hs wor s assumed ha Sc (Schmd number) s uny whch means ha he effecve spece dffusvy s equal o he vscosy. In Eq. 4, h, he enhalpy consss of sensble enhalpy and enhalpy of formaon. Moreover, he resuls of Chrso and Dally [4, 5] demonsraed ha for

4 he JHC confguraon, hermal radaon dd no have noceable effec on he resuls; so, he hermal radaon s gnored n hs sudy. In addon, s assumed ha Lews number s equal o uny. Generally, n he LES equaons, he sub-grd-scale sress τ s defned by, τ = ρ ( u u u u ). (5) For he SGS sress, he Smagornsy models s adoped, whch gves [16, 17], δ 1 u u τ τ 2µ S, S = SGS = +, µ SGS = ρc, τ = 2ρ. 3 2 (6) Where Δ s he fler sze compued from = 3 y z ; also, s compued by, C ρ S τ + ρ e 3/ 2 = 0. (7) In he above equaons, C and C e are 0.02 and 1.048, respecvely. The sub-grd scale mass flu and hea flu are closed by graden modelng as, ( µ SGS Y ρ u Y u Y ) =, ( µ SGS h ρ u h u h ) =. Sc Where Sc and Pr are model consans, Sc = Pr = 1.0. The RANS Governng Equaons and Sandard -ε Model Balance equaons for he mean quanes n RANS smulaons are obaned by averagng he nsananeous governng equaons. Ths averagng procedure nroduces unclosed quanes ha have o be modelled by urbulence models. Usng he Favre averages formalsm, he averaged balance equaons become [16, 17]: Pr (8) ρ + ( ρu ) = 0. ρu ( p + ρuu ) + = ( τ ρu u ) + ρg. ρy Y + ρuy = u Y + µ ρ ω ρh ( Dp µ h + ρu ) = + u h. Pr h ρ D ( ) 1,..., N. = (9) Closure for he Reynolds sress erms n he governmen equaons were acheved usng he ε urbulence model. Dally [5] showed ha he sandard -ε model wh a modfed consan C ε1 from 1.44 o 1.6 n he dsspaon rae equaon s he bes model among dfferen -ε models for numercal smulaon of MILD combuson. Therefore, s used as he RANS

5 model n hs sudy. In Eq. 9, assumpon, ρ u Y and ρ u h are closed usng a classcal graden µ Y µ h ρ u Y =, ρ u h =. Sc Pr I s also assumed ha Sc (urbulen Schmd number), and Pr (urbulen Prandl number) are uny. The urbulen vscosy s esmaed as: (10) 2 µ = ρcµ. ε (11) Followng he urbulence vscosy model proposed by Boussnesq, he urbulen Reynolds sresses ρ u are descrbed usng he vscous ensor τ epresson ha s obaned for u Newonan fluds. u u 2 u 2 ρ uu ρ uu µ = = + δ + ρ. 3 3 (12) Combuson Model The Parally Srred Reacor (PaSR) model s used n hs wor as he combuson model. In he PaSR approach, a compuaonal cell s spl no wo dfferen zones: n one zone all reacons occur, whle n he oher one here are no reacons (Fg. 2). Therefore, he composon changes due o mass echange wh he reacng zone. In addon, he reacon zone s reaed as a perfecly srred reacor (PSR), n whch all reacans are assumed o be perfecly med wh each oher. Ths allows us o neglec any flucuaons when calculang he chemcal source erms. Three average concenraons are presened n he reacor, he mean mure concenraon of he feed c 0, he mure concenraon n he reacon zone c, he mure concenraon a he e of he reacor c 1. Fgure 3. Concepual dagram of PaSR reacor (he reacon zone s paned) [18]. The whole combuson process could be regarded as wo processes. The frs s he nal concenraon n he reacon zone changes from c 0 o c as reacs; he second s he reacon mure c s med wh he no reacon mure c 0 by urbulence, he resuls n he averaged concenraon c 1. The reacon rae of hs compuaonal cell s deermned by he fracon of he reacor n hs cell. I seems que clear ha should be proporonal o he rao of he

6 chemcal reacon me τ c o he oal converson me n he reacor,.e. he sum of he mcromng me τ m and reacon me τ c [8, 18, 19], κ τ c = τ + τ c m. (13) The mcro-mng me τ m characerzes he echange process beween reacon mure and no reacon mure. In hs paper mcro-mng me was obaned from he -ε equaon, τ m =C m (μμ + μμμμ)/ρρɛ, he model consan C m was se o 1. The reacon me was derved from he lamnar reacon rae. Thus, he overall reacon rae ω and he homogenous reacon rae ω of hs compuaonal cell, whch represens he reacon rae of he speces accordng o he used nec mechansm, have he followng relaonshp, c 1 0 c = ω = ω. (14) d Resuls and Dscussons Fg. 2 llusraes he nsananeous emperaure and CH4 mole fracon maps whch are obaned usng he LES mehod. In hs fgure, s seen ha, far from he e e, he urbulence s much hgher. Ths fac, ncreasng urbulence, s also depced n Fg. 3, where he flucuaon of H2O concenraon s shown along he flame. CH 4 O 2 Temperaure Fgure 2. Predced nsananeous emperaure and speces profles on he cenre plane of he combuson Chamber usng LES. Fgure 3. Profles for nsananeous and Mean H 2 O, and H 2 O flucuaon on he cenre plane of he combuson Chamber usng LES.

7 The conour of CH 4 n Fg. 2 shows ha he fuel vore sze s ncreased when movng farher from he e e. The large fuel vorees cause he fuel m wh oygen ha comes from wnd unnel (where O 2 mass fracon s 23%). Ths condon s no suable for MILD combuson. In far dsances from he fuel nle, he flame emperaure s much hgher han he emperaure near he nle. One reason for hs emperaure rse s he appearance of hghly urbulen and wrnled flame, far from he nozzle. The ncrease of flame surface and urbulence nensy promoes he mng rae of fuel wh hgh-oygenzed odzer, whch, n urns, nensfes he burnng rae and he energy release. Fg. 4 shows he emperaure conours n dfferen locaons along he e as. Par (a) n Fg. 4 corresponds o a smulaon usng LES, whle par (b) n Fg. 4 shows he emperaure conours obaned ulzng he RANS approach. I s observed ha a symmerc flame s obaned by he RANS smulaon of he MILD flame (see Fg. 4-b). On he oher hand, conours of par (a) reveals ha he LES modelng predcs an asymmerc flame far from he nle. There has been a large dscrepancy beween he MILD flame emperaure obaned usng he -ε model wh he epermenal measuremen of Dally (for eample n 7, 13). The pas smulaons no only used (a he bes) he -ε model, hey were based on wodmensonal a-symmerc geomery, o smulae he Dally epermen symmerc seup. The presen LES modelng, ha s n essence a hree dmensonal approach, reveals ha he rue MILD flame feld n Dally seup s a hree-dmensonal phenomenon. Ths dfference can be a reason behnd he above menoned emperaure dscrepancy. z=30mm z=90mm z=30mm z=90mm z=120mm z=180mm z=120mm z=180mm a) Insananeous emperaure conour usng LES. b) Temperaure conour usng -ɛ mehod. Fgure 4. Temperaure conour n dfferen locaons. To furher clarfy hs fac, he radal emperaure profle nsde he flame, n aal locaon 30 mm from he fuel nozzle, s shown n Fg. 5. I s observed ha he emperaure profle predced by LES modelng s much closer o he epermenal values han he daa obaned by he -ε model.

8 Z=30mm Z=120mm Fgure 5. Comparson of radal dsrbuon of emperaure profle obaned from LES and - ε mehods wh epermenal resuls[1]. There s sll some dfference beween he LES predcon wh epermenal emperaure. Epermenal value of mamum emperaure n aal locaon z=30 mm s 1700 Kelvn whle he mamum emperaure predced by he LES echnque s 1900 Kelvn (and 2270elvn by he -ε mehod). Moreover, far from he nozzle e (z=120mm), he LES predcs emperaure and speces beer han he RANS approach. The mamum emperaure predced by he LES s 2200 Kelvn whle he RANS mehod predcs appromaely 2500 Kelvn (epermenal value of mamum emperaure a z=120 mm s 1700 Kelvn.) Ths dfference s arbued o he presen smulaons Knec modelng. Due o very hgh compuaonal cos of LES modelng, a smple wo-sep nec s used n hs sudy. I s predced ha he dfference beween epermenal daa and he smulaon predcon wll be furher reduced f a beer nec model s used. Concluson In hs wor, a numercal sudy of JHC flame of Dally has been performed. The resuls show ha he accuracy of numercal soluon hghly depends on he urbulen model. I s found ha he LES modelng predc he characerscs of MILD combuson much beer han he RANS approach. I s shown ha he a-symmerc assumpon of MILD flame feld n Dally epermenal seup s no correc far from he e e. The LES modelng, unle he RANS mehod, predcs an asymmerc MILD flame. The dfference n he predcon of he flame opology s suggesed as one of he reason of dfferen predcons of wo urbulence modelng approaches.

9 Nomenclaure ρ u g p Y h T c τ μ Sc ω Pr μ SGS μ Δ Pr Sc ɛ κ S densy velocy n -drecon gravy pressure mass fracon of speces enhalpy emperaure Concenraon for speces vscous ensor dynamc vscosy Schmd number for speces mass reacon rae of speces per un volume Prandl number subgrd scale vscosy he urbulen vscosy fler sze urbulen Prandl number urbulen Schmd number for speces urbulen nec energy nec energy dsspaon rae reacve fracon of speces Sran rae References [1]. Dally, B.B., Karres, A.N., Barlow, R.S., Srucure of Turbulen Non-Premed Je Flameless n a Dlued Ho Coflow, Proc. Comb. Ins. 29: (2002). [2]. Wunnng, J.G., Flameless combuson n hermal process echnology, 2nd Inernaonal Semnar on Hgh Temperaure Combuson, Socholm, Sweden, [3]. Cavalere, A., Joannon, M.D., MILD Combuson, Progress n Energy and Combuson Scence, 30: , [4]. Chrso, F.C., Dally, B.B., Applcaon of Transpor PDF Approach for Modelng MILD Combuson, 15 h Ausralasan Flud Mechancs Conference, Sydney, Ausrala, [5]. Chrso, F.C., Dally, B.B., Modelng Turbulen Reacng Jes Issung no a Ho and Dlued Coflow, Combuson and Flame 142: (2005). [6]. Galle, C., Parene, A., Togno, L., Numercal and epermenal nvesgaon of a mld combuson burner, Combuson and Flame 151(4): (2007). [7]. Golovchev, V.I., Nordn, N., Jarnc, R., Choma, J., 3-D Desel Spray Smulaons Usng a New Dealed Chemsry Turbulen Combuson Model, CEC/SAE Sprng Fuels & Lubrcans Meeng & Eposon, Pars, FRANC, [8]. Golovchec, V.I., Choma, J., Numercal Modelng of hgh emperaure ar Flameless combuson, he 4 h nernaonal symposum on hgh emperaure ar combuson and gasfcaon, Rome, Ialy, [9]. Zhou, L.X., Hu, L.Y., Wang, F., Large-eddy smulaon of urbulen combuson usng dfferen combuson models, Fuel 87: (2008). [10]. Mahesh, K., Consannescu, G., Ape, S., Iaccarno, G., Ham, F., Mon, P., Large-Eddy Smulaon of Reacng Turbulen Flows n Comple Geomeres, Journal of Appled Mechancs 73: (2006). [11]. Fureby, C., Tabor, G., Weller, H.G., Gosman, A.D., A comparave sudy of subgrd scale models n homogeneous soropc urbulence, Physcs of Fluds 9: (1997).

10 [12]. Fureby, C., On subgrd scale modelng n large eddy smulaons of compressble flud flow, Physcs of Fluds 8: (1996). [13]. OpenFOAM, OpenFoam user gude, verson1.5, 9 h Edon, [14]. Turns, S.R., An Inroducon o Combuson, second ed. McGraw Hll, [15]. Wesbroo, C., Drye, F., Smplfed Reacon Mechansms for he Odaon of Hydrocarbons Fuels n Flames, Combuson Scence and Technology, 27: 31-43(1981). [16]. Pones, T., Veynane, D., Theorecal and Numercal Combuson, Second Edon, Edwards, [17].hp://foam.sourceforge.ne/doc/Doygen/hml/classFoam_1_1compressble_1_1urbulen cemodel.hml. [18]. Hua, W., Yong-chang, L., Mng-ru, W., Yu-sheng, Z., Muldmensonal modelng of Dmehyl Eher (DME) spray combuson n DI desel engne, Journal of Zheang Unversy SCIENCE, 4: (2005). [19]. D Errco, G., Eorre, D., Lucchn, T., Comparson of Combuson and Polluan Emsson Models for Dl Desel Engnes, Inernaonal conference on nernal combuson engne, Napol, Ialy, 2007.