NUMERICAL SIMULATION OF A PREMIXED TURBULENT V-SHAPED FLAME

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1 THERMAL SCIENCE, Year 011, Vol. 15, No., pp NUMERICAL SIMULATION OF A PREMIXED TURBULENT V-SHAPED FLAME by Mohamed Issam EL KHAZEN a*, Hmaed BENTICHA a, Francos-Xaver DEMOULIN b, and Abdelmajd JEMNI a a Laboraore d Eudes de Sysèmes Thermques e Energéque, Monasr, Tunsa b Complexe de Recherche Inerprofessonnel en Aérohermochme CNRS, Unversé e INSA de Rouen, Cedex, France Orgnal scenfc paper UDC: 66.76: : DOI: 10.98/TSCI E In hs paper we smulae a urbulen premxed V-shape flame sablzed on a ho wre. The devce used s composed of a vercal combuson chamber where he mehane-ar mxure s conveced upwards wh a mean velocy of 4 m/s. The flow was smulaed runnng Fluen 6.3, whch numercally solved he saonary Favre-averaged mass balance; Naver-Sokes equaons; combuson progress varable, and k-ε equaons on a wo-dmensonal numercal mesh. We model gaseous mxure, gnorng Sore and Dufour effecs and radaon hea ransfer. The progress varable balance equaon was closed usng eddy break up model. The resuls of our smulaons allow us o analyze he nfluence of equvalence rao and he urbulen nensy on he properes of he flame (velocy, flucuaon, progress varable, hckness of flame).ths work gves us an dea on he par whch urbulence can play o decrease he rsks of exncon and nsables caused by he lean premxed combuson. Key words: premxed urbulen combuson, numercal smulaon, V-flame Inroducon The combuson s now one of he major processes o produce energy, wheher s sarng from coal, ol or gas. Combuson nervenes n he felds of ranspor (rocke moor, planes and auomobles), of he elecrcal producon (hermal power saon) or hermal devce (bolers and ndusral furnaces, domesc hearhs ). The growng energy demand of boh local and nernaonal level mples he need o mprove combuson effcency whle preservng he envronmen by reducng polluans emssons. In mos praccal applcaons, combuson akes place whn a urbulen flow where he phenomena of ransfer (mass, energy...) are more nense han n he lamnar regmes. The conrol of urbulen combuson s herefore fundamenal o all curren combuson sysems. Tha s why he urbulen combuson s he subjec of much research whose man concern deermnng he reacon rae, dfferen speeds flames, he sably and exncon crera or pollung emssons. *ncorrespondng auhor; e-mal: elkhazen_mohamedssam@yahoo.fr

2 31 THERMAL SCIENCE, Year 011, Vol. 15, No., pp Lean premxed combuson s a very promsng way o reduce he nrogen oxde polluan emssons. Unforunaely, hs operang mode leads o local exncon, source of unburn resdue and combuson nsables. Many expermenal and numercal sudes are led o he laboraory n order o undersand hese phenomena [1-3]. The effecs of he mxure and urbulence on he premxed flames are suded expermenally by Errard [4], Renou [5], Escude e al. [6], and Degardn [7]. In he oher hand, Bell e al. [8], Hauguel e al. [9], and Robn e al. [10] have presened a numercal work whch s exclusvely neresed n he numercal mehods and her felds of valdes and n he behavour of he flames wh regard, separaely, o he varaon of he flow, he composon and urbulence. In our knowledge here are no more numercal sudes whch rea hese parameers smulaneously. The am of hs work consss of a paramerc sudy of he effecs of he equvalence rao and urbulence nensy on he form and he hckness of a premxed V-shaped flame. Ths sudy s carred ou usng he numercal smulaons wh Fluen [11]. Our smulaons correspond o a real confguraon whch was suded n some expermens a he CORIA laboraory (France) [4-7]. Descrpon of he flow confguraon Fgure 1. Flow confguraon The physcal confguraon used n hs paper s a vercal, wo-dmensonal flow whch allows a paramerc approach of he characerscs of urbulence and composon of gases, n order o sudy he nfluence of each quany on he properes of he flame. The devce used consss of a vercal combuson chamber of 30 mm n lengh and mm secon where he premxure mehane-ar s conveced wh a mean velocy of 4 m/s, fg. 1. A ho wre (dameer equal o 0.8 mm) s placed a 90 mm downsream of he enrances of he gas. A V-shape flame s obaned when a premxed flame s sablzed on a ho wre. In hs case, he combuson s naed by he energy released by he wre; he mos localzed burnng kernel serves o sablze a premxed flame ha develops downsream. In a lamnar flow, he reacon layer propagaes agans he ncomng flud and a premxed V-shape flame s obaned. When he flow s urbulen, he wo wngs of he flame are wrnkled by he flucuaons of he velocy and he V shape of he flame s recovered on mean. Mahemacal model For he smulaons underaken n hs sudy, s necessary o smplfy he governng equaons. We adop a sandard se of assumpons ha are well jusfed for many gaseous combuson sysems and have been used n many prevous sudes. Accordngly, he followng phenomena are negleced n hs sudy: he Sore and Dufour effecs and radaon hea ransfer. The governng equaons used for hs sudy can be wren accordng [1, 13]: he mass equaon can be wren as follows:

3 THERMAL SCIENCE, Year 011, Vol. 15, No., pp he momenum conservaon equaons: ( u ) 0 x (1) uu j u u u p u u x x x x j j j j g () he fnal major equaon compleng he formulaon s he equaon of sae for deal gases: p RT 1 M M Y M ; (3) Turbulen model The Reynolds sress ensor represens correlaons beween flucuang veloces. I s an addonal sress erm due o urbulence. Ths erm s unknown and he number of unknowns n he equaons sysem eqs. (1), (), and (3) became larger han equaon number. So we need a model for uu j o close he equaons sysem. The sandard k-ε (proposed by Launder e al. [14, 15]) s model based on model ranspor equaons for he urbulence knec energy (k) and s dsspaon rae (ε). The equaon for k s derved from he exac equaon, whle he equaon for ε was obaned usng physcal reasonng and bears lle resemblance o s mahemacally exac counerpar. In he dervaon of he k-ε model, he assumpon s ha he flow s fully urbulen, and he effecs of molecular vscosy are neglgble. The urbulence knec energy and s rae of dsspaon are obaned from he followng equaons: k u x x x x j ( uk ) uu j j k j (4) u u ( u ) j ( u ) C1 C j j x x x x k k (5) j j k j xj xj 3 u u u u ; k (6) where C µ = 0.09, C 1 =1.44, C =1.9, ζ ε =1.30, and ζ k =1.00. In hs paper we op for he choce of he sandard k-ε model for s robusness, economy, and reasonable accuracy for a wde range of urbulen flows.

4 314 THERMAL SCIENCE, Year 011, Vol. 15, No., pp Turbulen combuson model Progress varable The progress varable s defned as a normalzed sum of he produc speces, c n n 1 Y Y, eq 1 (7) Relyng on hs defnon we can say ha: c = 0, where he mxure s cool and c = 1, when he mxure s burned, fg.. The value of c s defned as an nal condon, s usually specfed as 0 (unburn) or 1 (burn). Eddy break up model Fgure. Progress vrable To smulae he knec reacon rae of he combuson phenomena, we have consdered he eddy break up mode. Ths model s based on a phenomenologcal analyss of urbulen combuson. The reacon zone s vewed as a collecon of fresh and burn gases pockes. Followng he Kolmogrov cascade, urbulence leads o break down of fresh gases srucures. Accordngly, he mean reacon rae s manly conrolled by he urbulen mxng me. When oxdzer s n excess, he mean reacon rae s expressed as: EBU Y C (8) where Y denoes he fuel mass fracon flucuaons and C EBU s a model consan of he order of uny [16]. The urbulen mxng me, s esmaed from he urbulence knec energy k and s dsspaon rae e accordng o: = k/e, as an approxmaon of he characersc me of he negral lengh scales of urbulen flow feld. The reacon rae may be recas n erms of progress varable, c, as: EBU c C (9) Mass fracon flucuaon Y (or progress varable flucuaon c ) mus be modeled and may be esmaed from a balance equaon. Assumng nfnely hn flame fron, ~c s easly esmaed because c = c: c ( c c) ( c c) c(1 c ) (10) The square roo has been nroduced from dmensonal reasons n eqs. (8) and (9) bu, unforunaely, eqs. (9) and (10) lead o nconssences because he c ~ dervave of,

5 THERMAL SCIENCE, Year 011, Vol. 15, No., pp d /d c, s nfne boh when c 0 and when c 1 (Borgh, 1999, prvae communcaon). Then a correc verson of he eddy break up model, whou he square roo, s used for praccal smulaon: Inal condons CEBU c(1 c) k (11) Table 1 summarzes he urbulence condon n he mddle of he combuson zone and he combuson parameers for he dfferen flames presened n hs paper. Three cases of urbulence and four cases of chemsry condons were nvesgaed n erms of urbulence nensy I = u /U and equvalence rao varaons j. Values of urbulence nensy vary from 4% o 1.5% and he equvalence rao vares from j = 0.55 o 1 for sochomerc case. These nal condons were chosen such a ways o compare hem wh he expermenal resuls realzed n CORIA, [4]. Table 1. Numercal condons for mehane/ar flame correspondng o he dfferen smulaons u /U L 0 [mm] j ρ u ρ b S L [ms 1 ] 4% 3 9% % Numercal smulaon We have smulaed mehane-ar flames sablzed behnd a ho wre n a recangular channel performed n dfferen cases characerzed by dfferen equvalence rao and urbulence nensy. The mean nle velocy was equal o 4 m/s. The resuls were smulaed by runnng Fluen 6.3, whch numercally solved he saonary Favre-averaged mass balance; Naver-Sokes, combuson progress varable, and k-ε equaons on a wo-dmensonal numercal mesh conssng of nonunformly dsrbued nodes n x (axal) and y (ransversal) drecons, respecvely. The nodes were concenraed n he near-feld regon behnd he wre. Resuls and dscusson The mean felds of he progress varable c are presened n fgs. 3 and 4. The generc V-shaped flame s observed. Ths allows verfy ha he smulaons are ndeed saonary n mean. We noced ha he angle of he V-flame, s no only funcon of rae flow bu ncreases wh he equvalen rao and urbulence nensy.

6 316 THERMAL SCIENCE, Year 011, Vol. 15, No., pp Fgure 3. Feld of mean progress varable for urbulence nensy I = 9% and for wo value of equvalence rao, respecvely, j = 1 (a) and j = 0.55 (b) Fgure 4. Feld of mean progress varable for equvalence rao j = 1 and for wo value of urbulence nensy, respecvely, I = 9% (a) and I = 4% (b) Fgure 5 represens he ransverse dsrbuons of mean progress varable for sochomerc flame a urbulence nensy equal o 9%. I shows ha he hckness of he urbulen flame depends on he dsance o he ho wre, whch s perfecly comprehensble; s due o he V-shape of he flame. Bu here are wo oher parameers whch make ncrease he hckness of urbulen flame, fg. 6. Shows us ha hs hckness s maxmum for equvalen rao equal o 1 and becomes ncreasngly low for lean premx. I also ncreases when urbulence becomes ncreasngly mporan, fg. 7. To valdae our numercal resuls, we compared hem wh he expermenal resuls of Erard [4] and we observed a good agreemen concernng he profles of he progress varable for dfferen values he rchness, fg. 6.

7 THERMAL SCIENCE, Year 011, Vol. 15, No., pp Fgure 5. Transverse dsrbuons of mean progress varable for equvalence rao j = 1 and for urbulence nensy I = 9% Fgure 6. Progress varable a x = m for urbulence nensy I = 9% Fgure 7. Transverse dsrbuons of mean progress varable for equvalence rao j = 1 a x = m Fgure 8. Axal dsrbuons of mean velocy jus afer he wre for urbulence nensy I = 9% Whle on he profles of he progress varable a dfferen urbulence nensy, fg. 7, he dfference beween numercal and expermenal becomes more remarkable. Ths may be due o naccurae expermenal mehod of varaon of nensy of urbulence. However, hs dfference remans whn he lms of accepable and we can say ha our resuls are admssble. The mean velocy s reduced n wake of wre bu s offse by he acceleraon due o hermal expanson of burn gas, as can be seen on he fuel rch flames, fg. 8. We noce ha he velocy of burn gas ncreases wh equvalence rao and burn gases are deflecs o he axs of symmery, where he ransversal velocy V s equal o zero.

8 318 THERMAL SCIENCE, Year 011, Vol. 15, No., pp Fgure 9(a) shows ha he mean velocy s maxmum n he cener of flame. Ths maxmum velocy n he burn gas s relaed on he hea release and he graden of densy o he crossng of he flame fron. Fgure 9. Profles of he axal mean (a) and flucuaon (b) velocy for j = 0.55 and I = 9% urbulence The dynamc profles calculaed for several heghs show he spacng of he flame and he acceleraon of he burn gas when moves away from he heaed wre. We can see ha he je flame nduces good symmery a axal velocy The profles of u', fg. 9(b), show he presence of wo maxmum cenered on he flame fron. They also show ha he urbulen hckness of he flame ncreases wh he hegh. These profles hghlgh he spacng of he flame wh nenses maxmum becomng gradually broader a places furher away from he orgn of he flame, ho wre, snce he srucures are expanded. Axal velocy s larges because of man drecon flow bu he ransverse velocy, generaed by he flame, alhough weaker of a facor approxmaely 10, are also of a grea neres for he analyss of combuson. Fgure 10 wach ha he exsence of a non-null ransverse velocy upsream of he fron and n he flame proves ha combuson nduces a devaon of he sreamlnes n fresh gases as n burn gases. The sreamlnes are pushed back on boh sdes of fron flame n he ousde flow and he greaes deflecon s a he approach of he fron. The passage n he burn gases causes a Fgure 10. Transverse mean velocy for an equvalence rao, j = 0.55 and urbulence nensy, I = 9% devaon n he oppose drecon and ransversal velocy changes sgn. The burn gases move owards he cener of

9 THERMAL SCIENCE, Year 011, Vol. 15, No., pp he flame. Wh symmery, one fnds a null ransversal velocy n he cener and he poson of he graden dv/dx maxmum can be regarded as he average poson of he fron of flame. Conclusons In hs paper we have smulaed a urbulen premxed mehane-ar flame usng he Fluen code. For urbulence used he model k-ε and we model gaseous mxure, gnorng he Sore and Dufour effecs and radaon hea ransfer s negleced. The progress varable balance equaon was closed by usng eddy break up model he urbulen combuson model. A numercal procedure s nroduced o smulae a confguraon n whch urbulence neracs wh propagang premxed flame fron ha s sablzed by a ho wre. The resuls of our smulaons allow us o analyze he nfluence of equvalence rao and he urbulen nensy on he properes of he flame (velocy, flucuaon, progress varable, hckness of flame). Inal comparsons of our resuls o expermenally measured flame ndcae ha our mehodology s suffcenly accurae o model hs ype of flame. We have shown ha urbulence was a major phenomenon n he combuson. By srechng he flame fron, urbulence causes an ncrease n he surface of hs fron. I resul an ncrease of flame velocy and hus a faser combuson. Ths allows us o mprove he qualy of flame for low values of equvalence rao. However, he ncrease n combuson speed by he effec of urbulence mus be opmzed so as no o fall no he oppose effecs. Nomenclaure C EBU eddy break up model consan, [ ] c progress varable, [ ] g gravaonal body force, [m.s ] I urbulence nensy, [%] k urbulence knec energy, [m s ] M mxure molecular wegh, [gmol 1 ] M molecular wegh of speces, [gmol 1 ] n number of producs, [ ] uu j he Reynolds sresses, [m s ] p pressure, [Pa] R unversal gas consan, [kjkmol 1 K 1 ] S L lamnar flame speed, [m.s -1 ] T emperaure, [K] U me, [s] mean axal velocy (Reynolds average), [ms 1 ] u axal velocy, [ms 1 ] V mean ransversal velocy (Reynolds averaged), [ms 1 ] x axal co-ordnae, [m] Y fuel mass fracon, [ ] y ransversal co-ordnae, [m] Y mass fracon of speces, [ ] Y,eq equlbrum mass fracon of speces, [ ] Greek symbols δ Kronecher dela, [ ] ε urbulen dsspaon rae, [m s 3 ] n flud urbulen dffusvy, [m s 1 ] ρ flud densy, [kgm 3 ] ζε, ζ k k-e model consan, [ ] η sress ensor, [Pa] η urbulen mxng me, [s] j equvalence rao, [ ] reacon rae, [kgm 3 s 1 ] Subscrps, j co-ordnae drecon Superscrps Reynolds average ~ Favre average flucuaon References [1] Bengsson, K. U. M., Numercal and Expermenal Sudy of NO x Formaon n Hgh-Pressure Lean Premxed Combuson of Mehane, Ph. D. hess, ETH Zürch, Zürch, Swzerland, 1998

10 30 THERMAL SCIENCE, Year 011, Vol. 15, No., pp [] Corr, R. A., Male, P. C., Marnov, N. M., Evaluaon of NO x Mechansms for Lean, Premxed Combuson, ASME paper 91-GT-57, 1991 [3] Pavé, D., Conrbuon o he Sudy of he Srucure of Turbulen Premxed Lean Mehane-Ar Flame (n French), Ph. D. hess, Unversy of Orleans, Orleans, France, 00 [4] Erard, V., Spaal and Temporal Sudy of Thermal and Dynamc Felds of Unseady Turbulen Premxed Combuson (n French), Ph. D. hess, Unversy of Rouen, Rouen, France, 1996 [5] Renou, B., Conrbuon o he Sudy of he Propagaon of a Premxed Flame n an Unseady Turbulen Flow, Influence of he Lews Number (n French), Ph. D. hess, Unversy of Rouen, Rouen, France, 1999 [6] Galzz, C., Escudé, D., Turbulen Srafed V-Shaped Flames: Expermenal Analyss of he Flame Fron Topology, Proceedngs, European Combuson Meeng, Louvan-la-Neuve, Belgum, 005 [7] Degardn, O., Effecs of Heerogenees of Equvalence Rao on he Local Srucure of he Turbulen Flames (n French), Ph. D. hess, INSA of Rouen, Rouen, France, 006 [8] Bell, J. B., e al., Numercal Smulaon of a Premxed Turbulen V-Flame,19 h Inernaonal Colloquum on he Dynamcs of Explosons and Reacve Sysems, Kanagawa, Japan, 003 [9] Hauguel, R., Vervsch, L., Domngo, P., DNS of Premxed Turbulen V-Flame: Couplng Specral and Fne Dfference Mehods, Compe-Rendu-Mecanque, 333 (005), 1, pp [10] Robn, V., e al., Expermenal and Numercal Analyss of Srafed Turbulen V-Shaped Flames, Combuson and Flame, 153 (008), 1-, pp [11] ***, Fluen 6.3. User Manual, hp:// [1] Barrère, M., Prudhomme, R., Fundamenal Equaons of Aerohermochemsry, Ed. Masson, Pars, 1973 [13] Borgh, R., Desrau, M., Combuson and Flames (n French), Ed. Technp, Pars, 1995 [14] Launder, B. E., Spaldng, D. B., Mahemacal Models of Turbulence, Academc Press, London, 197 [15] Launder, B. E., Spaldng, D. B., The Numercal Compuaon of Turbulence Flows, Compuer Mehods n Appled Mechancs and Engneerng, 3 (1974),, pp [16] Borgh, R., Champon, M., Modelng and Theory of he Flames (n French), Ed. Technp, Pars, 000 Paper submed: Sepember 4, 009 Paper revsed: July 0, 009 Paper acceped: February 11, 010