CST036. -SST Turbulence Model for Separated Particle-Laden Flows

Transcription

1 CST36 The 9h Conference of Mechancal Engneerng Newor of Thaland 9- Ocober 5, Phue, Thaland Alcaon of - - Turbulence Model for Searaed Parcle-Laden Flows Nareera Srboonlucul *, Eacha Junasaro and Varangra Junasaro Dearmen of Mechancal Engneerng, Faculy of Engneerng, Kasesar Unversy, Banghen, Bango 9. School of Mechancal Engneerng, Insue of Engneerng, Suranaree Unversy of Technology, Nahon Rachasma 3. *Emal: g466539@u.ac.h Absrac Two-hase urbulen flows of dlue concenraon of dscree arcles occur n many ndusral and naural rocesses such as he combuson of lqud and fuels, cyclone searaors, neumac ransor of arculae maeral, and envronmenal arculae ransor. In hese alcaons, urbulence modulaon wll occur. Turbulence modulaon refers o he flud urbulence flows can be affeced by he resence of he arcles. Two-equaon Eddy Vscosy Models (EVM) such as -ε models are wdely emloyed models for comuaonal flud dynamcs (CFD). Ther maor advanage s he smlcy and suably for an easy ncororaon no he Naver-Soes numercal codes. Comuaon of a varey of flows has shown agreemen wh exermenal measuremens n some smle classes of flows. However, many resuls are msleadng and wrong esecally n comlex flows (e.g. searaon and recrculaon) because of lmaons of he lnear woequaon models. Recen advanced eddy-vscosy models (e.g. - model) ha reresen an nermedae closure level beween he lnear eddyvscosy and second-momen closures are esecally worh consderng because of demonsraed successful erformance n a number of more comlex flows. The obecve of hs arcle s o revew arcleladen characerscs whch affec he urbulence and o smulae he arcle-laden urbulen flow over a D bacward-facng se usng - model. The bacward-facng se s a basc geomery whch has many moran flow feaures such as flow searaon, flow reaachmen, and free shear e henomena. The smulaon resuls are valdaed agans exermenal daa obaned by Ruc and Maola []. The revewed nformaon s combned and wll be used o modfy he urbulence model o nclude he effec of arcles on carrer hase (flud hase). Keywords: Turbulence model, Parcle-laden flows, Bacward-facng se. Inroducon Parcle-laden flows are commonly found n boh engneerng and n naure. Alhough hey are commonly found, hey are no well undersood. Nowadays, he numercal models used for arcle-laden flows n engneerng analyss have wo caegores. The frs caegory s called Lagrangan aroach whch reas he dsersed hase (arcle hase) by racng a large number of arcles n Lagrangan frame. The second caegory s called Euleran aroach whch s also nown as he wo-flud aroach because he arclehase s descrbed by flud-le equaon such as, Reynolds averaged Naver-Soes (RANS). Ths wor focuses only n he Euleran aroach, RANS, whch concenraes n he arcle effec on urbulence no he behavor of arcles. The numercal models for engneerng analyss are based on he soluon of RANS equaons for he carrer hase. The models have been mroved such ha hey can roduce good redcon of he carrer hase. Ths has led o he modfcaon of ncreasngly accurae arcle dserson models because gas-arcle flows are characerzed by he coulng beween hases. The common model used for urbulen flows s he classcal -ε model. Tan e al. [] nvesgaed he erformance of Lagrangan and Euleran aroach of dlue gas-arcle flow over a bacwardfacng se. The numercal resuls agreed well wh he exermenal daa of Ruc and Maola []. The urbulence models n Euleran aroach were sandard - ε, RNG -ε and realzable -ε models. The wo successful models were RNG -ε and realzable -ε models because he good agreemen was acheved beween he model resuls and measuremen daa. Moreover, he advanage of he Euleran aroach was no only less comuaonal me bu also gave he beer erformance han he Lagrangan aroach. The bacward-facng se (Fgure ) s a smle geomery whch has many comlex flows such as searaon, reaachmen and recrculaon. For arcleladen flows, he arcles mae he flows more comlex. To mae sure ha he resul of he develoed arcle model s accurae, he smle geomery s used o reduce he effec from s body. Yu e al. [3] used large eddy smulaon (LES) for he flud hase whle arcle s moon was raced by a arcle rac model n a bacward-facng se. Ther wor could redc a small an-clocwse crculaon regon near he corner beween he se and he lower wall whch had no been reored n he exermenal wor of Fessler and Eaon [4] nor redced by he smulaon usng Reynolds-averaged equaons of Chan e al. [5]. Tan e al. [] found ha he RNG -ε and realzable -ε models could smulae a secondary recrculaon a he corner of he se bu he sandard -ε model could no redc.

2 CST36 Recenly, here s more advanced urbulence model han he -ε model ha can redc he comlex flows more successfully. The - model s he urbulence model ha can caure he searaed flows beer han he -ε model (Hanalc [6]). Thus here s he ossbly ha he - model s arorae o smulae searaed arcle-laden flows. A number of arcles are modeled by he seces ransor equaon whch he arcle dffusvy ( s an moran arameer. However, Soo D) [7] found ha he arcle dffuson of he dsersed hase was smaller han he carrer hase. Ths resul shows ha he arcle dffusvy can be negleced whle he urbulen dffusvy ( D / Sc) sll remans. The urbulen dffusvy s modeled hrough a Schmd number (Sc). Ths arcle evaluaes he Schmd number for a bacward-facng se by defnng Sc.35,.5, and.7. I s found n hs aer ha he numercal resuls are unchanged wh varyng Schmd number. Then he aer uses he - model o smulae a searaed arcleladen flow. The numercal resuls are comared wh he exermenal daa of Ruc and Maola [] for he arcle-laden urbulen flow over a bacward-facng se. Parcles dameer of m (ρs 8 g/m 3 ) s smulaed under he Reynolds numbers (based on he se hegh, h): Re64. Ths wor s n he urbulence aenuaon case because he flow s dlue where mass loadng s. and Soes number s smaller han uny. Inle h Maxmum negave velocy h Maxmum osve velocy 5h To Wall Boom Wall h Oule Fgure. The bacward-facng se geomery (h.5 m). Characersc of Parcle-Laden Flows The comlexy of momenum coulng n a arcle-laden flow deends on a number of arameers. The volume and mass of mxure are quanfed by he volume fracon and bul densy. The volume fracon s he volume of a hase er un volume of mxure. The bul densy s he mass of a hase er un volume of mxure. The volume fracons of each hase sum o uny whle he sum of he bul densy yelds he densy of he mxure (Crowe [8]). The rao of he mass of dsersed hase o he mass of he carrer hase s called loadng, w. A dlue dsersed hase flow s one whch he arcle moon s conrolled by he flud forces (drag and lf). A dense flow s one n whch he arcle moon s conrolled by collsons. The naure of dlue and dense flows can be comared by he rao of he arcle s nera, gven by arcle me consan ( ), and he me beween collsons ( c ). The arcle me consan s he me aes for a arcle a res n flowng sream o accelerae o - e - of he freesream velocy (U ). Thus he flow can be consdered dlue, f / c<. I means ha he arcle has suffcen me o resond o he local flud dynamcs forces before he nex collson so s moon s domnaed by he carrer hase. On he oher hand, f / c >, he arcle has no me o resond o flud forces before nex collson and he flow s dense. The arcles resonsveness o he carrer hase s deermned by he rao of he arcle me consan o he flud me scale ( f). Ths rao s a very moran arameer n gas-arcle flows called Soe number, S. S / f ; ρ d 8 f For bacward-facng se [5] f 5H /U, where H s he se hegh Parcles Ineracon wh Turbulence The effec of he urbulence on he urbulence of he carrer hase s moran n he develomen of numercal models for wo-hase flows. There has been a connung neres concernng he effec of arcles on he urbulence of he carrer hase. In Fgure, he dlue and dense dsersed hase can be searaed by he nerarcle sacng or he volume fracon. Gore and Crowe [9] ndcaed ha small arcles wll aenuae he urbulence whle large arcles wll generae urbulence. From Fgure 3, he daa suggesed ha he ranson occurs when he arcle sze was abou / of he negral lengh scale (he characersc lengh of he mos energec eddy). Elghobash [] has roosed he ma shown n Fgure 4 for he effec of arcles on carrerhase urbulence. For volume fracon less han -6 he resence of he arcles would have no effec on urbulence. For volume fracons beween -6 and -3, he arcles can augmen he urbulence, f he rao of arcle resonse me o he urbulence me scale s greaer han uny, or aenuae urbulence, f he rao s less han uny. For volume fracons greaer han -3, arcle-arcle collsons become moran, and he urbulence of he carrer hase can be affeced by he oscllaory moon due o arcle collsons. Ths effec s called four-way coulng. Fgure. Regmes of dsersed wo-hase flow as a funcon of arcle volume fracon [].

3 CST36 3 (α), Parcle mass loadng, and Parcle Reynolds number. Values of he arameer defne arcle s nfluence on urbulence, as conclude n Table. Table The comarson of he arcle arameer effec on urbulence. Turbulence Aenuaon S < Parcle dameer s smaller han he Kolmogorov scale (d <η) Parcle s smaller han % of he flud scale (d /l e <.) Low concenraon (α < O( -6 )) Parcle Reynolds number (Re < ) Fgure 3. A summary of exermenal daa on he effec of he arcle dameer/urbulence lengh scale on he urbulence nensy of he carrer hase [9]. Fgure 4. Proosed ma for arcle-modulaon. / e s he rao of he arcle resonse me o he urbulence me scale; α s he arculae hase volume fracon []. There are many flow and arcle arameers ha deermne he arcle s effec on he urbulence such as Soes number, Parcle dameer, Parcle concenraon Turbulence Augmenaon S > Parcle dameer s larger han he Kolmogorov scale (d <η) Parcle s larger han % of he flud scale (d /l e >.) Hgh concenraon (α > O( -3 )) Parcle Reynolds number (Re < 4) Ux Vx d Re where U x ν flud velocy Vx U e ( / ) f arcle velocy Turbulence aenuaon haens because he energy of he carrer hase ransfers o he arcles. The arcles are sll a frs, and hen, sarng movng by usng energy from he carrer hase unl hey reach he same velocy. On he oher hand, urbulence augmenaon resuls from he urbulence wae behnd he arcle, and hus he urbulence ncreases as he arcle sze ncrease. Invesgaed Models for Turbulence Modulaon The varous urbulence modulaon models found n he survey on he -ε model are concluded n Table. To modfy he urbulence model whch has he arcle effec, he added source erms are roosed. Ths added source erms n he urbulen nec energy () and dssaon rae of urbulen nec energy (ε) equaons were modeled o redc he arcle effec on urbulence. Table Comarson of he added source erm n and ε equaons. Model S S ε Commen Chen and Wood [] 5. ε α ex αε ρf ρ f Moafa and Monga [3] LI α ρ f LI ε 3 LI C ε α LI 35. / ε + ρ f LI + C ε 3. Tu and Flecher [4] B α ex ε Bε n,w B.9 ρ n α ex f w f ρ n n,w> f w f B.4 ε

4 CST36 4 Lghsone and Hodgson [5] Garca and Creso [6] α ρf + ρε εα ρf + Cε 3 urel L + I LI. 35 / ε LI L / 3 ε ε ε ( 3/ ) C I LI εφ 3 9 C,C ε 3.. Governng Equaons Mener [7] roosed o combne he wo models n such a way ha he model reduce o he - model close o he sold wall, and he -ε model away from he wall. The combnaon of he wo models has been accomlshed usng a blendng funcon. The Shear-Sress Transor () - model ρ, Ω Ω Ω max ΩF, α a u u Ω rae of roaon ensor x F / + F / ( ),, ( ρ) ( ρu ) + G F /, + ( F )/, x x + x Y () ( ρ) ( ρu ) ( 4 F anh Φ ), F anh ( Φ ) + + G Y + D 5 4ρ Φ mn max,, where ().9 y ρy,d + y + G reresens he generaon of urbulence nec energy D max ρ,, due o mean velocy gradens. u G ρ uu S, S S S 5 Φ max,.9 y ρ y u u where y s he dsance o he nex surface S + sran rae ensor Model consans a.3, α,,.76,,.,,., α G G he generaon of ν,.68, α / 9, R 95., κ 4., 9.,,.75,,.88 α α + Re / R α α, Re ρ / + Re / R Mass fracon equaon α F α, + ( F ) α, φ ( ρuφ) φ (3), κ, κ α,, α,,, whereφ s he mass fracon of arcles Y and Y reresen he dssaon of and due o urbulence Y ρ, ( ) Y ρ, F, + F, D reresens he cross-dffuson erm D ( F ) and ρ, reresen he effecve dffusvy of and +, φ reresens he effecve dffusvy of mass φ ρd +, Sc.7 Sc where Sc s he urbulen Schmd number Table 3 The Schmd number comarson. Researcher Schmd Number Laslandes and Sacré [8].35 (bacward-facng se) Launder and Saldng.7 (round e ) [9].5 (lane es, mxng layers) + The governng ransor equaons are dscrezed by usng he fne-volume aroach. QUICK scheme s used o aroxmae he convecve erms. The ressure-

5 CST36 5 velocy coulng s comued by he SIMPLE mehod. The smulaon s n he seady sae. Grd sacng s.5 mm. The convergence crera for he roeres (velocy, ressure,, and ) were acheve when he eraon resdual reduced by sx orders of magnude..5 Exermen Comarson of velocy a x/h5 3. Resuls and Dscusson Fgure 5. resens he arcle velocy rofle agans measuremens for a Reynolds number of 64, a locaon of x/h,, 3, 5, 7, and 9 behnd he se. The velocy rofles are normalzed by he free sream velocy, U. The acceable resuls were found a he x/h 5, 7, and U/U Comarson of velocy a x/h Comarson of velocy a x/h7 Exermen Exermen U/U U/U Comarson of velocy a x/h9 Comarson of velocy a x/h Exermen Exermen U/U U/U Comarson of velocy a x/h3 Fgure 5. Comarson beween he numercal resul and he exermenal daa of arcle velocy..5 Exermen Exermen.5 Normalzed maxmum negave velocy U/U Dsance from se (x/h) Fgure 6. Maxmum negave x-drecon velocy (normalzed wh free sream velocy, U ).

6 CST36 6 In Fgure 6, he maxmum negave velocy rofle of arcles n he recrculaon zone s shown. The reaachmen lengh of he - model s x/h 8. comared o he measures value of x/h Concluson Evenhough he arcle-laden urbulen flows are common naure. The undersandng of he behavor of he arcle s sll unclear n many suaons. Ths aer resens he characerscs of arcles and her behavor on he urbulence. The - model can demonsrae he naure of he arcle-laden searaed flows no only he arcle behavor bu also he reaachmen lengh. The second recrculaon a he corner of he se can be found n he smulaon. The numercal resuls can redc he flow behavor smlar o he exermenal daa. In he fuure wor, he urbulence models need o be furher modfed n order o gve a beer redcon by consderng he arcle effec on he urbulence. 5. Acnowledgemens Ths research was fnancally suored by Kasesar Unversy Graduae School Thess and Dssersaon Suor Fund, he Thaland Research Fund (TRF), and Kasesar Unversy Research and Develomen Insue (KURDI). 6. References [] B. Ruc, and B. Maola, Parcle Dserson n A Sngle-Sded Bacward-Facng Se Flow, In. J. Mulhase Flow, Vol. 4, No. 6, 988, [] Z.F. Tan, J.Y. Tu, and G.H. Yeoh, Numercal Smulaon and Valdaon of Dlue Gas-Parcle Flow Over a Bacward-Facng Se, Aerosol Scence and Technology, Vol. 39, 5, [3] K.F. Yu, K.S. Lau, and C.K. Chan, Numercal Smulaon of Gas-Parcle Flow n A Sngle-Sde Bacward-Facng Se Flow, Vol. 63, 4, [4] J.R. Fessler, and J.K. Eaon, Turbulence Modfcaon by Parcles n A Bacward-Facng Se Flow, J. Flud Mech., Vol. 394, 999, [5] C.K. Chan, H.Q. Zhang, and K.S. Lau, Numercal Smulaon of Gas-Parcle Flows Behnd A Bacward-Facng Se Usng Imroved Sochasc Searaed Flow Model, Comu. Mech., Vol. 7, No. 5,, [6] K. Hanalć, Closure Models for Incomressble Turbulen Flows, Dearmen of Aled Physcs, Delf Unversy of Technology, Neherlands. [7] S.L. Soo, Fluds Dynamcs of Mulhase Sysems, Bladsell, Walham, Mass, 967. [8] C.T. Crowe, REVIEW-Numercal Models for Dlue Gas-Parcle Flows, Journal of Fluds Engneerng, Vol. 4, 98, [9] R.A. Gore, and C.T. Crowe, Effec of Parcle Sze on Modulang Turbulen Inensy, In. J. Mulhase Flow, Vol. 5, No., 989, [] S.E. Elghobash, On Predcng Parcle-laden urbulen flows, Al. Sc. Res., Vol. 5, 994, [] M. Sommerfeld, Lecure Seres, Theorecal and Exermenal Modellng of Parculae Flows, von Karman Insue for Flud Dynamcs,. [] C.P. Chen, and P.E. Wood, Turbulence Closure Model for Dlue Gas-Parcle Flows, Canadan Journal of Chemcal Engneerng, Vol. 63, 985, [3] A.A. Mosafa and H.C. Monga, On The Ineracon of Parcles and Turbulen Flud Flow, Inernaonal Journal of Hea and Mass Transfer, Vol. 3, 988, [4] J.Y. Tu, and C.A.J. Flecher, An Imroved Model for Parculae Turbulence Modulaon n Confned Two-Phase Flows, Inernaonal Communcaons n Hea and Mass Transfer, Vol., 994, [5] S.M. Hodson, Turbulence Modulaon n Gas- Parcle Flows: A Comarson of Seleced Models, Unversy of Torono, 999. [6] J. Garca, and A. Creso, A Turbulen Model for Gas-Parcle Jes, Journal of Fluds Engneerng, Vol.,, [7] F. Mener, Two-equaon Eddy-Vscosy Turbulence Model for Engneerng Alcaons, AIAA Journal, Vol. 3, 994, [8] S. Laslandes, and C. Sacré, Transor of Parcles by A Turbulen Flow Around An Obsacle-A Numercal and Wnd Tunnel Aroach, Journal of Wnd Engneerng, Vol , 998, [9] B.E. Launder, and D.B. Sladng, Mahemacal Models of Turbulence, Academc Press, London, 97.