ModÃ©lisation de l'Ã©coulement diphasique dans les injecteurs Diesel

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is worth citing, because this is an attempt to createa transition model from large scale models to smallscale models.Interface location is not defined by the model• Methods that do not take in account the interfacelocation are the continuum models, and thetwo-fluids models. The continuum models, or mixturemodels, consider a single fluid whose densityis defined by an equation of state. G enerally, thisequation is a simple barotropic one. Some examplesare presented in table 2. The main attractivefeature of these models is this equation of state,but this is also their weakness : this equation needsto represent the whole cavitation physics, dependingon the configuration of the flow. Delannoy andKueny [54] have developped a pocket model on ahydrofoil. Their equation of state is barotropic,and considers three domains : the incompressibleliquid, the incompressible vapour, and the regionof compressible homogeneous mixture. This regionis a sine function of ρ versus P . Chen and Heister[55] have criticized this model by saying thattemporal terms in the equation of state must betaken in account. Pressure field history has to appearin the local density, as shown in the Rayleigh-Plesset equation [56]. The Chen and Heister algorithmdistinguishes three zones : the cavitatingregion, the region where P del considers also the two pure phasesas incompressible. Schmidt [21] has developped amodel particularly adapted to instationary cavitatingflows in common-rail injectors. This model considersthe liquid as compressible, and is based on theWallis [22] study on HEM 1 concerning sound velocityin two-phase flows. The liquid, the vapour andthe liquid/vapour mixture are considered as compressible.The numerical simulation results fit withthe Chaves experimental data on the exit velocity[7] for a typical axisymmetrical singled-hole nozzle.• The two-fluid models are usually used for largescaledflows, i.e. typically bubbly flows, in order totake in account each phase turbulence and the bubblesdrag. The approach consists in solving a setof Navier-Stokes equations for each phase, and tolink them one to each other using a mass transferterm in the mass conservation equation (see equation7), where N = 2 for a two-phase flow and k isthe phase subscript. For instance, Alajbegovic et al.[57] have made a two-fluid model using a simplifiedRayleigh-Plesset equation [58] as the mass transfer1 Ho m o g en eo u s E q u ilib riu m Mix tu reterm :∂α k ρ k∂t+ α kρ k v k,i∂x i=N∑l=1, l≠kΓ kl (7)Γ 21 = ρ 2 N ′ ′ ′ 4π R 2 ∂R∂t = −Γ 12 , (8)w here R is the av eraged b u b b le rad iu s and N ′ ′ ′ theb u b b le d ensity, w hich is link ed to the v oid fractionα 2 b y :{N ′ ′ ′ N′ ′ ′=′ ′ ′0 if α 2 ≤ 0.52(N 0 − 1)(1 − α 2 ) + 1 if α 2 > 0.5(9)T his heu ristic form u la is su p p osed to tak e in account the b u b b les coalescence as soon as the v oidfraction is great enou gh. In that case, the m od el isnot ad ap ted to high α 2 v alu es, for the “transitionfrom bu bbly to slu g, or even fi lm regim e” [59]. Lam -b ert [60] has also u sed a tw o-fl u id m od el to com p u tethe internal injector fl ow . A p articu lar attentionhas b een focu sed on tu rb u lence m od elling for thetw o p hases. T he liq u id is su p p osed com p ressib leand ob ey s to the T ait eq u ation :ρ l = ρ r ef[1 − C ln( B + PB + P r ef)] −1(10)T he resu lts lead to negativ e p ressu re v alu es (w hichcan b e encou ntered in ind u strial cases [24]), w hosev alu es are great (m ore or less 200 b ar) com p aringto u su al v alu es of the ord er of sev eral b ar. C onsequ ently, the fl ow d y nam ics resu lts are certainly d istorted. F ew com m ercial cod es d eal w ith cav itation.In the actu al F LUE NT v ersion, a tw o-fl u id m od el isp rop osed , and the cav itation can b e m od elled u singa m ass transfer term b ased on Alajb egov ic m ethod(see eq u ation8) [57, 61]. P sa t and the b u b b le d ensityare the p aram eters that can b e m od ifi ed b y theu ser. T he collap se is not tak en into accou nt b y thesolv er, i.e. b u b b les can only grow . F u rtherm ore, theb u b b les are consid ered as sp herical and m u st b e farsm aller than the com p u tational cell size. In fact,this m od el is p articu larly ad ap ted to large scaledfl ow s, w hich is not the case of Diesel injectors.C onsid ering the p articu larities of the ex istingm od els, w e can conclu d e that interface track ing andfront cap tu ring m ethod s are not ap p rop riate for theinjector fl ow confi gu ration. T he com p u tational cellnu m b er w ou ld b e too large for actu al com p u ter capab ilities. T he tw o-fl u id m ethod is not ad ap tedto large v ap ou r entities, i.e. w hen som e cells arefi lled of v ap ou r, w hich is ou r case in ou r confi gu ration.C onseq u ently, the right ap p roach shou ld b eto m od el the fl ow thank s to a continu u m m ethod ,b ased on an ap p rop riate eq u ation of state.
ConclusionPresent-day spray models suff er from the lackof knowledge of transient boundary conditions atthe orifice exit. W e have described the phenomenaoccuring in the injector that influence the spray.As a conclusion, in order of importance the causesof the asymmetrical and transient characteristics ofthe spray are due to :• Cavitation which leads to a decrease of theexit area and consequently increases the exitvelocity.• Non-stationary characteristic of cavitation andpressure fluctuations which lead to exit velocityprofile fluctuations.• V apour structures collapse in the dense regioncreating or increasing the perturbations at thejet surface in the dense core.As experimental investigations in real-sized injectorsare pretty hard to manage, the use of CFDseems to be judicious. The classical two-phase flowmodels have been presented, and the type of methodthat seems the most appropriate for injector flow(i.e. high-speed cavitating flow) modelling is thecontinuum one. A lot of improvements have tobe made on the present processing of this method: the cavitation physics have to be clearly understoodin order to take it in account in the equationof state expression. Nowadays, The S chmidt’sCavalry model [21] seems to be the most appropriateto model the injector flow. Nevertheless, theHEM method [22] considering the two-phase flowas homogeneous is clearly not usable in case of ahigh-speed heterogeneous flow. Consequently, theexpression of a new equation of state taking in accountthe vapour pockets history as discussed byChen and Heister [55], and the typical size of thedispersed entities should be done, in order to takein account the typical transient flow characteristicsat the injector exit.R eferences[1] B. CHAL L EN and R . BAR ANES CU. Dieselengine reference boo k 2 nd ed itio n. Butterw orthH einem ann, 1999.[2] W . BER GW ER K . Flow pattern in diesel nozzlespray holes. P roc Instn M ech E ngrs, 173(25):665–660, 1959.[3] A .J. R UIZ. A few useful relations for cav itatingorifices. In IC LASS’9 1 , 1991.[4] J.P . F R ANC, F. AVEL L AN, B. BEL A-HAD JI, J.Y . BIL L AR D , L . BR IANCON-M AR JOL L ET, D. F R ECHOU, D.H . F R U-M AN, A . K AR IM I, J.L . K UENY, and J.M.M ICHEL . La ca vita tio n. P resses U niv ersitairesde G renoble, 1995.[5] C . BAD OCK , R . W IR TH, S. K AM PM ANN,and C . TR OPEA. Fundam ental study of the influenceof cav itation on the internal flow and atomization of diesel spray s. In ILASS E uro pe, pages53–59, Manchester, 1998.[6] C . BAD OCK , R . W IR TH, and C . TR OPEA.T he influence of hy dro-grinding on cav itation insidea diesel injection nozzle and prim ary break -up under steady pressure conditions. In ILASS-E uro pe’9 9 , T oulouse, 1999.[7] H . CHAVES . E x perim ental study of cav itation inthe nozzle hole of diesel injectors using transparentnozzles. SAE pa per 9 5 0 2 9 0 , 1995.[8] W . EIF L ER . Untersuch ungen zur Strukturd es insta tio nä ren Dieselö leinsp ritzstra h les in Dsennah bereich m it d er M eth od e d er Hoch frequenz-Kinem a togra fie. P hD thesis, U niv ersität K aiserslautern,1990.[9] N . TAM AK I, M. S HIM IZU, K . NIS HID A,and H . HIR OYAS U. E ff ects of cav itation andinternal flow on atom ization of a liq uid jet. Ato m -iza tio n a nd Sp ra y s, 8:179–197, 1998.[10] C . AR COUM ANIS , H . F L OR A,M. GAVAIS ES , N . K AM PANIS , and R . HOR -R OCK S . Inv estigation of cav itation in a v erticalm ulti-hole injector. SAE pa per, (1999-01-0524),1999.[11] A .J. YUL E, A .M. D AL L I, and K .B. YEONG.T ransient cav itation and separation in a scaled-upm odel of a v co orifice. In ILASS - E uro pe ’9 8 , pages230–235, Manchester, 1998.[12] C . S OTER IOU, R . AND R EW S , andM. S M ITH. Direct injection diesel spray sand the eff ect of cav itation and hy draulic flip onatom ization. SAE pa per 9 5 0 0 8 0 , 1995.[13] H . CHAVES and F. OBER M EIER . C orrelationbetw een light absorption signals of cav itatingnozzle flow w ithin and outside of the hole of a transparentdiesel injection nozzle. In ILASS - E uro pe’9 8 , pages 224–229, Manchester, 1998.[14] C . AR COUM ANIS , M. GAVAIS ES , andB. F R ENCH. E ff ect of fuel injection processeson the structure of Diesel spray s. SAE tech nica lpa per 9 7 0 7 9 9 , 1997.[15] A -G . F AVENNEC and D.H . F R UM AN. E ff ectof the needle position on the cav itation in dieselinjectors. In P roceed ings o f th e 3 rd ASM E / JSM EJo int F luid s E ngineering C o nference, San Francisco,C alifornia, U SA , 1999.[16] O . GENGE. O laf genge hom epage. h ttp :/ / telema nn.ltt.rwth -a a ch en.d e/ ˜ genge/ .[17] J.H . K IM , K . NIS HID A, T . YOS HIZAK I, andH . HIR OYAS U. E ff et des flux transitoires dansl’injecteur sur la pulv érisation dans le cas d’un m o-teur diesel à injection directe. JSAE R eview, 29(4),O ctober 1998.[18] K . D ATE, H . NOBECHI, H . K ANO,M. K ATO, and T . OYA. E x perim ental analy sis
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ThèsePrésentéePour obtenirLE TIT
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RésuméDans les moteurs Diesel à
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Table des matièresNomenclature 9Ta
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TABLE DES MATIÈRES 76 Validation d
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NomenclatureLettres LatinesaVitesse
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Table des figures1 À gauche : prin
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TABLE DES FIGURES 134.1 Vitesse du
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Introduction généraleLES contrain
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INTRODUCTION GÉNÉRALE 17le quatri
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Chapitre 1Que se passe-t’il dans
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CHAPITRE 1 : QUE SE PASSE-T’IL DA
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Chapitre 2Phénoménologie et modé
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Chapitre 4Le modèle de mélange ho
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CHAPITRE 4 : LE MODÈLE DE MÉLANGE
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Chapitre 5Élaboration du code CavI
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Chapitre 6Validation du code CavIF6
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CHAPITRE 6 : VALIDATION DU CODE CAV
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Page 189 and 190: CAV2001:sessionB6.005 1NUMERICAL SI
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Page 201 and 202: CAV2001:sessionB6.005 13Fig. 12 - D
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ModÃ©lisation de l'Ã©coulement diphasique dans les injecteurs Diesel

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