on fuel flow characteristics in the nozzle for directinjection engines. SAE paper, (931002), 1993.[19] L.N. RANDALL. Rocket applications on the cavitatingventuri. ARS Journal, 1952.[20] W.H. NURICK. Orifice cavitation and its effecton spray mixing. J of Fluids Engineering, 98, 1976.[21] D.P. SCHMIDT. Cavitation in <strong>Diesel</strong> fuel injectornozz<strong>les</strong>. PhD thesis, University of Wisconsin -Madison, 1997.[22] WALLIS and GRAHAM. One-dimensional twophasefl ow. Mc Graw-Hill, 1969.[23] R. GILMORE. The collapse and growth of aspherical bubble in a viscous compressible liquid.Technical Report 26-4, Calif Inst of Tech HydrodynamicsLab, 1952.[24] Y. LECOFFRE. La cavitation - T raqueurs <strong>de</strong>bul<strong>les</strong>. Hermes, 1994.[25] C.D. OHL, A. PHILIPP, and W. LAUTER-BORN. Aufnahme <strong>de</strong>s kollapsvorganges laserindurzierterkavitäten mit 20 millionen bil<strong>de</strong>rn prosekun<strong>de</strong>. ?, 1997.[26] R.D. REITZ and F.B. BRACCO. Mechanismof atomization of a liquid jet. Phys. Fluids,25(10):1730–1742, 1982.[27] K. MOKADDEM, P. LESSART, and T. BAR-ITAUD. Liquid and vapour phase penetration ina di common rail diesel engine equipped with aninclined injector. In ILASS-Europe’99, Toulouse,1999.[28] D. WARKEN and P. KREHL. Application offlash radiography to the analysis of simulated liquidgun propellant jets. ?, 19? ?[29] C. BADOCK, R. WIRTH, A. FATH, andA. LEIPERTZ. Application of laser light sheettechnique for the investigation of cavitation phenomenain real size diesel injection nozz<strong>les</strong>. InILASS Europe, pages 236–241, Manchester, 1998.[30] A. FATH, K-U. Mü n ch , and A. LEIPERTZ.Spray break-up of diesel fuel close to the nozzle. InILASS Europe, pages 59–64, Lund, Swe<strong>de</strong>n, 1996.[31] P.H. SCHWEITZER. Mechanism of disintegrationof liquid jets. J. Apllied Physics, 8, 1937.[32] M.J. MAC CARTHY and N.A. MOLLOY. Reviewof stability of liquid jets and the influence ofnozzle <strong>de</strong>sign. T he Chemical Engineering Journal,7, 1974.[33] M.J. MAC CARTHY. PhD thesis, University ofNewcastle, Australia, 1972.[34] G.L. CHAHINE. Interaction between a collapsingbubble and a free surface. Technical report,Ecole Nationale Supérieure <strong>de</strong> Techniquesavancées-Paris, 1976.[35] D.H. FRUMAN. Cavitation <strong>dans</strong> <strong>les</strong> <strong>injecteurs</strong><strong>de</strong> moteurs diesel. Technical report, GSM, 1997.[36] D. HANKE and P. BALLMANN. Strongchanges of state in collapsing bubb<strong>les</strong>. Z AMM, 78,1998.[37] E. WINKLHOFER. V elocities and structure ofatomizing diesel sprays. In ?, ? , ?[38] D. BOULTON-STONE and P. BLAKE. Gasbubb<strong>les</strong> bursting at a free surface. J. Fluid Mech.,254:437–466, 1993.[39] M. CALLENAERE, J.P. FRANC, and J.M.MICHEL. Influence of cavity thickness and pressuregradient on the unsteady behaviour of partialcavities. In 3rd International Symposium on Cavitation,volume 1, pages 209–214, 1998.[40] R.T. KNAPP, J.W. DAILY, and F.G. HAM-MITT. Cavitation. McGraw-Hill, 1970.[41] J.L. REBOUD, B. STUTZ, and O. COUTIER.Two-phase flow structure of cavitation : experimentand mo<strong>de</strong>lling of unsteady effects. In 3rdInternational Symposium on Cavitation, volume 1,pages 203–208, 1998.[42] H. CHAVES, B. MULHEN, and F. OBER-MEIER. Comparison of high speed stroboscopicpictures of spray structures of a diesel spray withnumerical calculations based on a convective instabilitytheory. In ILASS - Europe ’99, Toulouse,1999.[43] J.M. FLORYAN and H. RASMUSSEN. Numericalmethods for viscous flows with movingboundaries. Appl. Mech. Review, 42(12):323–341,1989.[44] H. UNVERDI and S. TRYGGVASON. Afront-tracking method for viscous, incompressible,multi-fluid flow. Journal of Computational Physics,100:25–37, 1992.[45] J.U. BRACKBILL, D.B. KOTHE, andC. ZEMACH. A continuum method for mo<strong>de</strong>lingsurface tension. J. Comp. Phys., 100:335–354,1992.[46] A.J. CHORIN. Flame advection and propagationalgorithms. J. Comp. Phys., 35:1–11, 1980.[47] C.W. HIRT and B.D. NICHOLS. V olume offluid vof method for the dynamics of free boundaries.J. Comp. Physics, 39:201–225, 1981.[48] B. LAFAURIE, C. NARDONE, R. SCAR-DOVELLI, S. ZALESKI, and G. ZANETTI.Mo<strong>de</strong>lling merging and fragmentation in multiphaseflows with surfer. J. Comp. Physics, 113:134–147, 1994.[49] J. LI. Calcul d’interface affi ne par morceaux. C.R. Acad. Sci. Paris (Série IIb), 320:391–396, 1995.[50] W.F. NOH and P. WOODWARD. Slic : Simpleline interface calculation. In Proc. Fifth Int.Conf. on Numerical Methods in Fluid Dynamics.Springer-Berlin.[51] A. TOMIYAMA, Y. MAKINO, I. ZUN, andT. SAKAGUCHI. Bubble shape mo<strong>de</strong>lling for a3d two-way bubble tracking method. In ICMF’98,Lyon, France, 1998.[52] P. SMEREKA. Level set methods for twofluidflows. In Métho<strong>de</strong>s numériques pour <strong>les</strong>
écoulements <strong>diphasique</strong>s. Eco<strong>les</strong> CEA-EDF-INRIA,1996.[53] J.R. GRACE. Shapes and velocities of bubb<strong>les</strong>rising in infinite liquids. Trans. Chem. Eng.,51(116), 1973.[54] B. DELANNOY and H. KUENY. Two phaseflow approach in unsteady cavitation mo<strong>de</strong>ling.ASME Cavitation and Multiphase flow forum,98:153–158, 1990.[55] C. CHEN and A. VESHAGH. A simple unifiedfuel spray mo<strong>de</strong>l. SAE technical paper 930923,1993.[56] M.S. PLESSET and R.E. DEVINE. Effect of exposuretime on cavitation damage. Technical Report8531, Office of naval Research, Dept. of theNavy, 1965.[57] A. ALAJBEGOVIC, H.A. GROGGER, andH. PHILIPP. Calculation of nozz<strong>les</strong> using thetwo-fluid mo<strong>de</strong>l. In to be presented in the 7thannual Conference Computational Fluid DynamicsSociety of Canada, Canada, 1999.[58] H.A. GROGGER and A. ALAJBEGOVIC.Calculation of the cavitating flow in venturi geometriesusing two fluid mo<strong>de</strong>l. In Proceedingsof FEDSM’98, Washington D.C., USA, 1998. 1998ASME fluids engineering division summer meeting.[59] A. ALAJBEGOVIC. Private e-mail communication.may 1999.[60] L. LAMBERT. Modélisation <strong>de</strong>s jets d’injectionhaute pression <strong>de</strong>s moteurs <strong>Diesel</strong> et validationexpérimentale. PhD thesis, IFP, 1996.[61] D. COKLJAT, V.A. IVANOV, and S.A.VASQUEZ. Two-phase mo<strong>de</strong>l for cavitatingflows. In ICMF’98, Lyon, France, 1998.[62] T. IKOHAGI, M. YASUI, and R. OBA. Numericalsimulation of cavitating jet flows. In 2nd InternationalSymposium on Cavitation, Japan, 1994.[63] A. KUBOTA, H. KATO, and H. YAM-AGUCHI. A new mo<strong>de</strong>ling of cavitated flow :a numerical study of unsteady cavitation on a hydrofoilsection. J. Fluid Mech., 240, 1992.[64] A. CHEN and H. HEISTER. Two-phase mo<strong>de</strong>lingof cavitated flows. Comp. Fluids, 24(7), 1995.