Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-20T08:38:23.612Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling of cavitation in diesel injector nozzles

Published online by Cambridge University Press:  10 December 2008

E. GIANNADAKIS ,
M. GAVAISES  and
C. ARCOUMANIS
E. GIANNADAKIS
Affiliation:
Centre for Energy and the Environment, School of Engineering and Mathematical Sciences, City University, London, UK
M. GAVAISES
Affiliation:
Centre for Energy and the Environment, School of Engineering and Mathematical Sciences, City University, London, UK
C. ARCOUMANIS
Affiliation:
Centre for Energy and the Environment, School of Engineering and Mathematical Sciences, City University, London, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

A computational fluid dynamics cavitation model based on the Eulerian–Lagrangian approach and suitable for hole-type diesel injector nozzles is presented and discussed. The model accounts for a number of primary physical processes pertinent to cavitation bubbles, which are integrated into the stochastic framework of the model. Its predictive capability has been assessed through comparison of the calculated onset and development of cavitation inside diesel nozzle holes against experimental data obtained in real-size and enlarged models of single- and multi-hole nozzles. For the real-size nozzle geometry, high-speed cavitation images obtained under realistic injection pressures are compared against model predictions, whereas for the large-scale nozzle, validation data include images from a charge-coupled device (CCD) camera, computed tomography (CT) measurements of the liquid volume fraction and laser Doppler velocimetry (LDV) measurements of the liquid mean and root mean square (r.m.s.) velocities at different cavitation numbers (CN) and two needle lifts, corresponding to different cavitation regimes inside the injection hole. Overall, and on the basis of this validation exercise, it can be argued that cavitation modelling has reached a stage of maturity, where it can usefully identify many of the cavitation structures present in internal nozzle flows and their dependence on nozzle design and flow conditions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 616 , 10 December 2008 , pp. 153 - 193
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Afzal, H., Arcoumanis, C., Gavaises, M. & Kampanis, N. 1999 Internal flow in diesel injector nozzles: modelling and experiments. IMechE Paper S492/S2/99.Google Scholar
Ahmadi, M. & Sellens, R. W. 1993 A simplified maximum-entropy-based drop size distribution. Atom. Sprays 3, 291–310.CrossRefGoogle Scholar
Alajbegovic, A. 1999 Three-dimensional cavitation calculations in nozzles. In Proc. Second Annu. Meeting Inst. Multifluid Sci. Technol., Santa Barbara, CA (ed. Theofanus, T. G.), pp. III.97–III.103. Center of Risk Studies and Safety, University of California, Santa Barbara.Google Scholar
Alajbegovic, A., Grogger, H. A. & Philipp, H. 1999 a Calculation of cavitation in nozzles using the two-fluid model. In Proc. 7th Annu. Conf. Comp. Fluid Dyn. Soc. Canada, Halifax, NS, Canada (ed. Militzer, J.), pp. 7.3–7.8. CFD Society of Canada.Google Scholar
Alajbegovic, A., Grogger, H. A. & Philipp, H. 1999 b Calculation of transient cavitation in nozzle using the two-fluid model. In Proc. 12th Annu. Conf. Liquid Atom. Spray Systems, Indianapolis, IN.Google Scholar
Andrews, M. J. & O'rourke, P. J. 1996 The multiphase particle-in-cell (MP-PIC) method for dense particulate flows. Intl J. Multiphase Flow 22, 379–402.CrossRefGoogle Scholar
Apfel, R. E. 1970 The role of impurities in cavitation-threshold determination. J. Acoust. Soc. Am. 48, 1179–1186.CrossRefGoogle Scholar
Arcoumanis, C., Badami, M., Flora, H. & Gavaises, M. 2000 Cavitation in real-size multi-hole diesel injector nozzles. SAE Trans. J. Engines 109–3, 1485–1500.Google Scholar
Arcoumanis, C., Flora, H., Gavaises, M. & Kampanis, N. 1999 Investigation of cavitation in a vertical multi-hole injector. SAE Paper 1999-01-0524.CrossRefGoogle Scholar
Arcoumanis, C., Gavaises, M., Nouri, J. M., Abdul-Wahab, E. & Horrocks, R. W. 1998 Analysis of the flow in the nozzle of a vertical multi hole diesel engine injector. SAE Trans. J. Engines 107–3, 1245–1259.Google Scholar
Arcoumanis, C., Nouri, J. M. & Andrews, R. J. 1992 Application of refractive index matching to a diesel nozzle internal flow. In Proc. Sixth Intl Symp. Appl. Laser Techniques Fluid Mech., Lisbon, Spain (ed. Adrian, R. J. et al. ), pp. 10.4.1–10.4.7. Springer.Google Scholar
Arndt, R. E. A. & Maines, B. H. 2000 Nucleation and bubble dynamics in vortical flows. J. Fluids Engng: Trans. ASME 122, 488–493.CrossRefGoogle Scholar
Atchley, A. A. & Prosperetti, A. 1989 The crevice model of bubble nucleation. J. Acoust. Soc. Am. 86, 1065–1084.CrossRefGoogle Scholar
Avva, R. K., Singhal, A. & Gibson, D. H. 1995 An enthalpy based model of cavitation. In Cavitation and Multiphase Flow Forum (ed. Katz, J. & Matsumoto, Y.), ASME FED, pp. 63–70.Google Scholar
Badock, C., Wirth, R., Fath, A. & Leipertz, A. 1999 Investigation of cavitation in real size diesel injection nozzles. Intl J. Heat Fluid Flow 20, 538–544.CrossRefGoogle Scholar
Badock, C., Wirth, R. & Tropea, C. 1999 The Influence of hydro grinding on cavitation inside a diesel injection nozzle and primary breakup under unsteady pressure conditions. In Proc. ILASS-EUROPE, Toulouse, France (ed. Lavergne, G.).Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Bauer, D. 2005 Planung und Durchführung von Experimenten zur Validierung eines CFD-Codes für Kavitationsströmungen. Diplomarbeit. Technische Universität Bergakademie Freiberg, Germany.Google Scholar
Bergwerk, W. 1959 Flow pattern in diesel nozzle spray holes. Proc. Inst. Mech. Engrs 173, 655–660.CrossRefGoogle Scholar
Blessing, M., König, G., Krüger, C., Michels, U. & Schwarz, V. 2003 Analysis of flow and cavitation phenomena in diesel injection nozzles and its effect on spray and mixture formation. SAE Paper 2003-01-1358.CrossRefGoogle Scholar
Brennen, C. E. 1995 Cavitation and Bubble Dynamics. Oxford University Press.CrossRefGoogle Scholar
Briggs, L. J. 1950 Limiting negative pressure of water. J. Appl. Phys. 21, 721–722.CrossRefGoogle Scholar
Bunnell, R. A. & Heister, S. D. 2000 Three-dimensional unsteady simulation of cavitating flows in injector passages. J. Fluids Engng: Trans. ASME 122, 791–797.CrossRefGoogle Scholar
Bunnell, R. A., Heister, S. D., Yen, C. & Collicott, S. H. 1999 Cavitating injector flows: validation of numerical models and simulations of pressure atomizers. Atom. Sprays 9, 445–465.CrossRefGoogle Scholar
Chaves, H., Knapp, M., Kubitzek, A. & Obermeier, F. 1995 Experimental study of cavitation in the nozzle hole of diesel injectors using transparent nozzles. SAE Paper 950290.CrossRefGoogle Scholar
Chen, Y. L. & Heister, S. D. 1996 a Modeling cavitating flows in diesel injectors. Atom. Sprays 6, 709–726.CrossRefGoogle Scholar
Chen, Y. L. & Heister, S. D. 1996 b Modeling hydrodynamic nonequilibrium in cavitating flows. J. Fluids Engng: Trans. ASME 118, 172–178.CrossRefGoogle Scholar
Chesters, A. K. & Hofman, G. 1982 Bubble coalescence in pure liquids. Appl. Sci. Res. 38, 353–361.CrossRefGoogle Scholar
Delannoy, Y. & Kueny, J. L. 1990 Two phase flow approach in unsteady cavitation modelling. In Cavitation and Multiphase Flow Forum, ASME FED, pp. 153–158.Google Scholar
Dukowicz, J. K. 1980 A particle-fluid numerical model for liquid sprays. J. Comput. Phys. 33, 229.CrossRefGoogle Scholar
Dumont, N., Simonin, O. & Habchi, C. 2001 Numerical simulation of cavitating flows in diesel injectors by a homogeneous equilibrium modeling approach. In Proc. CAV2001, Fourth Intl Symp. Cavitation, Pasadena, CA (ed. Brennen, C. E.). California Institute of Technology.Google Scholar
Farrell, K. J. 2003 Eulerian/Lagrangian analysis for the prediction of cavitation inception. J. Fluids Enng: Trans. ASME 125, 46–52.CrossRefGoogle Scholar
Feng, Z. G. & Michaelides, E. E. 2001 Drag coefficients of viscous spheres at intermediate and high Reynolds numbers. J. Fluids Engng: Trans. ASME 123, 841–849.CrossRefGoogle Scholar
Fox, F. E. & Herzfeld, K. F. 1954 Gas bubbles with organic skin as cavitation nuclei. J. Acoust. Soc. Am. 26, 984–989.CrossRefGoogle Scholar
Gavaises, M. & Giannadakis, E. 2004 Modelling of cavitation in large-scale diesel injector nozzles. In Proc. 20th Annu Conf. Liquid Atom. Spray Systems (ILASS-Europe), Nottingham, UK, 6–8 September (ed. Azzopardi, B. J.), pp. 159–164. School of Chemical, Environmental and Mining Enginnering, University of Nottingham.Google Scholar
Gavaises, M., Papoulias, D., Andriotis, A., Giannadakis, E. & Theodorakakos, A. 2007 Link between cavitation development and erosion damage in Diesel fuel injector nozzles. SAE Paper 2007-01-0246.CrossRefGoogle Scholar
Giannadakis, E. 2005 Modelling of cavitation in automotive fuel injector nozzles. PhD thesis, Imperial College, University of London, London, UK.Google Scholar
Giannadakis, E., Gavaises, M., Roth, H. & Arcoumanis, C. 2004 Cavitation modelling in single-hole diesel injector based on Eulerian–Lagrangian approach. In Proc. THIESEL Intl Conf. Thermo-Fluid Dyn. Processes Diesel Engines, Valencia, Spain, pp. 47–60. La Editorial de la UPV.Google Scholar
Giannadakis, E., Papoulias, D., Gavaises, M., Arcoumanis, C., Soteriou, C. & Tang, W. 2007 Evaluation of the predictive capability of diesel nozzle cavitation models. SAE Paper 2007-01-0245.CrossRefGoogle Scholar
Gindroz, B. & Billet, M. L. 1998 Influence of the nuclei on the cavitation inception for different types of cavitation on ship propellers. J. Fluids Engng: Trans. ASME 120, 171–178.CrossRefGoogle Scholar
Goney, K. H. & Corradini, M. L. 2000 Isolated effects of ambient pressure, nozzle cavitation and hole inlet geometry on diesel injection spray characteristics. SAE Paper 2000-01-2043.Google Scholar
Grogger, H. A. & Alajbegovic, A. 1998 Calculation of the cavitating flow in venturi geometries using two fluid model. In Proc. FEDSM'98 — 1998 ASME Fluid Engng Div. Summer Meeting, Washington, DC.Google Scholar
Harvey, E. N., Barnes, D. K., Mcelroy, W. D., Whiteley, A. H., Pease, D. C. & Cooper, K. W. 1944 Bubble formation in animals. I. Physical factors. J. Cell. Comp. Physiol. 24, 1–22.CrossRefGoogle Scholar
He, L. & Ruiz, F. 1995 Effect of cavitation on flow and turbulence in plain orifices for high-speed atomization. Atom. Sprays 5, 569–584.CrossRefGoogle Scholar
Henry, M. E. & Collicott, S. H. 2000 Visualization of internal flow in a cavitating slot orifice. Atom. Sprays 10, 545–563.Google Scholar
Hinze, J. O. 1975 Turbulence, p. 309. McGraw-Hill.Google Scholar
Hsiao, C.-T., Chahine, G. L. & Liu, H. L. 2000 Scaling effect on bubble dynamics in a tip vortex flow: prediction of cavitation inception and noise. Rep. 98007-1, Dynaflow Inc, Jessup, MD, USA.Google Scholar
Hsiao, C.-T., Chahine, G. L. & Liu, H. L. 2003 Scaling effect on prediction of cavitation inception in a line vortex flow. J. Fluids Engng: Trans. ASME 125, 53–60.CrossRefGoogle Scholar
Johnson, V. E. & Hsieh, T. 1966 The influence of the trajectories of gas nuclei on cavitation inception. In Proc. Sixth Symp. Naval Hydrodyn., pp. 163–179. Office of Naval Research, Washington, DC.Google Scholar
Kamp, A. M., Chesters, A. K., Colin, C. & Fabre, J. 2001 Bubble coalescence in turbulent flows: a mechanistic model for turbulence-induced coalescence applied to microgravity bubbly pipe flow. Intl J. Multiphase Flow 27, 1363–1396.CrossRefGoogle Scholar
Kinjo, T. & Matsumoto, M. 1998 Cavitation processes and negative pressure. Fluid Phase Equil. 144, 343–350.CrossRefGoogle Scholar
Kodama, Y., Take, N., Tamiya, S. & Kato, H. 1981 The effect of nuclei on the inception of bubble and sheet cavitation on axisymmetric-bodies. J. Fluids Engng: Trans. ASME 103, 557–563.CrossRefGoogle Scholar
König, G. & Blessing, M. 2000 Database of cavitation effects in nozzles for model verification: geometry and pressure effects on cavitating nozzle flow. DaimlerChrysler AG.Google Scholar
Kubota, A., Kato, H. & Yamaguchi, H. 1992 A new modelling of cavitating flows: a numerical study of unsteady cavitation on a hydrofoil section. J. Fluid Mech. 240, 59–96.CrossRefGoogle Scholar
Laín, S., Bröder, D., Sommerfeld, M. & Göz, M. F. 2002 Modelling hydrodynamics and turbulence in a bubble column using the Euler-Lagrange procedure. Intl J. Multiphase Flow 28, 1381–1407.CrossRefGoogle Scholar
Liu, Z. H. & Brennen, C. E. 1998 Cavitation nuclei population and event rates. J. Fluids Engng: Trans. ASME 120, 728–737.CrossRefGoogle Scholar
Marcer, R., Le Cottier, P., Chaves, H., Argueyrolles, B., Habchi, C. & Barbeau, B. 2000 A validated numerical simulation of diesel injector flow using a VOF method. SAE Paper 2000-01-2932.CrossRefGoogle Scholar
Marcer, R. & Legouez, J. M. 2001 Simulation of unsteady cavitating flows in diesel injector with an improved VOF method. In Proc. ILASS-EUROPE, Zurich, Switzerland (ed. Ineichen, B.). I.C. Engines and Combustion Laboratory, ETH, Zurich.Google Scholar
Martínez-Bazán, C., Montañés, J. L. & Lasheras, J. C. 1999 a On the breakup of an air bubble injected into a fully developed turbulent flow. Part 1. Breakup frequency. J. Fluid Mech. 401, 157–182.CrossRefGoogle Scholar
Martínez-Bazán, C., Montañés, J. L. & Lasheras, J. C. 1999 b On the breakup of an air bubble injected into a fully developed turbulent flow. Part 2. Size PDF of the resulting daughter bubbles. J. Fluid Mech. 401, 183–207.Google Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883–889.CrossRefGoogle Scholar
Meyer, R. S., Billet, M. L. & Holl, J. W. 1992 Freestream nuclei and traveling-bubble cavitation. J. Fluids Engng: Trans. ASME 114, 672–679.CrossRefGoogle Scholar
Michaelides, E. E. 1997 Review: the transient equation of motion for particles, bubbles, and droplets. J. Fluids Engng: Trans. ASME 119, 233–247.CrossRefGoogle Scholar
Michaelides, E. E. 2003 Hydrodynamic force and heat/mass transfer from particles, bubbles, and drops: the Freeman scholar lecture. J. Fluids Engng: Trans. ASME 125, 209–238.CrossRefGoogle Scholar
Milton, S. G. & Arakeri, V. H. 1992 Studies on cavitation inception process in separated flows. J. Fluids Engng: Trans. ASME 114, 85–92.CrossRefGoogle Scholar
Mørch, K. A. 2000 Cavitation nuclei and bubble formation: a dynamic liquid–solid interface problem. J. Fluids Engng: Trans. ASME 122, 494–498.CrossRefGoogle Scholar
Moss, W. C., Levantin, J. L. & Szeri, A. J. 2000 A new damping mechanism in strongly collapsing bubbles. Proc. R. Soc. Lond. A 456, 2983–2994.CrossRefGoogle Scholar
Nurick, W. H. 1976 Orifice cavitation and its effects on spray mixing. J. Fluids Engng 98, 681–687.CrossRefGoogle Scholar
Papoulias, D., Giannadakis, E., Mitroglou, N., Gavaises, M. & Theodorakakos, A. 2007 Cavitation in fuel injection systems for spray guided direct injection gasoline engines. SAE Paper 2007-01-1418.CrossRefGoogle Scholar
Plesset, M. S. & Prosperetti, A. 1977 Bubble dynamics and cavitation. Annu. Rev. Fluid Mech. 9, 145–185.CrossRefGoogle Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1992 Numerical Recipes in Fortran 77. Cambridge University Press.Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1996 Numerical Recipes in Fortran 90. Cambridge University Press.Google Scholar
Rood, E. P. 1991 Mechanisms of cavitation inception: review. J. Fluids Engng: Trans. ASME 113, 163–175.CrossRefGoogle Scholar
Roth, H. 2004 Experimental and computational investigation of cavitation in diesel injector nozzles. PhD thesis, Imperial College, University of London, London, UK.Google Scholar
Roth, H., Gavaises, M. & Arcoumanis, C. 2002 Cavitation initiation, its development and link with flow turbulence in diesel injector nozzles. SAE Trans. J. Engines 111–3, 561–580.Google Scholar
Roth, H., Giannadakis, E., Gavaises, M., Arcoumanis, C., Omae, K., Sakata, I., Nakamura, M. & Yanagihara, H. 2005 Effect of multi-injection strategy on cavitation development in diesel injector nozzle holes. SAE Trans. J. Engines 114–3, 1029–1045.Google Scholar
Rusche, H. & Issa, R. 2000 The effect of voidage on the drag force on particles, droplets and bubbles in dispersed two-phase flow. In Proc. 2nd Japanese–European Two-Phase Flow Gp Meeting, Tsukuba, Japan.Google Scholar
Sauer, J. & Schnerr, G. H. 2000 Unsteady cavitating flow: a new cavitation model based on a modified front capturing method and bubble dynamics. In Proc. FEDSM'00 — 2000 ASME Fluid Engng Div. Summer Meeting, Boston, MA.Google Scholar
Schmidt, D. P. & Corradini, M. L. 2001 The internal flow of diesel fuel injector nozzles: a review. Intl J. Engine Res. 2, 1–22.CrossRefGoogle Scholar
Schmidt, D. P., Rutland, C. J. & Corradini, M. L. 1997 A numerical study of cavitating flow through various nozzle shapes. SAE Paper 971597.CrossRefGoogle Scholar
Schmidt, D. P., Rutland, C. J. & Corradini, M. L. 1999 A fully compressible, two-dimensional model of small, high-speed, cavitating nozzles. Atom. Sprays 9, 255–276.CrossRefGoogle Scholar
Schnerr, G. H. & Sauer, J. 2001 Physical and numerical modeling of unsteady cavitation dynamics. In Proc. ICMF 2001: Fourth Intl Conf. Multiphase Flows, New Orleans, LA.Google Scholar
Shyy, W., Thakur, S., Ouyang, H., Liu, J. & Blosch, E. 1997 Computational Techniques for Complex Transport Phenomena. Cambridge University Press.CrossRefGoogle Scholar
Singhal, A. K., Athavale, M. M., Li, H. Y. & Jiang, Y. 2001 Mathematical basis and validation of the full cavitation model. In Proc. FEDSM'01 — 2001 ASME Fluid Engng Div. Summer Meeting, New Orleans, LA.Google Scholar
Singhal, A. K., Athavale, M. M., Li, H. Y. & Jiang, Y. 2002 Mathematical basis and validation of the full cavitation model. J. Fluids Engng: Trans. ASME 124, 617–624.CrossRefGoogle Scholar
Soteriou, C., Andrews, R. J. & Smith, M. 1995 Direct injection diesel sprays and the effect of cavitation and hydraulic flip on atomization. SAE Paper 950080.CrossRefGoogle Scholar
Soteriou, C., Smith, M. & Andrews, R. J. 1998 Diesel injection: laser light sheet illumination of the development of cavitation in orifices. IMechE Paper C529/018/98.Google Scholar
Sou, A., Masaki, Y. & Nanajima, T. 2001 Numerical simulation of transient cavitating flow in a spray nozzle. In Proc. ILASS-Asia, Busan, Korea.Google Scholar
Sou, A., Nitta, S. & Nakajima, T. 2002 Bubble tracking simulation of cavitating flow in an atomization nozzle. In Proc. FEDSM'02 — 2002 ASME Fluid Engng Div. Summer Meeting, Montreal, QC, Canada.CrossRefGoogle Scholar
Sridhar, G. & Katz, J. 1995 Drag and lift forces on microscopic bubbles entrained by a vortex. Phys. Fluids 7, 389–399.CrossRefGoogle Scholar
Tamaki, N., Shimizu, M. & Hiroyasu, H. 2001 Enhancement of the atomization of a liquid jet by cavitation in a nozzle hole. Atom. Sprays 11, 125–137.Google Scholar
Temperley, H. N. V. & Trevena, D. H. 1994 Metastability of the liquid–vapor transition and related effects. J. Stat. Phys. 77, 501–508.CrossRefGoogle Scholar
Tamura, Y., Sugiyama, K. & Matsumoto, Y. 2001 Cavitating flow simulations based on the bubble dynamics. In Proc. CAV2001: Fourth International Symposium on Cavitation, Pasadena, CA, (ed. Brennen, C. E.). California Institute of Technology.Google Scholar
Trevena, D. H. 1987 Cavitation and Tension in Liquids. Adam Hilger.Google Scholar
Vaidyanathan, R., Senocak, I., Wu, J. Y. & Shyy, W. 2003 Sensitivity evaluation of a transport-based turbulent cavitation model. J. Fluids Engng: Trans. ASME 125, 447–458.CrossRefGoogle Scholar
Vinogradova, O. I., Bunkin, N. F., Churaev, N. V., Kiseleva, O. A., Lobeyev, A. V. & Ninham, B. W. 1995 Submicrocavity structure of water between hydrophobic and hydrophilic walls as revealed by optical cavitation. J. Colloid Interface Sci. 173, 443–447.CrossRefGoogle Scholar
Wallis, G. B. 1969 One-Dimensional Two-phase Flow, p. 143. McGraw-Hill.Google Scholar
Walther, J., Schaller, J. K., Heinold, O., Kunzi, U. & Müller, D. 2001 Data base of structure and dynamic behavior of cavitation. Robert Bosch GmbH.Google Scholar
Walther, J., Schaller, J. K., Wirth, R. & Tropea, C. 2000 Investigation of internal flow in transparent diesel injection nozzles using fluorescent particle image velocimetry (FPIV). In Proc. ICLASS, Pasadena, CA (ed. Chigier, N.), pp. 300–307.Google Scholar
van Wijngaarden, L. 1976 Hydrodynamic interaction between bubbles in a liquid. J. Fluid Mech. 77, 27–44.CrossRefGoogle Scholar
Xiao, C. & Heyes, D. M. 2002 Cavitation in stretched liquids. Proc. R. Soc. Lond. A 458, 889–910.CrossRefGoogle Scholar
Yakhot, V., Orszag, S. A., Thangam, S., Gatski, T. B. & Speziale, C. G. 1992 Development of turbulence models for shear flows by a double expansion technique. Phys. Fluids A 4, 1510–1520.CrossRefGoogle Scholar
Yuan, W., Sauer, J. & Schnerr, G. H. 2000 Modeling and computation of unsteady cavitation flows in injection nozzles. In 1st Intl Colloq. Microhydrodynamics, Paris, France.Google Scholar
Yuan, W. & Schnerr, G. H. 2001 Cavitation in injection nozzles: effect of injection pressure fluctuations. In Proc. CAV2001: Fourth Intl Symp. Cavitation, Pasadena, CA (ed. Brennen, C. E.). California Institute of Technology.Google Scholar