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The object of this paper is to propose a model to simulate steady and unsteady cavitating flows. In the engineering practice, cavitation flow is often modeled as a single-phase flow (mixture), where the cavitation area is handled as an area with the pressure lower than the vapor pressure. This approach always leads to the result, and the requirement of computer time is many times lower in comparison with multiphase flow models. The Reynolds-averaged Navier-Stokes equations are solved for the mixture of liquid and vapor, which is considered as a single-phase with variable density. The vaporization and condensation processes are controlled by barocline low. A transport equation with source terms is implanted in the code Computational Fluid Dynamics (CFD) to compute the volume fraction of the vapor. The CFD code used is ANSYS CFX. The influence of numerical and the physical parameters are presented. The numerical results are compared to previous experimental measures. For steady flow, a SST turbulence model is adopted and LES for the unsteady flow. Nomenclature ρ m : Mixture density (kg m −3 ) ρ v : Vapor density (kg m −3 ) ρ l : Liquid density (kg m −3 ) α : Volume fraction of vapor (−) µ m : Mixture viscosity (Pa s) µ v : Vapor viscosity (Pa s) µ l : Liquid viscosity (Pa s) V vap : Volume of vapor in control cell (m 3 ) V tot : Total volume in control cell (m 3 ) m : Source term (kg m −3 s −1 ) 277 Int. J. Model. Simul. Sci. Comput. 2011.02:277-297. Downloaded from www.worldscientific.com by WAYNE STATE UNIVERSITY on 03/23/15. For personal use only. 278 H. Kanfoudi & R. Zgolli n 0 : Bubble density (m −3 ) R : Radius of bubble (m) R 0 : Initial radius of bubble (m) p v : Saturation pressure (Pa) p g0 : Initial gas in the bubble (Pa) p : Local pressure (Pa) γ : Surface tension (N m −1 ) m + : Vaporization source term (kg m −3 s −1 ) m − : Condensation source term (kg m −3 s −1 ) α m : Volume fraction of liquid (−) σ : Cavitation number (−) c : Length of chord (m) C ref : Reference velocity (m s −1 ) p out : Outlet pressure (Pa) Cp : Pressure coefficient (−) L : Lift force (N) D : Drag force (N) A : Area of the hydrofoil (m 2 ) T : Period (s) t ref : Reference time (s) Int. J. Model. Simul. Sci. Comput. 2011.02:277-297. Downloaded from www.worldscientific.com by WAYNE STATE UNIVERSITY on 03/23/15. For personal use only.

Cavitating flows inside a diesel injection nozzle hole were simulated using a mixture model. A two-dimensional (2D) numerical model is proposed in this paper to simulate steady cavitating flows. The Reynolds-averaged Navier–Stokes equations are solved for the liquid and vapor mixture, which is considered as a single fluid with variable density and expressed as a function of the vapor volume fraction. The closure of this variable is provided by the transport equation with a source term Transport-equation based methods (TEM). The processes of evaporation and condensation are governed by changes in pressure within the flow. The source term is implanted in the CFD code ANSYS CFX. The influence of numerical and physical parameters is presented in detail. The numerical simulations are in good agreement with the experimental data for steady flow.

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