An homogeneous cavitation flow model capable of accounting for both the effects of thermal cavitation and the concentration of the active nuclei is considered; the model results in a barotropic state law. The local presence of both incompressible zones (pure liquid) and regions where the flow may become highly supersonic (cavitating mixture) renders the problem particularly stiff from a numerical viewpoint. The continuity and momentum equations for compressible inviscid flows are considered together with the barotropic state law. They are discretized by a finite-volume formulation applicable to unstructured grids. A shock-capturing upwind scheme is proposed for barotropic flows. The accuracy of the proposed method at low Mach numbers is ensured by ad-hoc preconditioning, which only modifies the upwind part of the numerical flux; thus, the time consistence is maintained and the proposed method can also be used for unsteady problems. Finally, an implicit time advancing is proposed to avoid severe time-step limitations encountered with explicit schemes. The proposed CFD tool is validated by quasi-1D simulations of nozzle flow. NOMENCLATURE Symbols : coefficient of pressure : latent heat of vaporization : temperature : speed : speed of sound : specific heat at constant pressure : cavitation model parameter : pressure : time : -component of the velocity : axial coordinate : void fraction : thermal diffusivity : isentropic compressibility module : specific heat ratio : cavitation model parameter : density : cavitation number Subscripts : liquid : vapor : at critical point : minimum : reference value : at saturation conditions : free-stream conditions
[1]
R. LeVeque.
Approximate Riemann Solvers
,
1992
.
[2]
H. Guillard,et al.
On the behaviour of upwind schemes in the low Mach number limit
,
1999
.
[3]
Cécile Viozat,et al.
Implicit Upwind Schemes for Low Mach Number Compressible Flows
,
1997
.
[4]
J. Steger,et al.
Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods
,
1981
.
[5]
Eli Turkel,et al.
Preconditioning and the Limit to the Incompressible Flow Equations
,
1993
.
[6]
E. Sinibaldi,et al.
A Preconditioned implicit Roe's scheme for barotropic flows: towards simulation of cavitation phenomena
,
2003
.
[7]
P. Roe.
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
,
1997
.
[8]
C. Brennen.
Cavitation and Bubble Dynamics
,
1995
.
[9]
E. Turkel,et al.
Preconditioned methods for solving the incompressible low speed compressible equations
,
1987
.
[10]
L. d'Agostino,et al.
A Modified Bubbly Isenthalpic Model for Numerical Simulation of Cavitating Flows
,
2001
.