NUMERICAL EXPERIMENTS WITH AN HOMOGENEOUS-FLOW MODEL FOR THERMAL CAVITATION

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