Investigation on numerical schemes in the simulation of barotropic cavitating flows

Abstract

A numerical methodology for the simulation of cavitating flows is considered. A homogeneous-flow cavitation model, accounting for thermal effects and active nuclei concentration, is considered, which leads to a barotropic state law. The continuity and momentum equations for compressible inviscid flows are discretized through a finite-volume approach, applicable to unstructured grids. The numerical fluxes are computed by shockcapturing schemes and adhoc preconditioning is used to avoid accuracy problems in the low-Mach regime. Second-order accuracy in space is obtained through MUSCL reconstruction. Time advancing is carried out by an implicit linearized scheme. Two different numerical fluxes are investigated here, viz. the Roe and the Rusanov schemes. For the Rusanov flux two different time linearizations are proposed; in the first one the upwind part of the flux function is frozen in time, while in the second one its time variation is taken into account, although in an approximated manner. The different schemes and the different linearizations are appraised for the quasi 1D-flow in a nozzle through comparison against exact solutions and for the flow around a hydrofoil mounted in a wind tunnel through comparison against experimental data. Non-cavitating and cavitating conditions are simulated. It is shown that, for cavitating conditions, the Rusanov scheme together with the more complete time linearization allows time steps much larger than for the Roe scheme to be used. Finally, the results obtained with this scheme are in good agreement with the exact solutions or the experimental data for all the considered test cases.