An unstructured preconditioned central difference finite volume multiphase Euler solver for computing inviscid cavitating flows over arbitrary two- and three-dimensional geometries

Abstract

In the present work, a numerical method is adopted and applied for simulating the inviscid cavitating flows around two- and three-dimensional geometries on unstructured meshes. The algorithm uses the preconditioned multiphase Euler equations discretized by a cell-centered central difference finite volume scheme with suitable dissipation terms. The interface capturing method with three transport equation-based cavitation models, namely the Merkle et al., Singhal et al. and Kunz et al. models are employed for the mass transfer between the liquid and vapor phases to be calculated. The simulations of the steady inviscid cavitating flows are performed around different two- and three-dimensional geometries, namely the NACA0012, NACA66(MOD) and two-element NACA4412-4415 hydrofoils, the hemispherical head shape body and the twisted NACA0009 hydrofoil, and the results are obtained over these geometries with the three cavitation models used for different flow conditions. The effects of different numerical parameters on the accuracy of the solution are also examined by a sensitivity study. The present results are compared with those of performed by other researchers which exhibit good agreement. It is indicated that the solution method adopted based on the preconditioned finite volume multiphase Euler flow solver on unstructured meshes is capable of accurately predicting the surface pressure distribution and the cavity shape over the arbitrary two- and three-dimensional geometries.