A dual-time implicit preconditioned Navier-Stokes method for solving 2D steady/unsteady laminar cavitating/noncavitating flows using a Barotropic model

Abstract

A two-dimensional, time-accurate, homogeneous multiphase, preconditioned Navier-Stokes method is applied to solve steady and unsteady cavitating laminar flows over 2D hydrofoils. A cell-centered finite-volume scheme employing the suitable dissipation terms to account for density jumps across the cavity interface is shown to yield an effective method for solving the multiphase Navier-Stokes equations. This numerical resolution is coupled to a single-fluid model of cavitation that the evolution of the density is governed by a barotropic sate law. A preconditioning strategy is used to prevent the system of equations to be stiff. A dual-time implicit procedure is applied for time accurate computation of unsteady cavitating flows. A sensitivity study is conducted to evaluate the effects of various parameters such as numerical dissipation coefficients and preconditioning on the accuracy and performance of the solution. The computations are presented for steady and unsteady laminar cavitating flows around the NACA0012 hydrofoil for different conditions. The solution procedure presented is shown to be accurate and efficient for predicting steady/unsteady laminar cavitating/noncavitating flows over 2D hydrofoils.