An improved progressive preconditioning method for steady non‐cavitating and sheet‐cavitating flows

Abstract

SUMMARYAn improved progressive preconditioning method for analyzing steady inviscid and laminar flows around fully wetted and sheet-cavitating hydrofoils is presented. The preconditioning matrix is adapted automatically from the pressure and/or velocity flow-field by a power-law relation. The cavitating calculations are based on a single fluid approach. In this approach, the liquid/vapour mixture is treated as a homogeneous fluid whose density is controlled by a barotropic state law. This physical model is integrated with a numerical resolution derived from the cell-centered Jameson's finite volume algorithm. The stabilization is achieved via the second-and fourth-order artificial dissipation scheme. Explicit four-step Runge-Kutta time integration is applied to achieve the steady-state condition. Results presented in the paper focus on the pressure distribution on hydrofoils wall, velocity profiles, lift and drag forces, length of sheet cavitation, and effect of the power-law preconditioning method on convergence speed. The results show satisfactory agreement with numerical and experimental works of others. The scheme has a progressive effect on the convergence speed. The results indicate that using the power-law preconditioner improves the convergence rate, significantly.

A high‐order nodal discontinuous Galerkin method to solve preconditioned multiphase Euler/Navier‐Stokes equations for inviscid/viscous cavitating flows

“…The computed surface pressure coefficient distribution by the present method is compared with that of Esfahanian et al, as shown in Figure , and the agreement between the numerical results is reasonable. The small difference between these two simulations may be due to different cavitation modeling approaches used and different numerical methods applied.…”

“…The small difference between these two simulations may be due to different cavitation modeling approaches used and different numerical methods applied. Esfahanian et al have used the finite volume method to solve the one‐fluid cavitation model with a barotropic state law and here the NDGM is applied to solve the multiphase transport equation–based model considering the mass transfer in the formulation.…”

SLAC – a semi-Lagrangian artificial compressibility solver for steady-state incompressible flows

“…The AC coefficient determines the stability and convergence rate of the AC scheme (Turkel, 1987;Malan et al, 2002;Esfahanian et al, 2012), and its choice is often case dependent. For example, for an inviscid and high Reynolds flow problem, Turkel(1987) showed that if b was close to the local convective velocity, the AC simulation achieved a better convergence rate ).…”

Effect of the Maximum Density Ratio Between Liquid and Vapor on Cavitating Simulation

“…Especially, the cavitation model is a critical method determining the accuracy of numerical simulation. Esfahanian et al (2012) applied a barotropic state equation that links the density variations to the local static pressure to solve the mixture density in the cavitating flow and this method is famous as the cavitation model based on state equation. The other popular approach to simulate cavitating flows is called as the cavitation model based on transport equation, which solves an additional transport equation for either the mass or volume fraction of vapor, with appropriate source/sink term(s) to regulate the mass transfer between the liquid and vapor phases.…”