Numerical simulation of unsteady flows with forced periodical oscillation around hydrofoils using locally power-law preconditioning method

Abstract

Abstract In the present study, a developed progressive preconditioning approach called locally power-law preconditioning method is implemented to analyze unsteady flows around hydrofoils at fixed and oscillating angles of attack. The preconditioning matrix is adopted locally from the velocity flow-field by a power-law relation. The unsteady preconditioned governing equations are solved by means of Jameson’s cell-centered finite volume numerical method and a dual-time implicit algorithm. Solution stability is obtained through second- and fourth-order artificial dissipation terms. Explicit four-stage Runge–Kutta time integration is applied to achieve the steady state condition in each pseudo time step. The results focus on velocity profiles, drag and lift coefficients and the impact of locally power-law preconditioner on the convergence rate. The results indicate that the locally power-law preconditioning method has an acceptable accuracy and improves the convergence rate to a large extent in unsteady regimes.