Numerical simulation of two-dimensional blade-vortex interactions using unstructured adaptive meshes

Abstract

A two-dimensional Euler flow solver has been developed for the simulation of unsteady, blade-vortex interaction problems on unstructured meshes. The Euler solver is based on a second-order-accurate implicit time integration using a point Gauss-Seidel relaxation scheme and a dual time-step subiteration. A vertex-centered, finite volume discretization is used in conjunction with the Roe's flux-difference splitting. An unsteady solution-adaptive dynamic mesh scheme is used by adding and deleting mesh points at every adaptation step to take account of not only spatial but also of temporal variations of the flow field. Unsteady flow around a harmonically oscillating airfoil and traveling vortex in a freestream were simulated to validate the accuracy of the dynamic mesh adaptation procedure. Three blade-vortex interaction problems, two at transonic freestream speeds and one with vortex-airfoil collision, were investigated. Computed results show good agreements with existing experimental and computational results within the accuracy of the present inviscid solver. It is found that the evolution of vorticies and propagation of acoustic waves can be accurately simulated using the present unstructured dynamic mesh adaptation procedure.