Numerical study on airfoils in steady and oscillating streams

Abstract

In this study, a numerical method has been developed in order to simulate steady and unsteady flow fields around airfoils. The unsteady flow field around the airfoil has been obtained by imposing periodically oscillating far field boundary conditions. In the interior domain, the Navier-Stokes equations have been solved by using Krylov subspace methods. The non-linear part of the problem has been linearized by Newtons method and GMRES is used as the linear solver with ILU preconditioner for efficient calculations. In order to reduce storage requirements, matrix free method is employed. The method of body-fitted curvilinear coordinate generation has been used to construct a finite-difference solution of the full, incompressible Navier-Stokes equations for the laminar viscous flow about arbitrary two-dimensional airfoils or any other two dimensional bodies. The governing equations in generelized curvilinear coordinate system were solved by using the stream function-vorticity formulation, which eliminates the pressure term. The velocity components have been calculated from the dependent variables, namely stream function and vorticity.