Numerical Solution of Navier-Stokes Equations for Rigid Airfoils in Arbitrary Unsteady Motion

Abstract

The existing code for the solution of the two-dimensional Navier-Stokes equations for steady cases at DLR is extended to the case of rigid airfoils in arbitrary unsteady motion. The original steady code uses the cell-vertex finite-volume formulation with artificial dissipation terms consisting of a blend of second and fourth differences. This spatial discretization leads to a system of ordinary differential equations in time which is solved by an explicit five-stage Runge-Kutta time stepping scheme. The implicit residual smoothing with variable coefficients is used to increase the CFL number. In the present research, a rigid body-fitted grid system fixed to the moving airfoil is generated for the solution of the flow field. The governing equations in integral form for moving control volume are derived to take the grid movement into account. Two numerical examples for pitching oscillation at low and high angles of attack are given, and compared with the experimental results.