Time-domain aeroelastic simulation on stationary body-conforming grids with small perturbation boundary conditions

Abstract

Small perturbation boundary conditions are formulated for solving the unsteady Euler equations on body-conforming stationary grids. The CFD solver with the approximate boundary conditions is coupled with elastic equations to predict the aeroelastic properties of airfoils. The accurate nonlinear Euler equations are solved in the field, while the movement of the solid surfaces is accounted for in the new boundary conditions without moving or deforming the computational grids. The first-order wall boundary conditions are used in solving the full Euler equations for steady, unsteady and aeroelastic cases, and the results are compared with Euler solutions with full boundary conditions on moving grids and known experimental data. The relative errors are analyzed quantitatively due to the variation of thickness or pitching angles of the airfoils for steady cases. Compared to a similar approximate boundary condition method on pure Cartesian grids, the present method on body-fitted grids eliminates the thickness limitation and the singularity at the leading edge of a round-nosed airfoil. It is shown that the simple first-order boundary conditions are adequate to represent airfoils with small deformation of both steady and unsteady cases.