Flutter Prediction by a Cartesian Mesh Euler Method with Small Perturbation Gridless Boundary Conditions

Abstract

A method for the prediction of transonic flutter by the Euler equations on a Cartesian mesh is presented. Surface boundary conditions are applied using a perturbation of a gridless treatment in such a manner that solutions are obtained on a stationary mesh. For steady problems, the gridless method applies surface boundary conditions using a weighted average of the flow properties within a cloud of nodes in the vicinity of the surface. Weight functions are derived based on a least squares fitting of the surrounding cloud of nodes. For unsteady calculations, a perturbation of the weight functions is incorporated to account for a fluctuating surface normal direction. Additionally, a varying surface normal velocity is introduced into the boundary treatment. The nature of the method provides for efficient and accurate solution of transient problems in which surface deflections are small (i.e. flutter calculations) without the need for a deforming mesh. Problem setup also requires minimal effort due to the use of patched embedded Cartesian grids. Although deviations in the airfoil angle of attack are small, the mean angle of attack can be large, being prescribed by the far field boundary condition. Results show good agreement with available experimental data and wing flutter computations using traditional moving mesh algorithms considering a two-degree of freedom structural wing model.