FUN3D-based Adjoint Optimization for Elastic Tandem Airfoils in Chaotic Flows

This proposal develops a two-dimensional, FUN3D-based, flow-structure-coupled adjoint optimization framework capable of handling chaotic dynamics, and validate this framework on an elastic tandem airfoil configuration in chaotic flow. To overcome the challenge of sensitivity analysis in chaotic flows, we will develop in this proposal the adjoint NI-LSS algorithm. This algorithm is the discrete adjoint of the tangent NI-LSS method that we developed previously. We have shown that the tangent NI-LSS method is superior to finite difference methods in sensitivity analysis of statistics in chaotic flows. The adjoint NI-LSS algorithm proposed here is consistent to the tangent NI-LSS algorithm to machine precision, allowing easy verification; it can have significantly lower computation cost than the tangent NI-LSS method in optimization with many design variables. The resulting sensitivities to shape and sizing design variables will be validated against very-long-time finite difference calculations. We plan to extend this two-dimensional, FUN3D-based, flow-structure-coupled adjoint optimization framework to three-dimensions in Phase II.