Comparison between gradient-free and adjoint based aerodynamic optimization of a flying wing transport aircraft in the preliminary design

This paper describes investigations of planform and shape optimizations for a flying wing transport aircraft with an Euler continuous adjoint method. For a prescribed lift the cost function will be the drag, which has to be minimized and implies a maximization of L/D. The results presented for the gradient based method using an adjoint solver are compared to an optimization performed with a gradient free approach. The different work-flows and procedures will demonstrate the advantages and disadvantages of each particular optimization approach. The optimization procedure uses a freeform deformation technique for the design param-eterization of the shape as well as for the surface mesh deformation required to determine the gradients. This combination of both tasks into one tool is advantageous because per-forming finite differences for evaluating the mesh sensitivities can be carried out with a constant grid topology. An example design case is also shown for demonstration purposes. Nomenclature CL lift coefficient CD drag coefficient CMY pitching moment coefficient L/D Lift-to-drag ratio D design vector F flux density tensor I cost function R residuals of the flow W vector of flow variables X vector of grid coordinates Λ vector of adjoint variables, Lagrangian multiplier n unit normal surface element in x, y and y-direction v velocity vector in x, y and y-direction Subscript k variable number I