Response surface method for airfoil design in transonic flow

A response surface method (RSM) applied to a transonic airfoil design problem is studied with other optimization methods. The objective function and constraints of RSM are modeled by quadratic polynomials, and the response surfaces are constructed by Navier-Stokes analyses in the transonic flow region. To assess the advantages of RSM, the design results by RSM are compared to those to a gradient-based optimization method (GBOM), namely, the discrete adjoint variable method. Comparisons are made for various sets of design variables and geometric constraints. It is observed that the response surface method is able to capture the nonlinear behavior of the objective function and smooth out high-frequency noises in transonic regime. These features enable the method to design a shock-free transonic airfoil with fewer design variables than in GBOM. In addition, RSM gives robust design results for the geometric constraints with different characteristics, whereas the GBOM depends heavily on the method of constraint specification. The results indicate that RSM could be used as an effective design tool for multidisciplinary design optimization problems, in which flowfields of design conditions are significantly nonlinear with many constraints imposed.