Response surface method for airfoil design in transonic flow

A response surface method (RSM) applied to a transonic airfoil design probl em is studied with other optimization methods. The objective function and c onstraints of RSM are modeled by quadratic polynomials, and the response su rfaces are constructed by Navier-Stokes analyses in the transonic how regio n. To assess the advantages of RSM, the design results by RSM are compared to those of a gradient-based optimization method (GBOM), namely, the discre te adjoint variable method. Comparisons are made for various sets of design variables and geometric constraints. It is observed that the response surf ace method is able to capture the nonlinear behavior of the objective funct ion and smooth out high-frequency noises in transonic regime. These feature s enable the method to design a shock-free transonic airfoil with fewer des ign variables than in GBOM. In addition, RSM gives robust design results fo r the geometric constraints with different characteristics, whereas the GBO M depends heavily on the method of constraint specification. The results in dicate that RSM could be used as an effective design tool for multidiscipli nary design optimization problems, in which flowfields of design conditions are significantly nonlinear with many constraints imposed.