Abstract
Aresponsesurfacemethod (RSM)appliedtoatransonicairfoildesignproblemisstudiedwithotheroptimization 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 e ow region. To assess the advantages of RSM, the design results by RSM are compared to those of a gradient-based optimization method (GBOM), namely, the discrete adjoint variable method. Comparisons are made for various sets of design variables and geometric constraints.Itisobserved thattheresponsesurfacemethodisabletocapturethenonlinearbehavioroftheobjective 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 specie cation. The results indicate that RSM could be used as an effective design tool for multidisciplinary design optimization problems, in which e owe eldsof design conditions are signie cantly nonlinear with many constraints imposed.
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