Efficient kriging-based aerodynamic design of transonic airfoils: Some key issues

Today's complex time-consuming Computational Fluid Dynamics (CFD) codes stimulated the use of surrogate models in aerodynamic design. In this paper, an efficient Kriging-based airfoil design system is developed, including functionalities of optimization design and inverse design. In this system, Design of Experiment techniques are used to select initial sample points in the design space and initial Kriging models are subsequently built for the cost function as well as the constraints, based on the sampled data; the Kriging models are refined repetitively by minimizing the Kriging approximated cost function or maximizing its Expected Improvement (EI) with genetic algorithm, until the global optimum is found. Four key issues about the design system is investigated: First, the performance of global optimization is tested for an analytical problem with extremely poor initial sampling; Second, the number of function evaluation needs to explore the global optimum for an analytical function is investigated with the number of design variables ranging from 2 to 40; Third, the optimization system is compared with the conventional quadratic response surface method (RSM) in drag minimization of transonic airfoil, which confirms that the Kriging-based optimization outperforms RSM method both in efficiency and percentage of drag reduction; Fourth, the design system is demonstrated for inverse design of a transonic airfoil, which also shows that it is very efficient and robust.