Aerodynamic Shape Optimization Using a Morphing- Body Optimization Method

Abstract

A morphing-body optimization method is introduced to accelerate adjoint-based shape optimization techniques. The optimization process solves the flow and adjoint equations around a continuously deforming body whose shape is controlled by the cost function. Effect of various parameters on the efficiency of the scheme is studied. It is found that, for the best performance of the algorithm, the morphing rate of the airfoil should be restricted, since larger rates foster oscillations and lower values are not computationally feasible. Moreover, the iterative procedure in the adjoint solver should be adapted to the iteration scheme in the flow solver and to the morphing rate. I. Introduction FD has changed our lives in many ways. It was initially used as merely an analysis tool. With the help of high speed computers, it became possible to carry out many numbers of analyses on the same machine and thus optimization techniques were incorporated into design of aerospace systems with the help of CFD. Application of control theory to optimization problems resulted in adjoint-based optimization techniques, which considerably reduced the computational cost. Jameson was the first to apply adjoint-based techniques to optimization using Euler equations 1 . He has been working extensively in different areas of adjoint-based aerodynamic shape optimization 2-5 . Moreover, a few methods have been developed to improve efficiency of adjoint-based optimization algorithms. Hazra has developed a pseudo-timestepping method using an artificial time stepping for the optimization process 6,7 . Jameson developed a reduced gradient approach which calculated gradient using boundary terms only 8 . In this paper, Morphing-Body Optimization (MBO) is introduced as a method to improve efficiency of adjoint-based optimization algorithms. It is analogous to the pseudo-time stepping method by Hazra 6 . However, the problem has been looked at from a different aspect. In fact, the problem is considered as unsteady solution of a morphing airfoil. Furthermore, effect of various parameters on the efficiency of the MBO method is investigated for various inverse design problems. Finally, flow and adjoint residuals are plotted for the unsteady process of airfoil deformation.