Adjoint Optimization of a Wing Using the Class-Shape-Refinement-Transformation Method

This paper will demonstrate the potential of the class-shape-refinement-transformation (CSRT) method for aerodynamically optimizing three-dimensional surfaces. The CSRT method was coupled to an in-house Euler solver and this combination was used in an optimization framework to optimize the ONERA M6 wing in transonic conditions. The gradients of the flow variables with respect to the design parameters were computed using an adjoint solver integrated in the Euler code. The optimization was performed by a trust region reflective algorithm. A two-step approach was used to optimize the wing. First, a general optimization was done using the Bernstein coefficients of the shape function. Second, a regional refinement was performed using the B-spline coefficients of the refinement function. It was shown that using this strategy a considerable improvement of the lift-to-drag ratio of 22% could be achieved. The work presented in this paper proves that the CSRT method is a very intuitive and effective way of parametrizing aircraft shapes, both in two as well as in three dimensions. The method allows for a two-step approach which has the potential to significantly increase the lift-to-drag ratio of various aircraft shapes. It was also shown that using an adjoint algorithm provides the computational efficiency necessary to perform true three-dimensional shape optimization.