A coupled CAD‐free parameterization‐morphing method for adjoint‐based shape optimization

Abstract

This article presents a fully differentiated CAD‐free shape parameterization coupled with a grid displacement method for performing adjoint‐based aerodynamic shape optimization efficiently. Both tools are integrated into an adjoint‐based aerodynamic shape optimization process, where the shape changes and the corresponding grid adaptation take place simultaneously, in a single step. The role of the proposed shape parameterization technique is to control the shape changes of the aerodynamic body under study during shape optimization, and to modify it according to the spatial distribution of the gradient. The latter frequently contains numerical noise, due to the limited resolution of spatial discretization schemes, which can result in irregular surfaces, if the raw gradient is used directly. The proposed parameterization undertakes the elimination of this noise, thus ensuring smooth surfaces during the shape optimization. More specifically, a subset of the nodes belonging to the design surface is selected as the design vector (handles) and is responsible for controlling the surface displacements. The analytical differentiation of the parameterization, considering the adjoint morphing technique for the computation of the grid sensitivities, allows for its integration within a gradient‐based optimization process, where the adjoint method is used to compute the gradient of the objective w.r.t. all nodal positions. The propagation of this gradient information to the handles is efficiently and accurately achieved through the inclusion of the differentiated parameterization expression. The developed CAD‐free process chain is successfully demonstrated in an automotive S‐section cooling duct and a serpentine‐like one, used for internal turbomachinery blade cooling.