Summary In any shape optimization framework and specifically in the context of computational fluid dynamics, a robust and reliable grid deformation tool is necessary to undertake the adaptation of the computational mesh to the updated boundaries at each optimization cycle. Grid deformation has its share of challenges, namely, to maintain high mesh quality (avoid distorted elements and tangles) even when dealing with extreme deformations. In this work a novel grid deformation algorithm, the finite transformation rigid motion mesh morpher (FT‐R3M) is proposed. FT‐R3M is essentially a mesh‐free grid deformation approach, since it does not require any inertial quantities and it gracefully propagates the movement of the boundaries (surface mesh) to the internal nodes of the mesh (volume mesh), by keeping the motion of its parts (referred to as stencils) as‐rigid‐as‐possible. It is an optimization‐based method, which means that the interior nodes of the computational mesh are displaced to minimize a distortion metric related to the elastic deformation energy, by favoring rigidity in critical directions, thus being able to handle mesh anisotropies very efficiently. Results are presented for three test cases; a rotated airfoil with a mesh appropriate for viscous flow; a simulation of a low Reynolds duct case; a beam.

In any optimization framework, a robust and reliable mesh morpher is necessary to undertake the adaptation of the CFD mesh to the updated boundaries at each optimization cycle. Morphing has its share of challenges, namely to maintain high mesh quality (avoid distorted elements and tangles) even during extreme deformations. In this work, the Finite Transformation Rigid Motion Mesh Morpher (FT-R3M) is presented, an improved version of the Rigid Motion Mesh Morpher [5], that eliminates the need for sub-cycling, making it more efficient in terms of CPU time. FT-R3M, which bears some similarities to [4], is a mesh-less mesh morphing tool, since it does not require any inertial quantities, that gracefully propagates the movement of the boundaries (surface mesh) to the internal nodes of the mesh (volume mesh), by keeping the motion of its parts (referred to as stencils) as-rigidas-possible. It is an optimization-based method, which means that the interior nodes of the computational mesh are displaced to minimize a distortion metric, namely the deformation energy. Since FT-R3M is minimizing the deformation energy between the initial and the final configuration, as opposed to R3M, in which the deformation energy is minimized from each sub-cycle to another, there is a significant gain in terms of the quality of the resulting mesh. The efficiency of the morpher proposed in this article will be demonstrated in small and medium-size cases.

Uncertainties, in the form of either non-predictable shape imperfections (manufacturing) or flow conditions which are not absolutely fixed (environmental) are involved in all aerodynamic shape optimization problems. In this paper, a workflow for performing aerodynamic shape optimization under uncertainties, by taking manufacturing uncertainties into account is proposed. The uncertainty quantification (UQ) for the objective function is carried out based on the non-intrusive Polynomial Chaos Expansion (niPCE) method which relies upon the CFD software as a blackbox tool. PCE is combined with an evolutionary algorithm optimization platform. CAD-free techniques are used to control the shape and simultaneously generate shape imperfections; next to this, a morphing/smoothing tool adapts the CFD mesh to any new shape. In the cases presented in this paper, all CFD evaluations are performed in the OpenFOAM environment.

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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.