Within an industrial setting, mesh adaptation has so far found very limited use. This is, in part, due to the complexity of the geometries and flow features that are to be dealt with. However, the successful utilisation of grid modification techniques, could help engineers achieve more accurate estimates of quantities of interest quickly and efficiently. For this reason, in this paper, adjoint error mesh adaptation technology is developed and applied to steady-3D turbo-machinery solutions. The grid modification strategy proposed comprises of a combined mesh movement and mesh refinement procedure, entirely based on errors related to the functional of interest. The node addition scheme makes use of the output to the flow adjoint solver and an interpolation to an embedded grid. The determined error is used in an edge-refinement approach developed in the in-house MeshPost software. The mesh relocation technique, instead, employs the sensitivity of the functional of interest with respect to the nodes’ coordinates to compute a Riemmannian metric. This parameter is then equi-distributed over the mesh by applying a spring-stiffness approach.

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The benefit of mesh adaptation to improve the optimisation process of turbomachinery components is here demonstrated for the first time. Mesh movement is used to automatically cluster and align the cells with significant flow features such as shocks, shock-induced separation and wakes for every geometry tested during a transonic compressor blade optimisation. Using mesh movement means that the same size grid is used while significantly improving the accuracy of the simulation and resulting adjoint gradients. A method is demonstrated to automatically carry out feature based mesh movement during every step of an adjoint optimisation process. Optimisations are carried out using the adaptation method and also using the starting mesh as a comparison. It is shown that (when tested on a very fine grid) the adaptation-optimisation process results in a better design, due to more accurate flow and gradient prediction throughout the optimisation process. A cost breakdown of the process is given to show that using adaptation during the optimisation process only increases the overall optimisation cost by a small amount, but results in greater efficiency of the final blade design.

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