The use of optimisation software combined with modern CFD simulation techniques can lead to the discovery of improved blade designs. This process can have high computational cost however, especially if large meshes are required to accurately simulate the critical flow features.

In this paper, the benefits of mesh adaptation to improve the design optimisation process are demonstrated. Grid adaptation \[1\] allows a coarser mesh to be used than would otherwise be necessary, whilst still accurately simulating the flow. This has the potential to drastically reduce the cost of an optimisation process.

 

Direction dependent anisotropic mesh movement is used in this work to automatically move the mesh towards the most critical regions of the flow. The movement is driven by the relative Mach number, allowing features such as shocks, boundary layers and wakes to be more accurately resolved while keeping a low total cell count. In this work mesh movement is combined with adjoint optimisation to demonstrate the cost reduction to the design process that can be achieved, while maintaining accuracy.

 

The geometry (a transonic compressor blade) is first simulated in Hydra RANS CFD \[2\] using a reasonably good quality but coarse multi-block structured mesh. A much finer (globally refined) mesh is also produced and simulated to provide a comparison. An adapted version of the coarse grid is then produced using flow-feature based mesh movement. It is shown how the adapted grid is able to improve the accuracy of the solution, matching closely the result of the finest grid, while maintaining a low node count. The adapted grid yields simulation results that are more accurate than the coarse grid, but with a comparatively small increase in computational cost.

 

A comparison of adjoint design parameter gradients (gradient of objective function (efficiency) with respect to each design parameter) is then carried out. It is shown that the adapted mesh gradients match more closely to the fine mesh gradients than those produced using the starting coarse mesh.

 

During each iteration of the optimisation, the current geometry is simulated using a baseline coarse mesh. Several adaptation steps are then carried out, to move the mesh based on the flow features. The objective function (efficiency) and adjoint gradients are then evaluated on the final adapted mesh. The optimiser selects the next design and a baseline coarse mesh is then re-generated for this design. The process is then repeated until an optimal design is found.

 

To demonstrate the benefit of using mesh adaptation within an optimisation process, separate blade optimisations are carried out using the coarse and fine meshes, and finally using the adaptation process during the optimisation. It is demonstrated how the optimisation including adaptation is able to produce comparable design benefit to the fine grid (when all optimised geometries are tested on the fine grid), but with a significant reduction in computational cost. Whilst the coarse grid can complete the optimisation in a further reduced time, due to the inaccuracies introduced, the optimised design does not provide as much benefit.

 

\[1\]  G Vivarelli, N Qin, S Shahpar, and D Radford. "Efficient Adjoint-Based Mesh Adaptation Applied to Turbo-Machinery Flows." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers Digital Collection, 2018.  
\[2\]  L. Lapworth, “Hydra-CFD: a framework for collaborative CFD development,” in International Conference on Scientific and Engineering Computation (IC-SEC), Singapore, 2004.


Using Feature-Based Mesh Adaptation to Improve the Adjoint Optimisation of Transonic Compressor Blades

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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