High-Resolution CAD-Based Shape Parametrisation of a U-Bend Channel

The parametrisation of the geometry in shape optimisation has an important influence on the quality of the optimum and the rate of convergence of the optimiser. Refinement studies for the parametrisation are not shown in the literature, as most methods use non-orthogonal parametrisations, which cause issues with convergence when the parametrisation is refined. The NURBS-based parametrisation with complex constraints (NSPCC) is the only CAD-based parametrisation method that guarantees orthogonal shape modes by constructing an optimal basis. We conduct a parametrisation refinement study for the benchmark turbomachinery cooling bend (U-bend) geometry, an intially symmetric geometry. Using an adjoint RANS solver, we optimise for mininmal total pressure drop. The results show significant effects of the control net density on the final shape, with the finest control net producing an asymmetric optimal shape resembling strakes that induces swirl ahead of the bend. These asymmetric modes have not been reported in the literature so far. We also demonstrate that the convergence rate of the optimiser is not significantly affected by the refinement of the parametrisation. The effectiveness of these shape features obtained with single-point optimisation is evaluated for a range of Reynolds numbers. It is shown that total pressure drop reduction is not sensitive to Reynolds number.