This paper introduces a multi-point design capability to discrete adjoint-based aerodynamic shape optimization for multistage turbomachines. The developed optimization framework allows to improve a compressor or turbine design not only for a certain operating point, but enables the inclusion of additional off-design operation points, therefore guaranteeing a robust design and annihilating the risk of improving the configuration for a specific design point while deteriorating the overall operability of the turbomachine. To keep the computational cost to a minimum, at every design cycle the flow and adjoint solutions are first calculated and stored for each operating point. This approach ensures that the subsequent finite-difference approximation of the residual sensitivity with respect to the design variables is obtained at a cost nearly independent of the number of investigated operating points. The objective function gradient is then assembled as a weighted sum of the sensitivities calculated for the different operating points. The developed multi-point optimization method is applied to a single-stage transonic compressor and both the back pressure and the rotor wheel speed are varied to investigate the use of adjoint-based design methods to efficiently explore robust turbomachinery designs.
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