Adjoint-Based Constrained Aerodynamic Shape Optimization for Multistage Turbomachines

This paper develops the discrete adjoint equations for a turbomachinery Reynolds-averaged Navier–Stokes solver and proposes a framework for fully automatic gradient-based constrained aerodynamic shape optimization in a multistage turbomachinery environment. The systematic approach for the development of the discrete adjoint solver is discussed. Special emphasis is put on the development of the turbomachinery-specific features of the adjoint solver (that is, on the derivation of flow-consistent adjoint inlet and outlet boundary conditions) and, to allow for a concurrent rotor–stator optimization and stage coupling, on the development of an exact adjoint counterpart to the nonreflective, conservative mixing-plane formulation used in the flow solver. The adjoint solver is validated by comparing its sensitivities with finite difference gradients obtained from the flow solver. A sequential-quadratic programming algorithm is used to determine an improved blade shape based on the gradient information provided by...

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