This paper develops the discrete adjoint equations for a turbomachinery RANS 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, i.e. on the derivation of flow-consistent adjoint inlet/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 non-reflective, 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 utilized to determine an improved blade shape based on the objective function gradient provided by the adjoint solution. The functionality of the proposed optimization method is demonstrated by the redesign of a single-stage transonic compressor. The objective is to maximize the isentropic efficiency while constraining the mass flow rate and the total pressure ratio.

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