The unsteady discrete adjoint method for the calculation of objective function gradients for transient turbomachinery compressible viscous flows is presented. The URANS state equations are used along with the one-equation Spalart-Allmaras model. The implementation relies on an existing unsteady three-dimensional unstructured grid solver and discrete adjoint capabilities previously developed for steady flows. The formulation of the adjoint equations is introduced within a generic time-dependent CFD optimal design problem. An adjoint sliding plane functionality is also presented in order to enable multi-row time-dependent adjoint calculations, exploiting the rotor-stator interface. Algorithmic Differentiation (AD) is used to compute differential terTwo testcases, a turbine vane and a turbine stage, are selected to demonstrate the feasibility of the method.
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