The Unsteady Discrete Adjoint Method for Turbomachinery Applications

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 terms. Two testcases, a turbine vane and a turbine stage, are selected to demonstrate the feasibility of the method.