Unsteady blade row interactions play an important role in the performance of the compressor stages. However, due to the large cost of the unsteady flow simulation, most aerodynamic optimizations of the compressor are based on the steady flow simulation. This paper adopts the time spectral method to reduce the cost of the unsteady flow simulation and a discrete adjoint solver based on the unsteady flow solver has been developed. The unsteady flow equations and the adjoint equations are solved using an in-house code. The in-house code is based on the finite volume method and solves the URANS (Unsteady Reynolds Averaged Navier-Stokes) equations on the multi-block structured mesh. For spatial discretization the 3rd order WENO (Weighted Essentially Nonoscillatory) upwind scheme is used for reconstruction and the convective flux is computed with Roe’s approximate Riemann solver. The widely used one-equation Spalart-Allmaras turbulence model is adopted for the flow simulation. For the adjoint solution, the constant-eddy viscosity assumption is adopted and only the main flow adjoint equations are solved. The adjoint equations are formed in a discrete manner, which leads to more accurate discrete objective function sensitivity than the continuous adjoint method. The present work serves as an essential part of the system for efficient unsteady aerodynamic optimization of turbomachinery.
Algorithm Developments for Discrete Adjoint Methods
