Performance sensitivity analysis and aerodynamic optimization of compressor cascades by a turbulence adjoint method

Sensitivity, which is useful for evaluating the contributions of input variations to output changes, favors designers exploiting the most sensitive design parameters and completing design optimization in aerospace. This study introduces the turbulence adjoint method due to its low computational cost in calculating sensitivities with high accuracy and then solves the adjoint partial differential equations with respect to both the Reynolds-averaged Navier-Stokes and turbulence model equations with the assistance of an automatic differentiation tool. By utilizing the turbulence adjoint method, the sensitivities of aerodynamic performance to the blade profile modifications of two-dimensional and three-dimensional compressor cascades are calculated, allowing for the investigations of the impact of geometric variations on the changes in the flow field. Ultimately, aerodynamic optimization of the compressor cascades is conducted. After optimization, the adiabatic efficiency of the two-dimensional cascade increases by 3.11%, and it increases by 1.15% for the three-dimensional cascade. The variations in flow fields of both the original and optimized cascades are illustrated to discover the origins of performance improvements. The changes in blade profile are almost consistent with those forecasted from sensitivity analysis, demonstrating the potential superiority of the adjoint method for aerodynamic design.