Assessment of turbulence adjoint method in sensitivity calculation and aerodynamic design optimization of turbomachinery cascades

Adjoint-based optimization faces the challenges from sensitivity accuracy when applying in design optimization of turbomachinery cascades with strong turbulence flow. In the study, sensitivities of aerodynamic parameters of different cascades are calculated using the discrete adjoint method, which are then used for design optimization of the cascades. The principles of adjoint method are firstly introduced and the procedures of sensitivity calculation using discrete adjoint method are described. Aerodynamic sensitivities of a high-pressure-turbine cascade and a controlled-diffusion compressor cascade are calculated by both the turbulence adjoint and constant-eddy-viscosity (CEV) adjoint methods. Through comparisons against the sensitivities by finite difference method, the improved accuracy in sensitivity calculation by turbulence adjoint method is demonstrated. Moreover, at the off-design condition of the compressor cascade with intensified turbulence flow, more improvements in sensitivity accuracy are gained. Finally, aerodynamic design optimizations of these two cascades are conducted. The results illustrate that more gains in performance improvements can be obtained by turbulence adjoint method, especially in the optimization of compressor cascade at the off-design condition. The impacts of aerodynamic shape optimization on performance variations of the cascades are addressed.