Adjoint boundary sensitivity method to assess the effect of nonuniform boundary conditions

The performance of turbomachinery is largely affected by the nonuniform boundary conditions caused by the coupling between neighboring parts, such as the inlet distortion and hot streak. Existing works study this problem by comparing the flow fields with uniform and nonuniform boundary conditions, which is cost extensive. In this work a new and efficient method is developed by computing the sensitivities of arbitrary performance metric relative to the boundary conditions and this method quantitatively describes how the disturbance on the boundary surface affects the performance. The adjoint method popular in the design optimization is extended to current field for the efficient computation of the sensitivity. The extra cost is independent of the number of parameters describing the nonuniform distribution. Accuracy of the adjoint boundary sensitivity is validated against analytical results for a converging–diverging nozzle case. Its applications in a representative case are detailed and discussed in this paper. Current method provides a new tool, also direct guides to minimize the negative effect and improve the performance utilizing the adjoint boundary sensitivity.