Receptivity and structural sensitivity study of the wide vaneless diffuser flow with adjoint method

The stability of the flow in the vaneless diffuser of a centrifugal compressor is studied with the linear theory. The characteristics of direct and adjoint perturbation modes are investigated, and the receptivity of the instability mode to momentum forcing or mass injection is identified based on the adjoint modes. Analysis shows that the perturbation with the largest amplitude is located at the outlet of the vaneless diffuser, while the highest-receptivity region is located in the middle of the vaneless diffuser along the radial direction. The large difference between the direct and adjoint modes indicates that the instability mechanism cannot be identified from a study of either eigenmode separately. Therefore, the structural sensitivity analysis is adopted to study the feedback of the instability mode. The structural sensitivity of the eigenvalue which is proportional to the perturbation pressure and velocity is used to explain the mechanism of flow control for the vaneless diffuser.