Stability and structural sensitivity analysis of the turbulent flow in the narrow vaneless diffuser with mean flow method

Abstract The performance and operating range of modern centrifugal compressors employed in the turbocharger are often limited by the vaneless diffusers. Despite of the simple geometry, the complex flow in the narrow vaneless diffusers makes it hard to identify the physicial mechanism of flow stability and requires more reliable model. In the present work, a three dimensional prediction model of the turbulent flow stability in the vaneless diffuser based on the mean flow method was proposed. The turbulent stability analysis was performed by linearizing the incompressible Navier–Stokes equations around the numerically computed mean flows. The predictions of flow instability frequency and coherent structure were attempted. Then the adjoint stability analysis was carried out and the adjoint global mode was also obtained. Combining the direct and adjoint global modes, the structural sensitivity of the leading eigenvalue for the vaneless diffuser was analyzed in order to localize the wavemaker region. Through validation against experimental data, the mean flow approach was proved to be capable of predicting the frequency of the flow instability in the narrow vaneless diffuser with mean flow approach. The receptivity analysis showed forcing or initial condition applied at the main flow upstream and the fully developed flow downstream the intersection region of the boundary layers on both walls of the vaneless diffuser may be most effective on the flow control. The structural sensitivity distribution indicated that the wavemaker region of the vaneless diffuser is localized at the centerline of the flow, especially near the radial position of r = 1.02–1.35. The viscosity and Reynolds stresses play a role of stabilizing the vaneless diffuser flow.