A numerical approach to predict the rotating stall in the vaneless diffuser of a centrifugal compressor using the eigenvalue method

A two-dimensional incompressible flow model is presented to study the occurrence of rotating stall in vaneless diffusers of centrifugal compressors. The diffuser considered has two parallel walls, and the undisturbed flow is assumed to be circumferentially uniform, isentropic, and to have no axial velocity. The linearized 2D Euler equations for an incompressible flow in a fixed frame of the coordinate system are considered. After discretization by a spectral collocation method based on Chebyshev-Gauss-Lobatto points, the generalized eigenvalue problem is solved through the QZ algorithm. The compressor stability is judged by the imaginary part of the eigenvalue obtained. Based on the 2D stability analysis, the influence of inflow angle, radius ratio and wave number are studied. The results from the present stability analysis are compared with some experimental measurement and Shen's model. It is showed that diffuser instability increases rapidly and the stall rotational speed decreases quickly with an increase in the diffuser radius ratio. The largest critical inflow angle can be obtained when the wave number is around 3 ∼ 5 for the radius ratio between 1.5 to 2.2. It is also verified that the stability model proposed in this paper agrees well with experimental data and has the capability to predict the onset of rotating stall, especially for wide diffusers.