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