A three-dimensional vaneless diffuser stall model

Abstract

A three-dimensional (3D) model is presented to study the occurrence of weak rotating waves in vaneless diffusers of centrifugal compressors. The model is an extension of the 2D one developed by Moore. 3D incompressible linearized Euler equations are cast on a rotating frame of reference travelling at the same circumferential speeds as the waves and the viscous effects are ignored. The diffuser is assumed to have two parallel walls and discharge into a large plenum. Solutions to the equations are obtained by a finite difference method and the singular value decomposition technique. Disturbances along the axial direction are found under zero undisturbed axial velocity. Resonant disturbances in the diffuser flow regardless of the compressor characteristics are also found as in the 2D cases found by Moore. Computational results show that both the critical flow angle and the propagation velocity of the wave are affected by the departure from the axial uniform distribution of the undisturbed radial velocity at the diffuser inlet, but the angle is less affected than the wave speed. The velocity distribution that satisfies Fj0rtoft's necessary conditions for flow instability is found slightly less stable and is more affected by the departure than those that do not. Shorter diffusers are affected more by the departure than the longer ones. The critical angle is shown to be increased non-linearly with the wave number and this helps to explain why wave numbers 2 to 4 are commonly observed in experiments. Finally, comparison with the experimental results in the open literature is made and a good agreement is shown.