Calculation of flow instability inception in high speed axial compressors based on an eigenvalue theory

This paper applies a theoretical model developed recently to calculate the flow instability inception point in axial high speed compressors system with tip clearance. After the mean flow field is computed by 3D steady computational fluid dynamics (CFD) simulation, a body force approach, which is a function of flow field data and comprises of one inviscid part and the other viscid part, is taken to duplicate the physical sources of flow turning and loss. Further by applying appropriate boundary conditions and spectral collocation method, a group of homogeneous equations will yield from which the stability equation can be derived. The singular value decomposition (SVD) method is adopted over a series of fine grid points in frequency domain, and the onset point of flow instability can be judged by the imaginary part of the resultant eigenvalue. The first assessment is to check the applicability of the present model on calculating the stall margin of one single stage transonic compressors at 85% rotational speed. The reasonable prediction accuracy validates that this model can provide an unambiguous judgment on stall inception without numerous requirements of empirical relations of loss and deviation angle. It could possibly be employed to check overcomputed stall margin during the design phase of new high speed compressors. The following validation case is conducted to study the nontrivial role of tip clearance in rotating stall, and a parameter study is performed to investigate the effects of end wall body force coefficient on stall onset point calculation. It is verified that the present model could qualitatively predict the reduced stall margin by assuming a simplified body force model which represents the response of a large tip clearance on the unsteady flow field.