When are Nonlinearities Important at Stall Inception?

Abstract

Recent experimental work has shown that in some compressors, the nonaxisymmetric disturbance leading to loss of stability appears as a localised phenomena, rather than a travelling sine wave which spans the entire circumference, suggesting that nonlinear effects appear very early in the evolution of the disturbance. In a regime dominated by nonlinear effects, the Fourier modes used to describe the spatial structure of non-axisymmetric disturbances, obtained from either experimental data or numerical data produced by a model, can interact very early in the rotating stall inception process. In this paper, we determine which parameters affect the rate of interaction of the various modes in a study of the Moore-Greitzer (MG) model. The relevant parameters are related back to the physics of compressors. Though the stall inception process may well be three-dimensional and involve physics not captured by the quasi two dimensional MG model, this study is of interest to those who wish to detect and control the magnitude of nonaxisymmetric disturbances, in order to decrease the stall margin in a compression system. Any control strategy which depends on eight detecting devices around the annulus of the compressor can resolve only the first three spatial Fourier modes. If disturbances leading to compression system instability develop as spikes, this approach will be completely unsuccessful at detecting the disturbances while they are still small enough to be controlled. The problem is further exacerbated by temporal nonlinearities, that is, the operating point may be linearly stable, but may lose stability to larger disturbances. It is observed in experiments and the Moore-Greitzer model that the compressor loses stability before the throttle is closed past the peak of the performance curve. Both spatial and temporal nonlinearities are discussed.