Quantitative characteristic of rotating stall and surge for Moore-Greitzer PDE model of an axial flow compressor

A commonly used mathematical model for axial flow compressors that captures the flow behavior of a compression system, known as the Moore-Greitzer model, consists of a PDE and two ODEs. The PDE describes the dynamical behavior of disturbances in the inlet region of the compression system, and the two ODEs describe the coupling of the disturbances with the mean flow. In this paper, we obtain a quantitative characteristic Delta, depending on the compressor geometry, to identify the type of oscillations of the system. More specifically, the sign of Delta indicates the physical oscillations predominated by rotating stall or by surge. In mathematical terminology, these three types of oscillations are distinctive Hopf bifurcations occurring in the system as the throttle coefficient decreases, and they present quite different dynamical behaviors in axial engine compressors. Estimations of oscillation frequencies corresponding to surge and rotating stall, respectively, are also given in the paper. Numerical simulations are provided to demonstrate different types of flow oscillation of the system.