Hysteresis behaviors of compressor rotating stall with cusp catastrophic model

Rotating stall is a complex nonlinear dynamic phenomenon which is always characterized by catastrophe and hysteresis in high aerodynamic-loading compressor. Exploring the key contributing factors and characteristic rules of hysteresis is very important for compressor design and flow instability control. In this paper, a novel model method is proposed to analyze the hysteresis behaviors to extend the understanding of compressor rotating stall. The equilibrium states of compressor system under different conditions are first described based on Moore-Greitzer model. Then, through assessing the stability of the equilibrium points by Liapunov's theorem, the ratio of shutoff head to compressor characteristic semi-height is found to affect the stall hysteresis: the size of hysteresis loop will gradually decrease, even disappear with the increase of the ratio. Combing the effects of both the ratio and throttle coefficient, the hysteresis behaviors of compressor stall under multi-parameters can be found to be consistent with the topological properties of cusp catastrophic model by Thom's catastrophe theory. Finally, according to topological invariant rules, from the perspective of potential function, the equilibrium surface equation of compressor system is developed by standard cusp catastrophic model to describe the various hysteresis behaviors of compressor rotating stall along different control routes.