Dynamics and Control of Entrained Solutions in Multi-Mode Moore-Greitzer Compressor Models

In this paper we investigate the behavior of higher order Galerkin expansions of the MooreGreitzer model of general transients in aeroengine compression systems. We assume steady state entrainment of the higher Fourier modes of the rotating stall cell which helps establish a framework for a simpli ed numerical analysis of the bifurcating solutions corresponding to rotating stall. For small values of the Greitzer surge parameter (B) we discuss general trends in the character of the pure stall solutions. The rotating stall characteristic is shown to exhibit deep hysteresis with a cubic compressor characteristic, establishing the fact that deep hysteresis to a certain extent is a multi-mode phenomena. Elimination of the hysteresis associated with the bifurcation into stall is accomplished in simulations with a combined feedback on the displacement from the peak of the compressor characteristic and the magnitude of the rst mode amplitude of the stall cell. Behavior for larger values of the B parameter is also investigated and novel surge/stall relaxation oscillations corresponding to classic surge are discovered. 2 List of Figures 1 Compressor and Throttle Characteristics . . . . . . . . . . . . . . . . . . . . . . . . 19 2 Dynamics of the Single Spatial Harmonic Approximation . . . . . . . . . . . . . . 20 3 Primary Stall Equilibria MG8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4 Stable Rotating Stall Cycle MG8 . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5 Primary Rotating Stall Characteristic Trends . . . . . . . . . . . . . . . . . . . . . 23 6 Relaxation Oscillations MG8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 7 Classic Surge Relaxation Oscillations MG8 . . . . . . . . . . . . . . . . . . . . . 25 8 Controlled Bifurcation Diagrams MG8 . . . . . . . . . . . . . . . . . . . . . . . . 26 3