Evaluation of Bleed Valve Rate Requirements in Nonlinear Control of Rotating Stall on Axial Flow Compressors

In this paper we evaluate the actuator rate requirements for control of rotating stall using a bleed valve and provide tools for predicting these requirements. Modiication of both the stable and unstable parts of the compressor characteristic via addition of continuous air injection serves to reduce the requirement of a bleed valve used for the purpose of rotating stall stabilization. Analytical tools based on low order models (2-3 states) and simulation tools based on a reduced order model (37 states) are described. A bleed actuator rate limit study is presented to compare the actuator requirements predicted by theory, simulation, and experiment. The comparisons show that the predictions obtained from theory and simulations share the same trend as the experiments, with increasing accuracy as the complexity of the underlying model increases. Some insights on the design of a bleed-compressor pair are given. A amplitude of rst Fourier mode A nom amplitude of rst Fourier mode of fully developed stall cell C x axial ow velocity noise level of the system expressed as a percentage of J throttle coeecient, T () = p J squared amplitude of rst Fourier mode, J = A 2 K X gain estimation from method X K RS gain for control of rotating stall in Liaw-Abed control law K SU gain for control of surge in Eveker et al. 9] control law R X rate estimation from method X U mean rotor speed u bleed valve control eeort u mag magnitude saturation of the bleed actuator as percentage of u rate bleed valve rate limit in rotor revolutions for valve to open from fully closed P pressure rise nondimensionalized axial ow velocity, = C x =U at peak of compressor characteristic T () nondimensionalized throttle characteristic as a function of nondimensionalized pressure rise, = P=(U 2) at peak of compressor characteristic c () nondimensionalized compressor characteristic as a function of