Numerical analysis of Moore-Greitzer equations to prevent from axial compressor instabilities: surge and rotating stall

Axial flow compressors are subject to two distinct aerodynamic instabilities, rotating stall and surge, which can severely limit the compressor performance. These instabilities are disruption of the normal operating condition and can severely lower the compressor performance. One of the famous models of predicting these instabilities is the Moore-Greitzer Model. This theory has been used extensively in stall and surge analysis. In this study a mathematical algorithm is used to convert the system of three simultaneous non-linear third order partial differential equations (PDE) to a system of three simultaneous ordinary differential equations (ODE), and then to solve this system through applying a third order polynomial introduced as the characteristic curve proposed for axial compressors. a control parameter called “B-Greitzer” is also used to predict the performance of the compressor. Results shows that the amplitude of disturbances are periodically increased as B > 0.3, and converges to a constant limit for values of B < 0.3. Moreover, it is observed the domain of stream function and pressure ratio are totally extended as the value of B-Greitzer is increased, and the turns of perturbation cycles are also increased. Finally, it is found that the value of B = 0.26 can be considered as a critical point to prevent the axial compressor from operating in rotating stall and surge modes.