Comparison Between Complete Hilbert Transform and Simplified Solutions of the Moore Rotating Stall Model

Abstract

The main objective of this work is the analysis and the comparison between different methods utilized to solve the Moore rotating stall model. To date only simplified relations between the axial flow perturbation g and the transverse one h have been utilized and presented in literature, such as h′ = −g or the truncated Fourier series. On the contrary, in this paper the accurate relation given by the Hilbert Transform is utilized, and to improve the numerical stability of the method, a new expression of the first derivative of transverse flow coefficient perturbation is proposed and utilized. A complete and detailed comparison between the results of the simplified methods and the solution proposed here is presented. This comparison is extended to a wide range of geometric and physical compressor parameters, and it allows the accuracy of simplified approaches to be tested. Finally, a correlative approach estimating overall rotating stall effects based on the complete solution proposed here is presented. It allows rotating stall influence to be quickly and easily taken into account in several axial compressor areas (design, optimization, active control, etc.).