Rotating Stall Model and Simulation of Two-Stage Centrifugal Compressors

Abstract

Often turbo-compressors exhibit the maximum efficiency condition very close to the stall limit, so that it would be highly interesting to have a deep comprehension of this phenomenon. Despite the large diffusion of the multi-stage centrifugal compressors in different fields of the technology, such as natural gas pipe-lines or chemical factories, at the best authors’ knowledge, to date no theoretical model exists for rotating stall in these machines. This paper deals with a model for simulating multi-stage centrifugal compressor flow pattern during rotating stall. The model is not able to capture the stall inception, so the velocity and pressure fields are calculated throughout the machine once rotating stall has developed. The model consists of an implementation of that proposed by Moore for single-stage centrifugal compressors, so the simplifying hypotheses are: irrotational upstream fluid flow, inviscid and incompressible flow, stationary flow in the frame rotating at the same frequency of the stall cell; infinite blades are supposed both in rotors and return channel. Even if these fluid-dynamic hypotheses are really strong, it is worth of note that the reference models for rotating stall simulation in turbo-compressors (namely the Moore’s models) are based, at the present time, on them. In a previous step of this research, the authors utilized a semi-empirical approach, with phases changes between first and second diffuser based on experimental data. Now this hypothesis is removed and the model is fully analytical. The mathematical model is solved by numerical way, leaving the original semi-analytical scheme of Moore, so allowing the stall cell propagation frequency to be calculated. The computer code is written in C language for Linux operating system. It was tested in single-stage configuration with results according to Moore’s theory; for two-stage setup, obtained results appear consistent and qualitatively according with experimental tests and, unlike the single stage analysis, only fast rotation waves were found.