Stability of Multi-Stage Axial Flow Compressors

Abstract

SummaryThe following theoretical investigation is concerned with the stability of the flow through a system composed of a multi-stage axial flow compressor followed by a throttle.Such an investigation was carried out by Pearson and Bowmer in 1949. In 1962 Pearson’s work on the analysis of axial flow compressor characteristics, and the accumulation of empirical data regarding factors affecting the surge line, re-awakened interest in the possibility of predicting the surge line of a multi-stage axial flow compressor-throttle system.In this paper the equations governing the stability of flow at any operating point in such a system are obtained by applying Kirchhoff’s laws to the associated electric circuit at that operating point, and the analysis is applied to a wide range of flows of the calculated characteristics of a seven-stage axial flow compressor.A study of the simplest compressor-throttle system is given, in which the equations of motion of the system are derived mechanically and electrically, and the range of validity of the equations and their stability are discussed in order to bring out the relation between the mathematics and physics of the simple system before applying these methods to multi-stage axial flow compressors.For the relatively simple electrical representation used in this paper for an axial compressor of n stages, there are shown to be 2n possible values of p, the transient rotational frequency, and these are determined over a sufficiently wide range of flows on the seven-stage compressor studied.As a result, a region of the compressor characteristic map can be marked out in which all the values of the transient rotational frequency have their real parts less than zero, corresponding to stability of operation, a region where at least one of the values of p is real and positive corresponding to non-oscillatory instability of operation, and an intermediate region where some of the values of the rotational frequency p are complex with positive real part, corresponding to oscillatory instability of operation.It is suggested that the non-oscillatory instability found here is associated with the surge and the line of inception of non-oscillatory instability with the surge line.