Three-Dimensional Design of Multi-Stage Axial-Flow Compressors

Abstract

The design of multi-stage axial-flow compressors, particularly where the blade rows are closely spaced, presents a problem to the designers owing to the mutual interference of the separate blade rows. The actuator disc approximation, applied to the design of single stages at a time has been shown to be useful, and this technique can be used for the multistage machine if the mutual interference of the separate stages may be neglected. Carmichael and Horlock (1)† have carried out calculations by including only the mutual interference of adjacent rows (see also Horlock (2) for an introduction to actuator disc theory). Using the theory of simple radial equilibrium of the flow at the trailing edges of the blade rows, it has been demonstrated, Howell (3), that the flow tends to a state which is termed the ‘ultimate steady flow’ after about two stages. The design of the third stage on a machine may be attempted, making use of this assumption, treating this stage as if it were flanked by many stages. The first part of the paper deals with an extremely simple method of design, for the ultimate steady flow, using the actuator disc theory, and a particular example of this method is compared with a more exact solution of the equations, based on a modified radial equilibrium approach. Both results are then compared with a set of experimental results taken from an experimental three-stage axial-flow compressor in the Department of Mechanical Engineering at the University of Birmingham. In the second part of the paper, the validity of the above assumptions regarding the ultimate steady flow state is discussed, along with the problem of the ‘entry stages’. These problems may be resolved by an exact solution for the flow through a series of identical stages in which parameters such as number of stages, blade row spacing and blade row axial length may be systematically varied. Such an approach is described, and the results of a series of calculations are presented. It is shown that the overall behaviour of the entry stages depends upon the ratio of blade row axial length to blade row spacing. Thus, for small values of this ratio, the flow tends slowly to the ultimate state, but for small axial clearance the ultimate state is reached virtually by the third stage. The influence on the entry stages of blade row spacing and of number of stages is also discussed. It is shown that the treatment of the practical multi-stage machine, even for closely spaced blading, reduces to the separate treatment of the first stage only (inlet guide vanes plus one rotor and one stator), plus the ultimate steady flow treatment to obtain the behaviour of the third stage; otherwise the exact approach may be applied to the first three stages taken as a group, although this involves more calculation. On a high-speed digital computer, such as the Ferranti ‘Mercury’ machine which was, in fact, used for the calculations, a 3-stage compressor design would take about 15 minutes.