A simple and unified model for spanwise mixing in multistage axial flow compressors

Abstract

A basic equation system for meridional throughflow fields in multistage axial flow compressors has been deduced, containing many unknown correlation terms, which describe different kinds of spanwise mixing mechanism in a unified form. The equation system shows that spanwise mixing of meridional flows in compressors is attributed to three kinds of mechanism: molecular motion, turbulent diffusion, and circumferential non-uniformities, the last of which includes secondary flow effects and others. Therefore the equation system unifies the two models for spanwise mixing analyses by Adkins & Smith (1981) and Gallimore & Cumpsty (1986). With three kinds of apparent mixing coefficients defined and introduced into the basic equation system, a novel, much simpler equation system, without additional unknown correlation terms included, has been obtained. This novel equation system makes throughflow computations including mixing far easier for multistage compressors. It has been rigorously shown that these apparent mixing coefficients contain full information of all the three kinds of mixing mechanism, so that the simpler equation system can also be taken as a unified model for meridional flows with all the kinds of the mixing effects. Calculations of the flow through multistage machines have been made by incorporating the new model into a streamline curvature throughflow calculation method and the improved agreement with experimental data has been obtained. It is believed that the simpler equation system can be applied to the flows not only in subsonic but in transonic and supersonic compressors if an appropriate model is proposed for the apparent mixing coefficients.