Three-dimensional incompressible and compressible Beltrami flow through a highly-loaded isolated rotor

Abstract

An analysis is proposed for the three-dimensional incompressible and compressible Beltrami flow through a heavily loaded isolated rotor. It is found that, in agreement with previous analyses on disturbances in swirling flows, the Beltrami vorticity-induced disturbances are not purely convected by the mean flow. The disturbances, which induce a persisting static pressure field, can be shown to grow linearly in strength close to the blade-row before beginning to decay inversely with axial distance downstream. This is again in agreement with previous analyses on swirling flow in which the disturbances had their origin in the viscous blade wakes. It is further shown that this analysis only agrees with the earlier analysis, in which vorticity-induced disturbances are assumed to be purely convected by the mean flow, in the limit of large numbers of blades and in a downstream region very close to the blade row. The two analyses differ considerably further downstream; that is, this analysis can predict the downstream evolution of the three-dimensional disturbances while the earlier cannot.