Reduced passage-averaged N-S equations of the three-dimensional flowfield in a multi-stage environment

The passage-averaged flow model was proved to be a more rigorous and complicated model than the mixing plane model in the flow prediction of multi-stage turbomachinery using the steady-state method. In the present work, the novel time- and passage-averaging operators are applied and a reduced average-passage N-S equation system is derived, in which the bodyforce and the blockage factor are eliminated. In order to consider the time-averaged effect of the periodic unsteadiness, a semi-empirical model with the interface approach is employed to evaluate the deterministic stresses instead of overlapping domain approach. Finally, two computations for a tested centrifugal compressor are performed and compared with the corresponding experimental data to verify the reduced passage-averaged equation system and the corresponding numerical method: one is the solution of the reduced passage-averaged equations with a semiempirical model and; the other is that of the steady Navier-Stokes equations with the mixing plane.