Abstract: The passage-averaged N-S equations proposed by ADAMCZYK is proved to be a more rigorous and complicated model than the mixing plane model in the flow prediction of multistage turbomachinery using steady state methods，in which the deterministic stresses represent the time-averaged effect of the flow unsteadiness. Like the RANS, the average-passage N-S equations do not contain sufficient information to determine its solution. Based on reduced passage averaged N-S equations, a semi-empirical deterministic stresses model is introduced instead of overlapping domain approach. By combining the interface approach with the deterministic stresses model, a steady simulation method is developed to predict the effect of the time-averaged unsteadiness in the centrifugal compressor stage. To verify the developed deterministic stresses model and the corresponding numerical method, two computations for two centrifugal compressors are performed: one is the solution of reduced passage-averaged N-S with the developed deterministic stresses model; the other is of the steady N-S equations with the mixing plane. Two computations cost the similar time. Compared with the mixing plane method, results with deterministic stresses model has a better agreement with the experiment due to considering the time averaged effects of the flow unsteadiness; deterministic stresses compensate the influence of the “artificial mixing” with the interface plane, and the deterministic stress model provides more realistic flow field prediction than the mixing plane model.

Key words: Centrifugal compressor, Deterministic stress, Multistage environment, Passage averaged N-S equations