Computational Fluid Dynamics (CFD) has been widely adopted at the compressor design process, but it remains a challenge to predict the flow details, performance and stage matching for multi-stage, high-speed machines accurately. The Reynolds Averaged Navier-Stokes (RANS) simulation with mixing plane for bladerow coupling is still the workhorse in the industry and the unsteady bladerow interaction is discarded. This paper examines these discarded unsteady effects via deterministic fluxes using semi-analytical and URANS calculations. The study starts from a planar duct under periodic perturbations. The study shows that under large perturbations, the mixing plane produces dubious mixed-out variables, e.g. whirl angle. The performance of the mixing plane can be considerably improved by including deterministic fluxes into the mixing plane formulation. This demonstrates the effect of deterministic fluxes at the bladerow interface. Furthermore the front stages of a 19-blade row compressor are investigated and URANS solutions are compared with RANS solutions. The magnitude of divergence of Reynolds stresses and deterministic stresses are compared. The effect of deterministic fluxes are demonstrated on whirl angle and radial profiles of total pressure and so on. The enhanced spanwise mixing due to deterministic fluxes are also observed. The effect of deterministic fluxes are confirmed via the non-linear harmonic method which includes the deterministic fluxes in the mean flow and the study of multistage compressor shows that unsteady effects, which are quantified by deterministic fluxes, are indispensable to have credible predictions of the flow details and performance of compressor even at its design stage.

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