This paper reports on the application of unsteady Reynolds averaged Navier-Stokes (U-RANS) and hybrid large-eddy simulation (LES)/Reynolds averaged Navier-Stokes (RANS) methods to predict flows in compressor cascades using an affordable computational mesh. Both approaches use the ζ-f elliptic relaxation eddy-viscosity model, which for U-RANS prevails throughout the flow, whereas for the hybrid the U-RANS is active only in the near-wall region, coupled with the dynamic LES in the rest of the flow. In this 'seamless' coupling the dissipation rate in the k-equation is multiplied by a grid-detection function in terms of the ratio of the RANS and LES length scales. The potential of both approaches was tested in several benchmark flows showing satisfactory agreement with the available experimental results. The flow pattern through the tip clearance in a low-speed linear cascade shows close similarity with experimental evidence, indicating that both approaches can reproduce qualitatively the tip leakage and tip separation vortices with a relatively coarse computational mesh. The hybrid method, however, showed to be superior in capturing the evolution of vortical structures and related unsteadiness in the hub and wake regions. [PUBLICATION ABSTRACT]
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