Navier-Stokes investigation of a transonic centrifugal compressor stage using an algebraic Reynolds stress model

A three-dimensional Navier-Stokes procedure has been developed and applied to a backswept transonic centrifugal compressor stage for which laser two-focus meridional passage velocity measurements are available. An explicit numerical procedure is employed which solves the governing compressible flow equations and a low Reynolds number form of the k-ϵ turbulence model. A two-layer k-ϵ/algebraic Reynolds stress model is employed to account for Reynolds stress anisotropics. Steady state full Navier-Stokes solutions are presented which are shown to capture detailed viscous dominated flow features including tip clearance and curvature induced and rotation induced secondary motions, with good accuracy. Relative helicity is used to help interrogate the computational results and provides insight into the secondary motions in the machine under consideration. Results are presented and interpreted for impeller-diffuser flow field calculations performed with and without the two-layer model. It is found that both modelling approaches provide good agreement with experimental meridional velocity and shroud static pressure measurements. Solutions which incorporate the algebraic Reynolds stress model show significant, though not dramatic, differences in predicted secondary flows, wall shear stress and performance parameters, when compared to the k-ϵ solution.