Three-Dimensional Navier–Stokes Computation of Turbomachinery Flows Using an Explicit Numerical Procedure and a Coupled k–ε Turbulence Model

Abstract

An explicit, three-dimensional, coupled Navier–Stokes/k–ε technique has been developed and successfully applied to complex internal flow calculations. Several features of the procedure, which enable convergent and accurate calculation of high Reynolds number two-dimensional cascade flows, have been extended to three dimensions, including a low Reynolds number compressible form of the k–ε turbulence model, local time-step specification based on hyperbolic and parabolic stability requirements, and eigenvalue and local velocity scaling of artificial dissipation operators. A flux evaluation procedure, which eliminates the finite difference metric singularity at leading and trailing edges on H- and C-grids, is presented. The code is used to predict the pressure distribution, primary velocity, and secondary flows in an incompressible, turbulent curved duct flow for which CFD validation quality data are available. Also, a subsonic compressor rotor passage, for which detailed laser, rotating hot-wire, and five-hole pressure probe measurements have been made is computed. Detailed comparisons between predicted and measured core flow and near-wall velocity profiles, wake profiles, and spanwise mixing effects downstream of the rotor passage are presented for this case. It is found that the technique provides accurate and convergent engineering simulation of these complex turbulent flows.