Explicit multigrid algorithm for quasi-three-dimensional viscous flows in turbomachinery

Abstract

A rapid quasi-three-dimensional analysis has been developed for blade-to-blade flows in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stream surface thickness. The BaldwinLomax eddy viscosity model is used for turbulent flows. The equations are solved using a two-stage RungeKutta scheme made efficient by the use of vectorization, a variable time step, and a flux-based multigrid scheme, all of which are described. Results of a stability analysis are presented for the two-stage scheme. Results for a flat-plate model problem show the applicability of the method to axial, radial, and rotating geometries. Results for a centrifugal impeller and a radial diffuser show that the quasi-three-dimensional viscous analysis can be a practical design tool.