Numerical simulation of three-dimensional viscous flow in diagonal flow impeller

A Navier-Stokes flow solver with an unfactored implicit upwind relaxation scheme has been developed for analyzing the three-dimensional internal flow field in a diagonal flow impeller with the hub and casing inclined to the axis of rotation. The three-dimensional, Reynolds-averaged Navier-Stokes equations are discretized in space using a cell-centered finite volume formulation and in time using the Euler implicit method. The inviscid fluxes are evaluated using a high-resolution upwind scheme based on a TVD formulation with the Roe's approximate Riemann solver to sharply capture the boundary layers and the tip leakage vortex. The viscous fluxes are determined in a central differencing manner, and the algebraic turbulence model of Baldwin and Lomax is employed. Unfactored implicit equations derived with no approximate factorization are solved by a point Gauss-Seidel relaxation method. The present relaxation scheme is stable up to a Courant numbers of about 100. The present Navier-Stokes flow solver was applied to a diagonal flow impeller of a fan with high specific speed. Inside the blade passage of the impeller there is a large growth of the casing wall boundary layer and a large production of the entropy along the tip leakage flow. In the inlet region of the blade passage the tip leakage vortex is formed. In contrast to axial flow impellers, however, the tip leakage vortex is found to disappear at the aft part of the blade passage. The disappearance of the tip leakage vortex results from the secondary flow toward the suction side near the casing, which is induced by the defect of the Coriolis force in the high loss region near the casing.