Computation of Incompressible Flow in Turbomachines Using the Primitive Variable Formulation

Abstract

The primitive variable approach is adapted here for the solution of incompressible flow in turbomachines using non-staggered grids. In this approach, a pressure Poisson equation with Neumann boundary conditions is solved in lieu of the continuity equation. Solutions for the Poisson equation exist only if a compatibility condition is satisfied. This condition is not automatically satisfied on non-staggered grids. Failure to satisfy the compatibility condition results in non-convergent solutions. A consistent finite difference method which satisfies this condition using a non-staggered grid in general curvilinear coordinates is developed. Numerical solutions are obtained for the pressure equation using the successive over-relaxation method. The velocity field is computed from the momentum equations by explicitly marching in time. The computed solutions are compared with the available numerical results for both inviscid and viscous laminar flows in cascades.