Three-Dimensional Solutions for Inviscid Incompressible Flow in Turbomachines

A primitive variable formulation is used for the solution of the incompressible Euler’s equation. In particular, the pressure Poisson equation approach using a non-staggered grid is considered. In this approach, the velocity field is calculated from the unsteady momentum equation by marching in time. The continuity equation is replaced by a Poisson-type equation for the pressure with Neumann boundary conditions. A consistent finite-difference method, which insures the satisfaction of a compatibility condition necessary for convergence, is used in the solution of the pressure equation on a non-staggered grid. Numerical solutions of the momentum equations are obtained using the second order upwind differencing scheme, while the pressure Poisson equation is solved using the line successive over-relaxation method. Three turbomachinery rotors are tested to validate the numerical procedure. The three rotor blades have been designed to have similar loading distributions but different amounts of dihedral. Numerical solutions are obtained and compared with experimental data in terms of the velocity components and exit swirl angles. The computed results are in good agreement with the experimental data.