A Calculation Method for Incompressible Viscous, Blade-to-Blade Flow through Radial Turbomachines with Log-Spiral Blade Surfaces

A finite difference method of blade-to-blade calculation for incompressible turbulent, viscous flow through radial turbomachines having log-spiral blades lying entirely in the r-θ plane is presented. A Newtonian stress system is incorporated into the calculation which employs a slip model for flow close to the blade surfaces. The effects of turbulence are simulated by use of an enhanced molecular viscosity. This problem is of a higher mathematical order than the usual free slip, inviscid calculation commonly applied in the design and analysis of these machines and raises interesting considerations of understanding with respect to mathematical closure and boundary conditions. Experimental results for flow through an actual machine of similar geometry to that analyzed are available and comparison of streamlines and velocity profiles are made.