Velocity Field Induced by Singularities in a Reaction Turbine Fluid Filament of Varying Thickness Approximated by Hyperbolic Law

Abstract

The flow in a hydraulic reaction turbine can be analyzed by considering the blade surfaces to be surfaces of discontinuity. For such an analysis the velocity field induced by a system of distributed singularities (sources and vortices) is to be determined. In this paper the runner space is divided into elementary runners, assuming the absolute flow in the runner to be irrotational and the stream surfaces to be surfaces of revolution. The axisymmetric fluid filament thus obtained is then conformally mapped on to a plane. The variable thickness of the resulting plane filament is approximated by hyperbolic law. The velocity field due to a singularity is obtained by solving the governing differential equation in a closed form. The solution is extended for a chain of singularities.