Analysis of Swirling Flow with Spiral Vortex Core in a Pipe

Abstract

A quasi-three dimensional analytical model is proposed to simulate swirling flow with spiral vortex core in a pipe. The vortex core is expressed as a helical vortex filament, and the boundary condition of zero normal velocity at the pipe wall is specified by distributing image helical vortex filaments on a cylindrical surface which is located outside the pipe. Thus, the velocity in a pipe is given by the superposition of velocity induced by helical vortex filaments and that of an exisymmetric base flow. The proposed model is applied to the swirling flow in the draft tube of a hydraulic turbine for predicting the flow pattern at the inlet section and the rotating frequency of the vortex core. The calculated results are compared with experimental ones, and reasonable agreement is obtained.