Study of dynamic vortex structures of an incompressible liquid

Abstract

The study of non-stationary vortex structures arising at the inlet of centrifugal pumps and at the outlet of turbines of the Kaplan and Francis type is the subject of the presented paper. Specific attention will be paid to spatial vortices, characterized by curvature and twist. Spiral vortices will also be monitored as sources of spatial vortex motion. Their core will be expressed by a mathematical model in curvilinear coordinates. Helicity, which indicates the degree of vorticity, will also be determined by computational simulation of turbulent motion. The swirling motion will be induced by a specially designed diffuser-shaped vortex generator, simulating the inlet to the turbine draft tube. A significant result of the study of vortex structures will be the dependence of the twist of the streamline in relation to the Hessian matrix, expressed as a function of the pressure function. This dependence will be significant for the optimization of the hydraulic machines.The study of non-stationary vortex structures arising at the inlet of centrifugal pumps and at the outlet of turbines of the Kaplan and Francis type is the subject of the presented paper. Specific attention will be paid to spatial vortices, characterized by curvature and twist. Spiral vortices will also be monitored as sources of spatial vortex motion. Their core will be expressed by a mathematical model in curvilinear coordinates. Helicity, which indicates the degree of vorticity, will also be determined by computational simulation of turbulent motion. The swirling motion will be induced by a specially designed diffuser-shaped vortex generator, simulating the inlet to the turbine draft tube. A significant result of the study of vortex structures will be the dependence of the twist of the streamline in relation to the Hessian matrix, expressed as a function of the pressure function. This dependence will be significant for the optimization of the hydraulic machines.