Discrete Vortex Model of Jet‐Forced Flow in Circular Reservoir

Abstract

A computer model of two-dimensional steady flow in a confined space is described in this paper. The simplest case of radial jet-forced flow within a circular cylinder with a single inlet and outlet is considered. The first stage in the numerical model consists of mapping the circular flow boundary onto a rectangle by means of a Schwarz-Christoffel transformation. As a result, two opposite sides of the rectangle represent the inlet and outlet. A potential uniform flow solution is then obtained for the flow in the rectangle and hence the cylinder. In the second stage of the flow simulation, discrete vortices are added at the inlet in order to model the inflow shear layers. Velocity components resulting from the discrete vortices and their images in the walls of the cylinder are superimposed on the potential uniform flow solution. The positions of the vorticese are updated using a finite-difference time-stepping scheme. Thus, a qualitative simulation of the complete flow is built up. The results show reasonable agreement with experimental observations.