Analysis of Moffat’s vortices in the straight channel with fittings at low Reynolds numbers

Abstract

The two-dimensional problem of a viscous incompressible fluid flow in a straight channel with a system of fittings of different geometries in the approximation of small Reynolds numbers is considered. The problem solved numerically in terms of “stream function – vorticity” on a uniform grid using a simple explicit method with upwind differences. The method of a successive over-relaxation was applied for solving of the Poisson equations for the stream function and pressure. It is shown that the flow before fittings and after them formed circulating zone (Moffat’s vortices). The quantitative dependence of the size and shape of the corner vortex structures from the axial velocity of the flow is determined. Losses levels of the pressure, that caused by the decrease in the effective channel cross section, is defined.