Hydrodynamics and stability of swirling flows in channels with solid walls

Abstract

The problem of swirling flow in an axisymmetric channel with solid walls is considered. The complete system of the Navier-Stokes equations in variables of stream function and vorticity was used to describe the hydrodynamics of the flow. The finite-difference relaxation method was used to calculate the main flow. The Poisson equation was solved by the method of incomplete reduction. The transfer equations were solved by the block iteration method. Calculation results are presented as streamlines. The main attention was paid to studying the formation of reverse flow zones in the axial region. The stability of the obtained calculated profiles was investigated by the method of small perturbations. The system of six differential equations was solved for complex amplitude functions by the Runge-Kutta method numerically. The stability of the calculated flows is studied. Growth rates and oscillation frequency of unstable perturbations are obtained. The calculation results show a significant effect of swirling on the stability of the flow. The areas ahead of the recirculation zones tend to be the most unstable. This fact shows the connection between the hydrodynamic instability of the flow and the phenomenon of vortex breakdown.

Keywords

• vortex flows
• navier-stokes equations
• flow instability
• finite-difference method
• recirculation zones