The dynamics of a swirling flow in a pipe and transition to axisymmetric vortex breakdown

Abstract

This paper provides a new study of the axisymmetric vortex breakdown phenomenon. Our approach is based on a thorough investigation of the axisymmetric unsteady Euler equations which describe the dynamics of a swirling flow in a finite-length constant-area pipe. We study the stability characteristics as well as the time-asymptotic behaviour of the flow as it relates to the steady-state solutions. The results are established through a rigorous mathematical analysis and provide a solid theoretical understanding of the dynamics of an axisymmetric swirling flow. The stability and steady-state analyses suggest a consistent explanation of the mechanism leading to the axisymmetric vortex breakdown phenomenon in high-Reynolds-number swirling flows in a pipe. It is an evolution from an initial columnar swirling flow to another relatively stable equilibrium state which represents a flow around a separation zone. This evolution is the result of the loss of stability of the base columnar state when the swirl ratio of the incoming flow is near or above the critical level.