Vortex breakdown control in confined swirling flows

Abstract

Confined steady flows, which display on-axis or off-axis vortex breakdown, have been numerically studied, with particular attention focused on means of controlling the vortex breakdown bubbles. Firstly, the model flow driven by one end disk of a cylindrical enclosure, which exhibits two distinct on-axis vortex bubbles, has been considered. The resulting computations revealed that, sloping slightly the stationary sidewall, beyond a threshold angle, provided an effective means of removing the secondary vortex structure, and the flow remains steady. Besides, this technique is shown to significantly modify the flow topology which displays off-axis bubbles, induced by the co-rotation of the end disks. Then, the effectiveness of adding a near-axis swirl, as suggested in recent experimental works, has been analysed numerically and found to substantially alter on-axis reverse flows.

Characterization of Swirling Flows in a Partly Open Cylinder

“…The solution algorithm is based on a three level time-marching finite difference scheme, used and tested on confined internal swirling flows with breakdown; which has been extended to account for stress-free surface conditions under reflection symmetry; see Saci et al (2008) for detailed accounts and implementation. With appropriate time and space mesh grids, the time dependent solutions of the circulation and the vorticity transport equations were calculated until an ultimate steady state is essentially reached.…”

“…The governing equations are the unsteady axisymmetric Navier-Stokes equations in cylindrical coordinates ( , , ), written in dimensionless form by scaling time, length and velocity with 1⁄ , and respectively. These are then expressed conveniently in a stream functionvorticity formulation (Piva et al 2005;Saci et al 2008); leading to the following non dimensional velocity field which satisfies continuity and the corresponding vorticity field, in terms of the stream function and angular momentum = ,…”

“…These are based on the no slip conditions applied to solid walls and regularity assumption on the cavity axis. Reflexion symmetry is considered on the partly open surface, assumed flat stress-free, (Herrada et al 2014;Hewitt et al 2008;Saci et al 2008) over the range of the flow parameters considered. Initial conditions consider the fluid at rest and the bottom disk is impulsively rotated to a constant angular speed.…”