Numerical computations of the flow in a finite diverging channel

Abstract

The flow in a finite diverging channel opening into a large space and resembling the experimental prototype of Putkaradze and Vorobieff (2006) was numerically investigated. The effects of the Reynolds number, initial condition, intersection angle, length of the wedge edges, and the outer boundary condition were examined. The numerical results showed that the flow in the wedge undergoes a change from symmetrical flow to unsymmetrical flow with a weak backflow, then a vortical (circulation) flow and finally an unsteady jet flow as the Reynolds number is increased for an intersection angle of 32° and a wedge edge of length 30 times the width of the inlet slit. For the unsteady flow, the jet attached to one side of the wedge constantly loses stability and rolls up into a mushroom-shaped vortex-pair near the outlet of the wedge. As the intersection angle is increased to 50°, a stable jet flow is observed as a new regime between the vortex and unsteady regimes. Both the intersection angle and the wedge length have negative effects on the stability of the flow, although the effect of the wedge length on the critical Reynolds number for the symmetry-breaking instability is not pronounced. The outer boundary condition was found not to affect the flow patterns inside the wedge significantly. At a certain Re regime above the onset of symmetry-breaking instability, the flows evolve into steady state very slowly except for the initial stage in the case of decreasing flow flux. Two different solutions can be observed within the normal observation time for the experiment, providing a possible explanation for the hysteresis phenomenon in the experiment.