Vortex breakdown in the shear-driven flow in a rectangular cavity

TL;DR

This study investigates vortex breakdown in shear-driven flow within a rectangular cavity, revealing how flow structures and stability depend on cavity width and Reynolds number through simulations and experiments.

Contribution

It provides new insights into the critical Reynolds number, vortex breakdown modes, and stability transitions in cavity flows, including the effects of asymmetries and width variations.

Findings

Vortex breakdown occurs above a critical Reynolds number dependent on cavity width.

Large widths produce symmetric vortex breakdown bubbles that merge with increasing Reynolds number.

Narrow widths exhibit complex modes, including reversed flow vortex breakdown.

Abstract

The vortex dynamics of laminar flow past a rectangular cavity is investigated using simulations and experiments. The flow is three-dimensional and characterized by a large, dominant vortex structure that fills most of the cavity at moderate Reynolds numbers with a weak, yet significant flow in the axial direction along the vortex core. Classical bubble-type vortex breakdown is observed within the cavity above a certain critical Reynolds number, which is a function of the channel width. The critical Reynolds number for the onset of breakdown is determined as a function of channel width, and the evolution and dynamical transitions of the breakdown regions are investigated as functions of the channel width and Reynolds number. At large cavity widths, two vortex breakdown bubbles emerge near the sidewalls symmetric about the centerplane, which grow and eventually merge as the Reynolds number increases. For large-enough widths, the vortex breakdown regions remain well-separated and their structures become independent of the cavity width. The stability and bifurcations of the stagnation points and their transitions to stable/unstable limit cycles are analyzed, and the criticality of the vortex flow is calculated, demonstrating that the vortex breakdown in the cavity agrees with Benjamin's interpretation of criticality. At the intermediate width regime, a single vortex breakdown bubble appears above the critical Reynolds number. In the narrow width regime, the flow exhibits more complicated modes. An additional vortex breakdown mode with reversed flow patterns is observed in this width regime, along with multiple shifts in the stability of stagnation points. The experimental and numerical results also demonstrate the sensitivity of the flow to the inlet conditions, such that relatively small asymmetries upstream can result in significant changes to the vortex breakdown behavior in the cavity.