Coupling of vortex breakdown and stability in a swirling flow

Swirling flows are ubiquitous over a large range of length scales and applications including micron-scale microfluidic devices up to geophysical flows such as tornadoes. As the viscous dissipation, shear, and centrifugal stresses interact, such flows can often exhibit unexpected fluid dynamics. Here, we use microfluidic experiments and numerical simulations to study the flow in a vortex T-mixer: a T-shaped channel with staggered, offset inlets. The vortex T-mixer flow is characterized by a single dominant vortex, the stability of which is closely coupled to the appearance of vortex breakdown. Specifically, at a Reynolds number of Re≈90, a first vortex breakdown region appears in the steady-state solution, rendering the vortex pulsatively unstable. A second vortex breakdown region appears at Re≈120, which restabilizes the vortex. Finally, a third vortex breakdown region appears at Re≈180, which renders the vortex helically unstable. Thus, a counterintuitive flow regime exists for the vortex T-mixer in which increasing the Reynolds number has a stabilizing effect on the steady-state flow. The pulsatively unstable vortex evolves into a periodically pulsating state with a Strouhal number of St≈0.5, and the helically unstable vortex evolves into a helically oscillating state with St≈1.75. These transitions can be explained within the framework of linear hydrodynamic stability. In addition, the vortex T-mixer flow exhibits multistability; multiple flow states are stable over various ranges of Re, including a narrow range of tristability for 160≤Re≤170, in which the steady state, the pulsatile oscillation, and the helical oscillation are all stable. This study provides experimental and numerical evidence of the close coupling between vortex breakdown and flow stability, including the restabilization of the flow with increasing Reynolds number due to the appearance of a vortex breakdown region, which will provide new insights into how vortex breakdown can affect the stability of a swirling flow.