Generating periodic vortex pairs using flexible structures

Abstract

In fluid dynamics, a planar starting flow through a narrow slit gives rise to a distinctive fluid mass in the form of counter-rotating vortex pairs, which do not undergo any propulsive detachment, known as ‘pinch-off’, from the tip-attached fluid layer. Our study envisions instigating the ‘pinch-off’ phenomenon in these vortex pairs using flexible plates as the slit edges to enhance momentum transport and self-propagation. In this study, considering a flow evolution model, we show that the growth rate of such ejected vortex pair scales as proportional to the square root of time. Using flexible plates to form the slit, we unearth a critical plate flexibility case with the Cauchy number, $Ca=0.01$, which induces a ‘pinch-off’ of the resultant vortex pair, a phenomenon absent in the case of rigid plates. We observe a train of vortex pairs generating one after the other, and the time period closely matches the plates’ oscillation period as the plates’ oscillation frequency locks-in with the shedding frequency of the vortex pairs. The streamwise speed of the leading vortex pair varies non-monotonically with $Ca$, showing an increase in the speed up to $Ca\approx 0.04$, and thereafter decreased speed due to upstream propagation of small-sized vortices. The new insights into inducing and controlling vortex pair behaviours pave the way for innovative applications in fluid transport and advanced flow manipulation techniques.