Interaction of a laminar vortex ring with a thin permeable screen

The canonical case of a vortex ring interacting with a solid surface orthogonal to its symmetry axis exhibits a variety of intricate behaviours, including stretching of the primary vortex ring and generation of secondary vorticity, which illustrate key features of vortex interactions with boundaries. Replacing the solid boundary with a permeable screen allows for new behaviour by relaxing the no-through-flow condition, and can provide a useful analogue for the interaction of large-scale vortices with permeable structures or closely spaced obstructions. The present investigation considers the interaction of experimentally generated vortex rings with a thin permeable screen. The vortex rings were generated using a piston-in-cylinder mechanism using piston stroke-to-diameter ratios ($L/ D$) of 1.0 and 3.0 (nominal) with jet Reynolds numbers ($R{e}_{j} $) of 3000 and 6000 (nominal). Planar laser-induced fluorescence and digital particle image velocimetry (DPIV) were used to study the interaction with wire-mesh screens having surface open-area ratios ($\phi $) in the range 0.44–0.79. Solid surfaces ($\phi = 0$) and free vortex rings ($\phi = 1$) were also included as special cases. Measurement of the vortex trajectories showed expansion of the vortex ring diameter as it approached the boundary and generation of secondary vorticity similar to the case of a solid boundary, but the primary vortex diameter then began to contract towards the symmetry axis as the flow permeated the screen and reorganized into a transmitted vortex downstream. The trajectories were highly dependent on $\phi $, with little change in the incident ring trajectory for $\phi = 0. 79$. Measurement of the hydrodynamic impulse and kinetic energy using DPIV showed that the change between the average upstream and downstream values of these quantities also depended primarily on $\phi $, with a slight decrease in the relative change as $L/ D$ and/or ${\mathit{Re}}_{j} $ were increased. The kinetic energy dissipation ($ \mrm{\Delta} E$) was much more sensitive to $\phi $, with a strongly nonlinear dependence, while the decrease in impulse ($ \mrm{\Delta} I$) was nearly linear in $\phi $. A simple model is proposed to relate $ \mrm{\Delta} E$ and $ \mrm{\Delta} I$ in terms of bulk flow parameters. The model incorporates the decrease in flow velocity during the interaction due to the drag force exerted by the screen on the flow.