The decay of confined vortex rings

Vortex rings are produced during the ejection of fluid through a nozzle or orifice, which occurs in a wide range of biological conditions such as blood flow through the valves of the heart or through arterial constrictions. Confined vortex ring dynamics, such as these, have not been previously studied despite their occurrence within the biological flow conditions mentioned. In this work, we investigate laminar vortex rings using particle image velocimetry and develop a new semi-empirical model for the evolution of vortex ring circulation subject to confinement. Here we introduce a decay parameter b which exponentially grows with increasing vortex ring confinement ratio, the ratio of the vortex ring diameter (DVR) to the confinement diameter (D), with the relationship b 1⁄4 4:38 expð9:5DVR=DÞ; resulting in a corresponding increase in the rate of vortex ring circulation decay. This work enables the prediction of circulation decay rate based on confinement, which is important to understanding naturally occurring confined vortex ring dynamics.