A Model for the Limiting Piston Stroke in Vortex Ring Formation

摘要

Many devices eject a mass of fluid either in one shot or periodically. Examples include heart valves and flapping wings. Often the goal is to maximize the volume of fluid moving as a coherent vortex ring away from the exit. M. Gharib (California Institute of Technology) used a piston to experimentally study fluid ejected from a pipe and found that the largest coherent mass of fluid was attained at a piston stroke (normalized by diameter) of 4 under a variety of circumstances, including different histories of the piston motion. For longer strokes, the mass broke up into smaller vortices and a trailing jet. He also found that this maximum stroke, when expressed as a time, corresponds to the ejection period of many biological systems, including normal hearts. The present contribution was a simple model that predicts the limiting stroke and the associated properties of the vortex such as circulation. Reasons for insensitivity to piston motion emerge from the model, and piston motions that maximize the ejected mass were obtained.