Visualization of Lagrangian Coherent Structures in Vortex Formation and Advection

In recent years, the formation of vortex rings generated through impulsively started jets using a piston-cylinder mechanism has been a popular topic of discussion, as these fluid structures are commonly found in nature. It is well known that there is a limiting stroke to diameter (L/D) ratio that causes two distinct modes of formation. For short stroke ratios, a single advecting vortex ring is created; however, above a ubiquitous L/D (~ 4) threshold, the flowfield generated consists of a leading vortex ring followed by a trailing jet. The transition between these two modes of formation is studied using particle image velocimetry (PIV) of a submerged piston-cylinder vortex ring generator. Finite Time Lyapunov Exponent analysis of the PIV flowfield identifies Lagrangian Coherent Structures that provide insight to the existence of this inherent threshold between the two ring generation modes. Results validate the findings of other researchers, in that when the stroke ratio is too large an adverse pressure gradient behind the leading vortex ring inhibits vorticity transport into the ring. Further analysis on the vortex wake and shedding of vorticity is presented, as well as the mechanisms by which a vortex ring reaches optimum strength.