Session M21: Vortex Dynamics VI

Vortex Ring Properties Before and After Interaction with a Screen

The interaction of a vortex ring with a screen was investigated using Molecular Tagging Velocimetry (MTV). The screen had a porosity of 65{\%} and a small wire diameter (D$_{w}$=0.0178 cm) with respect to the vortex ring diameter (D$_{w}$/ D$_{ring}$=5.23x10$^{-3})$. The results show that as the vortex ring approached the screen the initial interaction was much like that for a vortex ring/solid wall interaction. Specifically, the vortex ring slowed down and expanded as it approached the screen. A secondary vortex was formed that separated from the wall and orbited the primary vortex. Because the wall was porous the primary vortex ring passed through the wall, however, the secondary ring slowly convected back upstream. Data showed that the peak vorticity of the primary vortex dropped by nearly a factor of 4 after passing through while the radius increased in size only slightly (15{\%}). The circulation of the primary vortex before and after the interaction decreased by more than a factor of 2 confirming conclusions from prior flow visualization results. The secondary vortex was both smaller and weaker than the primary vortex as is observed for vortex/wall interactions.   

Vortex interaction during the pinch-off process in a starting jet

Experiments on starting jets at three Reynolds number (Re = 2600, 4100, 5600) were performed to investigate the effect of interaction of the leading vortex ring (LVR) with trailing secondary vortices on the pinch-off process. The velocity and vorticity fields of the starting jet of were obtained by using particle image velocimetry (PIV). It was found that after the formation number (i.e., the onset of the pinch-off process), secondary vortices develop in the trailing jet owing to the shear layer instability. These vortices then affect the dynamics of the trailing jet, especially the vorticity transportation into LVR. In the cases at higher Reynolds number, merging of LVR with the secondary vortices occurs during the pinch-off process, whose completion is indicative of the physical separation of LVR from its trailing jet. Therefore, although the formation number is relatively universal in all tested cases, the time of separation (i.e., the end of the pinch-off process) is actually sensitive to the Reynolds number due to its effect on the shear layer instability.   

Interaction between leading and trailing edge vortex shedding: effects of bluff body geometry

Elongated bluff bodies are distinguished from shorter bluff bodies (e.g., circular cylinders) by the fact that they have separating-reattaching flow at the leading edge as well as having vortex shedding at the trailing edge. Engineering examples of these bodies include heat exchanger fins and long-span suspension bridges. We have performed experiments on elongated bluff bodies of varying geometry. These experiments have been performed at Reynolds numbers O(10$^{4})$ based on the thickness of the model. Both surface pressure measurements (using 512 simultaneously sampled pressure taps) and PIV are used to quantify the flow fields of these bodies. The leading edge separation angle is controlled by changing the leading edge geometry. It is observed that the size of the leading edge separation bubble increases with increasing leading edge separation angle. As the size of the leading edge separation bubble increases, it is shown to continually decrease the shedding frequency for a given elongation ratio. It is suggested that the shedding frequency is diminished because the trailing edge vortex shedding is affected by the structures being shed from the leading edge separation bubble. The implications of this competition between leading and trailing edge flows will be explored.   

The formation of vortex rings from elliptical nozzles

It is known that there is a physical limit to the size of an axisymmetric vortex ring beyond which it rejects further vorticity flux, and a trailing jet forms behind it.\footnote{Gharib \emph{et al.}, J.~Fluid~Mech., {\bf 360}, p. 121, 1998.} This transition, termed ``vortex pinch-off,'' is predicted by an energy-maximization argument due to Kelvin and Benjamin.\footnote{Benjamin, In \emph{Applications of Methods of Functional Analysis to Problems in Mechanics}, Springer, 1976.} However, the Kelvin-Benjamin principle does not apply to non-axisymmetric flows, and the dynamics of the formation of non-axisymmetric vortex rings remain largely unknown. We consider the formation of vortex rings from elliptical nozzles, and compare it to that of axisymmetric vortex rings. By performing PIV on several planes along the perimeter of the elliptical nozzle, we study the effect of varying curvature on vortex formation.   

Early pinch-off in formation of consecutive vortex rings due to vortex interaction

The formation of an isolated vortex ring from a starting jet is a limited process described by the non-dimensional formation time. During formation, the vorticity flux of the jet shear layer is entrained into the forming ring until the formation time reaches a limit, upon which the ring pinches off from the trailing jet (Gharib et al. 1998). The limiting formation time can be attributed to the Kevin-Benjamin principle, which dictates that pinch-off occurs when the shear layer is no longer able to deliver the energy required for the existence of a steady vortex ring. In formation of consecutive vortex rings from a pulsed jet, due to interaction between vortex rings, the limiting ring growth process depends not only on the formation time, but also on the pulsing frequency of the jet. This experimental study on a classic piston-cylinder arrangement finds that when pulsing frequency is high and interaction between rings is strong, the forming ring pinches off at a significantly smaller formation time compared with that in isolated ring formation. A theoretical model is developed to explain the reduced limiting formation time in consecutive ring formation.   

Improving propulsive efficiency through passive mechanisms using a Starling vortex generator

Ruiz et al. (2011) demonstrated that pulsed propulsion with vortex rings, much like those seen in the wake of jellyfish and squid, can greatly enhance the overall efficiency of submersible vehicles. The objective of the present research is to achieve pulsed propulsion passively using a Starling vortex generator which consists of a collapsible tube within an airtight box. Recent work has shown that a Starling vortex generator is able to generate vortex rings, which indicates enhanced propulsion, while requiring less energy to generate pulsatility than the system by Ruiz et al. (2011). Current work is focused on conducting an experimental parameter study to determine an empirical scaling law suitable for design purposes, with the aim to integrate the device into a full-scale unmanned undersea vehicle.   

Experimental study of a vortex ring impacting a smart material-based cantilevered plate

Recent developments in lightweight smart materials have generated scientific and technological advancements in small scale energy harvesting for powering low-consumption electronic devices. Often, energy is harvested from base excitation of a cantilevered smart material strip. In this case, the encompassing fluid acts as a passive damper, reducing the vibration amplitude and frequency, which reduces the harvesting capacity. By comparison, relatively few research efforts to date have explored the feasibility of using smart materials for harvesting energy directly from fluid motion. In this paper we employ vortex rings as the source from which to extract energy and use an ionic polymer metal composite (IPMC) strip in a cantilevered configuration as the harvesting device. Vortex rings, generated using a piston/cylinder arrangement submersed in water, are fired at the IPMC harvester and the resulting impact is recorded using a high speed video camera. The vortex ring propagation and circulation are estimated using flow visualization and particle image velocimetry. The plate deflection and electrical output are recorded as functions of time and correlated to the vortex strength and geometry.