Session R12: Vortex VIII

A Fluid-solid Numerical Model for the Analysis of Bio-inspired UUV

Bio-inspired Unmanned Underwater Vehicles (UUVs) have potential applications for surveillance, monitoring climate change, magnetic field pattern, and migration of species. In past few years, several underwater organisms have been utilized as a source of inspiration for developing new generation of UUVs such as Mantra Ray, Squids, Dolphins and Jellyfish. In our research, we have utilized rowing form of jellyfish as a bio-inspiration and focused our attention on understanding the propulsion mechanism of medium to large diameter ($\sim$40-50 in) species. The motion of the jellyfish results a two-way coupled fluid-solid interaction problem. We provide new types of forcing functions in our model for actuating artificial jellyfish nodes employing flexible muscles such as SMA to make it energy efficient. The present simulation method uses 2-D fluid elements in the framework of the N-S based Immersed Boundary Method (IBM) and loosely coupled plane strain hyperelastic structural elements. This study will be useful in the accurate calculation of pressure distribution on the submerged autonomous vehicle and evaluation of maximum blocking stress in order to design novel actuator systems in terms of energy efficiency. Preliminary work towards achieving these final objectives will be presented.   

Vortex formation analysis of a piston-cylinder apparatus with passively varying output inspired by jellyfish

The flow analysis of a robotic jellyfish (Robojelly) has led to the observation of an increase in performance due to passive flexible margin. Flexible margin are common on animals using an oscillating mode of propulsion. The understanding of flexible margins is therefore important for a better understanding of animal propulsion and bio-inspired propulsion. This work focuses on analyzing the effects of stiffness and geometry of flexible margins. A piston-cylinder apparatus was used with flexible margin at the output to test the different flexible margin configurations. These results characterize the effects of the different flexible margin parameters on vortex circulation and size.   

Perturbation response of model vortex rings and dipoles

Jetting swimmers, such as squid or jellyfish, propel themselves by forming axisymmetric vortex rings. It is known that vortex rings cannot grow indefinitely, but rather ``pinch off'' once they reach their physical limit, and that a decrease in efficiency of fluid transport is associated with pinch-off. In contrast, two-dimensional vortex dipoles have been found to grow well beyond the physical limit observed in axisymmetric vortex rings. Previously, the Norbury and Pierrehumbert families of vortices have been used as models for axisymmetric vortex rings and two-dimensional dipoles respectively, and the response of these two families to shape perturbations has been characterized. In this study, we improve upon the Norbury and Pierrehumbert models, using nested contours to obtain more realistic models for experimentally-generated vortex rings and dipoles. The resulting vortices are subjected to shape perturbations akin to those previously introduced to members of the Norbury and Pierrehumbert families, and their response is characterized.   

Experimental Investigation of a Fluidic Oscillator for Application to Pulsed-Jet Propulsion

A fluidic oscillator with no moving parts is configured with nozzles at the exit ports and is investigated experimentally to assess its performance in a configuration appropriate for continuous pulsed-jet propulsion. Oscillation frequency was controlled via the length of an external feedback tube. Performance of the oscillator was quantified by pressure measurements throughout the device, time-averaged thrust measurements, and digital particle image velocimetry (DPIV) measurements of the jet flow. Feedback tube lengths in the range 0.4 -- 2 m and two flow rates (corresponding to mean jet Reynolds numbers of 9150 and 13500) were tested. Similar to prior studies, decreasing the feedback tube length and increasing the flow rate increased the oscillation frequency. However, no backflow was observed in the non-active outlet. Irregular oscillations were observed at higher frequency, but active occlusion of the feedback tube provided on/off switching of the oscillations.~ DPIV measurements showed formation of vortex rings at the initiation of a jet pulse, but these did not dominate the flow as the pulse durations were long for the frequency range studied.   

Dynamics of a Vortex Pair Impinging on a Horizontal Ground Plane

We study the effect of a solid boundary on the dynamics and instabilities of a pair of counter-rotating vortices. An isolated vortex pair is typically subject to a short-wave elliptic instability and a long-wave Crow (1971) instability. Near a wall, the boundary layer between the primary vortices and the wall can separate, leading to the generation of secondary vorticity. These secondary vortices can be subject to small-scale instabilities (Harris {\&} Williamson, 2012) as they come under the influence of the primary vortices. Using LIF, our facility is able to visualize both the primary and secondary vortices separately, depending on how we introduce the fluorescent dye. The long-wave Crow instability, when interacting with the wall, can cause significant axial flow, resulting in a periodic concentration of fluid at the peaks of each wavy vortex tube and a corresponding evacuation of fluid from the troughs. We are interested to determine the cause of these axial flows and to understand the vortex dynamics leading to what appear to be rebounding vortex ring structures. The vortex dynamics leading to strong axial flows seem to be a fundamental mechanism by which coherent vortex structures, such as vortex pairs or vortex rings (Lim, 1989), break up in the presence of a wall.   

Impact of a vortex dipole with a semi-infinite plate

Recently, several studies have been published on small-scale energy harvesting from fluids using electro-active polymers strips. Specifically, the feasibility of harvesting energy from vortex rings via impact with a cantilevered electro-active strip has recently been demonstrated. As a first step towards developing predictive models of the energy harvesting capacity of this modality, we develop a simplified two-dimensional representation of the vortex ring-deformable structure interaction, in which the vortex ring is modeled as a Lamb dipole, and the cantilevered deformable strip is replaced with a semi-infinite rigid plate. The interaction is explored numerically for a range of dipole Reynolds numbers from 500 to 3000, based upon the convection speed and dipole radius. The initial dipole trajectory results in an impact with the semi-infinite plate at its tip. As the dipole approaches, vorticity is induced in the boundary layer along the wall, which eventually separates and joins with half of the original dipole to form a secondary dipole. This interaction is similar to that of a dipole impacting an infinite wall. The other half of the original dipole merges with vorticity shed from the tip of the plate to produce another secondary dipole. The stagnation point is shifted away from the centerline of the original dipole, which differs from the case with an infinite wall. Of particular interest for the energy harvesting is the differential pressure across the semi-infinite plate, as it relates to the energy transferred to the wall in the event of a deformable, as opposed to rigid, structure, which will be discussed as well as the general flow features.   

Interaction of a Vortex Ring with a Thin Porous Surface

The interaction of vortex rings with thin porous screens was investigated using Molecular Tagging Velocimetry (MTV). The surface porosity, defined as the ratio of the open area to total area of the screen, was held constant at \textit{$\varphi $} = 65{\%} while the diameter of screen wires was varied. The three screens of varying wire diameter tested were: a fine wire (D$_{wire}$ = 0.0178 cm), a medium wire (D$_{wire}$ = 0.104 cm) and coarse wire (D$_{wire}$ = 0.204 cm). When the vortex interacted with the fine wire screen a secondary vortex formed on the upstream face of the screen that orbited the primary vortex and then convected back up stream. The primary vortex reformed immediately downstream of the screen with significantly lower strength. For medium and large wire screens additional vorticity was generated and shed from individual wires, changing the downstream vortex behavior. Secondary vortices were observed for these larger screens but they were weaker and remained in proximity to the screen. Vortex shedding from the screen wires was observed for the medium screen which delayed the reformation of the vortex ring downstream of the screen. Shed vortex pairs, from individual wires, were observed to dominate the downstream flow for the large wire screen and no vortex ring reformation was observed. Vorticity and circulation will be used to further understand the interaction process for each of these screens.   

Dynamics of the collision of a vortex ring with a vertical heated wall

We study the dynamics of the impact of a vortex ring with a vertical heated plate (at constant temperature). Laminar vortex rings were generated with a piston cylinder arrangement. The vertical wall is heated by a thermal bath which is held at constant temperature producing a laminar and stable thermal boundary layer. Measurements of the 2D velocity field were obtained with a PIV technique. The experimental results for the isothermal case are in agreement with previous investigations reported in the literature. To avoid azimuthal instabilities, we mainly conducted experiments for $L/D_0 = 1$ (where $L$ is the piston displacement and $D_0$ is the cylinder inner diameter) with different wall temperatures and vortex translation velocities. For this case, secondary vortices were not observed. Using ink visualization we observed the evolution of the vortex shape. The initial circular shape evolves into a ``cat head'' shape after reaching the wall. The top and bottom regions of the vortex reduce and increase their vorticity, respectively. The sides are stretched and convected. An analysis of the different mechanisms leading to this shape evolution is presented and discussed.   

A numerical study of vorticity-enhanced heat transfer

The Glezer lab at Georgia Tech has found that vorticity produced by vibrated reeds can improve heat transfer in electronic hardware. Vortices enhance forced convection by boundary layer separation and thermal mixing in the bulk flow. In this work, we simulate the heat transfer process in a 3-dimensional plate-fin heat sink. We propose a simplified model by considering flow and temperature in a 2-D channel, and extend the model to the third dimension using a 1-D heat fin model. We simulate periodically steady-state solutions. We determine how the global Nusselt number is increased, depending on the vortices' strengths and spacings, in the parameter space of Reynolds and Peclet numbers. We find a surprising spatial oscillation of the local Nusselt number due to the vortices.   

Dynamics of SQG Point Vortices and Passive Scalar Transport

The surface quasi-geostrophic (SQG) equations are a model for low-Rossby number geophysical flows in which the dynamics are governed by potential temperature dynamics on the boundary. We examine SQG point vortices, retaining the vertical velocity at first order in Rossby number. The dynamics of three SQG point vortices are determined qualitatively using a phase diagram technique. Trajectories of tracer particles are then investigated using techniques such as Poincar\'{e} sections. The effect of $O(Ro)$ corrections to horizontal velocities in the derivation of the SQG equations is also examined.