Session A12: Vortex Dynamics and Vortex Flows I

Vortical wake evolution and its effect on performance using Lagrangian coherent structures

In the field of bio-inspired hydrodynamics, positive thrust producing wakes and their evolution are of particular interest. Water tunnel experiments that utilize a vertically-mounted low-aspect-ratio flat panel are actuated in a purely pitching motion by employing a two-axis motion controller. Vortical wake structure data are collected using stereo particle image velocimetry (SPIV), and the velocity fields are analyzed using the Eulerian Q criterion and the Lagrangian finite time Lyapunov exponent (FTLE). We validate specific assumptions and results of previous work done with a similar geometry such as a negligible spanwise velocity at the midspan of the wake, and a strong spanwise induced velocity near the edges of the wake. The stereo analysis provides a quantitative measurement of the spanwise velocity at selected locations to determine how important three-dimensional effects are and where they are originating.   

Zero-Net Mass-Flux Actuator Cavity Vortex

Zero-Net Mass-Flux (ZNMT) devices are used commonly as synthetic jet actuators for flow control in various applications. The authors have recently proposed using larger ZNMF jet actuators for underwater propulsion; similar to squid and jellyfish. Generally the external flow generated by these devices is characterized according to momentum and energy transfer rates, and little attention is paid to the dynamics of flow inside the cavity. In fact the flow inside the cavity, especially during the refilling phase is not only highly dynamic but greatly influences the pressure distribution at the opening as well as the external flow during the following jetting phase. A completely transparent axisymmetric ZNMF cavity was constructed in order to investigate the internal vortex dynamics. The flow is seeded with reflective particles and illumined with a laser sheet bisecting the axis of symmetry. Standard 2D DPIV techniques are used to recover the velocity field in this cross section. During filling it is observed that a starting jet extending from the opening to the inside of the cavity rolls into a vortex ring much like the jetting phase. However, the effect of the cavity walls becomes apparent almost immediately. In this talk we characterize how the circulation within the cavity decays as a function of both cavity/orifice geometry and the mass flux program. In addition a load cell measures the total thrust acting on the device which is used to validate pressure calculations performed on the moving surface inside the cavity, showing excellent agreement.   

Evolution of the pressure thrust in a starting jet

It is known that the nozzle exit over-pressure is responsible for the improved propulsive performance of a starting jet. To illustrate the detailed evolution of the pressure thrust during the vortex ring formation process, starting jets with a straight nozzle configuration are investigated numerically for different velocity programs. It is found that the remarkable over-pressure contribution to the unsteady jet thrust is mainly associated with the initial acceleration phase of the starting flow. If the vortex ring does not gain appreciable translational velocity at the end of the acceleration phase, it will induce a locally lower pressure region near the nozzle edge due to a mechanism similar to that for the leading edge suction force on a delta wing. As a result of the lower pressure at the nozzle exit plane, the pressure thrust contributes adversely to the total jet thrust. This negative pressure thrust diminishes rapidly as the leading vortex ring translates downstream away from the nozzle exit. Finally, after the leading vortex ring pinches off from the trailing jet, its effect on the pressure variation at the nozzle exit plane becomes negligible and the propulsive characteristics of the flow approaches that of a steady jet.   

Impact of Cyclical Pulse Behavior on Toroidal Vortex Interaction

Vortex rings formed by impulsively started jets have been of great interest due to the possible applications to underwater vehicle propulsion and as a means of inducing fluid flow. So far, most research into vortex rings has only investigated the shedding of a single vortex ring at different formation numbers. This study investigated the behavior of vortex rings and the effects on the circulation when two vortex rings were shed one after the other from the same impulsively started jet. The computational fluid dynamics software ANSYS Fluent was used to perform this study. The geometry for the study was that of a pipe exiting into a volume of quiescent fluid and the impulsively started jet was modeled as a square wave velocity profile at the inlet of the pipe. The computational model was validated for a single vortex ring by comparing circulation data obtained to that found in previously published research. Once the model was validated, an analysis of vortex ring interaction was performed. This study considered formation numbers in the range of 1 to 4. The results showed that the second vortex ring either did not form or merged with the first vortex ring depending on the conditions. The combined vortex ring was found to have an increased circulation and an elongated shape.   

Nested contour-dynamic models for axisymmetric vortex rings and vortex wakes

Jetting swimmers, such as squid and jellyfish, propel themselves by forming 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. Previously, the Norbury family of vortices has been used as a model for axisymmetric vortex rings, and the response of this family to shape perturbations has been characterized. We improve upon the Norbury models, using nested patches of vorticity to construct a family of models for vortex rings generated by a piston-cylinder apparatus at different stroke ratios. The perturbation response of this family is considered by the introduction of a small region of vorticity at the rear of the vortex, which mimics the addition of circulation to a growing vortex ring by a feeding shear layer. Model vortex rings are found to either accept the additional circulation or shed it into a tail, depending on the perturbation size. A change in the behavior of the model vortex rings is identified at a stroke ratio of three. We hypothesize that this change in response is analogous to pinch-off, and that pinch-off might be understood and predicted based on the perturbation responses of model vortex rings.   

Optimal propulsive efficiency of vortex enhanced propulsion

The formation of coherent vortex rings in the jet wake of a vehicle has been shown to increase the propulsive efficiency of self-propelled vehicles. However, the effect of varying vortex ring formation characteristics has not been explored for vehicles at Reynolds numbers comparable to autonomous or manned submersible vehicles. In this work, we considered a range of vortex ring formation characteristics and found a peak in the propulsive efficiency where the vortex rings generated are coincident with the onset of vortex ring pinch off. This peak corresponds to a 22\% increase in the propulsive efficiency for the vortex-enhanced wake compared to a steady jet.   

Propulsion by active and passive airfoil oscillation

Oscillating airfoils have been the subject of much research both as a mechanism of propulsion in engineering devices as well as a model of understanding how fish, birds, and insects produce thrust and maneuvering forces. Additionally, the jet or wake generated by an oscillating airfoil exhibits a multitude of vortex patterns, which are an interesting study in their own right. We present PIV measurements of the vortex flow behind an airfoil undergoing controlled pitching oscillations at moderate Reynolds number. As a method of propulsion, oscillating foils have been found to be capable performers when undergoing both pitching and heaving motions [Anderson et al. 1998]. While an airfoil undergoing only pitching motion is a relatively inefficient propulsor, we examine the effect of adding passive dynamics to the system: for example, actuated pitching with a passive spring in the heave direction. Practically speaking, a mechanical system with such an arrangement has the potential to reduce the cost and complexity of an oscillating airfoil propulsor. To study an airfoil undergoing both active and passive motion, we employ our ``cyber-physical fluid dynamics'' technique [Mackowski {\&} Williamson, 2011] to simulate the effects of passive dynamics in a physical experiment.   

Formation of vortex pairs with hinged rigid flaps at the nozzle exit

Biological flows related to aquatic propulsion using pulsed jets, or flow through the valves in a human heart, have received considerable attention in the last two decades. Both these flows are associated with starting jets that occur through biological tissue/membranes that are flexible. Motivated by these flows, we explore in the present work, the effect of passive flexibility of the nozzle exit on vortex generation from a starting jet. The starting jet is generated using a two-dimensional piston cylinder mechanism, the cross-section of the cylinder being rectangular with large aspect ratio. The fluid is pushed out of this cylinder or channel using a computer controlled piston. We introduce flexibility at the channel exit by hinging rigid flaps, which are initially parallel to the channel. The hinge used is such that it provides negligible stiffness or damping, thus allowing for the maximum opening of the flaps due to fluid forces. Using this system, we study both the flap kinematics and the vorticity dynamics downstream of the channel exit. Visualizations show large flap motions as the piston starts and this dramatically changes the vorticity distribution downstream of the flaps, with the formation of up to three different kinds of vortex pairs. This idealized configuration opens new opportunities to look at the effect of flexibility in such biological flows.   

The Formation of Turbulent Vortex Rings by Synthetic Jets

Vortex rings formed by synthetic jets are found in many engineering and biological flows. For vortex rings formed both periodically and in isolation, a constraint on vortex formation (``pinch-off'') has been observed which is relevant to unsteady propulsion. However, there is no clear consensus on the physical mechanism of this constraint. We present analysis of time resolved, 2D Particle Image Velocimetry measurements of the velocity and material acceleration field in an axisymmetric, turbulent synthetic jet in air at maximum stroke ratios $L_m/D=2-15$. Using the acceleration field, pinch-off may be identified in a manner which is frame invariant and consistent with previous studies. An adverse pressure gradient behind the ring and induced by it plays a role in the pinch-off and separation of the ring from the jet. Recognising this, we revise an existing model for pinch-off: this revision fits our data well. Additionally, we show that as the ring forms, hydrodynamic impulse is delivered via two equally important mechanisms: a material flux and a vortex force. For large $L_m/D$, this vortex force may deliver a substantial impulse to the ring after pinch-off. This has implications for unsteady propulsion, models of vortex ring formation and existing explanations for pinch-off.