Session GG: Vortex Dynamics II

Geometry of unsteady flows

The ability to capture the dynamics of fluid flows continues to improve with advances in computational and empirical techniques. Interpretation of the data however is often quite heuristic. For steady flows, interpreting the flow structure is typically straightforward because streamlines and trajectories coincide. Therefore the Eulerian velocity field, or quantities derived from it, provide a clear description of the flow geometry. For unsteady flows, this is often not the case. A more natural choice is to understand the flow in terms of particle trajectories, i.e. the Lagrangian viewpoint. While the chaotic behavior of trajectories of unsteady systems makes direct interpretation difficult, more structured and frame-independent techniques have been developed. The method presented here uses finite-time Lyapunov exponent (FTLE) fields to locate Lagrangian Coherent Structures (LCS). The FTLE is a measure of divergence between fluid particle trajectories. LCS are maximizing curves (or surfaces in 3D) of FTLE fields, and can be thought of as distinguished material lines (surfaces) that separate regions of qualitatively different dynamics. We overview the theory and implementation of FTLE fields and LCS, and we apply this analysis to several distinct systems, including: vortex ring dynamics in laminar and turbulent flows, unsteady separation over an airfoil, and surface currents in the ocean.   

Practical considerations in the identification of vortices amidst vortex interactions

An isolated vortex is characterized by two features: the vorticity distribution and the concomitant strain distribution. Any vortex identification criterion determines the size of a vortex based on the relative variation of these two fields. In a flow composed of interacting vortices, the interaction modifies the distribution of vorticity and strain, and therefore affects the identification of these vortices using a vortex identification criterion. Considering flows resulting from superposition of vortices whose isolated fields are known \emph{a priori}, we study the influence of vortex interactions in the context of using local vortex identification parameters---$\lambda_{ci}$, $\lambda_{cr}/\lambda_{ci}$, $\Delta$, $Q$, and $\lambda_2$---to extract the individual vortices. Our results give useful guidelines for the application of local vortex identification criteria in complex flows.   

Trajectories of Vortex Rings Formed from Tube and Orifice Openings at Small Stroke Ratios

The sudden ejection of a jet of slug length $L$ and diameter $D$ from a tube or orifice opening engenders the formation of a vortex ring for $L$/$D\sim $ 1. For a vortex ring close to the tube/orifice exit at jet termination ($L$/$D<<$ 1), the results of Sheffield (\textit{Phys. Fluids}, \textbf{20}, 1977) suggest the vortex ring will travel back into the generator. Sheffield, however, only considered 2D (planar) flows and did not consider the vortex formation process. In the present investigation, $L$/$D<<$ 1 behavior is studied computationally for tube and orifice openings at a jet Reynolds number of 2000 and 0.02 $ [Preview Abstract]

Vortex Ring Interaction with a Permeable Flat Surface.

The interaction of vortex rings impinging on a permeable flat surface oriented normal to the ring motion is experimentally investigated. The vortex rings are formed using a piston-cylinder mechanism and visualized by laser induced fluorescence (LIF). Flow features such as the primary vortex ring trajectory, the formation of secondary vortices, flow separation, and mixing are observed for different jet Reynolds number and piston stroke-to-diameter ratios. Results show flow features similar to those observed during the interaction of a vortex ring with an impermeable flat surface---such as spreading of the primary ring as it approaches the surface and the appearance of a counter-rotating secondary vortex. Several new features are also observed, such as the emergence of an axisymmetric vortex ring on the back side of the permeable surface (having less momentum than the primary ring) and the entrainment of ambient fluid across the permeable surface.   

Experiments with a New, Unique Large-Scale Rig Investigating the Effects of Background System Rotation on Vortex Rings in Water

We introduce our unique, new large-scale experimental facility [1] designed for our long-term research program investigating the effects of background system rotation on the stability and the dynamics of vortex rings. The new rig constitutes a large water-filled tank positioned on a rotating turntable and its overall height and diameter are 5.7m and 1.4 m, respectively. First experimental and computational results of our program are summarized. We will show various videos of flow visualizations that illustrate some major, qualitative differences between rings propagating in rotating and non-rotating flows. Some of the investigated characteristics of the vortex rings include their translation velocity, the velocity field inside and surrounding the rings, and, in particular, their stability. We will briefly outline experiments employing the relatively new Ultrasonic-Velocity-Profiler technique (UVP). This technique appears to be particularly suited for some of our measurements and it was, as far as we are aware, not previously used in the context of vortex-ring studies. [1] http://www.eng.warwick.ac.uk/staff/pjt/turntabpics/voriskt.html   

Vortex ring impingement and particle suspension

Previous research has shown that the impact of a vortex ring with a solid surface can dislodge particles attached to that surface and suspend them in the surrounding fluid. A possible use for this phenomenon arises in the detection of trace explosives on clothing and belongings: Once liberated from the surface, suspended particles can be collected and interrogated. The current technology successfully uses round turbulent jets for this purpose, but also generates a large concomitant airflow due to entrainment. Here we present the results of initial experiments to construct vortex-ring generators producing a similar particle release from surfaces with much less entrainment than jets. A discussion of vortex-ring-generator design issues and semi-quantitative flow visualization results will be presented. Both normal and oblique vortex-ring impacts are considered.   

The Effect of Formation Parameters on Ambient Fluid Entrainment during Vortex Ring Formation

In this study, entrainment of ambient fluid during vortex ring formation from a piston-cylinder mechanism is investigated. During piston motion, the shear layer which separates at the nozzle lip rolls up and entrains some of the ambient fluid into the forming vortex ring. Consequently, both ejected and ambient fluid must be accelerated with the forming vortex ring. Understanding the entrainment mechanism is of interest because enhanced entrainment can improve the pumping and propulsive effectiveness of pulsed jets. Therefore, ambient fluid entrainment is examined using planar laser induced fluorescence (PLIF) for jet Reynolds number, and piston stroke-to-diameter ratios (L/D) in the ranges of 500 to 2000 and 0.5 to 2.0, respectively. Both trapezoidal and triangular piston velocity programs were used. It is observed that changing the initial acceleration of the velocity program affected the entrainment by as much as 20{\%} for a given L/D and Reynolds number. Also, decreasing L/D enhanced entrainment by as much as 20{\%}, but changing Reynolds number had a much weaker effect on entrainment.