Azimuthal instability of a vortex ring computed by a vortex sheet panel method

Feng, Hualong; Kaganovskiy, Leon; Krasny, Robert

doi:10.1088/0169-5983/41/5/051405

Cited by 19 publications

(11 citation statements)

References 38 publications

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“…In addition to the mode number, figure 15 highlights that increasing the Richardson number of a vortex-ring interaction increases the maximum amplitude of the instability as well as the complexity (or structure) of the perturbations. In reference to figure 15[c], the structure of this instability is reminiscent of the numerical results found by Feng et al (2009) and Archer et al (2008) in the absence of stratification. Note that the instability appears to be all but absent in Stock et al (2008) for the numerical simulation of a vortex ring impacting a stratified interface.…”

Section: Three-dimensional Instabilitysupporting

confidence: 58%

Three-dimensional visualization of the interaction of a vortex ring with a stratified interface

Olsthoorn

Dalziel

2017

J. Fluid Mech.

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The study of vortex-ring-induced stratified mixing has long played a key role in understanding externally forced stratified turbulent mixing. While several studies have investigated the dynamical evolution of such a system, this study presents an experimental investigation of the mechanical evolution of these vortex rings, including the stratification-modified three-dimensional instability. The aim of this paper is to understand how vortex rings induce mixing of the density field. We begin with a discussion of the Reynolds and Richardson number dependence of the vortex-ring interaction using two-dimensional particle image velocimetry measurements. Then, through the use of modern imaging techniques, we reconstruct from an experiment the full three-dimensional time-resolved velocity field of a vortex ring interacting with a stratified interface. This work agrees with many of the previous two-dimensional experimental studies, while providing insight into the three-dimensional instabilities of the system. Observations indicate that the three-dimensional instability has a similar wavenumber to that found for the unstratified vortex-ring instability at later times. We determine that the time scale associated with this instability growth has an inverse Richardson number dependence. Thus, the time scale associated with the instability is different from the time scale of interface recovery, possibly explaining the significant drop in mixing efficiency at low Richardson numbers. The structure of the underlying instability is a simple displacement mode of the vorticity field.

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Section: Three-dimensional Instabilitysupporting

confidence: 58%

Three-dimensional visualization of the interaction of a vortex ring with a stratified interface

Olsthoorn

Dalziel

2017

J. Fluid Mech.

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“…Examples of approaches of this type are found in vortex methods (e.g., Ref. [406]) and in vesicular flow problems (e.g., Ref. [407]), to mention just a few.…”

Section: Fast Methodologiesmentioning

confidence: 99%

Recent Advances and Emerging Applications of the Boundary Element Method

Liu

Mukherjee

Nishimura

et al. 2011

Applied Mechanics Reviews

146

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Sponsored by the U.S. National Science Foundation, a workshop on the boundary element method (BEM) was held on the campus of the University of Akron during September 1–3, 2010 (NSF, 2010, “Workshop on the Emerging Applications and Future Directions of the Boundary Element Method,” University of Akron, Ohio, September 1–3). This paper was prepared after this workshop by the organizers and participants based on the presentations and discussions at the workshop. The paper aims to review the major research achievements in the last decade, the current status, and the future directions of the BEM in the next decade. The review starts with a brief introduction to the BEM. Then, new developments in Green's functions, symmetric Galerkin formulations, boundary meshfree methods, and variationally based BEM formulations are reviewed. Next, fast solution methods for efficiently solving the BEM systems of equations, namely, the fast multipole method, the pre-corrected fast Fourier transformation method, and the adaptive cross approximation method are presented. Emerging applications of the BEM in solving microelectromechanical systems, composites, functionally graded materials, fracture mechanics, acoustic, elastic and electromagnetic waves, time-domain problems, and coupled methods are reviewed. Finally, future directions of the BEM as envisioned by the authors for the next five to ten years are discussed. This paper is intended for students, researchers, and engineers who are new in BEM research and wish to have an overview of the field. Technical details of the BEM and related approaches discussed in the review can be found in the Reference section with more than 400 papers cited in this review.

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“…Axisymmetric vortex rings formed along with a starting jet out of a circular nozzle are observed to ultimately become asymmetric. Feng et al numerically simulated the azimuthal instability for the ring and showed that the ring remains axisymmetric during early formation, but later on undergoes a wavy azimuthal instability [7]. Asymmetrization has been shown to be an indicator of performance and control of aircraft and other flight vehicles capable of extreme maneuvers [8].…”

Section: Introductionmentioning

confidence: 99%

A measure of axisymmetry for vortex rings

Falahatpisheh¹,

Kheradvar²

2015

European Journal of Mechanics - B/Fluids

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a b s t r a c tThere are many conditions in which a vortex ring deviates from axisymmetry. The shape of a three dimensional vortex ring represents the axisymmetry of propulsion, which has applications in animal locomotion (e.g., the free-swimming of a jellyfish), rocket and marine propulsion devices as well as blood flow through the heart valves. No fluid dynamics' measure is yet defined to quantify the axisymmetry of a three dimensional vortex ring with a single value. The non-axisymmetry exists, for instance, in the vortex ring formed downstream of the mitral valve of healthy hearts, and helps efficient blood momentum transfer from the left atrium toward the aorta. Here, we introduce an index that measures the deviation of a vortex ring from axisymmetry. This index examines the spectrum of the impulse of a naturally-formed vortex ring and expresses the deviation from axisymmetry in terms of the vortex's impulse. We show that the axisymmetry index is related to the second moment of the vorticity distribution of the ring, i.e., as the second moment of vorticity on one side increases compared to the other side, the axisymmetry index decreases accordingly.

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Azimuthal instability of a vortex ring computed by a vortex sheet panel method

Cited by 19 publications

References 38 publications

Three-dimensional visualization of the interaction of a vortex ring with a stratified interface

Three-dimensional visualization of the interaction of a vortex ring with a stratified interface

Recent Advances and Emerging Applications of the Boundary Element Method

A measure of axisymmetry for vortex rings

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