A universal time scale for vortex ring formation

Gharib, Morteza; Rambod, Edmond; Shariff, Karim

doi:10.1017/s0022112097008410

Cited by 961 publications

(1,144 citation statements)

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“…The present numerical simulations of the formation of laminar vortex rings confirm the experimental and analytical findings of Gharib et al (1998) and extend them to additional cases, including cases with thick shear layers. For thin shear layers, the formation number is confirmed to be approximately equal to four for a wide range of cases differing in the discharge time (piston stroke ratio), velocity programme, generator configuration and Reynolds number.…”

Section: Discussionsupporting

confidence: 81%

“…The finding of Gharib et al (1998) of the existence of a maximum in the circulation a vortex ring can acquire as the stroke ratio increases was also confirmed. A new finding of the present study is that the maximal vortex circulation (scaled by the maximal discharge velocity and the diameter of the orifice) is only weakly dependent on the discharge velocity profile or velocity programme.…”

Section: Discussionmentioning

confidence: 63%

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Circulation and formation number of laminar vortex rings

1998

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The formation time scale of axisymmetric vortex rings is studied numerically for relatively long discharge times. Experimental findings on the existence and universality of a formation time scale, referred to as the 'formation number', are confirmed. The formation number is indicative of the time at which a vortex ring acquires its maximal circulation. For vortex rings generated by impulsive motion of a piston, the formation number was found to be approximately four, in very good agreement with experimental results. Numerical extensions of the experimental study to other cases, including cases with thick shear layers, show that the scaled circulation of the pinched-off vortex is relatively insensitive to the details of the formation process, such as the velocity programme, velocity profile, vortex generator geometry and the Reynolds number. This finding might also indicate that the properly scaled circulation of steady vortex rings varies very little. The formation number does depend on the velocity profile. Non-impulsive velocity programmes slightly increase the formation number, while non-uniform velocity profiles may decrease it significantly. In the case of a parabolic velocity profile of the discharged flow, for example, the formation number decreases by a factor as large as four. These findings indicate that a major source of the experimentally found small variations in the formation number is the different evolution of the velocity profile of the discharged flow.

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Section: Discussionsupporting

confidence: 81%

Section: Discussionmentioning

confidence: 63%

Circulation and formation number of laminar vortex rings

1998

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“…where L is the length of a fluid slug ejected from the nozzle, D 0 is the nozzle diameter, U p is the average piston velocity and t p is the discharge time, as defined in Gharib, † Email address for correspondence: jodabiri@caltech.edu Rambod & Shariff (1998). This definition is based on the use of a piston-cylinder apparatus for producing vortex rings in a quiescent tank.…”

Section: Introductionmentioning

confidence: 99%

“…The formation time,t GRS , can be thought of physically as the non-dimensional piston travel distance (L) or alternatively as the non-dimensional pulse duration (t p ). Gharib et al (1998) demonstrated that vortex ring pinch off, a phenomenon where a forming vortex ring is kinematically separated from its trailing jet, occurs at a critical formation timet GRS ≈ 4. showed that for isolated vortex rings the pulse-averaged thrust normalized by the momentum flux is maximized at this critical formation time, known as the formation number F. Krueger, Dabiri & Gharib (2003 further showed that the formation number, F, can be reduced from its typical value of 4 when in the presence of coflow, such as that occurring in a self-propelled vehicle. Ruiz et al (2011) achieved significant increases in propulsive efficiency using vortex-enhanced propulsion, but did not explore the dependence of propulsive efficiency on vortex formation time.…”

Section: Introductionmentioning

confidence: 99%

Optimal vortex formation in a self-propelled vehicle

Whittlesey

Dabiri

2013

J. Fluid Mech.

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Previous studies have shown that the formation of coherent vortex rings in the nearwake of a self-propelled vehicle can increase propulsive efficiency compared with a steady jet wake. The present study utilizes a self-propelled vehicle to explore the dependence of propulsive efficiency on the vortex ring characteristics. The maximum propulsive efficiency was observed to occur when vortex rings were formed of the largest physical size, just before the leading vortex ring would pinch off from its trailing jet. These experiments demonstrate the importance of vortex ring pinch off in self-propelled vehicles, where coflow modifies the vortex dynamics.Key words: biological fluid dynamics, propulsion, vortex dynamics IntroductionThe presence of coherent vortical structures in the near-wake of a jet, hereafter referred to as 'vortex-enhanced propulsion', has been studied extensively and shown to increase propulsive performance in self-propelled vehicles (Siekmann 1962;Weihs 1977;Müller et al. 2000a;Krueger 2001;Finley & Mohseni 2004;Choutapalli 2007;Bartol et al. 2008;Krieg & Mohseni 2008, 2013Moslemi & Krueger 2010Ruiz, Whittlesey & Dabiri 2011). Weihs (1977, using many assumptions, analytically predicted an increase of 50 % in the average thrust through the use of vortex-enhanced propulsion. Later experimental work by Krueger & Gharib (2005) measured increases of up to 90 % of the propulsive thrust by optimization of the vortex ring characteristics. Ruiz et al. (2011) extended the results from stationary nozzles to a self-propelled vehicle, showing that vortex-enhanced propulsion can yield up to a 50 % increase in the propulsive efficiency over a steady jet.The vortices formed during vortex-enhanced propulsion can be characterized using the vortex formation time,t GRS , defined aŝ

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“…Other patterns were also observed. Gharib, Rambod & Shariff (1998) proposed an alternative paradigm to predict optimal performance of unsteady biological propulsors based on the generation of vortex rings using a piston and cylinder. They identified the formation number n = L/D (L = piston stroke, D = diameter) such that for n ≈ 4 both the vortex ring circulation and the time-averaged force were maximized.…”

Section: Introductionmentioning

confidence: 99%

The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel

2008

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Thrust performance and wake structure were investigated for a rigid rectangular panel pitching about its leading edge in a free stream. For Re C = O(10 4 ), thrust coefficient was found to depend primarily on Strouhal number St and the aspect ratio of the panel AR. Propulsive efficiency was sensitive to aspect ratio only for AR less than 0.83; however, the magnitude of the peak efficiency of a given panel with variation in Strouhal number varied inversely with the amplitude to span ratio A/S, while the Strouhal number of optimum efficiency increased with increasing A/S. Peak efficiencies between 9 % and 21 % were measured. Wake structures corresponding to a subset of the thrust measurements were investigated using dye visualization and digital particle image velocimetry. In general, the wakes divided into two oblique jets; however, when operating at or near peak efficiency, the near wake in many cases represented a Kármán vortex street with the signs of the vortices reversed. The three-dimensional structure of the wakes was investigated in detail for AR = 0.54, A/S = 0.31 and Re C = 640. Three distinct wake structures were observed with variation in Strouhal number. For approximately 0.20 < St < 0.25, the main constituent of the wake was a horseshoe vortex shed by the tips and trailing edge of the panel. Streamwise variation in the circulation of the streamwise horseshoe legs was consistent with a spanwise shear layer bridging them. For St > 0.25, a reorganization of some of the spanwise vorticity yielded a bifurcating wake formed by trains of vortex rings connected to the tips of the horseshoes. For St > 0.5, an additional structure formed from a perturbation of the streamwise leg which caused a spanwise expansion. The wake model paradigm established here is robust with variation in Reynolds number and is consistent with structures observed for a wide variety of unsteady flows. Movies are available with the online version of the paper.

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A universal time scale for vortex ring formation

Cited by 961 publications

References 16 publications

Circulation and formation number of laminar vortex rings

Circulation and formation number of laminar vortex rings

Optimal vortex formation in a self-propelled vehicle

The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel

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