Circulation and formation number of laminar vortex rings

Rosenfeld, M.; Rambod, Edmond; Gharib, Morteza

doi:10.1017/s0022112098003115

Cited by 177 publications

(193 citation statements)

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“…They assumed the physical process causing this constant formation number to be a maximum in total circulation attainable in the vortex ring. A numerical study by Rosenfeld et al (1998) demonstrates the invariance of this formation number to differences in the velocity programme and Reynolds number.…”

Section: Dependency Of Vectoring Behaviour On Strouhal Numbermentioning

confidence: 80%

Vectoring of parallel synthetic jets: a parametric study

2016

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The vectoring of a pair of parallel synthetic jets can be described using five dimensionless parameters: the aspect ratio of the slots, the Strouhal number, the Reynolds number, the phase difference between the jets and the spacing between the slots. In the present study, the influence of the latter four on the vectoring behaviour of the jets is examined experimentally, using particle image velocimetry. Time-averaged velocity maps are used to give a qualitative description of the variations in vectoring for a parametric sweep of each of the four parameters independently. A diverse set of vectoring behaviour is observed in which the resulting jet can be merged or bifurcated and either vectored towards the actuator leading in phase or the actuator lagging in phase. Three performance metrics are defined to give a quantitative description of the vectoring behaviour: the included angle between bifurcated branches, the vectoring angle of the total flow and the normalized momentum flux of the flow. Using these metrics, the influence of changes in the Strouhal number, Reynolds number, phase difference and spacing are quantified. Phase-locked maps of the swirling strength are used to track vortex pairs. Vortex trajectories are used to define three Strouhal number regimes for the vectoring behaviour. In the first regime, vectoring behaviour is dominated by the pinch-off time, which is written as function of Strouhal number only. In the second regime, the pinch-off time is invariant and the vectoring behaviour slightly changes with Strouhal number. In the third regime, given by the formation criterion, no synthetic jet is formed. Vortex positions at a single phase, shortly after creation of the lagging vortex pair, are used to propose a vectoring mechanism. This vectoring mechanism explains the observed qualitative and quantitative variations for all four parameters.

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Section: Dependency Of Vectoring Behaviour On Strouhal Numbermentioning

confidence: 80%

Vectoring of parallel synthetic jets: a parametric study

2016

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“…The universality of the formation number has been verified by a number of subsequent experimental (Dabiri & Gharib 2004a;Krueger, Dabiri & Gharib 2006;Pawlak et al 2007) and computational studies (Rosenfeld, Rambod & Gharib 1998;Mohseni, Ran & Colonius 2000). In particular, Rosenfeld et al (1998), Zhao, Frankel & Mongeau (2000) and Mohseni et al (2000), found the Reynolds number to have little impact on the formation number, provided that Re Γ is sufficiently large to ensure the formation process is completed before viscosity has a significant impact (Re Γ > 2000 according to Mohseni et al (2000)).…”

Section: Introductionmentioning

confidence: 85%

“…The Reynolds numbers considered here are comparable with those observed in jetting swimmers such as paralarval and juvenile squid (O'Dor 1988; Bartol et al 2009) and several species of jellyfish (Gladfelter 1973;Colin & Costello 2002;Peng & Dabiri 2009), which have been observed to operate at Reynolds numbers in the range of 10 2 -10 3 . We did not consider the effects of varying the Reynolds number, since they have been previously characterized for circular vortex rings, and found to have little impact on the formation number, in the intermediate range of Reynolds numbers (Rosenfeld et al 1998;Mohseni et al 2000;Zhao et al 2000).…”

Section: Experimental Methodsmentioning

confidence: 99%

“…In particular, Rosenfeld et al (1998), Zhao, Frankel & Mongeau (2000) and Mohseni et al (2000), found the Reynolds number to have little impact on the formation number, provided that Re Γ is sufficiently large to ensure the formation process is completed before viscosity has a significant impact (Re Γ > 2000 according to Mohseni et al (2000)). The concept of the universal formation number has also been extended to more complex vortex generator setups and computational frameworks, by extending the definition of the dimensionless vortex formation time to allow for variations such as the presence of bulk coflow (Krueger et al 2006) or bulk counterflow (Dabiri & Gharib 2004a), a time-varying exit diameter (Mohseni et al 2000;Dabiri & Gharib 2005), and differing velocity programs (Rosenfeld et al 1998;Mohseni et al 2000;Krueger & Gharib 2003;Olcay & Krueger 2010) and velocity profiles (Rosenfeld et al 1998).…”

Section: Introductionmentioning

confidence: 99%

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Pinch-off of non-axisymmetric vortex rings

O’Farrell

Dabiri

2014

J. Fluid Mech.

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The formation and pinch-off of non-axisymmetric vortex rings is considered experimentally. Vortex rings are generated using a non-circular piston-cylinder arrangement, and the resulting velocity fields are measured using digital particle image velocimetry. Three different nozzle geometries are considered: an elliptical nozzle with an aspect ratio of two, an elliptical nozzle with an aspect ratio of four and an oval nozzle constructed from tangent circular arcs. The formation of vortices from the three nozzles is analysed by means of the vorticity and circulation, as well as by investigation of the Lagrangian coherent structures in the flow. The results indicate that, in all three nozzles, the maximum circulation the vortex can attain is determined by the equivalent diameter of the nozzle: the diameter of a circular nozzle of identical cross-sectional area. In addition, the time at which the vortex rings pinch off is found to be constant along the nozzle contours, and independent of relative variations in the local curvature. A formation number for this class of vortex rings is defined based on the equivalent diameter of the nozzle, and the formation number for vortex rings of the three geometries considered is found to lie in the range of 3-4. The implications of the relative shape and local curvature independence of the formation number on the study and modelling of naturally occurring vortex rings such as those that appear in biological flows is discussed.

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“…An impulsive body force of this sort produces a leading vortex pair that pinches off from a trailing jet. The formation a the leading vortex ring (in the axisymmetric case) has been studied previously in experiments [25] and in computations that used a similar body force [21]. The toroidal radius of the ring is L and the leading ring is invariant to ␦ provided ␦/L is small.…”

Section: Two-dimensional Starting Jetmentioning

confidence: 99%

A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

Colonius¹,

Ran

2002

Journal of Computational Physics

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A new buffer region (absorbing layer, sponge layer, fringe region) technique for computing compressible flows on unbounded domains is proposed. We exploit the connection between coordinate mapping from bounded to unbounded domains and filtering of the equations of motion in Fourier space in order to develop a model to damp flow disturbances (advective and acoustic) that propagate outside an arbitrarily defined near field. This effectively simulates a free-space boundary condition. Damping the solution in the far field is accomplished in a simple and effective way by applying a filter (similar to that used in large-eddy simulation) on a mesh in Fourier space, followed by a secondary filtering of the equations on the physical grid and implementation of a model for the unresolved scales. The final form of the buffer region is given in real space, independent of any discretization of the equations. Here we use a dealiased, Fourier spectral collocation method to demonstrate the efficacy of the buffer region for several model problems: acoustic wave propagation, convection of a finite-amplitude vortex, and a viscous starting jet in two dimensions. The results compare favorably to previous nonreflecting and absorbing boundary conditions.

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Circulation and formation number of laminar vortex rings

Cited by 177 publications

References 13 publications

Vectoring of parallel synthetic jets: a parametric study

Vectoring of parallel synthetic jets: a parametric study

Pinch-off of non-axisymmetric vortex rings

A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

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