Formation Number of Vortex Rings

2021 ◽  
pp. 121-139
Author(s):  
Ionut Danaila ◽  
Felix Kaplanski ◽  
Sergei S. Sazhin
Keyword(s):  
Vortex Rings ◽  
Formation Number

scholarly journals Formation number of confined vortex rings

2018 ◽  
Vol 3 (9) ◽  
Author(s):  
I. Danaila ◽  
F. Luddens ◽  
F. Kaplanski ◽  
A. Papoutsakis ◽  
S. S. Sazhin
Keyword(s):  
Vortex Rings ◽  
Formation Number

Passive scalar mixing in vortex rings

2007 ◽  
Vol 582 ◽  
pp. 449-461 ◽  
Author(s):  
RAJES SAU ◽  
KRISHNAN MAHESH
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Vortex Ring ◽  
Nozzle Exit ◽  
Passive Scalar ◽  
Rate Of Change ◽  
Vortex Rings ◽  
Ambient Fluid ◽  
Stroke Length ◽  
Formation Number

Direct numerical simulation is used to study the mixing of a passive scalar by a vortex ring issuing from a nozzle into stationary fluid. The ‘formation number’ (Gharibet al. J. Fluid Mech.vol. 360, 1998, p. 121), is found to be 3.6. Simulations are performed for a range of stroke ratios (ratio of stroke length to nozzle exit diameter) encompassing the formation number, and the effect of stroke ratio on entrainment and mixing is examined. When the stroke ratio is greater than the formation number, the resulting vortex ring with trailing column of fluid is shown to be less effective at mixing and entrainment. As the ring forms, ambient fluid is entrained radially into the ring from the region outside the nozzle exit. This entrainment stops once the ring forms, and is absent in the trailing column. The rate of change of scalar-containing fluid is found to depend linearly on stroke ratio until the formation number is reached, and falls below the linear curve for stroke ratios greater than the formation number. This behaviour is explained by considering the entrainment to be a combination of that due to the leading vortex ring and that due to the trailing column. For stroke ratios less than the formation number, the trailing column is absent, and the size of the vortex ring increases with stroke ratio, resulting in increased mixing. For stroke ratios above the formation number, the leading vortex ring remains the same, and the length of the trailing column increases with stroke ratio. The overall entrainment decreases as a result.

Micro Pulsatile Jets for Thrust Optimization

2004 ◽  
Author(s):  
Tiffany J. Finley ◽  
Kamran Mohseni
Keyword(s):  
Actuation Voltage ◽  
Orifice Diameter ◽  
Vortex Rings ◽  
Wave Shape ◽  
Electromagnetic Actuation ◽  
Thrust Generation ◽  
Circular Orifice ◽  
Formation Number ◽  
Cylindrical Cavities ◽  
Maximum Thrust

Thrust optimization of micro-synthetic pulsatile jets is studied. Cylindrical cavities with a small circular orifice at one end, and a vibrating diaphragm at the other are used for thrust generation. The governing parameters are identified and the tradeoffs between electrostatic, piezoelectric, and electromagnetic actuation methods are investigated. Optimization of the micro jets requires a solution that gives maximum diaphragm displacement while minimizing voltage. The size of the orifice diameter is chosen to maintain a formation number of 4, at which the length of an expelled slug of fluid from the exit orifice is four times the diameter of orifice. This relationship maximizes the circulation and impulse in the leading vortex rings generated by the actuator. To examine the effects of cavity dimensions, a number of actuators are constructed out of aluminum with various cavity diameter, cavity height, and orifice diameters. Piezoelectric disks bonded to brass shims are used for actuation. The jets are tested in air at various actuation voltage and wave-shape functions. Maximum thrust generation is achieved at the resonant frequency of the cavity. Hot wire anemometry is used to further characterize the jet flow field. An investigation into electrostatic, piezoelectric, and electromagnetic diaphragm actuation methods revealed that electromagnetic actuation provides the maximum diaphragm displacement using a constant voltage.

scholarly journals Circulation and formation number of laminar vortex rings

1998 ◽  
Vol 376 ◽  
pp. 297-318 ◽  
Author(s):  
MOSHE ROSENFELD ◽  
EDMOND RAMBOD ◽  
MORTEZA GHARIB
Keyword(s):  
Velocity Profile ◽  
Time Scale ◽  
Vortex Generator ◽  
Formation Time ◽  
Vortex Rings ◽  
Axisymmetric Vortex ◽  
Parabolic Velocity Profile ◽  
Formation Number ◽  
Experimental Findings ◽  
Good Agreement

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.

scholarly journals The Formation and Evolution of Turbulent Swirling Vortex Rings Generated by Axial Swirlers

2019 ◽  
Vol 104 (4) ◽  
pp. 795-816 ◽  
Author(s):  
Chuangxin He ◽  
Lian Gan ◽  
Yingzheng Liu
Keyword(s):  
Propagation Velocity ◽  
Early Stage ◽  
Axial Direction ◽  
Vortex Rings ◽  
Eddy Simulation ◽  
Axis Parallel ◽  
3D Printed ◽  
Formation Number ◽  
Formation And Evolution ◽  
Swirling Vortex

AbstractThe present work investigates the formation process and early stage evolution of turbulent swirling vortex rings, by using planar Particle Image Velocimetry (PIV) and Large Eddy Simulation (LES). Vortex rings are produced in a piston-nozzle arrangement with swirl generated by 3D-printed axial swirlers in experiments. Idealised solid-body rotation is applied in LES to evaluate the effect of nozzle exit velocity profile in experiments. The Reynolds number (Re) based on the nozzle diameter D and the slug velocity U0 in the nozzle is 20,000. The swirl number S generated ranges from 0 (zero-swirl vortex ring) and 1.1, covering the two critical swirl numbers previously identified in a swirling jet. Both PIV and LES results show that the formation number F decreases linearly as S increases, with the maximum F ≈ 2.6 at S = 0 (produced by the swirler with straight vanes) and minimum F = 1.9 at S = 1.1. The corresponding maximum attainable circulation in the nozzle axis parallel plane also diminishes with increasing S. Evolution of compact rings produced by a stroke ratio L/D = 1.5 reveals that circulation decay rate is largely proportional to S. The trajectory of the vortex core in the axial direction, hence the ring axial propagation velocity, decreases as S, while that in the radial direction and the radial propagation velocity, increase with S. An empirical scaling function is proposed to scale these variables.

Numerical Modeling of Spores Dispersal of Sphagnum Moss Using ANSYS FLUENT

2017 ◽  
Author(s):  
Dwight L. Whitaker ◽  
Robert Simsiman ◽  
Emily S. Chang ◽  
Samuel Whitehead ◽  
Hesam Sarvghad-Moghaddam
Keyword(s):  
Vortex Ring ◽  
High Speed ◽  
Cost Effective ◽  
Video Data ◽  
Vortex Rings ◽  
Peat Moss ◽  
Ansys Fluent ◽  
Formation Number ◽  
Piston Stroke ◽  
First Time

The common peat moss, Sphagnum, is able to explosively disperse its spores by producing a vortex ring from a pressurized sporophyte to carry a cloud of spores to heights over 15 cm where the turbulent boundary layer can lift and carry them indefinitely. While vortex ring production is fairly common in the animal kingdom (e.g. squid, jellyfish, and the human heart), this is the first report of vortex rings generated by a plant. In other cases of biologically created vortex rings, it has been observed that vortices are produced with a maximum formation number of L/D = 4, where L is the length of the piston stroke and D is the diameter of the outlet. At this optimal formation number, the circulation and thus impulse of the vortex ring is maximized just as the ring is pinched off. In the current study, we modeled this dispersal phenomenon for the first time using ANSYS FLUENT 17.2. The spore capsule at the time of burst was approximated as a cylinder with a thin cylindrical cap attached to it. They were then placed inside a very large domain representing the air in which the expulsion was modeled. Due to the symmetry of our model about the central axis, we performed a 2D axisymmetric simulation. Also, due the complexity of the fluid domain as a result of the capsule-cap interface, as well as the need for a dynamic mesh for simulating the motion of the cap, first a mesh study was performed to generate an efficient mesh in order to make simulations computationally cost-effective. The domain was discretized using triangular elements and the mesh was refined at the capsule-cap interface to accurately capture the ring vortices formed by the expulsed cap. The dispersal was modeled using a transient simulation by setting a pressure difference between inside of the capsule and the surrounding atmospheric air. Pressure and vorticity contours were recorded at different time instances. Our simulation results were interpreted and compared to high-speed video data of sporophyte expulsions to deduce the pressure within the capsule upon dispersal, as well as the formation number of resulting vortex rings. Vorticity contours predicted by our model were in agreement with the experimental results. We hypothesized that the vortex rings from Sphagnum are sub-optimal since a slower vortex bubble would carry spores more effectively than a faster one.

A universal time scale for vortex ring formation

1998 ◽  
Vol 360 ◽  
pp. 121-140 ◽  
Author(s):  
MORTEZA GHARIB ◽  
EDMOND RAMBOD ◽  
KARIM SHARIFF
Keyword(s):  
Vortex Ring ◽  
Vortex Rings ◽  
Water Tank ◽  
Single Vortex ◽  
Piston Cylinder ◽  
Vortex Ring Formation ◽  
Image Velocimetry ◽  
Wide Range ◽  
Formation Number ◽  
Piston Stroke

The formation of vortex rings generated through impulsively started jets is studied experimentally. Utilizing a piston/cylinder arrangement in a water tank, the velocity and vorticity fields of vortex rings are obtained using digital particle image velocimetry (DPIV) for a wide range of piston stroke to diameter (L/D) ratios. The results indicate that the flow field generated by large L/D consists of a leading vortex ring followed by a trailing jet. The vorticity field of the leading vortex ring formed is disconnected from that of the trailing jet. On the other hand, flow fields generated by small stroke ratios show only a single vortex ring. The transition between these two distinct states is observed to occur at a stroke ratio of approximately 4, which, in this paper, is referred to as the ‘formation number’. In all cases, the maximum circulation that a vortex ring can attain during its formation is reached at this non-dimensional time or formation number. The universality of this number was tested by generating vortex rings with different jet exit diameters and boundaries, as well as with various non-impulsive piston velocities. It is shown that the ‘formation number’ lies in the range of 3.6–4.5 for a broad range of flow conditions. An explanation is provided for the existence of the formation number based on the Kelvin–Benjamin variational principle for steady axis-touching vortex rings. It is shown that based on the measured impulse, circulation and energy of the observed vortex rings, the Kelvin–Benjamin principle correctly predicts the range of observed formation numbers.

scholarly journals Pinch-off of non-axisymmetric vortex rings

2014 ◽  
Vol 740 ◽  
pp. 61-96 ◽  
Author(s):  
Clara O’Farrell ◽  
John O. Dabiri
Keyword(s):  
Aspect Ratio ◽  
Vortex Rings ◽  
Equivalent Diameter ◽  
Local Curvature ◽  
Cross Sectional ◽  
Piston Cylinder ◽  
Circular Arcs ◽  
Axisymmetric Vortex ◽  
Formation Number ◽  
Nozzle Geometries

AbstractThe 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.

Formation regimes of vortex rings in negatively buoyant starting jets

2013 ◽  
Vol 716 ◽  
pp. 470-486 ◽  
Author(s):  
C. Marugán-Cruz ◽  
J. Rodríguez-Rodríguez ◽  
C. Martínez-Bazán
Keyword(s):  
Vortex Ring ◽  
Richardson Number ◽  
Vortex Formation ◽  
Vortex Rings ◽  
Vortex Identification ◽  
Buoyant Flows ◽  
Formation Number ◽  
Secondary Vortices ◽  
Starting Jet ◽  
Negatively Buoyant

AbstractThe formation of vortex rings in negatively buoyant starting jets has been studied numerically for different values of the Richardson number, $\mathit{Ri}$, covering the range of weak to moderate buoyancy effects ($0\leq \mathit{Ri}\leq 0. 20$). Two different regimes have been identified in the vortex formation and the transition between them takes place at $\mathit{Ri}\approx 0. 03$. The vorticity distribution inside the vortex ring after pinching off from the trailing stem as well as the total amount of circulation it encloses (characterized by the formation number, $F$) show different behaviours with the Richardson number in the two regimes. The differences are associated with the different mechanisms by which the head vortex absorbs the circulation injected by the starting jet. While secondary vortices are engulfed by the leading vortex before separating from the trailing jet in the weak buoyancy effects regime ($0\lt \mathit{Ri}\lt 0. 03$), this phenomenon is not observed in the moderate buoyancy effects regime ($0. 03\lt \mathit{Ri}\lt 0. 2$). Moreover it is shown that the formation number of a negatively buoyant vortex ring can be determined by considering that its dynamics are similar to that of a neutrally buoyant vortex but propagating with velocity corresponding to the negatively buoyant one. Based on this simple idea, a phenomenological model is presented to describe quantitatively the evolution of the formation number with the Richardson number, $F(\mathit{Ri})$, obtained numerically. In addition, the limitations of different vortex identification methods used to evaluate the vortex properties in buoyant flows are discussed.

scholarly journals The formation number of vortex rings formed in uniform background co-flow

2006 ◽  
Vol 556 ◽  
pp. 147 ◽  
Author(s):  
PAUL S. KRUEGER ◽  
JOHN O. DABIRI ◽  
MORTEZA GHARIB
Keyword(s):  
Vortex Rings ◽  
Uniform Background ◽  
Formation Number
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