Formation number and pinch-off signals of disc vortex ring based on a Lagrangian analysis

2021 ◽  
Vol 129 ◽  
pp. 110452
Author(s):  
Yang Xiang ◽  
Zhuoqi Li ◽  
Suyang Qin ◽  
Hong Liu
Keyword(s):  
Vortex Ring ◽  
Lagrangian Analysis ◽  
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.

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.

scholarly journals Development of the trailing shear layer in a starting jet during pinch-off

2012 ◽  
Vol 700 ◽  
pp. 382-405 ◽  
Author(s):  
L. Gao ◽  
S. C. M. Yu
Keyword(s):  
Shear Layer ◽  
Vortex Ring ◽  
Critical Time ◽  
Piston Cylinder ◽  
Vortex Ring Formation ◽  
Image Velocimetry ◽  
Formation Number ◽  
Vorticity Flux ◽  
Secondary Vortices ◽  
Starting Jet

AbstractExperiments on a circular starting jet generated by a piston–cylinder arrangement, over a range of Reynolds number from $2600$ to $5600$, are conducted so as to investigate the development of the trailing shear layer during the leading vortex ring formation, as well as the corresponding effects on the pinch-off process. Results obtained by digital particle image velocimetry (DPIV) show that secondary vortices start to develop in the trailing jet only after the critical time scale, the ‘formation number’, is achieved. The subsequent growth of the secondary vortices reduces the vorticity flux being fed into the leading vortex ring and, as a consequence, constrains the growth of leading vortex ring with larger circulation. Evolution of perturbation waves into secondary vortices is found to associate with growth and translation of the leading vortex ring during the formation process. A dimensionless parameter ‘$A$’, defined as ${\Gamma }_{\mathit{ring}} / ({x}_{\mathit{core}} \mrm{\Delta} U$), is therefore proposed to characterize the effect of the leading vortex ring on suppressing the nonlinear development of instability in the trailing shear layer, i.e. the initial roll-up of the secondary vortices. In a starting jet, $A$ follows a decreasing trend with the formation time ${t}^{\ensuremath{\ast} } $. A critical value ${A}_{c} = 1. 1\pm 0. 1$ is identified experimentally, which physically coincides with the initiation of the first secondary vortex roll-up and, therefore, indicates the onset of pinch-off process.

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.

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.

A model for the pinch-off process of the leading vortex ring in a starting jet

2010 ◽  
Vol 656 ◽  
pp. 205-222 ◽  
Author(s):  
L. GAO ◽  
S. C. M. YU
Keyword(s):  
Vortex Ring ◽  
Complete Separation ◽  
Nozzle Geometry ◽  
Translational Velocity ◽  
Second Stage ◽  
Dimensionless Energy ◽  
Vortex Ring Formation ◽  
Formation Number ◽  
Stage Process ◽  
Starting Jet

Modifications have been made to an analytical model proposed by Shusser & Gharib (J. Fluid Mech., vol. 416, 2000b, pp. 173–185) for the vortex ring formation and pinch-off process in a starting jet. Compared with previous models, the present investigation distinguishes the leading vortex ring from its trailing jet so as to consider the details of the pinch-off process in terms of the properties of the leading vortex ring, which are determined by considering the flux of kinetic energy, impulse and circulation from the trailing jet into the leading vortex ring by convective transportation. A two-stage process has been identified before the complete separation of the leading vortex ring from its trailing jet. The first stage involves the growth of the leading vortex ring by absorbing all the ejected fluid from the nozzle until certain optimum size is achieved. The second stage is characterized by the appreciable translational velocity of the leading vortex ring followed by a trailing jet. The leading vortex ring is approximated as a Norbury vortex ring with growing characteristic core radius ϵ such that dimensionless energy α, as well as its translational velocity and penetration depth, can be estimated. By applying the Kelvin–Benjamin variational principle, the pinch-off process is signified by two time scales, i.e. the formation number, which indicates the onset of the pinch-off process, and the separation time, which corresponds to the time when the leading vortex ring becomes physically separated from the trailing jet and is therefore referred to as the end of the pinch-off process. The effect of nozzle geometry, i.e. a straight nozzle or a converging nozzle, has also been taken into account by using different descriptions of the growth of the trailing jet. The prediction of the formation number and the characteristics of the vortex ring are found to be in good agreement with previous experimental results on starting jets with straight nozzles and converging nozzles, respectively.

A Novel Assessment Technique for Prosthetic Valve Function: Employing a New Laboratory Approach to Characterize Projected Dynamic Valve Area and Vortex Formation Analysis

2008 ◽  
Author(s):  
Jennifer Bartell ◽  
Olga Pierrakos ◽  
Lawrence Scotten
Keyword(s):  
Vortex Ring ◽  
Heart Valves ◽  
Ring Formation ◽  
Prosthetic Heart Valves ◽  
Evaluation Tool ◽  
Vortex Ring Formation ◽  
Formation Number ◽  
Valve Annulus ◽  
Insight Into ◽  
Annulus Diameter

The study of heart valve performance (healthy, diseased, and prosthetic) has traditionally involved the examination of transvalvular characteristics, such as pressure gradients and effective and geometric orifice areas. However, recent research has shown that a key downstream flow characteristic, vortex ring formation, should not be overlooked because quantifying this mechanism provides insight into the assessment of valve performance [1]. Vortex ring formation, which is dependent on the valve design [1], is the roll-up of the shear layers shedding past valve leaflets. Governed by a universal time-scale or formation number (FN) that is based on the jet length to diameter ratio (L/D), vortex ring formation provides insight into the kinematics of optimizing effective fluid transport. It has been shown that growth of the leading vortex ring ceases at a FN between 3.5 and 4.5 in various biological systems [2], but most of these studies have assumed a constant or fixed orifice opening. However, incorporating a time-varying jet diameter rather than the constant valve annulus diameter has recently been identified by Dabiri and Gharib as a key factor in the characterization of vortex ring formation and provides a more complete picture of impulse generation and efficiency in vortical flows [2]. This dynamic formation number is governed by the following equation: (L/D)*=∫0tU¯/D¯dt(1) where U is velocity, D is diameter, t is time, and the overbar indicates a time average. Estimating (L/D)* can serve as a powerful evaluation tool in comparison to conventional methods of FN calculation that use either an averaged diameter or the valve annulus diameter. Ideally suited for unsteady flows, such as the opening phase and leaflet motions in heart valves, (L/D)* can provide insight into assessing the performance of natural and prosthetic heart valves (PHVs).

scholarly journals A model for vortex ring formation in a starting buoyant plume

2000 ◽  
Vol 416 ◽  
pp. 173-185 ◽  
Author(s):  
MICHAEL SHUSSER ◽  
MORTEZA GHARIB
Keyword(s):  
Vortex Ring ◽  
Time Scale ◽  
Ring Formation ◽  
Vortex Rings ◽  
Uniform Density ◽  
Dimensionless Time ◽  
Buoyant Plume ◽  
Piston Cylinder ◽  
Vortex Ring Formation ◽  
Formation Number

Vortex ring formation in a starting axisymmetric buoyant plume is considered. A model describing the process is proposed and a physical explanation based on the Kelvin–Benjamin variational principle for steady vortex rings is provided. It is shown that Lundgren et al.'s (1992) time scale, the ratio of the velocity of a buoyant plume after it has travelled one diameter to its diameter, is equivalent to the time scale (formation time) proposed by Gharib et al. (1998) for uniform-density vortex rings generated with a piston/cylinder arrangement. It is also shown that, similarly to piston-generated vortex rings (Gharib et al. 1998), the buoyant vortex ring pinches off from the plume when the latter can no longer provide the energy required for steady vortex ring existence. The dimensionless time of the pinch-off (the formation number) can be reasonably well predicted by assuming that at pinch-of the vortex ring propagation velocity exceeds the plume velocity. The predictions of the model are compared with available experimental results.

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