On the structure of vortex rings from inclined nozzles

2011 ◽  
Vol 686 ◽  
pp. 451-483 ◽  
Author(s):  
Trung Bao Le ◽  
Iman Borazjani ◽  
Seokkoo Kang ◽  
Fotis Sotiropoulos
Keyword(s):  
Vortex Ring ◽  
Vortex Sheet ◽  
Vortex Rings ◽  
Cylinder Wall ◽  
Primary Vortex ◽  
Vortical Structures ◽  
Ambient Flow ◽  
Piston Cylinder ◽  
Axial Stretching ◽  
Vortex Tubes

AbstractWe carry out numerical simulations to investigate the vortex dynamics of laminar, impulsively driven flows through inclined nozzles in a piston–cylinder apparatus. Our simulations are motivated by the need to provide a complete description of the intricate vortical structures and governing mechanisms emerging in such flows as documented in the experiments of Webster & Longmire (Phys. Fluids, vol. 10, 1998, pp. 400–416) and Troolin & Longmire (Exp. Fluids, vol. 48, 2010, pp. 409–420). We show that the flow is dominated by the interaction of two main vortical structures: the primary inclined vortex ring at the nozzle exit and the secondary stopping ring that arises due to the entrainment of the flow into the cylinder when the piston stops moving. These two structures are connected together with pairs of vortex tubes, which evolve from the continuous vortex sheet initially connecting the primary vortex ring with the interior cylinder wall. In the exterior of the nozzle the key mechanism responsible for the breakup of the vortical structure is the interaction of the stronger inclined primary ring with the weaker stopping ring near the longest lip of the nozzle. In the interior of the nozzle the dynamics is governed by the axial stretching of the secondary ring and the ultimate impingement of this ring on the cylinder wall. Our simulations also clarify the kinematics of the azimuthal flow along the core of the primary vortex ring documented in the experiments by Lim (Phys. Fluids, vol. 10, 1998, pp. 1666–1671). We show that the azimuthal flow is characterized by a pair of two spiral saddle foci at the long and short lips of the nozzle through which ambient flow enters and exits the primary vortex core.

Vortex Ring Formation in Wall-Bounded Domains

2010 ◽  
Author(s):  
Kelley C. Stewart ◽  
Pavlos P. Vlachos
Keyword(s):  
Vortex Ring ◽  
Propagation Velocity ◽  
Cylindrical Tube ◽  
Ring Formation ◽  
Vortex Rings ◽  
Frequency Noise ◽  
Bounded Domains ◽  
Piston Cylinder ◽  
Vortex Ring Formation ◽  
Wall Interaction

Vortex ring formation and propagation have been studied extensively in quiescent semi-infinite volumes. However, very little is known about the dynamics of vortex-ring formation in wall-bounded domains where vortex wall interaction will affect both the vortex ring pinch-off and propagation velocity. This study addresses this limitation and studies vortex formation in radially confined domains to analyze the effect of vortex-ring wall interaction on the formation and propagation of the vortex ring. Vortex rings were produced using a pneumatically driven piston cylinder arrangement and were ejected into a long cylindrical tube parallel to the piston cylinder arrangement which defined the confined downstream domain. Two different domains were studied with diameters twice and four times the size of the piston cylinder. A semi-infinite unbounded volume with no downstream cylinder was also investigated for comparison. The piston stroke-to-diameter ratio (L/D0) for the studied vortex rings was varied between 0.75 and 3 with corresponding Reynolds numbers, based on circulation, of approximately 500 to 8,000. Velocity field measurements were performed using planar Time Resolved Digital Particle Image Velocimetry (TRDPIV). The TRDPIV data were processed using an in-house developed cross-correlation PIV algorithm and post processed using Proper Orthogonal Decomposition to remove high frequency noise. The propagation velocity and vorticity were investigated and vortex identification was used to track the changing size, location, and circulation of the vortices. The combination of these parameters was used to investigate the effects of wall interaction on vortex ring formation and propagation.

Dynamics and Instability of a Vortex Ring Impinging on a Wall

2015 ◽  
Vol 18 (4) ◽  
pp. 1122-1146 ◽  
Author(s):  
Heng Ren ◽  
Xi-Yun Lu
Keyword(s):  
Vortex Ring ◽  
Axial Flow ◽  
Core Region ◽  
Vortical Flow ◽  
Vortex Rings ◽  
Flow Transition ◽  
Azimuthal Component ◽  
Vortical Structures ◽  
The Core ◽  
Eddy Simulation

AbstractDynamics and instability of a vortex ring impinging on a wall were investigated by means of large eddy simulation for two vortex core thicknesses corresponding to thin and thick vortex rings. Various fundamental mechanisms dictating the flow behaviors, such as evolution of vortical structures, formation of vortices wrapping around vortex rings, instability and breakdown of vortex rings, and transition from laminar to turbulent state, have been studied systematically. The evolution of vortical structures is elucidated and the formation of the loop-like and hair-pin vortices wrapping around the vortex rings (called briefly wrapping vortices) is clarified. Analysis of the enstrophy of wrapping vortices and turbulent kinetic energy (TKE) in flow field indicates that the formation and evolution of wrapping vortices are closely associated with the flow transition to turbulent state. It is found that the temporal development of wrapping vortices and the growth rate of axial flow generated around the circumference of the core region for the thin ring are faster than those for the thick ring. The azimuthal instabilities of primary and secondary vortex rings are analyzed and the development of modal energies is investigated to reveal the flow transition to turbulent state. The modal energy decay follows a characteristic –5/3 power law, indicating that the vortical flow has become turbulence. Moreover, it is identified that the TKE with a major contribution of the azimuthal component is mainly distributed in the core region of vortex rings. The results obtained in this study provide physical insight of the mechanisms relevant to the vortical flow evolution from laminar to turbulent state.

Self-similar shedding of vortex rings

2001 ◽  
Vol 435 ◽  
pp. 397-407 ◽  
Author(s):  
MONIKA NITSCHE
Keyword(s):  
Vortex Ring ◽  
Vortex Shedding ◽  
Vortex Pair ◽  
Vortex Sheet ◽  
Vortex Rings ◽  
Cylindrical Vortex ◽  
Spherical Vortex ◽  
Self Similar

The roll-up of an initially spherical vortex sheet into a vortex ring is computed using the vortex blob method. The ring sheds about 30% of its circulation into a tail which, in turn, rolls up into a ring that sheds circulation. The process repeats itself at smaller and smaller scales in a self-similar manner. The relation between the vortex shedding and the energy of the vortices is investigated. In contrast, an initially cylindrical vortex sheet rolls up into a vortex pair that sheds essentially no circulation.

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.

A Unified Energy Feature of Vortex Rings for Identifying the Pinch-Off Mechanism

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Yang Xiang ◽  
Hong Liu ◽  
Suyang Qin
Keyword(s):  
Vortex Ring ◽  
Critical Value ◽  
Ring Formation ◽  
Experimental Results ◽  
Vortex Rings ◽  
Piston Cylinder ◽  
Dimensionless Energy ◽  
Vortex Ring Formation ◽  
Energy Feature ◽  
Off Time

Owing to the limiting effect of energy, vortex rings cannot grow indefinitely and thus pinch off. In this paper, experiments on the vortex rings generated using a piston-cylinder apparatus are conducted so as to investigate the pinch-off mechanisms and identify the limiting effect of energy. Both theoretical and experimental results show that the generated vortex rings share a unified energy feature, regardless of whether they are pinched-off or not. Moreover, the unified energy feature is quantitatively described by a dimensionless energy number γ, defined as γ=(E/I2Γωmax) and exhibiting a critical value γring = 0.14 ± 0.01 for the generated vortex rings. This unified energy feature reflects the limiting effect of energy and specifies the target of vortex ring formation. Furthermore, based on the tendency of γ during vortex ring formation, criteria for determining the two timescales, i.e., pinch-off time and separation time, which correspond to the onset and end of pinch-off process, respectively, are suggested.

Axial interaction of a vortex ring with a cylinder

2016 ◽  
Vol 809 ◽  
pp. 1-30 ◽  
Author(s):  
Debopam Das ◽  
Akash Manghnani ◽  
Mohit Bansal ◽  
Prafulla Sohoni
Keyword(s):  
Vortex Ring ◽  
Vortex Sheet ◽  
Vortex Rings ◽  
Velocity Change ◽  
Core Diameter ◽  
Ring Diameter ◽  
Layer Region ◽  
Experimental Values ◽  
Induced Velocity ◽  
Axial Interaction

In this paper, axial interaction of a vortex ring with a thin circular cylinder has been studied. An apparatus to generate clean vortex rings, free of piston and stopping vortex effects, has been used. Flow visualization and particle image velocimetry (PIV) experiments are carried out to determine and compare the characteristics of free and interacting vortex rings in the Reynolds number (defined with the circulation of the free travelling vortex ring) range of $2270<Re_{\unicode[STIX]{x1D6E4}}<6790$. It is observed that due to the presence of the cylinder, there is an increase in the velocity of the vortex ring. Also, noticeable changes in the characteristic properties of vortex ring such as core circulation, core diameter and ring diameter have been observed. Changes in these parameters are explained by two changes in the flow field between the vortex ring and the cylinder due to axial interactions: (i) displacement of the streamlines and (ii) acceleration in the induced velocity field in this region. These two mutually opposing effects determine the changes in the primary vortex ring properties that take place during interaction. To justify these experimental observations quantitatively, an analytical study of the interaction under an inviscid assumption is performed. The inviscid analysis does predict the increase in velocity during the interaction, but fails to predict the values observed in the present experiments. However, when the theory is used to correct the velocity change through incorporation of the effects of an axisymmetric induced boundary layer region over the cylinder, modelled as an annular vortex sheet of varying strength, the changes in the translational velocities of the vortex rings match closely with the experimental values.

Interaction of a laminar vortex ring with a thin permeable screen

2012 ◽  
Vol 707 ◽  
pp. 260-286 ◽  
Author(s):  
Christian Naaktgeboren ◽  
Paul S. Krueger ◽  
José L. Lage
Keyword(s):  
Kinetic Energy ◽  
Vortex Ring ◽  
Large Scale ◽  
Symmetry Axis ◽  
Wire Mesh ◽  
Nonlinear Dependence ◽  
Vortex Rings ◽  
Solid Boundary ◽  
Primary Vortex ◽  
Special Cases

AbstractThe canonical case of a vortex ring interacting with a solid surface orthogonal to its symmetry axis exhibits a variety of intricate behaviours, including stretching of the primary vortex ring and generation of secondary vorticity, which illustrate key features of vortex interactions with boundaries. Replacing the solid boundary with a permeable screen allows for new behaviour by relaxing the no-through-flow condition, and can provide a useful analogue for the interaction of large-scale vortices with permeable structures or closely spaced obstructions. The present investigation considers the interaction of experimentally generated vortex rings with a thin permeable screen. The vortex rings were generated using a piston-in-cylinder mechanism using piston stroke-to-diameter ratios ($L/ D$) of 1.0 and 3.0 (nominal) with jet Reynolds numbers ($R{e}_{j} $) of 3000 and 6000 (nominal). Planar laser-induced fluorescence and digital particle image velocimetry (DPIV) were used to study the interaction with wire-mesh screens having surface open-area ratios ($\phi $) in the range 0.44–0.79. Solid surfaces ($\phi = 0$) and free vortex rings ($\phi = 1$) were also included as special cases. Measurement of the vortex trajectories showed expansion of the vortex ring diameter as it approached the boundary and generation of secondary vorticity similar to the case of a solid boundary, but the primary vortex diameter then began to contract towards the symmetry axis as the flow permeated the screen and reorganized into a transmitted vortex downstream. The trajectories were highly dependent on $\phi $, with little change in the incident ring trajectory for $\phi = 0. 79$. Measurement of the hydrodynamic impulse and kinetic energy using DPIV showed that the change between the average upstream and downstream values of these quantities also depended primarily on $\phi $, with a slight decrease in the relative change as $L/ D$ and/or ${\mathit{Re}}_{j} $ were increased. The kinetic energy dissipation ($ \mrm{\Delta} E$) was much more sensitive to $\phi $, with a strongly nonlinear dependence, while the decrease in impulse ($ \mrm{\Delta} I$) was nearly linear in $\phi $. A simple model is proposed to relate $ \mrm{\Delta} E$ and $ \mrm{\Delta} I$ in terms of bulk flow parameters. The model incorporates the decrease in flow velocity during the interaction due to the drag force exerted by the screen on the flow.

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.

scholarly journals Lattice Boltzmann Study of a Vortex Ring Impacting Spheroidal Particles

2014 ◽  
Vol 6 (4) ◽  
pp. 461-477 ◽  
Author(s):  
Chunlong Yu ◽  
Haibo Huang ◽  
Xiyun Lu
Keyword(s):  
Vortex Ring ◽  
Lattice Boltzmann ◽  
Prolate Spheroid ◽  
Vortex Rings ◽  
Secondary Vortex ◽  
Short Axis ◽  
Primary Vortex ◽  
Important Research Topic ◽  
Multiple Relaxation Time ◽  
Boltzmann Method

AbstractInteraction of vortex rings with solid is an important research topic of hydrodynamic. In this study, a multiple-relaxation time (MRT) lattice Boltzmann method (LBM) is used to investigate the flow of a vortex ring impacting spheroidal particles. The MRT-LBM is validated through the cases of vortex ring impacting a flat wall. The vortex evolution due to particle size, the aspect ratio of a prolate particle, as well as Reynolds (Re) number are discussed in detail. When the vortex ring impacting a stationary sphere, the primary and secondary vortex rings wrap around each other, which is different from the situation of the vortex ring impacting a plate. For the vortex ring impacting with a prolate spheroid, the secondary vortex ring stretches mainly along the long axis of the ellipsoid particle. However, it is found that after the vortex wrapping stage, the primary vortex recovers along the short axis of the particle faster than that in the long axis, i.e., the primary vortex ring stretches mainly along the short axis of the particle. That has never been address in the literature.

A study of the counter rotating vortex rings interacting with the primary vortex ring in shock tube generated flows

2013 ◽  
Vol 45 (2) ◽  
pp. 025506 ◽  
Author(s):  
T Murugan ◽  
S De ◽  
C L Dora ◽  
D Das ◽  
P Prem Kumar
Keyword(s):  
Shock Tube ◽  
Vortex Ring ◽  
Vortex Rings ◽  
Primary Vortex
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