Numerical Simulations of Two Coaxial Vortex Rings Head-on Collision

2016 ◽  
Vol 8 (4) ◽  
pp. 616-647 ◽  
Author(s):  
Hui Guan ◽  
Zhi-Jun Wei ◽  
Elizabeth Rumenova Rasolkova ◽  
Chui-Jie Wu
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Evaluation Procedure ◽  
Vortex Rings ◽  
Small Scale ◽  
Finite Volume Scheme ◽  
Induced Motion ◽  
Piecewise Parabolic ◽  
Physical Phenomena ◽  
Small Scale Structures

AbstractVortex rings have been a subject of interest in vortex dynamics due to a plethora of physical phenomena revealed by their motions and interactions within a boundary. The present paper is devoted to physics of a head-on collision of two vortex rings in three dimensional space, simulated with a second order finite volume scheme and compressible. The scheme combines non-iterative approximate Riemann-solver and piecewise-parabolic reconstruction used in inviscid flux evaluation procedure. The computational results of vortex ring collisions capture several distinctive phenomena. In the early stages of the simulation, the rings propagate under their own self-induced motion. As the rings approach each other, their radii increase, followed by stretching and merging during the collision. Later, the two rings have merged into a single doughnut-shaped structure. This structure continues to extend in the radial direction, leaving a web of particles around the centers. At a later time, the formation of ringlets propagate radially away from the center of collision, and then the effects of instability involved leads to a reconnection in which small-scale ringlets are generated. In addition, it is shown that the scheme captures several experimentally observed features of the ring collisions, including a turbulent breakdown into small-scale structures and the generation of small-scale radially propagating vortex rings, due to the modification of the vorticity distribution, as a result of the entrainment of background vorticity and helicity by the vortex core, and their subsequent interaction.

Large- and small-scale vortical motions in a shear layer perturbed by tabs

1999 ◽  
Vol 382 ◽  
pp. 307-329 ◽  
Author(s):  
JUDITH K. FOSS ◽  
K. B. M. Q. ZAMAN
Keyword(s):  
Shear Layer ◽  
Pitch Angle ◽  
Large Scale ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Small Scale ◽  
Streamwise Vortices ◽  
Streamwise Vorticity ◽  
Cross Sectional ◽  
Scale Population

The large- and small-scale vortical motions produced by ‘delta tabs’ in a two-stream shear layer have been studied experimentally. An increase in mixing was observed when the base of the triangular shaped tab was affixed to the trailing edge of the splitter plate and the apex was pitched at some angle with respect to the flow axis. Such an arrangement produced a pair of counter-rotating streamwise vortices. Hot-wire measurements detailed the velocity, time-averaged vorticity (Ωx) and small-scale turbulence features in the three-dimensional space downstream of the tabs. The small-scale structures, whose scale corresponds to that of the peak in the dissipation spectrum, were identified and counted using the peak-valley-counting technique. The optimal pitch angle, θ, for a single tab and the optimal spanwise spacing, S, for a multiple tab array were identified. Since the goal was to increase mixing, the optimal tab configuration was determined from two properties of the flow field: (i) the large-scale motions with the maximum Ωx, and (ii) the largest number of small-scale motions in a given time period. The peak streamwise vorticity magnitude [mid ]Ωx−max[mid ] was found to have a unique relationship with the tab pitch angle. Furthermore, for all cases examined, the overall small-scale population was found to correlate directly with [mid ]Ωx−max[mid ]. Both quantities peaked at θ≈±45°. It is interesting to note that the peak magnitude of the corresponding circulation in the cross-sectional plane occurred for θ≈±90°. For an array of tabs, the two quantities also depended on the tab spacing. An array of contiguous tabs acted as a solid deflector producing the weakest streamwise vortices and the least small-scale population. For the measurement range covered, the optimal spacing was found to be S≈1.5 tab widths.

scholarly journals Elongated Gravity Sources as an Analytical Limit for Flat Galaxy Rotation Curves

Universe ◽  
2021 ◽  
Vol 7 (9) ◽  
pp. 346
Author(s):  
Felipe J. Llanes-Estrada
Keyword(s):  
Galactic Plane ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Small Scale ◽  
Scaling Exponent ◽  
Rotation Curves ◽  
Central Mass ◽  
Filamentary Structure ◽  
Analytical Limit ◽  
Galaxy Rotation Curves

The flattening of spiral-galaxy rotation curves is unnatural in view of the expectations from Kepler’s third law and a central mass. It is interesting, however, that the radius-independence velocity is what one expects in one less dimension. In our three-dimensional space, the rotation curve is natural if, outside the galaxy’s center, the gravitational potential corresponds to that of a very prolate ellipsoid, filament, string, or otherwise cylindrical structure perpendicular to the galactic plane. While there is observational evidence (and numerical simulations) for filamentary structure at large scales, this has not been discussed at scales commensurable with galactic sizes. If, nevertheless, the hypothesis is tentatively adopted, the scaling exponent of the baryonic Tully–Fisher relation due to accretion of visible matter by the halo comes out to reasonably be 4. At a minimum, this analytical limit would suggest that simulations yielding prolate haloes would provide a better overall fit to small-scale galaxy data.

scholarly journals The Thinness of the Ocean in S–Θ–p Space and the Implications for Mean Diapycnal Advection

2007 ◽  
Vol 37 (6) ◽  
pp. 1714-1732 ◽  
Author(s):  
Trevor J. McDougall ◽  
David R. Jackett
Keyword(s):  
Dimensional Space ◽  
World Ocean ◽  
Three Dimensional ◽  
Small Scale ◽  
Lateral Motion ◽  
Hydrographic Data ◽  
Mixing Processes ◽  
The World ◽  
The Mean ◽  
Three Dimensional Space

Abstract It is shown that the ocean’s hydrography occupies little volume in the three-dimensional space defined by salinity–temperature–pressure (S–Θ–p), and the implications of this observation for the mean vertical transport across density surfaces are discussed. Although ocean data have frequently been analyzed in the two-dimensional temperature–salinity (S–Θ) diagram where casts of hydrographic data are often locally tight in S–Θ space, the relatively empty nature of the World Ocean in the three-dimensional S–Θ–p space seems not to have received attention. The World Ocean’s data lie close to a single surface in this three-dimensional space, and it is shown that this explains the known smallness of the ambiguity in defining neutral surfaces. The ill-defined nature of neutral surfaces means that lateral motion along neutral trajectories leads to mean vertical advection through density surfaces, even in the absence of small-scale mixing processes. The situation in which the ocean’s hydrography occupies a large volume in S–Θ–p space is also considered, and it is suggested that the consequent vertical diapycnal advection would be sufficiently large that the ocean would not be steady.

Vortex-Induced Motion: Model Testing of a Monocolumn Floater

2006 ◽  
Author(s):  
Marcos Cueva ◽  
Andre´ L. C. Fujarra ◽  
Kazuo Nishimoto ◽  
Lui´s Quadrante ◽  
Ana Paula Costa
Keyword(s):  
Three Dimensional ◽  
Mooring Line ◽  
Small Scale ◽  
Extensive Literature ◽  
Offshore Platforms ◽  
Spar Platforms ◽  
Vortex Induced Vibrations ◽  
Induced Motion ◽  
Electrical Cables ◽  
Line Design

The vortex-induced vibrations - VIV have been studied for several fields of engineering due to its occurrence in different structures, such as electrical cables, industries chimneys and offshore risers. Although available an extensive literature describing its fundamental issues, these vortex-induced phenomena still deserve investigation, particularly in the offshore platforms installed in regions with high current speed. Recently, the Vortex-Induced Motions - VIM, a particular case of vortex-induced vibration with high magnitude of response amplitude, have been observed in SPAR platforms installed in Gulf of Mexico - GoM, opening a new investigation field. For those motions, aspects such as asymmetric mooring restoring stiffness and the probable three-dimensionality of the flow turn the problem even more complex. Since 2003, in partnership with University of Sao Paulo and consultant companies, PETROBRAS has been studying the use of monocolumn floaters for oil production in Campos Basin and GoM. Considering the environmental conditions in these areas and assuming that monocolumn floaters can exhibit similar VIM behavior of SPAR platforms, it was started an experimental investigation focusing on VIM responses of small-scale monocolumn floaters in towing tank. Although based on the state of art procedures used for SPAR platforms, the monocolumn experiments considered the different geometry of this concept and the larger susceptibility to the three-dimensional effects, due to the smaller relation draft/beam. Special attention was given to the ratio roughness/beam in order to guarantee similarity between the experiments and its respective real cases. Additionally, different heading conditions were also tested. Thus, the present work presents a set of preliminary results and discussions concerning VIM of monocolumn floaters and its impact on the mooring line design and riser specification.

scholarly journals Head-on collisions of vortex rings upon round cylinders

2017 ◽  
Vol 833 ◽  
pp. 648-676 ◽  
Author(s):  
T. H. New ◽  
B. Zang
Keyword(s):  
Vortex Ring ◽  
Three Dimensional ◽  
Diameter Ratio ◽  
Vortex Rings ◽  
Strong Interactions ◽  
Small Scale ◽  
Secondary Vortex ◽  
Time Resolved ◽  
Flow Models ◽  
Flat Surfaces

Vortical structures and behaviour associated with vortex-ring collisions upon round cylinders with different cylinder-to-vortex-ring diameter ratios were studied using laser-induced fluorescence and time-resolved particle-image velocimetry techniques. Circular vortex rings of Reynolds number 4000 and three diameter ratios of $D/d=1$, 2 and 4 were considered in the present investigation. Results reveal that the collision behaviour is very different from that associated with flat surfaces, in which vortex disconnection and reconnection processes caused by the strong interactions between primary and secondary vortex rings produce small-scale vortex ringlets that eject away from the cylinders. For the cylinder with the largest diameter ratio used here, these vortex ringlets move towards each other along the collision axis, where they eventually collide to produce a vortex dipole that propagates upstream. However, as the diameter ratio decreases, these vortex ringlets are produced further away from the collision axis, which results in them ejecting away from the cylinder at increasingly larger angles relative to the collision axis. Trajectories of key vortex cores were extracted from the experimental results to demonstrate quantitatively the strong sensitivity of these vortical motions upon the diameter ratio. Furthermore, significant differences in the primary vortex-ring circulation along convex surfaces and straight edges after the collisions are observed. In particular, vortex flow models are presented here to better illustrate the highly three-dimensional flow dynamics of the collision behaviour, as well as highlighting the strong dependency of the secondary vortex-ring formation, vortex disconnection/reconnection processes, and ejection of the resulting vortex ringlets upon the diameter ratio. As such, these results are expected to shed more light on the more general scenario of vortex-ring collisions upon arbitrarily contoured solid boundaries.

scholarly journals ROTATING ELECTROMAGNETIC WAVES IN TOROID-SHAPED REGIONS

2010 ◽  
Vol 21 (01) ◽  
pp. 11-32 ◽  
Author(s):  
CLAUDIA CHINOSI ◽  
LUCIA DELLA CROCE ◽  
DANIELE FUNARO
Keyword(s):  
Fluid Dynamics ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Numerical Solutions ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Angular Speed ◽  
Vortex Rings ◽  
Bounded Region ◽  
Three Dimensional Space

Electromagnetic waves, solving the full set of Maxwell equations in vacuum, are numerically computed. These waves occupy a fixed bounded region of the three-dimensional space, topologically equivalent to a toroid. Thus, their fluid dynamics analogs are vortex rings. An analysis of the shape of the sections of the rings, depending on the angular speed of rotation and the major diameter, is carried out. Successively, spherical electromagnetic vortex rings of Hill's type are taken into consideration. For some interesting peculiar configurations, explicit numerical solutions are exhibited.

Large-scale structure in the mixing layer of a round jet

1978 ◽  
Vol 89 (3) ◽  
pp. 413-432 ◽  
Author(s):  
A. J. Yule
Keyword(s):  
Transition Region ◽  
Large Scale ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Careful Consideration ◽  
Vortex Rings ◽  
Small Scale ◽  
Potential Core ◽  
Round Jet ◽  
Large Eddies

Late transitional and turbulent flows in the mixing-layer region of a round jet are investigated for a range of Reynolds numbers by using flow-visualization and hotwire techniques. Attention is focused on the vortices in the transition region and the large eddies in the turbulent region. The interaction and coalescence of vortex rings in the transition region are described. The transition region is characterized by a growth of three-dimensional flow due to a wave instability of the cores of the vortex rings. The merging of these distorted vortices produces large eddies which can remain coherent up to the end of the potential-core region of the jet. A conditional sampling technique is used to measure eddies moving near the jet centre-line. These eddies differ significantly from the ring vortices as they are three-dimensional and contain irregular small-scale turbulence. However, when averaged, their structure is similar in cross-section to that of a vortex ring. These sampled eddies contribute greatly to local velocity fluctuations and statistical correlations. The experiments indicate a need for careful consideration of the meanings of terms such as ‘vortex’, ‘eddy’ and ‘turbulent flow’. In particular care must be taken to discriminate between the orderly, easily visualized, vortices in the transition regions of free shear flows and the less clearly visualized, but strong, large eddies in the fully developed turbulent regions.

scholarly journals Turbulent Vortex Ring/Free Surface Interaction

1995 ◽  
Vol 117 (3) ◽  
pp. 374-381 ◽  
Author(s):  
A. Weigand ◽  
M. Gharib
Keyword(s):  
Free Surface ◽  
Vortex Ring ◽  
Surface Interaction ◽  
Vortex Rings ◽  
Small Scale ◽  
Turbulent Vortex ◽  
Turbulent Transition ◽  
Vortex Loops ◽  
Scale Structures ◽  
Small Scale Structures

The interaction of turbulent vortex rings that approach a clean water surface under various angles is experimentally investigated. The temporal evolution of the vortex rings with an initial Reynolds number of Re0 = 7500 is characterized by the laminar/turbulent transition and asymptotic relaminarization of the flow. Using the shadowgraph technique, two major flow cases were identified as a result of the vortex-ring/free-surface interaction: a trifurcation case that results from the interaction during the transition stage, and a bifurcation case that evolves during the fully-developed turbulent stage. In contrast to the laminar interaction, the turbulent bifurcation pattern is characterized by the reconnection and mutual interaction of many small-scale structures. Simultaneous digital particle image velocimetry (DPIV) and shadowgraph measurements reveal that the evolution of the small-scale structures at the free surface is strongly dominated by the bifurcation pattern, which in turn is a consequence of the persisting laminar sublayer in the core regions of the reconnected turbulent vortex loops.

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