Evolution and breakup of vortex rings in straining and shearing flows

1994 ◽  
Vol 273 ◽  
pp. 285-312 ◽  
Author(s):  
J. S. Marshall ◽  
J. R. Grant
Keyword(s):  
Linear Theory ◽  
Vortex Pair ◽  
Small Strain ◽  
Oscillation Period ◽  
Numerical Calculations ◽  
Vortex Rings ◽  
Single Vortex ◽  
Discrete Vortex ◽  
Initial Plane ◽  
Shear Rates

A study of the effect of external straining and shearing flows on the evolution and form of breakup of vortex rings has been performed. Two orientations each of straining and shearing flows are considered. A theoretical analysis of the ring motion for small strain and shear rates is performed, and it is found that for shearing and straining flows in the plane of the ring, the ring may oscillate periodically. For a straining flow with compression normal to the initial plane of the ring, the linear theory predicts that the ring radius will expand with time. For shearing flow normal to the initial plane of the ring, the linear theory predicts tilting of the ring in the direction of the shear flow rotation.Numerical calculations are performed with both single vortex filaments and with a three-dimensional discrete vortex element method. The numerical calculations confirm the predictions of the linear theory for values of strain and shear rates below a certain critical value (which depends on the ratio R/σ0 of initial ring to core radii), whereas for strain and shear rates above this value the ring becomes very elongated with time and eventually pinches off. Three distinct regimes of long-time behaviour of the ring have been identified. Regime selection depends on initial ring geometry and orientation and on values of strain and shear rates. These regimes include (i) periodic oscillations with no pinching off, (ii) pinching off at the ring centre, and (iii) development of an elongated vortex pair at the ring centre and wider ‘heads’ near the ends (with pinching off just behind the heads). The boundaries of these regimes and theoretical reasons for the vortex behaviour in each case are described. It is also shown that the breakup of stretched vortex rings exhibits a self-similar behaviour, in which the number and size of ‘offspring’ vortices, at the point of pinching-off the ring, may be scaled by the product of the strain rate e (or shear rate s) and the oscillation period τ of a slightly elliptical ring with mean radius R.

scholarly journals Structure of the vortex wake in hovering Anna's hummingbirds ( Calypte anna )

2013 ◽  
Vol 280 (1773) ◽  
pp. 20132391 ◽  
Author(s):  
M. Wolf ◽  
V. M. Ortega-Jimenez ◽  
R. Dudley
Keyword(s):  
Flow Visualization ◽  
Vortex Structure ◽  
Force Production ◽  
Vortex Rings ◽  
Vortex Wake ◽  
Secondary Vortex ◽  
Single Vortex ◽  
Discrete Vortex ◽  
Weight Support ◽  
Calypte Anna

Hummingbirds are specialized hoverers for which the vortex wake has been described as a series of single vortex rings shed primarily during the downstroke. Recent findings in bats and birds, as well as in a recent study on Anna's hummingbirds, suggest that each wing may shed a discrete vortex ring, yielding a bilaterally paired wake. Here, we describe the presence of two discrete rings in the wake of hovering Anna's hummingbirds, and also infer force production through a wingbeat with contributions to weight support. Using flow visualization, we found separate vortices at the tip and root of each wing, with 15% stronger circulation at the wingtip than at the root during the downstroke. The upstroke wake is more complex, with near-continuous shedding of vorticity, and circulation of approximately equal magnitude at tip and root. Force estimates suggest that the downstroke contributes 66% of required weight support, whereas the upstroke generates 35%. We also identified a secondary vortex structure yielding 8–26% of weight support. Lift production in Anna's hummingbirds is more evenly distributed between the stroke phases than previously estimated for Rufous hummingbirds, in accordance with the generally symmetric down- and upstrokes that characterize hovering in these birds.

Simulation of particle dispersion in an axisymmetric jet

1988 ◽  
Vol 186 ◽  
pp. 199-222 ◽  
Author(s):  
J. N. Chung ◽  
T. R. Troutt
Keyword(s):  
Mixing Layer ◽  
Jet Flow ◽  
Particle Dispersion ◽  
Vortex Rings ◽  
Local Flow ◽  
Discrete Vortex ◽  
Turbulent Mixing Layer ◽  
Axisymmetric Jet ◽  
Free Jet ◽  
Global And Local

Particle dispersion in an axisymmetric jet is analysed numerically by following particle trajectories in a jet flow simulated by discrete vortex rings. Important global and local flow quantities reported in experimental measurements are successfully simulated by this method.The particle dispersion results demonstrate that the extent of particle dispersion depends strongly on γτ, the ratio of particle aerodynamic response time to the characteristic time of the jet flow. Particles with relatively small γτ values are dispersed at approximately the fluid dispersion rate. Particles with large γτ values are dispersed less than the fluid. Particles at intermediate values of γτ may be dispersed faster than the fluid and actually be flung outside the fluid mixing region of the jet. This result is in agreement with some previous experimental observations. As a consequence of this analysis, it is suggested that there exists a specific range of intermediate γτ at which optimal dispersion of particles in the turbulent mixing layer of a free jet may be achieved.

Application of modern soil models for numerical calculations of tank bases and foundations

2021 ◽  
pp. 257-269
Author(s):  
Георгий Владимирович Мосолов ◽  
Илья Леонидович Димов
Keyword(s):  
Small Strain ◽  
Petroleum Products ◽  
Numerical Calculations ◽  
Oil Storage ◽  
Soil Model ◽  
Modern Soil ◽  
Optimizing Design ◽  
Comparison Of The Results ◽  
Strain Model ◽  
Hardening Soil Model

Уже в ближайшем будущем от использования современных численных методов расчета будет зависеть прогресс в области проектирования оснований и фундаментов зданий и сооружений, поскольку возможности по совершенствованию строительных норм практически исчерпаны. Целью статьи является демонстрация возможностей численных расчетов с использованием современных моделей грунта на примере проектирования фундамента стандартного нефтяного резервуара для хранения нефти и нефтепродуктов. Приведено сравнение результатов расчетов осадки основания резервуара емкостью 30 000 м, выполненных в соответствии с действующими нормами проектирования и методом конечных элементов с применением программного комплекса PLAXIS. В частности, проведены численные расчеты с использованием современных моделей грунта: 1) модели грунта с упрочнением (Hardening Soil model, HS); 2) модели грунта с упрочнением и учетом малых деформаций (Hardening Soil small strain model, HSs). Показано, что использование указанных моделей при наличии требуемого объема исходных данных позволяет существенно уточнить вычисления, выполняемые по нормативным методикам. С учетом полученных результатов определена возможность оптимизации проектных решений при выборе типа фундамента резервуара. In the near future, the progress in design of bases and foundations of buildings and structures will depend on the use of modern numerical calculation methods since the opportunities to improve the building regulations are almost exhausted. This article aims to demonstrate the capabilities of numerical calculations with the use of modern soil models on the example of designing the foundation of a standard oil storage tank for crude oil and petroleum products. This article provides a comparison of the results of the base settlement of a 30,000 m tank calculations made in accordance with the current standards of design and the finite elements method with the use of the PLAXIS software package. In particular, the following numerical calculations with the use of modern soil models have been performed: 1) Hardening Soil model, HS; 2) Hardening Soil small strain model, HSs. It is shown that the use of these models in the presence of the required amount of baseline data can significantly refine the calculations performed according to normative methods. Considering the obtained results, the possibility of optimizing design solutions when selecting the type of foundation of a tank was determined.

Effect of velocity ratio on the interaction between plasma synthetic jets and turbulent cross-flow

2019 ◽  
Vol 865 ◽  
pp. 928-962 ◽  
Author(s):  
Haohua Zong ◽  
Marios Kotsonis
Keyword(s):  
Boundary Layer ◽  
High Speed ◽  
Velocity Ratio ◽  
Vortex Pair ◽  
Synthetic Jets ◽  
Low Energy ◽  
Vortex Rings ◽  
Wall Region ◽  
Mean Velocity ◽  
Counter Rotating Vortex Pair

Plasma synthetic jet actuators (PSJAs) are particularly suited for high-Reynolds-number, high-speed flow control due to their unique capability of generating supersonic pulsed jets at high frequency (${>}5$  kHz). Different from conventional synthetic jets driven by oscillating piezoelectric diaphragms, the exit-velocity variation of plasma synthetic jets (PSJs) within one period is significantly asymmetric, with ingestion being relatively weaker (less than $20~\text{m}~\text{s}^{-1}$) and longer than ejection. In this study, high-speed phase-locked particle image velocimetry is employed to investigate the interaction between PSJAs (round exit orifice, diameter 2 mm) and a turbulent boundary layer at constant Strouhal number (0.02) and increasing mean velocity ratio ($r$, defined as the ratio of the time-mean velocity over the ejection phase to the free-stream velocity). Two distinct operational regimes are identified for all the tested cases, separated by a transition velocity ratio, lying between $r=0.7$ and $r=1.0$. At large velocity and stroke ratios (first regime, representative case $r=1.6$), vortex rings are followed by a trailing jet column and tilt downstream initially. This downstream tilting is transformed into upstream tilting after the pinch-off of the trailing jet column. The moment of this transformation relative to the discharge advances with decreasing velocity ratio. Shear-layer vortices (SVs) and a hanging vortex pair (HVP) are identified in the windward and leeward sides of the jet body, respectively. The HVP is initially erect and evolves into an inclined primary counter-rotating vortex pair ($p$-CVP) which branches from the middle of the front vortex ring and extends to the near-wall region. The two legs of the $p$-CVP are bridged by SVs, and a secondary counter-rotating vortex pair ($s$-CVP) is induced underneath these two legs. At low velocity and stroke ratios (second regime, representative case $r=0.7$), the trailing jet column and $p$-CVP are absent. Vortex rings always tilt upstream, and the pitching angle increases monotonically with time. An $s$-CVP in the near-wall region is induced directly by the two longitudinal edges of the ring. Inspection of spanwise planes ($yz$-plane) reveals that boundary-layer energization is realized by the downwash effect of either vortex rings or $p$-CVP. In addition, in the streamwise symmetry plane, the increasing wall shear stress is attributed to the removal of low-energy flow by ingestion. The downwash effect of the $s$-CVP does not benefit boundary-layer energization, as the flow swept to the wall is of low energy.

DYNAMIC BEHAVIOR AND YIELDING OF FIELD-RESPONSIVE PARTICULATE SUSPENSIONS

2007 ◽  
Vol 21 (28n29) ◽  
pp. 4945-4951 ◽  
Author(s):  
HOWARD SEE ◽  
CLINTON JOUNG ◽  
CHARLES EKWEBELAM
Keyword(s):  
Magnetic Field ◽  
Small Strain ◽  
Large Strains ◽  
Careful Study ◽  
Particulate Suspensions ◽  
Shear Rates ◽  
Inert Particles ◽  
Steady Shear Flow ◽  
Particle Level ◽  
Low Shear

We have examined the small strain response of an inverse ferrofluid system, consisting of micron-sized inert particles dispersed in a ferrofluid, which is a magnetisable liquid consisting of single domain magnetite nanoparticles. Under a magnetic field the inert particles will form elongated aggregates in the field direction, analogous to a magnetorheological fluid. It was found that the fluid appeared to have a Bingham fluid-like yield stress when analysed using the flow curve. However careful study of the behavior at very low shear rates revealed an ever decreasing shear stress. In addition, the behavior of conventional magnetorheological fluids at large strains under steady shear flow and constant magnetic field was also studied, and the results compared to particle-level computer simulations.

scholarly journals About bubbles and vortex rings

2015 ◽  
Vol 780 ◽  
pp. 1-4 ◽  
Author(s):  
C. Martínez-Bazán
Keyword(s):  
Vortex Rings ◽  
Complex Mechanism ◽  
Complex Interplay ◽  
Single Vortex ◽  
Vortical Structures ◽  
Turbulent Eddies ◽  
Deformation Dynamics ◽  
Bubble Interaction ◽  
Elongation Process ◽  
Shed Light

Bubble interaction with turbulence has a number of applications in engineering processes and nature. The complex interplay between the vortical structures present in a turbulent flow and the bubbles drives their deformation dynamics, which may lead to bubble rupture under the appropriate conditions. Such a process includes nonlinear interaction among the turbulent eddies and between the eddies and the bubbles. Thus, the coupled evolution of a single vortex ring with a bubble represents an idealized scenario that can provide a framework to shed light on understanding such a common and complex mechanism. Jha & Govardhan (J. Fluid Mech., vol. 773, 2015, pp. 460–497) have performed elegant experiments generating controlled vortex rings and injecting bubbles of known volume. They have reported interesting results on the elongation process of the bubble and its impact on vortex dynamics.

scholarly journals A method of numerical simulation of flow separation at the inlet of a circular thin-walled pipe

2016 ◽  
pp. 189-196
Author(s):  
К.И. Логачев ◽  
О.А. Аверкова ◽  
А.К. Логачев ◽  
Е.И. Толмачева ◽  
А.С. Горлов
Keyword(s):  
High Speed ◽  
Separated Flow ◽  
Simulation Method ◽  
Quantitative Agreement ◽  
Vortex Rings ◽  
Incident Flow ◽  
Discrete Vortex ◽  
Qualitative And Quantitative ◽  
Thin Walled Pipe ◽  
Thin Walled

Разработан метод математического моделирования, вычислительный алгоритм и программа для расчета отрывного течения на входе в круглый всасывающий патрубок с тонкими стенками при наличии как высокоскоростного, так и низкоскоростного набегающего потока. Для построения дискретной модели используются стационарные дискретные вихревые кольца. Адекватность разработанного метода подтверждается удовлетворительным качественным и количественным согласованием с результатами расчетов других авторов. A mathematical simulation method, a computational algorithm and a software program are developed to calculate a separated flow at the inlet of a circular thin-walled pipe in the case of a high-speed or low-speed incident flow. In order to construct a discrete model, the stationary discrete vortex rings are used. The adequacy of the proposed method is confirmed by the satisfactory qualitative and quantitative agreement with the numerical results obtained by other authors.

Three-dimensional vortex dynamics in oscillatory flow separation

2011 ◽  
Vol 674 ◽  
pp. 408-432 ◽  
Author(s):  
MIGUEL CANALS ◽  
GENO PAWLAK
Keyword(s):  
Time Scale ◽  
Oscillatory Flow ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Outer Region ◽  
Vortex Pair ◽  
Propagation Distance ◽  
Oscillation Period ◽  
Number Range ◽  
Elliptical Instability

The dynamics of coherent columnar vortices and their interactions in an oscillatory flow past an obstacle are examined experimentally. The main focus is on the low Keulegan–Carpenter number range (0.2 < KC < 2), where KC is the ratio between the fluid particle excursion during half an oscillation cycle and the obstacle size, and for moderate Reynolds numbers (700 < Rev < 7500). For this parameter range, a periodic unidirectional vortex pair ejection regime is observed, in which the direction of vortex propagation is set by the initial conditions of the oscillations. These vortex pairs provide a direct mechanism for the transfer of momentum and enstrophy to the outer region of rough oscillating boundary layers. Vortices are observed to be short-lived relative to the oscillation time scale, which limits their propagation distance from the boundary. The instability mechanisms leading to vortex decay are elucidated via flow visualizations and digital particle image velocimetry (DPIV). Dye visualizations reveal complex three-dimensional vortex interactions resulting in rapid vortex destruction. These visualizations suggest that one of the instabilities affecting the spanwise vortices is an elliptical instability of the strained vortex cores. This is supported by DPIV measurements which identify the spatial structure of the perturbations associated with the elliptical instability in the divergence field. We also identify regions in the periphery of the vortex cores which are unstable to the centrifugal instability. Vortex longevity is quantified via a vortex decay time scale, and the results indicate that vortex pair lifetimes are of the order of an oscillation period T.

Analytic solution of liquid-drop impact problems

1981 ◽  
Vol 377 (1770) ◽  
pp. 289-308 ◽  
Keyword(s):  
Linear Theory ◽  
Wave Speed ◽  
Liquid Drop ◽  
Contact Region ◽  
Nonlinear Effects ◽  
Numerical Calculations ◽  
Escape Time ◽  
Good Representation ◽  
Time Step ◽  
Geometrical Acoustics

The pressure in an impacting liquid drop against both a rigid and an elastic target is calculated for the period when the contact region is expanding faster than the wave speed in the liquid. For very low speed impact a geometrical-acoustics model is shown to give a good representation of the solution, until the edge speed approaches the wave speed. A self-similar solution, that takes account of nonlinear effects, is used in the neighbourhood of the contact edge. Comparisons are made with linear theory and numerical calculations. It is shown that linear theory is totally inadequate in predicting the escape of the shock system from the contact edge and that numerical calculations have used too large a time step to calculate the time of escape correctly. The delay in escape time from the previous theoretical predictions of Heymann (1969) is attributed to the elasticity of the target, an effect that is taken into account in the present work.

scholarly journals Influence of asymmetric valve strategy on large-scale and turbulent in-cylinder flows

2017 ◽  
Vol 19 (6) ◽  
pp. 631-642 ◽  
Author(s):  
Daniel Butcher ◽  
Adrian Spencer ◽  
Rui Chen
Keyword(s):  
Large Scale ◽  
Vortex Pair ◽  
Velocity Fields ◽  
Valve Lift ◽  
Intake Valve ◽  
Single Vortex ◽  
Cyclic Variability ◽  
Stochastic Fluctuations ◽  
Particle Imaging ◽  
The Impact

Phase-locked particle imaging velocimetry measurements are carried out in a direct-injected spark-ignition single-cylinder optical research engine equipped with fully variable valve timing to assess the impact of asymmetric intake valve lift strategies on the in-cylinder flow. The engine was operated under a range of asymmetric strategies, with one valve following a full lift profile, while the second intake valve is scaled as a factor of the first, expressed as % maximum valve lift. Proper orthogonal decomposition combined with a proposed methodology allows instantaneous velocity fields to be decomposed into what are nominally demonstrated as coherent and turbulent constituent velocity fields. Analysis of the coherent fields reveals the behaviour of large-scale structures within the flow, subject to cyclic variation. In the case of 40% maximum valve lift, an increase in the flow cyclic variability is observed. This is found to be as a result of a switch between a flow dominated by a counter-rotating vortex pair and a single vortex. The impact of maximum valve lift on the bulk motion is further evident by an increase in the magnitude of swirl ratio from 0.5 to −6.0 (at 75°CA). Analysis of the turbulent constituent shows how the increased valve life asymmetry leads to increased turbulence during the intake stroke by over 250%. Finally, it is shown how the ensemble turbulence statistics may be misleading as stochastic fluctuations were found to be typically 66% of the total turbulent kinetic energy calculated from the ensemble statistic in the tested conditions.

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