The merging of two co-rotating vortices: a numerical study

The merging of two-dimensional co-rotating vortices is analysed through direct numerical simulations at large Reynolds numbers. It is shown how the Reynolds number affects each of the three phases that characterise this phenomenon. In the first phase, we examine the merging onset and focus on its definition. During the second rapid phase, the contributions of various flow regions upon the dynamics of a vortex are quantitatively studied. These regions are respectively the companion vortex, the filaments and an intermediate zone between vortices and filaments. The third phase is interpreted in terms of an advection diffusion process. Finally the final profile and circulation of the merged vortex is determined: the two thirds of the total circulation of the two initial vortices is contained in the newly formed vortex.     

Interaction of an obliquely rising vortex ring with a free surface in a viscous fluid

A vortex ring, which approaches a free surface under various initial conditions and different values of flow parameters, is investigated by means of numerical solutions of the Navier-Stokes equations. The study focuses on the connection process of the vortex ring with the free surface at low Reynolds number. Discrepancies between a numerical solution and experimental observations found recently with regard to the shape of the reconnected vorticity tubes have been resolved. The crucial parameter, which determines the essential differences at the low Reynolds number selected, is the angle of inclination at which the vortex ring rises toward the free surface. At an angle of inclination of 20° circular vorticity tubes at the free surface evolve, while at an angle of 45° the reconnection takes place in the form of an almost circular sheet. At higher Reynolds number this form of reconnection may change to the other form through instability. The possibility of vortex-ring reflection at the free surface is discussed.

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Sommario Usando soluzioni numeriche delle equazioni di Navier-Stokes, viene analizzato il comportamento di un vortice and anello che si avvicina ad una superficie libera, per diverse condizioni iniziali e valori dei parametri del flusso. Lo studio è incentrato sul processo di connessione del vortice adnanello con la superficie libera per bassi numeri di Reynolds. con riguardo alla forma dei tubi di vorticità riconnessi con la superficie, tutte le differenze tra osservazioni sperimentali e simulazioni numeriche sono state risolte. Per bassi numeri di Reynolds, il parametro cruciale dell' interazione è l'angolo di inclinazione tra vortice e superficie. Per un angolo di 20° si formano tubi circolari di vorticità alla superficie, mentre a 45° la riconnessione ha luogo in forma di strato sottile di vorticità. Per altri numeri di Reynolds la forma della riconnessione può cambiare in altre forme a causa dell'instabilità. Infine viene discussa la possibilità di riflessione del vortice ad anello alla superficie.

     

The variation in the maximum loading of a circular cylinder impacted by a 2D vortex with time of impact

Direct numerical simulation is used to study the loading of a rigid, circular cylinder impacted by a 2D vortex. The vortex travels within a stream of fluid characterized by Reynolds number of 150. Vortex impact occurs at twenty-five different times within one vortex shedding cycle. Substantial variation is observed in the maximum values of the drag and lift force coefficients. This variation is due to interaction between the impinging vortex and those attached to the cylinder. As the radius of the impinging vortex is increased from one to three times the cylinder’s diameter, the variation in maximum force coefficients with time of impact decreases. The variation decreases because the larger vortex alters the flow field and vortex shedding cycle prior to impacting the cylinder. For structures impacted by a vortex similar in size, significant under-prediction of the maximum loading may occur if variation in loading with vortex impact time is not considered.     

Formation of vortex breakdown in conical–cylindrical cavities

Numerical simulations in confined rotating flows were performed in this work, in order to verify and characterize the formation of the vortex breakdown phenomenon. Cylindrical and conical–cylindrical geometries, both closed, were used in the simulations. The rotating flow is induced by the bottom wall, which rotates at constant angular velocity. Firstly the numerical results were compared to experimental results available in references, with the purpose to verify the capacity of the computational code to predict the vortex breakdown phenomenon. Further, several simulations varying the parameters which govern the characteristics of the flows analyzed in this work, i.e., the Reynolds number and the aspect ratio, were performed. In these simulations, the limits for the transitional regime and the vortex breakdown formation were verified. Steady and transient cases, with and without turbulence modeling, were simulated. In general, some aspects of the process of vortex breakdown in conical–cylindrical geometries were observed to be different from that in cylinders.     

Modes of vortex formation and transition to three-dimensionality in the wake of a freely vibrating cylinder

The present work is aimed to give some insight into the relation between vortex shedding modes and transition to three-dimensionality in the wake of a freely vibrating cylinder by establishing a numerical model and analyzing the relevant results of two- and three-dimensional simulations. The compressible flow past an elastically-mounted cylinder is solved by using the immersed boundary method (IB method). The cylinder is free to vibrate in the transverse direction with zero structure damping. The response of displacement amplitude is studied with the variation of reduced velocity. Whether P+S mode exists in three-dimensional flow and the occurrence of 2P mode is caused by flow transition from two-dimensional to three-dimensional are problems of concern. Both 2P and P+S wake modes are observed in two- and three-dimensional simulations. The numerical results indicate that the flow transition from two-dimensional to three-dimensional is coupled with the cylinder vibration in the synchronization/lock-in regime. The wake formation given by three-dimensional simulations suggests that the P+S mode might exist in reality when the flow is reverted to two-dimensional by vortex induced vibration (VIV) at Re=300–350. When Reynolds number increases to 425, the wake formation undergoes transition to three-dimensionality and 2P mode is observed. The effect of mass ratio on the flow transition to three-dimensionality is studied. The relationship between wake modes and aerodynamic forces is discussed.     

The vorton method

After a general introduction to the vorton method, which is a vortex method resembling the 2-D point-vortex method, a set of equations describing dynamics of 3-D vortex singularities (vortons) is derived, avoiding the inconsistency in the derivation of other vorton equations which have been applied. Though inviscid, numerical simulations show reconnection phenomena.     

Experimental study of vortex–structure interaction noise radiated from rod–airfoil configurations

Vortex–structure interaction noise radiated from an airfoil embedded in the wake of a rod is investigated experimentally in an anechoic wind tunnel by means of a phased microphone array for acoustic tests and particle image velocimetry (PIV) for the flow field measurements. The rod–airfoil configuration is varied by changing the rod diameter (D), adjusting the cross-stream position (Y) of the rod and the streamwise gap (L) between the rod and the airfoil leading edge. Two noise control concepts, including “air blowing” on the upstream rod and a soft-vane leading edge on the airfoil, are applied to control the vortex–structure interaction noise. The motivation behind this study is to investigate the effects of the three parameters on the characteristics of the radiated noise and then explore the influences of the noise control concepts. Both the vortex–structure interaction noise and the rod vortex shedding tonal noise are analysed. The acoustic test results show that both the position and magnitude of the dominant noise source of the rod–airfoil model are highly dependent on the parameters considered. In the case where the vortex–structure interaction noise is dominant, the application of the air blowing and the soft vane can effectively attenuate the interaction noise. Flow field measurements suggest that the intensity of the vortex–structure interaction and the flow impingement on the airfoil leading edge are suppressed by the control methods, giving a reduction in noise.     

The vorton method

After a general introduction to the vorton method, which is a vortex method resembling the 2-D point-vortex method, a set of equations describing dynamics of 3-D vortex singularities (vortons) is derived, avoiding the inconsistency in the derivation of other vorton equations which have been applied. Though inviscid, numerical simulations show reconnection phenomena.     

Hierarchical instability of a vortex ring array in multipulse laser-matter interactions

In XeCl excimer Laser interactions with Co-coated steel surfaces, we have seemingly realized a quasi-linear array of vortex rings. These form from instabilities on an array of vortex filaments which emerge and then lead to a series of loops. Finally the collapse-and-reconnection process yields a cascade of nearby vortex rings. Since the filament array is subjected to randomly distributed local multipolar strains, unstable waves can develop on the vortex rings. These deformed shapes are frozen permanently by ultrafast cooling, following the last laser pulse. Using a modal analysis, an attempt is made to relate the wave structures to a parametric resonance instability which is caused by dipolar and a quadrupolar fields. Multipulse laser-matter interactions are thus capable of nonselective excitation of vortex ring instabilities of various sizes and various modal structures.     

Reconnections of vortex filaments

The process of break-down and reconnection of vortex filaments is considered by the method of three-dimensional vortex singularities (vortons) in various situations, including oblique interaction of a vortex ring with a boundary in shear flow, shedding of a vortex ring from a horseshoe vortex, instability of elliptic vortex ring, Crow instability of two perturbed antiparallel vortex filaments, merging and subsequent splitting of vortex rings. Special attention is paid to the global integrals (vorticity, momentum, angular momentum) and to the inviscid dissipation of energy. The visualization of the effective vortex core, created by the interference of the vorticity fields of vortons, is presented. The comparisons with other methods of simulation of three-dimensional vortex interactions and with the observations have been made.     

Kinematic properties of monopolar vortices in a strain flow

The advection properties of monopolar vortices subjected to background strain were investigated both experimentally and numerically. Dye-visualization studies in a stratified fluid demonstrated the deformation of the vortex core and the shedding of passive tracers from the edge of the vortex. The main kinematic characteristics of the vortex evolution could be well captured by a simple model, in which the monopole was represented by a (strength-varying) point vortex surrounded by a contour of passive tracers. Full numerical simulations of the vortex evolution showed an excellent agreement with the observed tracer distributions and also revealed that the spatial distribution of vorticity must be taken into account in order to explain the final tearing of the laboratory vortex.     

Control of vortex breakdown in a closed cylinder with a small rotating rod

Effective control of vortex breakdown in a cylinder with a rotating lid was achieved with small rotating rods positioned on the stationary lid. After validation with accurate measurements using a novel stereoscopic particle image velocimetry (SPIV) technique, analysis of numerical simulations using a high-order spectral element method has been undertaken. The effect of a finite length rod creates additional source terms of vorticity as the rod rotates. These additional source terms and their spatial locations influence the occurrence of the vortex breakdown.     

Flow above the free end of a surface-mounted finite-height circular cylinder: A review

The wake of a surface-mounted finite-height circular cylinder and the associated vortex patterns are strongly dependent on the cylinder aspect ratio and the thickness of the boundary layer on the ground plane relative to the dimensions of the cylinder. Above a critical aspect ratio, the mean wake is characterized by streamwise tip vortex structures and Kármán vortex shedding from the sides of the cylinder. Below a critical aspect ratio, a unique mean wake structure is observed. Recent experimental studies in the literature that used phase-averaged techniques, as well as recent numerical simulations, have led to an improved physical understanding of the near-wake vortex flow patterns. However, the flow above the free end of the finite circular cylinder, and its relationship to the near wake, has not been systematically studied. The effects of aspect ratio and boundary layer thickness on the free-end flow field are also not completely understood, nor has the influence of Reynolds number on the free-end flow field been fully explored. Common features associated with the free end include separation from the leading edge, a mean recirculation zone containing a prominent cross-stream arch (or mushroom) vortex, and reattachment onto the free-surface. Other flow features that remain to be clarified include a separation bubble near the leading edge, one or two cross-stream vortices within this separation bubble, the origins of the streamwise tip or trailing vortices, and various critical points in the near-surface flow topology. This paper reviews the current understanding of the flow above the free end of a surface-mounted finite-height circular cylinder, with a focus on models of the flow field, surface oil flow visualization studies, pressure and heat flux distributions on the free-end surface, measurements of the local velocity field, and numerical simulations, found in the literature.     

Self-similar collapse of 2D and 3D vortex filament models

In this article, a very simple toy model for a candidate blow-up solution of the Euler equation by Boratav and Pelz (vortex dodecapole) is investigated. In this model, vortex tubes are replaced with straight vortex filaments of infinitesimal thickness, and the entire motion is monitored by tracing the motion of a representative point on one vortex filament. It is demonstrated that this model permits a self-similar collapse solution which provides the time dependence of the length scale as (t _c ? t)^1/2, (t < t _c), where the collapse time t _c depends on the initial configuration. From the conservation of circulation, this time dependence implies that vorticity ω scales as (t _c ? t) ^?1, which agrees with the one observed in the direct numerical (pseudo spectral) simulations of the vortex dodecapole. Finally, possible modification of the model is considered.     

Vortex dynamics of turbulence–coherent structure interaction

We study the interaction between a coherent structure (CS) and imposed external turbulence by employing direct numerical simulations (DNS) designed for unbounded flows with compact vorticity distribution. Flow evolution comprises (i) the reorganization of turbulence into finer-scale spiral filaments, (ii) the growth of wave-like perturbations within the vortex core, and (iii) the eventual arrest of production, leading to the decay of ambient turbulence. The filaments, preferentially aligned in the azimuthal direction, undergo two types of interactions: parallel filaments pair to form higher-circulation “threads”, and anti-parallel threads form dipoles that self-advect radially outwards. The consequent radial transport of angular momentum manifests as an overshoot of the mean circulation profile—a theoretically known consequence of faster-than-viscous vortex decay. It is found that while the resulting centrifugal instability can enhance turbulence production, vortex decay is arrested by the dampening of the instability due to the “turbulent mixing” caused by instability-generated threads. Ensemble-averaged turbulence statistics show strong fluctuations within the core; these are triggered by the external turbulence, and grow even as the turbulence decays. This surprising growth on a normal-mode-stable vortex results from algebraic amplification through “linear transient growth”. Transient growth is examined by initializing DNS with the “optimal” modes obtained from linear analysis. The simulations show that the growth of transient modes reproduces the prominent dynamics of CS-turbulence interaction: formation of thread-dipoles, growth of core fluctuations, and appearance of bending waves on the column’s core. At the larger Reynolds numbers prevailing in practical flows, transient growth may enable accelerated vortex decay through vortex column breakdown.     

Characteristics of flow and liquid distribution in a gas–liquid vortex separator with multi spiral arms

Fischer–Tropsch (F–T) synthesis is an important route to achieve the clean fuel production. The performance of gas–liquid separation equipment involving in the progressive condensation and separation of light and heavy hydrocarbons in the oil-gas products has become a bottleneck restricting the smooth operation of the F–T process. In order to remove the bottleneck, a gas–liquid vortex separator with simple structure, low pressure drop and big separation capacity was designed to achieve the efficient separation between gas and droplets for a long period. The RSM (Reynolds Stress Model) and DPM (Discrete Phase Method) are employed to simulate the flow characteristics and liquid distribution in the separator. The results show that the separation efficiency is influenced by the flow field and liquid phase concentration in the annular zone. The transverse vortex at the top of spiral arm entrains the droplets with small diameter into the upper annular zone. The entrained droplets rotate upward at an angle of about 37.4°. The screw pitch between neighbor liquid threads is about 0.3 m. There is a top liquid ring in the top of annular zone, where the higher is the liquid phase concentration, the lower is the separation efficiency. It is found that by changing the operating condition and the annular zone height the vortex can be strengthened but not enlarged by the inlet velocity. The screw pitch is not affected by both inlet velocity and annular zone height. The liquid phase concentration in the top liquid ring decreases with both the increases of inlet velocity and annular zone height. The total pressure drop is almost not affected by the annular zone height but is obviously affected by the inlet velocity. When the height of annular zone is more than 940 mm, the separation efficiency is not changed. Therefore, the annular zone height of 940 mm is thought to be the most economical design.     

Adaptive Euler simulations of airfoil–vortex interaction

A grid redistribution method is used together with an improved spatially third‐order accurate Euler solver to improve the accuracy of direct Euler simulations of airfoil–vortex interaction. The presented numerical results of two airfoil–vortex interaction cases indicate that with combination of the two methods, the numerical diffusion of vorticity inherent in the direct Euler simulations is drastically reduced without increasing the number of grid points. With some extra works due to grid redistribution, the predicted vortex structure is well preserved after a long convection and much sharper acoustic wave front resulting from airfoil–vortex interaction is captured. Copyright © 2006 John Wiley & Sons, Ltd.     

On the theory of supersonic inviscid flow separation in gasdynamic problems

A general schematic flow representation that explains the mechanism of inviscid gas separation in time-dependent and three-dimensional gas flows is presented. The scenario of gas flow separation from a body surface or a mixing layer is described as a vortex which induces in the flowfield a velocity opposing to that of the main flow, thus decelerating it. Within the framework of this scenario the analytical conditions of separation are obtained for conical and self-similar gas flows which coincide with the results of experimental and numerical simulations.     

Investigation of passive oscillations of flexible splitter plates attached to a circular cylinder

This paper presents a numerical study to address wake control of a circular cylinder subjected to two-dimensional laminar flow regime using single and multiple flexible splitter plates attached to the cylinder. Three different cases are presented in the study, covering cylinders with one, two and three horizontally attached splitter plates while the locations of the plates around the cylinders are varied. The length of the splitter plates was equal to the cylinder diameter and Reynolds number was 100. Due to the flexibility of the plates, the problem was modeled as a Fluid–Structure Interaction (FSI) problem and the commercial finite element software, Comsol Multiphysics, was utilized to solve this problem using Arbitrary Lagrangian–Eulerian (ALE) method. Vortex shedding frequency and fluid forces acting on the cylinder are investigated, along with a comprehensive parametric study to identify the optimum arrangement of the plates for maximum drag reduction and maximum vortex shedding frequency reduction. The numerical results associated to the flexible splitter plates are also compared with the corresponding rigid splitter plate cases investigated in a previous study. Moreover, the tip amplitude of the plates and the maximum strains were measured in order to find an optimum position for placing a piezoelectric polymer to harvest energy from the flow.