Coaxial interactions of two vortex rings or of a ring with a body

Inviscid coaxial interactions of two vortex rings, including head-on collisions and leapfrogging motions, are considered using a contour dynamics technique. Interactions of vortex rings with solid bodies are also investigated by combining the contour dynamics technique with a boundary integral equation method. Numerical results show that a clean, successful passage motion is possible for two vortex rings with not too thick cores. In both cases of head-on collisions and leapfrogging motions, very large core deformations are observed when two vortex rings get close to each other. A head-tail structure is formed in the later stage of a head-on collision of two fat vortices. Numerical results also show that a vortex ring will stretch and slow down when it moves toward a solid boundary, will shrink and speed up when it moves away from a solid boundary, and will either translate steadily or approach an oscillating asymptotic state when it is far away from any boundaries. The project supported by The National Education Commission of China and NASA under cooperative grant agreement #NCC5-34.     

Dynamics of the flow around colliding spheres

An investigation of the flow resulting from the collision of two spheres at low Reynolds numbers is presented. Each sphere starts from rest and traverses a distance of 5 sphere diameters to the point of contact. Experimental and numerical results are compared for a symmetric collision; that is, a collision between two spheres of the same diameter and travelling with the same velocity. The flow consists of two axisymmetric recirculation zones which become a pair of colliding vortex rings, expanding radially from the collision point. Several examples of unbalanced collisions are also presented numerically, with one or both of the velocity and diameter of the spheres altered. These collisions break the symmetry, altering the post-collision expansion of the vortex rings.     

涡激诱导并列双圆柱碰撞数值模拟研究

圆柱类结构物的涡激振动是工程中较为常见的一种现象,如果圆柱结构物之间的距离较小, 就会产生涡激诱导碰撞现象,而涡激碰撞会比涡激振动对结构物疲劳破坏产生更严重的威胁.采用浸入边界法模拟流体中的动边界问题,避免了传统贴体网格方法在求解流体中存在固体间碰撞问题时出现数值求解不稳定问题,采用有限元方法对圆柱的运动和碰撞进行求解,通过数据回归方法建立了流体流动条件下的润滑模型,对不同间隙比下涡激诱导并列双圆柱振动及碰撞过程进行了数值模拟, 数值结果表明,如果两圆柱产生了碰撞将会有连续的碰撞发生, 碰撞时出现了多阶频率,振动主频率要比无碰撞时大, 两圆柱碰撞时的相对速度比自由来流速度小;当两圆柱相互接近时, 随着涡环分离角度的逐渐倾斜, 横向流体力先逐渐减小,当两圆柱间涡环开始相互影响发生挤压时, 横向流体力开始逐渐增大;当两圆柱开始反弹时, 两圆柱间形成了低压区, 改变了横向流体阻力的方向,使两圆柱又产生了接近运动,如此反复从而产生了碰撞后横向流体力和圆柱速度的振荡现象.      

Problem of the motion of annular vortices in an ideal fluid

The study discusses problems in the numerical modeling of axisymmetric flows of an incompressible fluid induced by a continuous vortex region or vortex sheet by means of a discrete system of vortex rings.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 68–75, May–June, 1987.     

The nonlinear interaction of vortex rings with a free surface

Nonlinear interactions of vortex rings with a free surface are considered in an incompressible, ideal fluid using the vortex contour dynamics technique and the boundary integral equation method. The flow is axisymmetric and the vorticity is linearly distributed in the vortex. Effects of the gravity and the surface tension as well as the initial geometric parameter of the vortex on the interaction process are investigated in considerable detail. The interaction process may be divided into three major stages: the vortex free-traveling stage, the collision stage, and the vortex stretching and rebounding stage. Time evolutions of both the vortex and free surface under various conditions are provided and analyzed. Two kinds of waves exist on the free surface during interaction. In a special case where the gravity and surface tension are very weak or the vortex is very strong, an electric-bulb-like ‘cavity’ is formed on the free surface and the vortex is trapped in the ‘cavity’ for quite a long time, resulting in a large amount of fluid above the mean fluid surface. The project supported by the National Education Commission of China and NASA under cooperative grant agreement # NCC5-34     

Vortex sound

Vortex motion is the only source of aerodynamic sound production in low Mach number flow: the unsteady part of the vorticity distribution contributes linearly to the sound field. The following fundamental model flows, which illustrate the vorticity as the predominant sound source in unsteady flows, are discussed: An initially planar elliptic vortex; two identical coaxial initially elliptic vortex rings, where a special case is the leap-frogging of two identical circular rings. For head-on collision of two identical circular vortex rings and for several cases of vortex-body interaction good agreement between theory and experiment exists. If the Mach number is not low, other mechanisms have also to be considered. Here the theory is not yet fully developed. Experimental results for a vortex-airfoil interaction in transonic flow show that local flow separation and boundary layer as well as compressibility effects play a basic role. However, if the motion of vorticity would be known in subsonic flow, essential parts of the sound field could be calculated by the theory. — In addition, it is shown that the general theory is well suited to provide a better understanding of the scattering of sound waves by vortex motion, at least for long wave lengths.     

A note on the cause of rebound in the head-on collision of a vortex ring with a wall

It is well documented that a trailing vortex pair approaching the ground, and a vortex ring colliding head-on with a rigid plane, experience a reversal in axial velocity which is commonly referred to as rebound. One explanation of this phenomenon suggests that it is essentially an inviscid process due to the effect of the finite core-size, whereas another and more widely accepted explanation attributes it to the influence of a secondary vortex which is generated at the surface by viscous effects. The aim of this paper is to assess experimentally the validity of these competing explanations. To achieve this, flow visualization studies of the collision of a vortex ring with a wall are compared with those of the head-on collision of two identical rings. The head-on collision is designed to mimic the inviscid, free-slip case of a ring/wall interaction. This paper describes the experimental findings.A version of this paper was presented at the 10th Australasian Fluid Mechanics Conference, University of Melbourne, Australia, 11–15 December 1989     

Formation and evolution of vortex rings induced by interactions between shock waves and a low-density bubble

The deformation and instability of a low-density spherical bubble induced by an incident and its reflected shock waves are studied by using the large eddy simulation method. The computational model is firstly validated by experimental results from the literature and is further used to examine the effect of incident shock wave strength on the formations and three-dimensional evolutions of the vortex rings. For the weak shock wave case (Ma?=?1.24), the baroclinic effect induced by the reflected shock wave is the key mechanism for the formation of new vortex rings. The vortex rings not only move due to the self-induced effect and the flow field velocity, but also generate azimuthal instability due to the pressure disturbance. For the strong shock wave case (Ma?=?2.2), a boundary layer is formed adjacent to the end wall owing to the approach of vortex ring, and unsteady separation of the boundary layer near the wall results in the ejection and formation of new vortex rings. These vortex rings interact in the vicinity of the end wall and finally collapse to a complicated vortex structure via azimuthal instability. For both shock wave strength cases, the evolutions of vortex rings due to the instability lead to the formation of the complicated structure dominated by the small-scale streamwise vortices.     

Numerical computation of a three-dimensional vortex sheet in a swirl flow

We consider an incompressible and inviscid fluid flow, called “swirl flow” that rotates around a certain axis in three-dimensional space. We investigate numerically the dynamics of a three-dimensional vortex sheet which is defined as a surface across which the velocity field of the swirl flow changes discontinuously. The vortex method and a fast summation method are implemented on a parallel computer. These numerical methods make it possible to compute the evolution of the vortex sheet for a long time and to describe the complex dynamics of the sheet.     

Numerical study of interaction of two vortex rings

Three-dimensional interaction of vortices with finite core is investigated numerically using the Rosenhead-Moore approximation. As the computational scheme in this approximation cannot deal with the structure of the vortex core, a bundle of vortex elements is employed to represent a single physical vortex tube. After the validity of this method was confirmed by comparing the numerical result for a single vortex ring composed of various number of the elements with the analytical solution, two cases of interaction of two vortex rings were studied. The first case is two vortex rings traveling along a common axis, and the second is two vortex rings moving side by side along parallel axes. Comparison with the experiments showed good agreement.     

Simple and efficient numerical methods for vortex sheet motion with surface tension

We present two simple and efficient explicit methods for the vortex sheet with surface tension. The first one is the standard point vortex method, which has been known to be unstable in the presence of surface tension, due to spurious growth of waves of high modes. We show, for the first time, that the standard point vortex method is able to calculate the vortex sheet motion with surface tension by employing a Fourier filtering. The second method is a modification of the Pullin method using central differences for numerical differentiations. This method is more convenient to implement than other spectral methods and is free from the aliasing instability. We give a linear stability analysis for the numerical methods and show results for the long‐time evolution of the vortex sheet. We also propose a new redistribution procedure to control point clustering, by setting limits of minimum and maximum distances between neighboring points. This procedure is found to be very efficient for long‐time computations of the explicit methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Natural and forced evolution of a counter rotating vortex pair

Naturally occurring instabilities such as the long wave Crow instability are one of the mechanisms that can bring about the break-up of aircraft wake vortex pairs. Encouraging the early onset of such instabilities by active or passive means offers the possibility of accelerating wake break-up and dissipation with favourable consequences in terms of safe aircraft separation and airport capacity. This paper describes an experimental investigation of the evolution of the Crow instability in a counter rotating vortex pair perturbed by a pulsed air sheet. Flow measurements were made using two-dimensional particle image velocimetry and two methods devised to detect wake break-up from the two-dimensional data. Pulsed excitation at a wavelength within the range amplified by the Crow instability resulted in wake break-up and the formation of vortex rings at a downstream distance reduced by up to 37% compared to the baseline case. For excitation at a wavelength outside the excited range early break-up was also observed but the extent of the accelerated break-up was reduced as the amplitude of the excitation was increased.     

PIV MEASUREMENT OF CLOSE IMPINGING JET ON FLAT PLATE 1)

运用时间分辨粒子成像测速系统(time-resolved particle image velocimetry, TR-PIV)对近距离下射流冲击平板时的流场进行了直接测量, 通过对两个正交的平面流场开展测量, 揭示了冲击距离和雷诺数对射流间隙内三维流动特征及涡系结构演化规律的影响. 结果表明: 射流间隙存在三种典型的涡系结构, 分别为双涡环模式、单涡环模式和卷吸模式, 但在大流量湍流状态下, 射流可能会冲破涡环, 形成随机的高速出流, 各流动模式的出现主要与射流流态及壁面约束作用有关. 运用涡量分析对三种典型涡系结构的能量传递和损失特性进行了比较. 结果表明: 近距离冲击时, 射流的能量通过涡环模式向外传递. 在双涡环模式下, 两个涡环的旋向相反, 端面的约束作用使得两个涡环都被严格约束在射流棒端面之内, 且一次涡环强度显著大于二次涡环强度. 最后, 运用本征正交分解方法对射流间隙内的流动模态及其能量分布进行了分析. 单涡和双涡模式前十阶模态分析结果表明: 能量脉动在较低阶时即以配对的模式出现, 这表明一次涡环与二次涡环均具有良好的对称性, 同时在双涡模式中, 一次涡环是占主导作用的大尺度流动结构. 卷吸模式的前三阶模态分析表明: 射流的能量集中在射流上游, 能量随紊动扩散急剧衰减.     

An experimental study of viscous vortex rings

The work focuses on the problem of stability and viscous decay of single vortex rings. A tentative classification scheme is proposed for vortex rings which is based on extensive hot-wire measurements of velocity in the ring core and wake, and flow visualization, viz. laminar, wavy, turbulence-producing, and turbulent. Prediction of vortex ring type is shown to be possible, at least approximately, based on the vortex ring Reynolds number alone. Linear growth rates of ring diameter with time are observed for all types of vortex rings, with different growth rates occurring for laminar and turbulent vortex rings. Data on the viscous decay of vortex rings are used to provide experimental confirmation of the accuracy of Saffman's equation for the velocity of propagation of a vortex ring.The work reported herein is supported through a grant of the Natural Sciences and Engineering Research Council of Canada. Special thanks are due to CAPES (Brazil) for the award of a scholarship to the senior author.     

近距离下射流冲击平板PIV实验研究

运用时间分辨粒子成像测速系统(time-resolved particle image velocimetry, TR-PIV)对近距离下射流冲击平板时的流场进行了直接测量, 通过对两个正交的平面流场开展测量, 揭示了冲击距离和雷诺数对射流间隙内三维流动特征及涡系结构演化规律的影响. 结果表明: 射流间隙存在三种典型的涡系结构, 分别为双涡环模式、单涡环模式和卷吸模式, 但在大流量湍流状态下, 射流可能会冲破涡环, 形成随机的高速出流, 各流动模式的出现主要与射流流态及壁面约束作用有关. 运用涡量分析对三种典型涡系结构的能量传递和损失特性进行了比较. 结果表明: 近距离冲击时, 射流的能量通过涡环模式向外传递. 在双涡环模式下, 两个涡环的旋向相反, 端面的约束作用使得两个涡环都被严格约束在射流棒端面之内, 且一次涡环强度显著大于二次涡环强度. 最后, 运用本征正交分解方法对射流间隙内的流动模态及其能量分布进行了分析. 单涡和双涡模式前十阶模态分析结果表明: 能量脉动在较低阶时即以配对的模式出现, 这表明一次涡环与二次涡环均具有良好的对称性, 同时在双涡模式中, 一次涡环是占主导作用的大尺度流动结构. 卷吸模式的前三阶模态分析表明: 射流的能量集中在射流上游, 能量随紊动扩散急剧衰减.      

Impact of buoyancy on vortex ring development in the near field

The development of a buoyant vortex ring in the near field was examined experimentally, and the findings were compared with those of a non-buoyant ring with a similar Reynolds number. The experiments were performed in a water tank, and the vortices were produced by a cylindrical tube of aspect ratio 2. Laser sheet flow visualization and PIV measurements were carried out. In the near field, the initial column of the buoyant fluid breaks down due to the presence of Rayleigh–Taylor instability at the buoyant fluid interface. Subsequently, a large diameter vortex ring with a large spreading rate, compared with the non-buoyant ring, emerges. The celerity of buoyant vortex continued to decrease throughout the range examined, in contrast to the constant celerity of the non-buoyant ring. The vorticity in the core of buoyant and non-buoyant vortex rings is symmetric and has a Gaussian distribution. However, the buoyant vortex ring evolves into a thin core ring, whereas the non-buoyant ring becomes a thick core ring shortly after the ring formation. This difference is brought on by the rapid entrainment and the significant growth of the buoyant ring following the breakup of the initial formation.     

A multi-vortex model of leading-edge vortex flows

A multi-vortex model of the vortex sheets shed from the sharp leading edges of slender wings is considered. The method, which is developed within the framework of slender-body theory, is designed to deal with those situations in which more than one centre of rotation is formed on the wing, for example on a slender wing with lengthwise camber or with a strake. Numerical results are presented, firstly for situations where comparison can be made with a vortex sheet model and secondly for cases, such as those described above, where a vortex sheet model is unable to describe the flow. Where comparison is available, agreement is good and in the cases where more than one vortex system is present interesting interactions are obtained.     

Numerical simulation of vortex sheet evolution

Recent research on the numerical simulation of vortex sheet evolution is discussed. Applications are presented to a periodic vortex sheet and to the vortex sheet shed behind a finite-span wing.     

Coaxial axisymmetric vortex rings: 150 years after Helmholtz

This article addresses the fascinating 150 years history of the classical Helmholtz paper that laid the foundation of the vortex dynamics. Among general theorems on vortex motion, this memoir contains the special section on circular vortex filaments and axisymmetric vortex rings, in particular. The objective of this article is both to clarify some purely mathematical questions connected with the Dyson model of coaxial vortex rings in inviscid incompressible fluid and to provide a historical overview of achievements in experimental, analytical, and numerical studies of vortex rings interactions. The model is illustrated by several examples both of regular and chaotic motion of several vortex rings in an unbounded fluid.