Numerical investigations into effects of three-dimensional wake patterns on unsteady aerodynamic characteristics of a circular cylinder at Re=1.3×105

In contrast with a wide range of applications concerning flows around a circular cylinder at upper subcritical Reynolds numbers (Re), there is no systematic understanding about the fundamentals of so-called random flow patterns, and their effects on intermittent modulations in the time history of pressure or force, and the decrease in their spanwise correlations. This paper employed the large-eddy simulation (LES) technique to predict flows past a circular cylinder at Re=1.3×10⁵ and to provide images based on flow visualization that can clarify the physical mechanism responsible for these outcomes. A reasonably sufficient spanwise length was adopted for the numerical model by taking into consideration the effect of aspect ratios (the spanwise length to the diameter). We found that even at such high Res, a three-dimensional pattern of vortical field is present in the wake resulting in total force modulation and weak spanwise correlation, e.g., obvious oblique shedding. The whole development process of the three-dimensional wake is exhibited as a universal. The results revealed that local phase variations in primary vortex shedding are the starting points of three-dimensional wake patterns, which are induced by the “irregular” streamwise vortex. The three-dimensional near wake following local phase variations is associated with a successive evolution composed of certain stages in order. Quantitative analyses based on the time series of sectional lift coefficients show that intermittent increase in primary shedding periods and sectional lift streak divisions are closely related to local phase variations and vortex division in the development process of the three-dimensional pattern. In addition to the phase difference along the span, the three-dimensional pattern also weakens vortex shedding in cross sections perpendicular to the axis of the cylinder, resulting in modulation of the sectional lift coefficient.     

The 3D Transition to Turbulence in Wake Flows by Means of Direct Numerical Simulation

The three-dimensional transition to turbulence in flows around bodies of non-rectangular configuration has been analysed physically by performing direct numerical simulation to solve the system of Navier-Stokes equations. The successive stages of 3D transition, beyond the first bifurcation, have been detected first in the incompressible regime, for a circular cylinder configuration. The generation of streamwise vorticity, organised according to spanwise periodic cells has been associated with the development of large-scale coherent spanwise undulations of the originally rectilinear (nominally 2D) alternating vortex rows. The wavelengths of these undulations have been determined as a function of Reynolds number. As this parameter increases, a further inherent change of the flow transition is obtained and analysed, the natural vortex dislocations pattern. Beyond this change, the increase of Reynolds number yields an abrupt shortening of the spanwise wavelength and the flow undergoes another transition step, whose critical Reynolds number is evaluated by the present DNS approach in association with the Ginzburg-Landau model. Therefore, the linear and non-linear parts of the flow transition have been quantified by means of the amplitude evolution versus time obtained by the present DNS, in conjunction with the mentioned global oscillator model. This revised version was published online in July 2006 with corrections to the Cover Date.     

Three-dimensional evolution of vortices and early features of coherent structure in the turbulent wake behind a 2-D circular cylinder

3-D evolution of Kármán vortex filaments and vortex filaments in braid regions in the turbulent wake of a 2-D circular cylinder is investigated numerically based on inviscid vortex dynamics by analyzing the response of the initially 2-D spanwise vortex filaments to periodic spanwise disturbance of varying magnitude, wavelength and initial phase angles. Our results reveal a kind of 3-D vortex system in the wake which consists of large scale horseshoe-shaped vortices and small scale γ-shaped vortex filaments as well as vortex loops. The mechanism and the dynamic process about the generation of streamwise vortical structure and the 3-D coherent structure are reported. currently published in the Chinese Edition of Acta Mechanica Sinica, Vol.25, No.3, 1993 The project supported by National Natural Science Foundation of China and the National Basic Research Project “Nonlinear Science”     

Dynamics of vortical structures in cylinder/wall interaction with moderate gap ratio

The interaction between the wake of a transverse circular cylinder and the underlying flat-plate boundary layer with a moderate gap ratio G/D=1.0 is investigated using both hydrogen-bubble-based and PIV-based visualization techniques. The spanwise rollers in the cylinder wake are found to be capable of inducing secondary vortices in the near-wall region. The mutual induction from the counter-clockwise rollers, which are closer to the wall, plays a primary role, so that these secondary vortices present linear lift-up motion at first. Their subsequent evolution dominantly determines the characteristics of the wake/boundary-layer interaction. Two different vortex interaction scenarios are observed: the secondary vortices can be either entrained into the rollers or pushed down towards the wall. This leads to a rapid three-dimensional destabilization process, through which streamwise vortices are generated. And it is suggested that these streamwise vortices are the dominant structures to promote the following boundary layer transition.     

Tomographic-PIV measurement of the flow around a zigzag boundary layer trip

Tomographic-PIV was used to measure the boundary layer transition forced by a zigzag trip. The resulting instantaneous three-dimensional velocity distributions are used to quantitatively visualize the flow structures. They reveal undulating spanwise vortices directly behind the trip, which break up into individual arches and then develop into the hairpin-like structures typical of wall-bounded turbulence. Compared to the instantaneous flow structure, the structure of the average velocity field is very different showing streamwise vortices. Such streamwise vortices are often associated with the low-speed streaks occurring in bypass transition flows, but in this case clearly are an artifact of the averaging. Rather, the present streaks in the separated flow region directly behind the trip are resulting from the waviness in the spanwise vortices as introduced by the zigzag trip. Furthermore, these streaks and the separated flow region are observed to be related to a large-scale, spanwise uniform unsteadiness in the flow that contributes significantly to the velocity fluctuations over large downstream distances (up to at least the edge of the present measurement domain).     

不定原点喷嘴射流中流体物理的实验研究(英文)

为了能够更好地了解不定源喷嘴(indeterminate origin nozzle)射流中的物理过程,本文应用平面激光诱导荧光技术对一个大尺度的水射流进行了实验研究。流场显示的实验结果表明不定源喷嘴在射流的剪切层引入了蘑菇形反向旋转的涡对。这些涡的矢量方向与射流方向相同或相反,被称为流向涡(streamwise vortex)。由于射流中存在开尔文-亥姆霍兹不稳定,每当一个横向涡(spanwise vortex,即涡的矢量方向与射流方向垂直)从喷嘴脱流时会产生瞬时的低压,该瞬时低压促使向内发展的流向涡对在喷嘴的凹槽处生成。这些涡对在向下游流动的过程中会重组并在喷嘴的尖峰面生成向外发展的涡对。这些流向涡极大地影响了射流的发展。流向涡与横向涡的相互作用促使射流更早地发展成为湍流。由于流向涡同时也在射流中引入了径向的剪切流动,因此导致了更多的湍流生成从而增强了射流与周围流体的混合。     

不定原点喷嘴射流中流体物理的实验研究

为了能够更好地了解不定源喷嘴（indeterminate origin nozzle）射流中的物理过程，本文应用平面激光诱导荧光技术对一个大尺度的水射流进行了实验研究。流场显示的实验结果表明不定源喷嘴在射流的剪切层引入了蘑菇形反向旋转的涡对。这些涡的矢量方向与射流方向相同或相反，被称为流向涡（streamwise vortex）。由于射流中存在开尔文一亥姆霍兹不稳定，每当一个横向涡（spanwisevortex，即涡的矢量方向与射流方向垂直）从喷嘴脱流时会产生瞬时的低压，该瞬时低压促使向内发展的流向涡对在喷嘴的凹槽处生成。这些涡对在向下游流动的过程中会重组并在喷嘴的尖峰面生成向外发展的涡对。这些流向涡极大地影响了射流的发展。流向涡与横向涡的相互作用促使射流更早地发展成为湍流。由于流向涡同时也在射流中引入了径向的剪切流动，因此导致了更多的湍流生成从而增强了射流与周围流体的混合。     

Vortex structure in laminar boundary layers on a concave wall

Naturally occurring Görtler vortices have been investigated, using laser anemometry, in the laminar concave-surface boundary layers of water channels with 90° bends. Distributions of streamwise and spanwise velocities are presented, supported by flow visualization. Amplification was found to cease at Görtler numbers in the region of 9, followed by increasing distortion and spanwise wandering of the vortices. Development of a vortex system from an imposed disturbance has also been predicted by numerical computations.     

圆柱尾迹涡的三维演化及结构特征

应用无粘涡丝运动学理论和局部诱导近似(LIA)方法,以Lagrange观点跟踪涡丝在背景流场中运动,用数值方法研究了中等Re数(≈10~3)下圆柱分离尾迹中Kármán涡和涡辫区涡丝的三维演化的机制和动力学过程,及其结构特征。背景流场考虑为尾迹时间平均速度流场和Kármán涡街流场。初始展向小扰动为指数形式和谐波形式。结果指出:Kármán涡和涡辫区中的涡丝具有展向不稳定性,形成流向涡量。在尾迹的初期输运过程中,表现出有序的大、小尺度涡结构。并进一步分析了其产生的机理。     

Effects of small changes in initial conditions on mixing layer three-dimensionality

Conclusions An experimental study which shows the effects of relatively small changes in the initial conditions on the development of the three-dimensional structure of a plane mixing layer originating from laminar boundary layers has been completed. It was shown that while the exact shapes and positions of the streamwise vortex structures are not the same for the two initial conditions, their overall distribution, reorganization and decay are very similar. The present results imply that while some of the specific details of the streamwise vortex structure may be facility dependent, a relatively strong structure, which produces significant three-dimensionality, should form in all mixing layers originating from laminar boundary layers. After some initial readjustments, the structure will appear in the form of counter-rotating pairs of streamwise vortices which, in the mean, grow with the mixing layer and decay in strength.The present results also serve as a warning that small changes in initial conditions may significantly affect the Reynolds stress distributions in the near-field. The most likely mechanism for this is through the effects of very small changes in initial boundary layer properties on the details (strength and location) of the spanwise vortex roll-up. Despite these relatively large differences in the near-field, both mixing layers attain comparable turbulence structure and growth rates in the far-field. In addition, the behavior of the streamwise vortex structure does not appear to be affected by the differences in the near-field Reynolds stress distributions.     

流向磁场作用下圆柱绕流的直接数值模拟

绕流是托卡马克装置中液态包层内常见的流动形态,对流场与热量分布有着重要的影响.本文通过直接数值模拟(DNS),研究了不同磁场强度下$Re=3900$的圆柱绕流,分析了磁场强度对于湍流尾迹的影响.无磁场情况下,直接数值模拟的结果与前人的实验及模拟结果吻合很好.圆柱下游的尾迹中,随着流向距离的增大, 流向速度剖面逐渐从U型进化呈V型, 并慢慢趋于平缓,这表明尾迹中的流动结构受圆柱影响逐渐减小.圆柱后方两侧的剪切层中,由于Kelvin-Helmholtz不稳定性的影响,可以清晰地看到小尺度剪切层涡的脱落.通过对无磁场的计算结果施加流向磁场,本文计算了哈特曼数($Ha$)分别为20, 40和80的工况,以研究磁场效应对于湍流的影响.结果表明磁场较弱时,流动依然呈三维湍流状态.随着磁场增强, 近圆柱尾流区受磁场抑制明显,回流区被拉长,剪切层失稳位置向下游转移.圆柱后方的涡结构由于受到竖直方向洛伦兹力的挤压作用,随着哈特曼数的增加尾迹区域逐渐变窄.相比于无磁场情况的涡结构,由于磁场的耗散作用,相应的涡结构尺度变小.该研究不仅扩展了现有磁场下湍流运动的参数范围,对于液态包层的设计及安全运行同样具有重要的理论指导意义和工程应用价值.      

DIRECT NUMERICAL SIMULATIONS ON THE TURBULENT FLOW PAST A CONFINED CIRCULAR CYLINDER WITH THE INFLUENCE OF THE STREAMWISE MAGNETIC FIELDS1)

绕流是托卡马克装置中液态包层内常见的流动形态,对流场与热量分布有着重要的影响.本文通过直接数值模拟(DNS),研究了不同磁场强度下$Re=3900$的圆柱绕流,分析了磁场强度对于湍流尾迹的影响.无磁场情况下,直接数值模拟的结果与前人的实验及模拟结果吻合很好.圆柱下游的尾迹中,随着流向距离的增大, 流向速度剖面逐渐从U型进化呈V型, 并慢慢趋于平缓,这表明尾迹中的流动结构受圆柱影响逐渐减小.圆柱后方两侧的剪切层中,由于Kelvin-Helmholtz不稳定性的影响,可以清晰地看到小尺度剪切层涡的脱落.通过对无磁场的计算结果施加流向磁场,本文计算了哈特曼数($Ha$)分别为20, 40和80的工况,以研究磁场效应对于湍流的影响.结果表明磁场较弱时,流动依然呈三维湍流状态.随着磁场增强, 近圆柱尾流区受磁场抑制明显,回流区被拉长,剪切层失稳位置向下游转移.圆柱后方的涡结构由于受到竖直方向洛伦兹力的挤压作用,随着哈特曼数的增加尾迹区域逐渐变窄.相比于无磁场情况的涡结构,由于磁场的耗散作用,相应的涡结构尺度变小.该研究不仅扩展了现有磁场下湍流运动的参数范围,对于液态包层的设计及安全运行同样具有重要的理论指导意义和工程应用价值.     

Modification of near-wall turbulence structure in a shear-driven three-dimensional turbulent boundary layer

 Most high Reynolds number flows of engineering interest are three-dimensional in nature. Key features of three-dimensional turbulent boundary layers (3DTBLs) include: non-colateral shear stress and strain rate vectors, and decreasing ratio of the shear stresses to the turbulent kinetic energy with increasing three-dimensionality. These are indicators that the skewing has a significant effect on the structure of turbulence. In order to further investigate the flow physics and turbulence structure of these complex flows, an innovative method for generating a planar shear-driven 3DTBL was developed. A specialized facility incorporating a relatively simple geometry and allowing for varying strengths of crossflow was constructed to facilitate studies where the skewing is decoupled from the confounding effects of streamwise pressure gradient and curvature. On-line planar particle image velocimetry (PIV) measurements and flow visualization results indicate that the experimental configuration generates the desired complex flow, which exhibits typical characteristics associated with 3DTBLs. Furthermore, spanwise shear results in modification of the near-wall turbulence structure. Analysis of near-wall flow visualization photographs revealed a reduction of mean streak length with increasing spanwise shear, while streak spacing remained relatively constant. In the most strongly sheared case, where the belt velocity is twice that of the freestream velocity, the mean streak length was reduced by approximately 50%. Received: 28 October 1997/Accepted: 4 February 1998     

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 simulation on evolution of subharmonic low-speed streaks in minimal channel turbulent flow

The evolution of low-speed streaks in the turbulent boundary layer of the minimum channel flow unit at a low Reynolds number is simulated by the direct numer- ical simulation （DNS） based on the standard Fourier-Chebyshev spectral method. The subharmonic sinuous （SS） mode for two spanwise-aligned low-speed streaks is excited by imposing the initial perturbations. The possibilities and the physical realities of the turbulent sustaining in the minimal channel unit are examined. Based on such a flow field environment, the evolution of the low-speed streaks during a cycle of turbulent sus- taining, including lift-up, oscillation, and breakdown, is investigated. The development of streamwise vortices and the dynamics of vortex structures are examined. The results show that the vortices generated from the same streak are staggered along the streamwise direction, while the vortices induced by different streaks tilt toward the normal direction due to the mutual induction effect. It is the spatial variations of the streamwise vortices that cause the lift-up of the streaks. By resolving the transport dynamics of enstrophy, the strength of the vortices is found to continuously grow in the logarithmic layer through the vortex stretching mechanism during the evolution of streaks. The enhancement of the vortices contributes to the spanwise oscillation and the following breakdown of the low-speed streaks.     

Effect of perforation on flow past a conic cylinder at $${\varvec{Re}}~=~100$$: wavy vortex and sign laws

In order to find the intrinsic physical mechanism of the original Kármán vortex wavily distorted across the span due to the introduction of three-dimensional (3-D) geometric disturbances, a flow past a peak-perforated conic shroud is numerically simulated at a Reynolds number of 100. Based on previous work by Meiburg and Lasheras (1988), the streamwise and vertical interactions with spanwise vortices are introduced and analyzed. Then vortex-shedding patterns in the near wake for different flow regimes are reinspected and illustrated from the view of these two interactions. Generally, in regime I, spanwise vortices are a little distorted due to the weak interaction. Then in regime II, spanwise vortices, even though curved obviously, are still shed synchronously with moderate streamwise and vertical interactions. But in regime III, violently wavy spanwise vortices in some vortex-shedding patterns, typically an \(\Omega \)-type vortex, are mainly attributed to the strong vertical interactions, while other cases, such as multiple vortex-shedding patterns in sub-regime III-D, are resulted from complex streamwise and vertical interactions. A special phenomenon, spacial distribution of streamwise and vertical components of vorticity with specific signs in the near wake, is analyzed based on two models of streamwise and vertical vortices in explaining physical reasons of top and bottom shear layers wavily varied across the span. Then these two models and above two interactions are unified. Finally two sign laws are summarized: the first sign law for streamwise and vertical components of vorticity is positive in the upper shear layer, but negative in the lower shear layer, while the second sign law for three vorticity components is always negative in the wake.     

Dynamics of large-scale eddies in turbulent flows

A model equation based on the equipartition of the turbulent dissipation is proposed for describing the dynamics of large-scale eddies in turbulent flows. The equation is reducible to the equation of motion of an inviscid fluid, so that the motion of the large-scale eddies can be described in terms of inviscid fluid dynamics. It is found that the large-scale eddies are always weakened by the background turbulence and their evolution is slowed down compared with the corresponding inviscid motion. In the case of turbulent mixing layer, its linear growth in downstream direction is accounted for by the exponential growth in time of the perturbation in an inviscid plane vortex sheet.     

Effect of streamwise and spanwise electric fields on transient growth in a two-fluid channel flow

A linear model of a two-fluid channel flow under streamwise/spanwise electric field is built. Both the fluids are assumed to be incompressible, viscous and perfectly dielectric. The effect of the streamwise and spanwise electric fields on transient behavior of small three-dimensional disturbances is studied. The numerical result shows that the streamwise electric field suppresses transient growth of the disturbance with spanwise uniform wave number. The spanwise electric field diminishes transient growth of the disturbance with streamwise uniform wave number. Two peaks of optimal growth are detected in the wave number plane. The peak at relatively large spanwise wave number is dominated by the lift-up mechanism and little influenced by electric field. Differently, the peak at relatively small wave number is associated with the characteristic of the interface and possibly influenced by electric field. The effect of the Weber number, the Reynolds number and the relative electrical permittivity on optimal growth is studied as well. A scaling law is obtained for relatively small Weber numbers and relatively large Reynolds numbers.     

圆柱尾迹影响旁路转捩末期发卡涡涡包的研究

基于TR-PIV技术, 通过侧视和俯视两种情况对圆柱尾迹影响下旁路转 捩末期发卡涡涡包的结构及特征尺寸进行了实验研究. 结合二维空间子波变换和\lambda _{ci}准则, 运用线性随机估计方法对速度信号进行条件平均. 在侧视情况下, 条件平均结 果显示, 在边界层中一系列发卡涡涡头与壁面构成17^{\circ}的倾角, 并且被尾迹涡所占据的低 速区域出现在涡包上方的主流区中. 在俯视的结果中, 沿流向方向拉伸(流向尺度 3\delta, 展向尺度0.55δ)的低速条带结构出现在法向高 度为y/δ =0.2的流向-展向平面中, 并且在该低速条带的两侧对称地出 现了沿流向分布的反向旋转的涡结构. 可以得出: 在圆柱尾迹影响下旁路转捩的末期, 由于 尾迹涡诱导作用的影响, 发卡涡涡包在形态上显示出了更大尺度的特征.