Numerical evaluation of passive control of VIV by small control rods

Flow past a circular cylinder with multiple small control rods is studied by numerical simulation for Re_D ranging from 1161.3 to 6387.1. The Reynolds-Averaged-Navier–Stokes (RANS) equations and shear stress transport (SST) k − ω turbulence model are used to calculate the vortex field, while a fourth-order Runge–Kutta method is employed for evaluating the structure dynamics of the cylinder group. Comparisons with experimental results demonstrate the validation of this method. This study is concerned with the vortex induced vibration (VIV) suppression efficacy of small control rods placed around a main cylinder. The effects of control rod number, diameter ratio, spacing ratio and Reynolds number on the hydrodynamics and vibration responses of the main cylinder are investigated. The reduced percents of in-line and cross-flow amplitudes and the increased percents of the whole cross-sectional area of cylinders and the drag coefficient are used to give a comprehensive evaluation. Results of simulation indicate that placing small rods with appropriate number at appropriate locations can achieve good suppression effectiveness at a wide range of Reynolds number. The numerical result for the case with nine control rods, diameter ratio of 0.15 and spacing ratio of 0.6 shows the best suppression effect among the cases investigated in this study.     

动波浪壁圆柱绕流三维数值模拟

利用计算流体力学软件Fluent开展了三维动波浪壁圆柱绕流的数值模拟,建立了三维运动波浪壁圆柱模型,通过C语言自编程序实现波浪壁面的运动控制,并保证壁面变形时网格的高质量。在来流速度u=0.125 m/s、雷诺数Re=12 500的情况下,开展了动波浪壁波动速度w=0、0.062 5、0.125、0.187 5 m/s四个工况的计算分析,并比较了不同波动速度对流场结构、升力、阻力特性的影响。结果表明:动波浪壁圆柱能有效抑制流动的分离,消除交替脱落的尾涡,从而消除周期振荡的升力;在消除卡门涡街的同时,圆柱后驻点处的涡量值随波动速度增加而增加,其原因在于波形移动加大了壁面流体的速度,从而减小了圆柱前后的压力差,减小了阻力;随着波动速度的增大,平均阻力系数呈明显下降趋势,当波动速度为来流速度的1.5倍时,平均阻力系数相对于光滑圆柱下降了53.76%。     

Vortex shedding suppression for flow over a circular cylinder near a plane boundary

In this study, the Navier-Stokes equations and the pressure Poisson equation for two-dimensional time-dependent viscous flows are solved with a finite difference method in a curvilinear coordinate system. With this numerical procedure, the vortex shedding flow past a circular cylinder near a wall is investigated. The flow is calculated for a broad range of gap ratios for different Reynolds numbers ranging from 80 to 1000. Based on the numerical solutions, the vortex shedding is observed using various methods, and the mechanism for the vortex shedding suppression at small gap ratios is analyzed. The critical gap ratio at which the vortex shedding is suppressed is identified at different Reynolds numbers.     

Flow past a circular cylinder between parallel walls at low Reynolds numbers

The flow about a circular cylinder placed centrally inside a channel is studied numerically with an unstructured collocated grid finite volume method based on the primitive variable formulation. The distance between the channel walls is allowed to vary to change the blockage ratio. Simulations are carried out over a range of Reynolds numbers that are consistent with the two-dimensional assumption. The study confirms that transition to vortex shedding regime is delayed when the channel walls are close to the cylinder because of the interaction between the vortices from the channel wall and cylinder wake. In the unsteady vortex shedding regime, the wake pattern is opposite to the classic Karman street in respect of the positions of the shed vortices. The cylinder drag coefficient and Strouhal number are considerably increased at smaller gaps while the root-mean-squared lift coefficient is significantly decreased. Several important flow parameters are correlated with the input parameters, namely Reynolds number and blockage ratio.     

Numerical investigation on the suppression of VIV for a circular cylinder by three small control rods

Laminar flow past a circular cylinder with 3 small control rods is investigated by numerical simulation. This study is concerned with the suppression efficacy of vortex induced vibration by small control rods located around a main cylinder. The effects of the attack angle and rod-to-cylinder gap ratio on the hydrodynamics and vibration responses of the main cylinder are investigated. The attack angle of α = 45° is performed as the critical angle for VIV suppression of 3 control rods. The 3 control rods have no effect on VIV suppression when the attack angle is less than the critical angle. The 3 control rods have an excellent VIV suppression efficacy when the attack angle is larger than the critical angle. The transverse vibration frequency of the cylinder with 3 control rods is less than that for an isolated cylinder for all the configurations. The numerical results for the configurations of α = 45° & 60°, G/D = 0.6–1.2 show excellent suppression efficient among the cases investigated in this study. The best suppression efficient is found at α = 45°, G/D = 0.9 for 3 control rods. 2 rods in behind of the main cylinder perform more efficient than that of 1 rod in front for VIV suppression as the gap ratio of G/D less than 1.0.     

不同雷诺数下倾斜圆柱绕流三维数值模拟研究

基于计算流体力学(CFD)开源代码OpenFOAM开展了不同雷诺数(Re=100、1500和3900)和倾斜角度(-60°≤α≤60°)工况下倾斜圆柱绕流流场的三维数值模拟,研究倾斜圆柱绕流的三维瞬时及时均尾流流场、流线拓扑、升阻力系数与旋涡脱落频率随雷诺数及倾斜角度变化的规律,探讨在顺流向及逆流向情况下独立性原则对倾斜圆柱绕流的适用性。研究结果表明:随着圆柱倾角的增大,倾斜圆柱尾流产生较为明显的轴向流,尾流旋涡脱落受到明显抑制,细碎旋涡逐渐消失,尾流宽度随之减小;随着雷诺数的增大,圆柱尾流涡管发生明显的变形,展向掺混使得大量细碎旋涡产生,呈现出明显的三维特性。在不同雷诺数下,阻力系数均值、升力系数均方根及无量纲涡脱频率在一定倾角范围内符合独立性原则。     

Computation of Viscous Uniform and Shear Flow over A Circular Cylinder by A Finite Element Method

The incompressible viscous uniform and shear flow past a circular cylinder is studied. The two-dimensional Navier-Stokes equations are solved by a finite element method. The governing equations are discretized by a weighted residual method in space. The stable three-step scheme is applied to the momentum equations in the time integration. The numerical model is firstly applied to the computation of the lid-driven cavity flow for its validation. The computed results agree well with the measured data and other numerical results. Then, it is used to simulate the viscous uniform and shear flow over a circular cylinder for Reynolds numbers from lO0 to lO00. The transient time interval before the vortex shedding occurs is shortened considerably by introduction of artificial perturbation. The computed Strouhal number, drag and lift coefficients agree well with the experimental data. The computation shows that the finite element model can be successfully applied to the viscous flow problem.     

不同倒角半径柱体绕流数值模拟及水动力特性分析

为研究倒角半径变化对柱体绕流水动力特性的影响,本文使用Fluent软件,采用大涡模拟对雷诺数Re=3 900下的6种不同倒角半径的三维柱体进行了研究。在模型验证基础上,分析了由方柱渐变到圆柱过程中后方流场速度的时均特性及瞬时涡脱落变化规律,给出了不同倒角半径下的升、阻力系数值及无量纲涡脱频率St数。分析结果表明:平均阻力系数随倒角半径的增加而降低,在倒角半径为0.2D时下降速率最大,相较方柱降幅达到50%;升力系数均方根在倒角半径为0.1D~0.2D时变化最显著,减小约93%; St数随倒角半径增加而增大,在倒角半径为0.4D时可达到最大值;回流区长度随倒角半径的增加呈先增大后减小的趋势,其长度在倒角半径为0.2D时达到最大;尾涡宽度在倒角半径为0.0D最大,后随倒角半径增加逐渐下降,且当倒角半径大于0.2D以后变化不大。本文研究结果可为柱体绕流研究及相关工程应用提供参考。     

Prediction of streamwise flow-induced vibration of a circular cylinder in the first instability range

The streamwise flow-induced vibration of a circular cylinder with symmetric vortex shedding in the first instability range is investigated, and a wake oscillator model for the dynamic response prediction is proposed. An approach is applied to calibrate the empirical parameters in the present model; the numerical and experimental results are compared to validate the proposed model. It can be found that the present prediction model is accurate and sufficiently simple to be easily applied in practice.     

不等直径串列双圆柱体绕流的数值模拟

利用Fluent软件模拟雷诺数为200时不同间距比G/D和直径比d/D情况下的圆柱绕流现象。根据模拟结果分析G/D和d/D对圆柱体的涡脱落形态,大、小柱体的升力,阻力系数和St数的影响,结果表明涡脱落形态随着G/D和d/D的变化呈现不同的形式,在G/D小于临界间距比时呈现单一涡脱落形态,在G/D大于临界间距比时,呈现双旋涡脱落形态;临界间距比随着d/D增大而增大。在临界间距比附近大、小柱体的升力和阻力系数值及St数变化较大,大、小柱体的St数具有相同的变化规律,St随着d/D的增大而减小。     

Viscous Effects on Wave Forces on A Submerged Horizontal Circular Cylinder

Numerical simulations are carried out for wave action on a submerged horizontal circular cylinder by means of a viscous fluid model, and it is focused on the examination of the discrepancies between the viscous fluid results and the potential flow solutions. It is found that the lift force resulted from rotational flow on the circular cylinder is always in anti-phase with the inertia force and induces the discrepancies between the results. The influence factors on the magnitude of the lift force, especially the correlation between the stagnation-point position and the wave amplitude, and the effect of the vortex shedding are investigated by further examination on the flow fields around the cylinder. The viscous numerical calculations at different wave frequencies showed that the wave frequency has also significant influence on the wave forces. Under higher frequency and larger amplitude wave action, vortex shedding from the circular cylinder will appear and influence the wave forces on the cylinder substantially.     

Comparison of flow patterns in the near wake of a circular cylinder and a square cylinder placed near a plane wall

The flow patterns in the near wake of a cylinder (either circular or square in shape, D=25 mm) placed in the proximity of a fully developed turbulent boundary layer (thickness δ=0.4D) are investigated experimentally using particle image velocimetry (PIV). The effects of changing the gap height (S) between the cylinder bottom and the wall surface, over the gap ratio range S/D=0.1–1.0, have been investigated. The results show that both the ensemble-averaged and instantaneous flow fields are strongly dependent on S/D. The flow patterns for the two types of cylinders share many similarities with respect to the change in S/D, such as the reduced recirculation length and increased velocity fluctuation in the near wake with increasing S/D, as well as the trend of suppression of vortex shedding at small S/D and onset of vortex shedding at large S/D. However, developments of the shear layers, in terms of wake width, flow curvature, etc., are considerably different for these two types of cylinders. In general, the wake development and momentum exchange for the square cylinder are slower those for the circular cylinder at the same gap ratio. Correspondingly, it is shown that the periodic vortex shedding is delayed and weakened in the case of square cylinder, as compared to that of the circular cylinder at the same S/D.     

Numerical Simulation on Flow Past Two Side-by-Side Inclined Circular Cylinders at Low Reynolds Number

A series of three-dimensional numerical simulations is carried out to investigate the effect of inclined angle on flow behavior behind two side-by-side inclined cylinders at low Reynolds number Re=100 and small spacing ratio T/D=1.5 (T is the center-to-center distance between two side-by-side cylinders, D is the diameter of cylinder). The instantaneous and time-averaged flow fields, force coefficients and Strouhal numbers are analyzed. Special attention is focused on the axial flow characteristics with variation of the inclined angle. The results show that the inclined angle has a significant effect on the gap flow behaviors behind two inclined cylinders. The vortex shedding behind two cylinders is suppressed with the increase of the inclined angle as well as the flip-flop gap flow. Moreover, the mean drag coefficient, root-mean-square lift coefficient and Strouhal numbers decrease monotonously with the increase of the inclined angle, which follows the independent principle at small inclined angles.     

Wave–current interaction with a vertical square cylinder

A three-dimensional numerical model is developed in this study to investigate the problem of wave–current–body interaction. The model solves the spatially averaged Navier–Stokes equations. Turbulence effects are modeled by a subgrid-scale (SGS) model using the concept of large eddy simulation (LES). The model is employed to study the wave–current interaction with a square cylinder that is mounted on the bottom and vertically pierces the free surface. The force analysis demonstrates that the presence of waves can reduce both the strength and frequency of vortex shedding induced by a uniform current due to the nonlinear wave–current interaction. The free surface elevation, strain rates of the mean flow, and eddy viscosity are found to closely correlate with the mechanism of vortex shedding. It is also shown that when the vortex shedding is neglected in the calculation such as by the potential flow approach, one may significantly underestimate the magnitude of in-line force. The energy spectral analysis reveals that there exist initiating, growing, and decaying regions for shedding vortices around the cylinder. In the vortex initiating region, both coherent and turbulent structures are nearly two-dimensional that become three-dimensional in the vortex growing region. The kinetic energy of both coherent and turbulent motions is dissipated in the vortex decaying region, within which the mean flow gradually returns back to two-dimensional.     

基于平行双板结构的圆管尾流抑制方法研究

通过数值模拟方法对基于平行双板的圆管尾流进行抑制研究。以二维不可压缩粘性流体方程为流动控制方程,并采用稳定化流体有限元方法求解。基于数值结果,详细探讨了平行双板的安装角度和板长等关键特征参数对尾流的抑制作用和影响。数值分析发现,平行双板结构对尾流的抑制作用明显优于传统单板控制。计算结果显示,基于平行双分隔板的尾流抑制最优位置为从圆管后驻点起向上游40°~50°处,并且与单板相比,在更短板长条件下,亦可完全抑制圆管的旋涡脱落,从而尾流从非定常涡旋流转入定常流动。当安装位置为θ≥80°时,被控圆管表面压力分布与无控圆管类似,说明此时平行双板控制无减阻效应。最后,基于数值模拟结果,对本方法的尾流高效控制效应,给出了相应的流动机制。     

Effect of peak perforation on flow past a conic cylinder at <Emphasis Type="Italic">Re</Emphasis>=100: drag,lift and Strouhal number

A flow past a circular-section cylinder with a perforated conic shroud, in which the perforation is located at the peak of the conic disturbance as the shroud installed on the cylinder and uniformly distributed with several circular holes, is numerically simulated at a Reynolds number of 100. Two factors in the perforation are taken into account, i.e. the attack angle relative to the direction of incoming flow and diameter of holes. The effect of such perforation on the drag, lift and vortex-shedding frequency is mainly investigated. Results have shown that variation of the attack angle has a little effect, especially on the drag and vortex-shedding frequency, except in certain cases due to the varied vortex-shedding patterns in the near wake. The increasing hole diameter still exhibits a little effect on the drag and frequency of vortex shedding, but really reduces the lift, in particular at larger wavelength, such as the lift reduction reaching almost 66%–68% after introducing the perforation.     

涡流发生器对潮流能水轮机翼型水动力学特性影响的数值模拟

为了改善潮流能水轮机叶片表面流动分离问题,提高其升阻比,本文通过在潮流能水轮机叶片表面加装涡流发生器,来研究涡流发生器对潮流能水轮机水动力学性能的影响。本文以NACA4418翼型为研究对象,分别建立了含VGs和不含VGs的三维模型,利用CFD方法研究了VGs的高度、长度以及相邻一对VGs之间的间距等多个方面对该翼型性能的影响。结果表明:VGs可以有效地提高翼型的最大升力系数;相邻VGs间距的增加对流动分离的抑制有积极影响。此外,通过对尾迹区流线和旋涡的分析,进一步揭示了尾迹区的流场特征。     

Effects of mass and damping ratios on VIV of a circular cylinder

In this study the basic characteristics of the dynamic response and vortex shedding from an elastically mounted circular cylinder in laminar flow is numerically investigated. The Reynolds number ranges from 80 to 160, a regime that is fully laminar. The governing equations of fluid flow are cast in terms of vorticity. The two-dimensional vorticity transport equation is solved using a vortex method. Effects of important parameters on the system response and vortex shedding are investigated; these include: mass ratio, damping ratio, Reynolds number and reduced velocity. The numerical results show that a decrease in either the mass ratio or damping ratio of the system can lead to an increase in both the oscillation amplitude and the reduced velocity range over which lock-in occurs. The results also suggest that the mass-damping parameter may characterize the system response adequately, although the effect of changing mass ratio appears to be a little more profound compared to damping ratio. Vorticity contour plots suggest that the vortex shedding occurs in the 2S mode, although a wake structure similar to the C(2S) mode appears at distances 15–20 diameters downstream in the lock-in region. The simulation results are in good agreement with previously published data.     

Effect of Peak Perforation on Flow Past A Conic Cylinder at Re=100: Drag, Lift and Strouhal Number

A flow past a circular-section cylinder with a perforated conic shroud, in which the perforation is located at the peak of the conic disturbance as the shroud installed on the cylinder and uniformly distributed with several circular holes, is numerically simulated at a Reynolds number of 100. Two factors in the perforation are taken into account, i.e. the attack angle relative to the direction of incoming flow and diameter of holes. The effect of such perforation on the drag, lift and vortex-shedding frequency is mainly investigated. Results have shown that variation of the attack angle has a little effect, especially on the drag and vortex-shedding frequency, except in certain cases due to the varied vortex-shedding patterns in the near wake. The increasing hole diameter still exhibits a little effect on the drag and frequency of vortex shedding, but really reduces the lift, in particular at larger wavelength, such as the lift reduction reaching almost 66%–68% after introducing the perforation.     

Direct numerical simulation of flow over a slotted cylinder at low Reynolds number

Direct numerical simulation was conducted to investigate the flow past a slotted cylinder at low Reynolds number (Re) of 100. The slotting of cylinder affects the boundary layer separation, vortex formation position, recirculation region length and wake width, which are determined by the type of slit. The streamwise slit (SS1), T-shaped slit (SS3) and Y-shaped slit (SS4) act as passive jets, while the transverse slit (SS2) achieves an alternate self-organized boundary layer suction and blowing. The flow rate in slits fluctuates over time due to the alternate vortex shedding and fluctuating pressure distribution around the cylinder surface. One fluctuation cycle of flow rate is caused by a pair of vortices shedding for SS2, SS3 and SS4, while it is created by each vortex shedding for SS1. The wall shear stress and flow impact on the slit wall partly contribute to the hydrodynamic forces acting on the slotted cylinder. Taking into account the internal wall of slit, the transverse slit plays the best role in suppressing the fluid forces with drag reduction of 1.7% and lift reduction of 17%.