不同剪切率来流作用下柔性圆柱涡激振动数值模拟

采用浸入边界法对细长柔性圆柱在线性剪切流条件下的涡激振动进行三维数值模拟.细长柔性圆柱振动采用三维索模型模拟,其两端铰接,质量比为6,长细比为50,无量纲顶张力为496.来流为线性剪切流,剪切率从0到0.024变化,最大雷诺数为250.研究发现:剪切流作用下柔性立管横流向振动表现为驻波模式,而顺流向振动表现为行波与驻波混合模式.随着剪切率增大,振动频谱呈现多频响应,振动能量逐渐向低频转移.阻力系数平均值随着展向变化,脉动阻力系数和升力系数的均方根值均表现为"双峰"模式.流固能量传递系数沿立管轴向的分布表明,振动激励区集中于高流速区,而振动阻尼区多位于低流速区.剪切率较小时,圆柱的泻涡为平行交叉模式;剪切率较大时,圆柱的泻涡为倾斜泻涡模式,且由于泻涡频率沿立管轴向变化,尾流发生涡裂现象,形成泻涡频率不同的胞格结构.     

不同剪切率来流作用下柔性圆柱涡激振动数值模拟

采用浸入边界法对细长柔性圆柱在线性剪切流条件下的涡激振动进行三维数值模拟。细长柔性圆柱振动采用三维索模型模拟,其两端铰接,质量比为6,长细比为50,无量纲顶张力为496。来流为线性剪切流,剪切率从0到0.024变化,最大雷诺数为250。研究发现:剪切流作用下柔性立管横流向振动表现为驻波模式,而顺流向振动表现为行波-驻波混合模式。随着剪切率增大,振动频谱呈现多频响应,振动能量逐渐向低频转移。阻力系数平均值随着展向变化,脉动阻力系数和升力系数的均方根值均表现为“双峰”模式。流固能量传递系数沿立管轴向的分布表明,振动激励区集中于高流速区,而振动阻尼区多位于低流速区。剪切率较小时,圆柱的泻涡为平行交叉模式;剪切率较大时,圆柱的泻涡为倾斜泻涡模式,且由于泻涡频率沿立管轴向变化,尾流发生涡裂现象,形成泻涡频率不同的胞格结构。      

串列布置三圆柱涡激振动频谱特性研究

对串列三圆柱体双自由度涡激振动问题进行了数值计算, 并分析了雷诺数、固有频率比和约化速度对串列三圆柱体结构动力响应及频谱特性的影响. 研究发现: 雷诺数、频率比对上游圆柱的振幅和流体力系数的影响较小. 中游圆柱频率锁定区域随着雷诺数的增大而增大, 其动力响应受上游圆柱尾流的影响较大, 但频率比的影响较小. 同时, 流体力系数在约化速度较小时受雷诺数和频率比的影响较大. 另外, 下游圆柱的振幅和流体力系数受雷诺数及频率比的影响较大. 雷诺数、频率比和约化速度对圆柱流体力系数能量谱密度(PSD)曲线中主峰幅值、频谱成分及波动性的影响较大. 流体力系数PSD曲线波动性的增强, 导致圆柱运动轨迹会从"8"字形转变成不规则形状. 当频率比为2.0时, 上游圆柱尾流出现P$+$S模式, 导致其发生非对称运动, 且升、阻力系数PSD曲线主峰重合. 最后, 激励荷载平均功率值随约化速度的变化趋势与对应的结构动力响应的变化类似. 在同一约化速度区间内, 结构振动响应的强弱与位移的平均功率值成正比. 对不同约化速度区间内的升力系数功率谱密度分析时, 振动频率比($f_{s}/f_{n, y})$对结构振动响应的影响更大.      

利用O型环抑制圆柱绕法流涡脱落的数值研究

圆柱绕流涡脱落诱发较大的振动和声,如何有效地抑制值得关注.利用大涡模拟技术求解了Navier-Stokes方程,得到了涡脱落频率,升力脉动幅值及平均阻力系数.计算表明二维模拟不能体现流动基本特征,三维计算与实验吻合较好.为了抑制涡脱落,在直径为D的圆柱表面装入间距为1D,直径为0.0167D的O型环.通过升力、速度谱分析以及柱向横截面流场分析可知,在光滑圆柱外表面加入O型环能诱发流体边界层分离,有效地抑制涡脱落现象,升力脉动和观测点速度脉动幅值几乎完全消失,阻力系数也略微降低,适合在实际工程中采用.     

利用O型环抑制圆柱绕流涡脱落的数值研究

圆柱绕流涡脱落诱发较大的振动和声,如何有效地抑制值得关注。利用大涡模拟技术求解了Navier—Stokes方程,得到了涡脱落频率,升力脉动幅值及平均阻力系数。计算表明二维模拟不能体现流动基本特征．三维计算与实验吻合较好。为了抑制涡脱落,在直径为D的圆柱表面装入间距为1D．直径为0．0167D的O型环。通过升力、速度谱分析以及柱向横截面流场分析可知．在光滑圆柱外表面加入O型环能诱发流体边界层分离,有效地抑制涡脱落现象．升力脉动和观测点速度脉动幅值几乎完全消失,阻力系数也略微降低,适合在实际工程中采用。     

错列角度对双圆柱涡激振动影响的数值模拟研究

为研究错列角度α对双圆柱涡激振动问题的影响,采用自主研发的基于CIP(constrained interpolation profile)方法的数值模型,对雷诺数Re=100、错列角度α=0?～90?(间隔15?)的等直径双圆柱涡激振动问题进行数值模拟.模型在笛卡尔网格系统下建立,采用具有三阶精度的CIP方法求解N-S(Navier--Stokes)方程,采用浸入边界法处理流-固耦合问题,避免了任意拉欧方法下的网格畸变和重叠动网格技术中的大量信息交换问题,保证了模型的计算效率.重点分析不同错列角度α上下游圆柱的升阻力系数、位移响应、涡脱频率和尾涡模态等.结果表明:折合速度Ur=2.0～3.0时,上下游圆柱升阻力随错列角度的增大基本呈单调增大的趋势;Ur=5.0～8.0时,随错列角度的增大,上下游圆柱阻力变化较小,升力呈"上凸"趋势,在α=15?～30?取得最大值;Ur=10.0～13.0时,随错列角度的增大,上下游圆柱阻力变化较小,升力呈"下凹"趋势,在α=30?～45?取得最小值,且柱体横流向振幅和升力没有明显的对应关系.最后,结合尾涡模态对以上规律的成因进行分析.研究结果可为相关海洋工程设计提供参考.     

剪切流下发生涡激振动的柔性立管阻力特性研究

利用缩尺模型试验的方法研究了线性剪切流下涡激振动发生时柔性立管的阻力特性.文中基于光纤光栅应变传感器测得的模型应变信息,采用梁复杂弯曲理论计算了立管的平均阻力,继而分析了阻力系数沿管长方向和雷诺数的分布特性以及涡激振动对阻力系数的放大效应,并提出了用于估算柔性立管发生涡激振动时阻力系数的经验公式.结果表明:涡激振动对阻力系数有放大效应,使得立管局部阻力系数高达3.2;平均阻力系数在1.0×104到1.2×105的雷诺数区间内的值为1.3~2.0,并随雷诺数的增大而减小.本文提出的经验公式可准确估算高雷诺数下涡激振动发生时柔性立管的阻力系数,此经验公式考虑了流速、涡激振动主导模态以及主导频率对阻力系数的影响.      

带整流罩隔水管流场特性的大涡模拟研究

为了深入揭示整流罩抑制涡激振动的机理，采用CFD软件FLUENT，结合大涡模拟方法，分别对附加整流罩前后隔水管模型的绕流流场进行模拟，将附加整流罩前后隔水管周围的流场特性、升力系数、阻力系数及其频谱特性等进行对比分析．结果表明，整流罩能有效抑制隔水管尾流区的漩涡脱落，隔水管背部的压力升高，升力系数和阻力系数显著降低，从而抑制了隔水管的涡激振动．     

带有柔性薄板三维方柱流固耦合的数值模拟研究

采用双向流固耦合方法,对带有柔性薄板三维方柱的流场变化特性进行了研究。通过对比单方柱,分析了带有柔性薄板三维方柱阻力系数、升力系数以及斯特劳哈尔数的变化规律。研究表明,在方柱尾流区域附加一柔性薄板可以使其阻力系数降低34.6%,同时其变化幅值大大减小;其升力系数的均方根减小84.8%,流场脉动大幅度减小;斯特劳哈尔数降低79.5%。研究结果表明,在三维方柱后设置柔性薄板可有效抑制涡脱落,从而改善三维方柱的尾流特性。     

两端铰接的细长柔性圆柱体涡激振动响应特性数值研究

目前细长柔性圆柱体涡激振动响应的研究方法主要包括实验方法、计算流体动力学方法以及半经验模型方法. 鉴于实验方法研究成本较高、计算流体动力学方法计算时间较长,本文基于尾流振子模型对线性剪切来流下两端铰接的细长柔性圆柱体涡激振动响应特性进行了半经验模型方法研究. 先建立了柔性圆柱体结构振子以及尾流振子之间的耦合模型,紧接着基于二阶精度中心差分格式对耦合模型先离散后迭代进行求解. 对不同剪切参数下柔性圆柱体涡激振动响应的振动波长、振动频率、振动位移以及响应频率随时间的变化特性等参数进行了分析. 分析结果表明:圆柱体的涡激振动响应由驻波和行波混合组成. 当无量纲弯曲刚度较小时,在圆柱体两端附近,驻波占主导;而在圆柱体中间段附近,行波占主导. 当无量纲弯曲刚度较大时,在圆柱体整个长度区间上均为驻波占主导. 随着剪切参数的增大,振动位移以及振动波长均逐渐减小,而振动频率和频率带宽均逐渐增大.      

Hydrodynamics of a flexible cylinder under modulated vortex-induced vibrations

Both amplitude modulation and frequency modulation of Vortex-induced Vibration (VIV) are observed in a recent model test of a flexible cylinder under oscillatory flow, but its hydrodynamics has not yet been broached in detail. This paper employs the Forgetting Factor Least Squares (FF-LS) method for identification of time-varying hydrodynamics of a flexible cylinder under modulated VIV. The FF-LS method’s applicability to accurately identify time-varying hydrodynamic coefficients is demonstrated through an elastically mounted rigid cylinder under flow with a given modulated motion. Furthermore, we propose a framework to predict instantaneous amplitude (envelope) and frequency using time-varying hydrodynamic coefficients to establish their analytical relationship. This prediction method is further extended to a highly tensioned flexible cylinder through Fourier series expansion in the spatial domain. By performing the identification procedure for all sampled data of a flexible cylinder undergoing oscillatory flow, we obtain the corresponding time-varying hydrodynamics in the cross-flow direction considering the amplitude and frequency modulation. The results show that, under modulated VIV, hydrodynamic coefficients of the flexible cylinder also show time-varying characteristics. We further investigate differences between identified hydrodynamic coefficients and those obtained from the database of a cylinder with modulated motion under flow. Prediction results using these identified time-varying coefficients reveal that the time-varying excitation coefficients mainly influence the amplitude modulation, and the time-varying added-mass coefficients contain the major information of frequency modulation. These results further suggest including the temporal derivative of the instantaneous amplitude as one determining parameter in building databases to improve the prediction of modulated VIV.     

ADDED MASS AND OSCILLATION FREQUENCY FOR A CIRCULAR CYLINDER SUBJECTED TO VORTEX-INDUCED VIBRATIONS AND EXTERNAL DISTURBANCE

This paper reports results from an experiment with a lightly damped elastically mounted rigid cylinder subjected to constant flow velocity. The cylinder was allowed to vibrate in the cross-flow direction and was fixed in the flow direction. The Reynolds numbers varied from 10⁴to 6×10⁴. The added mass for the freely vibrating cylinder agreed well with the results found by others in driven cylinder tests. The predicted natural frequency based on the measured added mass was approximately equal to the measured mean oscillation frequency. The added mass calculated from one oscillation cycle to the next varied considerably. The oscillation frequency from one oscillation to the next corresponded to the natural frequency including the added mass for the same cycle. By movement of the attachment point of the elastic members to the external structure a disturbance could be added to the normal vortex-induced vibrations (VIV) response. When an external disturbance was introduced at a frequency other than the VIV frequency, the added mass coefficient was found to be weakly influenced by the external harmonic disturbance.     

Application of wake oscillators to two-dimensional vortex-induced vibrations of circular cylinders in oscillatory flows

A nonlinear time-domain simulation model for predicting two-dimensional vortex-induced vibration (VIV) of a flexibly mounted circular cylinder in planar and oscillatory flow is presented. This model is based on the utilization of van der Pol wake oscillators, being unconventional since wake oscillators have typically been applied to steady flow VIV predictions. The time-varying relative flow–cylinder velocities and accelerations are accounted for in deriving the coupled hydrodynamic lift, drag and inertia forces leading to the cylinder cross-flow and in-line oscillations. The system fluid–structure interaction equations explicitly contain the time-dependent and hybrid trigonometric terms. Depending on the Keulegan–Carpenter number (KC) incorporating the flow maximum velocity and excitation frequency, the model calibration is performed, entailing a set of empirical coefficients and expressions as a function of KC and mass ratio. Parametric investigations in cases of varying KC, reduced flow velocity, cylinder-to-flow frequency ratio and mass ratio are carried out, capturing some qualitative features of oscillatory flow VIV and exploring the effects of system parameters on response prediction characteristics. The model dependence of hydrodynamic coefficients on the Reynolds number is studied. Discrepancies and limitations versus advantages of the present model with different feasible solution scenarios are illuminated to inform the implementation of wake oscillators as a computationally efficient prediction model for VIV in oscillatory flows.     

DNS-DERIVED FORCE DISTRIBUTION ON FLEXIBLE CYLINDERS SUBJECT TO VORTEX-INDUCED VIBRATION

We use direct numerical simulation (DNS) based on spectral methods to simulate turbulent flow past rigid and flexible cylinders subject to vortex-induced vibrations (VIV). We present comparisons of amplitude, and lift and drag forces, at Reynolds number 1000 for a short and a long cylinder, and we examine differences between a traveling wave response and a standing wave response. The DNS data suggest that the often-used empirical formula proposed by Skop, Griffin & Ramberg in 1977 overpredicts the drag coefficient. We propose an appropriate modification and present preliminary results that indicate that low-dimensional modeling may be an accurate and efficient approach in predicting forces in VIV. Given the lack of any benchmark experiments in VIV currently, the DNS results presented here, both distributions as well as span- and time-averaged quantities, should be helpful to experimentalists and modelers.     

Time domain simulation of vortex-induced vibrations in stationary and oscillating flows

This paper focuses on the further development of a previously published semi-empirical method for time domain simulation of vortex-induced vibrations (VIV). A new hydrodynamic damping formulation is given, and the necessary coefficients are found from experimental data. It is shown that the new model predicts the observed hydrodynamic damping in still water and for cross-flow oscillations in stationary incoming flow with high accuracy. Next, the excitation force model, which is one component of the total hydrodynamic force model, is optimized by simulating the VIV response of an elastic cylinder in a series of experiments with stationary flow. The optimization is performed by repeating the simulations until the best possible agreement with the experiments is found. The optimized model is then applied to simulate the cross-flow VIV of an elastic cylinder in oscillating flow, without introducing any changes to the hydrodynamic force modeling. By comparison with experiment, it is shown that the model predicts the frequency content, mode and amplitude of vibration with a high level of realism, and the amplitude modulations occurring at high Keulegan–Carpenter numbers are well captured. The model is also utilized to investigate the effect of increasing the maximum reduced velocity and the mass ratio of the elastic cylinder in oscillating flow. Simulations show that complex response patterns with multiple modes and frequencies appear when the maximum reduced velocity is increased. If, however, the mass ratio is increased by a factor of 5, a single mode dominates. This illustrates that, in oscillating flows, the mass ratio is important in determining the mode participation at high maximum reduced velocities.     

并列双圆柱流致振动的不对称振动和对称性迟滞研究

对雷诺数Re = 100 间距比s/D = 2.5 和5.0 的并列双圆柱流致振动进行了数值模拟研究, 其中圆柱质量比m = 2.0, 折合流速U_r 在2.0~10.0 之间, 两圆柱仅能做横流向振动. 研究发现, 当间距比s/D = 2.5 时, 在折合流速4.4 < U_r< 4.8区间内, 两圆柱流致振动响应出现不对称振动现象, 在折合流速4.4 < U_r< 4.8 区间内, 两圆柱流致振动响应出现对称性迟滞现象; 而当间距比s/D = 2.5时, 圆柱流致振动响应与单圆柱涡激振动响应相似, 没有出现不对称振动和对称性迟滞现象. 在不对称振动区间内, 两圆柱的升、阻力参数也出现了不相等的情况. 此外, 当两圆柱不对称振动时, 圆柱间隙流稳定地偏斜向其中的一个圆柱; 相应地, 尾涡也出现了宽窄不等的模式. 窄尾流圆柱的振幅和升、阻力均较宽尾流圆柱的大. 通过对比不对称振动现象发生前后的尾涡模式, 对新现象的产生机制进行了阐述.      

Shear flow induced vibrations of long slender cylinders with a wake oscillator model

A time domain model is presented to study the vibrations of long slender cylinders placed in shear flow. Long slender cylinders such as risers and tension legs are widely used in the field of ocean engineering. They are subjected to vortex-induced vibrations(VIV) when placed within a transverse incident flow. A three dimensional model coupled with wake oscillators is formulated to describe the response of the slender cylinder in cross-flow and in-line directions. The wake oscillators are distributed along the cylinder and the vortex-shedding frequency is derived from the local current velocity. A non-linear fiuid force model is accounted for the coupled effect between cross-flow and in-line vibrations. The comparisons with the published experimental data show that the dynamic features of VIV of long slender cylinder placed in shear flow can be obtained by the proposed model,such as the spanwise average displacement,vibration frequency,dominant mode and the combination of standing and traveling waves. The simulation in a uniform flow is also conducted and the result is compared with the case of nonuniform flow. It is concluded that the flow shear characteristic has significantly changed the cylinder vibration behavior.     

Vortex-induced vibrations of two mechanically coupled circular cylinders with asymmetrical stiffness in side-by-side arrangements

Vortex-induced vibrations of two mechanically coupled circular cylinders with asymmetrical stiffness in side-by-side arrangements are numerically investigated in a uniform flow at a low Reynolds number of 100. The oscillation system is restricted to the cross-flow direction, giving rise to a coupled two-degree-of-freedom response. Attention is placed on the two cylinders with a center-to-center gap ratio of 4 and a mass ratio of 10. The flow dynamics are described by the two-dimensional incompressible Navier–Stokes equations and resolved by the Characteristic-Based-Split finite element method. The stiffness of the first spring that connects the lower cylinder to the wall is chosen such that the vortex-induced vibration of the associated single cylinder with the same stiffness undergoes a pre-synchronization (state A), synchronization (state B) and post-synchronization (state C), respectively. In each state, the stiffness of the second spring connecting the lower and upper cylinders is varied to cover both synchronization and de-synchronization regimes. Numerical results show that the mechanically coupled system locks on the first-mode natural frequency in state A, while on the second-mode natural frequency in states B and C. In such a lock-in regime, the amplitude ratios of the two oscillating and coupled cylinders collapse well onto the corresponding first or second free-vibration mode. The overall coupling mechanism is further explained in terms of the hydrodynamic coefficients, frequency characteristics, wake patterns and effective added mass, quantifying the associated fluid-structure interactions against those governing a single-degree-of-freedom, single-cylinder system.     

Water surface wave radiation generated by multiple cylinders oscillating with identical frequency

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