An experimental investigation of dual-resonant and non-resonant responses for vortex-induced vibration of a long slender cylinder

Experimental results of the dual-resonant and non-resonant responses are presented for vortex-induced vibrations(VIV)of a long slender cylinder.The cylinder has a diameter of 10mm and a length of 3.31 m,giving an aspect ratio of 331.The cylinder was towed by a carriage with the velocity up to 1.5 m/s,with the Reynolds number varying from 2500 to 38000.Three different weights were used to provide the initial tension.Dual resonance means that resonance occurs simultaneously in both the cross-flow(CF)and in-line(IL)directions.The experiments were conducted in two stages.At the first stage,dual-resonant dynamic features of the cylinder subjected to vortex-induced excitation were investigated.The features of CF and IL vibration amplitude,motion orbits,phase angle differences,dominant frequencies and mode order numbers are presented.At the second stage of the experiments,particular emphasis was placed on non-resonant dynamic features.The variation of multi-mode modal displacement amplitudes was investigated in detail.     

基于浸入边界-多松弛时间格子玻尔兹曼通量求解法的流固耦合算法研究

针对流固耦合问题,发展了基于浸入边界-多松弛时间格子玻尔兹曼通量求解法(immersed boundary method multi-relaxation-time lattice Boltzmann flux solver,IB-MRT-LBFS)的弱耦合算法.依据多尺度Chapman-Enskog展开,建立不可压宏观方程状态变量和通量与格子玻尔兹曼方程中粒子密度分布函数之间的关系;采用强制浸入边界法处理流固界面使固壁表面满足无滑移边界条件,根据修正的速度求解动量方程力源项;结构运动方程采用四阶龙格-库塔法求解.格子模型与浸入边界法的引入使流固耦合计算可以在笛卡尔网格下进行,无需生成贴体网格及运用动网格技术,简化了计算过程.数值模拟了单圆柱横向涡激振动、单圆柱及串列双圆柱双自由度涡激振动问题.结果表明,IB-MRT-LBFS能够准确预测圆柱涡激振动的锁定区间、振动响应、受力情况以及捕捉尾流场结构形态,验证了该算法在求解流固耦合问题的有效性和可行性.     

基于有限差分法刚性圆柱体涡激振动响应特性数值研究

基于尾流振子模型对刚性圆柱体涡激振动响应特性进行数值研究.建立圆柱体结构振子及尾流振子之间的耦合方程,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.对不同质量比及不同阻尼比圆柱体涡激振动响应的无量纲位移、无量纲升力、频率比及锁定区间等参数进行分析.结果表明数值方法可以很好地模拟刚性圆柱体的涡激振动响应特性.随着质量比的增加,锁定开始点逐渐延后,锁定结束点逐渐提前,锁定区间宽度逐渐变窄.     

DPIV in the wake of a tandem arrangement of two flexible circular cylinders

Abstract  

Visualization of the wake of a system of two circular cylinders in tandem is presented through Digital Particle Image Velocimetry results in a plane perpendicular to the models’ axes. Both cylinder models have an aspect ratio (length over diameter) of almost 100, a mass ratio (mass divided by mass of displaced fluid) under 2, and they are flexible and free to move in the in-line and cross-flow directions. A supporting structure provided attachment of both models through universal joints at each end and the cylinders were exposed to a uniform flow profile over the lower 45% of their lengths, producing vortex-induced vibrations with wake interactions. The centre to centre separation between the models could be varied and data is shown here for three separations of 2, 3 and 4 diameters.     

Coherence and Reynolds stresses in the turbulent wake behind a curved circular cylinder

The turbulent wake behind a curved circular cylinder is investigated based on data obtained from a direct numerical simulation. Here, emphasis is placed in the assessment of two approaches for simplified modelling: reduced-order modelling (ROM) and Reynolds-averaged Navier–Stokes equations. To this end, the instantaneous vortical structures, the proper orthogonal decomposition (POD) of the flow, and relevant Reynolds stress components have been analysed. The results show that despite the complexity of the instantaneous vortical structures, the wake dynamics are governed by the quasi-periodic shedding of primary vortices. Between 24% and 50% of the kinetic energy in the POD is captured by the two most energetic modes, and about 200 modes are needed to capture 90% of the kinetic energy. These findings suggest that, as long as the large-scale structures of the von Kármán vortex shedding are concerned, the present case can be approached by ROM; but a detailed representation of the flow dynamics without an eddy viscosity model that accounts for the unresolved turbulent fluctuations would require a large amount of degrees of freedom. Concerning the Reynolds stresses, their magnitude varies considerably depending on the depth at which they have been sampled. This dependence is related to the strength of the vortex shedding, and the intensity of the secondary flows induced by the curvature of the cylinder. As a consequence of the combination of these two effects, the correlation between streamwise and vertical velocity fluctuations is highest in the wake behind the midspan of the curved cylinder, and the correlation between cross-flow and vertical velocity fluctuations reaches large values in the lower wake.     

Numerical Simulation of Two-Dimensional Flow over Three Cylinders by LatticeBoltzmann Method

The numerical simulation using the multiple relaxation time lattice Boltzmann method (MRT-LBM) is carried out for the purpose of investigating the two-dimensional flow around three circular cylinders. Among these three circular cylinders, one of the three cylinders on which a forced in-line vibrating is used to do this research and attempt to find out the effects of the movingcylinder and the other two rigid cylinders on the wake characteristics and vortex formation. As a benchmark problem to discuss the problem of lift coefficient r.m.s for these cylinders with spacing ratios T/D between other rigid side-by-side cylinders, and the calculation is carried out with two compared cases at Reynolds number of 100, two of the cylinders are rigid and the other one is an in-line vibrated cylinder lying downstream, in addition, forced vibrating amplitude and frequency are A/D= 0.5 and f_ν=0.4 (where A is the forced amplitude, D is the cylinder diameter, and f_ν stands for the vibrating frequency, respectively). The calculated results not onlyindicate that the spacing ratios T/D (T is the center-to-center spacing between the two upstream cylinders) have influence on the wake patterns and the formation of vortex shedding, but also analyze the lift coefficient r.m.s for the three cylinders with the spacing ratios S/D (where S is the center-to-center spacing between the center of upstream two side-by-side cylinders and downstream cylinder).     

Investigation of a hybrid approach combining experimental tests and numerical simulations to study vortex-induced vibration in a circular cylinder

In this study, a hybrid approach based on computational fluid dynamics (CFD) was used to investigate the aerodynamic forces associated with vortex-induced vibration (VIV) in a circular cylinder. The circular cylinder and the flow field were considered as two substructures of a system. Circular cylinder motion was produced in a wind tunnel test of the VIV prior to the numerical simulation; this motion was used as a known cylinder boundary condition and applied to the flow field. The flow field with the known moving boundary condition was then numerically simulated by the ANSYS CFX code. The transient aerodynamic coefficients of the circular cylinder with predetermined motion were obtained from the numerical simulation. To verify the feasibility and accuracy of the proposed hybrid approach and to calculate cylinder vibrations, the transient aerodynamic coefficients were applied to a single degree of freedom (SDOF) model of the circular cylinder. The oscillation responses of the circular cylinder from the calculated (SDOF model) and experimental results were compared, and the results indicate that the hybrid approach accurately simulated the transient aerodynamic coefficients of the circular cylinder. For further comparison, a nonlinear aerodynamic coefficient model based on a nonlinear least square technique was applied to the SDOF model. The nonlinear aerodynamic model can predict well the amplitude and lock-in region of the VIV of the circular cylinder model.     

Wake-body resonance of long flexible structures is dominated by counterclockwise orbits

We identify a dominant mechanism in the interaction between a slender flexible structure undergoing free vibrations in sheared cross-flow and the vortices forming in its wake: energy is transferred from the fluid to the body under a resonance condition, defined as wake-body frequency synchronization close to a natural frequency of the structure; this condition occurs within a well-defined region of the span, which is dominated by counterclockwise, figure-eight orbits. Clockwise orbits are associated with damping fluid forces.     

Non-linear control of torsional and bending vibrations of oilwell drillstrings

Drillstring dynamics is highly non-linear in nature and its model can only be described by a set of non-linear differential equations. In addition to this complexity, the drillstring dynamics are not linearly controllable and thus linear control methods are not suitable for suppressing the coupled torsional and lateral vibrations of a rotating drillstring. In this paper a non-linear dynamic inversion control design method is used to suppress the lateral and the torsional vibrations of a non-linear drillstring. It was found that the designed controller is effective in suppressing the torsional vibrations and reducing the lateral vibrations significantly.     

Control of a coupled map lattice model for vortex shedding in the wake of a cylinder

The flow behind a vibrating flexible cable at low Reynolds numbers can exhibit complex wake structures such as lace-like patterns, vortex dislocations and frequency cells. These structures have been observed in experiments and numerical simulations, and are predicted by a previously developed low-order coupled map lattice (CML). The discrete (in time and space) CML models consist of a series of diffusively coupled circle map oscillators along the cable span. Motivated by a desire to modify the complex wake patterns behind flexible vibrating cables we have studied the addition of control terms into the highly efficient CML models and explored the resulting dynamics. Proportional, adaptive proportional and discontinuous non-linear (DNL) control methods were used to derive the control laws. The first method employed occasional proportional feedback. The adaptive method used spatio-temporal feedback control. The DNL method used a discontinuous feedback linearization procedure, and the controller was designed for the resulting linearized system using eigenvalue assignment. These techniques were applied to a modeled vortex dislocation structure in the wake of a vibrating cable in uniform freestream flow. Parallel shedding patterns were achieved for a range of forcing frequency-forcing amplitude combinations studied to validate the control theory. The adaptive proportional and DNL methods were found to be more effective than the proportional control method due to the incorporation of a spatially varying feedback gain across the cylinder span. The DNL method was found to be the most efficient controller of the low-order CML model. The required control level across the cable span was correlated to the 1/1 lock-on behavior of the temporal circle map.     

Open loop control of vortex-induced vibration of a circular cylinder

In this paper both numerical and experimental investigations have been carried out to suppress the vortex-induced vibration (VIV) of a circular cylinder in an electrically low-conducting fluid. The electromagnetic forces (Lorentz forces) in the azimuthal direction were generated through the mounted electrodes and magnets locally on the surface of the cylinder, which have been proved having an accelerating effect to the fluid on the surface of the cylinder. Results of computations are presented for synchronous vibration phenomenon of a cylinder at Re=200, which are in good agreement with previous computational results. With the Lorentz forces loaded, the VIV of the cylinder has been suppressed successfully. Experimental results have also shown the same tendency and are in reasonable agreement with the numerical results.     

Natural and forced convective heat transfer on slender cylinders

This paper presents an experimental study of free and forced convective heat transfer along vertical slender cylinders. The local heat transfer coefficient is determined from the measurement of the surface temperature distribution performed by quantitative infrared thermography. It is found that the convective heat transfer is strongly dependent on the cylinder curvature and misalignment with the flow. The effect of proximity of two cylinders is emphasized in the case of forced convection. Correlations are proposed for the two types of convection. It is worth noting that circumstances exist where the turbulent heat transfer in free convection can be of the same order of magnitude as for laminar forced convection. The outcome of the study demonstrates the suitability of quantitative infrared thermography to solve complex problems and to provide a deeper understanding of the heat transfer on slender cylinders.     

A self-learning coupled map lattice for vortex shedding in cable and cylinder wakes

A coupled map lattice (CML) with self-learning features is developed to model flow over freely vibrating cables and stationary cylinders at low Reynolds numbers. Coupled map lattices that combine a series of low-dimensional circle maps with a diffusion model have been used previously to predict qualitative features of these flows. However, the simple nature of these CML models implies that there will be unmodeled wake features if a detailed, quantitative comparison is made with laboratory or simulated wake flows. Motivated by a desire to develop an improved CML model, we incorporate self-learning features into a new CML that is first trained to precisely estimate wake patterns from a target numerical simulation. A new convective-diffusive map that includes additional wake dynamics is developed. The new self-learning CML uses an adaptive estimation scheme (multivariable least-squares algorithm). Studies of this approach are conducted using wake patterns from a Navier-Stokes solution (spectral element-based NEKTAR simulation) of freely vibrating cable wakes at Reynolds numbers Re=100. It is shown that the self-learning model accurately and efficiently estimates the simulated wake patterns. The self-learning scheme is then successfully applied to vortex shedding patterns obtained from experiments on stationary cylinders. This constitutes a first step toward the use of the self-learning CML as a wake model in flow control studies of laboratory wake flows.     

The effect of higher harmonic forces on fatigue life of marine risers

Higher harmonic responses measured in flexible riser model tests conducted within the Norwegian Deepwater Programme (NDP) are studied to evaluate the effect of higher harmonics of force on the fatigue life of risers. A large third-harmonic contribution and sometimes a fifth-harmonic are observed for the majority of test cases. Since existing methods of fatigue life estimation account for the effect of hydrodynamic forces only at the frequency of vortex shedding, a new methodology is introduced which takes into account the influence of the higher harmonic components: First, a new response reconstruction technique is used to reconstruct the entire span-wise riser motion in both the cross-flow and in-line directions based on measurements at specific points along the length. Then, a force database obtained from forced in-line and cross-flow motions of rigid cylinders is used to estimate the higher harmonic components of the force along the entire riser length. A significant decrease in fatigue life is obtained when the higher harmonic components of the fluid forces are considered.     

Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics

We continue the study of a model for heat conduction [6] consisting of a chain of non-linear oscillators coupled to two Hamiltonian heat reservoirs at different temperatures. We establish existence of a Liapunov function for the chain dynamics and use it to show exponentially fast convergence of the dynamics to a unique stationary state. Ingredients of the proof are the reduction of the infinite dimensional dynamics to a finite-dimensional stochastic process as well as a bound on the propagation of energy in chains of anharmonic oscillators. Received: 12 March 2001 / Accepted: 5 August 2001     

微尺度串列双圆柱绕流的分子动力学并行模拟

本文采用基于空间分解算法的分子动力学并行模拟方法,研究了微尺度、低雷诺数（Re=40）下串列等大的双圆柱绕流现象。结果表明：随着间距比L＊／D＊的增加,流动存在3种特征状态：当L＊／D＊〈1．1时,同单一物体的绕钝体流动相似;当1．1〈L＊／0＊〈3．5时,涡脱落现象只在下游圆柱出现,在两圆柱之间有交替附着于下游圆柱的...     

A constrained-mode analysis of the fluidelastic instability of a double row of flexible circular cylinders subject to cross-flow: A theoretical investigation of system parameters

A new method of solution is proposed for a previously developed stability analysis of a double row of flexible cylinders subject to a fluid cross-flow. The double row of flexible cylinders may either be by itself or positioned in an array of rigid cylinders, the latter case being more representative of heat exchanger tube arrays. This new method of solution enables a long double row of fluid-dynamically coupled flexible cylinders to be adequately represented, from a stability viewpoint, by a two-cylinder kernel. This is done by prescribing a specific inter-cylinder modal pattern, and this is the reason for calling this the constrained-mode solution. A comparison of the critical flow velocities obtained via (i) this solution and (ii) the more complete long-row solution shows that the agreement between them is excellent. It is also shown that for some combinations of cylinder array geometry and mass-damping parameter the theoretical stability boundary of a single flexible cylinder surrounded by rigid cylinders is sensibly the same as that for a full array of flexible cylinders, the instability mechanism for these cases being virtually entirely due to negative fluid damping. However, for other cases where fluidelastic-stiffness effects are important, the flexibility of adjacent cylinders has a significant effect on the stability. The constrained-mode solution is capable of dealing with both of these instability mechanisms. By using the constrained-mode analysis, theoretical stability boundaries are obtained and compared with experimental data from similar cylinder arrays, plotted in terms of the critical reduced flow velocity versus the mass-damping parameter. Although the shape of the theoretical curve agrees well with the experimental data, theory consistently under estimates the experimental data points, by a factor of approximately 2. It is shown that the discrepancy may be partly due to small frequency differences between cylinders, which will inevitably be present in any cylinder array, raising the critical flow velocity of the experimental data points and bringing them closer to the theoretical values. This effect of frequency detuning is particularly important for high values of the mass parameter and low cylinder mechanical damping; however, it becomes less important for low values of the mass parameter and high values of cylinder mechanical damping.     

Flow characterization using a laser Doppler vibrometer

This paper shows how a scanning laser Doppler vibrometer (LDV), an instrument designed to measure vibrations of structures or objects, can be used in a non-traditional fashion to measure the flow around a cylinder. In particular the von Karmann vortex street which appears in the cylinder wake will be visualized. This is achieved by measuring the changes in the optical path induced by local fluctuation of air refraction index to which the laser vibrometer is sensitive.The measurements obtained with the LDV will be compared visually to measurements done with particle image velocimetry and also with CFD computations for one test case. The specific frequency of the Von Karmann street predicted by the vibrometer, will be compared numerically to the other techniques for two different sized cylinders at three different velocities.     

Mean velocity behaviour in the near wake of long slender cylinder with a sharp trailing edge at a high Reynolds number

A simple eddy viscosity model is applied to the governing equations to establish the behaviour of the mean velocity in the turbulent axisymmetric near wake. The near wake develops from a long slender cylinder which is kept parallel to the flow and is developing under zero streamwise pressure gradient. The upstream turbulent boundary layer on the body of revolution is fully developed. In the inner layer of the flow downstream of the trailing edge, the turbulent inner layer of the upstream boundary layer grows into the initial logarithmic layer, and as a consequence, the centreline velocity in the near wake is shown to increase logarithmically with streamwise distances for large streamwise distances. The analysis further leads to two regions of the near wake flow (the inner near wake and the outer near wake), similar to that of a fully developed turbulent boundary layer, for which the governing equations have been derived. The matching between these two regions leads to a logarithmic variation in the normal direction. Also shown is the variation of the square of the wake width which varies logarithmically with streamwise distance in the near wake. These features are validated by comparison with available experimental data.     

Resonant vibrations of bluff bodies cause multivortex shedding and high frequency forces

A flexibly mounted circular cylinder in cross-flow, with natural frequencies in the inline and transverse directions having a ratio close to 2:1, exhibits drastic changes in the vortex structures in its wake, the frequency content of the fluid forces, and the orbital shape of its resulting motions. Stable multivortex patterns form in the cylinder wake, associated with large high-frequency force components.