低雷诺数下弹性圆柱体涡激振动及影响参数分析

利用Fluent软件数值求解不可压缩粘性流体的N-S方程,研究均匀来流Re=200时弹性圆柱体的涡激振动.圆柱体运动简化为质量-弹簧-阻尼系统,将Newmark-β方法代码写入用户自定义函数(UDF)求解运动方程,柱体与流体间的非线性耦合作用通过动网格技术实现.详细分析了涡激力系数、柱体位移特征值和尾流涡结构随频率比的变化关系,获得"相位开关"、"拍"等现象.考虑流向振动对横向振动影响时,圆柱体最大横向振幅为0.65倍直径.当固定频率比,而质量比或折合阻尼增大时,圆柱体流向与横向振动均呈非线性衰减趋势,但增大质量比对流向平均位移的偏离起到更好的控制效果.     

Single-degree-of-freedom model of displacement in vortex-induced vibrations

In contrast to the approach of coupling a nonlinear oscillator that represents the lift force with the cylinder’s equation of motion to predict the amplitude of vortex-induced vibrations, we propose and show that the displacement can be directly predicted by a nonlinear oscillator without a need for a force model. The advantages of the latter approach include reducing the number of equations and, subsequently, the number of coefficients to be identified to predict displacements associated with vortex-induced vibrations. The implemented single-equation model is based on phenomenological representation of different components of the transverse force as required to initiate the vibrations and to limit their amplitude. Three different representations for specific flow and cylinder parameters yielding synchronization for Reynolds numbers between 104 and 114 are considered. The method of multiple scales is combined with data from direct numerical simulations to identify the parameters of the proposed models. The variations in these parameters with the Reynolds number, reduced velocity or force coefficient over the synchronization regime are determined. The predicted steady-state amplitudes are validated against those obtained from high-fidelity numerical simulations. The capability of the proposed models in assessing the performance of linear feedback control strategy in reducing the vibrations amplitude is validated with performance as determined from numerical simulations.

     

Multi-mode interactions in vortex-induced vibrations of flexible curved/straight structures with geometric nonlinearities

A general low-order fluid–structure interaction model capable of evaluating the multi-mode interactions in vortex-induced vibrations of flexible curved/straight structures is presented. Cross-flow motions due to unsteady lift forces of inclined sagged cables and tensioned beams in uniform currents are investigated. In contrast to a linear equation governing the transverse motion of straight beams or cables typically considered in the literature, coupled horizontal/vertical (axial/transverse) displacements and geometric nonlinearities of curved cable (straight beam) are accounted for. A distributed nonlinear wake oscillator is considered in the approximation of space–time varying hydrodynamics. This semi-empirical fluid force model in general depends on the mass-damping parameter and has further been modified to capture both the effects of varying initial curvatures of the inclined cylinder and the Reynolds number. Numerical simulations are performed in the case of varying flow velocities and parametric results highlight several meaningful aspects of vortex-induced vibrations of long flexible cylinders. These comprise multi-mode lock-in, sharing, switching and interaction features in the space and time domains, the estimated maximum modal and total amplitudes, the resonant nonlinear modes of flexible cylinders and their space–time modifications, and the influence of fluid/structure parameters. A shortcoming of single-mode or linear structural model is underlined. Some quantitative and qualitative comparisons of numerical/experimental results are discussed to demonstrate the validity and required improvement of the proposed modelling and analysis predictions.     

Random uncertainty modeling and vibration analysis of a straight pipe conveying fluid

A new procedure on random uncertainty modeling is presented for vibration analysis of a straight pipe conveying fluid when the pipe is fixed at both ends. Taking real conveying condition into account, several randomly uncertain loads and a motion constraint are imposed on the pipe and its corresponding equations of motion, which are established from the Euler–Bernoulli beam theory and the nonlinear Lagrange strain theory previously. Based on the stochastically nonlinear dynamic theory and the Galerkin method, the equations of motion are reduced to the finite discretized ones with randomly uncertain excitations, from which the vibration characteristics of the pipe are investigated in more detail by some previously developed numerical methods and a specific Poincaré map. It is shown that, the vibration modes change not only with the frequency of the harmonic excitation but also with the strength and spectrum width of the randomly uncertain excitations, quasi-periodic-dominant responses can be observed clearly from the point sets in the Poincaré’s cross-section. Moreover, the nonlinear elastic coefficient and location of the motion constraint can be adjusted properly to reduce the transverse vibration amplitude of the pipe.     

Slow motions of a circular cylinder experiencing slip near a plane wall

A theoretical study is presented for the two-dimensional creeping flow caused by a long circular cylindrical particle translating and rotating in a viscous fluid near a large plane wall parallel to its axis. The fluid is allowed to slip at the surface of the particle. The Stokes equations for the fluid velocity field are solved in the quasi-steady limit using cylindrical bipolar coordinates. Semi-analytical solutions for the drag force and torque acting on the particle by the fluid are obtained for various values of the slip coefficient associated with the particle surface and of the relative separation distance between the particle and the wall. The results indicate that the translation and rotation of the confined cylinder are not coupled with each other. For the motion of a no-slip cylinder near a plane wall, our hydrodynamic drag force and torque results reduce to the closed-form solutions available in the literature. The boundary-corrected drag force and torque acting on the particle decrease with an increase in the slip coefficient for an otherwise specified condition. The plane wall exerts the greatest drag on the particle when its migration occurs normal to it, and the least in the case of motion parallel to it. The enhancement in the hydrodynamic drag force and torque on a translating and rotating particle caused by a nearby plane wall is much more significant for a cylinder than for a sphere.     

Instantaneous Squeeze-Film Force Between a Heat Exchanger Tube and a Support Plate for Arbitrary Tube Motion

The instantaneous squeeze-film force between a heat exchanger tube and a support plate is studied. Based on a two-dimensional rectangular plate model, a short-sleeve squeeze-film model for arbitrary tube motion is developed. The instantaneous squeeze-film force is expressed in normal and tangential directions. The normal squeeze-film force consists of four nonlinear terms, the viscous, unsteady inertia, convective inertia and centripetal inertia terms. Three nonlinear terms, the viscous, unsteady inertia and Coriolis inertia terms, make up the tangential squeeze-film force. An experimental apparatus was developed in order to evaluate the theoretical models against measurements of a finite length squeeze film. A modified model based on the experimental data is obtained where the viscous terms for both directions are multiplied by the instantaneous Reynolds number. All the inertia terms are multiplied by constant coefficients. The modified model is in good agreement with most experimental cases for unsymmetrical linear motion, approximate circular motion and elliptical motion. The form of the modified model is suitable for predicting instantaneous squeeze-film forces in the simulation of heat exchanger tube vibration. Further work using different sized components and fluid properties is required in order to finalize coefficient values.     

A simplified method for time domain simulation of cross-flow vortex-induced vibrations

A new method for time domain simulation of cross-flow vortex-induced vibrations of slender circular cylindrical structures is developed. A model for the synchronization between the lift force and structure motion is derived from already established data for the cross-flow excitation coefficient. The proposed model is tested by numerical simulations, and the results are compared to experimental observations. When a sinusoidal cross-flow motion is given as input to the algorithm, the generated force time series are generally in good agreement with experimental measurements of cross-flow force in phase with cylinder velocity and acceleration. The model is also utilized in combination with time integration of the equation of motion to simulate the cross-flow vibration of a rigid cylinder. The resulting amplitude and frequency of motion as functions of reduced velocity are compared to published experimental results. In combination with the finite element method, the model is used to simulate cross-flow vibrations of a flexible cylinder in shear flow. Comparison with experiments shows that the model is capable of reproducing important quantities such as frequency, mode and amplitude, although some discrepancies are seen. This must be expected due to the complexity of the problem and the simple form of the present method.     

A unified view of energetic efficiency in active drag reduction,thrust generation and self-propulsion through a loss coefficient with some applications

An analysis of the energy budget for the general case of a body translating in a stationary fluid under the action of an external force is used to define a power loss coefficient. This universal definition of power loss coefficient gives a measure of the energy lost in the wake of the translating body and, in general, is applicable to a variety of flow configurations including active drag reduction, self-propulsion and thrust generation. The utility of the power loss coefficient is demonstrated on a model bluff body flow problem concerning a two-dimensional elliptical cylinder in a uniform cross-flow. The upper and lower boundaries of the elliptic cylinder undergo continuous motion due to a prescribed reflectionally symmetric constant tangential surface velocity. It is shown that a decrease in drag resulting from an increase in the strength of tangential surface velocity leads to an initial reduction and eventual rise in the power loss coefficient. A maximum in energetic efficiency is attained for a drag reducing tangential surface velocity which minimizes the power loss coefficient. The effect of the tangential surface velocity on drag reduction and self-propulsion of both bluff and streamlined bodies is explored through a variation in the thickness ratio (ratio of the minor and major axes) of the elliptical cylinders.     

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.      

Acoustic radiation force on a rigid cylinder in an off-axis Gaussian beam near an impedance boundary

The exact equations of the axial and transverse acoustic radiation force functions of a Gaussian beam arbitrarily incident on an infinite rigid cylinder close to an impedance boundary and immersed in an ideal fluid are deduced by expressing the incident wave, the scattering wave and the boundary reflected wave in terms of the cylindrical wave function. The effects of the beam waist, the sound reflection coefficient, the cylinder position and the distance from the impedance boundary on the acoustic radiation force are studied using numerical simulations. The simulation results show that the amplitude of the acoustic radiation force function increases with beam width. Moreover, the values of the acoustic radiation force in both the axial and transverse directions reach those of a plane wave when the beam width is considerably larger than the wavelength of the Gaussian beam. The properties of the impedance boundary and the position of the cylinder in the Gaussian beam have a considerable effect on the magnitude and direction of the force. The simulation results, particularly in the case of a transverse force, indicate the presence of a negative acoustic radiation force that is related to the nondimensional frequency and position of the cylinder in the Gaussian beam.     

DYNAMIC MODELING AND ANALYSIS OF THE LOWER LIMB PROSTHESIS WITH FOUR-BAR LINKAGE PROSTHETIC KNEE$^{\bf 1)}$

相比于单轴式膝关节,四连杆膝关节具有更好的仿生特性和运动安全性,因而在下肢假肢研究中得到广泛关注. 本研究以一款四连杆膝关节被动假肢为研究对象,主要关注足-地交互作用力以及膝关节单边接触力等强非线性因素对下肢假肢步态的影响. 为此,采用 Kelvin-Voigt 模型和库伦模型描述足-地接触力和摩擦力,并采用 Kelvin-Voigt 模型描述膝关节单边接触力,从而基于第一类拉格朗日方程建立假肢动力学模型. 本研究以步态实验测得的髋关节运动数据为模型的驱动信号,针对假肢的步态特征进行了数值分析. 计算结果显示,当膝关节液压阻尼器的刚度较小时,强非线性作用力会使假肢产生显著的亚谐波响应,进而导致步态周期失谐. 进一步研究发现,提胯行为能够避免步态周期失谐,这也为残疾人行走时的提胯等代偿行为提供了一种新的力学解释. 为了评价假肢步态与健康人实测步态的一致性,本研究进一步定义了步态相关系数并分析了膝关节液压阻尼器刚度、阻尼参数对相关系数的影响. 结果表明,通过合理的刚度、阻尼参数设计,两者步态的相关系数可达到 0.9 以上,这为四连杆膝关节被动假肢进一步优化提供了理论支撑.     

Control of cross-flow-induced vibrations of square cylinders using linear and nonlinear delayed feedbacks

We investigate the effectiveness of linear and nonlinear time-delay feedback controls to suppress high amplitude oscillations of an elastically mounted square cylinder undergoing galloping oscillations. A representative model that couples the transverse displacement and the aerodynamic force is used. The quasi-steady approximation is used to model the galloping force. A linear analysis is performed to investigate the effect of linear time-delay controls on the onset speed of galloping and natural frequencies. It is demonstrated that a linear time-delay control can be used to delay the onset speed of galloping. The normal form of the Hopf bifurcation is then derived to characterize the type of the instability (supercritical or subcritical) and to determine the effects of the linear and nonlinear time-delay parameters on their outputs near the bifurcation. The results show that the nonlinear time-delay control can be efficiently implemented to significantly reduce the galloping amplitude and suppress any dangerous behavior by converting any subcritical Hopf bifurcation into a supercritical one.     

Finite Oscillations of a Cylinder in a Coaxial Duct Subjected to Annular Compressible Flow

As a generalization considering small fluid-structural vibrations, the present paper examines the finite magnitude oscillatory motion of an elastically supported rigid cylinder in a cylindrical rigid duct conveying a compressible flow. The fluid is assumed to be inviscid and irrotational and free purely transverse vibrations of the body are dealt with. The governing equations of motion are the fully nonlinear Euler equations together with the continuity equation and a state equation (here for an ideal gas), the ordinary differential equation for the vibrating cylinder, and the kinematical transition and boundary conditions at the moving contact interface between fluid and body and the outside fluid border, respectively. A pertubation analysis is performed to calculate not only the dynamic characteristics for small coupled oscillations but also the corrections due to the inherent nonlinearities of the vibroacoustic problem. To make the calculation steps more transparent, the simpler problem of a two-dimensional channel flow between a rigid wall and an elastically supported rigid plate is also included in the present study. As an outlook, the influence of flexibility of the cylinder (or the plate) is addressed and the problem of forced vibrations is touched. This revised version was published online in July 2006 with corrections to the Cover Date.     

A semi-analytical approach to the study of an elastic circular cylinder confined in a cylindrical fluid domain subjected to small-amplitude transient motions

This paper deals with the transient motions experienced by an elastic circular cylinder in a cylindrical fluid domain initially at rest and subjected to small-amplitude imposed displacements. Three fluid models are considered, namely potential, viscous and acoustic, to cover different fluid–structure interaction regimes. They are derived here from the general compressible Navier–Stokes equations by a formal perturbation method so as to underline their links and ranges of validity a priori. The resulting fluid models are linear owing to the small-amplitude-displacement hypothesis. For simplicity, the elastic flexure beam model is chosen for the circular cylinder dynamics. The semi-analytical approach used here is based on the methods of Laplace transform in time, in vacuo eigenvector expansion with time-dependent coefficients for the transverse beam displacement and separation of variables for the fluid. Moreover, the viscous case is handled with a matched asymptotic expansion performed at first order. The projection of the fluid forces on the in vacuo eigenvectors leads to a fully coupled system involving the modal time-dependent displacement coefficients. These coefficients are then obtained by matrix inversion in the Laplace domain and fast numerical inversion of the Laplace transform. The three models, written in the form of convolution products, are described through the analysis of their kernels, involving both the wave propagation phenomena in the fluid domain and the beam elasticity. Last, the three models are illustrated for a specific imposed motion mimicking shock loading. It is shown that their combination permits coverage of a broad range of motions.     

四连杆膝关节假肢的动力学建模与分析

相比于单轴式膝关节,四连杆膝关节具有更好的仿生特性和运动安全性,因而在下肢假肢研究中得到广泛关注. 本研究以一款四连杆膝关节被动假肢为研究对象,主要关注足-地交互作用力以及膝关节单边接触力等强非线性因素对下肢假肢步态的影响. 为此,采用 Kelvin-Voigt 模型和库伦模型描述足-地接触力和摩擦力,并采用 Kelvin-Voigt 模型描述膝关节单边接触力,从而基于第一类拉格朗日方程建立假肢动力学模型. 本研究以步态实验测得的髋关节运动数据为模型的驱动信号,针对假肢的步态特征进行了数值分析. 计算结果显示,当膝关节液压阻尼器的刚度较小时,强非线性作用力会使假肢产生显著的亚谐波响应,进而导致步态周期失谐. 进一步研究发现,提胯行为能够避免步态周期失谐,这也为残疾人行走时的提胯等代偿行为提供了一种新的力学解释. 为了评价假肢步态与健康人实测步态的一致性,本研究进一步定义了步态相关系数并分析了膝关节液压阻尼器刚度、阻尼参数对相关系数的影响. 结果表明,通过合理的刚度、阻尼参数设计,两者步态的相关系数可达到 0.9 以上,这为四连杆膝关节被动假肢进一步优化提供了理论支撑.      

Acoustic radiation force on an elastic cylinder in a Gaussian beam near an impedance boundary

Acoustic radiation force (ARF) is studied by considering an infinite elastic cylinder near an impedance boundary when the cylinder is illuminated by a Gaussian beam. The surrounding fluid is an ideal fluid. Using the method of images and the translation-addition theorem for the cylindrical Bessel function, the resulting sound field including the incident wave, its reflection from the boundary, the scattered wave from the elastic cylinder, and its image are expressed in terms of the cylindrical wave function. Then, we deduce the exact equations of the axial and transverse ARFs. The solutions depend on the cylinder position, cylinder material, beam waist, reflection coefficient, distance from the impedance boundary, and absorption in the cylinder. To analyze the effects of the various factors intuitively, we simulate the radiation force for non-absorbing elastic cylinders made of stainless steel, gold, and beryllium as well as for an absorbing elastic cylinder made of polyethylene, which is a well-known biomedical polymer. The results show that the impedance boundary, cylinder material, absorption in the cylinder, and cylinder position in the Gaussian beam significantly affect the magnitude and direction of the force. Both stable and unstable equilibrium regions are found. Moreover, a larger beam waist broadens the beam domain, corresponding to non-zero axial and transverse ARFs. More importantly, negative ARFs are produced depending on the choice of the various factors. These results are particularly important for designing acoustic manipulation devices operating with Gaussian beams.     

On the orbital motion of a rotating inner cylinder in annular flow

In this paper, numerical calculations have been performed to analyse the influence of the orbital motion of an inner cylinder on annular flow and the forces exerted by the fluid on the inner cylinder when it is rotating eccentrically. The flow considered is fully developed laminar flow driven by axial pressure gradient. It is shown that the drag of the annular flow decreases initially and then increases with the enhancement of orbital motion, when it has the same direction as the inner cylinder rotation. If the eccentricity and rotation speed of the inner cylinder keep unchanged (with respect to the absolute frame of reference), and the orbital motion is strong enough that the azimuthal component (with respect to the orbit of the orbital motion) of the flow‐induced force on the inner cylinder goes to zero, the flow drag nearly reaches its minimum value. When only an external torque is imposed to drive the eccentric rotation of the inner cylinder, orbital motion may occur and, in general, has the same direction as the inner cylinder rotation. Under this condition, whether the inner cylinder can have a steady motion state with force equilibrium, and even what type of motion state it can have, is related to the linear density of the inner cylinder. Copyright © 2006 John Wiley & Sons, Ltd.     

VORTEX-INDUCED VIBRATIONS OF AN ELASTIC CIRCULAR CYLINDER

A numerical study of a uniform flow past an elastic circular cylinder using the discrete vortex method incorporating the vortex-in-cell (VIC) technique has been undertaken. The Reynolds number is kept at 200 for all calculations and the cylinder motion is modelled by a spring–damper–mass system. The fluid motion and the structural responses are solved in an iterative way so that the interactions between the fluid and the structure can be accounted for properly. Analyses of the cylinder responses, the damping, the induced forces, the vortex shedding frequency and the vortex structure in the wake have been carried out. The results show that fluid damping is responsible for a limit-cycle oscillation behaviour even when the system natural frequency is close to the vortex-shedding frequency. Reasonable agreement with previous experimental data and computational results is obtained in the comparison of the amplitude of the limit-cycle oscillations. The results further show that the cylinder oscillations could be as large as 0·57 diameter under certain flow conditions and structural properties. Finally, it is shown that a one-degree-of-freedom structural model yields results that are only in qualitative agreement with a two-degree-of-freedom model. In other words, the streamwise oscillations also have a substantial effect on the transverse vibrations and their characteristics.     

FLUID DAMPING OF AN ELASTIC CYLINDER IN A CROSS-FLOW

Damping characteristics of fluid–structure systems are difficult to measure or calculate. In the past, such data have been rather scarce. This study reports an attempt on the use of a numerical approach to derive damping ratios related to fluid–structure interactions. It is based on an autoregressive moving-average (ARMA) method, which is used to analyse the displacement time series obtained from a numerical simulation of an elastic cylinder in a uniform cross-flow. The damping ratios show a similar trend to those obtained in previous experiments. An alternative way to deduce damping ratios is to decompose the transverse force in the structural dynamics equation into a drag (or out-of-phase) and an inertia (or in-phase) component for analysis. The damping thus deduced is in fair agreement with that obtained from ARMA; however, at or near synchronization, where the natural frequency of the stationary cylinder is close to the vortex shedding frequency, there is a very substantial difference between the two results.     

Flow-induced vibrations of a tethered circular cylinder

One of the most basic examples of fluid-structure interaction is provided by a tethered body in a fluid flow. The tendency of a tethered buoy to oscillate when excited by waves is a well-known phenomenon; however, it has only recently been found that a submerged buoy will act in a similar fashion when exposed to a uniform flow at moderate Reynolds numbers, with a transverse peak-to-peak amplitude of approximately two diameters over a wide range of velocities. This paper presents results for the related problem of two-dimensional simulations of the flow past a tethered cylinder. The coupled Navier–Stokes equations and the equations of motion of the cylinder are solved using a spectral-element method. The response of the tethered cylinder system was found to be strongly influenced by the mean layover angle as this parameter determined if the oscillations would be dominated by in-line oscillations, transverse oscillations or a combination of the two. Three branches of oscillation are noted, an in-line branch, a transition branch and a transverse branch. Within the transition branch, the cylinder oscillates at the shedding frequency and modulates the drag force such that the drag signal is dominated by the lift frequency. It is found that the mean amplitude response is greatest at high reduced velocities, i.e., when the cylinder is oscillating predominantly transverse to the fluid flow. Furthermore, the oscillation frequency is synchronized to the vortex shedding frequency of a stationary cylinder, except at very high reduced velocities. Visualizations of the pressure and vorticity in the wake reveal the mechanisms behind the motion of the cylinder.