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.      

柔性圆柱涡激振动流体力系数识别及其特性

涡激振动是诱发海洋立管、浮式平台系泊缆和海底悬跨管道等柔性圆柱结构疲劳损伤的重要因素.目前,海洋工程中用于柔性圆柱涡激振动预报的流体力系数主要来源刚性圆柱横流向受迫振动的实验数据,存在一定缺陷和误差.本文综合考虑横流向与顺流向振动耦合作用,建立了柔性圆柱涡激振动流体力模型,运用有限元法和最小二乘法确定升力系数、脉动阻力系数和附加质量系数.为了准确识别柔性圆柱涡激振动流体力系数,设计并开展了拖曳水池模型实验,实验用柔性圆柱模型的质量比为1.82,长径比为195.5.通过与刚性圆柱流体力系数对比,深入分析了柔性圆柱流体力系数的特性.结果表明:柔性圆柱在一阶模态控制区,流体力系数随约化速度变化趋势与刚性圆柱大致相似;二阶模态控制区,升力系数和脉动阻力系数显著增大;附加质量系数在响应频率较低时与振动位移的相关性增强;当响应频率较低时,振动位移较大区域为能量耗散区,当响应频率较高时,振动位移较大区域为能量输入区.     

Slow motion of a slip spheroid along its axis of revolution

A combined analytical and numerical study of the Stokes flow caused by a rigid spheroidal particle translating along its axis of revolution in a viscous fluid is presented. The fluid is allowed to slip at the surface of the particle. The general solution for the stream function in prolate and oblate spheroidal coordinates can be expressed in an infinite-series form of semi-separation of variables. The slip boundary condition incorporating the shear stress at the particle surface is applied to this general solution to determine its unknown coefficients of the leading orders. The solution of these coefficients can be either numerical results obtained from a boundary-collocation method or explicit formulas derived analytically. The drag force exerted on the spheroidal particle by the fluid is evaluated with good convergence behavior for various values of the slip parameter and aspect ratio of the particle. The agreement between our hydrodynamic drag results and the relevant numerical solutions obtained previously using a singularity method is excellent. Although the drag force acting on the translating spheroid normalized by that on a corresponding sphere with equal equatorial radius increases monotonically with an increase in the axial-to-radial aspect ratio for a no-slip spheroid, it decreases monotonically as this aspect ratio increases for a perfect-slip spheroid. The normalized drag force exerted on a spheroid with a given surface slip coefficient in between the no-slip and perfect-slip limits is not a monotonic function of its aspect ratio. For a spheroid with a fixed aspect ratio, its drag force is a monotonically decreasing function of the slip coefficient of the particle.     

Multi-modes approach to modelling of vortex-induced vibration

In this work the fluid–structure interactions are considered by investigating a straight but slender pipe interacting with uniform water flow. Two configurations are studied, namely vertically and horizontally positioned pipes, which are modelled as an Euler–Bernoulli beam with flexural stiffness. Both pretension and length-wise mass distribution are considered. The structure is assumed to be moving only in the direction normal to flow (cross-flow motion) hence its in-line motion is neglected. The external fluid force acting on the structure is the result of the action of sectional vortex-induced drag and lift forces. Only mean drag force is considered, with time varying lift force modelled using a non-linear oscillator equation of the Van der Pol type. The obtained coupled system of non-linear partial differential equations is simplified employing Galerkin-type discretisation. The resulting ordinary differential equations are solved numerically providing multi-mode approximations of cross-flow displacement and non-dimensional lift coefficient. The comparison between the responses of vertical and horizontal structures shows that, as expected, due to a balancing between pretension and weight, in general a higher amplitude of vibration is observed for the vertical configuration than in the same location along the pipe for the horizontal configuration in the lower part of the structure. However, lower amplitudes are obtained in the upper part of the pipe. The horizontal configuration solutions are identical in symmetrical locations along the pipe due to constant pretension. The influence of the wake equation coefficients and the fluid force coefficients on the response amplitudes has been also considered together with the length of the pipe and pretension level, and the appropriate response curves are included. Finally, for the higher mode approximations it has been shown that the vibrations level at lower frequencies is predicted reasonably well by retaining only a small subset of modes.     

TWO-DIMENSIONAL VORTEX-INDUCED VIBRATION OF CABLE SUSPENSIONS

Resonant responses of suspended elastic cables driven by a steady current are investigated. Phenomenological fluid force models for alternate vortex-shedding are coupled with the nonlinear partial differential equations of cable motion. Decoupled cross-flow and in-line vortex-induced vibrations (VIV) are examined first using linearized and nonlinear cable models. The linearized cable model predicts well the basic characteristics of VIV and the nonlinear cable model captures the hysteresis often observed in experiments. Next, coupled cross-flow and in-line vibrations are evaluated by considering two principal coupling mechanisms: (i) cable structural nonlinearities, and (ii) coupled fluid lift and drag. Attention is focused on a “worst-case” resonant response where the natural frequencies for cable modes in the cross-flow and in-line directions are in the same 1:2 ratio as the excitation frequencies associated with lift and drag. The inclusion of cable structural nonlinearities alone leads to coupled responses that differ qualitatively (i.e., in number and stability of periodic motions) when compared to those of the decoupled model. The inclusion of coupled fluid lift and drag produces non-planar “figure eight” motions of the cable cross-section that exhibit similar characteristics to those previously measured on spring supported cylinders.     

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.      

Drag measurement and dynamic simulation of Martian wind-driven sensor platform concepts

The purpose of this work is to (a) determine the drag coefficient of three wind-driven systems (referred to as tumbleweeds) in a simulated Martian atmospheric boundary layer; two concepts from NASA Langley (LaRC) and one from Texas Tech University (TTU), and (b) perform a dynamic analysis of the TTU tumbleweed to establish the feasibility of operation in a simulated Martian environment. The TTU Wind Tunnel is used in order to determine the drag coefficient for the tumbleweeds in both the aerodynamic and atmospheric boundary layer (ABL) test sections. A comparison of the two mean drag coefficients for each tumbleweed model reveals the extent to which an ABL affects drag on the models. It appears that no transformation exists that can be used to transform aerodynamic-based drag coefficients into boundary-layer-based drag coefficients; therefore, reliance upon ABL tests is important. It is generally accepted that a complete ABL test under conditions of neutral atmospheric stability requires knowledge of the incoming (approach) mean velocity and turbulent intensity profile, spectral distribution, roughness height, and Reynolds number. Given the fact that limited data exists for the Martian flows, physical simulations of an atmospheric surface layer with knowledge of the mean velocity and general turbulence characteristics was developed in order to obtain drag coefficients for several tumbleweed wind platform designs. The tumbleweeds drag coefficients were effectively constant with the boundary layer affected coefficient less than the respective aerodynamically obtained coefficient. Of particular interest in this study is the TTU tumbleweed, which underwent extensive testing in order to obtain a force function to describe its aerodynamic characteristics in any orientation relative to the wind.     

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.     

The effect of an unsteady drag force on the structure of a non-equilibrium region behind a shock wave in a gas-particle mixture

For numerical analysis of shock wave propagation in gas-particle mixtures, drag coefficients of a sphere in steady flows are generally used. However, it is shown both experimentally and numerically that a shock loaded solid sphere experiences unsteady drag forces. The paper describes a model of unsteady drag force and its effect on the structure of the non-equilibrium region behind a shock front traveling in a dusty gas. The results are compared with those obtained by using a steady drag coefficient and are discussed. It is demonstrated that the large drag force at the early stage of the interaction between shock-wave induced flow and a solid particle affects the flow structure that is obtained with a steady drag force.      

Numerical investigations into the asymmetric effects on the aerodynamic response of a pitching airfoil

The effects of asymmetric sinusoidal motion on pitching airfoil aerodynamics were studied by numerical simulations for 2-D flow around a NACA0012 airfoil at Re=1.35×10⁵. Various unsteady parameters (amplitude of oscillation, d; reduced frequency, k) were applied to investigate the effect of asymmetry parameter S on the instantaneous force coefficients and flow patterns. The results reveal that S has a noticeable effect on the aerodynamic performance, as it affects the instantaneous force coefficient, maximum lift and drag coefficient, hysteresis loops and the flow structures.     

Numerical simulation of viscous oscillatory flow past four cylinders in square arrangement

The results of a numerical study of the viscous oscillating flow past four circular cylinders, for a constant frequency parameter equal to 50 and KC ranging between 0.2 and 10, are presented. The cylinders were placed on the vertices of a square, two sides of which were perpendicular and two parallel to the oncoming flow, for pitch ratios, P/D, ranging between 2 and 5. The finite-element method was employed for the solution of the Navier-Stokes equations, in the formulation where the stream function and the vorticity are the field variables, whereas the pressure distribution throughout the computational domain was obtained from the solution of Poisson’s equation. When the Keulegan-Carpenter number is lower than 4, the flow remains symmetrical with respect to the horizontal axis of symmetry of the solution domain and periodic at consecutive cycles. As KC increases to 4, the flow becomes aperiodic in different cycles, although symmetry with respect to the horizontal central line of the domain is preserved. For KC equal to 5, asymmetries appear intermittently in the flow, which are eventually amplified as KC increases still further. These asymmetries, in association with the aperiodicity of flow in different cycles, lead to an almost chaotic configuration as KC grows larger. For characteristic cases the flow pattern and the time histories of the in-line and transverse forces exerted on the cylinders are presented. The mean transverse forces acting on the cylinders, the r.m.s. values of the in-line and transverse forces, together with the drag and inertia coefficients of the in-line force, were evaluated for each pitch ratio in the range of Keulegan-Carpenter numbers examined and are presented in diagrams.     

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.     

顺桨风力机塔叶干涉翼型非稳气动力时频特性

由于风力机叶片与塔筒流场相互干涉,实际气动力与理想情况存在较大差异,这种干涉作用造成的气动力差异给叶片与塔筒结构可靠性带来不可忽视的影响.以翼型DU91-W2-250为研究对象,采用瞬态数值分析与本征正交分解方法,考虑叶片和塔筒流场相互干涉作用,分析顺桨工况翼型非稳气动力时频特性及其影响规律,量化不同雷诺数下塔叶相对位置及几何参数对气动力均值、波动幅度和频率的影响程度,通过流场模态能量分布形态分析,揭示流场干涉对气动力的影响机制.结果表明,翼型气动中心至塔筒几何中心的垂直距离、水平距离以及塔筒直径相对于翼型弦长的无量纲参数y*,x*和D*对气动力均有不同程度影响,其中y*对升阻力系数均值影响最大,对频率无明显影响,y*绝对值越大,C_l均值越接近单翼型C_l值,y*绝对值越小升阻力系数波动幅度越大,y*从-12增大到12,升力系数均值最小值为-0.48,最大值为1.16;x*减小和D*增大,反向阻力均值增大,波动幅度增大,波动频率略有下降,当x*小于临界值5时,带塔翼型阻力均值反向;在计算范围内,带塔翼型升力系数均值相对于单翼型升力系数最大偏差为...     

乘波体前体/进气道一体化设计研究

为了研究乘波体几何外形参数和飞行参数对前体/进气道一体化设计的影响,采用理论分析和数值模拟相结合的方法,以马赫数Ma=6和攻角α=0为设计状态、进气道总压恢复系数和前体阻力系数为目标函数,对乘波体前体/进气道进行了优化设计,并在此基础上研究了攻角、马赫数、前缘半径、前体宽度对气动参数的影响。结果表明:该乘波体前体/进气道构型具有良好的攻角特性,总压恢复系数比基准构型提高17.79%,阻力系数比基准构型降低78.5%,符合高超声速飞行器高升力、低阻力的要求,且非常适合小攻角高超声速巡航飞行;为了得到较高升阻比的前体,在前缘半径R≤2mm的范围内进行流场反设计时,可以将设计马赫数的取值比预期低一些。     

A NUMERICAL SIMULATION OF VORTEX SHEDDING FROM AN OSCILLATING CIRCULAR CYLINDER

Vortex shedding from an oscillating circular cylinder is studied by numerical solutions of the two-dimensional unsteady Navier–Stokes equations. A physically consistent method is used for the reconstruction of velocity fluxes which arise from discrete equations for the mass and momentum balances. This method ensures a second-order accuracy. Two phenomena are investigated and, in both cases, the cylinder oscillation is forced. The first is the flow induced by the harmonic in-line oscillation of cylinder in water at rest. The Reynolds number is equal to 100 and the Keulegan–Carpenter number is equal to 5. A comparison of phase-averaged velocity vectors between measurements and predictions is presented. Applying the widely used model of Morison to the computed in-line force history, the drag and the inertia coefficients are calculated and compared for different grid levels. Using these to reproduce the force functions, deviations from those originally computed are revealed. The second problem is an investigation of a transversely oscillating cylinder in a uniform flow at fixed Reynolds number equal to 185. The cylinder oscillation frequency ranges between 0·80 and 1·20 of the natural vortex-shedding frequency, and the oscillation amplitude is 20% of the cylinder diameter. As the frequency of excitation of the cylinder increases relative to the inherent vortex formation frequency, the initially formed concentration of vorticity moves closer to the cylinder until a limiting position is reached. At this point, the vorticity concentration abruptly switches to the opposite side of the cylinder. This process induces distinct changes of the topology of the corresponding streamline patterns.     

Investigation of turbulent flow past a yawed wavy cylinder

A large eddy simulation (LES) study was conducted to investigate the three-dimensional characteristics of the turbulent flow past wavy cylinders with yaw angles from 0° to 60° at a subcritical Reynolds number of 3900. The relationships between force coefficients and vortex shedding frequency with yaw angles for both wavy cylinders and circular cylinders were investigated. Experimental measurements were also performed for the validation of the present LES results. Comparing with corresponding yawed circular cylinders at similar Reynolds number, significant differences in wake vortex patterns between wavy cylinder and circular cylinder were observed at small yaw angles. The difference in wake pattern becomes insignificant at large yaw angles. The mean drag coefficient and the Strouhal number obey the independence principle for circular cylinders at yaw angle less than 45°, while the independence principle was found to be unsuitable for yawed wavy cylinders. In general, the mean drag coefficients and the fluctuating lift coefficients of a yawed wavy cylinder are less than those of a corresponding yawed circular cylinder at the same flow condition. However, with the increase of the yaw angle, the advantageous effect of wavy cylinder on force and vibration control becomes insignificant.     

Measurement of virtual mass and drag coefficients of a disk oscillating sinusoidally in a two-phase mixture

This paper presents an experimental determination of the virtual mass and drag coefficients of a disk oscillating sinusoidally in a two-phase mixture of air flowing through stagnant water. The purpose of this experiment was to determine the importance of virtual mass on the transient response of an INEL-type drag-disk flow meter.The results indicate that for a given void fraction, the virtual mass coefficient increases, and the drag coefficient decreases, with increasing amplitude parameter. Also, for a given amplitude parameter, the virtual mass coefficient decreases, and the drag coefficient increases, with increasing void fraction.Based on the measured virtual mass coefficients, it was concluded that when an INEL-type drag-disk is used for the measurement of transient two-phase flows, virtual mass effects may be neglected in the analysis of its response without appreciable error.     

Effect of damping and wave parameters on offshore structure under random excitation

This paper describes the linearized and nonlinear dynamic response of a tension leg platform (TLP) to random waves and current forces. The forcing term of the equation of motion is inherently nonlinear due to the nonlinear drag force. Two analysis procedures are used: nonlinear time domain analysis and linear frequency domain analysis. For the nonlinear analysis, the random wave particle velocities and accelerations are simulated for a given wave spectrum. The nonlinear equation of motion is then integrated directly to obtain the system response statistics. For the linear frequency domain analysis, the nonlinear drag force is linearized through an introduction of linearization coefficients. The main objective of this paper is to investigate the effect of the structural damping and wave parameters on both nonlinear and linear dynamic response of the TLP by parametric studies. The results of stochastic nonlinear and linear dynamic response of the TLP, with and without the presence of current, are presented and compared.     

Multi-frequency vortex-induced vibrations of a long tensioned beam in linear and exponential shear flows

The multi-frequency vortex-induced vibrations of a cylindrical tensioned beam of aspect ratio 200, free to move in the in-line and cross-flow directions within first a linearly and then an exponentially sheared current are investigated by means of direct numerical simulation, at a Reynolds number equal to 330. The shape of the inflow profile impacts the spectral content of the mixed standing-traveling wave structural responses: narrowband vibrations are excited within the lock-in area, which is limited to a single region lying in the high flow velocity zone, for the linear shear case; in contrast, the lock-in condition occurs at several spanwise locations in the exponential shear case, resulting in broadband responses, containing a wide range of excited frequencies and spatial wavenumbers. The broadband in-line and cross-flow vibrations occurring for the exponential shear current have a phase difference that lies within a specific range along the entire span; this differs from the phase drift noted for narrowband responses in linear shear flow. Lower vibration amplitudes, time-averaged and fluctuating in-line force coefficients are observed for the exponential shear current. The cross-flow force coefficient has comparable magnitude for both inflow profiles along the span, except in zones where the broadband vibrations are under the lock-in condition but not the narrowband ones. As in the narrowband case, the fluid forces associated with the broadband responses are dominated by high frequencies related to high-wavenumber vibration components. Considerable variability of the effective added mass coefficients along the span is noted in both cases.     

Short crested wave–current forces around a large vertical circular cylinder

An analytical solution for the diffraction of short crested incident wave along positive x-axis direction on a large circular cylinder with uniform current is derived. The important influences of currents on wave frequency, water run-up, wave force, inertia and drag coefficients on the cylinder profiles are investigated for short-crested incident wave. Based on the numerical results, we find wave frequency of short crested wave system is affected by incident angle and the strength of the currents. The wave frequency increases or decreases with increasing current speed following or opposing wave propagating direction. It shows that the effects of current speeds, current directions on water run-up on the circular cylinder with different radius for different wave numbers are very conspicuous when the incident wave changes from long crested plane waves to short-crested waves. With the increase of current speed, the water run-up on the cylinder becomes more and more high, and will exceed that of long crested plane wave and short crested wave case without currents even though the current speed is small. The total wave loads, inertia coefficient and drag coefficient exerted on a cylinder with currents would be larger compared to the wave loads exerted pure short-crested waves. Therefore, ocean engineers should consider the short crested wave–current load on marine constructs carefully.