Hydroelastic analysis of surface wave interaction with concentric porous and flexible cylinder systems

The present study deals with the hydroelastic analysis of gravity wave interaction with concentric porous and flexible cylinder systems, in which the inner cylinder is rigid and the outer cylinder is porous and flexible. The problems are analyzed in finite water depth under the assumption of small amplitude water wave theory and structural response. The cylinder configurations in the present study are namely (a) surface-piercing truncated cylinders, (b) bottom-touching truncated cylinders and (c) complete submerged cylinders extended from free surface to bottom. As special cases of the concentric cylinder system, wave diffraction by (i) porous flexible cylinder and (ii) flexible floating cage with rigid bottom are analyzed. The scattering potentials are evaluated using Fourier–Bessel series expansion method and the least square approximation method. The convergence of the double series is tested numerically to determine the number of terms in the Fourier–Bessel series expansion. The effects of porosity and flexibility of the outer cylinder, in attenuating the hydrodynamic forces and dynamic overturning moments, are analyzed for various cylinder configurations and wave characteristics. A parametric study with respect to wave frequency, ratios of inner-to-outer cylinder radii, annular spacing between the two cylinders and porosities is done. In order to understand the flow distribution around the cylinders, contour plots are provided. The findings of the present study are likely to be of immense help in the design of various types of marine structures which can withstand the wave loads of varied nature in the marine environment. The theory can be easily extended to deal with a large class of problems associated with acoustic wave interaction with flexible porous structures.     

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

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波浪与外壁开孔双筒柱群的相互作用

应用速度势的特征函数展开和透空壁内两壁间压力差和流体速度成正比的线性模型,建立 了波浪与外壁开孔同轴双筒桩柱群相互作用的线性解析解. 应用这一模型进行了数值计算, 用以检验孔隙系数对双筒柱上的波浪力和波面高度的影响. 结果表明,外壁孔隙系数的增加 对减小波浪力和柱外波面高度有很大影响.     

Hydrodynamic forces and moments due to interaction of linear water waves with truncated partial-porous cylinders in finite depth

An exact analytical method is employed for studying the diffraction problems in an ocean due to the presence of a specific type of cylinders. In this current work, two models are studied: (i) a floating surface-piercing truncated partial-porous cylinder, (ii) a surface-piercing truncated partial-porous cylinder placed at the bottom. In both cases, the configuration of the composite cylinder is such that it consists of an impermeable inner cylinder rising above the free surface and a coaxial truncated porous cylinder around the lower part of the inner cylinder with the top of the porous cylinder being impermeable. By using linear water wave theory, a three-dimensional representation of the problem is developed based on eigenfunction expansion method. The condition on the porous boundary is defined by applying Darcy’s law. Pressure and velocity satisfy continuity conditions across the linear interface between the adjacent fluid domains. Hydrodynamic force, moment and wave run-up are calculated by using the velocity potentials. Comparisons are carried out with results of wave diffraction by a floating and bottom-mounted compound cylinder, i.e., when the whole cylinder is non-porous. Handy agreements are observed from these comparisons. Through numerical tests, various experiments are carried out to investigate the impact of various parameters, such as porous coefficients, draft ratio, the ratio of inner and outer radii, the water depth etc., on hydrodynamic force, moment and wave run-up. The results clearly indicate that an appropriate optimal ratio for various parameters may be considered in designing practical ocean structures with minimum adverse hydrodynamic effect. The appearance of resonance in the results and role of porosity in mitigating resonance effect are explained. Proposal to select various appropriate parameters for the best possible effect is put forward.     

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.     

Dual cylinder inviscid vortex sound of low Mach number

The unsteady motions of an inviscid vortex under the influence of a cylinder pair in the presence of a low Mach number mean flow and the corresponding sound generation are examined in the present study. The two cylinders are in close proximity. A semi-analytical approach using the conformal mapping together with the potential theory is adopted. The results show that the vortex will interact intensively with the cylinders under the right combinations of mean flow direction and initial vortex position. Such interactions result in a high rate of change of vortex propagation velocity, strong fluctuating forces on cylinder and strong sound radiations. However, it is found that much stronger acoustic energy radiation will result when the vortex approaches the cylinder pair from the bottom than from the top, unless the mean flow is nearly perpendicular to the horizontal cylinder pair axis. Stronger sound radiation is also observed for the identical cylinder cases in general, except the flow direction is close to some critical values.     

Oscillations of elastically mounted cylinders in regular waves

Under the assumption of potential flow and linear wave theory, a semi-analytic method based on eigenfunciton expansion is proposed to predict the hydrody-namic forces on an array of three bottom-mounted, surface-piercing circular cylinders. The responses of the cylinders induced by wave excitation are determined by the equa-tions of motion coupled with the solutions of the wave radiation and diffraction problems. Experiments for three-cylinder cases are then designed and performed in a wave flume to determine the accuracy of this method for regular waves.     

Vortex shedding around a near-wall circular cylinder induced by a solitary wave

This study developed a two-dimensional generalized vortex method to analyze the shedding of vortices and the hydrodynamic forces resulting from a solitary wave passing over a submerged circular cylinder placed near a flat seabed. Numerical results for validation are compared with other numerical and experimental results, and satisfactory agreement is found. A series of simulations were performed to study the effects of gap-to-diameter ratio and incident wave height on vorticity pattern as well as the forces exerted on the cylinder. The range of the heights of incident waves is from 0.3h to 0.7h, where h is the still water depth. The range of the gap-to-diameter ratios is from 0.1 to 0.8. The results indicate that the flow pattern and the pressure distribution change significantly because of the close proximity of the seabed where the vorticity flux on the seabed-side surface of the cylinder is suppressed. Placing the cylinder nearer the seabed increases the drag and the positive lift on the cylinder. When the gap-to-diameter ratio increases, the pattern of vortices changes because of the interaction between the main recirculation zone and the shear layers separated from the gap. The maxima of drag, lift and total force increase linearly with the height of the incident wave.     

铰接圆柱体在二色波中的二阶低频力

考虑了铰接圆柱体的响应，给出了二色波中铰接在海底的圆柱体的二阶低频力。在未求出二阶速度势的情况下，利用其定解条件给出了二阶速度势的影响，给出了二阶低频力的解析表示式。二阶低频力主要由一阶速度势决定。二阶入射速度势以及圆柱的二阶响应对二阶低频力的影响可以忽略。     

Diffraction of regular waves by an arbitrarily oriented system of vertical circular cylinders

The linear theory of small-amplitude waves is used to construct a solution to the problem of the diffraction of surface gravity waves by a system of arbitrarily oriented vertical circular cylinders. Analytic expressions are obtained for the wave forces and overturning moments acting on each cylinder of the system. A system of two rows of cylinders with three cylinders in each row is considered as an example. It is shown that for certain relationships between the diameter of the cylinders, the distance between them, the angle of approach of the wave, and its wavelength, the maximal values of the hydrodynamic forces acting on the cylinders of the system with allowance for the interaction of the diffracted fields may be appreciably greater than when no allowance is made for it.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 177–181, January–February, 1984.     

Three-dimensional computation for flow-induced vibrations of an upstream circular cylinder in two tandem circular cylinders

It is well known from a lot of experimental data that fluid forces acting on two tandem circular cylinders are quite different from those acting on a single circular cylinder. Therefore, we first present numerical results for fluid forces acting on two tandem circular cylinders, which are mounted at various spacings in a smooth flow, and second we present numerical results for flow-induced vibrations of the upstream circular cylinder in the tandem arrangement. The two circular cylinders are arranged at close spacing in a flow field. The upstream circular cylinder is elastically placed by damper-spring systems and moves in both the in-line and cross-flow directions. In such models, each circular cylinder is assumed as a rigid body. On the other hand, we do not introduce a turbulent model such as the Large Eddy Simulation (LES) or Reynolds Averaged Navier-Stokes (RANS) models into the numerical scheme to compute the fluid flow. Our numerical procedure to capture the flow-induced vibration phenomena of the upstream circular cylinder is treated as a fluid-structure interaction problem in which the ideas of weak coupling is taken into consideration.     

Numerical investigation on flow around circular cylinders in tandem arrangement at a subcritical Reynolds number

Three-dimensional fluid computations have been performed to investigate the flows around two circular cylinders in tandem arrangements at a subcritical Reynolds number, Re=2.2×10⁴. The center-to-center space between the cylinders was varied from twice the cylinder diameter to five times that, and the flows and fluid-dynamic forces obtained from the simulations are compared with the experimental results reported in the literature. Special attention is paid to the characteristics of the vortices shed from the upstream cylinder such as the convection, the impingement onto the downstream cylinder and the interaction with the vortices from the downstream cylinder. The effects of the vortices from the upstream cylinder on the fluid-dynamic forces acting on the downstream cylinder are discussed.     

Diffraction of cnoidal waves by vertical cylinders in shallow water

Diffraction of nonlinear waves by single or multiple in-line vertical cylinders in shallow water is studied by use of different nonlinear, shallow-water wave theories. The fixed, in-line, vertical circular cylinders extend from the free surface to the seafloor and are located in a row parallel to the incident wave direction. The wave–structure interaction problem is studied by use of the nonlinear generalized Boussinesq equations, the Green–Naghdi shallow-water wave equations, and the linearized version of the shallow-water wave equations. The wave-induced force and moment of the Green–Naghdi and the Boussinesq equations are presented when the incoming waves are cnoidal, and the forces are compared with the experimental data when available. Results of the linearized equations are compared with the nonlinear results. It is observed that nonlinearity is very important in the calculation of the wave loads on circular cylinders in shallow water. The variation of wave loads with wave height, wavelength and the spacing between cylinders is studied. Effect of the neighboring cylinders, and the shielding effect of upwave cylinders on the wave-induced loads on downwave cylinders are discussed.     

串列双圆柱绕流问题的数值模拟

本文运用有限体积方法,对绕串列放置的双圆柱的二维不可压缩流动进行了数值计算。为研究两圆柱不同间距对圆柱相互作用和尾流特征的影响,选取间距比Ｌ／Ｄ（Ｌ为两圆柱中心间的距离,Ｄ为圆柱直径）在１．５～５．０之间每隔０．５共八个有代表性的间距进行了计算模拟。计算均在Ｒｅ＝２００条件下进行。计算结果表明：对该绕流问题,流动特征在很大程度上取决于间距的大小。且间距存在一临界值,间距比从小于临界值变化到大于临界     

Real-time nonlinear cylinder wave force reconstruction in stochastic wave field considering second-order wave effects

This study provides a novel method for reconstructing real-time nonlinear wave forces on a large-scale circular cylinder by considering second-order wave effects. Potential theory is utilized for deriving the expression of wave forces with the measured data of wave elevation. Approximate expressions of quadratic transfer functions are built with undetermined coefficients, which are resolved by using the historical data of measured wave elevation. Two different algorithms, including fast Fourier transform (FFT) and recursive least squares (RLS), are adopted for real-time reconstruction. Hydrodynamic tests are conducted in the wave flume on a circular cylinder to examine the effectiveness of the nonlinear reconstruction method. Comparative results demonstrate that the accuracy of real-time reconstructed wave forces is significantly enhanced by the present method. The over-prediction errors at force crests and the under-prediction errors at force troughs have been reduced. Furthermore, comparative results show that the nonlinear method implemented by the FFT algorithm provides more accurate results, whereas the RLS algorithm is more time cost efficient.     

RESONANCES IN WAVE DIFFRACTION/RADIATION FOR ARRAYS OF ELASTICALLY CONNECTED CYLINDERS

As shown by Maniar & Newman in 1997, for a long array of bottom-mounted cylinders in the open sea, resonant modes occur as “near-trapping” and large diffraction forces are excited on the cylinders. The mechanism of such a resonant phenomenon was subsequently explained by the present authors in connection with the Dirichlet trapped modes for an array of cylinders aligned perpendicular to the walls in a wave channel. This paper examines similar resonant phenomena for radiation problems. Considered is an array of elastically connected cylinders in a wave channel. The cylinders are surface-piercing and extend to the sea-bottom. They constitute an array in a line, and each cylinder is allowed to oscillate only in the direction parallel to the line. Nonradiating wave modes, which cause only added mass force and no hydrodynamic damping are demonstrated to exist for an array of cylinders across the wave channel. Each mode corresponds to a “dry-mode” for the periodic array of elastically connected cylinders. This result leads to the existence of pure-resonant modes for a periodic array of elastically connected cylinders across the channel. Trapped modes for the corresponding diffraction problem are obtained as the limiting case when the stiffness of the springs has an infinite value.     

Nonlinear free surface action with an array of vertical cylinders

Nonlinear diffraction of regular waves by an array of bottom-seated circular cylinders is investigated in frequency domain, based on a Stokes expansion approach. A complete semi-analytical solution is developed which allows an efficient evaluation of the second-order potentials in the entire fluid domain, and the wave forces on the structure. Expressions are derived for the second-order potential in the vicinity of individual cylinders. These expressions have a simple form, thus providing an effective means for investigating the wave enhancement due to nonlinear interactions with multiple cylinders. Based on the present method, the wave run-up and free-surface elevations around an array of two, three and four cylinders are investigated numerically.     

Forces on surface-piercing vertical circular cylinder groups on flooding staircase

Flooding into underground spaces has become a common threat and caused significant damages and casualties in the past decades. To improve the understanding of people walking through the flooding staircase, a 1:2-scale physical model of a staircase with rest platform was assembled. An instrument was developed to measure the hydrodynamic forces acting on individual vertical circular cylinders, as well as cylinder groups arranged side-by-side, in tandem and staggered cylinder arrays on the flooding staircase. The results show that the horizontal hydrodynamic force on a cylinder increases rapidly with the increasing of the inundated depth on the entrance of the staircase. With a side-by-side tight cylinder array, the force on the central cylinder is always larger than an isolated one. The force on the downstream cylinder in tandem cylinder array is always smaller. However, the drag coefficients of both cases are much larger than the corresponding ones in a horizontal bed channel. For the case of staggered cylinder array, the force on the downstream cylinder varies with the change of the transverse spacing and the longitudinal distance between cylinders.     

压电空心圆柱中波的传播

应用三维压电弹性体轴对称模型对压电空心圆柱中波的传播进行了研究. 发现在 圆柱中是否具有压电性质会对波的传播带来显著的差异. 当波长趋向于零时，在压电圆柱中 拟P波的波速渐进趋向于横观各向同性弹性体的准P波波速，而非压电圆柱中拟P波的波速 渐进趋向于一维杆模型中的P波波速；在压电圆柱中拟SV波存在驻波现象. 圆柱中的SH波 同电场无关，所以在压电圆柱和非压电圆柱中SH波具有相同的频散曲线. 应用积分变 换方法将圆柱的控制方程同其侧边界条件相结合，得到了一组动力学方程. 针对具体的侧边 界条件，得到相对应的波导条件和频散方程. 在此基础上通过数值计算模拟了圆柱受到端部 应力脉冲激励后的瞬态响应. 同时讨论了空心圆柱的半径比对轴向波传播的影响.