A shallow-depth sloshing absorber for structural control

Sloshing absorbers work on a similar principle to that of tuned vibration absorbers. A sloshing absorber consists of a tank, partially filled with liquid. The absorber is attached to the structure to be controlled, and relies on the structure's motion to excite the liquid. Consequently, a sloshing wave is produced at the liquid free surface possessing energy dissipative qualities. The primary objective of this paper is to demonstrate the effectiveness of employing liquid sloshing as a structural control mechanism. To this end, simple experimental observations are presented first. Then, numerical predictions obtained using smoothed particle hydrodynamics (SPH) are compared with experimental observations. The objective of this comparison is to demonstrate the modelling technique's ability to approximate the characteristics of such flows.     

A study of sloshing absorber geometry for structural control with SPH

A liquid sloshing absorber consists of a container, partially filled with liquid. The absorber is attached to the structure to be controlled, and relies on the structure's motion to excite the liquid. Consequently, a sloshing wave is produced at the liquid free-surface within the absorber, possessing energy dissipative qualities. The primary objective of this work is to numerically demonstrate the effect of a sloshing absorber's shape on its control performance. Smoothed Particle Hydrodynamics (SPH) is used to model fluid–structure interaction of the structure/sloshing absorber system in two dimensions. The structure to be controlled is a lightly damped single degree-of-freedom structure. The structure is subjected to a transient excitation and then allowed to respond dynamically, coming to rest either due to its own damping alone or with the added control of the sloshing absorber. It is identified that the control performance of the conventionally used rectangular container geometry can be improved by having inward-angled walls. This new arrangement is robust, and of significant advantage in situations when the external disturbance is of uncertain magnitude.     

基于SPH法的二维矩形液舱晃荡研究

液体晃荡是一种复杂的流体运动现象,自由液面的存在使得该现象具有很强的非线性和随机性。针对二维矩形液舱在不同振幅水平激励下的纵荡问题,应用SPH法对其进行了数值研究。首先计算了小振幅激励下的纵荡,计算结果分别与线性理论解、文献VOF法结果及文献SPH法结果作了比较分析,以验证所建数值模型的合理性;然后计算了液舱在大振幅水平激励下的纵荡,着重分析了不同振幅下液体晃荡的速度向量图、液面波动时程、压强波动时程、动量波动时程以及波动的频谱图,并将计算所得液面波动结果与小振幅激励下的液面波动结果作了比较。分析结果表明,在大振幅水平激励下,液面波动的波峰值较小振幅下的结果有较为明显的增大,而波谷值则无过大的变化,总体波动幅值比小振幅下的结果大;随着激励幅值的增大,液面波动幅值呈现明显增大的趋势,压强的整体波动幅值也呈增大趋势,动量波动的均值亦有明显增大;波动能量随着激励幅值的增大而增大并向第一阶频率区域集中。SPH法对处理液体大幅晃荡这种具有自由表面大变形的问题有十分优越的特性。     

Neural network-based reduced-order modeling for nonlinear vertical sloshing with experimental validation

In this paper, a nonlinear reduced-order model based on neural networks is introduced in order to model vertical sloshing in presence of Rayleigh–Taylor instability of the free surface for use in fluid–structure interaction simulations. A box partially filled with water, representative of a wing tank, is first set on vertical harmonic motion via a controlled electrodynamic shaker. Accelerometers and load cells at the interface between the tank and an electrodynamic shaker are employed to train a neural network-based reduced-order model for vertical sloshing. The model is then investigated for its capacity to consistently simulate the amount of dissipation associated with vertical sloshing under different fluid dynamics regimes. The identified tank is then experimentally attached at the free end of a cantilever beam to test the effectiveness of the neural network in predicting the sloshing forces when coupled with the overall structure. The experimental free response and random seismic excitation responses are then compared with that obtained by simulating an equivalent virtual model in which the identified nonlinear reduced-order model is integrated to account for the effects of violent vertical sloshing.

     

Autoparametric interaction of a liquid surface in a rectangular tank with an elastic support structure under 1:1 internal resonance

Autoparametric interaction of a liquid free surface in a rectangular tank with an elastic support structure, which is subjected to vertical excitation, is investigated. When the natural frequency of the structure is equal to the lowest natural frequency of liquid sloshing, this system is categorized as an autoparametric system with an internal resonance ratio 1:1. The structure is elastically supported so there is a higher possibility that the 1:1 internal resonance can be observed. The nonlinear theoretical analysis is conducted for a fluid assumed to be perfect in a tank with a finite liquid depth. The equations of motion for the first three sloshing modes are derived employing Galerkin’s technique and considering both the nonlinearity of the fluid motion, and the viscous damping effect. Then the theoretical frequency response curves for the harmonic oscillations of the structure and sloshing are determined using van der Pol’s method. The frequency response curves show that high amplitudes of the structure’s vibrations facilitate the liquid sloshing. Furthermore, the influence of the internal detuning parameter is investigated by showing the frequency response curves and bifurcation sets. Hopf bifurcations may occur followed by amplitude-modulated motions. The theoretical results are in quantitative agreement with the experimental data.     

低重环境下俯仰运动圆柱贮箱中液体非线性晃动

在低重力环境下,用变分原理建立了液体晃动的压力体积分形式的Lagrange函数,并将速度势函数在自由液面处作波高函数的级数展开,从而导出自由液面运动学和动力学边界条件非线性方程组;最后用四阶Runge-Kutta法求解非线性方程组。计算结果表明,随俯仰激励频率的逐渐变化,由于面外主模态和次生模态同时失稳,致使整个系统各阶模态和波高函数由稳态运动过渡为不稳定运动。     

基于修正光滑粒子流体动力学算法的低能量耗散数值波浪水池开发

目前, 无网格光滑粒子流体动力学SPH粒子法在波浪与结构物相互作用研究方面得到广泛应用, 但该方法模拟波浪远距离传播时, 常常面临严重的能量耗散问题, 导致波高非物理性降低, 给大范围海域、长时间作用下的波-物耦合作用研究带来一定困难. 对此, 本文采用一种核函数修正算法, 在确保粒子间相互作用对称性的同时, 改进压力梯度离散项的计算精度, 设法解决SPH方法中能量非物理性耗散的难题. 相较于前人减缓能量非物理性衰减的方法, 本文的修正SPH算法避免了自由液面搜索等复杂处理过程, 并能保证动量守恒特性. 数值结果中, 采用振荡液滴、规则波、不规则波等算例, 验证本修正SPH算法的准确性和有效性. 结果表明, 该修正SPH算法能准确模拟振荡液滴形态变化, 且动能保持较好守恒性. 通过数值水池与物理水池两者规则波与不规则波结果的对比分析表明, 基于本文修正SPH算法建立的数值波浪水池具有较好的抗能量衰减效果, 能实现长时间、远距离波浪传播的准确模拟. 此外, 本算法能在低光滑长度系数条件下, 实现精确模拟, 将极大缩减三维SPH模拟的时间, 从而节约计算成本.      

A comparative study of truly incompressible and weakly compressible SPH methods for free surface incompressible flows

In this paper, the performance of the incompressible SPH (ISPH) method and an improved weakly compressible SPH (IWCSPH) method for free surface incompressible flows are compared and analyzed. In both methods, the Navier–Stokes equations are solved, and no artificial viscosity is used. The ISPH algorithm in this paper is based on the classical SPH projection method with common treatments on solid boundaries and free surfaces. The IWCSPH model includes some advanced corrective algorithms in density approximation and solid boundary treatment (SBT). In density approximation, the moving least squares (MLS) approach is applied to re‐initialize density every several steps to obtain smoother and more stable pressure fields. An improved coupled dynamic SBT algorithm is implemented to obtain stable pressure values near solid wall areas and, thus, to minimize possible numerical oscillations brought in by the solid boundaries. Three representative numerical examples, including a benchmark test for hydrostatic pressure, a dam breaking problem and a liquid sloshing problem, are comparatively analyzed with ISPH and IWCSPH. It is demonstrated that the present IWCSPH is more attractive than ISPH in modeling free surface incompressible flows as it is more accurate and more stable with comparable or even less computational efforts. Copyright © 2013 John Wiley & Sons, Ltd.     

MPS与GPU结合数值模拟LNG液舱晃荡

液舱晃荡是一种在外部激励作用下部分装载的液舱内液体的波动现象,它会对液舱结构强度和运输船舶稳性产生危害.移动粒子半隐式法(moving particle semi-implicit,MPS)是一种典型的无网格粒子类方法,可以有效地模拟剧烈的液舱晃荡问题.但MPS方法存在计算效率低的缺点,难以模拟大规模三维问题,而GPU并行加速技术已广泛应用于科学计算领域.因此,本文将MPS方法与GPU并行加速技术相结合,采用CUDA程序语言编写,自主开发了MPSGPU-SJTU求解器,对三维液化天然气(liquefiednatural gas, LNG)型液舱晃荡进行了数值模拟.通过三种不同粒子间距的数值模拟,验证了求解器的收敛性,其中最大计算粒子数达到了200多万.与其他研究结果相比,MPSGPU-SJTU求解器能够准确地预测壁面砰击压力,并且捕捉晃荡过程中自由面的大幅度变形和强非线性破碎现象.相比CPU求解器的计算时间,GPU并行加速技术可以大幅度地减小计算时长,提高MPS方法的计算效率.本文将LNG型液舱与方型液舱的晃荡进行对比,结果表明在高充液率下LNG型液舱可以有效地减小晃荡幅值和壁面砰击压力.但在中低充液率下,LNG型液舱则会加剧晃荡,自由面呈现明显的三维特征.本文还进一步研究了水和LNG两种不同介质的液舱晃荡现象,数值模拟结果表明二者的流场基本相似,砰击压力则正比于液体密度.      

基于时域解耦算法的多液舱浮式结构物运动模拟

对于带有多个晃荡液舱的浮式结构物, 浮体的运动、外场水动力以及各舱内的液体晃荡力会实时相互决定, 发生复杂的耦合作用. 为准确模拟多液舱浮式结构物的运动, 本文引入一种有效的时域解耦算法. 该方法以模态分解法为基础, 通过对浮式结构物所受外域水动力和各液舱内非线性晃荡力进行模态分解, 最终形成时域解耦运动方程, 无需迭代求解过程即可显式计算浮式结构物的瞬时加速度. 该方法可避免传统迭代求解方法在迭代次数、截断误差和收敛特性等方面的不足, 减少解耦过程的计算耗时. 本文进一步结合边界元数值方法, 分别对单液舱浮式结构物和多液舱浮式结构物的工况开展数值模拟研究. 通过与单液舱浮式结构物的实验结果对比, 验证了本文时域解耦算法的有效性. 本文详细分析了晃荡力对单液舱浮式结构物运动的影响, 发现存在一个共振影响区间: 当外场波浪频率在该区间之外时, 可以在时域计算结果中观察到稳定的浮体运动; 在比该区间更低频的波况下, 液舱晃荡力与外场波浪力相位相反甚至可以相互抵消, 此时晃荡液舱的存在可以减弱浮体运动; 在比该区间更高频的波况下, 液舱内晃荡力与外场波浪力可以具有相同相位, 此时晃荡液舱的存在会加剧浮体的运动. 本文进一步研究了四液舱浮式结构物在波浪中的纵荡、垂荡和纵摇运动情况, 发现非线性液舱晃荡可对纵荡和纵摇运动产生影响, 但对垂荡运动影响很小.      

波浪与新型双排开孔圆筒防波堤相互作用三维数值模拟

双排开孔圆筒防波堤是基于圆筒、板式结构的一种复合式新型结构型式;基于不可压缩两相流模型建立三维数值波浪水槽,通过RNG k-ε湍流模型进行湍流封闭,并采用TruVOF方法捕捉自由液面,开展波浪与双排开孔圆筒防波堤相互作用数值模拟,探究相对排间距、开孔率对新型双排开孔圆筒防波堤消浪性能的影响,分析了后排开孔圆筒防波堤附近的复杂水动力现象和流动特性.结果表明,在本文研究工况范围内,沿程平均波高随相对排间距的增大先增大后减小,随开孔率的增大而增大,周期对沿程平均波高的影响没有明显规律;当B/D=9, e=23.11%时,新型双排开孔圆筒防波堤消浪效果最优,反射系数在0.4～0.46之间,透射系数在0.3～0.35之间,耗散系数在0.8～0.85之间;自由液面破碎、水气掺混、环状涡运动演化是新型双排开孔圆筒防波堤紊动耗能消波的主要原因;相对排间距会引起后排防波堤附近涡量分布以及剪切层形态的变化,从而导致不同的紊动特性,影响双排开孔圆筒防波堤消浪特性.研究结果可以为新型双排开孔圆筒防波堤工程设计与消浪机理研究提供理论支撑.     

Stable response of low-gravity liquid non-linear sloshing in a circle cylindrical tank

Under pitch excitation,the sloshing of liquid in circular cylindrical tank includes planar motion,rotary motion and rotary motion inside planar motion.The boundaries between stable motion and unstable motion depend on the radius of the tank,the liquid height,the gravitational intension,the surface tensor and the sloshing damping.In this article,the differential equations of nonlinear sloshing are built first. And by variational principle,the Lagrange function of liquid pressure is constructed in volume intergration form.Then the velocity potential function is expanded in series by wave height function at the free surface.The nonlinear equations with kinematics and dynamics free surface boundary conditions through variation are derived.At last,these equations are solved by multiple-scales method.The influence of Bond number on the global stable response of nonlinear liquid sloshing in circular cylinder tank is analyzed in detail.The result indicates that variation of amplitude frequency response characteristics of the system with Bond,jump,lag and other nonlinear phenomena of liquid sloshing are investigated.     

SPH方法Delaunay三角刨分与自由液面重构

光滑粒子法(SPH)作为一种拉格朗日型无网格方法,兼具欧拉网格方法和拉格朗日网格方法的优势,已经成功应用于科学和工程的众多领域。SPH方法后处理一般基于无规则分布的粒子,不如网格类方法后处理简便、直接。另外,SPH方法模拟自由液面流动等问题时,通过粒子位置难以重构自由液面的准确位置。发展一种基于Delaunay三角刨分的SPH后处理方法,即先基于SPH粒子位置利用Delaunay三角刨分建立三角网格,然后将粒子信息转化成网格单元/节点信息,从而可以在三角网格上进行后处理,实现基于网格方法的后处理功能,并可以在三角网格上直接提取或重构自由液面。将本文的方法应用到液滴碰撞和溃坝流SPH模拟结果的后处理中,得到了非常好的结果,表明本文的方法有效可靠。     

Damping computation of liquid sloshing with small amplitude in rigid container using FEM

An FEM (Finite Element Method) based damping estimation method of liquid sloshing with small amplitude in rigid container is proposed. Damping of the sloshing is affected by many factors and some of them are very complicated. Therefore, this paper aims to provide an estimation range, instead of computing the exact value of damping. This method will consider the dissipation at wall, in the interior, and at the contaminated free surface. Owing to the complexity of viscous damping at the free surface, damping of two extreme conditions are computed to estimate the range of actual damping. An iterative algorithm is designed to solve a special general eigenvalue problem. Comparing the computation results with experimental results, it is found that most of the experimental results are within the range of the numerical estimation. Therefore, the method is effective in estimating the range of the damping of liquid sloshing with small amplitude in rigid container. The project supported by the National Natural Science Foundation of China (10172048) The English text was polished by Keren Wang.     

微重力场中液体在带隔板球腔内的晃动

本文讨论微重力场中带球面隔板的球腔内液体晃动问题。选择Legendre函数作为Ritz方法的基函数,计算液体的自由晃动及腔体横向振动激励的受迫振动。计算结果表明,自由晃动频率随隔板位置的下降而趋于升高。液体晃动的动力学效应可用等效的质量—弹簧系统模拟。     

AN EFFICIENT LIQUID SLOSHING DAMPER FOR VIBRATION CONTROL

The next generation of tall structures are being designed to be lighter and more flxible, making them susceptible to wind, ocean waves and earthquake type of excitations. One approach to vibration control of such systems is through energy dissipation using a liquid sloshing damper. Such dampers are already in use for vibration control of tall structures in Japan and Australia. The present parametric study focuses on enhancing the energy dissipation efficiency of a rectangular liquid damper through introduction of a two-dimensional obstacle. A parametric free-vibration study, aimed at optimum size and location of the obstacle, is described first. Results suggest a significant increase in the energy dissipation, up to 60%, in the presence of the obstacle. An extensive wind tunnel test-program was undertaken which substantiated the effectiveness of the improved damper in suppressing both vortex resonance and galloping types of instabilities. Ability of the damper to control structural oscillations with a smaller amount liquid is quite attractive for real-life applications.     

自由液面晃动对旋转充液腔体运动稳定性的影响

针对旋转充液腔体的运动稳定性问题,本文考虑自旋速率范围较宽的情况。引入表示离心力与液体表面张力之比的常数C_f,以Stewartson—Wedemeyer理论和Murphy方法为基础,研究腔内液体晃动对共振不稳定频带的影响。结果表明只有当自旋速率较小,液体表面张力较大时,自由液面晃动对腔体运动稳定性才有明显影响;反之则可忽略自由液面晃动对腔体运动稳定性的影响。     

Motion stability dynamics for spacecraft coupled with partially filled liquid container

This paper presents a canonical Hamiltonian model of liquid sloshing for the container coupled with spacecraft. Elliptical shape of rigid body is considered as spacecraft structure. Hamiltonian system is an important form of mechanical system. It mostly used to stabilize the potential shaping of dynamical system. Free surface movement of liquid inside the container is called sloshing. If there is uncontrolled resonance between the motion of tank and liquid-frequency inside the tank then such sloshing can be a reason of attitude disturbance or structural damage of spacecraft. Equivalent mechanical model of simple pendulum or mass attached with spring for sloshing is used by many researchers. Mass attached with spring is used as an equivalent model of sloshing to derive the mathematical equations in terms of Hamiltonian model. Analytical method of Lyapunov function with Casimir energy function is used to find the stability for spacecraft dynamics. Vertical axial rotation is taken as the major axial steady rotation for the moving rigid body.     

Nonlinear simulation of a tuned liquid damper with damping screens using a modal expansion technique

Tuned liquid dampers utilize sloshing fluid to control wind-induced structural motions. However, as a result of the nonlinear free surface boundary conditions of fluid sloshing in a two-dimensional rectangular container, a closed-form solution describing the response behaviour is unavailable. Modal expansions, which couple the sloshing modes, are carried out to the first, third and fifth order to construct a system of coupled nonlinear ordinary differential equations that are solved using the Runge–Kutta–Gill Method. Modal damping is incorporated to account for energy losses arising from the fluid viscosity and the inclusion of damping screens. The model is in general agreement with a previous third-order model that incorporated screen damping in the fundamental sloshing mode only. Sinusoidal shake table experiments are conducted to validate the proposed models. Response time histories and frequency response plots assess the model’s prediction of wave heights, sloshing forces, and screen forces. The first-order model accurately predicts the resonant sloshing forces, and forces on a mid-tank screen. The higher-order models better represent the wave heights and forces on an off-centre screen. Experimental results from structure–TLD system tests under random excitation are used to evaluate the performance of the proposed models. The first-order model is able to predict the variance of the structural response and the effective damping the TLD adds to the structure, but as a minimum, a third-order model should be employed to predict the fluid response. It is concluded that a first-order model can be utilized for preliminary TLD design, while a higher-order model should be used to determine the required tank freeboard and the loading on damping screens positioned at off-centre locations.     

低重环境下俯仰运动圆柱贮箱内液体晃动

考虑低重环境下由于表面张力的影响使得圆柱贮箱内液体呈现弯曲自由液面的情况,以俯仰激励下液体晃动的占优模态振型函数为晃动速度势的基函数,利用傅里叶-贝塞尔级数对贮箱受俯仰激励时的自由液面处的运动边界条件进行展开,得到能描述晃动系统本质的广义状态方程,并分别给出了固有频率、晃动波高、晃动力和晃动力矩等晃动特征的计算方法. 通过具体算例得到了俯仰激励下贮箱内液体晃动特征的动态响应,同时验证了文中方法的收敛性、可行性和正确性.