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.     

浮式垂直轴风机的动力学建模、仿真与实验研究

考虑气动力和水动力的耦合研究浮式垂直轴风机系统的运动响应,将固定式垂直轴风机的气动载荷计算方法进一步推广到海上浮式垂直轴风机的气动载荷计算.考虑阻尼力、波浪力、风载荷、系泊力等,建立了浮式垂直轴风机系统的纵荡-垂荡-纵摇运动方程.考虑动态失速和浮式基础运动,基于双致动盘多流管理论,推导了风机叶片气动载荷计算公式,编制了数值计算程序.以Sandia 17 m风机为例,验证了气动载荷计算程序的正确性.最后进行了模型实验,其中模型的风机为Φ型达里厄垂直轴风机,支撑基础为桁架式Spar型浮式基础,将模型实验结果与数值计算结果进行了对比,验证了耦合计算程序.结果表明,数值计算得到的风机系统的垂荡、纵摇运动的RAO(幅值响应算子)曲线与模型实验结果吻合较好,验证了耦合程序的正确性.然而,由于数值计算与模型实验在运动自由度、阻尼、风载荷等方面存在差别,数值计算结果与模型实验结果仍有一定的差异.     

螺旋侧板和水深对浮式风机动态响应的影响

为研究漂浮式风力机平台动态响应的优化措施,提出平台附加螺旋侧板的方式。建立基于Spar平台的5MW风力机整机模型,利用有限元软件进行水动力计算,得到不同水深条件下,风力机平台在风、浪、流载荷联合作用下的频域特性,通过与不附加螺旋侧板情况下的动态特性参数对比,探讨螺旋侧板是否对结构的频响特性起到提升作用。结果表明,附加螺旋侧板后,结构的垂荡和纵摇的运动幅值和所受波浪力均得到了显著抑制;与纵荡和纵摇相比,垂荡运动的幅值和所受波浪力所受影响更显著;水深变化对结构响应的幅值有着显著影响。     

潮流能发电平台的水动力特性及动力响应分析

运用水动力学软件AQWA对潮流能发电平台进行了频域分析,得到不同重心高度、不同水深、遭遇不同浪向角条件下平台各自由度幅值响应算子随波浪圆频率的变化曲线。再对平台进行了风浪流联合作用下的时域耦合分析,研究不同系泊角度对平台运动响应和系泊缆张力的影响。计算结果表明:纵荡幅值响应算子峰值随浪向角的增大而逐渐减小,横荡幅值响应算子峰值随浪向角的增大而增大,纵荡、横荡上主要表现为与波浪的低频共振,浪向角较小会产生较大的垂荡运动、纵荡运动、纵摇运动,浪向角较大会导致较大的横摇运动;水深小于10m时,海底对波浪的反射作用对平台纵荡和艏摇运动影响比较明显;小范围内的重心高度变化对平台各自由度幅值响应算子影响较小。当系泊角度为45°时,系泊系统对平台运动响应的控制更好,且此时系泊系统的安全系数最大,主要系泊缆受力更加合理,平台更安全。     

传统Spar平台垂荡主共振时非线性耦合响应的研究

考虑瞬时波面影响,建立了Spar平台垂荡-纵摇运动的参数激励耦合运动方程,应用多尺度法导出了波浪频率接近垂荡固有频率时响应方程的一阶摄动解并做数值验证。计算结果显示:当波浪高度达到一定值时,纵摇运动中出现大量的亚谐频率成分;随着波浪高度进一步增大,纵摇运动将出现明显的幅值跳跃现象。研究结果表明,能量渗透现象是纵摇运动失稳的主要原因,波浪激励力矩对于纵摇本身的贡献很小。由于垂荡模态存在能量饱和现象,多余的垂荡能量将会向纵摇模态转移,导致出现大幅值的纵摇运动。     

ALE动网格法在流固耦合数值模拟中的应用

为了解决流固耦合问题中的物体大幅度运动带来的困难,采用ALE(Arbitrary Lagrange-Euler)动网格方法跟踪自由表面上浮体的运动.计算表明:浮体在无粘流体中的垂荡与弹簧-物体的振动模型理论解符合得较好;浮体在粘性流体中的自由横摇为阻尼运动,其横摇角度随时间的增加而减小,且在不同初始角度下运动系统的固有周期相当.在有外力力矩激励时,外力力矩的周期与系统的固有周期相当时浮体横摇运动趋于共振状态,运动幅度最大.计算结果验证了计算程序的可靠性与精度.本文方法为ALE方法应用于流体-多浮体耦合运动分析奠定了基础.     

系泊多体浮式码头的非线性动力特性

多体浮式码头由很多小的浮体模块组成,浮体间通过连接件相连,连接件可提供吸引和排斥力,首尾两端用缆索锚泊于海底.不同于传统分析方法,将每一个浮体模块当做一个独立振子,引入两个相对独立的耦合参数来分别表示浮体间的吸引作用和排斥作用,再考虑波浪和系泊缆作用,得到多体浮式码头动力响应的非线性分析模型.以长度600米的链式四浮体码头为例,利用四阶Runge-Kutta法求解码头运动微分方程,得到码头的运动响应情况和最佳的耦合参数范围区间.数值结果发现,吸引和排斥耦合的相互作用使得多体浮式码头模型表现出丰富的动力学现象,比如幅值跳跃、滞后同步、反向同步等.最后,为进一步揭示耦合多浮体系统的集体动力学行为,引入一个相似函数,该函数可表征两时间序列的相关性强弱,从而判断多体浮码头响应同步化协同效应程度.该方法尝试从网络动力学的角度去研究多体浮式码头的非线性动力特性,为多体浮式码头的初步设计提供理论参考.     

晃荡

本文列举了诸多工程领域中的液体共振运动现象,详细探讨了船舱中伴有剧烈流动的晃荡问题.描述了基于理论分析的非线性多模态方法,该方法便于波动稳定性分区、多分支解和物理稳定性的研究.强调了方形舱、垂向圆柱舱以及球形舱内伴有旋转和混沌(不规则波动)的三维流动的重要性.晃荡引起的砰击涉及到各种各样的内流条件,这些条件随液体深度与舱体长度之比而变化.针对棱柱状LNG舱,讨论了许多与流体力学和热力学参数、影响砰击载荷效应的水弹性以及模型实验缩尺比的物理现象.     

Sloshing

本文列举了诸多工程领域中的液体共振运动现象,详细探讨了船舱中伴有剧烈流动的晃荡问题.描述了基于理论分析的非线性多模态方法,该方法便于波动稳定性分区、多分支解和物理稳定性的研究.强调了方形舱、垂向圆柱舱以及球形舱内伴有旋转和混沌（不规则波动）的三维流动的重要性.晃荡引起的砰击涉及到各种各样的内流条件,这些条件随液体深度与舱体长度之比而变化.针对棱柱状LNG舱,讨论了许多与流体力学和热力学参数、影响砰击载荷效应的水弹性以及模型实验缩尺比的物理现象.     

晃荡（英文）

本文列举了诸多工程领域中的液体共振运动现象,详细探讨了船舱中伴有剧烈流动的晃荡问题.描述了基于理论分析的非线性多模态方法,该方法便于波动稳定性分区、多分支解和物理稳定性的研究.强调了方形舱、垂向圆柱舱以及球形舱内伴有旋转和混沌(不规则波动)的三维流动的重要性.晃荡引起的砰击涉及到各种各样的内流条件,这些条件随液体深度与舱体长度之比而变化.针对棱柱状LNG舱,讨论了许多与流体力学和热力学参数、影响砰击载荷效应的水弹性以及模型实验缩尺比的物理现象.     

Non-linear dynamic responses of elastic two-story structures with partially filled liquid tanks

This paper deals with the non-linear vibrations of an elastic two-story structure with two liquid tanks installed under horizontal harmonic excitation. The influence of the configuration of the two rectangular tanks on the response of the structure is investigated. In the theoretical analysis, Galerkin's method is applied to derive the equations of motion for the structure and the modal equations for sloshing, while considering the non-linear liquid forces. Then, van der Pol's method is used to determine the frequency response curves. Three cases are investigated: In the first case two tanks are installed, one on the top and one on the second story of the structure, in the second case one tank is installed on top, and in the third case two tanks are installed on top. The theoretical results of the first case are compared with those of the second and third cases. In the numerical calculations, it is found that Hopf bifurcations occur near the tuning frequency and then amplitude modulated motion appears in both the first and third cases. It is thus concluded that multiple tanks yield less effectiveness in suppressing the vibrations of the structure. The experimental data confirm the validity of the theoretical results for the first and third cases.     

燃料大幅晃动等几何分析仿真及航天器耦合动力学研究

现代航天器肩负许多周期长且复杂的航天任务,通常需要携带大量的液体燃料.贮箱中液体燃料大幅晃动会严重影响航天器的姿态稳定性和控制精度,是现代航天器耦合动力学建模和精确控制研究的重要问题.本文提出了一种新的液体大幅晃动数值仿真方法,采用等几何分析方法对贮箱内气体和液体整体进行建模和空间离散,采用压力修正的分步法对控制方程进行时间离散,结合水平集方法划分气体和液体区域并且实时追踪液体晃动自由面.提出了一种质量修正方法以消除水平集函数演化产生的液体质量误差.基于燃料大幅晃动等几何分析仿真方法,对携带太阳能帆板的充液航天器进行动力学建模和耦合运动数值仿真.对于太阳能帆板的振动问题则采用Kirchhoff-Love板理论建模和模态分析法数值求解.通过将数值仿真结果与解析解对比,证明了本文给出方法的正确性.本文还对燃料大幅晃动下的航天器刚-液-柔耦合运动进行了数值仿真,发现液体晃动对航天器的姿态变化和结构振动的幅值和频率具有不可忽视的影响.     

多储液腔航天器刚液耦合动力学与复合控制

采用复合控制方法对充液航天器的姿态和轨道机动进行高精度控制.通过傅里叶-贝塞尔级数展开法,将低重力环境下液体的弯曲自由表面的动态边界条件转化为简单的微分方程,其中耦合液体晃动方程的状态向量由相对势函数的模态坐标和波高的模态坐标组成.通过广义准坐标下的拉格朗日方程得到航天器刚体部分运动和液体燃料晃动的耦合动力学方程,提出了自适应快速终端滑模策略和输入整形技术相结合的复合控制器,并分别用于控制携带有一个燃料腔和四个燃料腔航天器的轨道机动和姿态机动.通过数值模拟来验证控制器的效率和精度.结果表明,对于多储液腔航天器,如果在设计航天器的姿态和轨道控制器时没有充分考虑燃料晃动效应,那么在受控航天器系统中将会出现刚-液-控耦合问题并导致航天器姿态不稳定.而本研究中的复合自适应终端滑模控制器可以实现航天器机动的高精度控制并有效抑制液体燃料晃动.     

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.     

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。     

Experimental findings of the suppression of rotary sloshing on the dynamic response of a liquid storage tank

In liquid storage tanks, rotary sloshing occurs when the frequency of the lateral harmonic load is near the lowest frequency of the tank–liquid system. Rotary sloshing is a type of sloshing that modifies the tank response, which may cause instabilities of the tank wall. However, the consequences of rotary sloshing for the development of strain in the tank wall have not been elucidated. This paper presents an experimental determination of the effects of rotary sloshing on the development of strain and acceleration at various locations of a storage tank. A low-density-polyethylene tank containing water was tested using a shake table. Nine excitations with frequencies near the first free-vibration frequency of the tank–water system were employed. To suppress rotary sloshing, a high-density foam floating lid was utilised as a barrier. Results reveal rotary sloshing boosts not only the development of both hoop and axial strain but also the acceleration in the horizontal direction perpendicular to the excitation. The lid reduced the maximum hoop and axial strain by 500% and 400%, respectively compared to that when rotary sloshing occurs. Moreover, the lid suppressed the nonplanar sloshing by erasing the first three free-vibration frequencies of the tank–water system without the lid.     

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.     

Linear wave-induced dynamic structural stress analysis of a 2D semi-flexible closed fish cage

Closed fish cages in the sea are proposed as a new concept in marine aquaculture, replacing the conventional net cages in order to meet ecological challenges related to fish lice and escapes. A closed fish cage can be compared to a floating tank structure with an internal free surface. Several types of closed cages have been suggested, and they are categorised according to structural properties as flexible membrane structures (fabric), semi-flexible structures (glass fibre) and rigid structures (steel or concrete). To be able to develop safe and reliable structures, more knowledge is required on the seakeeping behaviour of closed cages in waves and the structural response to the wave loads. This paper builds on a theory presented in Strand and Faltinsen (2019) on the linear wave loads on a 2D closed flexible fish cage. A modelling error has been found in Strand and Faltinsen (2019), however, all the main conclusions are in hold. The error has been corrected in the model in the present paper. The present paper extends the model to include bending in the structural model to be able to handle semi-flexible structures where bending stiffness is significant. In this paper, the linear theory of a 2D semi-flexible closed fish cage in waves is developed and analysed to investigate the structural response of the semi-flexible closed cage in waves. We have compared a quasi-static analysis with a fully coupled hydroelastic analysis to investigate if it is a valid and conservative assumption to assume that the stresses in the structure can be assumed quasi-static. If a hydroelastic analysis is necessary or not, is dependent on the stiffness of the structure. We have investigated what happens with the stress in the curved beam part of the closed fish cage for increasing and decreasing stiffness relative to a reference composite structure. One stiffer and two softer cases have been analysed. One major concern for the structural stresses in a closed cage is the effect of sloshing. Sloshing is internal wave motion inside the cage and have multiple resonance periods. The results indicate that to use the quasi-static assumption in structural stress calculation is conservative within the given frequency range for all examined stiffnesses and frequencies, except the frequencies very close to the second sloshing frequency. Close to the second sloshing frequency for all the examined stiffnesses, a localised peak can be observed in the coupled hydroelastic results. The second sloshing frequency is a frequency connected to a symmetric sloshing mode. Rigid body motion is not affected at the symmetric sloshing frequency for an assumed rigid structure, and are therefore also not visible in the stress results from the quasi-static analysis. The structural stress in irregular sea was calculated. These results show no indication of increased stress close to the second sloshing frequency. However, this is not a surprising result since the stress peak is very localised in frequency, and the accumulated effect on the stress standard deviation is therefore small.     

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.