Prediction of slamming pressure considering fluid-structure interaction. Part II: Derivation of empirical formulations

This is Part II in a series of papers. Part I [1] investigated the slamming responses of flexible flat stiffened steel and aluminum plates using the nonlinear explicit finite element code LS-Dyna with the Multi-Material Arbitrary Lagrangian-Eulerian (MMALE) solver. Subsequently, a simplified finite element FSI model of water hitting structures that is realistically close to the slamming phenomenon occurring on the bottom part of offshore structures was proposed. The proposed FSI methodology presented in Part I was verified by comparison with the relevant test data. It was evident that the use of the proposed numerical method presented in Part I was very effective for a benchmarking investigation of slamming load considering the hydroelastic effect. However, the method required much effort in terms of computation time and power analysis resources. The present study, Part II, aimed, as an alternative to the FSI analysis approach, to develop empirical formulae for prediction of slamming loads acting on deformable flat stiffened plates used in marine applications. This paper begins by describing the limitations of the existing approaches based on theoretical, experimental and even numerical studies conducted in the past for estimation of slamming loads. Next, it presents, based on the simulation methodology developed in Part I, rigorous parametric studies that had been performed on actual scantlings of marine-seagoing structures. The effects of structural geometry and water impact velocity on slamming pressure are then investigated in detail. Subsequently, the parametric results are analyzed and utilized to derive empirical formulations for the prediction of slamming loads acting on flat stiffened plates of marine structures. The accuracy and reliability of the proposed formulations are established by comparison with the results of the test and other existing formulations. The proposed formulations are expected to be used for the purposes of the design without any time-consuming FSI analysis of advanced and optimal structures that are robust to slamming.     

A study on slamming pressure on a flat stiffened plate considering fluid–structure interaction

Normally, the design slamming pressure on the bottomof a semi-submersible-type floating rig is determined in a simple way using the relative speed obtained from an air-gap analysis. However, few studies have taken a thorough, robust, and deep-background approach to the estimation of design pressure. To investigate the slamming pressure on the bottom of a semi-submersible rig, a simplified deformable stiffened plate of a zero-degree deadrise angle is simulated using the nonlinear FEM software LS-DYNA, which can take the influence of fluid–structure interaction (FSI) into account. Various parametric studies are carried out to examine the effects of structural flexibility, coupling stiffness, mesh size, velocity, stiffener size, and air cushion. The pressure response on the plate by the coupling of fluid and structure is studied and the FSI effect of each parameter is discussed. Then, equivalent transient and static loads that result in the same maximum or permanent deformation as FSI are evaluated for design purposes through a series of parametric studies.     

船首外飘砰击设计载荷直接计算

文章结合三维线性势流理论和砰击速度的长期分析方法,求解出船体外飘位置的设计砰击速度;以首垂线和静水面交点处的设计砰击速度为目标值,给出了用于确定船首外飘砰击设计载荷的等效设计波,进而得到了设计状态下船体外飘剖面与波面相对运动关系;将船体剖面与波面间的相对运动关系等效转化为船体剖面与静水面的相对运动,利用显式有限元方法实现了外飘剖面砰击设计载荷的预报。针对直接计算方法中涉及的设计砰击速度、砰击压力和砰击压力系数,对比分析了文中结果和相应的规范值或试验值,论证了文中船舶外飘砰击压力设计载荷直接计算方法的合理性。     

Equivalent design pressure for ship plates subjected to moving slamming impact loads

When a ship navigates at sea, the slamming impact can generate significant load pulses which move up along the hull plating. The effect of the moving pressure has so far not been explicitly considered in the Rules and Regulations for the Classification of Ships. Based on a modal superposition method and the Lagrange equation, this paper derives analytical solutions to study the elastic dynamic responses of fully clamped rectangular plates under moving pressure impact loads. The spatial variation of the moving slamming impact pressure is simplified to three types of impact loads, i.e. a rectangular pulse, a linearly decaying pulse and an exponentially decaying pulse. The dynamic responses of fully clamped rectangular plates under the moving slamming impact pressure are calculated in order to investigate the influence of the load pulse shapes and moving speed on the plate structural behaviour. It is found that the structural response of the plate increases with the increase of the moving speed. The response of the plate subjected to a moving pressure impact load is smaller than the case when the plate is subjected to a spatially uniform distributed impact load with the same load amplitude and load duration. In order to quantify the effect of the moving speed on the dynamic load, a Dynamic Moving Load Coefficient (DMLC) is introduced as the ratio between the dynamic load factor for the moving impact load and that under the spatially uniform distributed impact load. An expression for DMLC is proposed based on analyses of various scenarios using the developed analytical model. Finally an empirical formula which transforms the moving impact loads to an equivalent static load is proposed.     

参数横摇下大型集装箱船外飘砰击的近似计算方法（英文）

Since the research of flare slamming prediction is seldom when parametric rolling happens, we present an efficient approximation method for flare slamming analysis of large container ships in parametric rolling conditions. We adopt a 6-DOF weakly nonlinear time domain model to predict the ship motions of parametric rolling conditions. Unlike previous flare slamming analysis, our proposed method takes roll motion into account to calculate the impact angle and relative vertical velocity between ship sections on the bow flare and wave surface. We use the Wagner model to analyze the slamming impact forces and the slamming occurrence probability. Through numerical simulations, we investigate the maximum flare slamming pressures of a container ship for different speeds and wave conditions. To further clarify the mechanism of flare slamming phenomena in parametric rolling conditions, we also conduct real-time simulations to determine the relationship between slamming pressure and 3-DOF motions, namely roll, pitch, and heave.     

Hydroelastic analysis of a rectangular plate subjected to slamming loads

A hydroelastic analysis of a rectangular plate subjected to slamming loads is presented. An analytical model based on Wagner theory is used for calculations of transient slamming load on the ship plate. A thin isotropic plate theory is considered for determining the vibration of a rectangular plate excited by an external slamming force. The forced vibration of the plate is calculated by the modal expansion method. Analytical results of the transient response of a rectangular plate induced by slamming loads are compared with numerical calculations from finite element method. The theoretical slamming pressure based on Wagner model is applied on the finite element model of a plate. Good agreement is obtained between the analytical and numerical results for the structural deflection of a rectangular plate due to slamming pressure. The effects of plate dimension and wave profile on the structural vibration are discussed as well. The results show that a low impact velocity and a small wetted radial length of wave yield negligible effects of hydroelasticity.     

船艏底部砰击压力概率预报方法研究

在Ochi概率统计方法的基础上探索一种适合于非常规船型船艏底部砰击压力的概率预报方法。该方法在时域中计算船舶在波浪中的运动响应,基于Msc.Dytran计算砰击压力系数,在此基础上采用蒙特卡罗法对砰击压力的概率特性进行预报。分析了砰击时的船波相对速度和波面倾角对压力系数的影响。研究结果表明,船舶在静水和波浪中的砰击压力特性有很大差异,在波峰与波谷处发生砰击时产生的砰击压力大于在波面其它位置产生的压力值,相对速度对砰击压力系数的影响在波面不同位置呈现出不同的特点。     

波浪对有梁面板结构冲击作用数值模拟

采用计算机数值模拟方法,在FLUENT软件计算平台上建立了二维规则波数值波浪水槽,对透空有梁面板结构底面受到的波浪冲击作用进行研究。数学模型采用RANS方程和k-ε湍流模型,以VOF方法处理自由表面。通过对不同工况的数值模拟和试验结果比较,验证了模型的造消波性能和应用的有效性。通过计算,得到了波浪冲击过程中波陡、超高和板宽各因素对冲击压强的影响。最后在已有冲击压强计算公式基础上提出了修正公式,以更准确地预报波浪的冲击荷载,深入认识波浪冲击机理。     

大型集装箱船迎浪航行的外飘砰击压力研究

该文采用直接计算法研究一艘大型集装箱船迎浪航行时的外飘砰击压力特点。先基于三维势流理论Rankine面元法,应用DNV船级社的商业软件Wasim计算出该船在压载时不同海况下以不同航速航行时在非规则波中时域内的非线性运动响应时历,再根据Wagner型冲击理论计算得到该集装箱船艏外飘区域的外飘砰击压力。最后,依据概率随机理论,得到不同工况下的外飘砰击概率以及外飘砰击压力极值,并分析概率和极值特点。     

超大型集装箱船艏艉砰击强度直接计算方法

超大型集装箱船的船艏显著外飘、船艉宽平外悬,使其在恶劣海况下航行时容易发生严重的砰击。为确保船体艏艉部结构在砰击中不发生损坏,需要研究作用到艏艉外板上的砰击压力,并以此为设计载荷来校核外板和相连结构的强度。目前对集装箱船砰击局部强度的校核要求仍以经验公式为主,但是为提高对超大尺度船舶强度校核的可靠性,近年来推出了砰击的直接分析方法。本文初步分析了砰击直接分析方法的基本原理,并运用该方法对20,000 TEU集装箱船的艏、艉部砰击压力以及最小板厚要求进行了研讨,其结果可为超大型集装箱船的结构设计提供重要的参考。     

Hydroelastic slamming

An overview of the many water-impact (slamming) problems in ship and ocean engineering is given. Theoretical and experimental drop tests of horizontal and nearly horizontal elastic plates are reviewed. It is shown that maximum pressure cannot be used to estimate maximum slamming-induced stresses when maximum pressure is large, because dynamic hydroelastic effects then become important. Further, the significance of hydroelasticity increases with decreasing dead-rise angle, increasing impact velocity, and increasing the value of the highest local natural period of the structure. It is emphasized that the slamming problem must be hydrodynamically studied from a structural point of view. Comparisons between theory and full-scale measurements of slamming-induced local strains in the wet-deck of a catamaran are presented. The importance of the rigid body vertical accelerations and the influence of the side-hulls on the impact velocity are pointed out. Received: October 4, 2000     

平底结构砰击压力的分布

物体以一定的速度撞击水面,会受到水的砰击力的作用.这种砰击压力持续的时间通常很短,但量值有时会很大.本文利用仿真软件对平底刚性结构的入水问题进行了研究,建立了二维有限元模型,对平底结构分别以不同速度等速入水的情况进行了计算.计算发现,在结构入水前瞬间,作用在结构上的压力迅速增大,在到达原静水面位置稍后的位置处达到峰值.压力持续的时间随着结构入水速度的增加而减小;砰击面上的压力分布也不是均匀的,在平底中心处最大,向两侧逐渐减小.作者在对砰击压力的作用时间和在砰击面上的分布情况做了详尽的分析后,导出了砰击压力在砰击面上分布和持续时间的计算公式.     

基于船波相对运动的船艏砰击仿真方法

在分析船波相对运动表达式的基础上计算船艏典型剖面的船波相对运动,探讨船艏入水过程中的砰击问题,对比船体某剖面3种入水仿真模型计算所得的砰击载荷,讨论三维外形和航行速度对船艏剖面砰击外载荷的影响。在该分析中,船体在规则波浪中的运动用基于三维势流理论的水动力软件AQWA计算获得,船波相对运动通过理论推导计算获得,用对船艏结构施加强迫运动的方式模拟船波相对运动的真实过程。采用An—sys／Ls—Dyna软件的流固耦合分析进行入水仿真,流体划分为ALE体积网格,船艏视为刚体,划分为Lagrange有限元网格。对比结果表明：在三维模型中,相邻剖面引起剖面最大压力点处的液面变化对该点的砰击压力有增大效果,航速有增大剖面砰击压力的作用,减小船艏底部纵向斜升角有利于降低砰击压力。     

不规则波对平板冲击作用数值模拟研究

文章采用数值模拟方法,建立了基于FLUENT软件的二维不规则波浪数值模型,探讨了波浪对水平板结构的作用机理.模型中采用RANS方程和标准k-ε方程,采用VOF方法重建自由液面.通过数值模拟复演了波浪冲击水平板结构的过程,将数值模拟结果与实验数据进行比较,验证了模型的可靠性.经过计算和分析,研究了波浪冲击平板过程中的冲击压力和流场特性,得到了冲击压力和流场的分布规律.分析了波陡,净空及板宽等参数对冲击压力和流场的影响.最后,给出了波浪冲击压力与相应水质点垂直速度间的统计关系,并对河海大学原有冲击压力的计算公式进行了改进,提出了新的冲击压力公式.研究结果表明:冲击压力峰值与相应的水质点垂直速度的平方成正比,修正后的冲击压力公式更为合理、可行.论文工作将对准确预测冲击载荷,掌握更多的冲击机理具有重要意义.     

空气层对高速三体船连接桥砰击压力峰值影响二维仿真研究

利用LS-DYNA仿真软件研究了高速三体船连桥结构的砰击问题,建立了二维有限元模型,对高速三体船结构以不同的速度进行等速入水的情况进行了计算.研究发现,存在于高速三体船主船体和辅船体与水之间的空气层充当了缓冲垫,大大减小了连接桥的砰击压力峰值.通过对压力峰值与速度平方比值的无量纲系数的回归分析,发现该系数随着入水速度的增加成二次指数递减趋势;其次是假想不存在空气层进行仿真计算,与考虑空气层的计算进行比较分析,量化空气层对高速三体船连接桥砰击压力峰值的影响,并得出随着砰击速度的增加,空气层对压力峰值影响逐渐变小.     

三维回转体入水砰击载荷预报

采用数值仿真的方法研究了三维刚性回转体的入水问题,分析了不同回转角度的回转体的砰击压力峰值的变化规律,并研究了以一定初速度入水时,结构质量对砰击压力的影响。计算结果表明,恒速下降时,砰击压力峰值随角度的增加而下降;初速下降时,随着结构质量增加,砰击压力峰值先急剧增加,然后区域平稳。最后提出了不同回转角度、不同质量系数的回转体在初速下降与恒速下降时砰击压力峰值的预报公式。     

箱形驳船底部砰击载荷及结构加强要求研究

针对箱形驳船,建立了三维水动力计算模型,对箱形驳船系列在设计海况下的船体与波浪之间的相对运动和相对速度做了短期预报。运用Ochi船舶砰击理论,分析了箱形驳船在不同吃水和拖航速度时船首砰击的发生概率和砰击压力极值等,并讨论了吃水、拖航速度等因素对箱形驳船底部砰击特性的影响。在此基础上,提出了箱形驳船首部砰击加强的临界航速建议,为箱形驳船规范中有关底部砰击载荷的修订提供参考和依据。     

砰击载荷作用下船底肋骨等效设计压力的确定

通过一个船体二维分段的自由落体试验,测量模型入水速度、砰击压力和结构响应,获得模型底部板架在砰击载荷作用下的响应特征;对结构模型在均布静压力作用下的应力响应进行有限元分析;比较试验和计算得到的应力响应,获得作用在模型肋骨上的砰击压力的折减系数,从而使该结构在设计时仍可按常规的静力计算方法进行强度校核。该折减系数与船体入水速度成线性关系,在已知船体设计入水速度和试验压力分布时,可以获得船体设计均布静压力。     

Bottom slamming on heaving point absorber wave energy devices

Oscillating point absorber buoys may rise out of the water and be subjected to bottom slamming upon re-entering the water. Numerical simulations are performed to estimate the power absorption, the impact velocities and the corresponding slamming forces for various slamming constraints. Three buoy shapes are considered: a hemisphere and two conical shapes with deadrise angles of 30° and 45°, with a waterline diameter of 5 m. The simulations indicate that the risk of rising out of the water is largely dependent on the buoy draft and sea state. Although associated with power losses, emergence occurrence probabilities can be significantly reduced by adapting the control parameters. The magnitude of the slamming load is severely influenced by the buoy shape. The ratio between the peak impact load on the hemisphere and that on the 45° cone is approximately 2, whereas the power absorption is only 4–8% higher for the 45° cone. This work illustrates the need to include slamming considerations aside from power absorption criteria in the buoy shape design process and the control strategy.     

Development of simplified method for prediction of structural response of stiffened plates under explosion loads

During their lifetime, marine structures may be exposed to accidental loadings such as from collisions or explosions, as well as environmental loadings such as from slamming, sloshing and green water. Such loadings can cause damage to structures. Therefore, to minimize such damage, advanced and robust design guidelines should be formulated. Among those loads, in this study, explosions imparting an impulsive pressure loading containing a rapid increase in pressure and a short duration that can cause serious casualties, property losses, and marine pollution were considered. In this paper, a practical and robust method for damage assessment of marine structures exposed to explosion loads based on a single degree of freedom (SDOF) system and numerical simulations is proposed. The SDOF method was improved by introduction of new and better idealization resistance for the system and consideration of the effect of strain-rate, and subsequently was verified by a numerical method developed using the commercial ABAQUS software package. The numerical method was itself validated by comparison with relevant pulse pressure test data available in the open literature (good correlation was shown). Based on the validated numerical models, a rigorous parametric study of the structural response of stiffened plates having actual scantlings of offshore structures was performed. The numerically obtained maximum deformations were compared with the results from the improved SDOF method in a parametric study, and the variation of both methods was verified. Finally, simple yet accurate and reliable formulations for prediction of structural response were empirically derived. These formulations are expected to be usefully employed as a first-hand tool for prediction of damage extent of marine structures (including offshore structures) due to explosion loads.