CFD simulation of 3-dimensional motion of a ship in waves: application to an advancing ship in regular heading waves

A new computational fluid dynamics simulation method has been developed for the unsteady motion of a ship advancing in waves. The objective is to evaluate the added resistance and predict the performance of a ship in waves. In this study, a finite volume method, in the framework of a boundary-fitted grid system, is employed. The motion of the ship is solved with six degrees of freedom by using the hydrodynamic forces and moments obtained from the solution of the simulation method. The marker–density–function method is employed to calculate the nonlinear free surface. This method is applied to the coupled motion problem of heaving and pitching. Received for publication on Nov. 15, 1999; accepted on Nov. 18, 1999     

三维流体动力方法计算穿浪双体船的船体响应

穿浪双体船船型复杂,航速较高,要准确预报其波浪载荷比较困难,但同时对于结构设计而言又非常重要。基于线性势流理论,采用三维流体动力学方法在时域上计算了穿浪双体船的运动响应和波浪载荷,时域计算结果经过傅立叶变换,在频域上分析了其响应特征。通过与规则波中试验结果和数值计算结果进行比较分析,表明用该方法计算穿浪双体船的船体响应可以获得比较满意的结果,可应用于同类船舶的波浪载荷预报。     

Numerical simulation of three-dimensional breaking waves

Three-dimensional (3D) wave breaking around bodies of complex geometry has been numerically investigated by use of two types of Navier-Stokes solvers, namely the finite-difference and the finite-volume methods employing rectangular and curvilinear coordinate systems, respectively. Both methods employ the density-function technique to capture the free surface location and can cope with complicated free surface configurations such as breaking waves. The accuracy of the density-function method is examined through the comparison with experimental results, and it is confirmed to be satisfactory when the grid spacing and the time increment are sufficiently small. New computational methods are applied to several problems including 3D breaking waves around ships and wave diffraction around offshore structures. The computed results show good agreement with experimental results indicating that wave breaking phenomena are successfully simulated. The qualitative accuracy, however, could be improved by including the dissipating effect of breaking waves.     

Dynamic interaction of parallel moving ships in close proximity

Nowadays,there are many studies conducted in the field of marine hydrodynamics which focus on two vessels traveling and floating in sufficiently close proximity to experience significant interactions.The hydrodynamic behavior of parallel moving ships in waves is an interesting and important topic of late.A numerical investigation has been carried out for the prediction of wave exciting forces and motion responses of parallel moving ships in regular waves.The numerical solution was based on 3D distribution technique and using the linear wave theory to determine the exciting forces and ship＇s motion.The speed effects have been considered in the Green function for more realistic results.The numerical computations of wave exciting forces and motion responses were carried out for a Mariner and Series 60 for the purpose of discovering different Froude numbers and different separation distances in head sea conditions.Based on the numerical computations,it was revealed that the sway,roll and yaw have a significant effect due to hydrodynamic interaction.     

The choice of speed and clearance for RAS on 3D method

In this paper, a 3D source distribution technique is used to calculate the coupled motions between two ships which advance in the wave with the same speed. The numerical results of coupled motions for a frigate and a supply ship have a good agreement with the experimental results. Based on the 3D coupled motions of two ships, a spectral analysis is employed to clearly observe the effect of speed, clearance and wave heading on the significant relative motion amplitude (SRMA) of two ships.The method presented in this paper will be helpful to select suitable clearance, speed and wave heading for underway replenishment at sea(RAS).     

深海系泊浮体物面非线性时域耦合动力分析

文章基于三维时域势流理论和弹性细长杆理论,研究并提出了深海系泊浮体物面非线性时域耦合动力分析方法。该方法采用时域物面非线性理论方法在瞬态位置直接时域模拟系泊浮体所需水动力,结合有限元方法计算系泊缆索的动力响应,利用异步耦合方法实现浮体和系泊缆索的时域耦合动力求解。既满足系泊浮体时域水动力耦合,又满足系泊浮体和系泊缆索动力耦合。通过对二阶非线性不规则波作用下深海系泊半潜式平台的时域耦合响应特性进行研究,将不同海况下物面非线性时域耦合静力响应和动力响应与间接时域耦合动力响应的三种方法计算结果进行比较。研究结果表明,系泊缆索动力响应明显,平台瞬态空间位置对垂荡低频运动影响较大,有必要在平台瞬时湿表面采用动力响应方法进行深海系泊浮体时域耦合响应分析。     

浅水中航行船舶的水动力系数

本文利用切片理论数值研究了浅水中前进船舶的水动力系数.为计及水深的影响,采用简单格林函数方法求解剖面水动力系数,提出了满足辐射条件的一种较方便的数值方法.计算了一数学船型的水动力系数,并与有关文献结果比较验证了数值方法的可行性.数值结果显示了水底效应对航行船舶水动力的影响,为进一步研究浅水航行船舶的耐波性提供了基础.     

两船在波浪中耦合运动的三维频域理论研究

本文采用三维势流理论求解两船在波浪中相互干扰的耦合运动。基于源分布方法，两船船体表面被划分成若干面元，在每一面元上进行等源强分布。为了验证该理论以及算法的可行性，计算了有限水深中两圆柱的水动力干扰，其数值计算结果与其他理论结果吻合较好。其次计算了两船在波浪中无航速与有航速情况的水动力干扰，其结果与单船结果以及双船试验结果进行比较。同时深入研究了纵横向间距以及航速变化对水动力干扰的影响，得出间距与航速不仅是水动力干扰的重要参数，而且对两船中的小船影响尤为重要。本文的研究提出了一种有效而又简单的方法预报两船在波浪中的耦合运动，为分析海上航行补给所涉及的水动力问题提供了有效的手段。     

Time-domain simulation for water wave radiation by floating structures （Part A）

Direct time-domain simulation of floating structures has advantages： it can calculate wave pressure fields and forces directly; and it is useful for coupled analysis of floating structures with a mooring system. A time-domain boundary integral equation method is presented to simulate three-dimensional water wave radiation problems. A stable form of the integration free-surface boundary condition （IFBC） is used to update velocity potentials on the free surface. A multi-transmitting formula （MTF） method with an artificial speed is introduced to the artificial radiation boundary （ARB）. The method was applied to simulate a semi-spherical liquefied natural gas （LNG） carrier and a semi-submersible undergoing specified harmonic motion. Numerical parameters such as the form of the ARB, and the time and space discretization related to this method are discussed. It was found that a good agreement can be obtained when artificial speed is between 0.6 and 1.6 times the phase velocity of water waves in the MTF method. A simulation can be done for a long period of time by this method without problems of instability, and the method is also accurate and computationally efficient.     

顶浪中船舶水动力计算与运动模拟研究

基于计算流体动力学(CFD)方法建立数值波浪水池,对顶浪中航行船舶的水动力与运动进行数值计算研究。推导出一种船舶在波浪中航行的数值模拟的波浪环境表达方法并进行模拟验证,计算不同航速下顶浪中Wigley-III船模所受的水动作用力,以及顶浪中航行的Wigley-III船模的运动。通过将计算结果与DUT(Delft University of Technology)相关的试验数据进行比较,吻合良好。研究表明:基于数值波浪水池的数值模拟较试验更容易实现和控制,能够获得船体周围详细的流场信息,在波浪中舰船水动力性能与运动的研究等方面具有广泛的适用性。     

Analysis of hydrodynamic characteristics for arbitrary multihull ships advancing in waves

Multihull vessels have emerged as popular alternatives to conventional monohull ships for high-speed crafts. However, the bridging structures connecting the hulls are vulnerable to various wave actions and the wave impact on the bottom of them is the most serious problems associated with multihulled vessels. In this study, prediction of relative wave elevations under the bridging structures is investigated for multihull ships traveling with forward speed in waves. A computer code YNU-SEA using the three-dimensional (3D) Green function method with forward speed has been developed and used to analyze the hydrodynamic radiation and diffraction forces and motion responses for high-speed catamarans in waves. The results of the present calculations are compared with those of previous calculations as well as with experimental results. The numerical results reveal that the present computer code can be used as a powerful tool for the accurate numerical computation of seakeeping problems for multihull ships advancing in waves. Numerical calculations of wave pattern are also carried out including wave interactions between the hulls to analyze the effects of hull form on the free surface flow around catamarans advancing in waves. The analysis of the wave pattern allows the determination of relative wave height including radiation and diffraction waves. Finally, some discussions are included based on these numerical results which may be helpful for the accurate prediction of relative wave height and wave breaking load on the deck associated with multihull ships.     

桁架式Spar平台与系泊/立管系统的全时域非线性耦合动态分析

开发了对浮式平台系统进行耦合动态分析的全时域程序。采用二阶时域方法计算水动力荷载,在此方法中,对物面边界条件和自由水面边界条件进行泰勒级数展开,利用Stokes摄动展开分别建立相应的一阶、二阶边值问题,而且此边值问题的计算域不随时间变化。采用高阶边界元方法计算每一时刻流场中的速度势,利用四阶预报校正法对二阶自由水面边界条件进行数值积分。在自由表面加入一个人工阻尼层来避免波浪的反射。对于系泊缆索/立管/张力腿的动力分析,在一个总体坐标系中对控制方程进行描述,采用基于细长杆理论的有限元方法进行求解。在耦合动态分析中,采用Newmark方法对平台和系泊缆索/立管/张力腿的运动方程同时进行求解。利用开发的耦合分析程序对一个桁架式Spar平台的运动响应进行了数值模拟,给出了平台的位移和系泊缆索/立管上端点的张力,并得到了一些重要结论。     

基于细长体公式的Truss SPAR在波流中的运动响应预报方法

利用细长体公式和刚体非线性运动方程建立Truss SPAR在波浪与流中运动响应预报方法。通过波浪自由表面和SPAR中心线方程构造辅助函数,迭代计算Truss SPAR瞬时湿长度。根据SPAR主体形状特点和流场中水质点运动规律,分段高效积分Truss SPAR上的水动力载荷。通过Runge-Kutta-Fehlberg方法求解运动方程,得Truss SPAR在波浪与流中的运动响应。对一座Truss SPAR在不同波流工况中的运动响应进行了预报,结果显示波浪和流使Truss SPAR产生了明显漂移运动和振荡运动,漂移运动的大小与流的方向有关,而振荡运动的幅值与波浪的方向有关。     

A free surface frequency domain green function with viscous dissipation and partial reflections from side walls

The free-surface Green function method is widely used in solving the radiation or diffraction problems caused by a ship or ocean structure oscillating on the waves. In the context of inviscid potential flow, hydrodynamic problems such as multi-body interaction and tank side wall effect cannot be properly dealt with based on the traditional free-surface frequency domain Green function method, in which the water viscosity is omitted and the energy dissipation effect is absent. In this paper, an open-sea Green function with viscous dissipation was presented within the theory of visco-potential flow. Then the tank Green function with a partial reflection from the side walls in wave tanks was formulated as a formal sum of open-sea Green functions representing the infinite images between two parallel side walls of the source in the tank. The new far-field characteristics of the tank Green function is vitally important for improving the validity of side-wall effects evaluation, which can be used in supervising the tank model tests.     

Efficient calculation of slamming pressures on ships in irregular seas

An efficient method for calculation of the slamming pressures on ship hulls in irregular waves is presented and validated for a 290-m cruise ship. Nonlinear strip theory was used to calculate the ship–wave relative motions. The relative vertical and roll velocities for a slamming event were input to the slamming calculation program, which used a two-dimensional boundary element method (BEM) based on the generalized 2D Wagner formulation presented by Zhao et al. To improve the calculation efficiency, the method was divided into two separate steps. In the first step, the velocity potentials were calculated for unit relative velocities between the section and the water. In the next step, these precalculated velocity potentials were used together with the real relative velocities experienced in a seaway to calculate the slamming pressure and total slamming force on the section. This saved considerable computer time for slamming calculations in irregular waves, without significant loss of accuracy. The calculated slamming pressures on the bow flare of the cruise ship agreed quite well with the measured values, at least for time windows in which the calculated and experimental ship motions agreed well. A simplified method for calculation of the instantaneous peak pressure on each ship section in irregular waves is also presented. The method was used to identify slamming events to be analyzed with the more refined 2D BEM method, but comparisons with measured values indicate that the method may also be used for a quick quantitative assessment of the maximum slamming pressures.     

Monolithic coupling of the pressure and rigid body motion equations in computational marine hydrodynamics

In Fluid Structure Interaction(FSI) problems encountered in marine hydrodynamics, the pressure field and the velocity of the rigid body are tightly coupled. This coupling is traditionally resolved in a partitioned manner by solving the rigid body motion equations once per nonlinear correction loop, updating the position of the body and solving the fluid flow equations in the new configuration. The partitioned approach requires a large number of nonlinear iteration loops per time–step. In order to enhance the coupling, a monolithic approach is proposed in Finite Volume(FV) framework,where the pressure equation and the rigid body motion equations are solved in a single linear system. The coupling is resolved by solving the rigid body motion equations once per linear solver iteration of the pressure equation, where updated pressure field is used to calculate new forces acting on the body, and by introducing the updated rigid body boundary velocity in to the pressure equation. In this paper the monolithic coupling is validated on a simple 2D heave decay case. Additionally, the method is compared to the traditional partitioned approach(i.e. "strongly coupled" approach) in terms of computational efficiency and accuracy. The comparison is performed on a seakeeping case in regular head waves, and it shows that the monolithic approach achieves similar accuracy with fewer nonlinear correctors per time–step. Hence, significant savings in computational time can be achieved while retaining the same level of accuracy.     

Numerical and experimental analysis of bow flare slamming on a Ro–Ro vessel in regular oblique waves

A method for the prediction of slamming loads on ship hulls is presented and validated for a 20-knot, 120-m car carrier. A nonlinear strip theory is used to calculate the relative motions of ship and wave. The relative vertical and roll velocities for a slamming event are given as input to the slamming calculation program, which is based on a generalized two-dimensional Wagner formulation and solved by the boundary element method. The method is fast and robust. Model tests of a car carrier have been carried out in regular head, bow, and bow quartering waves of various heights. Slamming on two panels in the upper part of the bow flare has been studied. It has been found that the water pile-up around the bow due to the forward speed of the vessel significantly increases the slamming pressures. A simplified way of including this effect is presented. When the calculated slamming pressures are corrected for 3D effects, they compare well with the measured data. Since the effect of the wave elevation due to the forward speed and the effect of three-dimensional flow act in opposite directions, excluding both of them produced results that also agreed quite well with the experiments, especially for the most severe slamming events.     

Nonstationary response of floating structures to random waves

Even if ocean waves are treated as a stationary random process, dynamic responses of floating structures to random waves at the transient state are always nonstationary. When nonstationary response statistics is desired, a common technique is to apply Monte Carlo simulations; however, its implementation is costly in computational time. Analytically, this article develops an efficient method for computing nonstationary response statistics, including evolutionary power spectrum and time-varying mean-square values. Assuming a hydrodynamic software has been employed to get various frequency response functions, a prerequisite of the proposed method is to get the elevation-to-motion transfer function formulated in its pole-residue form. The proposed method is applicable to arbitrary wave spectrum and has been based on pole-residue operations implemented in the Laplace domain to obtain closed-form solutions for the response evolutionary power spectrum. Numerical examples choose a single-degree-of-freedom Spar model and a six-degree-of-freedom Floating Production Storage and Offloading model to a Pierson–Moskowitz wave spectrum, and the correctness of the computed mean-square values is verified by Monte Carlo simulations.     

迎浪状态下三体船垂荡和纵摇运动参数

运用基于势流理论的三维频域格林函数方法对三体船的垂荡、纵摇运动进行参数研究,讨论三体船附体位置对垂荡、纵摇运动的影响。将计算结果与实验结果进行对比,比较结果表明数值计算是可靠的。设计了十二种不同附体位置配置方案,并计算出各个方案在三个航速下的垂荡和纵摇频率响应函数曲线。计算结果表明:(1)航速对三体船的垂荡、纵摇运动影响剧烈,随着航速提高,运动幅值增加明显;(2)当三体船的航速为零时,附体位置对垂荡、纵摇的影响不明显,随着三体船航速的增加,附体位置对垂荡、纵摇影响也随之变大;(3)附体纵向位置变化对垂荡、纵摇的影响要大于其横向位置变化的影响。     

数值波浪水池及顶浪中船舶水动力计算

基于粘流理论建立了三维数值波浪水池,模拟了非线性波浪,并对规则波顶浪中前进的拘束船模的水动力进行了计算.数值模拟中,控制方程-RANS方程和连续性方程使用有限体积法离散,非线性自由面采用VOF方法处理;在入口边界模拟柔性造波板运动产生入射波,使用位于波浪水池尾部的人工阻尼区消波.给出了非线性规则波的模拟结果以及规则波顶浪中前进的拘束船模的水动力计算结果,并与理论解及DUT(Delfi University of Technology)的试验数据进行了比较,二者吻合良好.