应用比例边界有限元法求解狭缝对双箱水动力的影响

比例边界有限元法(SBFEM)是一种半解析数值分析的新方法,既融合了有限元法和边界元法的优点,又有其特有的优点。用该方法可求解有限水深下狭缝对双箱水动力作用的影响,为波浪与多浮体超大型结构的相互作用探索一些规律。整个计算域划分成2个无限子域和4个有限子域,并利用加权余量法在各个子域上推导了SBFEM的积分方程;计算了4个数值算例并与边界元等其它数值方法进行了比较,验证了该方法是一种用很少单元便能得到精确结果的高效方法。应用SBFEM对不同箱体宽度、不同狭缝宽度、不同吃水深度条件的双箱作了计算,得出了狭缝对双箱水动力干涉影响的一些规律,对超大型浮体水动力分析和结构设计具有一定的参考价值。     

Hydrodynamic coefficients of a floating,truncated vertical cylinder in shallow water

The paper seeks to apply the methodology of matched asymptotic expansions to obtain analytical solutions for hydrodynamic properties of a circular cylindrical platform (truncated circular cylinder) in extremely shallow water. By matching potentials of the fluid flows outside and under the cylinder bottom with the inner flow near its edge the radiation problems are solved for heave, surge and pitch motions. Closed asymptotic formulae are derived for all hydrodynamic coefficients of the floating cylinder, which include the first-order terms in the gap height. The formulae are discussed and shown to compare well with numerical results published in literature.     

混合模块大型浮式结构系统耦合动力响应分析

针对具有天然岛礁庇护或人工庇护的温和海洋环境,提出了一种混合模块大型浮式结构系统,即水动力性能更优的半潜式模块作为内侧主模块,消波效果更优的箱式模块作为外侧浮式防波模块和波浪能发电模块.波浪能装置利用外侧箱式模块与内侧半潜式模块的相对纵摇运动进行发电.考虑模块间多体水动力耦合效应和连接器机械耦合效应,基于ANSYS-AQWA程序重点研究了典型海况下混合5模块串联浮式结构系统的动力响应特征.结果表明,外侧箱式模块和波浪能发电装置能有效减弱内侧半潜式主模块运动响应、连接器动力响应和系泊缆绳张力,并且提供一定的能源供给.所得研究成果可为模块化超大型浮式结构系统的防波—发电集成系统设计提供参考.     

Hydrodynamic characteristics of floating toroidal bodies

The paper deals with the linearized exciting wave forces and hydrodynamic coefficients of a toroidal body floating in water of finite depth. For the solution of the diffraction and the radiation problems the flow field around the body is subdivided into ring-shaped fluid regions, in each of which axisymmetric eigenfunction expansions for the velocity potential is made. By implementing Galerkin's method the various potential solutions are matched and numerical results concerning the exciting wave forces and the hydrodynamic coefficients in all modes of motion are obtained.     

高等级海况条件下移动式海上基地动力响应分析

针对半潜式超大型浮式结构中典型的移动式海上基地(Mobile Offshore Base,MOB)在高等级海况下的动力响应问题展开研究。在MOB结构"刚性模块-柔性连接构件(Rigid Modules and Flexible Connectors,RMFC)"模型的前提下,根据动力学基本原理,经理论推导并计算得到MOB分别在6、7、8级海况的随机波激励下,其上各模块的动力响应位移结果。详细分析了MOB结构同一模块在不同海况条件下的动力响应位移随浪向角及连接构件刚度的变化规律。研究成果可为半潜式超大型浮式结构动力响应研究及结构优化设计提供一定的技术支撑。     

Hydrodynamic coefficients in heave of two concentric surface-piercing truncated circular cylinders

The paper aims at presenting a solution of the linearized hydrodynamic radiation problem for two concentric, free surface-piercing truncated vertical cylinders that are forced to independently oscillate in heave in finite depth waters. For the solution of the problem, the flow field around the two bodies is subdivided into ring-shaped fluid regions, in each of which axisymmetric eigenfunction expansions for the velocity potential are made. By implementing Galerkin's method, the various potential solutions are matched and extensive numerical results concerning the hydrodynamic and interaction coefficients in heave for various geometrical configurations presented and discussed.     

Wave driven free surface motion in the gap between a tanker and an FLNG barge

When two vessels are moored side-by-side with a narrow gap between them, intense free surface motions may be excited in the gap as a result of complex hydrodynamic interactions. These influence the motions of the two vessels, and the forces in any moorings. The present paper uses first and second order wave diffraction analysis to investigate this phenomenon. Key theoretical aspects of the numerical analysis are first summarised, including the vital need to suppress “irregular frequency” effects; and results are given to validate the code used. The case of a tanker alongside a large floating FLNG barge is then considered in detail.     

Asymptotic analysis of the interaction between linear long waves and a submerged floating breakwater of wavy surfaces

In this work, we carried out an asymptotic analysis, up to the second order in a regular expansion, of the interaction of linear long waves with an impermeable, fixed, submerged breakwater composed of wavy surfaces. Below the floating breakwater, there is also a step with a wavy surface. The undulating surfaces are described by sinusoidal profiles. The effects of three different geometric parameters — the amplitude of the wavy surfaces and the submerged length and width of the structure — on the reflection and transmission coefficients are analyzed. The hydrodynamic forces are also determined. The governing equations are expressed in dimensionless form. Using the domain perturbation method, the small wavy surfaces of the breakwater are linearized. The wavy surfaces of the breakwater generate larger values of the reflection coefficient than those obtained for breakwaters with flat surfaces, and the largest values of this coefficient are obtained when the length of the breakwater is of the same order of magnitude as the wavelength. The asymptotic solution is compared with the theoretical solutions that have been reported in the specialized literature and with a numerical solution. The present mathematical model can be used as a practical reference for the selection of the geometric configuration of a submerged floating breakwater under shallow flow conditions.     

多模块超大型浮体中连接器刚度对其运动响应的影响

多模块超大型浮体一般由连接器连接,实现海上浮动机场等功能。实际操作中,为约束超大型浮体模块之间的相对运动,连接器通常将承受非常巨大的载荷,给连接器的制造带来巨大的困难。通过对不同环境力情况下不同刚度连接器的研究,分析了连接器刚度对超大型浮体模块之间相对运动与连接器自身承受载荷的影响。研究发现,随着柔性连接器刚度的增加,连接器对超大浮体模块之间相对运动的约束逐渐增强,同时连接器也将承受更大的载荷;此外,较大的连接器刚度,并不利于抵抗模块之间的冲击载荷;最后,连接器刚度的改变会影响其固有振动频率,因此需要尽可能避开共振区域,否则系统容易出现较大的振动,导致模块间相对运动过大,连接器过载。研究结果确定了连接器刚度最佳匹配原则,以指导连接器的工程设计。     

Wave radiation by a floating rectangular structure in oblique seas

The linear wave radiation by a long floating rectangular structure in oblique seas of finite depth is investigated by use of the method of separation of variables and the eigenfunction expansion matching method. Analytical expressions for the radiated potentials, wave forces and hydrodynamic coefficients are given. The correctness of these expressions is verified through two specific examples investigated previously by other numerical methods. Using the present analytical solution, the hydrodynamic effects of the angle of incidence, the draft and the width of the structure on the wave forces and hydrodynamic coefficients are discussed in detail which may provide some useful information for the design of rectangular structures in oblique seas.     

Modelling of multi-bodies in close proximity under water waves—Fluid forces on floating bodies

This work presents two-dimensional numerical results of the dependence of wave forces of multiple floating bodies in close proximity on the incident wave frequency, gap width, body draft, body breadth and body number based on both viscous fluid and potential flow models. The numerical models were validated by the available experimental data of fluid oscillation in narrow gaps. Numerical investigations show that the large amplitude responses of horizontal and vertical wave forces appear around the fluid resonant frequencies. The convectional potential flow model is observed to un-physically overestimate the magnitudes of wave forces as the fluid resonance takes place. By introducing artificial damping term with appropriate damping coefficients μ∈[0.4, 0.5], the potential flow model may work as well as the viscous fluid model, which agree with the damping coefficients used in our previous work for the predication of wave height under gap resonance. In addition, the numerical results of viscous fluid model suggest that the horizontal wave force is highly dependent on the water level difference between the opposite sides of an individual body and the overall horizontal wave force on the floating system is generally smaller than the summation of wave force on each body.     

Wave radiation and diffraction by a two-dimensional floating body with an opening near a side wall

The radiation and diffraction problem of a two-dimensional rectangular body with an opening floating on a semi-infinite fluid domain of finite water depth is analysed based on the linearized velocity potential theory through an analytical solution procedure. The expressions for potentials are obtained by the method of variation separation, in which the unknown coefficients are determined by the boundary condition and matching requirement on the interface. The effects of the position of the hole and the gap between the body and side wall on hydrodynamic characteristics are investigated. Some resonance is observed like piston motion in a moon pool and sloshing in a closed tank because of the existence of restricted fluid domains.     

Hydroelastic analysis of pontoon-type circular VLFS with an attached submerged plate

This paper is concerned with the hydroelastic analysis of a pontoon-type, circular, very large floating structure (VLFS) with a horizontal submerged annular plate attached around its perimeter. The coupled fluid–structure interaction problem may be solved by using the modal expansion method in the frequency domain. It involves, firstly, the decomposition of the deflection of a circular Mindlin plate with free edges into vibration modes that are obtained analytically. Then the hydrodynamic diffraction and radiation forces are evaluated by using the eigenfunction expansion matching method which can also be done in an exact manner. The hydroelastic equation of motion is solved by the Rayleigh–Ritz method for the modal amplitudes, and then the modal responses are summed up to obtain the total response. The effectiveness of the attached submerged annular plate in reducing the motion of VLFS has been confirmed by the analysis.     

Radiation and diffraction of linear water waves by an infinitely long submerged rectangular structure parallel to a vertical wall

The radiation and the diffraction of linear water waves by an infinitely long floating rectangular structure submerged in water of finite depth with leeward boundary being a vertical wall are analyzed in this paper by using the method of separation of variables. Analytical expressions for the radiated and diffracted potentials are derived as infinite series with unknown coefficients determined by the eigenfunction expansion matching method. The expressions for wave forces and hydrodynamic coefficients are given. A comparison is made between the results obtained by the present analytical solution and those obtained by the boundary element method. By using the present analytical solution, the hydrodynamic influences of the submergence, the width, the thickness of the structure, and the distance between the structure and the wall on the wave forces and hydrodynamic coefficients are discussed in detail.     

Analytical Study on Transmission and Reflection of Non-Linear Shallow Water Waves

The analytical study is made by using the method of matched asymptotic expansions on the transmission and reflection of solitary waves and cnoidal waves on two-dimensional floating bodies. The solutions give explicitly the variation pattern of the transmitted waves and the characteristics of the reflected waves, including the wave profile, amplitude, phase shift and evolution. The effects of the gap between the body and the sea bottom on the transmission and reflection of those waves are also discussed.     

Waves at the sea surface generated by a flow over an underwater obstacle

We study wave perturbations appearing at the surface of a two-layer fluid flowing around an underwater obstacle in the lower layer of the fluid. The obstacle is modeled as a point source. A class of asymptotic solutions was obtained that demonstrate that realistic conditions of the open sea and the given parameters of the source in the neighborhood of the source of hydrodynamic perturbations allow for the formation of two types of surface waves. The waves of the first type only slightly depend on the stratification, and, in the conditions of the real sea, they are almost not observed. The characteristics of the second type of waves were repeatedly recorded in field experiments during radar and optical monitoring of the sea surface.     

两层流体中矩形箱浮体的附加质量和阻尼系数

研究了两层流体中矩形箱浮体的辐射问题。基于特征函数匹配理论,针对矩形箱浮体的三种振荡运动模式(横荡、垂荡和横摇),建立两层流体中矩形箱浮体辐射势的求解方法,导出矩形箱浮体附加质量和阻尼系数的计算公式。对所建立的求解模型进行了数值计算分析,结果表明在矩形箱浮体的某个振荡频率范围内,流体的分层效应对其附加质量和阻尼系数有显著影响的。     

Numerical simulation of flow around a circular cylinder close to a flat seabed at high Reynolds numbers using a k–ε model

High Reynolds number flows around a circular cylinder close to a flat seabed have been computed using a two-dimensional standard high Reynolds number k–ε turbulence model. The effects of gap to diameter ratio, Reynolds number and flat seabed roughness for a given boundary layer thickness of the inlet flow upstream of the cylinder have been investigated. Hydrodynamic quantities and the resulting bedload transport have been predicted, and the vortex shedding mechanisms have been investigated. Predictions of hydrodynamic quantities around a cylinder located far away from the bed (so that the effect of the bed is negligible) are in satisfactory agreement with published experimental data and numerical results obtained for the flow around an isolated cylinder. Results for lower Reynolds number flows have also been computed for comparison with the high Reynolds number flow results. Overall it appears that the present approach is suitable for design purposes at high Reynolds numbers which are present near the seabed in the real ocean.     

Diffraction–radiation of multiple floating structures in directional waves

The dynamics of multiple floating structures have been studied using the finite element method. The emphasis is on the hydrodynamic behaviour of multiple bodies under a multi-directional wave field. A two-dimensional numerical model has been adopted to evaluate hydrodynamic coefficients and forces in an oblique wave field. The responses in sway, heave and roll modes are reported. The linear filter technique is then used to extrapolate the responses under directional waves. The effect of mean wave direction and directional homogeneity on the hydrodynamic behaviour of the structure is studied. Based on the present study, it is found that the two-dimensional model is applicable to investigate the wave-structure interaction problems of the type herein considered.     

有航速浮体时域分析的混合边界元法

给出了一种联合瞬态格林函数和Rankine源进行有航速浮体时域水动力分析的混合——边界元方法。在三维混合边界元方法中,通过一个匹配面将流体域划分为内域和外域,在内域中使用Rankine源以模拟直壁或非直壁船体及线性或非线性自由面条件,在外域中使用瞬态格林函数以满足自由面条件和远方辐射条件。使用该方法计算了一个有航速潜没圆球的波浪力,和解析结果的比较证明了该方法的正确性。进一步给出了一个有航速Wigley船的水动力结果,计算结果稳定,没有外传波向内反射的现象发生。