不同Legendre函数递推公式对计算球谐函数定积分的影响

针对球谐函数定积分计算中Legendre函数递推问题展开研究,分析了标准向前列推法、Belikov法、跨阶次法、X数法以及顾及麦克劳林级数展开式对球谐函数定积分计算的影响。利用Eigen6c-4地球重力场模型计算扰动引力梯度径向分量,分析不同方法之间的差异。实验表明,不考虑麦克劳林级数展开式时4种方法的相对精度在高纬度地区较差,但计算模型扰动引力径向分量的精度一致,结合麦克劳林级数式可提高高纬度地区定积分计算的相对精度,但会降低中低纬度地区定积分计算的精度,并且对高纬度地区扰动引力径向分量的影响极小,但会严重降低低纬度地区扰动引力梯度计算的精度。     

南海温跃层深度计算方法的比较

基于1986-2008年的中国近海及邻近海域再分析产品(CORA)气候平均海温资料,分别运用S-T法、垂向梯度法和最大曲率点3种温跃层定义计算了南海温跃层上界深度,揭示了南海温跃层季节变化特征。对3种不同定义确定的温跃层上界深度进行比较发现:采用不同定义计算南海温跃层上界深度存在差异,S-T法确定的温跃层上界深度最浅,垂向梯度法其次,最大曲率点法最深;在深水区(水深200 m)运用S-T法计算的温跃层上界深度与垂向梯度法的结果比较一致,都与实际温跃层深度符合较好;在浅水区(水深200 m),垂向梯度法和最大曲率点法可以准确判定无跃区,但对于温跃层深度计算,3种定义误差均较大。     

抛锚贯入深度计算方法比较研究

文中分析了两种计算船舶抛锚贯入深度的方法,分析不同方法的特点及对于不同土参数的敏感性。以海洋20 m水深和25 m水深为例,分别使用两种方法计算不同海底土参数状况下抛锚的贯入深度。基于正交试验原理分别分析了能量法与微分方程法计算抛锚贯入深度时的参数敏感性。结果表明,基于能量方法计算得到的贯入深度大于微分法计算得到的贯入深度,且能量法对于内摩擦角最敏感,而微分法对于土的有效重度最敏感。     

用直接法分析超大型浮体的水弹性响应

探讨了浮舟桥型超大型浮体结构的水弹性响应分析问题。将超大型浮体结构简化成弹性平板模型,用压力分布法计算流体压力,用直接法计算流体-结构系统,给出了它们的数学计算模型。计算表明本计算方法和程序是正确的,并能保证充分的精度,进而计算了更大尺度的超大型浮体,分析了波长、波向等对响应振幅的影响。     

东海夏季跃层深度计算方法的比较

基于31°N和PN断面高分辨率的温度、盐度和密度(CTD)资料,分别选取1992,1998和2001年东海夏季长江径流量偏小、偏大和正常的3个年份,运用4种跃层计算方法计算了2个断面的温跃层和密度跃层上界的深度。计算结果与实际跃层上界深度比较发现,在3种不同条件下,采用垂向梯度法计算的东海夏季跃层上界深度,无论在浅海海区还是深海海区均较为理想。长江径流量偏小和正常的年份,在东海的浅海海区(水深<200m)运用S-T法计算的跃层上界深度与垂向梯度法的结果比较一致,都与实际跃层深度符合较好。在具有高分辨率资料的情况下,垂向梯度法是4种方法中计算东海夏季跃层上界深度的最佳方法。在缺乏高分辨率资料且长江径流量不大时,夏季东海浅海海区也可以运用S-T法计算温跃层和密度跃层上界深度。     

水下运动物体间相互作用力的计算探讨

本文首先用体内奇点分布法建立了水下多个运动回转体的数学模型,基此提出了一种新的计算多物体相互作用力的方法──等价拓展体法,达到考虑粘性、简化边界层计算的目的。以上方法都以两个运动回转体为例作了数值计算与比较。     

浮式结构物二阶波浪力求解方法比较研究

对远场法、近场法和中场法这几种常用的二阶波浪力计算方法进行了总结,并结合算例对它们之间的差异进行了研究,重点分析了网格密度、浮体形状、水深等因素的影响。此外,还对全QTF法和Newman近似这两种不规则波中的二阶力计算方法进行了讨论,比较了不同水深条件下两种方法求得的二阶波浪力谱之间的差异。研究结果表明,远场和中场法给出的结果基本一致,且具有较好的数值稳定性;而近场法受网格密度、浮体形状等因素影响较大;Newman近似给出的结果在频率较低时与全QTF法接近,但在频率较高时存在一定的误差。     

海岸线分维数计算方法及其比较研究

海岸线是分形领域最传统的研究课题 ,但是在目前的海岸线研究中却忽略了一个重要且根本性的问题 ,那就是海岸线分维数不同计算方法之间是否存在着一定的差异 ,根据不同计算方法计算所得的分维数之间是否具有可比性。在概述海岸线分维数计算方法的基础上 ,分析了它们之间的异同 ,并进行了实证研究。指出 :使用量规法、网格法计算所得海岸线分维数结果之间存在着客观的差异 ,文中利用量规法计算所得的海岸线分维数结果大于使用网格法计算所得的海岸线分维数结果。     

有限水深中零航速浮体波浪力计算奇点积分的数值处理方法

使用三维源汇分布法Ⅲ计算有限水深中零航速浮体所受到的波浪力,对两种不同形式的格林函数中所共同存在的奇点问题分别进行了处理。公式推导表明,使用级数形式的格林函数可以使计算更加快捷。最后,对不同尺度的圆柱体进行了验算,在对计算结果与解析解进行了比较之后,工程计算也证明选择格林函数级数计算公式是更令人满意的方案。     

海岸线分维数计算方法及其比较研究

海岸线是分形领域最传统的研究课题，但是在目前的海岸线研究中却忽略了一个重要且根本性的问题，那就是海岸线分维数不同计算方法之间是否存在着一定的差异，根据不同计算方法计算所得的分维数之间是否具有可比性，在概述海岸线分维数计算方法的基础上，分析了它们之间的异同，并进行了实证研究，指出：使用量规法、网格法计算所得海岸线分维数结果之间存在着客观的差异，文中利用量规法计算所得的海岸线分维数结果大于使用网格法计算所得的海岸线分维数结果。     

Response Characteristics of Load on Vessels in Waves

Considering the requirement of direct design and fatigue test for ships and floating structures byuse of FEM technique,a computational procedure of spectral analysis for wave load on the hull surface is de-veloped in this paper.The response of hydrodynamic pressure on the body surface to a designated sea state forships and floating structures is calculated by use of the revised strip method with the hull bound perturbationflow concept.The spectral function of wave load for the defined point on the body surface can be determinedfrom the Wiener-Khinhin theorem and the characteristic load value can be also obtained from spectral mo-ment analysis.A container ship is taken as a computational example and the sample of wave load with a cer-tain probability and corresponding encountered frequency is provided.     

Wall effect of underwater explosion load based on wave motion theories

Owing to the existence of the flow field boundary, the shock wave load near the boundary is different from the freefield shock wave load. In the present paper, the hull plate load subjected to underwater shock wave is investigated based onwave motion theories; in addition, the experimental study of the hull plate load is carried out. According to the theoreticalanalysis of the hull plate pressure, we find that the hull plate pressure oscillates repeatedly and decays rapidly with timepassing, the maximum hull plate pressure is 2/（1＋n） times the maximum free field pressure, where n is the ratio ofimpedance, and the impulse is much smaller than the free field impulse. Compared with the experimental study, thetheoretical results agree well with the experimental data.     

Design of ship's bow form by potential-based panel method

A surface panel method treating a boundary-value problem of the Dirichlet type with the free surface is presented to design a three-dimensional body corresponding to a prescribed pressure distribution. The free surface boundary condition is linearized with respect to the oncoming flow, and computed by four-point finite difference scheme. Sample designs for submerged spheroids and Wigley hull are carried out to demonstrate the stable convergence, the effectiveness and the robustness of the method. The design of a 5500TEU container carrier is performed with respect to reduction of the wave resistance. To reduce the wave resistance, calculated pressure on the hull surface is modified to have the lower fluctuation, and is applied as a Dirichlet type dynamic boundary condition on the hull surface. The designed hull form is verified to have the lower wave resistance than the initial one not only by computation but also by experiment.     

万米级深海陶瓷耐压结构水下内爆流场数值模拟

耐压结构是深海潜器的重要组成部分,但在深海的高压环境中却存在内爆的风险。为研究陶瓷耐压结构水下内爆的流场特性,使用针对可压缩多相流问题开发的开源代码,采用直接数值模拟,应用自适应直角网格,对两种压力条件下的耐压结构水下内爆进行了数值模拟。通过低压模拟结果与理论解和试验值比较,验证了模拟方法的有效性,进而开展万米级深海陶瓷耐压结构水下内爆模拟。分析发现：陶瓷耐压结构发生内爆后,其内部气腔存在多次压缩—反弹现象,深海环境压力越大则反弹越不明显;气腔反弹阶段,在结构外部将产生数倍于深海环境压力的冲击波,且传播速度接近声速;冲击波压力峰值与到球心距离呈负指数幂函数关系;在相同深海环境压力下,耐压结构外部监测点的冲击波压力与球体半径呈正比例关系。     

Computation of wave-making resistance of a catamaran in deep water using a potential-based panel method

This paper presents a potential-based boundary element method for solving a nonlinear free-surface flow problem for a Wigley catamaran moving with a uniform speed in deep water. Since the interior flow of each monohull of the catamaran is different from the exterior flow, both monohulls must be considered as lifting bodies. The pressure Kutta condition is imposed at the trailing-edge of the lifting body by determining the dipole distribution, which generates required circulation on the lifting part. The effects of wave interference and hull separation on the hydrodynamic characteristics of the catamaran hull are analyzed and the validity of the computer scheme is examined by comparing the wave resistance with the numerical results of others. The present method could be a useful design tool for screening the suitable combinations of hull parameters and hull spacing at the preliminary design stage of catamaran hull.     

Numerical investigation of wave elevation and bottom pressure generated by a planing hull in finite-depth water

A numerical investigation of the bottom pressure and wave elevation generated by a planing hull in finite-depth water is presented. While the existing literature addresses the free-surface deformation and pressure field at the seafloor independently, this work proposes a direct comparison between the two hydrodynamic quantities. The dependence of the pressure disturbances at the ocean floor from the waves generated at the free-surface by a planing hull is studied for several values of both the depth and hull Froude numbers. The methodology employed is Smoothed Particle Hydrodynamics (SPH), a numerical technique based on the discretization of the continuum fields of hydrodynamics through mesh-less particles. The SPH code herein chosen is initially validated against experimental data for transom-stern flow. Subsequently, numerical simulations are presented for a planing hull in high-speed regimes. The results show a direct correlation between surface wave dynamics and hydrodynamic pressure disturbances at the seafloor as the value of the Froude number is varied. This is assessed by studying the inverse dependence of the low-pressure wake angle with the Froude number and by comparison of SPH results with similar works in the cited literature.     

Numerical calculation of free-surface potential flow around a ship using the modified Rankine source panel method

A modified Rankine source panel method is presented for solving a linearized free-surface flow problem with respect to the double-body potential. The method of solution is based on the distribution of Rankine sources on the hull as well as its image and on the free surface. An iterative algorithm is used for determining the free surface and wave resistance using upstream finite difference operator. A verification of numerical modeling is made using the Wigley hull and the validity of the computer program is examined by comparing the details of wave profiles and wave making resistance with Series 60 model.     

设计相关动载荷作用下的水下耐压结构拓扑优化

常规耐压结构拓扑优化设计研究主要集中于静水压条件下的设计相关载荷拓扑优化理论及方法。但是,在深海环境下,耐压结构可能面临内爆所产生的冲击载荷,其载荷呈现高频率的周期性变化。为研究载荷变化对耐压结构优化设计的影响,在BILE模型的基础上,结合修正的SIMP插值模型,开展不同频率、设计相关动载荷作用下的水下耐压结构拓扑优化理论及方法研究。设计相关动载荷的难点在于不仅载荷的作用位置和方向在优化过程中发生变化,且其大小也随优化过程进行而发生变化,这是与常规设计相关静载荷本质的不同。通过经典的拱形结构优化算例验证BILE模型在动力学拓扑优化中的可行性,进而研究设计相关动载荷作用下的水下耐压结构的最佳拓扑形式。研究表明,在低频时,圆环型耐压结构无明显变化,但多球交接耐压结构在交接处会出现明显材料聚集;高频时,两者均发生明显变化,得到耐压结构新形式。关于设计相关动载荷作用下的水下耐压结构拓扑优化研究,将对新型水下耐压结构的探索具有一定的工程应用价值。     

The effect of appendages on the hydrodynamic characteristics of an underwater vehicle near the free surface

An underwater vehicle typically has various appendages such as sail, rudders and hydroplanes. These appendages affect the hull hydrodynamic characteristics, including the resistance components and the form of the generated wave due to the motion of the vehicle near the free surface. The effect of the appendages on the hydrodynamic characteristics of an underwater vehicle near the free surface is studied. Initially the DARPPA SUBOFF submarine without the appendages is selected and hydrodynamic characteristics, including the friction resistance, viscous pressure resistance, wave resistance and shape of the created wave on the free surface are calculated for Froude numbers in the range of 0.128–0.84 and non-dimensional submergence depths 1.3, 2.2, 3.3 & 4.4. Then, by adding the appendages and comparing these two conditions, the effect of appendages is obtained. The results of computations indicate that the appendages cause a mean increase of about 16% in the total resistance. This increment is due to viscosity of fluid and also the interaction of the main hull with the appendages. There are no significant changes in the wave pattern and wave making resistance due to the presence of appendages.     

Finite-element computation of wave impact load due to a violent sloshing

A nonlinear sloshing problem is numerically simulated. During excessive sloshing, the sloshing-induced impact load can cause a critical damage on the tank structure. Recently the problem becomes an important research topic in LNG (Liquefied Natural Gas) Tanker and FPSO (Floating Production Storage Offloading) design. In this study, the wave impact load on the structure is obtained numerically by imposing the exact nonlinear free surface conditions and compared with that predicted by Morison's formula. As a theoretical model, a three-dimensional free surface flow in a tank is formulated in the scope of potential flow theory with the exact nonlinear free-surface conditions. A finite-element method based on Hamilton's principle is employed as a numerical method. The problem is treated as an initial-value problem. The nonlinear problem is numerically solved through an iterative scheme at each time step.