WAVE EQUATION MODEL FOR SHIP WAVES IN BOUNDED SHALLOW WATER

1.　 INTRODUCTIONIn the recentyears,waves in coastal shallow water,generated by marine traffic and in-tensified by port expansion,interaction with structures and reflection of land boundaries,has become a crucial factor affecting waterenvironmentsand engineering operation.In com-parison with the wind waves and ocean swells,waves inside harbor exhibitanomalous waveheight in certain areas.The dominantship waves are hardly dissipated in the harbor due tothe interaction with shorelines,and may…     

浅水域中两船交错运行时的非定常波浪干涉

本文以Green-Naghdi（G-N）方程为基础,采用波动方程／有限元法计算两艘船舶在浅水域交错运动时的非定常波浪干涉特性。把运动船舶对水面的扰动作为移动压强直接包含在Green—Naghdi方程里,以描述运动船体和水面的相互作用。本文以S60 CB=0．6船为算例,给出在两艘船交错运动时,自由面波高,波浪阻力及横向力的变化特征。计算结果发现,当两艘船船首接近时,波浪阻力增加。接着,两艘船船身相向平行航行时,阻力减少。两艘船船尾相遇时,波浪阻力又增加。最后随着两船的远离,波浪阻力趋于正常。两船之间的侧向力呈现相似的变化规律。两船先承受横向排斥力,接着相互吸引,尔后又排斥。最后两船远离,横向力消失。计算结果表明,在两船间距较小和船速较大时,两船间的吸引力相当显著,应该予以充分重视。     

二维浅水狭航道船舶变速航行的有限元计算

本文从二维浅水波方程出发,采用有限元计算船舶变速驶进、驶出大坝升船机承船厢时的水动力学过程.二维浅水波方程理论把行驶船舶对水面的作用力直接加在二维浅水波方程里,以此来计算水表面波动和水平流速.水动力波产生的水动压力又影响到船舶的运动.本文研究船舶和水体的相互作用.它描述了水面波动、水平流速、船舶的纵倾角、船和厢底的最小间隙、以及承船厢受的水体总重量、水动力矩等重要物理量在船舶行驶过程中的变化规律.本文算例的结果和文献[5]给出的实验数据大体一致.计算结果还发现,船舶驶出承船厢时下沉和纵倾的幅度比船只驶进承船厢时要稍大一点.工程上应当予以重视.     

An iterative Rankine BEM for wave-making analysis of submerged and surface- piercing bodies in finite water depth

A 3-D iterative Rankine Boundary Element Method （BEM） for seakeeping problem in time domain is developed in the framework of linear potential theory. Waves generated by both submerged and surface-piercing bodies moving at a constant forward speed in otherwise calm water, and the resultant steady wave pattern, wave profile and resistance are computed to validate this newly-developed code. A rectangular computational domain moving with the same forward speed as the body is introduced, in which an artificial damping beach is installed at an outer portion of the free surface except the downstream side for satisfying the radiation condition. The velocity potential on the ship hull and the normal velocity on the free surface are obtained directly by solving the boundary integral equation, with the Rankine source used as the kernel function. An iterative time-marching scheme is employed for updating both kinematic and dynamic free surface boundary conditions to stabilize the calculation. Extensive results including the wave patterns, wave profiles and wave resistances for a submerged spheroid and a Wigley hull with forward speed are presented to validate the efficiency of the proposed 3-D time-domain higher-order approach. Finally, the sensitivity of ship-generated waves to the water depth is investigated. Computed results show satisfactory agreement with the corresponding experimental data and other numerical solutions.     

解浅水船波问题的方法

本文提出以六重模速度势线化自由面条件解浅水船波问题的方法。作为算例,对Wigley船型进行了实际计算。根据计算结果,讨论了浅水对波形及兴波阻力的影响,给出了浅水影响起始傅氏数、临界傅氏数与水深关系曲线。结果表明,所给水动特性与实验结果吻合,本文方法能较好地对浅水船波问题进行数值模拟。     

基于CFD的船-舵水动力干扰数值研究

该文采用基于RANS方程求解的CFD方法,对匀速直航的船-舵系统的黏性绕流场进行数值模拟,计算了不同船速和不同舵角下的船-舵水动力干扰系数,计算中忽略了自由面兴波及螺旋桨的影响。文中以KVLCC1船、舵模型为研究对象,首先将数值计算的船舶水动力及船-舵水动力干扰系数结果与模型试验数据进行比较,验证了所采用数值方法的有效性;随后,对船-舵系统、裸船体和敞水舵分别进行计算,通过水动力计算结果的比较以及流场分析,对船-舵水动力相互作用进行了数值研究。     

内河航道中船行波在岸坡爬高的数值模拟

该文基于RANS方程、RNG k-ε湍流模型建立数值波浪水池,用VOF法追踪自由面的位置,并模拟了内河航道中船行波的生成、传播、爬高和岸壁反射过程,且与典型断面航道中船行波在岸坡最大爬高和回落的现场测量值进行了比较,验证了数值模型的有效性。通过对航道中船行波进行数值模拟,获得了船行波的波形及其在岸坡上爬高与回落的最大值。分析了船舶吃水、航速和航道岸坡倾角对特征波高以及最大爬高与回落的影响。最后建立了计算船行波特征波高、爬高和回落的经验公式。     

ANALYTIC SOLUTION FOR WAVE DIFFRACTION OF A SUBMERGED HOLLOW SPHERE WITH AN OPENING HOLE

An investigation is carried out on the interaction of surface waves with a submerged sphere having an opening hole in finite-depth water in this article. Based on the linear wave theory, the method of multipole expansions is used to obtain the fluid velocity potential in the form of double series of the associated Legendre functions with the unknown coefficients of an infinite set. In terms of the body surface boundary condition and the matching condition between the inner and outer flows at the hole, the complex matrix equations for the coefficients of the series are established. The infinite sets of matrix equations are solved by truncating the series at a finite number. The hydrodynamic pressure on the structure surface and the exciting forces acting on the structure are graphically presented. The dynamic pressure on the wave front surface of the sphere varies slightly with angle of opening hole increasing, while that on the wave back surface does obviously. When the angles of opening hole are increasing, the absolute values of the complex exciting forces tend to fall as a whole.     

WAVE MAKING COMPUTATION IN TIME DOMAIN FOR MULTI-HULL SHIPS

1. INTRODUCTION For high-speed displacement ships, the wave making at the free surface is an important hydro- dynamic performance. The wave making reduction has attracted more attention for ship designers. The ship wave resistance and ship hull form improvement have been widely investigated. The thin ship theory adopting the Havelock source distribution on the ship centerline plane can be used to analyze the ship wave making profile and the ship wave resistance may be obtained by ship wav…     

不平水底浅水波问题的位移法

该文研究考虑不平水底的二维浅水波问题的位移法。利用水平位移与竖向坐标无关的假定,建立了基于位移的浅水波方程和相应的Hamilton变分原理。针对文中提出的基于位移的浅水波方程,利用有限元和保辛算法建立了相应的计算格式。最后给出一个具有抛物线型河床的浅水周期晃荡算例。数值算例表明该方法可以有效模拟带动边界和不平水底浅水波问题。     

浮体在浅水中运动产生的孤立波

本文对在浅水中以跨临界速度运动的浮体产生的兴波问题作了数值计算，用作者提出的求解浮体波动问题的新方法，将浮体与流体接触的物面作为自由表面处理，使Ｂｏｕｓｓｉｎｅｓｑ方程用于此问题的全域直接数值求解，数值结果使我们得到了新颖的浮体运动产生的孤立波解。     

Hydrodynamic interaction.among hull,rudder and bank for a ship sailing along a bank in restricted waters

By applying a CFD tool to solve the RANS equations, the viscous flow around a model of hull-rudder system towed along a bank in shallow water is numerically simulated. Hydrodynamic forces and moments acting on the ship are calculated for different ship-bank distances and rudder angles. A container ship, KCS, is taken as an example for the numerical study. Under the assumption of low ship speed, the influences of free surface elevation and ship squat are assumed to be negligible. Based on the calculation results, the hydrodynamic interaction among the hull, rudder and bank is analyzed.     

开阔海域越洋海啸波高计算的一种简化方法

该文研究了开阔海域中越洋海啸波高的简化计算方法。基于选取具有一系列断裂带长宽比的震源参数,采用Okada弹性变形理论生成初始海底变形,运用基于有限体积法的非线性浅水方程数值模型,模拟地震激发海啸在4 000 m水深的平底地形上的传播过程。通过监测布置在相对震源中心不同距离及方位角上测点的波面时间序列,研究海啸波高在不同距离及方位角上的分布规律,给出不同断裂带长宽比下越洋海啸传播过程中首波幅值的分布关系式;进一步分析了断裂带长宽比对模型参数的影响,得出了归一化的越洋海啸波高计算经验公式,并与日本2011年海啸实际记录进行对比,验证了该近似方法的有效性。     

移动边界浅水问题的数值研究

移动边界问题是水力计算中难点之一 ,本文用拉格朗日坐标系来描述浅水方程 ,并用二阶Godunov算法求解有移动边界的浅水问题的数值解。在拉格朗日坐标系下 ,移动边界条件十分容易处理 ,数值计算结果表明 ,该方法十分有效     

Hydrodynamic model of vessel-generated currents

The drawdown and return currents of vessels navigating in channels have previously been described by empirical relations or by using physical models. The empirical solutions are generally limited in scope to idealized channel shapes. Physical models are unrestricted in this respect, but have limitations related to expense and scale effects. In this paper, vessel effects are modelled numerically. The vessel's displacement is represented by a moving pressure field. The movement of the pressure field is spatially varied in time, representing a vessel navigating along a channel. The hydrodynamics are described using the two-dimensional shallow water equations, which are modified to account for the effects of the imposed pressure field. A Petrov—Galerkin finite-element scheme using characteristic-based weighting is used to solve the governing equations. This Petrov—Galerkin test function is specifically designed to model flow fields containing large gradients such as those found in the vicinity of the moving vessel. The numerical results for return flows and water surface elevations are compared with flume results of vessel passages.     

二维溃坝波传播和绕流特性的高精度数值模拟

本文建立了二维浅水方程的高分辨率差分模型，即将浅水方程作空间差分分裂，分别沿x、y方向应用组合型的通量限制二阶TVD格式，采用Van Leer的MUSCL型限量函数，用以解决二维溃坝的计算问题.首先分别与一维理论解和其它二维结果的比较，表明本文的方法非常成功.然后对全溃和部分溃情况下的溃坝波传播和绕流问题进行了数值研究，给出了精细的数值结果，揭示了其复杂的运动特性.     

Ship hull optimization based on wave resistance using wavelet method

The ship hull surface optimization based on the wave resistance is an important issue in the ship engineering industry. The wavelet method may provide a convenient tool for the surface hull optimization. As a preliminary study, we use the wavelet method to optimize the hull surface based on the Michel wave resistance for a Wigley model in this paper. Firstly, we express the model's surface by the wavelet decomposition expressions and obtain a reconstructed surface and then validate its accuracy. Secondly, we rewrite the Michel wave resistance formula in the wavelet bases, resulting in a simple formula containing only the ship hull surface's wavelet coefficients. Thirdly, we take these wavelet coefficients as optimization variables, and analyze the main wave resistance distribution in terms of scales and locations, to reduce the number of optimization variables. Finally, we obtain the optimal hull surface of the Wigley model through genetic algorithms, reducing the wave resistance almost by a half. It is shown that the wavelet method may provide a new approach for the hull optimization.     

浅水波-流对直立桩柱作用的分层数值解法

本文采用分层方式，用水气比拟方程计算由于存在桥墩等障碍物而造成的浅水波高度的变化，以此给出水下粘性层内计算域上表面的压力，用传统的N-S方程计算粘性层内的流动，得到了波一流联合作用下桥墩上的压力分布和河床上压力与剪应力分布随时间周期性的变化过程，并得到了一些有意义的结论。     

An iterative Rankine boundary element method for wave diffraction of a ship with forward speed

A 3-D time-domain seakeeping analysis tool has been newly developed by using a higher-order boundary element method with the Rankine source as the kernel function. An iterative time-marching scheme for updating both kinematic and dynamic free-surface boundary conditions is adopted for achieving numerical accuracy and stability. A rectangular computational domain moving with the mean speed of ship is introduced. A damping beach at the outer portion of the truncated free surface is installed for satisfying the radiation condition. After numerical convergence checked, the diffraction unsteady problem of a Wigley hull traveling with a constant forward speed in waves is studied. Extensive results including wave exciting forces, wave patterns and pressure distributions on the hull are presented to validate the efficiency and accuracy of the proposed 3-D time-domain iterative Rankine BEM approach. Computed results are compared to be in good agreement with the corresponding experimental data and other published numerical solutions.     

Numerical simulations of wake signatures around high-speed ships

Navier-Stokes equations are solved to obtain the near field flow and to reveal the generation of droplets due to the breaking of the bow wave. With an adaptive refinement of the Octree mesh, the fine scale flow characteristics, the wave breaking and the splashing are well simulated. For high-speed ships, the V-shape ship wave pattern with the angle smaller than the classical Kelvin angle is confirmed by the present numerical results, which can also be applied to the catamaran. Comparisons of the vertical velocity distributions induced by the mono-hull ship and the catamaran are made at different locations in the wake regions.