A potential based panel method for 2-D hydrofoils

A potential based panel method for the hydrodynamic analysis of 2-D hydrofoils moving beneath the free surface with constant speed without considering cavitation is described. By applying Green's theorem and the Green function method, an integral equation for the perturbation velocity potential is obtained under the potential flow theory. Dirichlet type boundary condition is used instead of Neumann type boundary condition. The 2-D hydrofoil is approximated by line panels which have constant source strength and constant doublet strength distributions. The free surface condition is linearized and the method of images is used for satisfying this free surface condition. All the terms in fundamental solution (Green function) of perturbation potential are integrated over a line panel. Pressure distribution, lift, residual drag and free surface deformations are calculated for NACA4412, symmetric Joukowski and van de Vooren profile types of hydrofoil. The results of this method show good agreement with both experimental and numerical methods in the literature for the NACA4412 and symmetric Joukowski profile types. The lift and residual drag values of the van de Vooren profile are also presented. The effect of free surface is examined by a parametric variation of Froude number and depth of submergence.     

A potential based panel method for 2-D hydrofoils

A potential based panel method for the hydrodynamic analysis of 2-D hydrofoils moving beneath the free surface with constant speed without considering cavitation is described. By applying Green's theorem and the Green function method, an integral equation for the perturbation velocity potential is obtained under the potential flow theory. Dirichlet type boundary condition is used instead of Neumann type boundary condition. The 2-D hydrofoil is approximated by line panels which have constant source strength and constant doublet strength distributions. The free surface condition is linearized and the method of images is used for satisfying this free surface condition. All the terms in fundamental solution (Green function) of perturbation potential are integrated over a line panel. Pressure distribution, lift, residual drag and free surface deformations are calculated for NACA4412, symmetric Joukowski and van de Vooren profile types of hydrofoil. The results of this method show good agreement with both experimental and numerical methods in the literature for the NACA4412 and symmetric Joukowski profile types. The lift and residual drag values of the van de Vooren profile are also presented. The effect of free surface is examined by a parametric variation of Froude number and depth of submergence.     

High-speed submerged and surface piercing cavitating hydrofoils, including tandem case

The iterative method that is originally developed before both for two- and three-dimensional single cavitating hydrofoils moving with a constant speed under free surface is applied to the case of high-speed (Froude number up to 6.5) and some figures are given. The method is also extended to include the surface piercing hydrofoils (vertical struts) and the case of tandem hydrofoils into the calculations. The iterative nonlinear method based on the Green's theorem allows separating the cavitating hydrofoil problem(s) and the free surface problem. These two (or three in the case of tandem hydrofoil) problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. The cavitating hydrofoil surface(s) and the free surface are modeled with constant strength dipole and constant strength source panels. The source strengths on the free surface are expressed in terms of perturbation potential by applying the linearized free surface conditions. No radiation condition is enforced for downstream and transverse boundaries. The cavitation number is expressed in terms of Froude number and the submergence depth of the hydrofoil from the free surface. An algebraic grid on the free surface has been described to get a smooth transition between the panels along the direction of uniform inflow and to have a long distance in the downstream direction depending on the wave-length (or Froude number) while keeping the number of panels fixed. First, the method is validated in the case of surface piercing hydrofoil. Then, the effects of high Froude number and the submergence depth of the hydrofoil from free surface on the results are discussed and some figures are given for interested engineers and designers. The method is later applied to the case of tandem hydrofoils and the effects of one hydrofoil on the other are discussed.     

群岛峡道浓盐水排放扩散的三维数值模拟

采用三维潮流温盐数学模型对六横岛附近海域的水动力环境及盐度场分布进行数值模拟,并以实测资料进行验证,所建立模型可以较好地反映该海域潮流动力特征及盐度场的分布情况。利用验证后的三维数学模型,对海水淡化工程浓盐水排放后盐度场分布进行计算,将排放后的盐度分布与工程前进行对比分析,并推算盐升面积及垂向盐度增量。结果表明,海水淡化工程排放的浓盐水对六横岛海域盐度分布的影响主要集中在排水口附近的底层,影响区域呈带状分布,最大盐度增量为1.2左右,且排水口附近海域出现盐度垂向分层。     

Sloshing in a three-dimensional rectangular tank: Numerical simulation and experimental validation

Pressure variations and three-dimensional effects on liquid sloshing loads in a moving partially filled rectangular tank have been carried out numerically and experimentally. A numerical algorithm based on the volume of fluid (VOF) technique is used to study the non-linear behavior and damping characteristics of liquid sloshing. A moving coordinate system is used to include the non-linearity and avoid the complex boundary conditions of moving walls. The numerical model solves the complete Navier–Stokes equations in primitive variables by using of the finite difference approximations. In order to mitigate a series of discrete impacts, the signal computed is averaged over several time steps. In order to assess the accuracy of the method used, computations are compared with the experimental results. Several configurations of both baffled and unbaffled tanks are studied. Comparisons show good agreement for both impact and non- impact type slosh loads in the cases investigated.     

内孤立波作用下半潜平台荷载及其周围流场数值模拟研究

内孤立波对海洋平台的安全运行存在一定的威胁,基于三维数值水槽对内孤立波传播引起的半潜平台受力及其周围流场的分布进行了数值模拟研究.通过与试验对比,分析了入射波幅和分层流体深度比对半潜平台上内孤立波荷载特性的影响规律,验证了数值模拟结果是准确可靠的.研究表明,内孤立波引起的平台荷载会随着内孤立波波幅的增加而增大,随着分层流体深度比的增加而减小.基于对平台周围剖面速度场和三维涡场的演化规律研究,发现在内孤立波传播过程中,平台周围会出现明显的速度减小区,平台周围会有大量的漩涡产生并发生脱落现象.     

基于大涡模拟的波状前缘水翼空化抑制研究

为了降低空化造成的水动力性能损失,基于仿生学原理,参考座头鲸鳍肢剖面形状,将前缘波浪构型引入到水翼设计中,研究波状前缘水翼的非定常空化特性,并探究前缘参数改变对空化控制的效果和规律。选用NACA63₄-021水翼为基准模型,进行前缘参数化重构,设计出3种不同的波状水翼进行对比研究。采用大涡模拟（LES）方法对空化流场进行精细化数值模拟,针对基准水翼和不同波幅与波长参数下的波状水翼开展了空化周期、升阻力系数、压力脉动以及流向涡结构的对比分析。结果发现,波状水翼在抑制空化和降低压力脉动方面都取得了显著效果。其中,3种不同的波状水翼空化抑制率分别为15.7%、18.6%和27.9%,压力脉动幅值分别降低了55.3%、67.3%和74.6%。分析表明,波浪前缘的引入使得空化的分区效应更加凸显,空化从波谷处初生,增大波幅或减小波长都可以加强对空化的抑制效果,并可以提高升力系数以及显著降低水翼表面的压力脉动。前缘波浪构型还将诱发向下游发展的对转涡结构,不同前缘参数的波状水翼涡结构的演化是相似的,空泡发展与溃灭的整个过程对涡结构的发展也具有显著影响。     

Wave motions around different submerged structures

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崎头洋附近群岛水域泥沙特征及悬沙来源分析

依据实测水文泥沙资料分析舟山群岛南部崎头洋附近海域的悬沙与底沙特征,建立该水域二维潮流数学模型,同时根据底沙及悬沙的粒径分布和潮流的运动路径对该海域的悬沙来源做进一步分析.指出崎头洋附近群岛海域的悬沙除部分来源于潮汐动力作用下的底沙起动再悬浮之外,主要是杭州湾附近灰鳖洋水域的泥沙在潮汐动力作用下经群岛西北方向水道进入群岛内部水域的,进而在潮动力作用下经由东南方向水道进入东海及象山港附近水域.     

The motions of a ship in swallow water

A general formulation is given of the hydrodynamic forces on a ship, oscillating about a state of rest in 6df in response to excitation by a harmonic wave in shallow water. A method is described to obtain a numerical approximation of the velocity potential, describing the flow around the moving ship by means of a distribution of discrete three-dimensional sources.With this method it is possible to take the influence of a quay into account.Calculated values of wave excited forces, hydrodynamic coefficients and motions of a 200,000 tdw tanker in shallow water are presented and compared with experimental results.     

Diffraction of multidirectional random waves by multiple rectangular submarine pits

A numerical model is presented to predict the interaction of multidirectional random surface waves with one or more rectangular submarine pits. The water depth is assumed uniform and the method involves the superposition of diffraction solutions based on linearized shallow water wave theory obtained by a two-dimensional boundary integral approach. The incident wave conditions are specified using a discrete form of the Mitsuyasu directional spectrum. The present numerical model has been validated through comparisons with previous theoretical results for regular waves. Good agreement was obtained in all cases. Based on these comparisons it is concluded that the present numerical model is an accurate and efficient tool to predict the wave field around multiple submarine pits and navigation channels in many practical situations.     

Nonlinear simulations of wave-induced motions of a freely floating body using WCSPH method

Nonlinear interactions between waves and floating bodies are investigated using the weakly compressible Smoothed Particle Hydrodynamic (WCSPH) method. An improved algorithm based on the dynamic boundary particles (DBPs) is proposed to treat the moving boundary of the floating body. The force exerted on the floating body boundary particle by the particles surrounding it is evaluated using the volume integration of the stress tensors obtained from the momentum equation in its compact support. The improved WCSPH model is validated by the experimental results. The numerical test cases of the vertical oscillation of a rectangular box, the damped rolling oscillation of a floating box and the wave forces on a fixed rectangular box are then carried out to demonstrate the performance of the proposed model. Finally the evolution in time of the dynamic response of the freely floating body under nonlinear waves are discussed and compared with experimental results.     

长江口南支潮流的一个数值模拟

为了能够精确地拟合天然水域不规则的水陆边界,并能保持有限差分数值计算在矩形网格中进行,本文利用Thompson的数值网格生成技术,在长江口南支七丫口至横沙河段设计了一个椭圆型边界拟合坐标系,并在这个坐标系下建立了平面二维潮流数学模型。通过数值求解此数学模型,实现了计算区域内现状潮流的一个数值模拟,模拟结果表明,模式的设计是成功的。     

A composite numerical model for wave diffraction in a harbor with varying water depth

A composite numerical model is presented for computing the wave field in a harbor. The mild slope equation is discretized by a finite element method in the domain concerned. Out of the computational domain, the water depth is assumed to be constant. The boundary element method is applied to the outer boundary for dealing with the infinite boundary condition. Because the model satisfies strictly the infinite boundary condition, more accurate results can be obtained. The model is firstly applied to compute the wave diffraction in a narrow rectangular bay and the wave diffraction from a porous cylinder. The numerical results are compared with the analytical solution, experimental data and other numerical results. Good agreements are obtained. Then the model is applied to computing the wave diffraction in a square harbor with varying water depth. The effects of the water depth in the harbor and the incoming wave direction on the wave height distribution are discussed.     

基于MPS方法模拟低雷诺数方柱绕流问题

柱体绕流问题是流体力学领域一个非常经典的问题。当流体流经柱体时,由于黏性的存在,会发生许多复杂的流动现象,如流动分离、涡旋周期性生成与脱落等,经常被作为标准验证算例。同时,柱体绕流广泛存在于实际工程中,并在一定工况下可能对工程产生巨大危害,因此对柱体绕流进行深入研究具有重要意义。研究中,拟将一种无网格类方法——半隐式移动粒子方法(moving particle semi-implicit method,简称MPS)引入到柱体绕流问题的数值研究中,并对不同雷诺数下二维方柱绕流问题进行数值模拟。首先,使用基于MPS方法自主开发的MLParticle-SJTU求解器,结合入口边界条件和出口边界条件,模拟了雷诺数Re分别为40、200和1 000时均匀来流条件下的方柱绕流。随后,将模拟的绕流结果与文献中试验和数值计算结果进行了对比,结果吻合较好,并且在雷诺数为200和1 000时,可以清晰地捕捉到方柱尾流中的卡门涡街现象,验证了MPS方法在柱体绕流问题模拟上的有效性和适用性。     

A composite numerical model for wave diffraction in a harbor with varying water depth

A composite numerical model is presented for computing the wave field in a harbor. The mild slope equation is discretized by a finite element method in the domain concerned. Out of the computational domain, the water depth is assumed to be constant. The boundary element method is applied to the outer boundary for dealing with the infinite boundary condition. Because the model satisfies strictly the infinite boundary condition, more accurate results can be obtained. The model is firstly applied to compute the wave diffraction in a narrow rectangular bay and the wave diffraction from a porous cylinder. The numerical results are compared with the analytical solution, experimental data and other numerical results. Good agreements are obtained. Then the model is applied to computing the wave diffraction in a square harbor with varying water depth. The effects of the water depth in the harbor and the incoming wave direction on the wave height distribution are discussed.     

Research on the Effects of in-Line Oscillatory Flow on the Vortex-Induced Motions of A Deep Draft Semi-Submersible in Currents

A Deep Draft Semi-submersible (DDS) under certain flow conditions could be subjected to Vortex-Induced Motions (VIM), which significantly influences the loads on and life fatigue of the moorings and the risers. To investigate the VIM of a DDS with four rectangular section columns in waves coupled with a uniform current, a numerical study using the computational fluid dynamics (CFD) method was conducted. The issues of the VIM of multi-column floaters can be conveniently converted to the issues of oscillating cylinders in fluid cross flows. This paper looks into the CFD numerical simulation of infinite cylinders having rectangular sections in a two-dimensional sinusoidal time-dependent flow field coupled with a uniform current. The resulted hydrodynamic forces and motion responses in different oscillatory flows plus currents both aligned in the same direction for the incidence of 135° of the DDS relative to the flow are compared with the ones in current only cases. The results show that the VIM response of this geometric arrangement of a DDS with four rectangular columns in a current combined with oscillatory flows is more evident than that in the current only case. The oscillatory flows and waves have the significant influence on the VIM response, forces and trajectory, in-plane motions of the DDS.     

Numerical simulation of the motion of an ice keel in a stratified flow

The results of the three-dimensional numerical simulation for the study of the stratification effect and wave processes associated with it on the drag of the underwater part of the hummocked ice are considered. The numerical model is based on the sampling of equations on a rectangular grid using the immersed boundary method that makes it possible to explicitly describe the interaction of moving ice with a stratified flow. The dependence of the drag force on the Froude number was established based on these calculations. This dependence has expressed points of maximum and minimum. The form of this dependence is common for the considered models of ice keels. The obtained estimations of drag force consistent with the known results of laboratory experiments show the need for the construction of parametrizations of the drag coefficient on the ice–ocean boundary, taking into account wave effects.     

Numerical simulation of fluid–structure interaction using a combined volume of fluid and immersed boundary method

In this work, a combined immersed boundary (IB) and volume of fluid (VOF) methodology is developed to simulate the interactions of free-surface waves and submerged solid bodies. The IB method is used to account for the no-slip boundary condition at solid interfaces and the VOF method, utilizing a piecewise linear interface calculation, is employed to track free surfaces. The combined model is applied in several case studies, including the propagation of small-amplitude progressive waves over a submerged trapezoidal dike, a solitary wave traveling over a submerged rectangular object, and wave generation induced by a moving bed. Numerical results depicting the free-surface evolutions and velocity fields are in good agreement with either experimental data or numerical results obtained by other researchers. In addition, the simplification of the initial free-surface deformation used in most tsunami earthquake source study is justified by the present model application. The methodology presented in the paper serves as a good tool for solving many practical problems involving free surfaces and complex boundaries.