具有惯性表面的两层流体的柯西-泊松问题(英文)

This paper is concerned with the generation of waves due to initial disturbances at the upper surface of a two-layer fluid, as the upper layer is covered by an inertial surface and the lower layer extends infinitely downwards. The inertial surface is composed of thin but uniform distribution of non-interacting material. In the mathematical analysis, the Fourier and Laplace transform techniques have been utilized to obtain the depressions of the inertial surface and the interface in the form of infinite integrals. For initial disturbances concentrated at a point, the inertial surface depression and the interface depression are evaluated asymptotically for large time and distance by using the method of stationary phase. They are also depicted graphically for two types of initial disturbances and appropriate conclusions are made.     

存在底部起伏影响的近壁面处双层多孔栅栏陷波研究（英文）

Trapping of oblique surface gravity waves by dual porous barriers near a wall is studied in the presence of step type varying bottom bed that is connected on both sides by water of uniform depths. The porous barriers are assumed to be fixed at a certain distance in front of a vertical rigid wall. Using linear water wave theory and Darcy's law for flow past porous structure, the physical problem is converted into a boundary value problem. Using eigenfunction expansion in the uniform bottom bed region and modified mild-slope equation in the varying bottom bed region, the mathematical problem is handled for solution. Moreover, certain jump conditions are used to account for mass conservation at slope discontinuities in the bottom bed profile. To understand the effect of dual porous barriers in creating tranquility zone and minimum load on the sea wall, reflection coefficient, wave forces acting on the barrier and the wall, and surface wave elevation are computed and analyzed for different values of depth ratio, porous-effect parameter, incident wave angle, gap between the barriers and wall and slope length of undulated bottom. The study reveals that with moderate porosity and suitable gap between barriers and sea wall, using dual barriers an effective wave trapping system can be developed which will exert less wave force on the barriers and the rigid wall. The proposed wave trapping system is likely to be of immense help for protecting various facilities/infrastructures in coastal environment.     

采用高阶边界元法的楔形体变速度入水数值模拟(英文)

A high order boundary element method was developed for the complex velocity potential problem. The method ensures not only the continuity of the potential at the nodes of each element but also the velocity. It can be applied to a variety of velocity potential problems. The present paper, however, focused on its application to the problem of water entry of a wedge with varying speed. The continuity of the velocity achieved herein is particularly important for this kind of nonlinear free surface flow problem, because when the time stepping method is used, the free surface is updated through the velocity obtained at each node and the accuracy of the velocity is therefore crucial. Calculation was made for a case when the distance S that the wedge has travelled and time t follow the relationship s=Dtα, where D and α are constants, which is found to lead to a self similar flow field when the effect due to gravity is ignored.     

Numerical analysis of the hydroelastic behavior of a vertical plate due to solitary waves

Interactions of a vertical elastic plate with fully nonlinear water waves were simulated. Utilizing the mixed Eulerian Lagrangian method for the free-surface flow and the finite element method for the deflection of an elastic plate, a fully coupled scheme for accurately determining fluid–plate motions was developed. Using this scheme, some modifications to the solvers for both fluid and plate were made. A hybrid wave-absorbing beach was installed to prevent wave reflection from the end of the wave tank. A fourth-order Runge–Kutta time-marching scheme with a uniform time step was applied to achieve numerical stability. The method was validated by simulating the wave generated by the initial deformation of a vertical plate and comparing the result with the corresponding analytical solution. For further validation, the hydroelastic behavior of a vertical plate induced by a pulse-type wave (where the initial pulse-type elevation of the free surface is specified) was computed, and the result was compared with another numerical result from a mode-expansion method. The interaction of a surface-piercing plate with nonzero initial free surface was then simulated, and the result was compared with the corresponding linear analytical solution. Finally, the hydroelastic response of a surface-piercing vertical plate due to a solitary wave (generated by actuating the vertical plate at the right end of the tank only at the beginning) was computed and investigated systematically.     

Water wave scattering by a sphere submerged in uniform finite depth water with an ice-cover

Using the multipole method, we formulate the problem of water wave scattering by a submerged sphere in uniform finite water depth with an ice-cover, the ice-cover being modelled as an elastic plate of very small thickness. This leads to an infinite system of linear equations which are solved numerically by standard techniques. The vertical and horizontal forces on the sphere are obtained and depicted graphically against the wave number for various values of the depth of water and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover and also the effect of varying depth of water on these quantities. When the flexural rigidity is taken to be zero, the numerical results exactly coincide with the curves of the vertical and horizontal forces on the sphere for the cases of uniform finite depth water with a free surface.     

Second-order wave run-up on a vertical cylinder adjacent to a plane wall based on the application of quadratic transfer function in bi-directional waves

A numerical model was developed in this study to simulate the wave diffraction caused by an arbitrarily shaped structure in the presence of bi-directional incident waves based on a higher-order boundary element method (HOBEM). Based on the developed model, the wave elevation quadratic transfer function (QTF) in bi-directional waves, which is defined as the second-order wave elevation caused by two incident waves of unit amplitude from two directions, can be determined. The developed model was subsequently used to investigate the wave interaction with a cylinder situated near a vertical wall. The image principle was applied to transform the original problem into an equivalent one of wave diffraction caused by two symmetrical cylinders in open seas exposed to bi-directional incident waves. The second-order wave run-up on the cylinder can then be determined using the wave elevation QTF obtained from an analysis of the equivalent problem. A detailed numerical analysis was then conducted. Numerical results revealed that the presence of the vertical wall can apparently disturb the wave diffraction process from the cylinder, and lead to significantly amplified second-order wave elevation within the region between the wall and cylinder. In addition, the respective contribution from the first- and second-order components to the overall wave elevation around the cylinder was discussed.     

Time-domain TEBEM method for mean drift force and moment of ships with forward speed under the oblique seas

A numerical method for solving 3D unsteady potential flow problem of ship advancing in waves is put forward. The flow field is divided into an inner and an outer domain by introducing an artificial matching surface. The inner domain is surrounded by ship wetted surface and matching surface as well as part of the free surface. The free surface condition for the inner domain is formulated by perturbation about the double-body flow or uniform incoming flow assumption. The outer domain is surrounded by matching surface and the rest free surface as well as infinite far-field radiation boundary. The free surface condition for the outer domain is formulated by perturbation about uniform incoming flow. The simple Green function and transient free surface Green function are used to form the boundary integral equation (BIE) for the inner and outer domains, respectively. Taylor Expansion Boundary Element Method (TEBEM) is utilized to solve the double-body flow and inner domain and outer domain unsteady flow BIE. Matching conditions for the inner domain flow and outer domain flow are enforced by the continuity of velocity potential and normal velocity on the matching surface. Direct pressure integration on ship wetted surface is used to obtain the first-order and second-order wave forces (moments). The numerical predictions on the displacement, added resistance, sway mean drift force and yaw mean drift moment of the modified KVLCC2 ship at different forward speeds are investigated by the proposed TEBEM method. It is also compared with the other numerical results. The physical tank experiment results are also developed to validate the accuracy of numerical tank results. Compared with the experiment solutions, a good agreement can be obtained by TEBEM method.

     

Dynamic adaptive finite element analysis of acoustic wave propagation due to underwater explosion for fluid-structure interaction problems

In this paper, an investigation into the propagation of far field explosion waves in water and their effects on nearby structures are carried out. For the far field structure, the motion of the fluid surrounding the structure may be assumed small, allowing linearization of the governing fluid equations. A complete analysis of the problem must involve simultaneous solution of the dynamic response of the structure and the propagation of explosion wave in the surrounding fluid. In this study, a dynamic adaptive finite element procedure is proposed. Its application to the solution of a 2D fluid-structure interaction is investigated in the time domain. The research includes: a) calculation of the far-field scatter wave due to underwater explosion including solution of the time-depended acoustic wave equation, b) fluid-structure interaction analysis using coupled Euler-Lagrangian approach, and c) adaptive finite element procedures employing error estimates, and re-meshing. The temporal mesh adaptation is achieved by local regeneration of the grid using a time-dependent error indicator based on curvature of pressure function. As a result, the overall response is better predicted by a moving mesh than an equivalent uniform mesh. In addition, the cost of computation for large problems is reduced while the accuracy is improved.     

考虑流固耦合问题的水下爆炸声波传播的动态自适应有限元分析（英文）

In this paper, an investigation into the propagation of far field explosion waves in water and their effects on nearby structures are carried out. For the far field structure, the motion of the fluid surrounding the structure may be assumed small, allowing linearization of the governing fluid equations. A complete analysis of the problem must involve simultaneous solution of the dynamic response of the structure and the propagation of explosion wave in the surrounding fluid. In this study, a dynamic adaptive finite element procedure is proposed. Its application to the solution of a 2D fluid-structure interaction is investigated in the time domain. The research includes: a) calculation of the far-field scatter wave due to underwater explosion including solution of the time-depended acoustic wave equation, b) fluid-structure interaction analysis using coupled Euler-Lagrangian approach, and c) adaptive finite element procedures employing error estimates, and re-meshing. The temporal mesh adaptation is achieved by local regeneration of the grid using a time-dependent error indicator based on curvature of pressure function. As a result, the overall response is better predicted by a moving mesh than an equivalent uniform mesh. In addition, the cost of computation for large problems is reduced while the accuracy is improved.     

具有初始挠度的板架结构承载特性分析

为探讨具有初始挠度的板架结构轴向受压时的承载特性,本文采用MSC.Nastran建立了具有初始挠度的板架结构模型,分析了初始挠度及其大小对结构的影响,根据应力等效原理拟合了挠曲板架结构轴向受压时的相当面积公式。结果表明,随着初始挠度的增加,板架主要变形方式逐渐由压缩转换为弯曲,其承载能力大幅下降;初始挠度越大,板架承载能力越弱;相当面积折减系数随着初始挠度的增加呈现先缓慢减小随后迅速降低最终平减小的变化趋势,结构中横向(垂直于轴向)应力随着初始挠度的增加不断增大。     

浸没式竖直薄平板微振动引起的冰覆海洋波动研究（英文）

In this paper we study the problem of generation of surface waves produced due to a) rolling of the plate and b) presence of a line source in front of a fixed vertical plate. The amplitudes of radiated waves at large distance from the plate, in both cases, are obtained by a suitable application of Green's integral theorem. These are then studied graphically for various values of the ice cover parameter.     

Study on fast calibration of a ULA＇s gain and phase error

Array calibration is important in engineering practice. In this paper, fast calibration methods for a ULA＇s gain and phase errors both in far and near fields are proposed. In the far field, using a single sound source without exact orientation, this method horizontally rotates the array exactly once, performs eigen value decomposition for the covariance matrix of received data, then computes the gain and phase error according to the formulas. In the near field, using the same single sound source, it is necessary to rotate the array horizontally at most three times, build equations according to geometric relations, then solve them. Using the formula proposed in this paper, spherical waves are modified into plane waves. Then eigen values decomposition is performed. These two calibration methods were shown to be valid by simulation and are fast, accurate and easy to use. Finally, an analysis of factors influencing estimation precision is given.     

用naoe-FOAM-SJTU求解器数值模拟船舶在波浪上的操纵运动问题（英文）

Ship maneuvering in waves includes the performance of ship resistance, seakeeping, propulsion, and maneuverability. It is a complex hydrodynamic problem with the interaction of many factors. With the purpose of directly predicting the behavior of ship maneuvering in waves, a CFD solver named naoe-FOAM-SJTU is developed by the Computational Marine Hydrodynamics Lab(CMHL) in Shanghai Jiao Tong University. The solver is based on open source platform OpenFOAM and has introduced dynamic overset grid technology to handle complex ship hull-propeller-rudder motion system. Maneuvering control module based on feedback control mechanism is also developed to accurately simulate corresponding motion behavior of free running ship maneuver. Inlet boundary wavemaker and relaxation zone technique is used to generate desired waves. Based on the developed modules, unsteady Reynolds-averaged Navier-Stokes(RANS) computations are carried out for several validation cases of free running ship maneuver in waves including zigzag, turning circle, and course keeping maneuvers. The simulation results are compared with available benchmark data. Ship motions, trajectories, and other maneuvering parameters are consistent with available experimental data, which indicate that the present solver can be suitable and reliable in predicting the performance of ship maneuvering in waves. Flow visualizations, such as free surface elevation, wake flow, vortical structures, are presented to explain the hydrodynamic performance of ship maneuvering in waves. Large flow separation can be observed around propellers and rudders. It is concluded that RANS approach is not accurate enough for predicting ship maneuvering in waves with large flow separations and detached eddy simulation(DES) or large eddy simulation(LES) computations are required to improve the prediction accuracy.     

球体波能转换装置捕获能量的理论研究

球体波能转换装置在波浪的激励下可以同时在水平和竖直两个模式振荡。基于线性微幅波浪和势流理论,将波浪与球体相互作用简化为球体固定不动,波浪绕过球体和球体在静止流体中运动。线性叠加以后得到总的速度势,计算出球体波能转换装置的平均功率和能量俘获宽度因子的解析表达式。理论研究表明:装置与波浪运动的相位差是影响波能的最重要的参数,最优相位差为-π/2,并且给出了最优相位差调节的理论表达式。另外,对波长、波幅、球体半径、水深和球心距静水面的距离等因素也进行了分析。     

Multi-fidelity optimization of a high-speed foil-assisted semi-planing catamaran for low wake

The wakes of high-speed passenger-only ferries that operated through Rich Passage, on the Seattle-Bremerton ferry route, caused beach erosion and damage to habitat. A task was initiated to design a low-wake high-speed vessel using multi-fidelity CFD based design optimization by using low-fidelity potential flow solvers for initial global design optimization and by using URANS solvers for high-fidelity tuning of the optimized design. This simulation based design process involved a close collaboration between ship designers, and hydrodynamics and CFD specialists, whose collective expertise guided the evolution of the design based on both hydrodynamic and structural aspects. The initial hull shape optimization using potential flow code was carried out by blending three different initial concepts provided by the designers. Subsequently, URANS was used to evaluate the potential flow optimized hull and to further optimize the hull configuration parameters, namely, the centre-of-gravity, demihull spacing, foil location, foil angle and slenderness ratio at different displacement conditions. The URANS based configuration optimization also took into account the far field wakes’ energy spectrum with an objective of reducing the energetic, low frequency far field wakes which are associated with beach flattening on the mixed sand and gravel beaches. Calculation of the far field wake using URANS would require an unfeasibly large domain size; therefore, a Havelock code with a source distribution matching the URANS calculated near field wave elevation was used to propagate the wakes into the far field. The end result of the optimization was a design with significantly reduced far field wake, which is currently being built for experimental testing.     

水锤冲击时管路系统流固耦合响应的特征线分析方法研究

本文以Wiggert 和Hatfield[3]的特征线分析方法为基础,研究管路在水锤冲击下考虑泊松耦合时流体和结构的瞬态响应.推导了分别对应于管中流体压缩波和管壁中纵波的特征关系式和相容方程,并联合采用空间插值和显式时间插值进行数值求解.针对经典的水锤压力冲击的算例,将边界和初始条件离散化,编制了MATLAB程序进行计算,获得管道中流体压力和流速及轴向应力和振动速度的时程曲线,计算结果与理论分析相当吻合.根据计算结果,提出了对于实际管路设计和水锤防护有益的结论.鉴于特征线法本身的优势,有望在管路系统抗冲击设计分析和防护研究中得到进一步的应用.     

重力式码头建设对水沙环境的影响

针对重力式码头和工程区域的特点,建立二维潮流泥沙数学模型,采用实测资料对模型进行验证,研究工程建设对东山湾水动力、泥沙环境的影响,为项目选址及方案布置提供依据.结果表明,工程建设前后东山湾大范围潮流场格局基本不变,变化主要位于工程附近;悬浮泥沙增量影响范围集中在工程东侧;工程前沿回淤范围较小,最大淤积强度约为12cm/a.总体来说,工程的选址及方案设计是可行的.     

Higher-order boundary element method for the interaction of a floating body with both waves and slow current

A hybrid boundary element method is suggested to solve the problem of the interaction of floating structures with both waves and slow current. A pulsating source and its mirror image referring to the sea bottom are adopted as the Green's function. The velocity potentials are expanded into an eigenfunction expansion in the outer region of the fluid domain while higher order elements are used to discretize the boundary surface surrounding the inner region. The method is validated by comparing calculated results for a circular cylinder with the semi-analytical solutions. The method is then applied to ellipsoids of various breadth and draft to investigate the influence of body shape on the wave drift damping.     

阻振质量对板平面弯曲波传播的阻抑

研究了无限板上受点激励时阻振质量对结构声传递的阻抑,采用基于能量观点的隔振度来定义阻振质量的阻抑作用.通过理论分析验证了隔振度简化公式的可行性.发现板平面弯曲波分别和阻振质量的弯曲波和扭转波达到最佳耦合时,平面弯曲波发生最大透射.算例分析和试验研究论证了理论分析的正确性,为阻振质量应用于结构声传递途径的控制提供了理论和试验基础.     

A parametric study on water-entry of a twin wedge by boundary element method

High speed catamarans are used for pleasure, racing as well as passenger transportations. Optimal design of these crafts requires knowledge of sea loads exerted on their structures. The total load may be estimated by integration of loads exerted on a series of two-dimensional sections along the hull. In order to access the cross-sectional loads, the problem may be simplified to solve the water-entry problem of a twin hull. In this paper, water-entry problem of a twin wedge at constant vertical water-entry speed is studied. The problem is solved in the framework of potential theory using boundary element method where gravity effect on the flow is neglected. A simplified model based on Wagner theory is employed. Free surface elevation and pressure distribution on the body in different deadrise angles have been evaluated. A parametric study has been done to investigate effects of deadrise angle, distance between demi-hulls and free surface elevation on maximum pressure coefficient. Finally, a regression formula for maximum pressure coefficient has been proposed. Results of parametric study reveal that as time advances the interaction between two demi-hull gets more severe, besides the interaction effect on pressure coefficient is nonlinear.