Interactions between nonlinear water waves and non-wall-sided 3D structures

Interactions between water waves and non-wall-sided cylinders are analyzed based on velocity potential theory with fully nonlinear boundary conditions on the free surface and the body surface. The finite element method (FEM) is adopted together with a 3D mesh generated through an extension of a 2D Delaunay grid on a horizontal plane along the depth. The linear matrix equation for the velocity potential is constructed by imposing the governing equation and boundary conditions through the Galerkin method and is solved through an iterative method. By imposing the gradient of the potential equal to the velocity, the Galerkin method is used again to obtain the velocity field in the fluid domain. Simulations are made for bottom mounted and truncated cylinders with flare in a numerical tank. Periodic waves and wave groups are generated by a piston type wave maker mounted on one end of the tank. Results are obtained for forces, wave profiles and wave runups. Further simulations are made for a cylinder with flare subjected to forced motion in otherwise still open water. Results are provided for surge and heave motion in different amplitudes, and for a body moving in a circular path in the horizontal plane. Comparisons are made in several cases with the results obtained from the second order solution in the time domain.     

Viscous free surface effect on coastal embankment hydrodynamics

A finite-differnece method was used to calculate the nonlinear hydrodynamic pressures acting on the coastal embankment faces by seismic-wave actions. The nonlinearity of free surface flow, convective acceleration, viscosity and surface tension of fluid are included in the analysis. The kinematic and dynamic free surface boundary conditions are employed for calculating the horizontal fluid velocity, pressure at the free surface and the surface profile of the fluid. The time-dependent water surface is transformed to the horizontal plane, and the flow field is mapped onto a rectangular, making it convenient to model the complex sea bottom geometry and the wavy water surface by the finite-difference method. Fully nonlinear and weakly nonlinear dynamic free surface conditions are used and compared. The effects of surface tension of fluid are also discussed. The nonslip boundary condition is applied on the most part of the interface between fluid and solid face, except the region near the intersection between free surface and wall face. The numerical results are presented for various water depths and ground motion intensities, and their associate viscous effects on coastal embankment hydrodynamics are discussed.     

Free fall water entry of a wedge tank into calm water in three degrees of freedom

The hydrodynamic problem of a two dimensional wedge tank filled with liquid entering a calm water surface is analysed based on the incompressible velocity potential theory. The motion effect of inner liquid on the entry process is investigated through comparison with the result containing equivalent solid mass or the liquid being frozen. The problem is solved through the boundary element method in the time domain. Two separated computational regions are constructed. One is the inner domain for the internal liquid, and the other is the outer open domain for the open water. The former is solved in the physical coordinate system, and the latter is solved in a stretched coordinate system. The solutions of two separated domains are connected through the motion of the body. The auxiliary function method is extended to decouple the nonlinear mutual dependence between fluid loads from two separated domains and the body motion. Detailed results for wedge motion, external impact pressure and free surface, and for internal pressure, free surface deformation and liquid motion are provided. Through comparison with the results of a wedge tank with frozen ice, in-depth discussion on the effect of the inner liquid is provided.     

Generation of surface and internal waves in a bounded basin by a moving baric front

We consider a plane problem of generation of surface and internal waves in a bounded rotating basin of variable depth by a front of atmospheric pressure moving over the basin. The fluid is assumed to be two-layer. The system of nonlinear long-wave equations is solved numerically by the method of finite differences for the distribution of depths corresponding to a zonal section of the Black-Sea basin. It is shown that the baric front moving over the basin generates barotropic and baroclinic oscillations of the fluid. The intensity of disturbances depends on the velocity of motion and the width of the front. There exists a velocity of motion of the front for which internal waves are generated especially efficiently. When the front leaves the basin, we observe the formation of a packet of internal waves propagating from one lateral boundary of the basin to the other boundary with reflections from the boundaries.     

Fully Nonlinear Time Domain Analysis for Hydrodynamic Performance of An Oscillating Wave Surge Converter

The hydrodynamic behaviour of an oscillating wave surge converter (OWSC) in large motion excited by nonlinear waves is investigated. The mechanism through which the wave energy is absorbed in the nonlinear system is analysed. The mathematical model used is based on the velocity potential theory together with the fully nonlinear boundary conditions on the moving body surface and deforming free surface. The problem is solved by the boundary element method. Numerical results are obtained to show how to adjust the mechanical properties of the OWSC to achieve the best efficiency in a given wave, together with the nonlinear effect of the wave height. Numerical results are also provided to show the behaviour of a given OWSC in waves of different frequencies and different heights.     

A Numerical Study on Water Waves Generated by A Submerged Moving Body in A Two-Layer Fluid System

This is a numerical study on the time development of surface waves generated by a submerged body moving steadily in a two-layer fluid system, in which a layer of water is underlain by a layer of viscous mud. The fully nonlinear Navier-Stokes equations are solved on FLUENT with the Volume-of-Fluid (VOF) multiphase scheme in order to simulate the free surface waves as well as the water-mud interface waves as functions of time. The numerical model is validated by mimicking a reported experiment in a one-layer ...     

Water entry of a finite width wedge near a floating body

The problem of a two-dimensional finite-width wedge entering water near a freely floating body is considered through the velocity potential theory for the incompressible liquid with the fully nonlinear boundary conditions on the free surface. The problem is solved by using the boundary element method in the time domain. The numerical process is divided into two phases based on whether the interaction between the wedge and floating body is significant. In the first phase, when the single wedge enters water at initial stage, only a small part near its tip is in the fluid, the problem is studied in a stretched coordinate system and the presence of the floating body has no major effect. In the second phase, the disturbance by water entry of the wedge has reached the floating body, and both are considered together in the physical system. The auxiliary function method is adopted to decouple the nonlinear mutual dependence between the motions of the wedge and floating body, both in three degrees of freedom, and the fluid flow, as well as the interaction effects between them. Case studies are undertaken for a wedge entering water in forced or free fall motion, vertically or obliquely. Results are provided for the accelerations, velocities, pressure distribution and free surface deformation, and the interaction effects are discussed.     

Wave pattern induced by a moving atmospheric pressure disturbance

A moving low atmospheric pressure is a main feature of tropical cyclones, which can induce a system of forced water waves and is an important factor that cause water level rise during a storm. A numerical model based on the nonlinear shallow water equations is applied to study the forced waves caused by an atmospheric pressure disturbance moving with a constant velocity over water surface. The effects of the moving speed, the spatial scale and the central pressure drop of the pressure disturbance are discussed. The results show that the wave pattern caused by a moving low-pressure is highly related with its moving speed. The wave pattern undergoes a great change as the moving speed approaches the wave velocity in shallow water. When the moving speed is less than the wave velocity, the distribution of water surface elevation is nearly the same as that of the pressure disturbance, and the maximum of the water surface elevation is located at the center of pressure. When the moving speed is larger than the wave velocity, a triangle shaped wave pattern is formed with a depression occurs in front of the pressure center, and the maximum of the water surface elevation lags behind the center of pressure. As the moving speed increases, the maximum of the water surface elevation firstly increases and then decreases, which reaches a peak when the moving speed is close to the wave velocity. The maximum of water surface elevation is approximately in proportion to the central pressure drop, and slightly affected by the spatial scale of pressure disturbance. Both the central pressure drop and the spatial scale of the pressure disturbance do not significantly affect the forced wave pattern. However, a clear difference can be noticed on the ratio of the maximum water surface elevation in moving pressure situation to that in static situation, when the moving speed is close to the wave velocity. A pressure disturbance with smaller spatial scale and smaller central pressure drop will give a larger ratio when the moving speed is close to the wave velocity.     

用时域法求解二维二阶非线性水波

本文用二阶理论在时域范围内计算二维二阶非线性水波,一、二阶问题分别满足各自的自由表面条件和物面条件,流场内的速度势通过求解有限元方程得到,计算采用八结点四边形等参单元,采用人工阻尼来吸收反射波,对楔形体在水面上的振荡问题进行了计算,计算结果与有关文献相比符合较好。     

Time domain three-dimensional fully nonlinear computations of steady body–wave interaction problem

Three-dimensional fully nonlinear waves generated by moving disturbances with steady forward speed without motions are solved using a mixed Eulerian–Lagrangian method in terms of an indirect boundary integral method and a Runge–Kutta time marching approach which integrates the fully nonlinear free surface boundary conditions with respect to time.A moving computational window is used in the computations by truncating the fluid domain (the free surface) into a computational domain. The computational window maintains the computational domain and tracks the free surface profile by a node-shifting scheme applied within it. An implicit implement of far field condition is enforced automatically at the truncation boundary of the computational window.Numerical computations are applied to free surface waves generated by Wigley and Series 60 hulls for the steady problem. The present numerical results are presented and compared with existing linear theory, experimental measurements, and other numerical nonlinear computations. The comparisons show satisfactory agreements for these hydrodynamic problems.     

CFD simulation of flow features and vorticity structures in tuna-like swimming

The theoretical research on the propulsive principle of aquatic animal becomes more important and attracted more researchers to make efforts on it.In the present study,a computational fluid dynamic (CFD) simulation of a three-dimensional traveling-wave undulations body of tuna has been developed to investigate the fluid flow features and vorticity structures around this body when moving in a straight line.The undulation only takes place in the posterior half of the fish,and the tuna-tail is considered as a lunate fin oscillating with the mode combined swaying with yawing.A Reynolds-averaged Navier-Stokes (RANS) equation is developed,employing a control-volume method and a k-omega SST turbulent model;meanwhile an unstructured tetrahedral grid,which is generated for the three-dimensional geometry,is used based on the deformation of the hind parts of the body and corresponding movement of the tail.We calculated the hydrodynamic performance of tuna-like body when a tuna swims in a uniform velocity,and compared the input power coefficient,output power coefficient and propulsive efficiency of the oscillating tuna-tail with or without body vortex shedding.Additionally,the load distribution on the body,flow features and vorticity structures around the body were demonstrated.The effect of interaction between the body-generated vortices and the tail-generated vorticity on the hydrodynamic performance can be obtained.     

Numerical simulation of nonlinear wave and force generated by a wedge-shape wave maker

Nonlinear waves and forces induced by a wedge-shape wave maker were simulated in a potential-theory-based fully nonlinear 2D Numerical Wave Tank (NWT). The NWT is developed in a time domain by using Boundary Element Method (BEM) including Mixed Eulerian–Lagrangian method (MEL) and Runge–Kutta 4th-order (RK4) integration as a time marching process. For ensuring accurate nonlinear free surface both material-node and semi-Lagrangian approach are independently developed for crosschecking. The acceleration-potential scheme is used for obtaining accurate time derivative of velocity potential. The developed NWT is utilized to calculate water particle velocity and a series of higher-harmonic force components on the wave maker. The added-mass and radiation-damping coefficients of the wave maker are also obtained from the least-square method. The simulation results are compared with the experimental and numerical results of other researchers. To compare the relative importance of free-surface and body-surface nonlinearities, a body nonlinear formulation is independently developed. Force by body nonlinear method is in good agreement with fully nonlinear result in case of low body-stroke frequency.     

Response of a thin plate resting on a fluid-layer to a moving point load

This paper is concerned with the vibrations of a thin plate resting on a fluid-layer subjected to a moving point force. The frequency is assumed to be low and the fluid is deep. Both the fluid and the point force are always in contact with the plate. Hankel Transform and complex integration techniques are used to calculate the lateral displacements withrespect to a moving coordinate system and a coordinate transformation is used to achieve the results with respect to a fixed point. Numerical results are discussed with respect to the velocity of the moving force, its direction of movement and the fluid depth.     

湍流局地平衡假设的新推论--齐次湍流动能输运方程封闭模型与应用(Ⅱ)

在湍流局地平衡假设下 ,建立了齐次湍能输运方程封闭模型 (HKE) ,并在平板边界层的两种经典流动中加以检验 ,给出 HKE封闭下的流速、湍流动能和湍流混合系数剖面的形式解。结果表明 ,HKE可以避免在流速剪切为零时的无湍流混合问题 ,其解与 L aufer湍流实验吻合 ,因而HKE模型比混合长理论有更合理的内涵。文中还给出 HKE封闭的浅海动力学模型 ,以湍应力和水位梯度力的平衡为运动的基本受力平衡 ,进行了模型的量阶分析和运动分析 :当阻尼频率和运动频率同量阶时 ,惯性运动不可忽略 ;在潮振荡占优的浅海中 ,对流非线性相对于惯性运动为小量 ;当阻尼频率足够大时 ,科氏力项相对于湍应力也可能为小量。     

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.     

Numerical and Experimental Investigation of Interactions Between Free-Surface Waves and A Floating Breakwater with Cylindrical-Dual/Rectangular-Single Pontoon

This paper investigates the hydrodynamic performance of a cylindrical-dual or rectangular-single pontoon floating breakwater using the numerical method and experimental study. The numerical simulation work is based on the multi-physics computational fluid dynamics (CFD) code and an innovative full-structured dynamic grid method applied to update the three-degree-of-freedom (3-DOF) rigid structure motions. As a time-marching scheme, the trapezoid analogue integral method is used to update the time integration combined with remeshing at each time step. The application of full-structured mesh elements can prevent grids distortion or deformation caused by large-scale movement and improve the stability of calculation. In movable regions, each moving zone is specified with particular motion modes (sway, heave and roll). A series of experimental studies are carried out to validate the performance of the floating body and verify the accuracy of the proposed numerical model. The results are systematically assessed in terms of wave coefficients, mooring line forces, velocity streamlines and the 3-DOF motions of the floating breakwater. When compared with the wave coefficient solutions, excellent agreements are achieved between the computed and experimental data, except in the vicinity of resonant frequency. The velocity streamlines and wave profile movement in the fluid field can also be reproduced using this numerical model.     

Statistical characteristics of long waves nearshore

The random long wave runup on a beach of constant slope is studied in the framework of the rigorous solutions of the nonlinear shallow water theory. These solutions are used for calculation of the statistical characteristics of the vertical displacement of the moving shoreline and its horizontal velocity. It is shown that probability characteristics of the runup heights and extreme values of the shoreline velocity coincide in the linear and nonlinear theory. If the incident wave is represented by a narrow-band Gaussian process, the runup height is described by a Rayleigh distribution. The significant runup height can also be found within the linear theory of long wave shoaling and runup. Wave nonlinearity nearshore does not affect the Gaussian probability distribution of the velocity of the moving shoreline. However the vertical displacement of the moving shoreline becomes non-Gaussian due to the wave nonlinearity. Its statistical moments are calculated analytically. It is shown that the mean water level increases (setup), the skewness is always positive and kurtosis is positive for weak amplitude waves and negative for strongly nonlinear waves. The probability of the wave breaking is also calculated and conditions of validity of the analytical theory are discussed. The spectral and statistical characteristics of the moving shoreline are studied in detail. It is shown that the probability of coastal floods grows with an increase in the nonlinearity. Randomness of the wave field nearshore leads to an increase in the wave spectrum width.     

Analytical Solutions to the Flow Field Induced by Uniformly Moving Multiple Helical Vortex Filaments

This paper presents analytic solutions for the flow field of inviscid fluid induced by uniformly and rigidly moving multiple helical vortex filaments in a cylindrical pipe. The relative coordinate system is set on the moving vortex filaments. The analytical solutions of the flow field are obtained on the assumption that the relative velocity field induced is time-independent and helically symmetrical. If the radius of the cylindrical pipe approaches infinity, these solutions are also available for tmbounded space. The results show that both the absolute velocity field and pressure field are periodical in time, and may reduce to time-independent when the helical vortex filaments are immobile or slip along the filaments themselves. Furthermore, the solution of velocity field is reduced to Okulov‘s formula for the case of a single static vortex filament in a cylindrical pipe. The calculated locations of pressure peak and valley on the pipe wall agree with experimental results.     

Simulation of nonlinear wave run-up with a high-order Boussinesq model

This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions. As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability to accurately simulate a moving wet–dry boundary is of considerable practical importance within coastal engineering, and the extension described in this work significantly improves the nearshore versatility of the present high-order Boussinesq approach.     

A 3D fully coupled analysis of nonlinear sloshing and ship motion

This study investigates the coupling effects of six degrees of freedom in ship motion with fluid oscillation inside a three-dimensional rectangular container using a novel time domain simulation scheme. During the time marching, the tank-sloshing algorithm is coupled with the vessel-motion algorithm so that the influence of tank sloshing on vessel motions and vice versa can be assessed. Several factors influencing the dynamic behavior of tank–liquid system due to moving ship are also investigated. These factors include container parameters, environmental settings such as the significant wave height, current velocity as well as the direction of wind, wave and flow current acting on the ship. The nonlinear sloshing is studied using a finite element model whereas nonlinear ship motion is simulated using a hybrid marine control system. Computed roll response is compared with the existing results, showing fair agreement. Although the two hull forms and the sea states are not identical, the numerical result shows the same trend of the roll motion when the anti-rolling tanks are considered. Thus, the numerical approach presented in this paper is expected to be very useful and realistic in evaluating the coupling effects of nonlinear sloshing and 6-DOF ship motion.