Similarity solution of oblique impact of wedge-shaped water column on wedged coastal structures

The initial stage of plunging wave impact obliquely on coastal structures is analysed. The problem is modelled through an oblique collision of an asymmetrical water wedge and an asymmetrical solid wedge. The gravity effect on the flow is ignored based on the assumption that the ratio of the incoming speed of the wave to the acceleration due to gravity is much larger than the time scale of interest. Similarity solution method based on the velocity potential theory is then used. The problem of this similarity flow is solved by a boundary element method through the Cauchy theorem in the complex plan. Results for the wave elevation and pressure distribution are provided, including the forces and moments, effects of different impact angles and the effects of oblique impact are investigated. In particular, negative pressure near the tip of the solid wedge is observed and its implications are discussed.     

楔形体在波浪中自由入水的数值模拟

物体入水时波浪的影响不可忽略,基于流体力学模型采用VOF法,并利用自定义函数,模拟了楔形体的自由入水过程;同时结合推波板原理及海绵层消波理论实现了数值水槽的造消波,完成了波浪中楔形体自由入水的模拟,计算了楔形体入水时所受的水作用力、自由液面变化及物面压强分布等,研究了不同波高、周期以及在波浪不同位置入水时对楔形体的影响。结果表明:本文建立的数值模型可很好地模拟楔形体入水造成的射流及空泡的形成发展过程,波浪对楔形体入水的影响主要由波浪内部流场变化及表面波形决定,在波浪不同位置处入水对楔形体受力及入水形态均有较大影响。     

改进的移动粒子半隐式法模拟楔形体入水砰击

移动粒子半隐式法(Moving-Particle Semi-Implicit Method,MPS)是一种新的基于拉格朗日(Lagrange)理念的无网格方法,适用于模拟自由液面的大变形和水流的喷射现象。用基于大涡模拟的改进MPS法首先模拟了矩形体的入水砰击,砰击压力的计算结果证明了这种方法的正确性,然后模拟了楔形体的匀速入水砰击,并与实验结果进行了对比,验证了大涡模拟改进MPS法在砰击问题中的适用性。     

Simulation of freefall water entry of a finite wedge with flow detachment

A two-dimensional finite wedge entering water obliquely in freefall with three degrees of freedom is considered through the velocity potential theory for the incompressible liquid. The problem is solved by using the boundary element method in the time domain. The scheme of the stretched coordinate system is adopted at the initial stages when only a small part of the wedge near its tip has entered water. The auxiliary function method is adopted to decouple the nonlinear mutual dependence between the body motions in three degrees of freedom and the fluid flow. When the liquid has detached from the knuckle of the wedge, the free jet is treated through the momentum equation. The developed method is verified through existing results for one degree of freedom in vertical motion. Various case studies are undertaken for a wedge entering water vertically, obliquely and with rotational angles. Results are provided the accelerations, velocities, pressure distribution and free surface deformation, and the physical implications are discussed.     

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.     

An accurate and efficient SPH modeling of the water entry of circular cylinders

The present work is dedicated to the enhancement and application of the recently developed δ⁺-SPH scheme for two and three dimensional water entry problems. The cylinder surface presents a circular shape and therefore the position where the flow separation happens is tightly related to the implementation of the boundary condition. A special treatment for the particle shifting between fluid and solid wall is highlighted. Adaptive particle refinement (APR) is applied in this work to reduce the computational cost. It is found that, APR and the δ⁺-SPH scheme benefit to each other. That is to say the former reduces the computing cost of the latter while in return the latter solves the problem of particle disorder of the inactive particles of the former. Thanks to the combination of APR and δ⁺-SPH especially in three dimensional (3D) cases, the overall computational cost is significantly reduced while sufficiently fine particle resolution can be obtained in the flow region characterized by large pressure gradient close to the structure surface. The fairly good agreements between the SPH results and the experimental data prove the present SPH model to be a reliable tool in accurately solving the fluid–structure interacting problems in ocean engineering.     

Axisymmetric liquid block impact on a solid surface

The hydrodynamic problem of collision of an axisymmetric water block and solid boundary has been analyzed based on the velocity potential theory. The three dimensional axisymmetric hydrodynamic problem is converted to a quasi two dimensional one and is solved in axisymmetric coordinate system using the boundary element method. Numerical simulations are made for collision of a solid cone with a liquid cone or a spheroidal liquid block. The results in the former are compared with those obtained from similarity solution and excellent agreement is found. Numerical results are then presented for the collision between different solid cones and various spheroidal liquid blocks.     

An experimental study on water entry of asymmetric wedges

The aim of the paper is to provide an experimental reference for investigation of asymmetric water entry of wedges. Parameters of the study include initial deadrise angle, inclination angle and impact speed. Initial deadrise angles of the wedges were 20° and 30° with inclination angles ranging from 0° to 15° in 5° increments. Wedges were freely fallen from three different heights. Time histories of impact pressure and body acceleration were recorded. Sampling rate of measurements were set to 25 KHz. Main configuration of each test including mass of the wedge and water level were kept unchanged during all experiments. Additionally, several calibration tests were conducted to assess the repeatability and accuracy of the recorded data. The experimental results are compared with different entry theories and other available experiments. The comparison shows a reasonable agreement and indicates that the inclination angle can dramatically affect the impact pressure experienced by the wedges. Finally, the results show that the traditional asymmetric theories are not appropriate for all inclination angles.     

A Numerical Study on the Asymmetric Water Entry of A Wedge Section

The effect of the asymmetric water entry over a submerged part of a ship on the hydredynamic impact is investigated numerically. A wedge hotly is considered and the problem is assumed to be two-dimensional. The results of symmetric and asymmetric impacts are compared. The effect is found significant in the numerical simulation. The maximum hydrodynamic pressure at a heel angle of 10 degrees becomes about 95% more than that of the symmetric entry. The result of the present work proves the importance of asymmetrical hydrodynamic impact loading for structural design of a ship. Besides, the numerical procedure is not limited to a wedge type cross section and it is possible to apply it for any real geometry of ships and high-speed craft.     

Numerical analysis of the bubble jet impact on a rigid wall

The main characteristic of the bubble dynamics near a rigid wall is the development of a high speed liquid jet, generating highly localized pressure on the wall. In present study, the bubble dynamic behaviors and the pressure impulses are investigated through experimental and numerical methods. In the experiment, the dynamics of a spark-generated bubble near a steel plate are captured by a high-speed camera with up to 650,000 frames per second. Numerical studies are conducted using a boundary integral method with incompressible assumption, and the vortex ring model is introduced to handle the discontinued potential of the toroidal bubble. Meanwhile, the pressure on the rigid wall is calculated by an auxiliary function. Calculated results with two different stand-off parameters show excellent agreement with experimental observations. A double-peaked or multiple-peaked structure occurs in the pressure profile during the collapse and rebounding phase. Generally, the pressure at the wall center reaches the first peak soon after the jet impact, and the second peak is caused by the rapid migration of the bubble toward the wall, and the subsequent peaks may be caused by the splashing effect and the rebounding of the toroidal bubble. At last, both agreements and differences are found in the comparison between the present model and a hybrid incompressible–compressible method in Hsiao et al. (2014). The differences show that the compressibility of the flow is another influence factor of the jet impact. However, the main features of the jet impact could be simulated using the present model.     

Momentum and gravity effects during the constant velocity water entry of wedge-shaped sections

Computational fluid dynamics analysis was used to investigate the added mass momentum, flow momentum and gravity effects during the constant velocity water entry of wedge-shaped sections with deadrise angles from 5° to 45°. It is shown that the added mass continues to increase for a time after chine immersion and that added mass can be estimated in terms of a constant added mass coefficient and an effective wetted width. A momentum theory is presented in which the water entry force is explained as the sum of the rate of change of added mass momentum, which becomes zero at immersion to chine depth ratios greater than about three, and the rate of change of flow momentum, which continues at deep immersions. The effect of gravity on the water entry force is given as the hydrostatic force together with the force necessary to create the potential energy in the water pile up. Hydrodynamic forces are not significantly changed by the effect of gravity on the flow fields.     

Effective boundary element method for the interaction of oblique waves with long prismatic structures in water of finite depth

An effective boundary element method (BEM) is presented for the interaction between oblique waves and long prismatic structures in water of finite depth. The Green's function used here is the basic Green's function that does not satisfy any boundary condition. Therefore, the discretized elements for the computation must be placed on all the boundaries. To improve the computational efficiency and accuracy, a modified method for treatment of the open boundary conditions and a direct analytical approach for the singularity integrals in the boundary integral equation are adopted. The present BEM method is applied to the calculation of hydrodynamic coefficients and wave exciting forces for long horizontal rectangular and circular structures. The performance of the present method is demonstrated by comparisons of results with those generated by other analytical and numerical methods.     

Numerical study on the cavity characteristics and impact loads of AUV water entry

The high-speed water entry process of an autonomous underwater vehicle (AUV) has a strong impact nonlinearity, and a cavity formed by air and water will often be generated as part of the entry process. The shape of the water-entry cavity plays an important role in the load characteristics and stability of the water-entry trajectory. In this paper, a numerical model for describing the cavity and impact load characteristics of a high-speed water-entry AUV is established. The simulation results such as cavity shape and impact load are compared with experimental data. The good agreement between the numerical results and those of the experiments reveals the accuracy and capability of the numerical algorithm. Subsequently, the arbitrary Lagrange-Euler (ALE) numerical algorithm is used to simulate and analyse the variation laws of the cavity characteristics and impact loads with different head shapes, water-entry velocities, water-entry angles and angles of attack. The results obtained in this study can provide a good reference for the trajectory control and structural design of the AUV.     

Scattering of oblique waves by permeable vertical flexible membrane wave barriers

The interaction of obliquely incident surface gravity waves with a vertical flexible permeable submerged membrane wave barrier is investigated in the context of three-dimensional linear water wave theory. From the general formulation of the submerged membrane barrier, the performance of bottom-standing, surface-piercing and fully extended membrane wave barriers are analyzed for various values of wave and structural parameters. The analytic solution of the physical problem is obtained using eigenfunction expansion method and a coupled boundary element-finite difference method has been used to get the numerical solution. In the boundary element method, since the boundary condition on the membrane barrier is not known a priori, the membrane response and velocity potentials are solved simultaneously using appropriate discretization with the help of finite difference scheme. The convergence of the analytic and numerical solution techniques is discussed. The study reveals that for suitable combination of wave and structural parameters, approximately (45–50)% incident wave energy can be dissipated irrespective of membrane barrier configurations. Further, in certain situations, nearly full wave reflection and zero transmission occur for all barrier configurations. The study will be useful in the design of flexible permeable membrane to act as an effective wave barrier for creation of tranquility zone in the marine environment.     

海运石脑油储罐水相区阴极保护电场的数值模拟

采用边界元方法对石脑油储罐罐底水相区的阴极保护系统设计方案进行了数值模拟.结果表明,传统设计方案中电场参数分布不均匀、过保护现象明显;通过适当减少牺牲阳极数量并调整其布设位置,可对其阴极保护设计进行优化,过保护现象明显减小,且电位和电流密度分布也更为均匀.     

Numerical solution of the asymmetric water impact of a wedge in three degrees of freedom

Impact problems associated with water entry have important applications in various aspects of naval architecture and ocean engineering. Estimation of hydrodynamic impact forces especially during the first instances after the impact is very important and is of interest. Since the estimation of hydrodynamic impact load plays an important role in safe design and also in evaluation of structural weight and costs, it is better to use a reliable and accurate prediction method instead of a simple estimation resulted by analyzing methods. In landing of flying boats, some phenomena such as weather conditions and strong winds can cause asymmetric instead of symmetric descent. In this paper, a numerical simulation of the asymmetric impact of a wedge, as the step of a flying boat, considering dynamic equations in two-phase flow is taken into account. The dynamic motion of the wedge in two-phase flow is solved based on finite volume method with volume of fluid (VOF) scheme considering dynamic equations. Then the effects of different angles of impact and water depth on the velocity change and slamming forces in an asymmetric impact are investigated. The comparison between the simulation results and experimental data verifies the accuracy of the method applied in the present study.     

Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations

A one-dimensional high-resolution finite volume model capable of simulating storm waves propagating in the coastal surf zone and overtopping a sea wall is presented. The model (AMAZON) is based on solving the non-linear shallow water (NLSW) equations. A modern upwind scheme of the Godunov-type using an HLL approximate Riemann solver is described which captures bore waves in both transcritical and supercritical flows. By employing a finite volume formulation, the method can be implemented on an irregular, structured, boundary-fitted computational mesh. The use of the NLSW equations to model wave overtopping is computationally efficient and practically flexible, though the detailed structure of wave breaking is of course ignored. It is shown that wave overtopping at a vertical wall may also be approximately modelled by representing the wall as a steep bed slope. The AMAZON model solutions have been compared with analytical solutions and laboratory data for wave overtopping at sloping and vertical seawalls and good agreement has been found. The model requires more verification tests for irregular waves before its application as a generic design tool.     

Application of an improved semi-Lagrangian procedure to fully-nonlinear simulation of sloshing in non-wall-sided tanks

The semi-Lagrangian procedure is widely used for updating the fully-nonlinear free surface in the time domain. However, this procedure is only available to cases when the body surface is vertical near the waterline. Present study introduces an improved semi-Lagrangian procedure which removes this ‘vertical-wall’ limitation. Coupling with the boundary element method, the improved semi-Lagrangian procedure is applied to the simulation of fully-nonlinear sloshing waves in non-wall-sided tanks. From the result comparison with the open source CFD software OpenFOAM, it is confirmed that this numerical scheme could guarantee a sufficient accuracy. Further series studies on 2D and 3D fully-nonlinear sloshing waves in wedged tanks are performed. Featured phenomena are observed which are distinct from those in wall-sided tanks.     

近岸波浪破碎区不规则波浪的数值模拟

基于近岸不规则波浪传播的抛物型缓坡方程和两类波浪破碎能量损耗因子,对近岸波浪破碎区不规则波浪的波高分布进行了数值模拟,并结合实验结果对数值模拟结果进行了验证分析,结果表明采用两类波浪破碎能量损耗因子所模拟的破碎区波高与实测值均吻合良好,波浪破碎能量损耗因子及波浪破碎指标对破碎区波浪波高分布影响较明显。     

Analytical and experimental investigation on the hydrodynamic performance of onshore wave-power devices

The hydrodynamic performance of the oscillating water column type shoreline-mounted wave-power device is numerically studied within linear wave theory by using a boundary element method based on the Wehausen and Laitone 3D shallow water Green's function. In order to verify the numerical model, a 1:12 physical model with different bottom slopes was constructed and tested in a wave basin under regular wave conditions. The effects of the bottom slope on the hydrodynamic performance are investigated by both analytical and experimental methods.