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.     

柔性水囊潜堤消波特性的溃坝水槽试验研究

柔性水囊潜堤由橡胶制成,内部充水,具有结构简单、造价低廉等优点,能较好满足人工岛、跨海桥梁、海洋平台等基础设施建设工程对简单便携、拆装方便的临时防波堤的需求。为了探究柔性水囊潜堤的消波特性,在溃坝水槽内开展溃坝波与半圆柱形柔性水囊潜堤相互作用的试验研究,重点探究柔性水囊潜堤与溃坝波相互作用过程中水位变化特性,并与半圆柱刚性潜堤的性能进行比较;同时分析柔性水囊潜堤内部初始水压和浸没深度等参数对其消波性能的影响。结果表明：柔性水囊潜堤能够用作临时防波堤来衰减波浪;与半圆柱刚性潜堤相比,柔性水囊潜堤在降低溃坝波无量纲最大水位、提高消波性能方面更具优势;内部初始水压是影响柔性水囊潜堤消波性能的重要因素,适当降低内部初始水压,有利于增强柔性潜堤的变形程度,进而增加波能耗散,可获得更好的消波效果;而增加浸没深度即潜深,会使得柔性水囊潜堤对溃坝波的影响程度降低,消波效果减弱。     

Dynamic Analysis of A 5-MW Tripod Offshore Wind Turbine by Considering Fluid–Structure Interaction

Fixed offshore wind turbines usually have large underwater supporting structures. The fluid influences the dynamic characteristics of the structure system. The dynamic model of a 5-MW tripod offshore wind turbine considering the pile–soil system and fluid structure interaction (FSI) is established, and the structural modes in air and in water are obtained by use of ANSYS. By comparing low-order natural frequencies and mode shapes, the influence of sea water on the free vibration characteristics of offshore wind turbine is analyzed. On basis of the above work, seismic responses under excitation by El-Centro waves are calculated by the time-history analysis method. The results reveal that the dynamic responses such as the lateral displacement of the foundation and the section bending moment of the tubular piles increase substantially under the influence of the added-mass and hydrodynamic pressure of sea water. The method and conclusions presented in this paper can provide a theoretical reference for structure design and analysis of offshore wind turbines fixed in deep seawater.     

Fully Coupled Fluid-Structure Interaction Model Based on Distributed Lagrange Multiplier/Fictitious Domain Method

This paper,with a finite element method,studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations.With this fully coupled model,the rigid structure is taken as "fictitious" fluid with zero strain rate.Both fluid and structure are described by velocity and pressure.The whole domain,including fluid region and structure region,is modeled by the incompressible Navier-Stokes equations which are discretized with fixed Eulerian mesh.However,to keep the structure's rigid body shape and behavior,a rigid body constraint is enforced on the "fictitious" fluid domain by use of the Distributed Lagrange Multiplier/Fictitious Domain(DLM/FD) method which is originally introduced to solve particulate flow problems by Glowinski et al.For the verification of the model presented herein,a 2D numerical wave tank is established to simulate small amplitude wave propagations,and then numerical results are compared with analytical solutions.Finally,a 2D example of fluid-structure interaction under wave dynamic forces provides convincing evidences for the method excellent solution quality and fidelity.     

Far-Field Noise Induced by Bubble near Free Surface

The motion of a bubble near the free surface is solved by the boundary element method based on the linear wave equation, and the influence of fluid compressibility on bubble dynamics is analyzed. Based on the solution of the bubble motion, the far-field radiation noise induced by the bubble is calculated using Kirchhoff moving boundary integral equation, and the influence of free surface on far-field noise is researched. As the results, the oscillation amplitude of the bubble is weakened in compressible fluid compared with that in incompressible fluid, and the free surface amplifies the effect of fluid compressibility. When the distance between the bubble and an observer is much larger than that between the bubble and free surface, the sharp wave trough of the sound pressure at the observer occurs. With the increment of the distance between the bubble and free surface, the time of the wave trough appearing is delayed and the value of the wave trough increase. When the distance between the observer and the bubble is reduced, the sharp wave trough at the observer disappears.     

Numerical study of nonlinear freak wave impact underneath a fixed horizontal deck in 2-D space

Freak waves are extreme and unexpected surface waves with huge wave heights that may lead to severe damage to ships and offshore structures. However, few researches have been conducted to investigate the impact underneath fixed horizontal decks caused by freak waves. To study these phenomena, a 2-D numerical wave tank is built in which nonlinear freak waves based on the Peregrine breather solution are generated. As a validation, a regular-wave-induced underneath impact is simulated and compared to the existing experimental measurements. Then the nonlinear freak-wave-induced impact is investigate with different values of deck clearance above the mean free surface. In addition, a comparative simulation of a “large” regular wave based on the 2nd-order Stokes wave theory with the same crest height and wave length of the nonlinear freak wave is carried out to reveal the unique features of the nonlinear freak-wave-induced impact. By applying a fluid–structure interaction (FSI) algorithm in which the bottom deck and front side wall are simplified as Euler beams in 2-D and discretized by the finite element method (FEM), the hydroelastic effects are considered during the impact event. The vertical force acting underneath the bottom deck, the transversal force acting on the front side wall, the structural displacements of the elastic deck and wall are analyzed and discussed respectively, from which meaningful conclusions are drawn.     

Propulsive efficiency and structural response of a sandwich composite propeller

Studying the sandwich composite propeller (SCMP) is of great significance since the sandwich structure is lightweight and possesses high strength. This study proposes and verifies a fluid–structure interaction (FSI) method for a 3D underwater sandwich composite structure to calculate the performance of the propeller. The Reynolds-averaged Navier–Stokes formula-based computational fluid dynamics is adopted to solve for propeller loads, whereas the finite element method (FEM) is applied to solve for propeller deformations. ANSYS Workbench’s system coupling is utilized to deliver the loads and deformations in the FSI. The paper also compares the propulsive performance and structural response of the SCMP and conventional composite propeller (CMP). The impact of the structural form and core material on the SCMP is explored. The results show that the weight reduction effect of the SCMP is better than that of the CMP, the propulsive efficiency of the SCMP is higher at low advance coefficients and lower at high advance coefficients, and the maximum pitch angles of the SCMP decrease at all conditions, unlike the case for the CMP. Moreover, the thinner the facing of the SCMP, the greater the influence of the higher twist–deformation ratio of the resulting structural form on the intrinsic frequency.     

Motion Characteristics of Cavitation Bubble near the Rigid Wall with the Driving of Acoustic Wave

The dynamics of cavitation bubble is analyzed in the compressible fluid by use of the boundary integral equation considering the compressibility.After the vertical incidence of plane wave to the rigid wall,the motion characteristics of single cavitation bubble near the rigid wall with initial equilibrium state are researched with different parameters.The results show that after the driving of acoustic wave,the cavitation bubble near the rigid wall will expand or contract,and generate the jet pointing to the wall.Also,the existence of the wall will elongate time for one oscillation.With the compressible model,the oscillation amplitude is reduced,as well as the peak value of inner pressure and jet tip velocity.The effect of the wall on oscillation amplitude is limited.However with the increment of initial vertical distance,the effect of wall on the jet velocity is from acceleration to limitation,and finally to acceleration again.     

The dynamic behavior of a gas bubble near a wall

In this paper, a numerical model based on the potential flow theory is established to simulate the interaction of a gas bubble with a nearby wall. The time-integration boundary integral method is used to solve the dynamics of a gas bubble. With this method the numerical calculations show an excellent agreement with the experimental data. Employing the numerical code based on the presented algorithm, the dynamics of a gas bubble close to a rigid wall is investigated systematically, especially the relationship between various characteristic parameters and the Bjerknes effect due to the presence of a nearby wall. It is found that Blake's criterion, which is usually used to predict the direction of the bubble jet, has a great degree of accuracy for the bubble relatively far away from the wall and bubble near a wall, there is a significant error, attributed to its simplifications and assumptions. Further studies show that an oblique jet will be formed when a bubble close to an inclined wall collapses, direction and width of which have a close relationship with the characteristic parameters used to characterize the bubble. For the bubble near a horizontal wall, a liquid jet pointing directly to the wall is developed generally when the Bjerknes attraction and buoyancy are in the same direction; and at the same time, if the Bjerknes attraction is in the opposite direction of buoyancy, the direction of the jet will depend on a criterion. Then the interaction of gas bubble between complicated walls of some a submarine is also studied, which shows the most dangerous induced loading condition of structure in water, and the evidently effects of bubble jet on loading. The special phenomena mentioned above have a great significance for the further study on the interaction of the bubble with its boundaries.     

Dynamic Analysis of A 5-MW Tripod Offshore Wind Turbine by Considering Fluid–Structure Interaction

Fixed offshore wind turbines usually have large underwater supporting structures.The fluid influences the dynamic characteristics of the structure system.The dynamic model of a 5-MW tripod offshore wind turbine considering the pile–soil system and fluid structure interaction(FSI) is established,and the structural modes in air and in water are obtained by use of ANSYS.By comparing low-order natural frequencies and mode shapes,the influence of sea water on the free vibration characteristics of offshore wind turbine is analyzed.On basis of the above work,seismic responses under excitation by El-Centro waves are calculated by the time-history analysis method.The results reveal that the dynamic responses such as the lateral displacement of the foundation and the section bending moment of the tubular piles increase substantially under the influence of the added-mass and hydrodynamic pressure of sea water.The method and conclusions presented in this paper can provide a theoretical reference for structure design and analysis of offshore wind turbines fixed in deep seawater.     

Pressure characteristics of bubble collapse near a rigid wall in compressible fluid

High speed liquid jet and shockwave can be produced when a bubble collapses near a rigid wall, which may cause severe damage to solid structures. A hybrid algorithm was adopted to simulate bubble motion and associated pressures near a wall combining Level Set-Modified Ghost Fluid-Discontinuous Galerkin (LS-MGF-DG) method and boundary element method (BEM). Numerical results were compared with experimental data to validate the presented algorithm. Jet formation was simulated by BEM and the induced pressure on the wall was calculated with auxiliary function. The pressure at the point on the wall where the jet points to reaches its peak value after the jet penetrates the bubble. Bubble collapse and rebounding were simulated by the LS-MGF-DG method. Shock-wave is induced when the bubble collapse toroidally to a minimum volume and the pressure at wall center reaches the maximum due to shockwave superposition. A third pressure peak is found associated with the bubble rebounds and bubble splitting. In the case studied, a higher pressure was found due to collapse shockwave than bubble jet and affects a larger area of the wall. In addition, the three pressure peaks due to jet impact, collapse impact as well as bubble rebounding and splitting decrease with the increase of the standoff distance.     

Wave interaction with a semi-porous cylindrical breakwater mounted on a storage tank

The interaction of linear water waves with a semi-porous cylindrical breakwater surrounding a rigid vertical circular cylinder mounted on a storage tank is investigated theoretically. The cylindrical breakwater structure is porous in the vicinity of the free-surface, while at some distance below the water surface it becomes impermeable. Under the assumptions of linearized potential flow, the coupled problem of flow in the interior and exterior fluid regions is solved by an eigenfunction expansion approach. Analytical expressions are obtained for the wave motion in both the interior and exterior flow regions. Numerical results are presented which illustrate the effects of the various wave and structural parameters on the hydrodynamic loads and interior and exterior wave fields. It is found that for certain parameter combinations the semi-porous, cylindrical breakwater may result in a significant reduction in the wave field and hydrodynamic forces experienced by the interior structure.     

基于FLOW-3D的三维数值波流水槽的构建及应用研究

为获得具有自由液面的三维波流水槽,基于FLOW-3D有限差分程序,选用RNG?-?紊流模型,基于线性波速度入口法造波,采用VOF方法对自由液面进行追踪。构建具有自由液面的三维波流联合作用数值水槽,对比压力出流边界与Sammerfeld辐射边界发现,在波流水槽内采用压力出流边界能够保持流体体积守恒,波形稳定;加入的孔隙结构,不仅能保证良好的消波效果,而且流体能够顺利通过,对消除反射波影响效果良好;与实验结果对比发现,垂向时均流速与实验数据拟合较好。波流场中桩柱前形成明显下潜水流及漩涡,是形成局部冲刷主要原因。本文所构建的波流数值模型波形稳定、具有良好的波流特性,能较好反应波浪与水流之间的相互作用,可进一步模拟波流场与结构物之间的相互作用或波流作用下泥沙冲刷等研究。     

完全非线性波浪与二维固定结构物作用的IGN-BEM耦合分析模型

为高效准确地对完全非线性波浪与二维固定结构物的相互作用进行模拟分析,建立了二维完全非线性时域耦合模型。耦合模型将计算域划分为靠近结构物的内域和远离结构物的外域,每个区域均采用满足完全非线性自由水面边界条件的波浪模型进行求解。在内域使用Laplace方程描述流体运动并采用高阶边界元法（BEM）对其进行求解;而在没有结构物的外域,波浪运动的控制方程为Irrotational Green-Naghdi（IGN）方程并采用有限元法（FEM）对其进行求解。内域和外域通过一段重叠区域进行耦合,从而实现模型间变量的传递。首先利用耦合模型分别对规则波的传播、直墙前立波的生成以及相关物理模型试验进行模拟,数值结果与精确解和试验结果的良好吻合验证了耦合模型耦合方式的合理性以及处理非线性问题的准确性;然后使用耦合模型模拟分析了波浪与固定结构物间的相互作用,并将结果与线性解析解以及完全非线性BEM模型的结果进行了对比分析,进一步证明了耦合模型的正确性与高效性。     

水下平板与波浪相互作用完全非线性数值模拟(英文)

利用完全非线性数值波浪水槽技术研究水下平板与波浪的相互作用。假定水下平板厚度极薄、刚性,位于有限水深并且非常接近自由水面。应用四阶龙格库塔方法追踪每一时刻的波面形状,采用阻尼层来吸收反射波以保证算法的稳定性,同时引入平滑和重组的方法抑制自由表面控制点的较高梯度。通过对波浪与浮动圆柱相互作用的数值模拟证实了数值波浪水槽方法的有效性,计算结果与线性理论吻合良好。在波浪数值水槽方法中引入造波板模拟波浪产生并与水下平板发生相互作用,应用傅立叶解析方法对波面变形、波浪力作了分析。结果表明在板非常接近自由水面的情况下会表现出现很强的非线性,揭示了线性理论的局限性。     

Numerical Simulation of Sloshing Using the MPS-FSI Method with Large Eddy Simulation

A numerical model has been developed to study sloshing of turbulent flow in a tank with elastic baffles. The Moving-Particle Semi-implicit method(MPS) is a kind of meshless Lagrangian calculation method. The large eddy simulation(LES) approach is employed to model the turbulence by using the Smagorinsky Sub-Particle Scale(SPS)closure model. This paper uses MPS-FSI method with LES to simulate the interaction between free surface flow and a thin elastic baffle in sloshing. Then, the numerical model is validated, and the numerical solution has good agreement with experimental data for sloshing in a tank with elastic baffles. Furthermore, under external excitations,the MPS is applied to viscous laminar flow and turbulent flow, with both the deformation of elastic baffles and the wave height of the free surface are compared with each other. Besides, the impact pressure with/without baffles and wave height of free surface are investigated and discussed in detail. Finally, preliminary simulations are carried out in the damage problem of elastic baffles, taking the advantage of the MPS-FSI method in computations of the fluid–structure interaction with large deformation.     

Long waves dissipation and harmonic generation by coastal vegetation

In this paper, we study the harmonic generation and energy dissipation as water waves propagating through coastal vegetation. Applying the homogenization theory, linear wave models have been developed for a heterogeneous coastal forest in previous works (e.g. [17], [10], [11]). In this study, the weakly nonlinear effects are investigated. The coastal forest is modeled by an array of rigid and vertically surface-piercing cylinders. Assuming monochromatic waves with weak nonlinearity incident upon the forest, higher harmonic waves are expected to be generated and radiated into open water. Using the multi-scale perturbation theory, micro-scale flows in the vicinity of cylinders and macro-scale wave dynamics are separated. Expressing the unknown variables (e.g. velocity, free surface elevation) as a superposition of different harmonic components, the governing equations for each mode are derived while different harmonics are interacting with each other because of nonlinearity in the cell problem. Different from the linear models, the leading-order cell problem for micro-scale flow motion, driven by the macro-scale pressure gradient, is now a nonlinear boundary-value-problem, while the wavelength-scale problem for wave dynamics remains linear. A modified pressure correction method is employed to solve the nonlinear cell problem. An iterative scheme is introduced to connect the micro-scale and macro-scale problems. To demonstrate the theoretical results, we consider incident waves scattered by a homogeneous forest belt in a constant shallow depth. Higher harmonic waves are generated within the cylinder array and radiated out to the open water region. The comparisons of numerical results obtained by linear and nonlinear models are presented and the behavior of different harmonic components is discussed. The effects of different physical parameters on wave solutions are discussed as well.     

Analysis of hydrodynamic behavior of a submersible net cage and mooring system in waves and current

Failure of net cage and mooring system is of great concern to the marine aquaculture industry. To avoid the structure failure in storm waves and current during typhoon events, net cage can submerge below the water surface in practice. A submersible net cage and mooring system is analyzed by numerical simulation and physical model test. The numerical model is established based on the lumped mass method and principle of rigid body kinematics. A series of physical model tests are conducted to validate the numerical model of single net cage and grid mooring system in waves and current. Numerical results correspond well with data obtained from physical model test. The results indicate that when net cage is submerged below the water surface, the deformation of net cage in waves can be improved significantly, and the tension force on the anchor line, bridle line and grid line will decrease significantly. However, the tension force on the buoy line in the submergence condition is larger than that in the floating condition. Different relative submergence ratios are also considered in our numerical simulation, and a relative submergence ratio equal to 0.1 is suggested here. The tension reduction ratio (56%) for the four-cage system is larger than that for the single-cage (52%) and double-cage systems (44%).     

Reduction of hydroelastic responses of a very-long floating structure by a floating oscillating-water-column breakwater system

The hydroelastic responses of a very-long floating structure (VLFS) placed behind a reverse T-shape freely floating breakwater with a built-in oscillating water column (OWC) chamber are analyzed in two dimensions. The Bernoulli–Euler beam equation is coupled with the equations of rigid and elastic motions of the breakwater and the VLFS. The interaction of waves between the floating rigid breakwater and the elastic VLFS is formulated in a consistent manner. It has been shown numerically that the structural deflections of the VLFS can be reduced significantly by a suitably designed reverse T-shape floating breakwater.