Coupled analysis of nonlinear sloshing and ship motions

A coupled numerical model considering nonlinear sloshing flows and the linear ship motions has been developed based on a boundary element method. Hydrodynamic performances of a tank containing internal fluid under regular wave excitations in sway are investigated by the present time-domain simulation model and comparative model tests. The numerical model features well the hydrodynamic performance of a tank and its internal sloshing flows obtained from the experiments. In particular, the numerical simulations of the strong nonlinear sloshing flows at the natural frequency have been validated. The influence of the excitation wave height and wave frequency on ship motions and internal sloshing has been investigated. The magnitude of the internal sloshing increases nonlinearly as the wave excitation increases. It is observed that the asymmetry of the internal sloshing relative to still water surface becomes more pronounced at higher wave excitation. The internal sloshing-induced wave elevation is found to be amplitude-modulated. The frequency of the amplitude modulation envelope is determined by the difference between the incident wave frequency and the natural frequency of the internal sloshing. Furthermore, the coupling mechanism between ship motions and internal sloshing is discussed.     

Experimental studies of a damaged ship section in forced heave motion

This work documents a detailed series of experiments performed in a wave flume on a thin walled prismatic hull form. The model consists of a rectangular opening located on the side. The length of the model is slightly smaller than the flume breadth to achieve two-dimensional (2D) behavior in the experiments. Forced oscillatory heave tests in calm water have been carried out by varying the model-motion parameters and examining both intact and damaged conditions. Video recordings, measurements of the wave elevation inside the damaged compartment and of the force on the model were performed in all the experiments. The effect of damage opening in the model on hydrodynamic loads is examined by comparing with an intact section. A theoretical analysis is used to explain the behavior of added mass and damping coefficients in heave for a 2D damaged section. The presented results demonstrate occurrence of sloshing and piston mode resonances in the tests and their influence on the hydrodynamics loads of a damaged ship. Detailed physical investigations are presented at these resonance frequencies for the damaged section. Effect of filling level in the damage compartment, damage-opening length and air compressibility in the airtight compartment is examined. Nonlinear effects are documented and appear dominant, especially, for lowest filling level where we have shallow-water depth conditions in the damaged compartment. Resonance phenomena that can lead to significant local loads are identified for the shallow water condition. Air compressibility in the airtight compartment and floodwater act as a coupled system and influence inflow/outflow of floodwater in the compartment. It has a significant effect on local floodwater behavior in the damaged compartment.     

Shared-Memory parallelization of consistent particle method for violent wave impact problems

A shared-memory parallelization is implemented to the recently developed Consistent Particle. Method (CPM) for violent wave impact problems. The advantages of this relatively new particle method lie in four key aspects: (1) accurate computation of Laplacian and gradient operators based on Taylor series expansion, alleviating spurious pressure fluctuation and being able to model two-phase flows characterized by large density difference, (2) a thermodynamics-based compressible solver for modelling compressible air that eliminates the need of determining artificial sound speed, (3) seamless coupling of the compressible air solver and incompressible water solver, and (4) parallelization of the numerical model based on Open Multi-Processing (OpenMP) and a parallel direct sparse solver (Pardiso) to significantly improve computational efficiency. Strong and weak scaling analyses of the parallelized CPM are conducted, showing an efficiency speedup of 100 times or more depending on the size of simulated problem. To demonstrate the accuracy of the developed numerical model, three numerical examples are studied including the benchmark study of wave impact on seawall, and our experimental studies of violent water sloshing under rotational excitations and sloshing impact with entrapped air pocket. CPM is shown to accurately capture highly deformed breaking waves and violent wave impact pressure including pressure oscillation induced by air cushion effect.     

Hydrodynamic performance of a pile-supported OWC breakwater: An analytical study

A pile-supported OWC breakwater is a novel marine structure in which an oscillating water column (OWC) is integrated into a pile-supported breakwater, with a dual function: generating carbon-free energy and providing shelter for port activities by limiting wave transmission. In this work we investigate the hydrodynamics of this novel structure by means of an analytical model based on linear wave theory and matched eigenfunction expansion method. A local increase in the back-wall draft is adopted as an effective strategy to enhance wave power extraction and reduce wave transmission. The effects of chamber breadth, wall draft and air chamber volume on the hydrodynamic performance are examined in detail. We find that optimizing power take-off (PTO) damping for maximum power leads to both satisfactory power extraction and wave transmission, whereas optimizing for minimum wave transmission penalizes power extraction excessively; the former is, therefore, preferable. An appropriate large enough air chamber volume can enhance the bandwidth of high extraction efficiency through the air compressibility effect, with minimum repercussions for wave transmission. Meanwhile, the air chamber volume is found to be not large enough for the air compressibility effect to be relevant at engineering scales. Finally, a two-level practical optimization strategy on PTO damping is adopted. We prove that this strategy yields similar wave power extraction and wave transmission as the ideal optimization approach.     

Comparison of four numerical models for simulating seepage from salt marsh sediments

A boundary integral equation method (BIEM) model and three differently formulated finite element method (FEM) models were implemented to explore the spatial and temporal patterns in marsh pore water seepage that each generated. The BIEM model is based on the Laplace equation coupled to a dynamic free-surface condition that assumes that, as the water-table changes, the aquifer instantaneously loses or gains an amount of water equal to the change in head times the specific yield. The FEM models all implement a simplified Richards equation that allows gradual desaturation or resaturation and thus flow in both the saturated and unsaturated zones of the aquifer. Two of the FEM models are based on the governing equation for the USGS model SUTRA and thus take into account fluid and aquifer compressibility. One of these was modified to take into account the effect of tidal loading on the total stress, which is assumed to be constant in the derivation of the original version of SUTRA. The third FEM model assumes that neither the fluid or aquifer matrix is compressible so that changes in storage are due solely to changes in saturation. The unmodified SUTRA model generated instantaneous boundary fluxes that were up to two orders of magnitude greater, and spatially more uniform, than those of the other models. The FEM model without compressibility generated spatial and temporal patterns of the boundary fluxes very similar to those produced by the BIEM model. The SUTRA model with the tidal stress modification gave fluxes similar in magnitude to the BIEM and no compressibility models but with distinctly different distributions in space and time. These results indicate that accurate simulation of seepage from marsh soils is highly sensitive to aquifer compressibility and to proper formulation of the effect of tidal loading on the total stress in the aquifer. They also suggest that accurate simulation may require total stress correction not only for tidal loading but for changes in the water table as well. Finally, to aid the development of methods for the measurement of compressibility, we present a schematic, pore-scale model to illustrate the factors that may govern the compressibility of marsh soils.     

Experimental hydrodynamic investigation of a fixed offshore Oscillating Water Column device

Oscillating Water Column (OWC) is one of the pioneer devices in harnessing wave energy; however, it is not fully commercialized perhaps due to the complicated hydrodynamic behavior. Previous studies are significantly devoted to OWC devices located in nearshore and coastal regions where incident wave energy would experience dissipation more than offshore. In this paper, a 1:15 scaled fixed offshore OWC model is tested in a large towing tank of National Iranian Marine Laboratory. Wave spectrum shape effect on the efficiency of the OWC model is addressed. Moreover, the paper investigates the effects of the geometric and hydrodynamic factors on OWC device efficiency and uncovers new points in nonlinear interaction occurring inside the chamber; i.e. sloshing. The results indicate that shape of the spectrum inside the chamber is affected by the type of incident wave spectrum, especially for long waves. Pierson–Moskowitz spectrum leaded to higher efficiency rather than JONSWAP spectrum at longer incident wave periods. According to efficiency analysis, increasing wave height may lead to air leakage from the chamber followed by vortex generation, which is a reason for decreasing the efficiency of the OWC device. Furthermore, no shift in the resonant period of the OWC model, due to wave height increase, was observed at the opening ratios equal or smaller than 1.28%. Spectral analysis of water fluctuation inside the OWC chamber illustrates two modes of sloshing. The first mode can be seen at short period waves while the second mode is visible at long period waves. The sloshing modes approximately vanish by increasing draft value.     

Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating tank

A time-independent finite-difference method and a fifth-order Runge–Kutta–Felhberg scheme were used to analyze the dynamic responses of sea-wave-induced fully non-linear sloshing fluid in a floating tank. The interaction effect between the fully non-linear sloshing fluid and the floating tank associated with coupled surge, heave and pitch motions of the tank are analyzed for the first time in the present pilot study. For the analysis of fluid motion in the tank, the coordinate system is moving (translating and rotating) with tank motion. The time-dependent water surface of the sloshing fluid is transformed to a horizontal plane and the flow field is mapped on to a rectangular region. The Euler equations as well as the fully non-linear kinematic free surface condition were used in the analysis of the sloshing fluid. The strip theory for linearized harmonic sea-wave loading was adopted to evaluate the regular encounter wave force. In addition, the dynamic coefficients used in the dynamic equations of tank motion were also derived based on strip theory and a harmonic motion of the tank. The characteristics of free and forced tank motions with and without the sloshing effect are studied. By the damping effect, the response of free oscillation will damp out and that of forced oscillation will approach a steady state. Without sea-wave action, the contribution of the sloshing load would enlarge the angular response of tank motion as well as the rise of free surface and the sloshing effect will delay the damping effect on angular displacement. On the contrary, under sea-wave action, the sloshing effect will decrease the dynamic response of tank motion and rise of free surface. The interaction, sloshing and coupling effects are found to be significant and should be considered in the analysis and design of floating tanks.     

A probabilistic assessment of design sloshing pressure time histories in LNG tanks

The violent motion (sloshing) of liquefied natural gas (LNG) in cargo tanks has attracted significant attention. Transformations of the LNG market have led to the increased transport of LNG in partially filled tanks, but established technology is mainly based on engineering experience with completely filled containers. This paper investigates a large sample of sloshing pressure measurements. It focuses on the magnitude of individual sloshing impact events, and their associated temporal and spatial patterns. The durations of these impacts are comparable to the natural frequency of an LNG container wall, so the details of their time histories are important in determining the structural response. Experiments are performed on tanks with high (92.5%) and low (30%) filling levels, for various wave headings. The common post-processing approach of representing impact pressure histories by a triangular profile is studied, and an alternative approach is presented. Two statistical models are used to describe the distribution of maximal pressures in sloshing impacts: a three-parameter Weibull model and a generalized Pareto model. The latter is found to be of questionable utility due to small sample sizes. It is observed that for low filling levels the sloshing impacts are of greater magnitude, having longer durations, smaller ratios of rise time to duration, and larger spatial extents. All these factors should in principle increase the structural response.     

容器固有频率对液体晃荡的影响

针对矩形容器内液体晃荡问题,采用了时域高阶边界元方法建立自由水面满足完全非线性边界条件的数学模型。求解中采用混合欧拉-拉格朗日方法追踪流体瞬时水面,运用四阶龙格库塔方法更新下一时间步的波面和速度势。通过将计算得到的波面结果与实验数据、解析解和已发表结果对比,吻合良好,验证了本方法的准确性。进而采用谱分析方法分析了波面时间历程,得到容器各阶固有频率对液体晃荡的影响。研究发现,基频对液体晃荡的影响最大,且非线性越强,更高阶容器固有频率的影响越大。     

PSME model of parametric excitation of two-layer liquid in a tank

Internal waves driven by external excitation constitute important phenomena that are often encountered in environmental fluid mechanics. In this study, a pseudospectral σ-transformation model is used to simulate parametric excitation of stratified liquid in a two-layer rectangular tank. The σ-transformation maps the physical domain including the liquid free surface, the interface between the liquid layers, and the bed, onto a pair of fixed rectangular computational domains corresponding to the two layers. The governing equation and boundary conditions are discretised using Chebyshev collocation formulae. The numerical model is verified for two analytical sloshing problems: horizontal excitation of constant density liquid in a rectangular tank, and vertical excitation of stratified liquid in a rectangular tank. A detailed analysis is provided of liquid motions in a shallow water tank due to excitations in the horizontal and the vertical directions. Also, the effect of pycnocline on the wave motions and patterns is studied. It is found that wave regimes and patterns are considerably influenced by the pycnocline, especially when the excitation frequency is large. The present study demonstrates that a pseudospectral σ-transformation is capable to model non-linear sloshing waves in a two-layer rectangular tank.     

The air–water sloshing problem: Fundamental analysis and parametric studies on excitation and fill levels

The problem of liquid sloshing has gained recent attention with the proliferation of liquefied natural gas (LNG) carriers transporting liquids in partially filled tanks. Impact pressures caused by sloshing depend on the tank fill level, period and amplitude of oscillation of the tank. In this paper, we first present the rudiments of a linear potential theory for sloshing motions in a two-dimensional rectangular tank, due to small amplitude sway motions. Although this topic is fundamental, we clarify inconsistencies in the published literature and texts.Numerical investigations were carried out on the sloshing motions in a two-dimensional tank in the sway excitation. The fluid domain was modeled using a finite volume approximation, and the air–water interface was tracked using a volume-of-fluid (VOF) technique. Computational results for free surface elevation and impact pressure are found to be in good agreement with theory and published data. The fill levels were varied from 10% to 95%, and the excitation time periods were varied from 0.8 to 2.8 s for a constant sway amplitude of 0.25 m (peak–peak) at 1:30 scale. The results of the parametric study are compared with theoretical predictions and suggestions are made on incorporating sloshing effects in standard seakeeping analysis for LNG carriers.     

Sloshing waves and resonance modes of fluid in a 3D tank by a time-independent finite difference method

A 3D time-independent finite difference method is developed to solve for wave sloshing in a three-dimensional tank excited by coupled surge and sway motions. The 3D equations of fluid motion are derived in a moving coordinate system. The three-dimensional tank, with an arbitrary depth and a square base, is subjected to a range of excitation frequencies with motions that exhibit multiple degrees of freedom. For demonstration purposes the numerical scheme is validated by a benchmark study. Five types of sloshing waves were observed when the tank is excited by various excitation frequencies. A spectral analysis identified the resonant frequencies of each type of wave and the results show a strong correlation between resonant modes and the occurrence of the sloshing wave types. The method can be used to simulate fluid sloshing in a 3D tank with six-degrees of freedom.     

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.     

半球形多向波聚合波道振荡水柱气室优化设计

为了解决振动水柱式波浪能转换装置收集多向波浪问题,本文设计了半球形多向聚合波道振荡水柱气室结构,以适合远海单点波浪能采集和发电。在规则波正向入射条件下,基于流体仿真分析软件(FLUENT)、流体动力学连续性假设和粘性不可压缩流体动量守恒的运动方程(Navier-Stokes方程)建立半球形振荡气室和三维数值波浪水槽模型。仿真结果表明:增设气室后壁,合理设计波道开口角度实现多向迎波捕获波浪能,优化前壁形状可降低波浪触底反射带来的能量耗散,同时提高了气室内空气压强和出气口速度,有效提升波浪能俘获效率,为后续发电的二次能量转换提供高效的空气动力。     

A parametric sensitivity study on LNG tank sloshing loads by numerical simulations

A series of parametric sensitivity studies on unmatched dimensionless scale parameters is carried out on the liquified natural gas (LNG) tank sloshing loads by using a computational fluid dynamics (CFD) program. First, a brief dimensional analysis is conducted to identify the governing and non-matched non-dimensional parameters, assuming that Froude scaling law is adopted. Then the sensitivity of impact pressure is checked through numerical simulations against non-matched parameters, such as fluid viscosity, liquid-gas density ratio, and ullage pressure and compressibility. The CFD simulations are also verified against experimental results. It is concluded that the effects of viscosity and density ratio are insignificant, while the compressibility of ullage space plays an appreciable role, as was pointed out by Bass et al. [Bass, R.L., Bowles, E.B., Trudell, R.W., Navickas, J., Peck, J.C., Yoshimura, N., Endo, S., Pots, B.F.M., 1985. Modeling criteria for scaled LNG sloshing experiments. Transactions of the ASME 107, 272-280].     

Numerical simulations of sloshing flows with an elastic baffle using a SPH-SPIM coupled method

In this work, sloshing flows were successfully simulated by using a coupled numerical scheme between smoothed particle hydrodynamics (SPH) and smoothed point interpolation method (S-PIM) (SPH-SPIM coupled method). SPH is a Lagrangian particle method to solve flow fields while S-PIM is developed to deal with the structure dynamics. A coupling scheme is proposed, the key of which is that the fluid and solid fields are not necessary to be discretized by the same resolution. The stability, accuracy, convergence and conservation of the SPH-SPIM coupled method were validated by the case of hydrostatic water column on an elastic plate. Then, a wave impact problem was simulated to verify that the present SPH method worked well for sloshing flows. Finally, two sloshing problems with an elastic baffle were simulated, which validated the accuracy and stability of the method in predicting the fluid-structure interaction (FSI) features during the process of sloshing. It has been found that both the shape of the free surface and the large deformation of the elastic baffle can be well captured by the present method, which shows the potential of the present method to be a good candidate for simulating sloshing problems.     

Nonlinear modeling of liquid sloshing in a moving rectangular tank

A nonlinear liquid sloshing inside a partially filled rectangular tank has been investigated. The fluid is assumed to be homogeneous, isotropic, viscous, Newtonian and exhibit only limited compressibility. The tank is forced to move harmonically along a vertical curve with rolling motion to simulate the actual tank excitation. The volume of fluid technique is used to track the free surface. The model solves the complete Navier–Stokes equations in primitive variables by use of the finite difference approximations. At each time step, a donor–acceptor method is used to transport the volume of fluid function and hence the locations of the free surface. In order to assess the accuracy of the method used, computations are verified through convergence tests and compared with the theoretical solutions and experimental results.     

随机波作用下埋管海床动态响应及液化研究

基于广义Biot动力理论和Longuet-Higgins线性叠加模型,构建波浪-海床-管线动态响应的有限元计算模型,求解随机波作用下,多层砂质海床中管线周围土体孔隙水压力和竖向有效应力的分布。采用基于超静孔隙水压力的液化判断准则,得出液化区的最大深度及横向范围,从而判断海床土体液化情况。考虑海洋波浪的随机性,将海床视为多孔介质,海床动态响应计算模型采用u-p模式,孔隙水压力和位移视为场变量。并考虑孔隙水的可压缩性、海床弹性变形、土体速度、土体加速度以及流体速度的影响,忽略孔隙流体惯性作用。参数研究表明:土体渗透系数、饱和度以及有效波高等参数对海床土体孔隙水压力、竖向有效应力和液化区域分布有显著影响。     

Boundary element analysis of liquid sloshing characteristics in axisymmetric tanks with various porous baffles

This paper aims to investigate the effects of the porous baffles on the suppression of sloshing for the tanks with axisymmetric geometries under lateral excitation. Based on the assumptions of inviscid, irrotational, incompressible liquid and small amplitude sloshing, an axisymmetric boundary element method (BEM) for 3D Laplace equation is derived by using the Green's theorem together with the weighted residual method. And a zoning method is employed to model fluid domain in the tanks with complex porous baffles. Meanwhile, the porous baffles are treated motioning together with the tanks, and the velocity across the porous baffle is assumed to be linearly proportional to the pressure gradient between each side of the porous baffle. And the mechanism of suppressing the sloshing response is mainly the energy dissipation of the fluid passing through the porous baffle. Moreover, the linear free surface boundary conditions are also used to solve the governing equations. Compared with other numerical methods, the most prominent advantage of the BEM in solving axisymmetric potential problem is that only the boundaries of half the cross-section instead of the entire problem domain should be discretized, which can cut down large amount of memory and time costs. The present method is verified by comparing the numerical results with the existing literatures, and excellent agreements are obtained. Meanwhile, the proposed models are applied to investigate the effects of the porous baffles on sloshing response in circular cylindrical, annular cylindrical and conical tanks. The effects of the porous baffle length, porous-effect parameter, installation angle and baffle height on the sloshing force, natural frequency and surface elevation are studied. Additionally, some typical sloshing pressure distributions, velocity potential contours and velocity fields are plotted. The results show that swirls at the tips of the baffles can be observed in many cases, and the top-mounted porous baffle makes more significant suppression effects on sloshing response than that of bottom-mounted porous baffle, while increasing the number of ring porous baffles can achieve better restraint effects on sloshing response. And increasing the baffle length of the horizontal wall-mounted ring porous baffle can significantly decrease the sloshing frequencies, as well as the first non-dimensional natural frequency decreases with decrease in porous-effect parameter of the coaxial porous baffle. In addition, remarkable effects on sloshing can be obtained when reasonable designed by selecting the optimal porous-effect parameter, installation angle and baffle height. And this paper can be a useful guide for the seismic design and analysis of many actual liquid storage tanks (such as the Advanced Passive PWR, large water cooling tower, etc.).     

A coupled numerical model for simulation of wave breaking and hydraulic performances of a composite seawall

A numerical model is developed by combining a porous flow model and a two-phase flow model to simulate wave transformation in porous structure and hydraulic performances of a composite type low-crest seawall. The structure consists of a wide submerged reef, a porous terrace at the top and an impermeable rear wall. The porous flow model is based on the extended Navier-Stokes equations for wave motion in porous media and k−ε turbulence equations. The two-phase flow model combines the water domain with the air zone of finite thickness above water surface. A unique solution domain is established by satisfying kinematic boundary condition at the interface of air and water. The free surface advection of water wave is modeled by the volume of fluid method with newly developed fluid advection algorithm. Comparison of computed and measured wave properties shows reasonably good agreement. The influence of terrace width and structure porosity is investigated based on numerical results. It is concluded that there exist optimum value of terrace width and porosity that can maximize hydraulic performances. The velocity distributions inside and in front of the structure are also investigated.