基于MPS方法数值模拟三维LNG液舱的晃荡问题

该文基于自主开发的无网格粒子方法求解器MLParticle-SJTU,将MPS方法(moving particle semi-implicit)应用到三维LNG液舱的晃荡问题中,分别研究了LNG液舱在单自由度纵摇和横摇激励下,装载高度和激励频率对液舱晃荡作用的影响。首先,对装载高度为70%H的LNG液舱在单自由度纵摇和横摇激励下的晃荡问题分别进行了数值模拟,并将计算结果与实验结果进行比较,验证了MPS方法的可靠性。其次,对比不同装载高度,不同激励频率下液舱晃荡的拍击压力和流场分布情况,分析了装载高度和激励频率对晃荡作用的影响,并分析了一阶固有频率和共振频率随装载高度的变化规律。数值结果表明:激励频率对晃荡幅度影响较大;当激励频率在一阶固有频率附近时,会发生剧烈的晃荡现象;52.5%H为危险装载高度,在共振频率下,产生的拍击压力最大。     

用MPS方法数值模拟低充水液舱的晃荡

液体晃荡是一种非线性的自由面流动现象.在低充水率下,由于液体具有很大的运动空间,晃荡现象具有强烈的非线性特征,自由面的变形较大,剧烈时甚至会翻卷和破碎,这给数值模拟带来很大挑战.本文基于移动粒子半隐式法(Moving Particle Semi-Implicit,MPS)对低充水率的液舱晃荡问题进行了数值模拟.结果表明:当激励频率等于共振频率时,液体撞击到了液舱的顶板,并出现了飞溅现象,此时液体对侧舱壁产生了较大的抨击压力;在低于共振频率时,自由面出现了破碎波及波前的翻卷和融合等现象,抨击压力相对较小.计算结果表明,MPS方法能够很好地预测晃荡引起的拍击现象,数值计算得到的压力能够与实验结果很好地吻合.在自由面的追踪上,MPS方法具有很大的灵活性,能够很好地处理自由面的破碎、融合及液体的飞溅等流动现象.     

Dynamic Characteristics of Liquid Forced Sloshing in A Turning Spherical Tank with A Spacer Under Low Gravity

Under the condition of low gravity the characteristics of liquid forced sloshing in a turning spherical tank with a spacer were investigated. The static shape of the liquid surface was analyzed. By expanding the characteristic functions, the frequencies and velocity potential of liquid free-sloshing were derived. The governing equations and boundary conditions for the forced sloshing of liquid under the tank turning were established. The transverse force of liquid acting on the tank and the moment of force to the centre of the tank which is caused by the force of liquid acting on the spacer were given. Numerical results were compared with the ones of the spherical tank without a spacer. The results show that when a spacer is inserted in the tank, the sloshing frequency of liquid and the transverse force of liquid acting on the tank will decrease, but the moment of force to the centre of the tank which is caused by the force of liquid acting on the spacer will occur.     

THE EQUIVALENT MECHANICAL MODELS OF LIQUID SLOSHING IN A SPHERICAL TANK WITH SPACER UNDER LOW GRAVITY

The dynamics of liquid sloshing in a spherical tank with spacer under low gravity was investigated. By extending the characteristic functions, the frequencies of liquid free-sloshing, reaction force and moments on the wall of tank were obtained. By mechanical equivalent principle, the equivalent models of spring-vibrator-damper of liquid sloshing were given. The numerical results obtained show when a spacer is inserted in the tank, the sloshing frequency of liquid and the sloshing mass of liquid will decrease.     

超谐共振横摇下液舱晃荡特性数值研究

该文从船舶非线性横摇运动方程出发,采用多尺度法,获得其在正横规则波中的超谐共振稳态解,并将其作为液舱运动的外部激励。在此基础上,基于Open FOAM开源代码,采用基于VOF的两相流模型模拟液舱内气液运动,研究了船舶在超谐共振横摇条件下的液舱晃荡动特性问题。结果表明,在超谐共振横摇条件下,自由液面易出现翻卷、破碎等强非线性现象,舱壁压力时历表现出多峰型特征,其峰值要远大与简谐激励的情况,而且舱内液体晃荡在两个谐波成分的差频附近发生共振响应。     

带自由液面 Navier-Stokes 流动问题的ALE 分步有限元方法

将任意的拉格朗日 欧拉 (ArbitraryLagrange Euler,简称ALE)描述引入到Navier Stokes方程中 ,以速度和压力为基本变量 ,在时间域上采用分步求解格式 ,利用Galerkin加权余量法推导了分步格式的ALE有限元数值离散方程。并对带有自由液面的Navier Stokes流动问题的定解条件进行了分析讨论。最后利用所得到的ALE分步有限元方法对二维及三维不可压粘性液体大幅晃动问题进行了算例数值模拟 ,数值计算结果验证了本文方法及计算机仿真软件的正确性与可靠性     

Dynamic characteristics of liquid sloshing in a transversely vibrating spherical tank with a spacer under low gravity

The dynamic characteristics of liquid sloshing in a transversely vibrating spherical tank with spacer under low gravity were investigated. By expanding the characteristic functions, the frequencies and velocity potentials of liquid free-sloshing were obtained. The dynamic equations and boundary conditions of liquid sloshing in the traverse vibrational spherical tank with spacer under low gravity were derived. By modifying the velocity potentials of liquid free-sloshing, the velocity potentials of liquid sloshing in the traverse vibrating spherical tank with a spacer were obtained. Furthermore, the forces and the moments acting on tank wall were given. The numerical results show when a spacer is inserted in the tank, the sloshing frequencies of liquid and the forces acting on tank wall will decrease, but the moment of force to the centre of the tank which is caused by the force of liquid acting on the spacer will occur.     

DYNAMIC CHARACTERISTICS OF LIQUID SLOSHING IN A RECTANGULAR TANK UNDER LOW GRAVITY

1. INTRODUCTION The stability and the directional precision of liquid-filled spacecraft are influenced by the sloshing of liquid in the tank of spacecraft, which has been studied since 1960’s[1]. The major studies have been focused on the sloshing of liq…     

柱形容器内储液的驻留运动和地震响应

为合理制订大型油罐的设计规范,求解了柱形容器内粘性流体的驻留运动。按频域和任意水平地震输入的时历分析两种方式给出了储液波高和动水压力计算结果。与大型振动台试验结果的比较表阴,理论方法可以很好预估储液地震响应。     

ANALYTICAL SOLUTIONS FOR THE SLOSHING LOADING ON CIRCULAR CYLINDRICAL LIQUID TANKS WITH INTERIOR SEMI-POROUS BARRIERS

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The analysis of second-order sloshing resonance in a 3-D tank

Based on the potential theory and perturbation techniques, the problem of second-order sloshing in a three-dimensional tank in combination with surge and sway motions is analyzed. When excitation is applied in both horizontal directions, the second-order resonance can occur when the sum frequency or the difference frequency of any two excitation components is equal to one of the natural frequencies. The resonance can also occur when the sum or difference frequency of one of the excitation frequencies and one of the natural frequencies is equal to another natural frequency.     

Capillary effect on the sloshing of a fluid in a rectangular tank submitted to sinusoidal vertical dynamical excitation

Surface tension effects on fluid sloshing in a tank subjected to external excitation has been less studied. This work aims at understanding this phenomenon in order to derive practical solutions to problems faced in several engineering. A tank containing a fluid with a free surface is submitted to gravity and capillary forces and subject to external dynamic excitation. Introduction of vertical sinusoidal dynamical excitation leads to a problem of paramtric oscillations governed by the Mathieu equation. Analysis of the Mathieu equation shows the existence of stable and unstable regions in the stability diagram. Some results induced by harmonic excitations on the fluid sloshing are presented. When the external dynamical excitation amplitude ~ is small, periodic solutions appear in stable regions and when e increases, the fluid behavior is not perfectly periodic and the amplitudes are not regular. Nonlinear effects make the behavior of the fluid complicated and render it almost unpredictable. In stable regions, the solution remains bounded at any time. When changing the perturbation parameter 6, the phase difference increases and also with the increase of the surface tension.     

SIMULATION OF TANK SLOSHING BASED ON OPENFOAM AND COUPLING WITH SHIP MOTIONS IN TIME DOMAIN

Tank sloshing in ship cargo is excited by ship motions, which induces impact load on tank wall and then affects the ship motion. Wave forces acting on ship hull and the retardation function are solved by using three-dimensional frequency domain theory and an impulse response function method based on the potential flow theory, and global ship motion is examined coupling with nonlinear tank sloshing which is simulated by viscous flow theory. Based on the open source Computational Fluid Dynamics (CFD) development platform Open Field Operation and Manipulation (OpenFOAM), numerical calculation of ship motion coupled with tank sloshing is achieved and the corresponding numerical simulation and validation are carried out. With this method, the interactions of wave, ship body and tank sloshing are completely taken into consideration. This method has quite high efficiency for it takes advantage of potential flow theory for outer flow field and viscous flow theory for inside tank sloshing respectively. The numerical and experimental results of the ship motion agree well with each other.     

A numerical study of violent sloshing problems with modified MPS method

A numerical study on violent liquid sloshing phenomenon in a partially filled rectangular container is carried out by using moving particle semi-implicit(MPS) method. The present study deals with the implementation of five modifications all together over the original MPS method. The modifications include improved source terms for pressure Poisson equation, special approximation technique for the representation of gradient differential operator, collective action of mixed free surface particle identification boundary conditions, effecting Neumann boundary condition on solving the PPE and fixing judiciously the parting distance among particles to prevent collision. The suitability of the kernel function used in the original MPS method along with these five modifications is investigated for violent sloshing problems. The present model ensures a good agreement between numerical results with the existing experimental observations. The model is successfully applied to a partially filled tank undergoing horizontal sinusoidal excitation to compute the sloshing wave amplitudes and pressure on tank walls. The assessment of dynamic behaviour manifested in terms of base shear, overturning moment and impact pressure load exerted on tank ceiling induced by violent sloshing motion using MPS method is not reported in the open literature and has been efficiently carried out in the present study.     

不同液舱结构形式对晃荡的影响分析

本文就不同液舱结构形式对晃荡所产生的影响进行了分析研究。根据晃荡问题的特点及其液舱结构形式,建辛了数学模型。采用有限差分法离散流体运动方程,VOF法追踪自由表面,通度系数概念处理液舱内的障碍物。最后通过编制的计算程序,计算分析了不同结构形式液舱的防晃效果。     

NUMERICAL SIMULATION OF SLOSHING IN RECTANGULAR TANK WITH VOF BASED ON UNSTRUCTURED GRIDS

A new method for sloshing simulation in a sway tank is present, in which the two phase interface is treated as a physical discontinuity, which can be captured by a well-designed high order scheme. Based on Normalized Variable Diagram (NVD), a high order discretization scheme with unstructured grids is realized, together with a numerical method for free surface flow with a fixed grid. This method is implemented in an in-house code General Transport Equation Analyzer (GTEA) which is an unstructured grids finite volume solver. The present method is first validated by available analytical solutions. A simulation for a 2-D rectangular tank at different excitation frequencies of the sway is carried out. A comparison with experimental data in literature and results obtained by commercial software CFX shows that the sloshing load on the monitor points agrees well with the experimental data, with the same grids, and the present method gives better results on the secondary peak. It is shown that the present method can simulate the free surface overturning and breakup phenomena.     

Level-set法在液体晃荡研究中的应用

Level—set法是一种简便、通用、高效的计算分析空间运动界面的数值方法,本文尝试性地将Level—set方法应用于液体晃荡的研究,详细论述了应用该方法模拟液体晃荡的数学模型及数值解法。为了验证该方法处理晃荡问题的正确合理性,首先在势流假定下模拟了释放初始液面引起的自由晃荡,并将液面波动的数值结果与理论解析解进行了比较;然后模拟了二维矩形液箱做简谐横摇运动引起的液体受迫晃荡,计算结果以箱壁不同高度处的压强时间历经给出,并与实验结果进行了定量比较。计算结果初步表明采用Level—set方法研究液体晃荡现象是正确可行的。     

薄膜型LNG液舱中浮式制荡板的数值模拟研究

薄膜型液舱广泛用于FLNG(浮式液化天然气储存装置)、FSRU(浮式储存和再气化装置)和LNGC等LNG储运装置,液舱晃荡是目前国际上的一个重要的研究热点。晃荡会产生沿舱壁的爬高和冲击,各国研究人员相继提出了各类制荡措施,以确保液舱安全。该文根据港口工程中浮式防波堤的原理,提出在液舱壁面附近安装浮式制荡板的新设想。首先,针对日本学者提出的在液舱中部放置浮式制荡板的方案,建立带有浮式制荡板的二维液舱晃荡数学模型,并与其试验结果进行对比,验证了该数学模型的有效性;然后,采用该数学模型,对文中提出的方案,进行数值模拟和分析,探讨新型浮式制荡装置对制荡效果的影响,为下一步的结构优化和实船应用奠定基础。     

EXPERIMENTAL INVESTIGATION OF EFFECTS OF INNER-TANK SLO-SHING ON HYDRODYNAMICS OF AN FLNG SYSTEM

The present research focuses on experimentally clarifying the effect of inner-tank sloshing on the hydrodynamics of an Floating Liquefied Natural Gas(FLNG)system.Through the comparisons of the results obtained from the model tests carried out with the vessel model ballasted with liquid and solid cargo separately,the effects of the inner-tank sloshing on the hydrodynamics of an FLNG system are highlighted and presented.Statistical languages of the maximum,minimum,mean values and the standard deviations and power density spectra calculated with the help of the algorithm of Fast Fourier Transformation(FFT)are provided.It is concluded that the effects of the inner-tank sloshing on the responses of the FLNG system are sensitive to wave excitation frequencies,and that the effects of the inner-tank sloshing play an important role,particularly in the roll motion of the FLNG hull.The outcome of the proposed technique would offer constructive feedback,which can lead to more practical applications and can serve as a reference for the verification of the potential numerical simulations by other researchers.     

HYDROELASTIC VIBRATIONS AND LIQUID SLOSHING SUPPRESSION IN A RECTANGULAR TANK WITH ELASTIC SPACER

In this paper, the couple vibration of liquid and elastic spacer in a rectangular tank is investigated. Two different velocity potential functions corresponding respectively to the liquid above and below the elastic spacer are assumed.Complicated boundary conditions corresponding to two velocity potential functions and vibrations of elastic spacer are given. Using the method of energy, the equation of couple frequency is obtained. Through numerical computation the natural frequencies that change according to the location and stiffness of the spacer are shown.