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.     

Numerical study of the wave-induced slamming force on the elastic plate based on MPS-FEM coupled method

Slamming is the phenomenon of structure impacting the water surface. It always results in the extremely high load on the structure. This paper is mainly concerned with the slamming force caused by the wave-plate interaction. In this paper, the process of solitary wave impacting onto the horizontal plate is simulated with the help of the moving particle semi-implicit and finite element coupled method(MPS-FEM). The MPS method is adopted to calculate the fluid domain while the structural domain is solved by FEM method. In the first series of simulations, the profiles of the solitary waves with various amplitudes, which are generated in the numerical wave tank, are compared with the theoretical results. Thereafter the interaction between the solitary waves and a rigid plate is simulated. The effects of wave amplitude, as well as the elevation of the plate above the initial water level, on the slamming force are numerically investigated. The calculated results are compared with the available experimental data. Finally, the interactions between the solitary waves and the elastic plate are also simulated. The effects of the structural flexibility on the wave-induced force are analyzed by the comparison between the cases with elastic and the rigid plate.     

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.     

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.     

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.     

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.     

Comparative study of MPS method and level-set method for sloshing flows

This paper presents a comparative study of a meshless level-set method in the simulation of sloshing flows. The numerical moving particle semi-implicit （MPS） method and a grid based schemes of the MPS and level-set methods are outlined and two violent sloshing cases are considered. The computed results are compared with the corresponding experimental data for validation. The impact pressure and the deformations of free surface induced by sloshing are comparatively analyzed, and are in good agreement with experimental ones. Results show that both the MPS and level-set methods are good tools for simulation of violent sloshing flows. However, the second pressure peaks as well as breaking and splashing of free surface by the MPS method are captured better than by the level-set method.     

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.     

Numerical Simulation and Analysis on the Hemodynamics of An Elastic Aneurysm

Intracranial aneurysms are pathological dilatations which endanger people＇s health. Hemodynamics is thought to be an important factor in the pathogenesis and treatment of aneurysms. To date, the bulk of investigations into hemodynamics have been conducted by making use of mathematically idealized models for rigid aneurysms and associated arteries. However the walls of aneurysms and associated arteries are elastic in vivo. This study shows the differences of the simulation between elastic and rigid wall models. The numerical simulation of elastic aneurysm model is made fi＇om a representative Digital Subtraction Angiography （DSA） image and calculated with CFD software to get the wall deformation and the velocity field. Then the results are analyzed. By comparing the simulation results of the two models from their velocity vectors and shear stress distribution, many differences can be noted. The main difference exists in the distribution of velocity magnitude at some sections, with one outlet having obviously off-center distribution for the elastic wall model. The currents of the distribution of wall shear stress along the wall of aneurysm simulated in rigid and elastic wall models were similar. But there were apparent differences between the two models on the values of wall shear stress especially at the neck of aneurysm. The off-center distribution of velocity magnitude affects the distribution of wall shear stress and the exchange of substance through the wall. The analysis demonstrated clearly that the results of 2-D elastic numerical simulation were in good agreement with the clinical and pathological practice. The results of this study play an important role in the formation, growth, rupture and prognosis of an aneurysm on clinic application.     

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.     

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     

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。     

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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