Analytical and numerical study of the effects of an elastically-linked body on sloshing

In order to investigate the effects of an elastically-linked moving body on liquid sloshing inside a tank, an analytical formulation and a numerical approach were proposed to assess hydrodynamic loads in a partially filled rectangular tank with a body connected to the tank by springs. The analytical approach was developed based on the potential theory to calculate fluid velocity field, and the dynamics of the liquid sloshing coupled to the moving body are described as a mechanical system with two degrees of freedom. The coupling between the fluid and the moving body is given by a damping force calculated based on the body geometry and the fluid velocity field. The proposed numerical approach is based on the Moving Particle Semi-implicit (MPS) method, which is a Lagrangian particle-based method and very effective to model nonlinear hydrodynamics due to fluid–structure interaction. In the numerical approach, the rigid body is modeled as a cluster of particles and the motions are calculated considering its mass, moment of inertia, hydrodynamic loads and springs restoring forces. The elastic link between the body and tank is modeled by applying Hooke’s law. Simple cases of floating body motion were used to validate the numerical method. Finally, analytical and numerical results were compared. Despite its simplicity, the analytical approach proposed in the present work is an efficient approach to provide qualitative understanding and a first estimate of the moving body effects on the sloshing inside the tank. On the other hand, the numerical approach can provide more detailed information about the coupling phenomena, and it is an effective mean for the assessment of the reduction of the sloshing loads due to the moving body with elastic link. Finally, the effectiveness of the concept as a sloshing suppressing device is also investigated.     

基于拉格朗日描述的罐车内液体晃动模拟

基于拉格朗日描述的柔性多体系统动力学理论,采用绝对节点坐标有限元方法描述液体大变形运动,开展铁路液罐车内液体晃动模拟研究.本方法能够模拟液体自由表面的连续性变化,并适用于研究具有复杂外形容器的内部液体晃动问题.基于流体力学牛顿体基础理论,推导液体粘性方程和满足体积不可压缩的条件方程;采用基于绝对节点坐标方法描述的实体单元进行液体网格划分;采用罚函数方法描述液体与罐体之间的接触关系,组建液体-罐体耦合多体系统动力学方程.仿真计算液罐车内液体的横向和纵向晃动行为,发现液体自由表面形状呈非线性变化,不同断面处的高度和形状不同.     

液体晃动条件下飞艇水箱动力响应仿真分析

为了增加重载飞艇的载重能力,在满足结构强度要求下飞艇上的贮水水箱需要采用薄壁结构、轻质材料等方法来减轻重量。水箱在空中受到风载荷或其他载荷的作用,会导致水箱中的液体发生晃动,水箱在液体晃动和外部载荷共同作用下,可能会遭到破坏。考虑流固耦合作用对水箱结构的影响,分别从液体小幅晃动和大幅晃动两种情况对水箱动力响应进行研究。对于大幅晃动的情况,以试验所得风载荷加速度函数作为激励,利用计算流体动力学（CFD）方法进行仿真分析。分析结果表明,小幅晃动条件下,即使水箱发生共振,其结构也不会遭到破坏;大幅晃动条件下,1.3 mm以下壁厚钢材料水箱和2.1 mm以下壁厚铝合金材料水箱结构会遭到破坏。该分析结果可为水箱部分设计参数的确定提供参考依据。     

谐波平衡法求解俯仰运动矩形贮箱中液体非线性晃动

针对俯仰运动贮箱中液体的晃动用变分原理建立了一类新的Lagrange函数,以此为基础可以解析方式来研究俯仰运动贮箱中液体的非线性晃动．首先将速度势函数Φ在自由液面处作波高函数叩的Taylor级数展开,从而导出自由液面运动学和动力学边界条件非线性方程组;然后用谐波平衡法(HBM)假设其解为各次主导谐波叠加的形式,并代入方程组中得到含有未知系数相应多个代数方程式;最后用Broyden法对代数方程组求解．以无挡板开口二维、刚性矩形贮箱为例,研究了液体的大幅晃动,就液体晃动的幅值而言,在一定激励频率范围内,理论计算值与试验结果吻合较好,同时液面波高出现明显的零点漂移现象．     

微重环境下Cassini贮液腔中液体晃动特性研究

针对我国某一型号大型卫星液体燃料Cassini贮箱（腰为圆柱,两底为半球）,应用有限元方法研究了微重环境下液体的小幅晃动问题和横向受迫晃动问题,采用Galerkin方法得到了系统的有限元离散方程；得到了晃动固有频率和等效力学模型参数.针对周期脉冲激励,推导了液体作用于贮箱壁的晃动力和晃动力矩计算公式并给出了数值计算结果和分析结论.     

Step-by-step improvement of MPS method in simulating violent free-surface motions and impact-loads

The violent free-surface motions and the corresponding impact loads are numerically simulated by using the Moving Particle Semi-implicit (MPS) method, which was originally proposed by Koshizuka and Oka [10] for incompressible flows. In the original MPS method, there were several defects including non-optimal source term, gradient and collision models, and search of free-surface particles, which led to less-accurate fluid motions and non-physical pressure fluctuations. In the present study, how those defects can be remedied is illustrated by step-by-step improvements in the respective processes of the revised MPS method. For illustration, two examples are studied; (i) dam breaking problem and (ii) liquid sloshing inside a rectangular tank. The improvement of each step is explained and numerically demonstrated. The numerical results are also compared against the experimental results of Martin and Moyce [12] for dam-breaking problem and Kishev et al. [9] for sloshing problem. The numerical results for violent free-surface motions and impact pressures are in good agreement with their experimental data.     

基于浅水波理论液体晃动初值问题的数值模拟

针对日益受到关注的液体晃动问题,提出了一种基于浅水波理论的研究方案.该方案采用浅水波理论而非势流理论导出系统控制方程,并通过哈密顿体系表达;利用中心有限差分法和Stormer-Verlet算法进行空间和时间离散;模拟了不同初值条件下的液体晃动情况并对比分析了影响系统非线性响应的主要因素.结果表明,基于浅水波理论能有效解决液体晃动问题;与Euler格式对比,Stormer-Verlet算法精度较高;除共振外对于系统非线性响应的影响容器初始位移比初始速度更显著;非共振情况一定条件下,充液容器运动过程中液体晃动能起到阻尼作用.     

圆柱形贮箱液晃系统稳定性边界分析

本文研究了纵向激励下液晃系统的稳定性边界.首先利用等效摆模型获得纵向激励下液体晃动的等效动力学Mathieu方程,然后利用摄动法得到随阻尼、储液高度及贮箱直径变化时的液晃系统的稳定区域.结果表明,液体晃动阻尼、储液量及贮箱尺寸对晃动稳定性具有显著影响.     

多腔充液晃动的等效特性

用等效力学模型法研究了多腔体充液晃动问题.在单腔体等效模型的基础上给出了多腔体充液体的等效模型,并分析了液体分散到多个腔体后对飞行器带来的影响.结果表明,从频带的改善到作用力的减少等方面,一般情况下多个腔体的力学特性更有利于飞行器的动力学与控制设计.     

Comprehensive model of electrokinetic flow and migration in microchannels with conductivity gradients

A comprehensive model of electrokinetic flow and transport of electrolytes in microchannels with conductivity gradients is developed. The electrical potential is modeled by a combination of an electrostatic and an electrodynamic approach. The fluid dynamics are described by the Navier–Stokes equations, extended by an electrical force term. The chemistry of the system is represented by source terms in the mass transport equations, derived from an equilibrium approach. Moreover, the interaction between ionic species concentration and physicochemical properties of the microchannel substrate (i.e. zeta-potential) is taken into consideration by an empirical approach. Approximate analytical solutions for all variables are found which are valid within the electrical double layer. By using the method of matched asymptotic expansions, these solutions provide boundary conditions for the numerical simulation of the bulk liquid. The models are implemented in a Finite-Element-Code. As an example, simulations of an electrophoretic injection/separation process in a micro-electrophoresis device are performed. The results of the simulations show the strong coupling between the involved physicochemical phenomena. Simulations with a constant and a concentration-depend zeta-potential clarify the importance of a proper modeling of the physicochemical substrate characteristics.