二维晃动模态的统一Ritz计算格式

基于线性势流理论,推导了液体二维晃动的特征值方程,对于任意二维容器,通过引入第一Green公式,将矩形截面晃动模态的精确解作为基函数,提出了特征值问题Ritz统一计算格式,避免不同截面(不同的边界条件)需要引入不同基函数的复杂性,使得Ritz方法适用于任意截面内液体的二维晃动模态分析,可同时求解晃动频率与振型。本文方法分别用于求解半顶角为45°的三角形渠道、半椭圆形截面内液体的晃动频率,计算结果与其它解析方法的结果吻合良好,其计算精度完全满足工程要求。     

容器内液体晃动的变分有限元方法

提出了用变分有限元方法计算容器内液体晃动谐振频率的方法和步骤。这种方法可适用于各种形状复杂的容器内液体晃动问题，按照此方法对二维矩形容器问题进行了实际计算，对计算结果和解析方法获得的解进行了比较。     

截面任意形状的柱形和环形容器内液体晃动特性的精确解法

本文研究截面任意形状的柱形和环形容器内液体的晃动特性，利用Ｆｏｕｒｉｅｒ级数匹配法将液体速度势沿容器壁面展开得频率方程，由行列式搜根法数值计算各阶固有振动频率，结果是精确的，方法具有通用性。     

环形调频液体阻尼器（TLD）的计算模型

本文建立了液体在刚性环形容器内晃动的计算模型，这一模型可以用于调频液体阻尼器（ＴＬＤ）及结构─ＴＬＤ相互作用的研究。为了验证计算模型，进行了一系列的振动台试验，研究液体晃动第一振型的频率和动力反应。用模型计算的结果与试验结果符合良好，计算模型基本合理。     

液固耦合内流问题及防晃研究进展

对液固耦合内流问题以及液体晃动特性的研究在宇航工程中有着十分重要的意义，大型液体运载火箭以及战略弹道导弹中的推进剂与储箱的藕合效应和推进刑的晃动特性对它们的飞行动力稳定性有着很大的影响。为了使导弹和航天运载器具有良好的飞行稳定性，就必须对其内部液体推进剂的晃动加以抑制，避免使液体的晃动与整体结构的固有振动发生耦合，防止结构的固有振动频率和液体的晃动频率落入控制系统的频带之中。本文概述了近年来在液固耦合作用以及在推进剂防晃研究方面所取得的进展。     

二维晃动自然频率与阻尼比系数的试验识别

液体的晃动模态（自然频率、振型与阻尼比系数）是贮液结构设计以及振动控制的重要参数。在液体晃动的模态试验中,需要激发液面的模态运动,但液面的对称模态运动一般比较难以激发出来,使得对称模态参数（特别是阻尼比系数）难以精确识别。本文采用参数激振的方法对矩形、U形和圆形截面容器进行竖向激振,可容易激发出液体表面的前四阶模态(包括对称模态)运动,撤除激励后液体表面按某一特定的振型作自由衰减振动,通过激光测量液体表面波高的自由衰减曲线,从而精确得到液体晃动的自然频率与对应的阻尼比系数,测得晃动频率与理论频率结果吻合良好,表明本文试验识别方法有效。     

内置有水平挡板的矩形储液器非线性晃动分析

该文以内置有水平挡板的矩形储液器为研究对象,对储液器的非线性晃动问题展开研究。利用势流理论和虚功原理,推导了由水平挡板引起的储液器非线性阻尼比(非线性体现于波高有关)的计算公式,同时考虑水平挡板对储液器晃动频率的影响而对非线性阻尼比计算公式进行了修正。结合液体晃动的非线性分析理论,研究了水平挡板处于不同位置、挡板长度不同时储液器的液面波高与晃动力变化情况。利用Fluent软件进行了数值模拟,并与理论模型分析的结果进行对比。结果表明：当水平挡板靠近储液器底部或长度较小时,储液器内液体的非线性晃动现象较明显,利用非线性三阶模态方程推导得到的波高、晃动力与数值模拟结果较接近,而仅考虑一阶线性响应会明显低估储液器液面波高,但其求解的晃动力却与考虑非线性值的状况基本一致;随着挡板到自由液面距离的变小或挡板长度的增大,储液器液面波高、晃动力幅值减小,液体晃动呈线性变化,说明水平挡板靠近自由液面或增大其长度时能够提高储液器的阻尼比,进而也更能抑制液体的非线性晃动。同时水平挡板逐渐靠近自由液面或长度逐渐增大时,储液器晃动频率逐渐减小,减小的幅度分别可达到5.7%～28%。     

液阻悬置惯性通道阻尼特性的实验与计算分析

以一轿车动力总成惯性通道型液阻悬置为研究对象,讨论了线性与非线性集总参数模型和模型中物理参数的特点及应用范围;应用流体力学有限元分析的方法,计算得到了惯性通道两端压力差与其中液体流动流量的关系,设计并制作了实验台,对计算结果进行了验证.利用惯性通道中液体流动的动量方程和惯性通道两端的压力差与其流量的关系,采用最小二乘方法,得到了惯性通道中液体流动的阻尼参数.该方法得到的阻尼参数,在较大激振频率和激振振幅范围内反应了惯性通道的阻尼特性.利用非线性的集总参数模型和本文方法得到的惯性通道阻尼特性参数,对一液阻悬置的动态特性进行了计算分析,计算结果和实验结果具有较好的一致性.     

罐式集装箱液体晃动过程的数值模拟研究

罐车制动过程中,液体晃动产生的水击压力对罐车的安全性能具有很大的影响。基于此,本文运用FLUENT软件中的VOF模块模拟研究罐车在制动过程中罐内液体水击产生过程,并研究了罐车液体充装率、密度和黏度对罐体水击压强的影响。研究表明：制动过程中液体晃动水击内壁压力随着充装率的增加先增大后减小,充装率为0.85时,达到最大。且液体晃动水击内壁压力随着液体密度的增加而增大,随着液体黏度的增加而减小。按实际刹车制动过程液体晃动水击内壁压力计算的液化气体罐式集装箱的罐体最大应力要比按JBT4781-2005标准计算的最大应力增加33.2%,应依据实际刹车制动过程液体晃动水击内壁压力进行强度设计.     

液固纵向耦合系统的受迫响应

建立了柱形贮箱中液体与弹性体纵向耦合振动的一类动力学模型，并运用Ｂｅｒｎｏｕｌｉ积分及Ｄ′Ａｌｅｍｂｅｒｔ原理导出了相应的动力学方程。发现在小幅晃动情况下，航天器的振动将构成对液体的有滞后相角的参数激励，这一滞后相角是弹性体阻尼及外激励的函数。对该动力学方程运用多尺度方法，得到液体各阶模态晃动的摄动解，从而得出固液系统纵向耦合特征的若干规律性认识     

A successive boundary element model for investigation of sloshing frequencies in axisymmetric multi baffled containers

This study presents a developed successive Boundary Element Method to determine the symmetric and antisymmetric sloshing natural frequencies and mode shapes for multi baffled axisymmetric containers with arbitrary geometries. The developed fluid model is based on the Laplace equation and Green's theorem. The governing equations of fluid dynamic and free surface boundary condition are also applied to proposed model. A zoning method is presented to model arbitrary arrangement of baffles in multi baffled axisymmetric tanks. The influence of each zone on neighboring zones is applied by introducing interface influence matrix which correlates the velocity potential of interfaces to their flux. By discretizing the flow boundaries, the integral equation governed on the boundary is formulated into a general matrix eigenvalue problem. The proposed method has a considerable effect on decreasing computational cost and a good accuracy in determining the sloshing natural frequencies. The obtained results for different types of container based on the application of the presented study are validated in comparison with the literature and very good agreement is achieved. Finally, the effect of baffle parameters on the sloshing natural frequencies was investigated and some conclusions are outlined.     

A 3D BEM model for liquid sloshing in baffled tanks

The present work aims at developing a boundary element method to determine the natural frequencies and mode shapes of liquid sloshing in 3D baffled tanks with arbitrary geometries. Green's theorem is used with the governing equation of potential flow and the walls and free surface boundary conditions are applied. A zoning method is introduced to model arbitrary arrangements of baffles. By discretizing the flow boundaries to quadrilateral elements, the boundary integral equation is formulated into a general matrix eigenvalue problem. The governing equations are then reduced to a more efficient form that is merely represented in terms of the potential values of the free surface nodes, which reduces the size of the computational matrices considerably. The results obtained using the proposed model are verified in comparison with the literature and very good agreement is achieved. Finally, a number of example tanks having common configurations are used to investigate the effect of baffle on sloshing frequencies and some conclusions are outlined. Copyright © 2008 John Wiley & Sons, Ltd.     

Sloshing in a vertical circular cylindrical tank with an annular baffle. Part 1. Linear fundamental solutions

The paper centres around fundamental solutions of the linearised problem on fluid sloshing in a vertical circular cylindrical tank having a thin rigid-ring horizontal baffle. It develops an analytically oriented approach, which provides accurate approximations of natural frequencies and modes. The singular asymptotic behaviour of the velocity potential at the sharp baffle edge is also captured. A numerical analysis quantifies the natural frequencies and modes versus vertical position and width of the annular baffle. Forthcoming parts will use these approximate fundamental solutions in both nonlinear modal modelling and estimating the damping due to vorticity stress near the baffle.     

Large-displacement nonlinear sloshing in 2-D circular rigid containers — prescribed motion of the container

The two-dimensional large-displacement non-linear sloshing analysis of liquids in circular rigid containers is revisited. The updating of the free surface position is carried out using an adaptive technique for repositioning the computational nodes on the free surface avoiding the use of remeshing algorithms. Smoothing and volume correction approaches using polar co-ordinates are also presented. The fluid is modelled with potential flow theory using modified Rayleigh damping. All non-linear terms in the boundary conditions are taken into account. The known prescribed motion of the container is arbitrary. Boundary elements are used to solve the potential equations and standard techniques are used for the time integration. The analysis can be applied to arbitrarily shaped containers and is limited to the case of non-breaking waves. © 1998 John Wiley & Sons, Ltd.     

Analysis of the small amplitude sloshing of a liquid in a rigid container of arbitrary shape using a low‐order boundary element method

A boundary element method for estimating the natural sloshing frequencies and forces developed due to an inviscid, incompressible liquid oscillating in a rigid‐walled tank is presented here. The amplitude of oscillation is assumed to be small enough to allow linearization of the boundary condition at the free surface. Both free and forced oscillation cases are studied. Comparison with results available in the literature shows good agreement. The present method offers significant economy of computing resources compared to the finite element method. Copyright © 2000 John Wiley & Sons, Ltd.     

汽车燃油箱减振元件设计方法研究

汽车刹车之后油箱的燃油晃动噪声会引起车内驾驶员和乘客的不适,采用油箱减振元件是降低车内燃油晃动噪声的较为方便的手段。通过理论推导研究燃油晃动时油箱对车身的传递力,得出减振元件的效果主要由车身、油箱的局部机械导纳以及减振元件的柔度确定的结论。根据传递路径分析方法,设计了车身的力和加速度传递函数测量实验和整车制动实验,计算了减振元件工作时车身的受力情况。根据理论研究结果提出了一套油箱减振元件设计方法。     

Computational slosh dynamics: theory and industrial application

 The effect of liquid sloshing upon the performance, control, and acoustics of vehicles is becoming more pronounced with the increasing size of fuel tanks. Especially the fundamental natural frequency and the viscous damping rate are important quantities from an engineering point of view. Theory and industrial application for calculating numerically sloshing effects of viscous liquids within fuel tanks are presented for various container geometries. The numerical treatment uses the volume-of-fluid method for calculating the free surface flows. The efficiency and the error level of the chosen numerical approach are evaluated by academic benchmark tests. The industrial application presented covers a typical contemporary automotive fuel tank and its sloshing problems. Received: 27 May 2002 / Accepted: 6 January 2003 This work has been performed as a part of the automotive slosh research at KAUTEX TEXTRON GmbH & Co. KG, Bonn. In addition, the author expresses his thanks for submitting helpful papers by W. Eidel and H. Bauer, Neubiberg.