微重力环境下充液球腔非线性耦合动力学研究

采用球坐标系描述球腔中的液体动力学特性并建立一种轴对称贮腔类液刚耦合系统动力学模型．采用模态展开方法分析了微重环境下球形贮箱中的液体晃动问题,给出了球形贮箱内液体晃动速度势函数和波高函数的Gauss超几何级数解析表达式．采用变分原理推导了系统动力学系模型,利用Galerkin 方法对变分方程进行特征频率分析．运用Lagrange方法及非线性动力学方法导出了微重力环境下贮箱中液体与航天器结构耦合的动力学方程组,并对该方程组进行了数值计算,绘出了非线性耦合充液系统自由度随时间的变化历程．     

圆柱贮箱液体非线性晃动的多维模态分析方法

将Faltinsen等提出的多维模态理论应用到求解圆柱贮箱液体非线性晃动问题中．根据Narimanov-Moiseiev的三阶渐近假设关系,通过选取主导模态以及确定它们的阶次关系,将一般形式的无穷维模态系统降为五维渐近模态系统,即描述自由液面波高的广义坐标之间相互耦合的二阶非线性常微分方程组．通过对这个模态系统的数值积分,得到了与以前的理论分析和实验结果相吻合的非线性现象．研究结果表明,多维模态方法是用来求解液体非线性晃动动力学的一个很好的工具．在我们的下一步工作中,将继续发展这种方法,用来研究更为复杂的晃动问题．     

小Bond数条件下圆柱贮箱中液体晃动的模部分析

运用模部分析方法考察了小Bond数条件下圆柱贮箱中弯曲静液面对液体晃动模态的重构作用.研究表明,圆柱贮箱中的液体作小幅晃动时,参与晃动的各阶基本模态的正交性若仅由Bessel模部来给出,则弯曲静液面将使各阶模态加权耦合,形成新的特征模态;参与晃动的各阶基本模态的正交性若由三角函数模部来给出,则弯曲静液面将独立改变各阶模态的固有频率,各阶模态之间不耦合.运用新的重构模态来研究圆柱贮箱中液体的横向受迫晃动,给出了其模态选择特征.     

带弹性附件充液矩形贮箱俯仰运动动态响应

首先建立了俯仰运动矩形贮箱刚-液-弹耦合系统在外力矩作用下的耦合动力学模型,给出满足边界条件的速度势函数和液面波高的级数表达式,采用伽辽金法离散,将动力学模型转化为常微分方程组,得到刚-液-弹耦合系统的固有频率,给出简单的近似表达式,分析了转动中心距静液面不同位置时刚-液-弹耦合系统各阶固有频率的变化规律,系统转动中心距静液面较近时,耦合后液体反对称模态和刚体的固有频率对比耦合前减小,较远时则增大,最后进行数值验证,比较分析了液体和弹性体对刚体姿态的影响．     

液固耦合系统中液体的有限幅晃动力及晃动力矩

研究弹簧-质量系统与圆柱贮箱类液体有限幅晃动系统间的非线性耦合动力学问题。在建立了六自由度非线性耦合动力学模型的基础上,导出了液体有限幅晃动力和力矩解析表达式。指出在终了构形上积分及压力表达式中的非线性项是有限幅晃动作用力、作用力矩非线性的根源。x、y方向结果之间良好的对称性在很大程度上证明了结果的正确性。通过耦合机理分析可知,这样的理论结果应具有较大的普适性。数值仿真结果与有关实验结果进行了对比。分析认为,在终了构形上求晃动力、晃动力矩较为合理。舍去的高维模态基底及高阶非线性项以及液体晃动阻尼的复杂性是导致偏差的重要原因。     

旋转充液腔体的非线性稳定理论及其对Columbus问题的应用

对于任意形状、充满粘性液体的腔体绕惯性主轴整体旋转的一般情形,本文首先导出大扰动运动方程组,然后按照直接方法建立了弱非线性稳定理论,并应用于Columbus问题,得到和实验完全一致的结论。     

伴随变分方法在液体表面张力不稳定问题中的应用

本文应用一次近似变分直接方法对于旋转液体柱、柱形液体环,柱面内外液体膜等各种情形的表面张力不稳定问题作了统一的处理,得到“柱芯-液体-液体-柱壳”系统旋转运动稳定的充要条件,使以往的研究结果均可作为特例导出。同时阐明了旋转不稳定的物理机理,澄清以往研究中存在的一些争论。     

一类弹性储液箱同液体耦合晃动问题的分岔行为分析

建立了弹性圆柱型储液箱同液体耦合系统在外激励下的非线性振动方程组．采用多尺度法、奇异性理论研究此非线性振动系统共振解的分岔行为,通过对其分岔行为的分析和讨论,得到了这一系统的多种转迁集和分岔图,建立了系统参数与其拓扑分岔解的联系,并且分析了不同参数下系统的分岔特性,为实现储液器参数的优化控制提供了理论依据．     

微重力环境中摆转运动引起的流体晃动力及力矩

本文以部分充液的贮箱系统作为研究对象，用数值方法计算研究了在扰动力作用下流体系统的晃动力学问题。文中给出了由于系统摆转而在流体中引起的扰动加速度的数学表达式。晃动力的计算是在与贮箱固结在一起的非惯性坐标系中，对依赖于初始与边界条件的三维非稳态偏微分方程组进行数值求解，计算了在伴随系统的摆转运动而在流体中产生的扰动加速度作用下，流体施加于贮箱上的力与力矩的波动规律。     

关于充液腔体旋转运动稳定问题的变分原理及其应用

对于任意形状、充满粘性液体的腔体绕惯性主轴整体旋转的一般情形,导得小扰动运动的一组线性微分一积分方程组.在稳定理论基础上发展的一系列方法都处理不了这个问题.本文应用文献[1]中的方法导得这个问题变分原理的一般形式,并得到一系列稳定判据,以前不少作者的结果均是本文的特例^[3-6]。本文的变分方法在充液腔体运动稳定性问题中具有较广泛的应用,对于线性非自伴本征值问题原则上都能应用。     

An analytical solution for free liquid sloshing in a finite-length horizontal cylindrical container filled to an arbitrary depth

A general series-type theoretical formulation based on the linearized potential theory, the method of separation of variables, and the translational addition theorem for cylindrical Bessel functions is developed to study three-dimensional natural sloshing in a partially filled horizontally-mounted circular cylindrical tank of finite span. Assuming time-harmonic variations, the potential solutions associated with the Symmetric/Antisymmetric (S/A) modes of free liquid surface oscillations are first analytically expanded as series of bounded spatial functions with unknown modal coefficients. The impenetrability conditions of the rigid end-plates along with the free surface dynamic/kinematic boundary condition are then imposed. The zero-normal-velocity requirement of the lateral tank boundary is subsequently applied by innovative use of Graf's translational addition theorem for modified cylindrical Bessel functions. After truncation, four independent sets of homogeneous algebraic equations are obtained that are then numerically worked out for the natural sloshing eigen-frequencies and free surface oscillation mode shapes. Extensive numerical data include the first thirty six longitudinal/transverse Antisymmetric/Symmetric (AA, SA, AS, SS) dimensionless sloshing frequencies, for a wide range of liquid fill depths and container span to radius ratios. Also, the influence of fill depth on the free surface oscillation mode shapes is addressed through selected 2D images. Comprehensive numerical simulations illustrate the strong effects of container length and liquid fill depth on the calculated sloshing frequencies. It is revealed that the frequency branches with the same transverse mode number form a cluster that progressively merge together amid the tank fill-depth limits as the tank span ratio increases. On the other hand, when the tank length substantially decreases, the number of “frequency cross-overs” between various frequency clusters at certain liquid fill depths considerably increases. Moreover, primary advantages of proposed methodology in comparison to other approximate/numerical methods are explicitly pointed out, convergence of solution is tested, and accuracy/reliability of the results is demonstrated by comparisons with available data.     

拓扑优化技术在抑制流体晃荡中的数值模拟研究

流体晃荡问题广泛存在于船舶与海洋工程领域,任何部分载液的储罐运载装备在运动过程中均存在晃荡问题.当外界激励频率接近液舱内流体自由液面的固有频率时,很容易产生剧烈的晃荡,产生极大的冲击力,进而引起结构损害.因此,研究有效的减晃方案,以抑制流体晃荡带来的冲击具有重要意义.该文研究了基于自主研制的数值程序模拟长方体液舱内的流体晃荡问题.该数值程序采用有限差分法求解均质不可压缩的三维非定常Navier-Stokes方程,利用VOF/PLIC方法对自由液面进行捕捉,并结合基于最优控制理论的拓扑优化程序对液舱内隔板进行优化设计.数值计算了液舱内固定形状的双隔板以及拓扑优化的双隔板的晃荡问题,分析了增设双隔板后流场的运动学和动力学特性.结果表明,拓扑优化后的双隔板抑制流体晃荡的效果更好,为船舶与海洋工程领域和航空航天领域中的晃荡问题提供了一种新的研究思路.     

Seismic-generated unsteady motions in shallow basins and channels. Part I: Smooth analytical solutions

In this paper time-dependent water motions generated by seismic-type horizontal excitation in shallow basins and channels are modelled by the two-dimensional depth-averaged shallow water equations in which a specific source term is added in order to include an earthquake-induced forcing effect. Sinusoidal excitation is considered as a first approximation, and the response of shallow basins and channels to this simple external forcing is characterized. The nondimensional form of the governing equations shows that the Strouhal number and a ratio representing the amplitude of the forcing acceleration are the influential dimensionless parameters. Novel exact solutions of sinusoidally-forced smooth waves in a prismatic tank, a rectangular open channel, and a parabolic basin are presented. In the first two cases, a sway motion occurs, and reflections take place at the side walls. In the last case, the water sloshes back and forth flowing up the sloping sides of the basin; the free surface remains planar and a moving circular shoreline is present. These analytical solutions provide useful standards for assessing the accuracy of the numerical models used to solve the two-dimensional shallow water equations with source terms.     

气液耦合系统中固有频率的实验研究

流体砰击现象广泛存在于海洋环境、航空航天等自然界与工程中.流体砰击大尺度结构过程中,自由液面破碎时会包裹气体进入流场,气液混合易导致局部砰击荷载增大,引起结构破坏的危险.砰击过程中,气室压力对自由液面固有模态的影响尚未有系统的研究报道.该文采用物理模型实验方法在二维储舱内设计并开展一系列实验,系统研究了两种不同的气室压力对耦合系统的固有频率和阻尼的影响.实验中采用高速摄影机记录了自由液面振荡过程,通过自主研制的图像处理软件提取自由液面波高.结果表明:在低气室压力下,晃荡能量主要集中于一阶固有频率;在高气室压力下,晃荡能量主要集中于二阶固有频率.随着气室压强的增大,影响液体晃荡的主要固有频率提高,而对应的阻尼比却随之降低.因此,气体可压缩性是研究流体晃荡的一个重要因素.     

A numerical investigation of energy dissipation with a shallow depth sloshing absorber

A liquid sloshing absorber consists of a container, partially filled with liquid. The absorber is attached to the structure to be controlled, and relies on the structure’s motion to excite the liquid. Consequently, a sloshing wave is produced at the liquid free surface within the absorber, possessing energy dissipative qualities. The behaviour of liquid sloshing absorbers has been well documented, although their use in structural control applications has attracted considerably less attention.     

Free Cavitational Deceleration of a Circular Cylinder in a Liquid after Impact

The problem is considered about the vertical continuous impact and subsequent free deceleration of a circular cylinder semi-immersed in a liquid. The specificity of this problem is that, under certain conditions, some areas of low pressure near the body appear and the attached cavities are formed. The separation zones and the motion law of the cylinder are unknown in advance and have to be determined in solving the problem. The study of the problem is conducted by a direct asymptotic method effective for small spans of time. Some nonlinear problem with unilateral constraints is formulated that is solved together with the equation defining the law of motion of the cylinder. In the case when the space above the external free surface of a liquid is filled with a gas with low pressure (vacuum), an analytical solution of the problem is constructed. To determine the main hydrodynamic characteristics (the separation point and acceleration of the cylinder), we derive a system of transcendental equations with elementary functions. The solution of this system agrees well with the results obtained by the direct numerical method.     

Dynamics of a rotor partially filled with a viscous incompressible fluid

A rotor partially filled with a viscous incompressible fluid is modeled as planar system. Its structural part, i. e. the rotor, is assumed to be rigid, circular, elastically supported and running with a prescribed time-dependent angular velocity. Both parts, structure and fluid, interact via the no-slip condition and the pressure. The point of departure for the mathematical formulation of the fluid filling is the Navier-Stokes equation, which is complemented by an additional equation for the evolution of its free inner boundary. Further, rotor and fluid are subjected to volume forces, namely gravitation. Trial functions are chosen for the fluid velocity field, the pressure field and the moving boundary, which fulfill the incompressibility constraint as well as the boundary conditions. Inserting these trial functions into the partial differential equations of the fluid motion, and applying the method of weighted residuals yields equations with time derivatives only. Finally, in combination with the rotor equations, a nonlinear system of 12 differential-algebraic equations results, which sufficiently describes solutions near the circular symmetric state and which may indicate the loss of its stability. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Seismic-generated unsteady motions in shallow basins and channels. Part II: Numerical modelling

In this paper, unsteady motions generated by seismic-type excitation are simulated by a 2D depth-averaged mathematical model based on the classic shallow water approximation. A suitable time-dependent forcing term is added in the governing equations, and these are solved by a MUSCL-type shock-capturing finite volume scheme with a splitting treatment of the source term. The HLL approximate Riemann solver is used to estimate the numerical fluxes. The accuracy of the numerical scheme is assessed by comparison with novel exact solutions of test cases concerning sinusoidally-generated sloshing in a prismatic tank, a rectangular open channel, and a parabolic basin. A sensitivity analysis is performed on the influence of the relevant dimensionless parameters. Moreover, numerical results are validated against experimental data available in literature concerning shallow water sloshing in a swaying tank. Finally, real‐scale applications to a reservoir created by a dam and an urban water-supply storage tank are presented. The results show that the model provides accurate solutions of the shallow water equations with a seismic-type source term and can be effectively adopted to predict the main flow features of the unsteady motion induced by horizontal seismic acceleration when the long wave assumption is valid.