Stable response of low-gravity liquid non-linear sloshing in a circle cylindrical tank

Under pitch excitation,the sloshing of liquid in circular cylindrical tank includes planar motion,rotary motion and rotary motion inside planar motion.The boundaries between stable motion and unstable motion depend on the radius of the tank,the liquid height,the gravitational intension,the surface tensor and the sloshing damping.In this article,the differential equations of nonlinear sloshing are built first. And by variational principle,the Lagrange function of liquid pressure is constructed in volume intergration form.Then the velocity potential function is expanded in series by wave height function at the free surface.The nonlinear equations with kinematics and dynamics free surface boundary conditions through variation are derived.At last,these equations are solved by multiple-scales method.The influence of Bond number on the global stable response of nonlinear liquid sloshing in circular cylinder tank is analyzed in detail.The result indicates that variation of amplitude frequency response characteristics of the system with Bond,jump,lag and other nonlinear phenomena of liquid sloshing are investigated.     

燃料大幅晃动等几何分析仿真及航天器耦合动力学研究

现代航天器肩负许多周期长且复杂的航天任务,通常需要携带大量的液体燃料.贮箱中液体燃料大幅晃动会严重影响航天器的姿态稳定性和控制精度,是现代航天器耦合动力学建模和精确控制研究的重要问题.本文提出了一种新的液体大幅晃动数值仿真方法,采用等几何分析方法对贮箱内气体和液体整体进行建模和空间离散,采用压力修正的分步法对控制方程进行时间离散,结合水平集方法划分气体和液体区域并且实时追踪液体晃动自由面.提出了一种质量修正方法以消除水平集函数演化产生的液体质量误差.基于燃料大幅晃动等几何分析仿真方法,对携带太阳能帆板的充液航天器进行动力学建模和耦合运动数值仿真.对于太阳能帆板的振动问题则采用Kirchhoff-Love板理论建模和模态分析法数值求解.通过将数值仿真结果与解析解对比,证明了本文给出方法的正确性.本文还对燃料大幅晃动下的航天器刚-液-柔耦合运动进行了数值仿真,发现液体晃动对航天器的姿态变化和结构振动的幅值和频率具有不可忽视的影响.     

ACTUATION OF SLOSHING MODULATED FORCE AND MOMENT ON LIQUID CONTAINER DRIVEN BY JITTER ACCELERATIONS ASSOCIATED WITH SIEW MOTION IN MICROGRAVITY

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EQUIVALENT DYNAMICS MODELING AND ANALYSIS OF LIQUID-FILLED SPACECRAFT WITH FUEL CONSUMPTION 1)

在轨航天器贮腔内的液体可能表现出多种不同的运动模式, 主要包括液体相对于贮腔的整体性刚体运动、自由液面横向晃动、液体起旋后逐步发生明显的旋转晃动及液体自旋运动; 复合三自由度刚体摆晃动模型能够较为全面地描述这些液体运动模式, 同时为研究起旋阶段的液体晃动动力学问题提供了有效手段. 本文对非线性液体晃动刚体摆复合模型作进一步发展, 考虑模型等效参数随贮腔充液比的变化, 提出了变参数的刚体摆复合模型, 该模型适用于研究燃料消耗下非线性晃动类充液航天器大范围运动耦合动力学问题. 采用刚体摆复合模型对球形贮腔内的液体晃动进行等效后, 基于混合坐标意义下的拉格朗日方程推导了一类充液航天器轨道-姿态-晃动全耦合的动力学方程组, 并展开了充液航天器大角度三轴稳定姿态机动和零冲量轨道机动仿真以及航天器耦合动力学响应特性分析. 研究表明: 液体相对于贮腔的运动会造成航天器主刚体位置发生偏移, 当航天器在执行零冲量机动时, 燃料消耗会造成航天器的轨道平动速度无法收敛到零; 贮腔偏心布放时, 航天器在执行轨道机动过程中贮腔内液体易发生剧烈而且形式复杂的晃动行为, 进而可能造成航天器刚体运动的不稳定.     

燃料消耗下充液航天器等效动力学建模与分析

在轨航天器贮腔内的液体可能表现出多种不同的运动模式, 主要包括液体相对于贮腔的整体性刚体运动、自由液面横向晃动、液体起旋后逐步发生明显的旋转晃动及液体自旋运动; 复合三自由度刚体摆晃动模型能够较为全面地描述这些液体运动模式, 同时为研究起旋阶段的液体晃动动力学问题提供了有效手段. 本文对非线性液体晃动刚体摆复合模型作进一步发展, 考虑模型等效参数随贮腔充液比的变化, 提出了变参数的刚体摆复合模型, 该模型适用于研究燃料消耗下非线性晃动类充液航天器大范围运动耦合动力学问题. 采用刚体摆复合模型对球形贮腔内的液体晃动进行等效后, 基于混合坐标意义下的拉格朗日方程推导了一类充液航天器轨道-姿态-晃动全耦合的动力学方程组, 并展开了充液航天器大角度三轴稳定姿态机动和零冲量轨道机动仿真以及航天器耦合动力学响应特性分析. 研究表明: 液体相对于贮腔的运动会造成航天器主刚体位置发生偏移, 当航天器在执行零冲量机动时, 燃料消耗会造成航天器的轨道平动速度无法收敛到零; 贮腔偏心布放时, 航天器在执行轨道机动过程中贮腔内液体易发生剧烈而且形式复杂的晃动行为, 进而可能造成航天器刚体运动的不稳定.      

Autoparametric interaction of a liquid surface in a rectangular tank with an elastic support structure under 1:1 internal resonance

Autoparametric interaction of a liquid free surface in a rectangular tank with an elastic support structure, which is subjected to vertical excitation, is investigated. When the natural frequency of the structure is equal to the lowest natural frequency of liquid sloshing, this system is categorized as an autoparametric system with an internal resonance ratio 1:1. The structure is elastically supported so there is a higher possibility that the 1:1 internal resonance can be observed. The nonlinear theoretical analysis is conducted for a fluid assumed to be perfect in a tank with a finite liquid depth. The equations of motion for the first three sloshing modes are derived employing Galerkin’s technique and considering both the nonlinearity of the fluid motion, and the viscous damping effect. Then the theoretical frequency response curves for the harmonic oscillations of the structure and sloshing are determined using van der Pol’s method. The frequency response curves show that high amplitudes of the structure’s vibrations facilitate the liquid sloshing. Furthermore, the influence of the internal detuning parameter is investigated by showing the frequency response curves and bifurcation sets. Hopf bifurcations may occur followed by amplitude-modulated motions. The theoretical results are in quantitative agreement with the experimental data.     

晃荡液舱内水动冲击力的分段仿射模型

针对舱内晃荡液体与舱壁的相互作用,对舱内水动冲击力的等效力学模型进行了研究。基于混合系统理论,建立了强非线性液体晃荡的等效摆分段仿射模型,重点对矩形液舱的简化等效力学模型进行了分析。利用计算流体动力学软件Flow3D对矩形液舱内的强非线性液体晃荡进行了数值仿真。理论分析表明：分段仿射模型更符合刚性碰撞的假定,可以更有效地描述等效摆和舱壁碰撞时的速度跃变。仿真结果的对比表明：受到激励时,等效摆分段仿射模型所产生的力与Flow3D计算的结果比较接近,利用此模型可以恰当地描述强非线性液体晃荡。     

俯仰激励下三维液体大幅晃动问题研究

主要研究俯仰激励下三维液体大幅晃动问题,将任意Lagrange-Euler法 (arbitrary Lagrange-Euler, ALE)运动学描述引入到Navier-Stokes方程中,推导了俯仰激励下液体大幅晃 动数值模拟计算公式,并利用Galerkin加权余量法推导了有限元数值离散方程和分步有限 元计算格式,采用ALE分步有限元方法对圆筒形贮腔中的液体大幅晃动进行了数值模拟计 算. 得到了波高、晃动力及晃动力矩等晃动特性的时间变化历程,并对结果进行了分析,揭 示了俯仰激励下三维液体大幅晃动问题的非线性现象.     

Non-linear multimodal model for tuned liquid dampers of arbitrary tank geometry

Tuned liquid dampers (TLDs) utilize sloshing fluid to absorb and dissipate structural vibrational energy. Simple TLD tank geometries may not always be feasible due to space limitations. While the non-linear modelling of sloshing fluid is currently limited to tanks of simple geometries, this paper develops a non-linear multimodal model which describes the sloshing behaviour of a fluid in a flat-bottom tank of arbitrary geometry. The mode shapes of the sloshing fluid are found by solving the Helmholtz equation over the tank domain using the finite element method. The Bateman-Luke variational principle is used to develop a system of ordinary differential equations which account for the coupling of the sloshing modes through the non-linear free surface boundary conditions. Damping is incorporated into the model by considering the drag produced on a set of damping screens inserted in the fluid. The system of ordinary differential equations is solved using the Runge-Kutta-Gill Method to predict the wave heights and sloshing forces. In general, the mode shapes in an arbitrary tank will have components in two orthogonal (x- and y-) directions. This out-of-plane behaviour is an important consideration for TLD design. The model is validated with existing models for the special cases of rectangular and circular tanks. Lastly, new shake table tests are conducted on a tank of complex geometry.     

Motion stability dynamics for spacecraft coupled with partially filled liquid container

This paper presents a canonical Hamiltonian model of liquid sloshing for the container coupled with spacecraft. Elliptical shape of rigid body is considered as spacecraft structure. Hamiltonian system is an important form of mechanical system. It mostly used to stabilize the potential shaping of dynamical system. Free surface movement of liquid inside the container is called sloshing. If there is uncontrolled resonance between the motion of tank and liquid-frequency inside the tank then such sloshing can be a reason of attitude disturbance or structural damage of spacecraft. Equivalent mechanical model of simple pendulum or mass attached with spring for sloshing is used by many researchers. Mass attached with spring is used as an equivalent model of sloshing to derive the mathematical equations in terms of Hamiltonian model. Analytical method of Lyapunov function with Casimir energy function is used to find the stability for spacecraft dynamics. Vertical axial rotation is taken as the major axial steady rotation for the moving rigid body.     

俯仰激励下液体大幅晃动问题研究

主要研究俯仰激励下液体大幅晃动问题，将ALE(arbitrary Lagrange-Euler)运动学描述引入到Navier-Stokes方程中，推导了俯仰激励下液体大幅晃动数值模拟计算公式，并利用Galerkin加权余量法推导了有限元数值离散方程，采用ALE有限元方法对方形贮腔中的液体大幅晃动进行了数值模拟计算，对结果进行了比较分析，揭示了俯仰激励下液体大幅晃动问题的非线性现象。     

三维液体非线性晃动及其复杂现象

主要讨论三维液体非线性晃动问题 。将ALE（任意的拉格朗日-欧拉）运动学描述引人到Navier-Stokes方程的分步有限元计算格式中;在时间域上采用分步离散方法中的速度修正格式,利用Galerkin加权余量方法得到了系统的有限元离散方程;推导了考虑表面张力效应时有限元边界条件的弱积分形式;模拟了三维液体的非线性晃动问题,得到了一系列三维液体非线性晃动的复杂现象.进一步模拟了考虑表面张力效应以及在微重力环境下三维液体的非线性晃动,揭示了考虑表面张力效应以及在微重力环境下液体非线性晃动的重要特征.井将所得结论与现有的实验结果进行了比较.从而证实了该方法的有效性与正确性.     

Mathematical modelling and control of a nonholonomic spherical robot on a variable-slope inclined plane using terminal sliding mode control

In this paper, the three degrees-of-freedom motion of a two-dimensional rectangular liquid tank under wave action is simulated by the boundary element method in time domain. The coupling effects between tank motion and internal sloshing flow are investigated in partially filled conditions. The fourth-order Runge–Kutta method is adopted to update the wave shape and velocity potential on the free surface. The fully nonlinear mutual dependence of the incident wave, tank motion and internal sloshing flow is decoupled through an auxiliary function method, by which the liquid tank acceleration can be obtained directly without knowing the pressure distribution. The corresponding validation of numerical model is carried out and indicates that the accuracy of the present method is satisfactory to evaluate the dynamic responses of tank and sloshing motion. The corresponding response amplitude operators of tank motions for various wave frequencies, amplitudes and filling conditions are obtained, and the nonlinear coupling effects of sloshing flow on the tank responses are analyzed. It is found that the coupling effects have significant influence on sway and roll motion while have little impact on heave motion. The most important coupling effects on roll motion are the split of peak. In addition, due to the nonlinearity of sloshing flow, the roll motion amplitude is not linearly proportional to wave amplitude.     

低重环境下俯仰运动圆柱贮箱中液体非线性晃动

在低重力环境下,用变分原理建立了液体晃动的压力体积分形式的Lagrange函数,并将速度势函数在自由液面处作波高函数的级数展开,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;最后用四阶Runge-Kutta法求解非线性方程组。计算结果表明,随俯仰激励频率的逐渐变化,由于面外主模态和次生模态同时失稳,致使整个系统各阶模态和波高函数由稳态运动过渡为不稳定运动。     

矩形贮箱内液体非线性晃动动力学建模与分析

基于理想流体的假设,根据H-O原理建立了充液贮箱刚体平动与液体非线 性晃动的耦合动力学方程,通过引入改进的势函数描述刚体和液体之间的动边界. 利用伽辽 金方法对动力学方程进行了离散. 针对液体非线性晃动情况,与ALE有限元方法、边界元方 法的结果进行了比较,验证了方法的可行性. 对刚体平动和液体非线性晃动耦合的情 况,数值模拟了多种外力激励下系统的响应. 利用等效力学模型解释了耦合系统固有频率升 高的现象.     

Sloshing simulation of standing wave with time-independent finite difference method for Euler equations

The numerical solutions of standing waves for Euler equations with the nonlinear free surface boundary condition in a two-dimensional(2D) tank are studied.The irregular tank is mapped onto a fixed square domain through proper mapping functions. A staggered mesh system is employed in a 2D tank to calculate the elevation of the transient fluid.A time-independent finite difference method,which is developed by Bang-fuh Chen,is used to solve the Euler equations for incompressible and inviscid fluids.The numer...     

基于时域解耦算法的多液舱浮式结构物运动模拟

对于带有多个晃荡液舱的浮式结构物, 浮体的运动、外场水动力以及各舱内的液体晃荡力会实时相互决定, 发生复杂的耦合作用. 为准确模拟多液舱浮式结构物的运动, 本文引入一种有效的时域解耦算法. 该方法以模态分解法为基础, 通过对浮式结构物所受外域水动力和各液舱内非线性晃荡力进行模态分解, 最终形成时域解耦运动方程, 无需迭代求解过程即可显式计算浮式结构物的瞬时加速度. 该方法可避免传统迭代求解方法在迭代次数、截断误差和收敛特性等方面的不足, 减少解耦过程的计算耗时. 本文进一步结合边界元数值方法, 分别对单液舱浮式结构物和多液舱浮式结构物的工况开展数值模拟研究. 通过与单液舱浮式结构物的实验结果对比, 验证了本文时域解耦算法的有效性. 本文详细分析了晃荡力对单液舱浮式结构物运动的影响, 发现存在一个共振影响区间: 当外场波浪频率在该区间之外时, 可以在时域计算结果中观察到稳定的浮体运动; 在比该区间更低频的波况下, 液舱晃荡力与外场波浪力相位相反甚至可以相互抵消, 此时晃荡液舱的存在可以减弱浮体运动; 在比该区间更高频的波况下, 液舱内晃荡力与外场波浪力可以具有相同相位, 此时晃荡液舱的存在会加剧浮体的运动. 本文进一步研究了四液舱浮式结构物在波浪中的纵荡、垂荡和纵摇运动情况, 发现非线性液舱晃荡可对纵荡和纵摇运动产生影响, 但对垂荡运动影响很小.      

Neural network-based reduced-order modeling for nonlinear vertical sloshing with experimental validation

In this paper, a nonlinear reduced-order model based on neural networks is introduced in order to model vertical sloshing in presence of Rayleigh–Taylor instability of the free surface for use in fluid–structure interaction simulations. A box partially filled with water, representative of a wing tank, is first set on vertical harmonic motion via a controlled electrodynamic shaker. Accelerometers and load cells at the interface between the tank and an electrodynamic shaker are employed to train a neural network-based reduced-order model for vertical sloshing. The model is then investigated for its capacity to consistently simulate the amount of dissipation associated with vertical sloshing under different fluid dynamics regimes. The identified tank is then experimentally attached at the free end of a cantilever beam to test the effectiveness of the neural network in predicting the sloshing forces when coupled with the overall structure. The experimental free response and random seismic excitation responses are then compared with that obtained by simulating an equivalent virtual model in which the identified nonlinear reduced-order model is integrated to account for the effects of violent vertical sloshing.

     

重力环境下液体大幅晃动运动脉动球模型及实验研究

现代航天器通常携带大量的液体推进剂, 在航天器的姿态发生变化的过程中, 由于惯性力和重力的作用, 可能会导致液体燃料发生剧烈晃动, 由此产生附加的晃动力会对航天器造成重要影响. 为了得到液体晃动的规律并满足星载计算机实时计算的要求, 本文研究并验证了一种用于等效液体大幅晃动的动力学模型. 首先将液体大幅晃动运动脉动球模型MPBM推广到重力环境中, 通过脉动球的牛顿?欧拉动力学方程和“呼吸运动”过程中能量关系式, 推导出晃动力法向分量的表达式. 同时, 引入不参与晃动的液体的等效模型, 使得液体质心位置的计算更加准确. 通过和文献中实验数据以及CFD软件的计算结果进行比较, 分别验证了推广的MPBM模型在大幅晃动、零动量机动工况下的有效性, 并基于该等效模型, 研究了脉冲激励的不同时序对航天器中液体晃动响应的影响. 最后, 设计并搭建了用于精确测量液体晃动力的实验平台, 验证了MPBM模型在等效非球形储箱的液体晃动时也同样可以很好地反应出晃动力的变化趋势. 本文的研究工作对进一步研究重力环境中充液航天器刚–液耦合动力学行为具有重要的参考价值.