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Numerical study of three-dimensional free surface dynamics

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Acta Mechanica Sinica 2006年第2期22卷 120-126页

作者： baozeng yue Zhaolin Wang Department of Mechanics School of Science Beijing Institute of TechnologyBeijing 100081 China Institute of Astronautics and Aeronautics Tsinghua University Beijing 100084 China

The dynamic problem of three-dimensional free surface is numerically studied in this paper. The ALE （Arbitrary Lagrange-Euler） kinematic description is introduced into the control equation system. The ALE description method is used to track free surface. Accurate formulations for calculating the normal vector on the free surface are presented. The discrete numerical equations by finite element method are developed by Galerkin weighted residual method. The boundary condition about free-surface tension is represented in the form of weak integration that can be computed by a differential geometry method derived in the present paper. The effect of contact angle is incorporated in the numerical algorithm. Furthermore, the numerical computations are performed and the comparison between computational and analytical results validated the effectiveness of the method. The results of this paper provide a fundamental understandings of the dynamics of liquid free surfaces, in which the surface tension and contact angle boundary conditions are taken into account. Finally, numerical simulation of largescale amplitude sloshing of liquid in a cylindrical container is performed and a numerical analysis of the effect of an annular ring-shaped rigid damping baffle on liquid sloshing oscillations in a cylindrical tank is also carried out.

关键词： Free surface Surface tension Numerical simulation Finite element

Attitude tracking control of flexible spacecraft with large amplitude slosh

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Acta Mechanica Sinica 2017年第6期33卷 1095-1102页

作者： Mingle Deng baozeng yue School of Aerospace Engineering Beijing Institute of Technology Beijing 100081 China

This paper is focused on attitude tracking control of a spacecraft that is equipped with flexible appendage and partially filled liquid propellant tank. The large amplitude liquid slosh is included by using a moving pulsating ball model that is further improved to estimate the settling location of liquid in microgravity or a zero-g environment. The flexible appendage is modelled as a three-dimensional Bernoulli–Euler beam, and the assumed modal method is employed.A hybrid controller that combines sliding mode control with an adaptive algorithm is designed for spacecraft to perform attitude tracking. The proposed controller has proved to be asymptotically stable. A nonlinear model for the overall coupled system including spacecraft attitude dynamics,liquid slosh, structural vibration and control action is established. Numerical simulation results are presented to show the dynamic behaviors of the coupled system and to verify the effectiveness of the control approach when the spacecraft undergoes the disturbance produced by large amplitude slosh and appendage vibration. Lastly, the designed adaptive algorithm is found to be effective to improve the precision of attitude tracking.

关键词： Attitude tracking Large amplitude liquid slosh Flexible spacecraft Dynamic coupling Adaptive sliding mode control

Large-scale amplitude liquid sloshing in container under pitching excitation

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Chinese Science Bulletin 2008年第24期53卷 3816-3823页

作者： yue baozeng Department of Mechanics School of Science Beijing Institute of Technology Beijing 100081 China

Large-scale amplitude liquid sloshing in container under pitching excitation is numerically studied in this ***,the kinematics of the ALE description is introduced and the fluid dynamics equations are revised in the ALE ***,the boundary condition about free-surface tension is represented in the form of weak integration that can be computed by the differential geometry method derived in the present paper and the normal vector on free surface is calculated using accurate formulas presented in this *** the numerical discretized equations of fractional step finite element method are developed by Galerkin weighted residual ***,the numerical simulation of large-scale amplitude sloshing of the liquid both in rectangular container and cylindrical container is carried *** computed time evolution of the wave height,and free surface profiles at different time are *** among the present numerical results with other published numerical results and experimental data confirm the effectiveness and validity of the method developed in this paper.

关键词：纵摇激发数字模拟液体晃动自由面张力

Heteroclinic bifurcations in attitude maneuver of coupled slosh-spacecraft with flexible appendage

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Science China(Technological Sciences) 2011年第8期54卷 2090-2099页

作者： yue baozeng SONG XiaoJuan Department of Mechanics School of Aerospace Engineering Beijing Institute of Technology Beijing 100081 China

In this paper, the chaotic dynamics in an attitude transition maneuver of a slosh-spacecraft coupled with flexible appendage in going from minor axis to major axis spin under the influence of dissipative effects due to fuel slosh and a small flexible appendage constrained to only torsional vibration is investigated. The slosh-spacecraft coupled with flexible appendage in attitude maneuver carrying a sloshing liquid is considered as multi-body system with the sloshing motion modeled as a spherical pendulum. The focus in this paper is that the dynamics of the liquid and flexible appendage vibration are coupled. The equations of motion are derived and transformed into a form suitable for the application of Melnikov’s method. Melnikov’s integral is used to predict the transversal intersections of the stable and unstable manifolds for the perturbed system. An analytical criterion for chaotic motion is derived in terms of system parameters. This criterion is evaluated for its significance to the design of spacecraft. The dependence of the onset of chaos on quantities such as body shape and magnitude of damping values, fuel fraction and torsional vibration frequency of flexible appendage are investigated. In addition, we show that a spacecraft carrying a sloshing liquid, after passive reorientation maneuver, will end up with periodic limit motion other than a final major axis spin because of the intrinsic non-linearity of fuel slosh. Furthermore, an extensive numerical simulation is carried out to validate the Melnikov’s analytical result.

关键词： chaotic attitude maneuver liquid-filled spacecraft flexible appendage liquid slosh

Hamilton–Pontryagin spectral-collocation methods for the orbit propagation

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Acta Mechanica Sinica 2021年第11期37卷 1696-1713,I0003页

作者： Zhonggui Yi baozeng yue Mingle Deng School of Aerospace Engineering Beijing Institute of TechnologyBeijing100081China China Academy of Space Technology Beijing100094China

According to the discrete Hamilton–Pontryagin variational principle,we construct a class of variational integrators in the real vector spaces and extend to the Lie groups for the left-trivialized Lagrangian mechanical systems by employing the spectral-collocation method to discretize the corresponding Lagrangian and kinematic *** constructed framework can be transformed easily to the well-known symplectic partitioned Runge–Kutta methods and the higher order symplectic partitioned Lie Group methods by choosing same interpolation nodes and quadrature *** numerical experiments about the orbit propagation of Kepler two-body system and the rigid-body flow propagation of a free rigid body are conducted,*** simulating results reveal that the constructed update schemes can possess simultaneously the excellent exponent convergence rates of spectral methods and the attractive long-term structure-preserving properties of geometric numerical algorithms.

关键词： Hamilton-Pontryagin principle Spectral-collocation method Lie groups Variational integrator Orbit propagation

Chebyshev spectral variational integrator and applications

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Applied Mathematics and Mechanics(English Edition) 2020年第5期41卷 753-768页

作者： Zhonggui YI baozeng yue Mingle DENG School of Aerospace Engineering Beijing Institute of TechnologyBeijing 100081China China Academy of Space Technology Beijing 100094China

The Chebyshev spectral variational integrator(CSVI) is presented in this paper. Spectral methods have aroused great interest in approximating numerically a smooth problem for their attractive geometric convergence rates. The geometric numerical methods are praised for their excellent long-time geometric structure-preserving *** to the generalized Galerkin framework, we combine two methods together to construct a variational integrator, which captures the merits of both methods. Since the interpolating points of the variational integrator are chosen as the Chebyshev points,the integration of Lagrangian can be approximated by the Clenshaw-Curtis quadrature rule, and the barycentric Lagrange interpolation is presented to substitute for the classic Lagrange interpolation in the approximation of configuration variables and the corresponding derivatives. The numerical float errors of the first-order spectral differentiation matrix can be alleviated by using a trigonometric identity especially when the number of Chebyshev points is large. Furthermore, the spectral variational integrator(SVI) constructed by the Gauss-Legendre quadrature rule and the multi-interval spectral method are carried out to compare with the CSVI, and the interesting kink phenomena for the Clenshaw-Curtis quadrature rule are discovered. The numerical results reveal that the CSVI has an advantage on the computing time over the whole progress and a higher accuracy than the SVI before the kink position. The effectiveness of the proposed method is demonstrated and verified perfectly through the numerical simulations for several classical mechanics examples and the orbital propagation for the planet systems and the Solar system.

关键词： geometric numerical method spectral method variational integrator Clenshaw-Curtis quadrature rule barycentric Lagrange interpolation orbital propagation

Nonlinear phenomena of three-dimensional liquid sloshing in microgravity environment

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Chinese Science Bulletin 2006年第20期51卷 2425-2431页

作者： yue baozeng WANG Zhaolin Department of Mechanics School of Science Beijing Institute of Technology Beijing 100081 China Institute of Astronautics and Aeronautics Tsinghua University Beijing 100084 China

The dynamic problem of three-dimen- sional liquid sloshing is numerically studied in this paper. The arbitrary Lagrange-Euler (ALE) kinematic description is introduced into the control equations system. The discrete numerical equations of finite element method are developed by Galerkin weighted residual method. The boundary condition about free-surface tension is represented in the form of weak integration that can be computed by our dif- ferential geometry method derived. The normal vec- tor on free surface is calculated by using accurate formula presented in this paper. The numerical computations are performed and the comparison not only between numerical results and analytical results but also between numerical results and experimental results validated the effectiveness of the method. Finally, large amplitude sloshing of three-dimensional liquid in low-gravity environment is simulated and some important nonlinear characteristics are ob- tained. From the numerical results, it is concluded that the character of nonlinear sloshing of the liquid under low-gravity environment is much different from that of the liquid sloshing under normal gravity envi- ronment.

关键词：表面张力微重力环境数值模拟航天器运动学非线性现象

Chaotification in the stretch-twist-fold (STF) flow

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Chinese Science Bulletin 2013年第14期58卷 1655-1662页

作者： yue baozeng AQEEL Muhammad Department of Mechanics School of Aerospace Engineering Beijing Institute of Technology Department of Mathematics COMSATS Institute of Information Technology

Chaotic behavior and detailed parameter analysis of stretch-twist-fold (STF) flow are investigated. STF flow is associated with fluid particle motion which naturally arises in the dynamo theory. It proposes a mechanism, by which a celestial bodies, such as earth and sun, can maintain and amplify the magnetic field continuously. Parameter analysis is performed using linearization theory for different choices of parameters. The existence of Heteroclinic trajectory of Sil'nikov type is proved using an undetermined coefficient method. It connects two non trivial equilibrium points. As a consequence, the Sil'nikov criterion guarantees that STF flow has Smale horseshoes chaos.

关键词：混沌行为扭折待定系数法发电机理 Sil 线性化平衡点

Stage separation of recoverable liquid launch vehicle by using moving pulsating ball analogue for propellant sloshing

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Chinese Journal of Aeronautics 2024年第2期37卷 360-370页

作者： Yu LU baozeng yue Bailong HAO Bole MA Feng LIU Yuanyuan CHANG School of Aerospace Engineering Beijing Institute of TechnologyBeijing 100081China Beijing Institute of Astronautical Systems Engineering Beijing 100076China

In the process of stage separation of recoverable liquid launch vehicles,because of the large amount of residual fuel in the storage tanks,the influence of liquid sloshing on separation safety must be *** calculation simplicity and operation practicability,the Moving Pulsating Ball Model(MPBM)of large amplitude liquid sloshing is introduced into the calculation of launch vehicle stage *** the dynamic equation of the model with the energy relationship during"breathing movement",the formula calculating the force of liquid on the rigid body is *** with the calculations of commercial CFD calculation software,the accuracy of MPBM model is ***,all the external forces and moments are applied to the rigid body of the stages,so that the translational and rotational dynamic equations of the stages are obtained *** to the relative position of the two stages,the geometric shape of the interstage section and the engine of the second stage,the minimum clearance in the separation process can be decided to guarantee that the separation process is safe.

关键词： Moving Pulsating Ball Model(MPBM) Dynamics of stage separation Large amplitude sloshing Recoverable liquid launch vehicle Flight dynamics