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 n...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.展开更多
Large-scale amplitude liquid sloshing in container under pitching excitation is numerically studied in this paper.Firstly,the kinematics of the ALE description is introduced and the fluid dynamics equations are revise...Large-scale amplitude liquid sloshing in container under pitching excitation is numerically studied in this paper.Firstly,the kinematics of the ALE description is introduced and the fluid dynamics equations are revised in the ALE form.Secondly,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 paper.Then the numerical discretized equations of fractional step finite element method are developed by Galerkin weighted residual method.Furthermore,the numerical simulation of large-scale amplitude sloshing of the liquid both in rectangular container and cylindrical container is carried out.The computed time evolution of the wave height,and free surface profiles at different time are obtained.Comparisons 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.展开更多
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 t...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.展开更多
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 mechanis...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.展开更多
基金the National Natural Science Foundation of China （Grant Nos. 10272022 ＆ 10572022） the Basic Research Foundation of Beijing Institute of Technology （Grant No. 000Y07）.
文摘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.
基金Supported by the National Natural Science Foundation of China (Grant Nos.10572022,10772022)
文摘Large-scale amplitude liquid sloshing in container under pitching excitation is numerically studied in this paper.Firstly,the kinematics of the ALE description is introduced and the fluid dynamics equations are revised in the ALE form.Secondly,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 paper.Then the numerical discretized equations of fractional step finite element method are developed by Galerkin weighted residual method.Furthermore,the numerical simulation of large-scale amplitude sloshing of the liquid both in rectangular container and cylindrical container is carried out.The computed time evolution of the wave height,and free surface profiles at different time are obtained.Comparisons 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.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10772026, 11072030)the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20080070011)+1 种基金the Scientific Research Foundation of Ministry of Education of China for Returned Scholars (Grant No. 20080732040)the Program of Beijing Municipal Key Discipline Construction
文摘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.
基金supported by the National Natural Science Foundation of China (10772026, 11072030)the Ph.D. Programs Foundation of Ministry of Education of China (20080070011)+1 种基金the Scientific Research Foundation of Ministry of Education of China for Returned Scholars (20080732040)the Program of Beijing Municipal Key Discipline Construction
文摘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.
