环型圆管内对流动力学行为及数值分析  

Dynamic behavior and numerical analyze of convection dynamics in a circular tube

作　　者：王贺元 杨跃男[1] 柏孟卓[1] WANG Heyuan;YANG Yuenan;BAI Mengzhuo(College of Mathematics and Systems Science,Shenyang Normal University,Shenyang 110034,China)

机构地区：[1]沈阳师范大学数学与系统科学学院,沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2020年第5期447-450,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11572146)。

摘　　要：研究竖直放置的环型圆管内底部加热流体的对流动力学行为及其数值仿真问题。采用理论分析和Matlab数值仿真的方法,讨论了环型圆管内流体对应的类洛伦兹方程组的耗散性与吸引子的存在性问题,并且对该类洛伦兹方程组的定常解以及全局稳定性进行了分析与论证。通过数值模拟由不稳定周期到达混沌所展现的动力学行为,数值仿真给出了该系统的分岔图以及最大Lyapunov指数图,由图可确定随着雷诺数的增大,该系统存在音叉式分岔点和霍普夫分岔点。进而证明了当环型圆管底部加热到一定程度后圆管内的液体发生对流现象。动力学行为及Matalab数值仿真结果表明系统存在吸引子且产生混沌,解释了环型圆管内的对流动力学行为。The convection dynamics and numerical simulation of heated liquid in a vertical circular tube are studied.By using the methods of theoretical analysis and numerical simulation,the dissipation and the existence of the attractor of the Lorentz equations is discussed,and the steady solution of this kind of Lorentz equations and global stability are analyzed and demonstrated.Numerical simulation shows the dynamic behavior from unstable period to chaos.And the numerical simulation also shows the bifurcation diagram of the system and the largest Lyapunov index figure.It can be determined by the graph as r increases the system of the tuning fork type bifurcation and the Hopf bifurcation points.Then it is proved that the fluid in the circular tube will flow when heated to a certain degree.The results of dynamic behavior and Matalab numerical simulation show that there are attractors and chaos in the system,which explains the convection dynamics in the circular tube.

关 键 词：动力学行为 数值仿真 稳定性 混沌 

分 类 号：O193[理学—数学] O241[理学—基础数学]