圆内开缝圆自然对流的Ruelle-Takens混沌道路

使用热格子Boltzmann方法针对圆内开缝圆自然对流的流动与换热进行数值模拟，通过相空间、功率谱等进行非线性动力学特性分析，研究其流动与换热的稳定性.结果表明：随着瑞利数Ra的增加，流场的相图从开始稳定的平衡点经历Hopf分岔后转变为极限环，表明流场进入一个倍周期性振荡状态；随着瑞利数进一步增加，稳定的极限环分岔为二维环面，系统相空间结构复杂化；当瑞利数Ra大于某一临界值时，二维环面分岔突变进入混沌状态，系统在相空间中出现非常复杂的轨线结构.总体上，通过系统不同瑞利数所对应的非线性动力学特性的表现形式，表明系统经过Ruelle-Takens道路到达混沌，展现出自然对流从稳定的流动和换热发展到非线性运动特征的混沌历程.

Ruelle-Takens Chaotic Natural Convection in a Horizontal Annulus with an Internally Slotted Circle

Natural convection in a two-dimensional horizontal annulus with an internally slotted circle is analyzed with lattice Boltzmann method (LBM). Flow instability is studied with nonlinear dynamic analysis techniques such as phase diagram and power spectrum. It shows that, with the increase of Rayleigh number Ra, the flow field changes from the beginning of a stable equilibrium point to a limit cycle after Hopf bifurcation. And the flow field may exhibit a change from steady-state to periodic oscillation. As the Rayleigh number is further increased, the stable limit cycle change to a two-dimensional torus. As the Rayleigh number Ra is greater than a critical value, chaotic state appears, and the system has a very complicated trajectory structure in the phase space. In general, the nonlinear dynamic characteristics and expressions at different Rayleigh numbers in the system show that the system evolves to chaos through Ruelle-Takens road. It shows evolution from a stable natural convection to chaotic motion with nonlinear characteristics.