Zheng Laiyun, Zhao Bingxin, Yang Jianqing, Tian Zhenfu, Ye Ming
School of Mechanical Engineering, Ningxia University, Yinchuan 750021, China.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China.
Entropy (Basel). 2020 Feb 29;22(3):283. doi: 10.3390/e22030283.
This paper studied the Rayleigh-Bénard convection in binary fluid mixtures with a strong Soret effect (separation ratio ψ = - 0.6 ) in a rectangular container heated uniformly from below. We used a high-accuracy compact finite difference method to solve the hydrodynamic equations used to describe the Rayleigh-Bénard convection. A stable traveling-wave convective state with periodic source defects (PSD-TW) is obtained and its properties are discussed in detail. Our numerical results show that the novel PSD-TW state is maintained by the Eckhaus instability and the difference between the creation and annihilation frequencies of convective rolls at the left and right boundaries of the container. In the range of Rayleigh number in which the PSD-TW state is stable, the period of defect occurrence increases first and then decreases with increasing Rayleigh number. At the upper bound of this range, the system transitions from PSD-TW state to another type of traveling-wave state with aperiodic and more dislocated defects. Moreover, we consider the problem with the Prandtl number P r ranging from 0.1 to 20 and the Lewis number L e from 0.001 to 1, and discuss the stabilities of the PSD-TW states and present the results as phase diagrams.
本文研究了在底部均匀加热的矩形容器中具有强索雷特效应（分离比ψ = - 0.6）的二元流体混合物中的瑞利 - 贝纳德对流。我们使用高精度紧致有限差分法来求解用于描述瑞利 - 贝纳德对流的流体动力学方程。获得了一种具有周期性源缺陷的稳定行波对流状态（PSD - TW），并详细讨论了其性质。我们的数值结果表明，新型PSD - TW状态由埃克豪斯不稳定性以及容器左右边界处对流涡旋产生和湮灭频率的差异维持。在PSD - TW状态稳定的瑞利数范围内，缺陷出现的周期随瑞利数增加先增大后减小。在该范围的上限处，系统从PSD - TW状态转变为具有非周期性且更错位缺陷的另一种行波状态。此外，我们考虑了普朗特数Pr范围为0.1至20以及刘易斯数Le范围为0.001至1的问题，讨论了PSD - TW状态的稳定性，并将结果表示为相图。
