Lin Wenxian, Armfield S W
Solar Energy Research Institute, Yunnan Normal University, Kunming, Yunnan 650092, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jul;72(1 Pt 2):016306. doi: 10.1103/PhysRevE.72.016306. Epub 2005 Jul 18.
The flow behavior associated with cooling an initially quiescent isothermal Newtonian fluid with Prandtl number (Pr) less than one in a vertical cylinder by unsteady natural convection with an imposed lower temperature on vertical sidewalls is investigated by scaling analysis and direct numerical simulation. The flow is dominated by three distinct stages of development, i.e., the boundary-layer development stage adjacent to the sidewall, the stratification stage, and the cooling-down stage, respectively. The first stage can be further divided into three distinct substages, i.e., the start-up stage, the transitional stage, and the boundary-layer steady-state stage, respectively. A scaling analysis is carried out to obtain scaling laws for the basic flow features in terms of the flow control parameters, i.e., the Rayleigh number Ra, Pr, and the aspect ratio of the cylinder A , respectively. A series of direct numerical simulations with selected values of A , Ra, and Pr in the ranges of 1/3< or = A< or =3, 10(6) < or =Ra < or = 10(10) , and 0.01< or =Pr< or =0.5 are carried out, and it is found that the numerical results agree well with the scaling laws. These numerical results are further used to quantify these scaling laws for Ra, A , and Pr in the above-mentioned ranges.
通过尺度分析和直接数值模拟，研究了在垂直圆柱体内，通过对垂直侧壁施加较低温度的非稳态自然对流，冷却初始静止的普朗特数（Pr）小于1的等温牛顿流体时的流动行为。该流动由三个不同的发展阶段主导，即分别为靠近侧壁的边界层发展阶段、分层阶段和冷却阶段。第一阶段可进一步细分为三个不同的子阶段，即启动阶段、过渡阶段和边界层稳态阶段。进行尺度分析以获得根据流动控制参数，即瑞利数Ra、Pr和圆柱的纵横比A表示的基本流动特征的尺度律。对A、Ra和Pr在1/3≤A≤3、10⁶≤Ra≤10¹⁰以及0.01≤Pr≤0.5范围内的选定值进行了一系列直接数值模拟，结果发现数值结果与尺度律吻合良好。这些数值结果进一步用于量化上述范围内Ra、A和Pr的这些尺度律。
