﻿ 长方体腔内关于密度极值温度对称加热-冷却时冷水瑞利-贝纳德对流稳定性
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 力学学报  2015, Vol. 47 Issue (5): 722-730  DOI: 10.6052/0459-1879-15-171 0

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Hu Yupeng, Li Yourong. NUMERICAL INVESTIGATION ON FLOW STABILITY OF RAYLEIGH-BĖNARD CONVECTION OF COLD WATER IN A RECTANGULAR CAVITY COOLED AND HEATED SYMMETRICALLY RELATIVE TO THE TEMPERATURE OF DENSITY MAXIMUM[J]. Chinese Journal of Ship Research, 2015, 47(5): 722-730. DOI: 10.6052/0459-1879-15-171.
[复制英文]

文章历史

2015-05-12收稿
2015-07-14录用
2015-07-20网络版发表

1. 中国工程物理研究院总体工程研究所, 绵阳621900;
2. 重庆大学动力工程学院, 重庆400044

|引 言

1 物理数学模型

 图 1 物理模型 Fig.1 Physical model

 $\rho = {\rho _{\rm{m}}}{\rm{ }}\left( {1 - \gamma {{\left| {T - {T_{\rm{m}}}} \right|}^q}} \right)$ (1)

 $\nabla \cdot V = 0$ (2)
 ${\partial _\tau }V + V \cdot \nabla V = - \nabla P + {\nabla ^2}V + (Ra/Pr){\left| {\Theta - {\rm{ }}{\Theta _{\rm{m}}}} \right|^q}{e_Z}$ (3)
 ${\partial _\tau }{\rm{ }}\Theta + V \cdot \nabla {\rm{ }}\Theta = {\nabla ^2}\Theta /Pr$ (4)

 $N{u_{{\rm{ave}}}} = - \frac{1}{{{L^2}{\tau _{\rm{P}}}}}\int {_\tau ^{\tau + {\tau _{\rm{p}}}}} {\rm{ }}\int {_0^L} \int {_0^L} {\left| {\frac{{\partial \Theta }}{{\partial Z}}} \right|_{Z = 0}}{\rm{d}}X{\rm{d}}Yd\tau$ (5)

2 结果分析与讨论

 图 2 L=1时绝热侧壁不同Ra下稳态流型. 左：Z=0.5截面等Z向速度线：实线为向上流动，速度为正， 虚线为向下流动，速度为负. 右：温度分别为$\Theta =0.3$(蓝)、0.5(绿)及0.7(红)对应的等温面(下同) Fig.2 Flow patterns for different Ra at L=1 for insulating sidewalls. left: contours of vertical velocity in the Z=0.5 plane. Solid lines denote a positive value and dotted lines denote a negative value. right: isothermal surfaces of $\Theta =0.3$ (blue), 0.5 (green) and 0.7 (red)(similarly hereinafter)

 图 3 L=1时导热侧壁不同$Ra$下稳态${\rm{FP}}_{{\rm{L1 - insu}}}^1$流型 Fig.3 Flow patterns of stable ${\rm{FP}}_{{\rm{L1 - insu}}}^1$ state at different $Ra$ for conducting sidewalls at L=1

 图 4 L=1时热壁$Nu_{\rm ave}$随$Ra$的变化 Fig.4 The variation of the average Nusselt number at the hot wall at $L=1$

 图 5 $L =2$ 时绝热侧壁不同$Ra$下稳态流型 Fig.5 Flow patterns for different $Ra$ at $L =2$ for conducting sidewalls at $L =2$

 图 6 $L =2$时一个周期内流型的演变过程 Fig.6 Flow evolution in a period at $L =2$
 图 7 $L =2$时监测点($X =0.5$，$Y =0.5$，$Z =0.5$)温度随时间演变 Fig.7 Time record of local temperature at a monitoring point ($X =0.5$，$Y =0.5$，$Z =0.5$) at $L =2$

 图 8 $L =2$时热壁 $Nu_{\rm ave}$随$Ra$的变化 Fig.8 The variation of the average Nusselt number at the hot wall at $L=2$

 图 9 不同条件下壁面传热能力比较 Fig.9 Comparison of the heat transfer ability for different conditions
3 结 论

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NUMERICAL INVESTIGATION ON FLOW STABILITY OF RAYLEIGH-BĖNARD CONVECTION OF COLD WATER IN A RECTANGULAR CAVITY COOLED AND HEATED SYMMETRICALLY RELATIVE TO THE TEMPERATURE OF DENSITY MAXIMUM
Hu Yupeng, Li Yourong
1. Institute of systems Engineering, China Academy of Engineering Physics, Mianyang 621900, China;
2. College of Power Engineering, Chongqing University, Chongqing 400044, China
Fund: The project was supported by the National Natural Science Foundation of China (51376199) and the Innovation and Developing Foundation of ISE.CAEP (14cxj20).
Abstract: In order to understand the special phenomena and laws of Rayleigh-Bénard convection of fluids with density extremum, a series of three-dimensional numerical simulations on Rayleigh-Bénard convection of cold water in a rectangular cavity when its horizontal walls were cooled and heated symmetrically relative to the temperature of the density extremum by using finite volume method is carried out. Flow structures and their bifurcation series are obtained, and the effects of the density extremum character, the Rayleigh number, the thermal boundary condition and the aspect ratio on Rayleigh-Bénard convection are discussed. The results demonstrate that the system of Rayleigh-Bénard convection of cold water with density extremum is much more stable than that of common fluid, and the flow structures and their bifurcation series are much more complex. Multiple flow patterns can coexist at a constant Rayleigh number and hysteresis phenomenon is observed in the flow evolution. The system loses its stability more easily and the heat transfer ability enhances with the increase of the aspect ratio. The system for conducting sidewalls is much more stable than that for insulating sidewalls and the heat transfer ability weakens. Furthermore, heat transfer correlations are proposed according to the multiple linear regression.
Key words: density extremum    Rayleigh-Bènard    nard convection    flow Patterns    bifurcation character    heat transfer