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二维局部受热腔体内电热对流问题模拟和分析

刘镇涛 肖莉 和琨 汪垒

刘镇涛, 肖莉, 和琨, 汪垒. 二维局部受热腔体内电热对流问题模拟和分析. 力学学报, 2021, 53(9): 2477-2492 doi: 10.6052/0459-1879-21-205
引用本文: 刘镇涛, 肖莉, 和琨, 汪垒. 二维局部受热腔体内电热对流问题模拟和分析. 力学学报, 2021, 53(9): 2477-2492 doi: 10.6052/0459-1879-21-205
Liu Zhentao, Xiao Li, He Kun, Wang Lei. Numerical study on two-dimensional electro-thermal convection in a partially heated cavity. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2477-2492 doi: 10.6052/0459-1879-21-205
Citation: Liu Zhentao, Xiao Li, He Kun, Wang Lei. Numerical study on two-dimensional electro-thermal convection in a partially heated cavity. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2477-2492 doi: 10.6052/0459-1879-21-205

二维局部受热腔体内电热对流问题模拟和分析

doi: 10.6052/0459-1879-21-205
基金项目: 国家自然科学基金资助项目(12002320)
详细信息
    作者简介:

    汪垒, 副教授, 主要研究方向: 复杂流体流动传热、格子Boltzmann方法、物理信息神经网络. E-mail: leiwang@cug.edu.cn

  • 中图分类号: O361.4

NUMERICAL STUDY ON TWO-DIMENSIONAL ELECTRO-THERMAL CONVECTION IN A PARTIALLY HEATED CAVITY

  • 摘要: 近些年, 基于电场的主动强化传热技术因其对特殊环境的良好适用性而获得广泛关注, 该问题由于涉及电场、电荷分布场、流场和温度场等多物理场的强烈非线性耦合, 目前相关的理论分析和实验研究工作相对较少. 本文采用格子Boltzmann方法对二维局部受热腔体内电热对流问题进行了模拟和分析, 详细探究了无量纲参数如热瑞利数$Ra$、电瑞利数$T$、电极板的长度$h$和电极板中心到下壁面的距离$\delta$对传热效率的影响, 并对电热对流问题中的分岔结构进行了分析. 数值结果表明, 随着电瑞利数$T$的增加, 传热效率逐渐增强, 且电瑞利数$T$的分岔类型为亚临界型, 而热瑞利数$Ra$表现为超临界型. 当电瑞利数$T$足够大时, 库仑力占据绝对优势, 浮升力对传热的影响减弱, 传热效率的变化不再依赖于热瑞利数$Ra$. 另外, 对比不同电极板位置的传热效率时发现电极板处于中间时传热效率最佳, 并且电极板长度越短传热效率越高. 本文的研究结果拓展了已有二维电热对流模型, 可为其他非均匀温度边界电热对流问题的理论分析提供参考.

     

  • 图  1  物理模型示意图

    Figure  1.  Schematic diagram of the physical model

    图  2  电荷密度$ q $, 水平方向电场强度$ E_{x} $的数值解与解析解对比

    Figure  2.  Comparisons of the charge density q and horizontal electric field strength $ E_{x} $ between the analytical solutions and numerical solutions

    图  3  (a) 热瑞利数 Ra = 400, 变化电瑞利数 T 的分岔结构和(b) 电瑞利数T = 80, 变化热瑞利数Ra 的分岔结构 ($ C = 10 $, $ M = 10 $, $ Pr = 10 $, $ h = 0.5H $, $ \delta = 0.5H $)

    Figure  3.  (a) The distributions of the maximum speed $ V_{{\rm{max}}} $ vs. electric Rayleigh number $ T $. (b) The distributions of the maximum speed $ V_{{\rm{max}}} $ vs. Rayleigh number $ Ra $ ($ C = 10 $, $ M = 10 $, $ Pr = 10 $, $ h = 0.5H $, $ \delta = 0.5H $)

    图  4  在不同电瑞利数T下, (a) 平均努塞特数$Nu_{{\rm{av}}}$和(b) 最大速度$V_{{\rm{max}}}$随时间变化的曲线 ($ Ra = 1\times10^{4} $, $ C = 10 $, $ M = 10 $, $ Pr = 10 $, $ h = 0.5H $, $ \delta = 0.5H $)

    Figure  4.  The distributions of (a) the average Nusselt number $Nu_{{\rm{av}}}$ vs. time and (b) the maximum speed $V_{{\rm{max}}}$ vs. ${\rm{time}}$ under different electric Rayleigh number $ T $ ($ Ra = 1\times10^{4} $, $ C = 10 $, $ M = 10 $, $ Pr = 10 $, $ h = 0.5H $, $ \delta = 0.5H $)

    图  5  电瑞利数(a) $ T = 0 $, (b) $ T = 200 $, (c) $ T = 500 $, (d) $ T = 800 $, (e) $ T = 1200 $时的电荷密度分布(上)、温度分布(中)和流线分布(下)图($ Ra = 1\times10^{4} $, $ C = 10 $, $ M = 10 $, $ Pr = 10 $, $ h = 0.5H $, $ \delta = 0.5H $)

    Figure  5.  The distributions of the charge density (top), temperature (middle) and streamlines (bottom) under different electrical Rayleigh number T. (a) $ T = 0 $, (b) $ T = 200 $, (c) $ T = 500 $, (d) $ T = 800 $, (e) $ T = 1200 $ ($ Ra = 1\times10^{4} $, $ C = 10 $, $ M = 10 $, $ Pr = 10 $, $ h = 0.5H $, $ \delta = 0.5H $)

    图  6  (a) 探究不同电瑞利数T下的平均努塞特数$Nu_{{\rm{av}}}$的变化过程和(b) 探究不同热瑞利数$ Ra $下的平均努塞特数$Nu_{{\rm{av}}}$的变化过程($ C = 10 $, $ M = 10 $, $ Pr = 10 $, $ h = 0.5H $, $ \delta = 0.5H $)

    Figure  6.  (a) The distributions of the average Nusselt number $Nu_{{\rm{av}}}$ vs. electrical Rayleigh number T under different Rayleigh number $ Ra $.(b) The distributions of the average Nusselt number $Nu_{{\rm{av}}}$ vs. Rayleigh number $ Ra $ under different electrical Rayleigh number T ($ C = 10 $, $ M = 10 $, $ Pr = 10 $, $ h = 0.5H $, $ \delta = 0.5H $)

    图  7  电极板在不同位置下, 随着电瑞利数$ T $增加, 平均努塞特数$Nu_{{\rm{av}}}$的变化曲线 ($ Ra = 1\times10^{4} $, $ C = 10 $, $ Pr = 10 $, $ M = 10 $, $ h = 0.5H $)

    Figure  7.  The distributions of the average Nusselt number $Nu_{{\rm{av}}}$ vs. electrical Rayleigh number $ T $ under different heating locations $ \delta $ ($ Ra = 1\times10^{4} $, $ C = 10 $, $ Pr = 10 $, $ M = 10 $, $ h = 0.5H $)

    图  8  电极板在上半区域和下半区域时的电荷密度分布图(上)、温度分布图(中)和流线分布图(下) ($ T = 250 $, $ Ra = 1\times10^{4} $, $ C = 10 $, $ Pr = 10 $, $ M = 10 $, $ h = 0.5H $)

    Figure  8.  The distributions of the charge density (top), temperature (middle) and streamlines (bottom) as the electrode plate is at the top and bottom positions ($ T = 250 $, $ Ra = 1\times10^{4} $, $ C = 10 $, $ Pr = 10 $, $ M = 10 $, $ h = 0.5H $)

    图  9  电极板在(a)下半区域, (b)中间, (c)上半区域, 电荷密度分布(左)、温度分布(中)和流线分布(右)图 ($ T = 800 $, $ Ra = 1\times10^{4} $, $ C = 10 $, $ Pr = 10 $, $ M = 10 $, $ h = 0.5H $)

    Figure  9.  The distributions of the charge density (left), temperature (middle) and streamlines (right) as the electrode plate is at the top, middle and bottom positions ($ T = 800 $, $ Ra = 1\times10^{4} $, $ C = 10 $, $ Pr = 10 $, $ M = 10 $, $ h = 0.5H $)

    图  10  电极板长度不同时, 随着电瑞利数$ T $增加, 平均努塞特数$Nu_{{\rm{av}}}$的变化曲线 ($ Ra = 1\times10^{4} $, $ C = 10 $, $ Pr = 10 $, $ M = 10 $, $ \delta = 0.5H $)

    Figure  10.  The distributions of the average Nusselt number $Nu_{{\rm{av}}}$ vs. electrical Rayleigh number $ T $ under different length of electrode plate $ h $ ($ Ra = 1\times10^{4} $, $ C = 10 $, $ Pr = 10 $, $ M = 10 $, $ \delta = 0.5H $)

    图  11  不同长度下, (a) $ h = 0.5H $, (b) $ h = 0.75H $, (c) $ h = H $, 电荷密度分布图(左)、温度分布图(中)和流线分布图(右) ($ T = 250 $, $ Ra = 1\times10^{4} $, $ C = 10 $, $ Pr = 10 $, $ M = 10 $, $ \delta = 0.5H $)

    Figure  11.  The distributions of the charge density (left), temperature (middle) and streamlines (right) under different length of electrode plate. (a) $ h = 0.5H $, (b) $ h = 0.75H $, (c) $ h = H $ ($ T = 250 $, $ Ra = 1\times10^{4} $, $ C = 10 $, $ Pr = 10 $, $ M = 10 $, $ \delta = 0.5H $)

    图  12  不同长度下, (a) $ h = 0.5H $, (b) $ h = 0.75H $, (c) $ h = H $, 电荷密度分布图(左)、温度分布图(中)和流线分布图(右) ($ T = 300 $, $ Ra = 1\times10^{4} $, $ C = 10 $, $ Pr = 10 $, $ M = 10 $, $ \delta = 0.5H $)

    Figure  12.  The distributions of the charge density (left), temperature (middle) and streamlines (right) under different length of electrode plate. (a) $ h = 0.5H $, (b) $ h = 0.75H $, (c) $ h = H $ ($ T = 300 $, $ Ra = 1\times10^{4} $, $ C = 10 $, $ Pr = 10 $, $ M = 10 $, $ \delta = 0.5H $)

    图  13  固定普朗特数Pr, 在不同无量纲离子迁移率M下, 平均努塞特数$ Nu_{{\rm{av}}} $的变化曲线 ($ Ra = 1\times10^{4} $, $ T = 300 $, $ C = 10 $, $ \delta = 0.5H $, $ h = 0.5H $)

    Figure  13.  The distributions of the average Nusselt number $ Nu_{{\rm{av}}} $ vs. dimensionless ion mobility $ M $ under different Prandtl number $ Pr $ ($ Ra = 1\times10^{4} $, $ T = 300 $, $ C = 10 $, $ \delta = 0.5H $, $ h = 0.5H $)

    图  14  不同M值下的电荷密度分布(左)、温度分布(中)和流线分布(右)图. (a) $ M = 25 $, (b) $ M = 30 $, (c) $ M = 50 $ ($ Pr = 50 $,$ Ra = 1\times10^{4} $, $ T = 300 $, $ C = 10 $, $ \delta = 0.5H $, $ h = 0.5H $)

    Figure  14.  The distributions of the charge density (left), temperature (middle) and streamlines (right) under different dimensionless ion mobility $ M$. (a) $ M = 25 $, (b) $ M = 30 $, (c) $ M = 50 $ ($ Pr = 50 $,$ Ra = 1\times10^{4} $, $ T = 300 $, $ C = 10 $, $ \delta = 0.5H $, $ h = 0.5H $)

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出版历程
  • 收稿日期:  2021-05-14
  • 录用日期:  2021-08-07
  • 网络出版日期:  2021-08-08
  • 刊出日期:  2021-09-18

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