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射流通道内方柱发热器件的几何设计

饶凯 谢志辉 关潇男 孟凡凯 戈延林

饶凯,谢志辉,关潇男,孟凡凯,戈延林. 射流通道内方柱发热器件的几何设计 [J]. 应用数学和力学,2022,43(9):955-965 doi: 10.21656/1000-0887.420166
引用本文: 饶凯,谢志辉,关潇男,孟凡凯,戈延林. 射流通道内方柱发热器件的几何设计 [J]. 应用数学和力学,2022,43(9):955-965 doi: 10.21656/1000-0887.420166
RAO Kai, XIE Zhihui, GUAN Xiaonan, MENG Fankai, GE Yanlin. Geometry Design of Square Column Heating Devices in Jet Channels[J]. Applied Mathematics and Mechanics, 2022, 43(9): 955-965. doi: 10.21656/1000-0887.420166
Citation: RAO Kai, XIE Zhihui, GUAN Xiaonan, MENG Fankai, GE Yanlin. Geometry Design of Square Column Heating Devices in Jet Channels[J]. Applied Mathematics and Mechanics, 2022, 43(9): 955-965. doi: 10.21656/1000-0887.420166

射流通道内方柱发热器件的几何设计

doi: 10.21656/1000-0887.420166
基金项目: 国家自然科学基金(51979278; 51579244; 51506220)
详细信息
    作者简介:

    饶凯(1989—),男,硕士生(E-mail:superior2345@ qq.com

    谢志辉(1977—),男,教授,博士生导师(通讯作者. E-mail:zhihui-xie@163.com

    关潇男(1997—),男,硕士生(E-mail:2601282251@qq.com

    孟凡凯(1982—),男,讲师(E-mail:782601028@qq.com

    戈延林(1979—),男,副教授(E-mail:geyali9@hotmail.com

  • 中图分类号: O35; TK123

Geometry Design of Square Column Heating Devices in Jet Channels

  • 摘要:

    基于构形理论,建立了二维射流通道内导热基座上方柱离散热源的散热优化模型。给定离散热源的总纵截面面积和热源高度为约束条件,以系统最高温度和熵产率为优化目标,以各热源的长度比为优化变量进行了几何设计,并分析了射流速度和热源间距对热源最优构形的影响。当射流速度和热源间距给定时,均存在最优长度比使系统最高温度和熵产率最低,但对应不同射流速度和热源间距的最优长度比不同。研究结果可为方柱发热器件的热设计提供理论指导。

  • 图  1  热源几何模型图

    Figure  1.  The geometric model for heat sources

    图  2  整体网格图

    Figure  2.  The overall grid pattern

    图  3  γ= 0.2时,UjTmaxβ关系的影响

    Figure  3.  Effects of Uj on the relationship of Tmax vs. β for γ= 0.2

    图  4  γ= 0.3时,UjTmaxβ关系的影响

    Figure  4.  Effects of Uj on the relationship of Tmax vs. β for γ= 0.3

    图  5  γ= 0.4时,UjTmaxβ关系的影响

    Figure  5.  Effects of Uj on the relationship of Tmax vs. β for γ= 0.4

    图  6  γ=0.2, β= 2,Uj =3 m/s时,温度的等值线图

    Figure  6.  The temperature contour map for γ=0.2, β=2, Uj=3 m/s

    图  7  γ=0.3, β=0.8, Uj = 3 m/s时,温度的等值线图

    Figure  7.  The temperature contour map for γ=0.3, β=0.8, Uj=3 m/s

    图  8  γ=0.4, β=0.4, Uj = 3 m/s时,温度的等值线图

    Figure  8.  The temperature contour map for γ=0.4, β=0.4, Uj =3 m/s

    图  9  γ=0.2时,Uj${\dot S_{ {\rm{gen}}}}$β关系的影响

    Figure  9.  Effects of Uj on the relationship of ${\dot S_{ {\rm{gen}}}}$ vs. β for γ=0.2

    图  10  γ=0.3时,Uj${\dot S_{ {\rm{gen}}}}$β关系的影响

    Figure  10.  Effects of Uj on the relationship of ${\dot S_{ {\rm{gen}}}}$ vs. β for γ=0.3

    图  11  γ=0.4时,Uj${\dot S_{ {{\rm{gen}}}}}$β关系的影响

    Figure  11.  Effects of Uj on the relationship of ${\dot S_{ {{\rm{gen}}}}}$ vs. β for γ=0.4

    图  12  γ=0.2, β=2, Uj = 3 m/s时,通道纵截面的速度分布图

    Figure  12.  The velocity profile of the channel longitudinal section for γ=0.2, β=2, Uj = 3 m/s

    图  13  γ=0.3, β=0.8, Uj = 3 m/s时,通道纵截面的速度分布云图

    Figure  13.  The velocity profile of the channel longitudinal section for γ=0.3, β=0.8, Uj = 3 m/s

    图  14  γ=0.4, β=0.4, Uj = 3 m/s时,通道纵截面的速度分布云图

    Figure  14.  The velocity profile of the channel longitudinal section for γ=0.4, β=0.4, Uj = 3 m/s

    表  1  网格独立性检验

    Table  1.   The grid independence test

    order numbernumber of units NTmax/K$| {( {T_{ {\rm{\max} } }^{j + 1} - T_{ {\rm{\max} } }^j} )/T_{ {\rm{\max } } }^j} |/\text{%}$
    129 085432.67
    269 132434.120.34
    3108 055434.970.2
    下载: 导出CSV

    表  2  模型有效性验证

    Table  2.   Validation of the model

    $\tilde H$0.10.2
    b0.465 20.483 5
    $\tilde T$[22]7.233 913.650 9
    $\tilde T$7.191 513.534 3
    下载: 导出CSV

    表  3  不同Uj时,Tmax,min及对应的几何参数

    Table  3.   Tmax,min and its corresponding geometric parameters for different Uj values

    Uj/(m·s−1)γβoptTmax,min/K
    10.22433
    10.30.8417.5
    10.40.4410.5
    20.22376
    20.30.8362.8
    20.40.4360.2
    30.22354.3
    30.30.8342.6
    30.40.4341.5
    下载: 导出CSV

    表  4  不同Uj时,${\dot S_{ {\rm{gen}},\min }}$及对应的几何参数

    Table  4.   ${\dot S_{ {\rm{gen}},\min }}$ and its corresponding geometric parameters for different Uj values

    Uj/(m·s−1)γβopt${\dot S_{ {\rm{gen,\min } } } }/({\rm{W \cdot K} }^{-1})$
    10.20.40.12575
    10.30.90.14298
    10.40.40.13021
    20.20.30.07972
    20.30.80.088153
    20.40.30.083012
    30.20.40.060294
    30.30.80.06559
    30.40.40.07022
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-06-16
  • 修回日期:  2022-07-05
  • 网络出版日期:  2022-09-28
  • 刊出日期:  2022-09-30

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