• •
收稿日期:
2024-05-30
修回日期:
2024-08-03
出版日期:
2024-09-12
通讯作者:
刘萍
作者简介:
刘萍(1978—),女,博士,教授,pingliu@mail.ustc.edu.cn
基金资助:
Ping LIU(), Yusheng QIU, Shijing LI, Ruiqi SUN, Chen SHEN
Received:
2024-05-30
Revised:
2024-08-03
Online:
2024-09-12
Contact:
Ping LIU
摘要:
为提高微通道散热器的传热效率,需要对微通道进行结构优化设计。以热阻Rt和泵功Pp为目标函数,在Re=100的条件下,采用多目标遗传算法对文丘里管微通道的结构参数,如通道深度,收缩角度,喉颈宽度和扩散角度进行优化,通过遗传迭代计算得到Pareto优化解集,利用k-means聚类法对优化解集进行比较分析,通过强化传热因子
中图分类号:
刘萍, 邱雨生, 李世婧, 孙瑞奇, 申晨. 微通道内纳米流体传热流动特性[J]. 化工学报, DOI: 10.11949/0438-1157.20240582.
Ping LIU, Yusheng QIU, Shijing LI, Ruiqi SUN, Chen SHEN. Heat transfer and flow characteristics of nanofluids in microchannels[J]. CIESC Journal, DOI: 10.11949/0438-1157.20240582.
名称 | Al2O3 |
---|---|
颜色 | 白色 |
热导率 (W/(m | 40 |
纳米颗粒直径 (nm) | 40 |
密度 (kg/m3) | 3970 |
恒压热容 (J/(kg | 765 |
模拟体积分数 | 1%~5% |
表1 纳米颗粒参数[28]
Table 1 Nanoparticle parameters
名称 | Al2O3 |
---|---|
颜色 | 白色 |
热导率 (W/(m | 40 |
纳米颗粒直径 (nm) | 40 |
密度 (kg/m3) | 3970 |
恒压热容 (J/(kg | 765 |
模拟体积分数 | 1%~5% |
设计变量 | a(°) | b(°) | c(mm) | h(mm) |
---|---|---|---|---|
最小值 | 40 | 14 | 0.04 | 0.18 |
最大值 | 42 | 16 | 0.05 | 0.20 |
表2 设计变量及其范围
Table 2 Design variables and their ranges
设计变量 | a(°) | b(°) | c(mm) | h(mm) |
---|---|---|---|---|
最小值 | 40 | 14 | 0.04 | 0.18 |
最大值 | 42 | 16 | 0.05 | 0.20 |
设计 序号 | 设计变量 | 目标变量 | ||||
---|---|---|---|---|---|---|
a(°) | b(°) | c(mm) | h(mm) | Rt/(K | Pp/(10-4W) | |
1 | 40.7373 | 14.6294 | 0.0494 | 0.1997 | 14.2379 | 0.6460 |
2 | 40.2388 | 14.5699 | 0.0437 | 0.1920 | 14.1493 | 0.8483 |
3 | 41.1666 | 14.8625 | 0.0458 | 0.1926 | 14.2133 | 0.7662 |
4 | 40.9078 | 14.4708 | 0.0441 | 0.1985 | 14.0928 | 0.7988 |
5 | 41.5828 | 15.5224 | 0.0400 | 0.1804 | 14.1536 | 1.0789 |
6 | 41.6110 | 15.8708 | 0.0427 | 0.1992 | 14.0577 | 0.8336 |
7 | 41.3162 | 14.0744 | 0.0448 | 0.1905 | 14.1883 | 0.8180 |
8 | 40.0497 | 15.0459 | 0.0433 | 0.1806 | 14.2568 | 0.9222 |
9 | 40.1199 | 14.2140 | 0.0415 | 0.1957 | 14.0597 | 0.9231 |
10 | 40.5807 | 15.4502 | 0.0491 | 0.1821 | 14.4176 | 0.7261 |
11 | 41.0542 | 15.9823 | 0.0469 | 0.1815 | 14.3761 | 0.7870 |
12 | 41.3999 | 14.1514 | 0.0471 | 0.1930 | 14.2440 | 0.7269 |
13 | 40.6769 | 15.6827 | 0.0417 | 0.1848 | 14.1704 | 0.9594 |
14 | 41.7788 | 14.0057 | 0.0443 | 0.1875 | 14.2051 | 0.8594 |
15 | 41.6770 | 15.3273 | 0.0475 | 0.1892 | 14.3024 | 0.7365 |
16 | 41.9615 | 15.4293 | 0.0487 | 0.1899 | 14.3273 | 0.7013 |
17 | 41.1339 | 14.9891 | 0.0456 | 0.1889 | 14.2434 | 0.7971 |
18 | 40.6108 | 15.5937 | 0.0408 | 0.1938 | 14.0603 | 0.9404 |
19 | 40.2764 | 15.6346 | 0.0450 | 0.1830 | 14.3052 | 0.8440 |
20 | 41.2482 | 15.1137 | 0.0403 | 0.1831 | 14.1320 | 1.0481 |
表3 设计变量和目标变量值
Table 3 Design variables and target variable values
设计 序号 | 设计变量 | 目标变量 | ||||
---|---|---|---|---|---|---|
a(°) | b(°) | c(mm) | h(mm) | Rt/(K | Pp/(10-4W) | |
1 | 40.7373 | 14.6294 | 0.0494 | 0.1997 | 14.2379 | 0.6460 |
2 | 40.2388 | 14.5699 | 0.0437 | 0.1920 | 14.1493 | 0.8483 |
3 | 41.1666 | 14.8625 | 0.0458 | 0.1926 | 14.2133 | 0.7662 |
4 | 40.9078 | 14.4708 | 0.0441 | 0.1985 | 14.0928 | 0.7988 |
5 | 41.5828 | 15.5224 | 0.0400 | 0.1804 | 14.1536 | 1.0789 |
6 | 41.6110 | 15.8708 | 0.0427 | 0.1992 | 14.0577 | 0.8336 |
7 | 41.3162 | 14.0744 | 0.0448 | 0.1905 | 14.1883 | 0.8180 |
8 | 40.0497 | 15.0459 | 0.0433 | 0.1806 | 14.2568 | 0.9222 |
9 | 40.1199 | 14.2140 | 0.0415 | 0.1957 | 14.0597 | 0.9231 |
10 | 40.5807 | 15.4502 | 0.0491 | 0.1821 | 14.4176 | 0.7261 |
11 | 41.0542 | 15.9823 | 0.0469 | 0.1815 | 14.3761 | 0.7870 |
12 | 41.3999 | 14.1514 | 0.0471 | 0.1930 | 14.2440 | 0.7269 |
13 | 40.6769 | 15.6827 | 0.0417 | 0.1848 | 14.1704 | 0.9594 |
14 | 41.7788 | 14.0057 | 0.0443 | 0.1875 | 14.2051 | 0.8594 |
15 | 41.6770 | 15.3273 | 0.0475 | 0.1892 | 14.3024 | 0.7365 |
16 | 41.9615 | 15.4293 | 0.0487 | 0.1899 | 14.3273 | 0.7013 |
17 | 41.1339 | 14.9891 | 0.0456 | 0.1889 | 14.2434 | 0.7971 |
18 | 40.6108 | 15.5937 | 0.0408 | 0.1938 | 14.0603 | 0.9404 |
19 | 40.2764 | 15.6346 | 0.0450 | 0.1830 | 14.3052 | 0.8440 |
20 | 41.2482 | 15.1137 | 0.0403 | 0.1831 | 14.1320 | 1.0481 |
模型 | ||
---|---|---|
热阻Rt | 0.9956 | 0.9983 |
泵功PP | 0.9999 | 0.9999 |
表4 模型可信度检验
Table 4 Model credibility test
模型 | ||
---|---|---|
热阻Rt | 0.9956 | 0.9983 |
泵功PP | 0.9999 | 0.9999 |
设计序号 | 1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|---|
目标变量 | a(°) | 41.45783427 | 41.34520548 | 41.38383064 | 41.40335531 | 41.39160136 |
b(°) | 14.70096577 | 14.53238701 | 14.46657789 | 14.45850405 | 14.45775171 | |
c(mm) | 0.04151237 | 0.043408283 | 0.04510961 | 0.0470403 | 0.04897439 | |
h(mm) | 0.1998938 | 0.199907562 | 0.19991469 | 0.19993298 | 0.19992672 | |
拟合结果 | Rt/(K | 14.003928 | 14.06209062 | 14.1127671 | 14.16854199 | 14.22269925 |
Pp/(10 -4W) | 0.89170968 | 0.816684084 | 0.75664856 | 0.69696176 | 0.647391251 | |
模拟结果 | Rt/(K | 13.97747222 | 14.0375 | 14.11241667 | 14.15291667 | 14.20372222 |
Pp/(10 -4W) | 0.89612137 | 0.81757886 | 0.76453825 | 0.70817871 | 0.65827214 | |
误差 | Rt | 0.19% | 0.18% | 0.002% | 0.11% | 0.13% |
Pp | 0.49% | 0.11% | 1.03% | 1.58% | 1.65% |
表5 Pareto优化值与模拟值对比
Table 5 Comparison of Pareto optimization value and simulation value
设计序号 | 1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|---|
目标变量 | a(°) | 41.45783427 | 41.34520548 | 41.38383064 | 41.40335531 | 41.39160136 |
b(°) | 14.70096577 | 14.53238701 | 14.46657789 | 14.45850405 | 14.45775171 | |
c(mm) | 0.04151237 | 0.043408283 | 0.04510961 | 0.0470403 | 0.04897439 | |
h(mm) | 0.1998938 | 0.199907562 | 0.19991469 | 0.19993298 | 0.19992672 | |
拟合结果 | Rt/(K | 14.003928 | 14.06209062 | 14.1127671 | 14.16854199 | 14.22269925 |
Pp/(10 -4W) | 0.89170968 | 0.816684084 | 0.75664856 | 0.69696176 | 0.647391251 | |
模拟结果 | Rt/(K | 13.97747222 | 14.0375 | 14.11241667 | 14.15291667 | 14.20372222 |
Pp/(10 -4W) | 0.89612137 | 0.81757886 | 0.76453825 | 0.70817871 | 0.65827214 | |
误差 | Rt | 0.19% | 0.18% | 0.002% | 0.11% | 0.13% |
Pp | 0.49% | 0.11% | 1.03% | 1.58% | 1.65% |
网格数 | Nu | f | 相对误差 | |
---|---|---|---|---|
Nu | f | |||
105450 | 18.23633 | 11.70182 | 7.91% | 6.78% |
203823 | 18.26503 | 12.19808 | 8.08% | 2.83% |
512410 | 17.69948 | 12.34234 | 4.73% | 1.68% |
1156491 | 17.23667 | 12.43544 | 1.99% | 0.93% |
1640613 | 16.89959 | 12.55278 | — | — |
表6 网格无关性验证
Table 6 Grid independence verification
网格数 | Nu | f | 相对误差 | |
---|---|---|---|---|
Nu | f | |||
105450 | 18.23633 | 11.70182 | 7.91% | 6.78% |
203823 | 18.26503 | 12.19808 | 8.08% | 2.83% |
512410 | 17.69948 | 12.34234 | 4.73% | 1.68% |
1156491 | 17.23667 | 12.43544 | 1.99% | 0.93% |
1640613 | 16.89959 | 12.55278 | — | — |
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