微通道内纳米流体传热流动特性

doi:10.11949/0438-1157.20240582

摘要/Abstract

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R_t和泵功P_p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 $η$ 对各聚类点综合性能进行评价，得到最优的微通道结构。采用数值模拟方法，研究优化后的微通道结构的流动与传热特性。结果表明：当去离子水中加入纳米颗粒后微通道内的压降具有小幅度上升，但其流动阻力在相同Reynolds数的条件下并没有发生较大的变化。在文丘里管微通道喉部位置会产生喉部效应，强化纳米颗粒与微通道中流动工质的融合。熵产分析表明，传热熵随着Reynolds数的增大而减小，摩擦熵随着Reynolds数的增大而增大，不过总熵值中主要是传热熵占据主导地位。纳米流体随着体积分数的增加不可逆损失均小于去离子水。

关键词: 遗传算法, 优化设计, 微通道, 纳米流体, 强化传热, 数值模拟

Abstract:

In order to improve the heat transfer efficiency of microchannel heat sink, it is necessary to optimize the structure of microchannel. Taking thermal resistance R_t and pump power P_p as the objective function, under the condition of Re = 100, the multi-objective genetic algorithm is used to optimize the structural parameters of the Venturi microchannel, such as channel depth, contraction angle, throat width and diffusion angle. The Pareto optimal solution set is obtained by genetic iteration calculation, and the optimal solution set is compared and analyzed by k-means clustering method. The comprehensive performance of each clustering point is evaluated by the enhanced heat transfer factor η, and the optimal microchannel structure is obtained. The flow and heat transfer characteristics of the optimized microchannel structure were studied by numerical simulation. The results show that when nanoparticles are added to deionized water, the pressure drop in the microchannel increases slightly, but its flow resistance does not change significantly under the same Reynolds number. The throat effect will be generated at the throat position of the Venturi microchannel to strengthen the fusion of nanoparticles and the flowing working fluid in the microchannel. The entropy generation analysis shows that the heat transfer entropy decreases with the increase of Reynolds number, and the friction entropy increases with the increase of Reynolds number, but the total entropy is mainly dominated by heat transfer entropy. With the increase of volume fraction, the irreversible loss of nanofluids is less than that of deionized water.

Key words: genetic algorithm, optimal design, microchannel, nanofluid, heat transfer enhancement, numerical simulation

中图分类号:

TK 122

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, 2025, 76(1): 184-197.

Ping LIU, Yusheng QIU, Shijing LI, Ruiqi SUN, Chen SHEN. Heat transfer and flow characteristics of nanofluids in microchannels[J]. CIESC Journal, 2025, 76(1): 184-197.

图/表 25

图1 文丘里管微通道结构

Fig.1 Microchannel structure of Venturi tube

表1 Al2O3纳米颗粒参数［28］

Table 1 Al2O3 nanoparticle parameters［28］

参数	数值
颜色	白色
热导率/(W/(m·K))	40
纳米颗粒直径/nm	40
密度/(kg/m³)	3970
比定压热容/(J/(kg $∙$ K) )	765
模拟体积分数/%	1~5

表1 Al2O3纳米颗粒参数［28］

Table 1 Al2O3 nanoparticle parameters［28］

参数	数值
颜色	白色
热导率/(W/(m·K))	40
纳米颗粒直径/nm	40
密度/(kg/m³)	3970
比定压热容/(J/(kg $∙$ K) )	765
模拟体积分数/%	1~5

表2 设计变量及其范围

Table 2 Design variables and their ranges

范围	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
设计序号	a/(°)	b/(°)	c/mm	h/mm	R_t/(K/W)	P_p/(10^-4 W)
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4 模型可信度检验

Table 4 Model credibility test

模型	$R^{2}$	$R_{a d j}^{2}$
热阻R_t	0.9956	0.9983
泵功P_p	0.9999	0.9999

表4 模型可信度检验

Table 4 Model credibility test

模型	$R^{2}$	$R_{a d j}^{2}$
热阻R_t	0.9956	0.9983
泵功P_p	0.9999	0.9999

图2 多目标遗传算法优化操作过程

Fig.2 Multi-objective genetic algorithm to optimize the operation process

图3 热阻和泵功的Pareto解集

Fig.3 Pareto solution set of thermal resistance and pump power

表5 Pareto优化值与模拟值对比

Table 5 Comparison of Pareto optimization value and simulation value

项目		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	R_t/(K/W)	14.003928	14.06209062	14.1127671	14.16854199	14.22269925
拟合结果	P_p/(10^-4 W)	0.89170968	0.816684084	0.75664856	0.69696176	0.647391251
模拟结果	R_t/(K/W)	13.97747222	14.0375	14.11241667	14.15291667	14.20372222
模拟结果	P_p/(10^-4 W)	0.89612137	0.81757886	0.76453825	0.70817871	0.65827214
误差	Error（R_t）/%	0.19	0.18	0.002	0.11	0.13
误差	Error（P_p）/%	0.49	0.11	1.03	1.58	1.65

图4 不同聚类点的强化传热因子η随Reynolds数的变化(1 atm=101.325 kPa)

Fig.4 The change of heat transfer enhancement factor of different clustering points with Reynolds number

图5 聚类点2与基础微通道随Reynolds数变化的温度云图

Fig.5 The temperature cloud diagram of cluster point 2 and basic microchannel changing with Reynolds number

图6 聚类点2与基础微通道随Reynolds数变化的压力云图

Fig.6 The pressure cloud diagram of cluster point 2 and basic microchannel changing with Reynolds number

图7 不同通道间的Nusselt数对比

Fig.7 The comparison of Nusselt number among different channels

图8 热阻随Reynolds数的变化趋势

Fig.8 The variation trend of thermal resistance with Reynolds number

表6 网格无关性验证

Table 6 Grid independence verification

网格数/个	Nu	f	相对误差/%
网格数/个	Nu	f	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	—	—

图9 数值模拟结果与文献[29]结果对比

Fig.9 The numerical simulation results compared with the results of Ref.[29]

图10 不同Re下压降∆P的变化

Fig.10 The change of pressure drop ΔP under different Re

图11 摩擦阻力系数随Reynolds数的变化

Fig.11 The variation of frictional resistance coefficient with Reynolds number

图12 结果分布云图

Fig.12 Results distribution cloud chart

图13 Nusselt数随Reynolds数的变化

Fig.13 Variation of Nusselt number with Reynolds number

图14 流动热阻随Reynolds数的变化

Fig.14 The change of flow thermal resistance with Reynolds number

图15 纳米流体强化传热因子随Reynolds数的变化

Fig.15 Variation of heat transfer enhancement factor of nanofluids with Reynolds number

图16 微通道整体温度与出口温度分布云图

Fig.16 Microchannel overall temperature and outlet temperature distribution cloud diagram

图17 传热熵产随Reynolds数的变化

Fig.17 The change of heat transfer entropy generation with Reynolds number

图18 摩擦熵产随Reynolds数的变化

Fig.18 The variation of friction entropy generation with Reynolds number

图19 熵产增大数随Reynolds数的变化

Fig.19 The change of entropy generation increment with Reynolds number

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