Numerical study and structural optimization of microchannel flow and heat transfer characteristics of bionic homocercal fin microchannels

doi:10.11949/0438-1157.20231069

Abstract

Abstract:

Motivated by the vital role of fish tail fins in fluid flow, microchannel with homocercal fin is designed. Three key structural parameters are identified: the relative length of the tail fin depression along its major axis $D t / W c h$ , the relative width of the tail fin $b t / W c h$ and the angle determining the maximum height of the fin $α t$ . The effects of structural parameters on average friction coefficient, average Nusselt number, overall performance factor, thermal resistance, and pump power of the bionic microchannel are analyzed numerically. The optimal solution to the structural parameters of the conformal caudal fin was obtained through uniform test analysis, regression fitting and genetic algorithm multi-objective optimization. The results show that the overall performance factor of the bionic homocercal fin microchannel ranges from 1.74 to 1.89, indicating significantly better comprehensive heat transfer performance compared to the rectangular smooth channel. Increasing the relative length $D t / W c h$ and angle $α t$ and decreasing width $b t / W c h$ improves the microchannel’s heat transfer performance, with the relative length $D t / W c h$ and the angle $α t$ having the greatest influence. Optimal microchannel performance is achieved when the structural parameters are $D t / W c h$ =0.476, $b t / W c h$ =0.135, and $α t$ =146.96°.

Key words: microchannel, tail fin, bionic, numerical simulation, heat transfer

摘要：

基于鱼类尾鳍在流动过程中的重要作用，仿生设计并建立了正形尾鳍结构微通道物理模型，研究了仿生尾鳍肋间距对微通道综合传热性能的影响，提取了尾鳍结构凹陷长轴相对长度 $D t / W c h$ 、决定尾鳍结构最大宽度的 $b t / W c h$ 以及决定尾鳍结构最大高度的张角 $α t$ 三个结构参数，数值分析了结构参数对仿生微通道平均摩擦因数、平均Nusselt数、综合性能因子以及热阻和泵功的影响规律；并通过均匀试验分析回归拟合和遗传算法多目标优化得到了正形尾鳍结构参数的最优解。结果表明，综合性能因子随着仿生肋间距的增大而减小，当间距为4 mm时，正形尾鳍结构微通道的综合性能因子变化范围为1.74~1.89，综合传热性能明显优于矩形光滑通道；随着 $D t / W c h$ 的增加、 $b t / W c h$ 的减小或 $α t$ 的增加，尾鳍结构微通道的综合传热性能提升，其中凹陷长轴相对长度 $D t / W c h$ 和高度张角 $α t$ 影响较大。结构参数为 $D t / W c h$ =0.476、 $b t / W c h$ =0.135、 $α t$ =146.96°时，微通道性能有较大提升。

关键词: 微通道, 尾鳍, 仿生, 数值模拟, 传热

CLC Number:

TK 124

Juan LI, Yaowen CAO, Zhangyu ZHU, Lei SHI, Jia LI. Numerical study and structural optimization of microchannel flow and heat transfer characteristics of bionic homocercal fin microchannels[J]. CIESC Journal, 2024, 75(5): 1802-1815.

李娟, 曹耀文, 朱章钰, 石雷, 李佳. 仿生正形尾鳍结构微通道流动与传热特性数值研究及结构优化[J]. 化工学报, 2024, 75(5): 1802-1815.

Figures/Tables 35

Fig.1 3D structure of microchannel and parameters

Table 1 Geometric dimensions of the biomimetic structure

几何参数	尺寸
尾鳍结构圆直径(D_t)	1.2 mm
尾鳍结构凹陷长半轴长(a_t)	0.6 mm
尾鳍结构凹陷短半轴长(b_t)	0.24 mm
尾鳍结构高度张角(α_t)	180°

Table 2 Physical properties of solid and liquid

材料	密度/(kg/m³)	比热容/(J/(kg·K))	热导率/(W/(m·K))
去离子水	998.2	4183	—
6063铝合金	2690	900	218

Table 3 Experimental conditions

工况	进口Reynolds数	进口流速/(m/s)	体积流量/(ml/min)
1	400	0.5034	90.60
2	550	0.6922	124.59
3	700	0.8809	158.58
4	850	1.0697	192.54
5	1000	1.2585	226.53
6	1150	1.4472	260.49
7	1300	1.6360	294.48

Fig.2 Grid division of microchannel with shark-tail structure (MC-T)

Table 4 Validation of grid independence

序号	网格数量/个	平均摩擦因数(f_ave,sim)	摩擦因数误差	平均Nusselt数(Nu_ave,sim)	Nusselt数误差
1	118万	0.1875	2.01%	7.09	6.27%
2	170万	0.1860	1.29%	6.86	3.12%
3	200万	0.1849	0.62%	6.76	1.76%
4	252万	0.1841	0.10%	6.70	0.55%
5	314万	0.1840	—	6.68	—

Table 5 Thermal entry region Nusselt number

x^*	Nu_x_,4	x^*	Nu_x_,4	x^*	Nu_x_,4
0.0001	26.7	0.00714	7.63	0.025	5.87
0.0025	10.4	0.00833	7.32	0.033	5.77
0.005	8.44	0.01	7	0.05	5.62
0.00556	8.18	0.0125	6.63	0.1	5.45
0.00625	7.92	0.0167	6.26	1	5.35

Fig.3 Validation of numerical simulation

Fig.4 Variation of average Nusselt number with Reynolds number

Fig.5 Variation of total thermal resistance with Reynolds number

Fig.6 Variation of comprehensive performance factor with Reynolds number

Table 6 Different interval parameter of MC-T

参数	a型	b型	c型	d型	e型
尾鳍结构数量	19	17	15	14	13
间距/mm	4	4.5	5	5.5	6

Fig.7 Schematic diagram of MC-T structure

Fig.8 Variation of average friction coefficient with interval

Fig.9 Variation of average Nusselt number with interval

Fig.10 Variation of comprehensive performance factor with interval

Fig.11 Effect of Dt/Wch on average friction coefficient

Fig.12 Effect of Dt/Wch on average Nusselt number

Fig.13 Effect of Dt/Wch on comprehensive performance factor

Fig.14 Effect of Dt/Wch on total thermal resistance and pumping power

Fig.15 Effect of bt/Wch on average friction coefficient

Fig.16 Effect of bt/Wch on average Nusselt number

Fig.17 Effect of bt/Wch on comprehensive performance factor

Fig.18 Effect of bt/Wch on total thermal resistance and pumping power

Fig.19 Effect of αt on average friction coefficient

Fig.20 Effect of αt on average Nusselt number

Fig.21 Effect of αt on comprehensive performance factor

Fig.22 Effect of αt on total thermal resistance and pumping power

Table 7 U11（113） uniform design

试验编号	因素1	因素2	因素3
1	1	5	7
2	2	10	3
3	3	4	10
4	4	9	6
5	5	3	2
6	6	8	9
7	7	2	5
8	8	7	1
9	9	1	8
10	10	6	4
11	11	11	11

Table 8 Uniform design table for MC-T

试验编号	$D t / W c h$	$b t / W c h$	$α t$ /(°)	$R t o t$ /(K/W)	$W p$ /(W)
1	0.40	0.129	156	0.767	0.0044
2	0.42	0.159	132	0.798	0.0042
3	0.44	0.123	174	0.698	0.0047
4	0.46	0.153	150	0.682	0.0045
5	0.48	0.117	126	0.688	0.0045
6	0.50	0.147	168	0.665	0.0049
7	0.52	0.111	144	0.679	0.0048
8	0.54	0.141	120	0.649	0.0047
9	0.56	0.105	162	0.586	0.0056
10	0.58	0.135	138	0.641	0.0051
11	0.60	0.165	180	0.606	0.0061

Table 8 Uniform design table for MC-T

试验编号	$D t / W c h$	$b t / W c h$	$α t$ /(°)	$R t o t$ /(K/W)	$W p$ /(W)
1	0.40	0.129	156	0.767	0.0044
2	0.42	0.159	132	0.798	0.0042
3	0.44	0.123	174	0.698	0.0047
4	0.46	0.153	150	0.682	0.0045
5	0.48	0.117	126	0.688	0.0045
6	0.50	0.147	168	0.665	0.0049
7	0.52	0.111	144	0.679	0.0048
8	0.54	0.141	120	0.649	0.0047
9	0.56	0.105	162	0.586	0.0056
10	0.58	0.135	138	0.641	0.0051
11	0.60	0.165	180	0.606	0.0061

Table 9 Coefficients of multivariate quadratic regression equations for Rtot and Wp

系数	MC-T
系数	$R t o t$	$W p$
$a 0$	1.9605	0.0148
$a 1$	-3.4258	-0.0165
$a 2$	1.212×10^-3	-0.1758
$a 3$	-2.969×10^-3	5.31×10^-5
$a 11$	4.6921	-7.045×10^-3
$a 22$	-10.5677	0.1775
$a 33$	-4.09×10^-3	3.28×10^-5
$a 12$	1.3994	0.5492
$a 13$	0.0355	-4.135×10^-4
$a 23$	-1.7×10^-6	-1.62×10^-8

Table 9 Coefficients of multivariate quadratic regression equations for Rtot and Wp

系数	MC-T
系数	$R t o t$	$W p$
$a 0$	1.9605	0.0148
$a 1$	-3.4258	-0.0165
$a 2$	1.212×10^-3	-0.1758
$a 3$	-2.969×10^-3	5.31×10^-5
$a 11$	4.6921	-7.045×10^-3
$a 22$	-10.5677	0.1775
$a 33$	-4.09×10^-3	3.28×10^-5
$a 12$	1.3994	0.5492
$a 13$	0.0355	-4.135×10^-4
$a 23$	-1.7×10^-6	-1.62×10^-8

Table 10 Pareto optimized solution set for MC-T

序号	$D t / W c h$	$b t / W c h$	$α t$ /(°)	$W p$ /W	$R t o t$ /(K/W)
1	0.400	0.140	120.00	0.0147	0.652
2	0.405	0.139	124.36	0.0150	0.631
3	0.409	0.139	130.28	0.0153	0.609
4	0.413	0.136	132.32	0.0156	0.598
5	0.420	0.137	134.77	0.0158	0.586
6	0.423	0.137	137.00	0.0160	0.578
7	0.440	0.138	133.14	0.0162	0.572
8	0.428	0.134	141.58	0.0165	0.562
9	0.470	0.138	134.14	0.0170	0.546
10	0.480	0.137	135.10	0.0172	0.536
11	0.464	0.137	148.69	0.0175	0.523
12	0.468	0.137	155.99	0.0179	0.513
13	0.513	0.137	141.85	0.0183	0.502
14	0.551	0.125	142.22	0.0189	0.479
15	0.554	0.121	146.30	0.0193	0.469
16	0.566	0.119	154.31	0.0201	0.456
17	0.574	0.117	157.30	0.0205	0.450
18	0.600	0.121	163.78	0.0210	0.445
19	0.599	0.108	161.88	0.0219	0.439
20	0.600	0.105	163.78	0.0225	0.438

Table 10 Pareto optimized solution set for MC-T

序号	$D t / W c h$	$b t / W c h$	$α t$ /(°)	$W p$ /W	$R t o t$ /(K/W)
1	0.400	0.140	120.00	0.0147	0.652
2	0.405	0.139	124.36	0.0150	0.631
3	0.409	0.139	130.28	0.0153	0.609
4	0.413	0.136	132.32	0.0156	0.598
5	0.420	0.137	134.77	0.0158	0.586
6	0.423	0.137	137.00	0.0160	0.578
7	0.440	0.138	133.14	0.0162	0.572
8	0.428	0.134	141.58	0.0165	0.562
9	0.470	0.138	134.14	0.0170	0.546
10	0.480	0.137	135.10	0.0172	0.536
11	0.464	0.137	148.69	0.0175	0.523
12	0.468	0.137	155.99	0.0179	0.513
13	0.513	0.137	141.85	0.0183	0.502
14	0.551	0.125	142.22	0.0189	0.479
15	0.554	0.121	146.30	0.0193	0.469
16	0.566	0.119	154.31	0.0201	0.456
17	0.574	0.117	157.30	0.0205	0.450
18	0.600	0.121	163.78	0.0210	0.445
19	0.599	0.108	161.88	0.0219	0.439
20	0.600	0.105	163.78	0.0225	0.438

Fig.23 Pareto optimized solution set and five clustering points

Fig.24 Comparison of optimized and unoptimized solution

Table 11 Comparison of results before and after optimization

项目		$D t / W c h$	$b t / W c h$	$α t$ /(°)	$R t o t$ /(K/W)	$W p$ /W
优化前		0.6	0.12	180	0.576	0.00560
点1	优化后	0.405	0.139	120.37	0.786	0.00398
点1	模拟值	0.405	0.139	120.37	0.773	0.00404
点2	优化后	0.437	0.132	120.91	0.744	0.00416
点2	模拟值	0.437	0.132	120.91	0.756	0.00398
点3	优化后	0.476	0.135	121.01	0.698	0.00438
点3	模拟值	0.476	0.135	121.01	0.703	0.00456
点4	优化后	0.511	0.133	146.96	0.649	0.00483
点4	模拟值	0.511	0.133	146.96	0.633	0.00497
点5	优化后	0.554	0.112	174.99	0.592	0.00558
点5	模拟值	0.554	0.112	174.99	0.604	0.00534

Table 11 Comparison of results before and after optimization

项目		$D t / W c h$	$b t / W c h$	$α t$ /(°)	$R t o t$ /(K/W)	$W p$ /W
优化前		0.6	0.12	180	0.576	0.00560
点1	优化后	0.405	0.139	120.37	0.786	0.00398
点1	模拟值	0.405	0.139	120.37	0.773	0.00404
点2	优化后	0.437	0.132	120.91	0.744	0.00416
点2	模拟值	0.437	0.132	120.91	0.756	0.00398
点3	优化后	0.476	0.135	121.01	0.698	0.00438
点3	模拟值	0.476	0.135	121.01	0.703	0.00456
点4	优化后	0.511	0.133	146.96	0.649	0.00483
点4	模拟值	0.511	0.133	146.96	0.633	0.00497
点5	优化后	0.554	0.112	174.99	0.592	0.00558
点5	模拟值	0.554	0.112	174.99	0.604	0.00534

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