Calculation model of flow and heat transfer characteristics of printed microchannel heat exchanger

doi:10.11949/0438-1157.20220942

Abstract

Abstract:

As the energy problem becomes more and more prominent, it is urgent to develop high-efficient energy equipment. Microchannel heat exchanger has attracted much attention in thermal management system due to its excellent performance. In this paper, a calculation model is proposed for the theoretical calculation of flow and heat transfer characteristics of microchannel heat exchanger. Based on the establishment of experimental database of literature, 10 and 6 kinds of heat transfer and flow calculation correlation formulas are compared and analyzed respectively. And numerical simulation and model solving research are carried out for a heat exchanger structure. The empirical solution of heat transfer characteristics obtained by using the correlation formula proposed by Stephan et al. and Sarmiento et al. is in good agreement with experimental solutions. The empirical solution of flow characteristics obtained by using the correlation formula, which are proposed by Kim et al., Muzychka et al., is in good agreement with the experimental solution. The numerical simulation and model calculation of the heat exchange unit are carried out, and the error of most points in the numerical solution and the empirical solution is within 10% , which verifies the accuracy and reliability of the calculation model proposed in this paper in the theoretical solution.

Key words: microchannel heat exchanger, flow and heat transfer characteristics, calculation model, numerical simulation, numerical solution, experimental solution, empirical solution

摘要：

随着能源问题的日益突出，亟需研制高效能源设备，微通道换热器以其优良的性能在热管理系统中备受关注。针对微通道换热器流动与传热特性理论计算提出了一个计算模型，基于文献建立实验数据库，分别对比分析了10种和6种传热与流动计算关联式，并针对一种换热器结构进行了数值仿真与模型求解。研究得出：采用Stephan等、Sarmiento等提出关联式所得关于传热特性的经验解与实验解的吻合度较好；采用Kim等、Muzychka等提出的关联式所得关于流动特性的经验解与实验解的吻合度较好；对换热单元进行数值仿真和模型计算，数值解与经验解中绝大多数点的误差在10%以内，验证了本文提出计算模型在理论求解中的准确性与可信度。

关键词: 微通道换热器, 流动与传热特性, 计算模型, 数值仿真, 数值解, 实验解, 经验解

CLC Number:

TK 124

Zhiqiang YU, Jianze WU, Yatao REN, Mingjian HE, Xikui YU, Hong QI. Calculation model of flow and heat transfer characteristics of printed microchannel heat exchanger[J]. CIESC Journal, 2022, 73(12): 5324-5342.

余智强, 吴建泽, 任亚涛, 何明键, 于喜奎, 齐宏. 印刷板式微通道换热器流动与传热特性的理论模型[J]. 化工学报, 2022, 73(12): 5324-5342.

Figures/Tables 23

Fig.1 Structure of PCHE[2]

Fig.2 Simplified schematic diagram of heat transfer calculation

Table 1 Nusselt number correlation of laminar heat transfer in microchannels

序号	文献	公式
(1)	[26]	$N u ¯ d = 1 C 1 L t h * C 2 + C 3 + C 4, L t h * < Z t h *, 1 < ε < 10 C 1 = - 2.757 × 10 - 3 φ 3 + 3.274 × 10 - 2 φ 2 - 7.464 × 10 - 5 φ + 4.476 C 2 = 6.391 × 10 - 1 C 3 = 1.604 × 10 - 4 φ 2 - 2.622 × 10 - 3 φ - 2.568 × 10 - 2 C 4 = 7.301 - 1.311 × 10 / φ + 1.519 × 10 / φ 2 - 6.094 / φ 3$
(2)	[27]	$N u ¯ d = 4.36 + 0.00668 1 / L t h * 1 + 0.04 1 / L t h * 2 / 3, R e < 2300$
(3)	[28]	$N u ¯ d = 0.1165 d w 0.81 b w + e - 0.79 R e 0.62 P r 1 / 3, 层流 0.072 d w 1.15 1 - 2.421 φ - 0.5 2 R e 0.8 P r 1 / 3, 湍流$
(4)	[11]	$N u ¯ d = 0.0475 R e d 0.6332, 1200 ≤ R e ≤ 1850 3.6802 × 10 - 4 R e d 1.2822, 1850 < R e ≤ 2900$
(5)	[24]	$N u ¯ d = 1.953 1 / L t h, d * 1 / 3, L t h, d * ≤ 0.03 4.364 + 0.0722 1 / L t h, d , L t h, d > 0.03, R e d < 2300$
(6)	[29]	$N u ¯ d = N u d, H, 1 3 + 0.63 + N u d, H, 2 - 0.6 3 + N u d, H, 2 3 1 / 3, R e d < 2300, 0.7 < P r < 1000 N u d, H, 1 = 4.364, N u d, H, 2 = 1.953 R e d P r d L 3, N u d, H, 3 = 0.924 P r 3 R e d d L$
(7)	[18]	$N u ¯ d = 4.36 + 0.086 1 / L t h, d * 1.33 1 + 0.1 P r R e d d / L 0.83, 0.7 < P r < 7, L t h, d * > 0.3, R e d < 2300$
(8)	[19]	$N u ¯ d = 3.63 + 0.086 1 / L t h, d * 1.33 1 + 0.1 P r R e d d / L 0.83, 0.7 < P r < 7, L t h, d * > 0.3, R e d < 2300$

Table 1 Nusselt number correlation of laminar heat transfer in microchannels

序号	文献	公式
(1)	[26]	$N u ¯ d = 1 C 1 L t h * C 2 + C 3 + C 4, L t h * < Z t h *, 1 < ε < 10 C 1 = - 2.757 × 10 - 3 φ 3 + 3.274 × 10 - 2 φ 2 - 7.464 × 10 - 5 φ + 4.476 C 2 = 6.391 × 10 - 1 C 3 = 1.604 × 10 - 4 φ 2 - 2.622 × 10 - 3 φ - 2.568 × 10 - 2 C 4 = 7.301 - 1.311 × 10 / φ + 1.519 × 10 / φ 2 - 6.094 / φ 3$
(2)	[27]	$N u ¯ d = 4.36 + 0.00668 1 / L t h * 1 + 0.04 1 / L t h * 2 / 3, R e < 2300$
(3)	[28]	$N u ¯ d = 0.1165 d w 0.81 b w + e - 0.79 R e 0.62 P r 1 / 3, 层流 0.072 d w 1.15 1 - 2.421 φ - 0.5 2 R e 0.8 P r 1 / 3, 湍流$
(4)	[11]	$N u ¯ d = 0.0475 R e d 0.6332, 1200 ≤ R e ≤ 1850 3.6802 × 10 - 4 R e d 1.2822, 1850 < R e ≤ 2900$
(5)	[24]	$N u ¯ d = 1.953 1 / L t h, d * 1 / 3, L t h, d * ≤ 0.03 4.364 + 0.0722 1 / L t h, d , L t h, d > 0.03, R e d < 2300$
(6)	[29]	$N u ¯ d = N u d, H, 1 3 + 0.63 + N u d, H, 2 - 0.6 3 + N u d, H, 2 3 1 / 3, R e d < 2300, 0.7 < P r < 1000 N u d, H, 1 = 4.364, N u d, H, 2 = 1.953 R e d P r d L 3, N u d, H, 3 = 0.924 P r 3 R e d d L$
(7)	[18]	$N u ¯ d = 4.36 + 0.086 1 / L t h, d * 1.33 1 + 0.1 P r R e d d / L 0.83, 0.7 < P r < 7, L t h, d * > 0.3, R e d < 2300$
(8)	[19]	$N u ¯ d = 3.63 + 0.086 1 / L t h, d * 1.33 1 + 0.1 P r R e d d / L 0.83, 0.7 < P r < 7, L t h, d * > 0.3, R e d < 2300$

Table 2 Correlation coefficient［20， 30］

条件	系数
边界条件
均匀壁温（UWT）	C₁=3.24，C₃= 0.409, $f (P r) = 0.564 1 + 1.664 P r 1 / 6 9 / 2 2 / 9$
均匀热流（UHF）	C₁=3.86，C₃= 0.501, $f (P r) = 0.886 1 + 1.909 P r 1 / 6 9 / 2 2 / 9$
Nu类型
局部Nu	C₂ = 1，C₄ = 1
平均Nu
UWT	C₂ = 3/2，C₄ = 2
UHF	C₂ = 4/3，C₄ = 3/2
形状参数
上边界	γ = 1/10
下边界	γ = -3/10

Table 2 Correlation coefficient［20， 30］

条件	系数
边界条件
均匀壁温（UWT）	C₁=3.24，C₃= 0.409, $f (P r) = 0.564 1 + 1.664 P r 1 / 6 9 / 2 2 / 9$
均匀热流（UHF）	C₁=3.86，C₃= 0.501, $f (P r) = 0.886 1 + 1.909 P r 1 / 6 9 / 2 2 / 9$
Nu类型
局部Nu	C₂ = 1，C₄ = 1
平均Nu
UWT	C₂ = 3/2，C₄ = 2
UHF	C₂ = 4/3，C₄ = 3/2
形状参数
上边界	γ = 1/10
下边界	γ = -3/10

Fig.3 Schematic diagram of pressure loss distribution

Table 3 The Fanning friction coefficient f of the microchannel

序号	文献	公式
(1)	[8]	$f d = 1 R e d 3.44 L h y * 2 + 24 1 + φ 2 1 - 192 φ π 5 t a n h π 2 φ 2 1 / 2, R e d ≤ 1800$
(2)	[24]	$f d = 24 1 - 1.3553 1 φ + 1.9467 1 φ 2 - 1.7012 1 φ 3 + 0.9564 1 φ 4 - 0.2537 1 φ 5 R e d$
(3)	[9]	$f d = 15.78 + 0.004868 R e d 0.8416 R e d, R e < 2500$
(4)	[44]	$f d = λ D a r c y 4 = 1.82 l g R e d - 1.64 - 2 4$
(5)	[45]	$f d = 3.43 L h y * + 15.77 + 1.463 / 4 L h y * - 3.43 / L h y * 1 + 0.00051 L h y * 2 R e d, 100 ≤ R e d ≤ 1000$
(6)	[8]	$f A = 1 R e A 3.44 L h y * 2 + 12 φ 1 + φ 1 - 192 φ π 5 t a n h π 2 φ 2 1 / 2, R e A ≤ 1800$

Table 3 The Fanning friction coefficient f of the microchannel

序号	文献	公式
(1)	[8]	$f d = 1 R e d 3.44 L h y * 2 + 24 1 + φ 2 1 - 192 φ π 5 t a n h π 2 φ 2 1 / 2, R e d ≤ 1800$
(2)	[24]	$f d = 24 1 - 1.3553 1 φ + 1.9467 1 φ 2 - 1.7012 1 φ 3 + 0.9564 1 φ 4 - 0.2537 1 φ 5 R e d$
(3)	[9]	$f d = 15.78 + 0.004868 R e d 0.8416 R e d, R e < 2500$
(4)	[44]	$f d = λ D a r c y 4 = 1.82 l g R e d - 1.64 - 2 4$
(5)	[45]	$f d = 3.43 L h y * + 15.77 + 1.463 / 4 L h y * - 3.43 / L h y * 1 + 0.00051 L h y * 2 R e d, 100 ≤ R e d ≤ 1000$
(6)	[8]	$f A = 1 R e A 3.44 L h y * 2 + 12 φ 1 + φ 1 - 192 φ π 5 t a n h π 2 φ 2 1 / 2, R e A ≤ 1800$

Fig.4 Internal angle of channel

Fig.5 Flow chart

Table 4 Composition of database and research content

文献	通道截面	当量直径	Re_d	换热工质	流动形式	研究方法
[17]	矩形	0.002 m	400~1300	去离子水/去离子水	交错流	实验
[19]	矩形	0.003 m	300~2500	空气/水	交错流	实验
[2, 20, 45]	半圆形	0.00122 m	800~2600	氦气/氦气	准逆流	实验+仿真
[50]	半圆形	0.00122 m	800~4000	氦气/氦气	准逆流	实验
[49]	圆形	0.00183 m	300~2400	空气/水	交错流	实验

Fig.6 Comparative analysis of outlet temperature Tout

Fig.7 Comparative analysis of total heat transfer coefficient UA (or entire thermal resistance 1/UA) and efficiency ε

Fig.8 Comparative analysis of the total heat exchange amount Q

Fig.9 Comparison and analysis of Fanning friction coefficient f of heat exchanger with numerical simulation

Fig.10 Comparison and analysis of Fanning friction coefficient f of heat exchanger with experimental measurement

Fig.11 Structure of heat transfer core

Table 5 Fitting polynomial of aviation fuel RP-3［52-55］

系数	ρ/(kg/m³)	c_p /(J/(kg·K))	μ/(Pa·s)	λ/(W/(m·K))
r₁	0	-1.02757×10^-6	1.06×10^-12	0
r₂	0	0.001576781	-1.74792×10^-9	-6.50×10^-10
r₃	-0.000432735	-0.877885341	1.09093×10^-6	5.15×10^-7
r₄	-0.673250175	214.3414755	-0.000307156	-0.000300975
r₅	1029.120329	-17433.41997	0.033481934	0.193770047
精度R²	0.9997	0.9987	0.9977	0.9984

Fig.12 Semicircular microchannel cross section[2]

Fig.13 Heat transfer unit and boundary type

Table 6 Heat exchange plate geometry

名称	尺寸
板片厚度	0.0008 m
通道半径	0.0006 m
换热板长	0.200 m
通道节距	0.00165 m
边缘厚度	0.008 m
每层通道数	33个
通道长度	0.220 m
转折角度	40°

Table 7 Working condition

q_v,c/(m³/h)	v_in,c/(m/s)	q_v,h/(m³/h)	v_in,h/(m/s)	T_in,c/℃	T_in,h/℃
1.0	0.4255	2.0	0.8510	40.0	160
1.5	0.6383	2.0	0.8510	40.0	160
2.0	0.8510	2.0	0.8510	50.0	160
2.5	1.0638	2.0	0.8510	50.0	160
3.0	1.2765	2.0	0.8510	60.0	160
3.5	1.4893	2.0	0.8510	60.0	160
4.0	1.7021	2.0	0.8510	70.0	160
4.5	1.9148	2.0	0.8510	70.0	160
5.0	2.1276	2.0	0.8510	80.0	160

Fig.14 Grid independence verification

Fig.15 Numerical solution of outlet temperature compared with empirical solution

Fig.16 Comparison of numerical and empirical solutions of pcost and f

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