微通道换热器拓扑结构优化与性能研究

doi:10.11949/0438-1157.20231236

摘要/Abstract

摘要：

换热器结构拓扑优化可将传热强化设计问题转化为数学优化问题进行求解，对于设计新颖高效换热器具有重要价值。然而，拓扑优化数学模型难以直接解释优化结果的几何特征及相应强化机理。以传热量为目标，对微通道换热器进行拓扑优化设计，研究了不同参数对换热器强化结构特征和换热器性能的影响。结果表明，拓扑优化换热器的通道结构呈现多级分叉构型，分叉的数量随着入口 $R e$ 数、翅片传热效率和流体 $P r$ 数的增大而增多。在此基础上，采用（火积）耗散和边界层理论分析了拓扑优化分叉通道与流体边界层厚度的内在联系，为换热器结构强化设计提供了新的思路。

关键词: 优化设计, 微通道, 传递过程, 分级通道结构, 边界层理论

Abstract:

The structure topology optimization of the heat exchanger transforms the design problem of enhancing heat transfer into a mathematical optimization problem, which is important in finding novel design for high performance heat exchanger. However, the mathematical model of topology optimization cannot directly explain the geometric features and enhancing mechanisms of the design. The topology optimization design is conducted for the heat transfer enhancement of microchannel heat exchanger. The impacts of different factors on the optimized structures and heat transfer performance are investigated. The optimization results show that the channels of the topology-optimized heat exchanger present a "hierarchical bifurcation" configuration, and the number of bifurcations increases with the increase of the inlet $R e$ number, the vertical heat transfer of fins, and the $P r$ number of liquid. Based on these findings, entransy dissipation theory and boundary layer theory are applied to reveal the mechanism of heat transfer enhancement, which may shad lights on the design of heat transfer enhancement.

Key words: optimal design, microchannel, transport processes, hierarchical channel pattern, boundary layer theory

中图分类号:

TK 124

陈彦松, 阮达, 刘渊博, 郑通, 张帅帅, 马学虎. 微通道换热器拓扑结构优化与性能研究[J]. 化工学报, DOI: 10.11949/0438-1157.20231236.

Yansong CHEN, Da RUAN, Yuanbo LIU, Tong ZHENG, Shuaishuai ZHANG, Xuehu MA. Topology optimization and performance research of microchannel heat exchangers[J]. CIESC Journal, DOI: 10.11949/0438-1157.20231236.

图/表 10

图1 微通道换热器模型示意图：(a) 电子元件冷板对流换热器换热；(b) 简化的二维模型

Fig.1 Heat exchanger model diagram (a) Electronic components cold plate convection heat exchanger heat exchange; (b) Simplified 2D model

表1 各案例参数一览表

Table 1 List of parameters for different cases

编号	$Δ p$ (Pa)	$h z$ (W/(m²·K))
案例组I(1~10)	1~10	$103$
案例组II(1~10)	1~10	$5 × 103$
案例组III(1~10)	1~10	$104$
案例组IV(1~10)	1~10	$5 × 104$

表1 各案例参数一览表

Table 1 List of parameters for different cases

编号	$Δ p$ (Pa)	$h z$ (W/(m²·K))
案例组I(1~10)	1~10	$103$
案例组II(1~10)	1~10	$5 × 103$
案例组III(1~10)	1~10	$104$
案例组IV(1~10)	1~10	$5 × 104$

图2 不同压降条件下的典型拓扑优化结果

Fig.2 Topology optimization results under pressure drop conditions for different cases

图 3 不同拓扑优化案例的性能指标

Fig.3 The optimization results and corresponding conditions for optimizing different cases

图 4 无量纲压降Δp˜与入口雷诺数Rein的关系

Fig.4 Plot of dimensionless pressure drop Δp˜ versus inlet Reynolds number Rein

表2 不同流体介质的物性参数及边界条件

Table 2 Physical parameters and boundary conditions for different fluid media

物质名称	动力黏度 $μ$ Pa·s	密度 $ρ$ kg/m³	热导率 $k l$ W/(m·K)	等压热熔 $c p, l$ J/(kg·K)	$P r$ 数	初始 $R e i n$	入口压力Pa
液态金属	0.0024	6440	16.5	200	0.029	996.9	9.085
水	0.0010	998	0.600	4180	6.99	1000.0	10.24
FC40 (3M)	0.0041	1855	0.065	1100	69.4	997.8	92.05
乙二醇	0.0214	1116.5	0.2495	2383	204.6	995.8	4172

表2 不同流体介质的物性参数及边界条件

Table 2 Physical parameters and boundary conditions for different fluid media

物质名称	动力黏度 $μ$ Pa·s	密度 $ρ$ kg/m³	热导率 $k l$ W/(m·K)	等压热熔 $c p, l$ J/(kg·K)	$P r$ 数	初始 $R e i n$	入口压力Pa
液态金属	0.0024	6440	16.5	200	0.029	996.9	9.085
水	0.0010	998	0.600	4180	6.99	1000.0	10.24
FC40 (3M)	0.0041	1855	0.065	1100	69.4	997.8	92.05
乙二醇	0.0214	1116.5	0.2495	2383	204.6	995.8	4172

图5 不同流体介质微通道换热器的优化结果

Fig.5 Distribution diagram of solid-liquid region (γ) for topological optimization of different working fluids

图6 不同Pr数对应的边界层区域以及场协同关系

Fig.6 Boundary layer regions corresponding to different Pr numbers and field synergy relations

图7 典型拓扑优化换热器内楔形结构的几何示意图

Fig.7 Geometrical sketch of typical wedge structures in topology optimized heat exchanger.

表3 不同楔形结构开角条件下流动和传热边界层达到充分发展时对应的η临界值

Table 3 The η Critical Values of Flow and Heat Transfer Boundary Layer at Fully Developed Conditions for Different Wedge Angles

$β (°)$	$η U$	$η t P r = 0.029$	$η t P r = 6.99$	$η t P r = 69.4$	$η t P r = 204.6$
$-$ 30	6.11	24.19	3.08	1.51	1.08
$-$ 20	5.56	23.58	2.76	1.31	0.93
$-$ 10	5.20	23.10	2.58	1.20	0.85
0	4.91	22.66	2.45	1.13	0.78
20	4.46	21.88	2.26	1.03	0.72
40	4.09	21.12	2.12	0.95	0.66
60	3.78	20.38	1.99	0.89	0.62
80	3.50	19.63	1.88	0.84	0.58
90	3.37	19.25	1.83	0.81	0.56
100	3.25	18.87	1.78	0.78	0.54
120	3.01	18.10	1.68	0.73	0.51
140	2.79	17.30	1.59	0.69	0.48

表3 不同楔形结构开角条件下流动和传热边界层达到充分发展时对应的η临界值

Table 3 The η Critical Values of Flow and Heat Transfer Boundary Layer at Fully Developed Conditions for Different Wedge Angles

$β (°)$	$η U$	$η t P r = 0.029$	$η t P r = 6.99$	$η t P r = 69.4$	$η t P r = 204.6$
$-$ 30	6.11	24.19	3.08	1.51	1.08
$-$ 20	5.56	23.58	2.76	1.31	0.93
$-$ 10	5.20	23.10	2.58	1.20	0.85
0	4.91	22.66	2.45	1.13	0.78
20	4.46	21.88	2.26	1.03	0.72
40	4.09	21.12	2.12	0.95	0.66
60	3.78	20.38	1.99	0.89	0.62
80	3.50	19.63	1.88	0.84	0.58
90	3.37	19.25	1.83	0.81	0.56
100	3.25	18.87	1.78	0.78	0.54
120	3.01	18.10	1.68	0.73	0.51
140	2.79	17.30	1.59	0.69	0.48

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