非均匀泡沫铜强化相变材料蓄热特性的数值分析

doi:10.19799/j.cnki.2095-4239.2025.0132

摘要/Abstract

摘要：

泡沫铜的高导热可以强化相变材料的导热传热，但其孔隙结构会阻碍相变材料的对流传热。为了优化其对相变材料的传热强化效能，本工作提出构建梯度孔隙的泡沫铜优化其对相变材料传热特性，并通过数值仿真方法研究了泡沫铜孔隙梯度方向和跨度对相变材料传热的影响。结果表明，一维水平方向梯度均可以强化相变材料的传热，正向梯度的传热速率随孔隙跨度的增加而增加，而负向梯度的传热速率随孔隙跨度的增加而降低，在负向4%的跨度下最大提高了5.8%。一维垂直方向梯度下，正向梯度表现出较好的强化效果，且在跨度10%时传热速率最大提高了11.5%。二维梯度孔隙传热特性研究结果显示，底部设置较低的孔隙率可以增加传热速率，最大提高了5.5%。综合发现，一维垂直正向梯度泡沫铜在10%的孔隙跨度下具有更好的强化效果。

关键词: 相变材料, 泡沫铜, 梯度设计, 相变传热, 数值仿真

Abstract:

Copper foam, owing to its high thermal conductivity, enhances the conductive heat transfer of phase change materials (PCMs); however, its porous structure can inhibit convective heat transfer. To optimize the overall heat transfer enhancement, this study proposes the use of copper foam with a gradient-porosity structure to improve the thermal performance of PCMs. Numerical simulations were conducted to investigate the influence of gradient direction and porosity span on the heat transfer behavior. The results indicate that one-dimensional horizontal gradient porosity improves heat transfer, with the heat transfer rate increasing with porosity span for positive gradients and decreasing for negative gradients. The maximum improvement observed was 5.8% for a negative gradient span of 4%. For one-dimensional vertical gradients, positive gradients yielded superior enhancement, with a maximum increase of 11.5% at a 10% span. In the case of two-dimensional gradients, placing lower porosity at the bottom led to improved heat transfer performance, with a maximum increase of 5.5%. Overall, vertically oriented one-dimensional positive gradient copper foam with a 10% porosity span demonstrated the most effective heat transfer enhancement.

Key words: phase change materials, copper foam, design of gradient, phase change heat transfer, numerical simulation

中图分类号:

TK 11

袁艳平, 高启发, 张楠, 孙钦荣. 非均匀泡沫铜强化相变材料蓄热特性的数值分析[J]. 储能科学与技术, 2025, 14(8): 3100-3109.

Yanping YUAN, Qifa GAO, Nan ZHANG, Qinrong SUN. Numerical analysis of thermal storage characteristics of gradient-porosity copper foam-enhanced phase change materials[J]. Energy Storage Science and Technology, 2025, 14(8): 3100-3109.

图/表 12

图1

表1

图2

图3

图4

图5

图6

图7

图8

图9

图10

图11

参考文献 34

[1]	GE R H, LI Q, LI C, et al. Evaluation of different melting performance enhancement structures in a shell-and-tube latent heat thermal energy storage system[J]. Renewable Energy, 2022, 187: 829-843. DOI: 10.1016/j.renene.2022.01.097.
[2]	ZUO H Y, ZHOU Y, WU M Y, et al. Development and numerical investigation of parallel combined sensible-latent heat storage unit with intermittent flow for concentrated solar power plants[J]. Renewable Energy, 2021, 175: 29-43. DOI: 10.1016/j.renene. 2021.04.092.
[3]	张云峰, 张学文, 钟威, 等. 石蜡与低熔点合金双级联相变材料强化板翅式散热器换热性能的数值模拟[J]. 储能科学与技术, 2024, 13(5): 1460-1470. DOI: 10.19799/j.cnki.2095-4239.2023.0843.
	ZHANG Y F, ZHANG X W, ZHONG W, et al. Numerical simulation of heat transfer performance of plate-fin radiator reinforced with double cascade phase change material of paraffin and low melting point alloy[J]. Energy Storage Science and Technology, 2024, 13(5): 1460-1470. DOI: 10.19799/j.cnki.2095-4239.2023.0843.
[4]	RATHOD M K, BANERJEE J. Thermal performance enhancement of shell and tube Latent Heat Storage Unit using longitudinal fins[J]. Applied Thermal Engineering, 2015, 75: 1084-1092. DOI: 10.1016/j.applthermaleng.2014.10.074.
[5]	YANG X H, XU F F, WANG X Y, et al. Solidification in a shell-and-tube thermal energy storage unit filled with longitude fins and metal foam: A numerical study[J]. Energy and Built Environment, 2023, 4(1): 64-73. DOI: 10.1016/j.enbenv.2021.08.002.
[6]	柴进, 王军, 倪奇强. 纳米颗粒协同肋片强化相变材料传热性能试验[J]. 储能科学与技术, 2022, 11(10): 3161-3170. DOI: 10.19799/j.cnki.2095-4239.2022.0021.
	CHAI J, WANG J, NI Q Q. Experiment on heat transfer performance of phase change materials strengthened by nanoparticles and fins[J]. Energy Storage Science and Technology, 2022, 11(10): 3161-3170. DOI: 10.19799/j.cnki.2095-4239.2022.0021.
[7]	XIAO X, JIA H W, WEN D S, et al. Experimental investigation of a latent heat thermal energy storage unit encapsulated with molten salt/metal foam composite seeded with nanoparticles[J]. Energy and Built Environment, 2023, 4(1): 74-85. DOI: 10.1016/j.enbenv.2021.08.003.
[8]	代建龙, 李果, 曹一通, 等. 多孔金属泡沫强化石蜡相变蓄热性能[J]. 储能科学与技术, 2024, 13(11): 3764-3771. DOI: 10.19799/j.cnki.2095-4239.2024.0449.
	DAI J L, LI G, CAO Y T, et al. Enhancing phase change heat storage performance of paraffin using porous metal foam[J]. Energy Storage Science and Technology, 2024, 13(11): 3764-3771. DOI: 10.19799/j.cnki.2095-4239.2024.0449.
[9]	XU Y, ZHENG Z J, CHEN S, et al. Parameter analysis and fast prediction of the optimum eccentricity for a latent heat thermal energy storage unit with phase change material enhanced by porous medium[J]. Applied Thermal Engineering, 2021, 186: 116485. DOI: 10.1016/j.applthermaleng.2020.116485.
[10]	ZHANG Z L, ZHANG N, YUAN Y P, et al. Investigations on transient thermal performance of phase change materials embedded in metal foams for latent heat thermal energy storage[J]. International Journal of Energy Research, 2021, 45(15): 20763-20782. DOI: 10.1002/er.7137.
[11]	TIAN W, DANG S, LIU G, et al. Thermal transport in phase change materials embedded in metal foam: Evaluation on inclination configuration[J]. Journal of Energy Storage, 2021, 33: 102166. DOI: 10.1016/j.est.2020.102166.
[12]	YING Q F, WANG H, LICHTFOUSE E. Numerical simulation on thermal behavior of partially filled metal foam composite phase change materials[J]. Applied Thermal Engineering, 2023, 229: 120573. DOI: 10.1016/j.applthermaleng.2023.120573.
[13]	JOSHI V, RATHOD M K. Constructal enhancement of thermal transport in metal foam-PCM composite-assisted latent heat thermal energy storage system[J]. Numerical Heat Transfer, Part A: Applications, 2019, 75(6): 413-433. DOI: 10.1080/10407782. 2019.1599270.
[14]	XU Y, REN Q L, ZHENG Z J, et al. Evaluation and optimization of melting performance for a latent heat thermal energy storage unit partially filled with porous media[J]. Applied Energy, 2017, 193: 84-95. DOI: 10.1016/j.apenergy.2017.02.019.
[15]	LI X Y, DUAN J T, SIMON T, et al. Nonuniform metal foam design and pore-scale analysis of a tilted composite phase change material system for photovoltaics thermal management[J]. Applied Energy, 2021, 298: 117203. DOI: 10.1016/j.apenergy.2021.117203.
[16]	朱孟帅, 张华, 闫勤学, 等. 泡沫金属填充率对相变材料强化换热的机理研究[J]. 制冷学报, 2021, 42(5): 127-133. DOI: 10.3969/j.issn. 0253-4339.2021.05.127.
	ZHU M S, ZHANG H, YAN Q X, et al. Study on the effect of foamed metal copper filling ratio on the enhanced heat transfer mechanism of phase change materials[J]. Journal of Refrigeration, 2021, 42(5): 127-133. DOI: 10.3969/j.issn.0253-4339.2021.05.127.
[17]	HU C Z, LI H Y, TANG D W, et al. Pore-scale investigation on the heat-storage characteristics of phase change material in graded copper foam[J]. Applied Thermal Engineering, 2020, 178: 115609. DOI: 10.1016/j.applthermaleng.2020.115609.
[18]	YANG X H, WANG W B, YANG C, et al. Solidification of fluid saturated in open-cell metallic foams with graded morphologies[J]. International Journal of Heat and Mass Transfer, 2016, 98: 60-69. DOI: 10.1016/j.ijheatmasstransfer.2016.03.023.
[19]	YANG X H, WEI P, WANG X Y, et al. Gradient design of pore parameters on the melting process in a thermal energy storage unit filled with open-cell metal foam[J]. Applied Energy, 2020, 268: 115019. DOI: 10.1016/j.apenergy.2020.115019.
[20]	WANG Z F, WU J N, LEI D Q, et al. Experimental study on latent thermal energy storage system with gradient porosity copper foam for mid-temperature solar energy application[J]. Applied Energy, 2020, 261: 114472. DOI: 10.1016/j.apenergy.2019.114472.
[21]	MENG X, LIU S H, ZOU J L, et al. Inclination angles on the thermal behavior of Phase-Change Material (PCM) in a cavity filled with copper foam partly[J]. Case Studies in Thermal Engineering, 2021, 25: 100944. DOI: 10.1016/j.csite.2021.100944.
[22]	HUANG S, LU J, LI Y C. Numerical study on the influence of inclination angle on the melting behaviour of metal foam-PCM latent heat storage units[J]. Energy, 2022, 239: 122489. DOI: 10.1016/j.energy.2021.122489.
[23]	GHAHREMANNEZHAD A, XU H J, SALIMPOUR M R, et al. Thermal performance analysis of phase change materials (PCMs) embedded in gradient porous metal foams[J]. Applied Thermal Engineering, 2020, 179: 115731. DOI: 10.1016/j.applthermaleng.2020.115731.
[24]	YANG X H, YU J B, GUO Z X, et al. Role of porous metal foam on the heat transfer enhancement for a thermal energy storage tube[J]. Applied Energy, 2019, 239: 142-156. DOI: 10.1016/j.apenergy.2019.01.075.
[25]	MAHDI J M, MOHAMMED H I, HASHIM E T, et al. Solidification enhancement with multiple PCMs, cascaded metal foam and nanoparticles in the shell-and-tube energy storage system[J]. Applied Energy, 2020, 257: 113993. DOI: 10.1016/j.apenergy. 2019.113993.
[26]	NIE C D, LIU J W, DENG S X. Effect of geometry modification on the thermal response of composite metal foam/phase change material for thermal energy storage[J]. International Journal of Heat and Mass Transfer, 2021, 165: 120652. DOI: 10.1016/j.ijheatmasstransfer.2020.120652.
[27]	CALMIDI V V, MAHAJAN R L. Forced convection in high porosity metal foams[J]. Journal of Heat Transfer, 2000, 122(3): 557-565. DOI: 10.1115/1.1287793.
[28]	FOURIE J G, DU PLESSIS J P. Pressure drop modelling in cellular metallic foams[J]. Chemical Engineering Science, 2002, 57(14): 2781-2789. DOI: 10.1016/S0009-2509(02)00166-5.
[29]	CALMIDI V V. Transport phenomena in high porosity fibrous metal foams[D]. Boulder: University of Colorado at Boulder, 1998.
[30]	BHATTACHARYA A, CALMIDI V V, MAHAJAN R L. Thermophysical properties of high porosity metal foams[J]. International Journal of Heat and Mass Transfer, 2002, 45(5): 1017-1031. DOI: 10.1016/S0017-9310(01)00220-4.
[31]	ŽUKAUSKAS A. Heat transfer from tubes in crossflow[J]. Advances in Heat Transfer, 1972, 8: 93-160. DOI: 10.1016/S0065-2717(08)70038-8.
[32]	BOOMSMA K, POULIKAKOS D. On the effective thermal conductivity of a three-dimensionally structured fluid-saturated metal foam[J]. International Journal of Heat and Mass Transfer, 2001, 44(4): 827-836. DOI: 10.1016/S0017-9310(00)00123-X.
[33]	POURAKABAR A, ALI RABIENATAJ DARZI A. Enhancement of phase change rate of PCM in cylindrical thermal energy storage[J]. Applied Thermal Engineering, 2019, 150: 132-142. DOI: 10.1016/j.applthermaleng.2019.01.009.
[34]	WEI X Y, ZHANG N, ZHANG Z L, et al. Melting evaluation of phase change materials impregnated into cascaded metal foams with regionalized enhancement[J]. Journal of Thermal Science, 2025, 34(1): 223-241. DOI: 10.1007/s11630-024-2064-3.

材料	物性	类值
泡沫铜	密度/(kg/m³)	8979
	比热容/[J/(kg·K)]	381
	热导率/[W/(m·K)]	401
石蜡	密度/(kg/m³)	900
	比热容/[J/(kg·K)]	2200
	相变潜热/(J/kg)	197700
	相变区间/K	314.15～321.15
	动力黏度/[kg/(m·s)]	0.0031
	热导率/[W/(m·K)]	0.2
	热膨胀系数/K^-1	0.0006