孔隙尺度下Laguerre Voronoi开孔泡沫的对流传热特性

doi:10.16085/j.issn.1000-6613.2025-0119

化工进展 ›› 2025, Vol. 44 ›› Issue (8): 4394-4407.DOI: 10.16085/j.issn.1000-6613.2025-0119

• 微介观过程与材料的模拟与仿真 • 上一篇

孔隙尺度下Laguerre Voronoi开孔泡沫的对流传热特性

戴贵龙¹^,²(), 王孝宇¹(), 皇甫江飞¹, 龚凌诸²

^1.福建理工大学建筑新能源与节能福建省高校重点实验室，福建福州 350118
^2.福建理工大学福州市绿色化工与清洁生产行业技术创新中心，福建福州 350118

收稿日期:2025-01-20 修回日期:2025-03-17 出版日期:2025-08-25 发布日期:2025-09-08
通讯作者: 戴贵龙
作者简介:戴贵龙（1983—），男，博士，副教授，研究方向为多孔介质流固耦合传热、辐射传热。E-mail：daiguilong611@126.com
王孝宇（2000—），男，硕士研究生，研究方向为多孔介质流固耦合传热。E-mail：1476473619@qq.com。
基金资助:
国家自然科学基金(52176181);福建省自然科学基金(2024J01828);福建省自然科学基金(2022Y3008)

Convection heat transfer characteristics of pore-scale Laguerre Voronoi open-cell foam

DAI Guilong¹^,²(), WANG Xiaoyu¹(), HUANGFU Jiangfei¹, GONG Lingzhu²

^1.Key Laboratory of New Energy and Energy-Saving in Building, Fujian University of Technology, Fuzhou 350118, Fujian, China
^2.Fuzhou Green Chemical and Cleaner Production Industry Technology Innovation Center, Fujian University of Technology, Fuzhou 350118, Fujian, China

Received:2025-01-20 Revised:2025-03-17 Online:2025-08-25 Published:2025-09-08
Contact: DAI Guilong

摘要/Abstract

摘要：

为提高人工设计开孔泡沫的对流传热性能，提出了一种新型泡沫多孔Laguerre Voronoi（LV）模型，该模型能够有效还原实际泡沫的周期性和随机性，避免了流动贯穿，同时还可对孔隙堵塞问题进行定量调控，具有良好的对流传热性能。基于参数式一体化建模方法，重建了一系列具有不同几何参数的LV泡沫，通过孔隙尺度数值模拟分析了入口流速、表观及孔隙结构参数（孔隙率、水力直径、元胞直径、相对肋筋直径）对LV泡沫对流传热性能的影响，结合实验测量验证数值结果可靠性，并与现有研究中提出的Lord-Kelvin（L-K）模型、传统工艺模型及X射线计算机断层成像（X-CT）扫描模型进行对比。在此基础上，基于孔隙参数及表观参数分别拟合了两类对流传热关联式，对关联式的适用性、预测精度及误差分布特性进行了详细分析。结果表明，相比L-K模型，LV泡沫具有更为真实的孔隙结构，对流传热性能更佳；容积传热系数随入口流速增大而单调增大，随相对肋筋直径增大（或孔隙率减小）成抛物线分布，其对称轴与雷诺数相关。本文提出的两类对流换热关联式适用于广泛的几何参数和雷诺数范围，最大相对误差均小于20%，具有良好的预测精度，可用于高效预测开孔泡沫的对流传热性能。

关键词: 多孔介质, 孔隙尺度模拟, 对流, 传热, 关联式

Abstract:

To enhance the convective heat transfer performance of artificially designed open-cell foams, a novel porous foam model, the Laguerre Voronoi (LV) model, is proposed. This model effectively captures both the periodicity and randomness of real foams, avoiding flow-through and enabling quantitative control over pore blockage issues, while demonstrating excellent convective heat transfer performance. Using a parameterized integrated modeling approach, a series of LV foams with different geometric parameters are reconstructed. Pore-scale numerical simulations are conducted to investigate the influence of inlet velocity, apparent, and pore structure parameters (porosity, hydraulic diameter, cell diameter, and relative strut diameter) on the convective heat transfer performance of LV foams. Experimental measurements are used to validate the reliability of the numerical results, and comparisons are made with existing models, including the Lord-Kelvin (L-K) model, traditional process models, and X-ray computed tomography (X-CT) scan models. Based on this, two types of convective heat transfer correlations are fitted using pore and apparent parameters. The applicability, prediction accuracy, and error distribution characteristics of the correlations are analyzed in detail. The results show that, compared to the L-K model, LV foam exhibits more realistic pore structures and higher convective heat transfer performance. The volumetric heat transfer coefficient increases monotonically with the inlet velocity and follows a parabolic distribution with increasing relative strut diameter (or decreasing porosity), with its symmetry axis related to the Reynolds number. The two convective heat transfer correlations proposed in this paper are applicable to a wide range of geometric parameters and Reynolds numbers, with the maximum relative error less than 20%, showing good prediction accuracy and providing an efficient tool for predicting the convective heat transfer performance of open-cell foams.

Key words: porous media, pore-scale numerical simulation, convection, heat transfer, correlation

中图分类号:

TK124

戴贵龙, 王孝宇, 皇甫江飞, 龚凌诸. 孔隙尺度下Laguerre Voronoi开孔泡沫的对流传热特性[J]. 化工进展, 2025, 44(8): 4394-4407.

DAI Guilong, WANG Xiaoyu, HUANGFU Jiangfei, GONG Lingzhu. Convection heat transfer characteristics of pore-scale Laguerre Voronoi open-cell foam[J]. Chemical Industry and Engineering Progress, 2025, 44(8): 4394-4407.

图/表 18

图1 LVT与VT对比

图2 Laguerre Voronoi建模流程

图3 边界条件及尺寸说明（dc=4mm，ds/dc=0.34）

表1 LV泡沫几何参数

d_c/mm	d_s/d_c	ϕ/%	a_sf/m^-1	d_h/mm
3	0.11	96.8	367.12	10.60
	0.25	85.3	708.21	4.80
	0.30	80.1	786.51	4.10
	0.32	78.1	803.64	3.90
	0.35	74.7	839.51	3.60
	0.45	61.8	901.96	2.70
4	0.10	96.9	301.85	12.84
	0.25	83.5	598.05	5.59
	0.31	76.2	673.91	4.52
	0.34	71.9	709.12	4.05
	0.38	67.6	727.36	3.72
	0.45	56.6	761.86	2.97
5	0.10	96.8	245.77	15.76
	0.24	84.3	473.60	7.12
	0.30	77.5	526.40	5.89
	0.32	74.4	551.30	5.40
	0.36	69.9	567.52	4.93
	0.45	56.0	599.60	3.74

图4 模型验证（u0=0.5m/s）

表2 泡沫样品几何及物性参数

D/mm	L/mm	ϕ	d_s/d_c	d_c/mm	ρ_s/kg·m^-3	c_s/J·kg^-1·K^-1	λ_s/W·m^-1·K^-1
25	40	0.629	0.41	4.0	2670	900	120

图5 对流换热实验平台1—空压机；2—截止阀；3—稳压罐；4—旁通阀；5—针阀；6—流量计；7—空气加热器；8—热电偶；9—保温层；10—3D打印泡沫样品；11—数据采集装置

图6 实测与计算流固动态温度响应

图7 数值结果与实验结果对比

图8 LV泡沫与文献模型的传热性能对比

图9 不同入口流速下的速度分布（dc=4mm、ds/dc=0.34）

图10 不同相对肋筋直径下的速度分布（dc=4mm、u0=0.5m/s）

图11 不同入口流速下的温度分布（dc=4mm、ds/dc=0.34）

图12 不同相对肋筋直径下的温度分布（dc=4mm、u0=0.5m/s）

图13 孔隙参数分析

图14 表观参数分析

表3 对流换热关联式及评价

尺度	结构参数	表达式	拟合评价
尺度	结构参数	表达式	R²	平均绝对百分比误差（MAPE）/%
孔隙（元胞）	$d c, d s / d c$	$N u s f, c = 2.2 d s d c 2 - 2.7 d s d c + 1.2 R e c 0.562 P r 0.33$	0.981	7.9
孔隙（元胞）	$d c, d s / d c$	$N u v, c = - 8.3 d s d c 2 + 4.8 d s d c + 0.4 R e c 0.613 P r 0.33$	0.974	11.6
表观（骨架）	$d h, ϕ$	$N u s f, h = (16.2 ϕ 2 - 20.4 ϕ + 7.0) R e h 0.510 P r 0.33$	0.987	14.3
表观（骨架）	$d h, ϕ$	$N u v, h = (74.0 ϕ 2 - 93.2 ϕ + 30.7) R e h 0.504 P r 0.33$	0.988	17.7

表3 对流换热关联式及评价

尺度	结构参数	表达式	拟合评价
尺度	结构参数	表达式	R²	平均绝对百分比误差（MAPE）/%
孔隙（元胞）	$d c, d s / d c$	$N u s f, c = 2.2 d s d c 2 - 2.7 d s d c + 1.2 R e c 0.562 P r 0.33$	0.981	7.9
孔隙（元胞）	$d c, d s / d c$	$N u v, c = - 8.3 d s d c 2 + 4.8 d s d c + 0.4 R e c 0.613 P r 0.33$	0.974	11.6
表观（骨架）	$d h, ϕ$	$N u s f, h = (16.2 ϕ 2 - 20.4 ϕ + 7.0) R e h 0.510 P r 0.33$	0.987	14.3
表观（骨架）	$d h, ϕ$	$N u v, h = (74.0 ϕ 2 - 93.2 ϕ + 30.7) R e h 0.504 P r 0.33$	0.988	17.7

图15 孔隙及表观关联式误差分布特性

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孔隙尺度下Laguerre Voronoi开孔泡沫的对流传热特性

Convection heat transfer characteristics of pore-scale Laguerre Voronoi open-cell foam

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