Laguerre-Voronoi开孔泡沫流动-传热综合性能孔隙尺度模拟

doi:10.11949/0438-1157.20241502

摘要/Abstract

摘要：

为提高泡沫多孔介质的流动-传热综合性能，基于Laguerre-Voronoi镶嵌（LVT）算法，建立了具有人工可控孔隙结构的LV开孔泡沫模型。采用经实验验证的孔隙尺度方法，对比分析了边界无封闭骨架（O-LV）和边界有封闭骨架（E-LV）两类LV泡沫的流动、传热及综合性能，并提炼了压降和传热的关联式。结果表明，当径、轴向元胞数大于等于5层时，数值结果满足元胞独立性要求；相比传统陶瓷及L-K泡沫，LV泡沫具有更好的综合性能；在表观流速为0.1~5.0 m/s时，增设封闭骨架能够有效改善壁面效应，且综合性能最大可提升6.0%~9.3%；两类LV泡沫关联式均具有良好的预测精度（R²≥0.98，MAPE≤27%），其孔隙率和Reynolds数的适用范围分别为0.529<ϕ<0.967，14<Re_h<3835和0.614<ϕ<0.970，15<Re_h<4487。在此基础上推导出了LV泡沫综合性能表达式，由孔隙率和Reynolds数即可预测其综合性能，为高效吸热器及反应器的进一步设计提供了参考。

关键词: 多孔介质, 孔隙尺度模拟, 性能优化, 流动, 传热

Abstract:

In order to improve the flow-heat transfer comprehensive performance of foam porous media, an LV open-cell foam model with artificial controllable pore structure was established based on the Laguerre-Voronoi tessellation (LVT) algorithm. This design effectively mitigates the flow penetration phenomenon and enables quantitative control of closed pores, thereby achieving superior overall flow and heat transfer performance. Based on this, two LV open-cell foam models were designed, fabricated, and studied: one with open boundaries (O-LV) and the other with closed boundaries (E-LV). The thermal performance of these models was investigated using experimentally validated pore-scale methods. Extensive numerical simulations were conducted to derive correlations between heat transfer and pressure drop, and a comprehensive performance expression was formulated. When the radial and axial cell layers are greater than or equal to five, the numerical results meet the cell independence requirement. The results show that the E-LV foam performs better at higher porosities (ϕ≥75%), while the O-LV foam performs better at lower porosities (ϕ<75%). The fitting correlations for heat transfer and pressure drop for both LV foams demonstrate high predictive accuracy (R²≥0.98, MAPE≤27%). Specifically, the correlation for E-LV foam is applicable for porosities ranging from 0.529 to 0.967 and Reynolds numbers between 14 and 3835, while the correlation for O-LV foam is applicable for porosities ranging from 0.614 to 0.970 and Reynolds numbers between 15 and 4487. On this basis, a comprehensive performance expression for LV foams was derived, enabling the prediction of their comprehensive performance from porosity and Reynolds numbers. This facilitates the further design of efficient heat exchangers and reactors.

Key words: porous media, pore-scale simulation, performance optimization, flow, heat transfer

中图分类号:

TK 124

王孝宇, 戴贵龙, 邓树坤, 龚凌诸. Laguerre-Voronoi开孔泡沫流动-传热综合性能孔隙尺度模拟[J]. 化工学报, 2025, 76(7): 3259-3273.

Xiaoyu WANG, Guilong DAI, Shukun DENG, Lingzhu GONG. Pore-scale simulation of heat transfer and pressure drop performance in Laguerre-Voronoi open-cell foams[J]. CIESC Journal, 2025, 76(7): 3259-3273.

图/表 21

图1 LV泡沫建模流程

Fig.1 Modeling flowchart of the LV foams

表1 LV泡沫结构参数

Table 1 Structural parameters of the LV foams

d_c/m	d_s/d_c	ϕ_O-LV	ϕ_E-LV	a_{sf, O-LV}/m^-1	a_{sf, E-LV}/m^-1	d_{h, O-LV}/m	d_{h, E-LV}/m
0.003	0.10	0.970	0.967	365.1	399.4	0.0106	0.0097
	0.25	0.843	0.833	710.4	796.5	0.0047	0.0042
	0.30	0.802	0.782	784.3	890.2	0.0041	0.0035
	0.36	0.736	0.704	842.1	955.4	0.0035	0.0029
	0.45	0.616	0.581	903.0	1031.1	0.0027	0.0023
0.004	0.10	0.969	0.967	302.3	333.2	0.0128	0.0116
	0.25	0.839	0.808	597.1	649.2	0.0056	0.0050
	0.30	0.797	0.755	670.9	727.9	0.0048	0.0042
	0.36	0.732	0.671	715.6	781.1	0.0041	0.0034
	0.45	0.614	0.538	762.0	841.3	0.0032	0.0026
0.005	0.10	0.968	0.965	246.3	274.7	0.0157	0.0141
	0.25	0.838	0.807	475.1	521.3	0.0071	0.0062
	0.30	0.793	0.754	524.5	588.1	0.0060	0.0051
	0.36	0.731	0.664	566.9	635.6	0.0052	0.0042
	0.45	0.617	0.529	600.0	675.1	0.0041	0.0031

图2 边界条件与模型尺寸

Fig.2 Boundary conditions and model dimensions

图3 模型验证

Fig.3 Model validation

图4 LV泡沫结构参数对比

Fig.4 Comparison of structural parameters between O-LV and E-LV foams

表2 实验样品的几何参数

Table 2 Geometric parameters of experimental samples

样品类型	D/mm	L/mm	ϕ	d_s/d_c	d_c/mm
E-LV	25	40	0.629	0.41	4.0
O-LV	25	40	0.566	0.41	4.0

图5 测压实验平台

Fig.5 Experimental apparatus for pressure drop measurement

图6 模型可靠性验证（dc=4 mm，ds/dc=0.41）

Fig.6 Validation of computational model reliability (dc=4 mm, ds/dc=0.41)

图7 纵截面流速矢量图（dc=4 mm，ds/dc=0.30，U=2.0 m/s)

Fig.7 Velocity vector diagrams within longitudinal section (dc=4 mm, ds/dc=0.30, U=2.0 m/s)

图8 流速云图（dc=4 mm，ds/dc=0.30，U=2.0 m/s)

Fig.8 Velocity contour maps of cross and longitudinal sections (dc=4 mm, ds/dc=0.30, U=2.0 m/s)

图9 平均流速及孔隙率分布（dc=4 mm，ds/dc=0.30，U=2.0 m/s）

Fig.9 Distribution of average velocity and porosity in O-LV and E-LV foams (dc=4 mm, ds/dc=0.30, U=2.0 m/s)

图10 静压云图（dc=4 mm，ds/dc=0.30，U=2.0 m/s）

Fig.10 Static pressure contour maps of cross and longitudinal sections (dc=4 mm, ds/dc=0.30, U=2.0 m/s)

图11 平均静压分布（dc=4 mm，ds/dc=0.30，U=2.0 m/s）

Fig.11 Distribution of average static pressure in O-LV and E-LV foams (dc=4 mm, ds/dc=0.30, U=2.0 m/s)

图12 温度云图（dc=4 mm，ds/dc=0.30，U=2.0 m/s）

Fig.12 Temperature contour maps of cross and longitudinal sections (dc=4 mm, ds/dc=0.30, U=2.0 m/s)

图13 平均温度分布（dc=4 mm，ds/dc=0.30，U=2.0 m/s）

Fig.13 Distribution of average temperature in O-LV and E-LV foams (dc=4 mm, ds/dc=0.30, U=2.0 m/s)

图14 典型泡沫模型流动和传热性能对比

Fig.14 Comparison of flow and heat transfer performance in typical foam models

图15 Colburn因子变化特性曲线

Fig.15 Characteristic curves of the Colburn factor varying with apparent velocity

图16 阻力系数变化特性曲线

Fig.16 Characteristic curves of the friction coefficient varying with apparent velocity

图17 综合性能j/f变化特性曲线

Fig.17 Characteristic curves of the comprehensive performance varying with apparent velocity

表3 传热和压降经验关联式及评价指标

Table 3 Empirical correlations and evaluation indicators of the heat transfer and pressure drop

模型	经验关联式	评价指标
模型	经验关联式	R²	MAPE
E-LV	$N u v = 11.3 ϕ 2.95 R e h 0.496 P r 0.33$	0.99	20.6%
E-LV	$Δ p L = 320 μ f U ϕ d h 2 + 0.81 ρ f U 2 ϕ 2 d h$	0.98	26.5%
O-LV	$N u v = 13.9 ϕ 4.74 R e h 0.480 P r 0.33$	0.99	20.4%
O-LV	$Δ p L = 362 μ f U ϕ d h 2 + 0.79 ρ f U 2 ϕ 2 d h$	0.98	27.0%

表3 传热和压降经验关联式及评价指标

Table 3 Empirical correlations and evaluation indicators of the heat transfer and pressure drop

模型	经验关联式	评价指标
模型	经验关联式	R²	MAPE
E-LV	$N u v = 11.3 ϕ 2.95 R e h 0.496 P r 0.33$	0.99	20.6%
E-LV	$Δ p L = 320 μ f U ϕ d h 2 + 0.81 ρ f U 2 ϕ 2 d h$	0.98	26.5%
O-LV	$N u v = 13.9 ϕ 4.74 R e h 0.480 P r 0.33$	0.99	20.4%
O-LV	$Δ p L = 362 μ f U ϕ d h 2 + 0.79 ρ f U 2 ϕ 2 d h$	0.98	27.0%

图18 拟合关联式误差分析

Fig.18 Error analysis of fitting correlations

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