Study on the Scale Characteristics of Permeability of TPMS Porous Materials

doi:10.16182/j.issn1004731x.joss.20-0966

Abstract

Abstract:

Triply Periodic Minimal Surface (TPMS) has been widely used in the design of porous materials, however, there is insufficient research on the scale characteristics of permeability. Four commonly used TPMS units are chosen as the research object, based on the introduction of their mathematical models and porosity control methods, a numerical simulation model based on CFD (computational fluid dynamics) is established; TPMS units and cubic porous structures with different porosities are analyzed, the quantitative correlation between their scales and permeability is clarified, i.e., within the selected scale range, the permeability of various TPMS units and cubic porous structures is the quadratic function of scaled. For the design of the permeability of TPMS porous materials, the research results can provide simulation method to support the selection of TPMS unit type and size.

Key words: TPMS, permeability, scale characteristics, computational fluid dynamics, porous material

CLC Number:

TP391.9

Tong Wu, Qinghui Wang, Zhijia Xu. Study on the Scale Characteristics of Permeability of TPMS Porous Materials[J]. Journal of System Simulation, 2022, 34(5): 1015-1024.

Figures/Tables 23

Table 1

Simplified implicit expressions for common TPMS

TPMS	简化隐式表达式
P	$φ (r) = cos (X) + cos (Y) + cos (Z) = C$
G	$φ (r) = sin (X) cos (Y) + ? ? ? ? ? sin (Y) cos (Z) + sin (Z) cos (X) = C$
F-RD	$φ (r) = cos (X) cos (Y) cos (Z) + ? ? ? ? ? ? ? ? ? cos (2 X) cos (2 Y) cos (2 Z) ? ???? ? ? ? ? ? ? cos (2 X) cos (2 Y) ? cos (2 Y) cos (2 Z) ? ? ? ? ? ? ? ? ? ? ? cos (2 Z) cos (2 X) = C$
I-WP	$φ (r) = 2 [cos (X) cos (Y) + ? ? ? ? ? cos (Y) cos (Z) + cos (Z) cos (X)] ? ? ? ? ? ? [cos (2 X) + cos (2 Y) + cos (2 Z)] = C$

Table 1

Fig. 1

Fig. 2

Table 2

TPMS unit porosity and threshold fitting formula

TPMS	拟合公式
P	$P = 28.731 C + 49.997$
G	$P = 32.811 C +49 .969$
F-RD	$P = 13.300 C + 53.100$
I-WP	$P = 10.914 C +34 .689$

Table 2

Table 3

Threshold value ranges and corresponding porosity ranges of four TPMS units

TPMS	阈值范围	对应孔隙率范围
P	$[? 0.7, 0.9]$	$[29.885, 75.855]$
G	$[? 0.7, 0.8]$	$[27.001, 76.218]$
F-RD	$[? 1.0, 1.7]$	$[39.800, 75.710]$
I-WP	$[? 0.9, 1.0]$	$[24.866, 45.603]$

Table 3

Fig. 3

Table 4

TPMS model basic scale parameter range table

模型种类	单元数量N	特征尺度?L_c/mm	?出口与入口间距?L/mm
P单元	1	$L 0$	$L 0$
立方多孔结构	1~5	$N ? L 0$	$N ? L 0$

Table 4

Fig. 4

Fig. 5

Table 5

Mesh independence analysis results

网格数量	入口到出口之间的压降 $Δ P$ /Pa
??211 944	0.439 2
1 063 476	0.491 4
1 879 838	0.496 5

Table 5

Fig. 6

Table 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Table 7

Relationship between TPMS cell permeability and scale

TPMS	孔隙率/%	拟合表达式
P	50	$K = 10.066 L 2 + 0.207 L ? 0.409$
G	50	$K = 1.691 L 2 + 0.064 L ? 0.126$
F-RD	50	$K = 0.823 L 2 + 0.003 L ? 0.006$
I-WP	45	$K = 2.407 L 2 + 0.092 L ? 0.181$

Table 7

Fig. 12

Fig. 13

Fig. 14

Fig. 15

Fig. 16

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尺度/mm	入口速度/(mm/s)	计算雷诺数
1	5.000	5
5	1.000	5
10	0.500	5
15	0.300	4.5
20	0.250	5
30	0.140	4.2
40	0.100	4