Numerical Investigation of Effective Thermal Conductivity of Strut-Based Cellular Structures Designed by Spatial Voronoi Tessellation
Abstract
:1. Introduction
2. Materials and Methods
2.1. Design of Cellular Structures
2.2. Heat Transfer Finite Element Modeling
2.3. Mesh Independence Tests
3. Results
3.1. Effects of Filling Material on the Effective Thermal Conductivity
3.2. Effect of the Number of Seed Points on the Effective Thermal Conductivity
3.3. Effect of Porosity and Orientation on the Effective Thermal Conductivity
3.4. Temperature Distribution
4. Discussion
5. Conclusions
- (1)
- As the porosity decreases, the effective thermal conductivity of the strut-based cellular structures increases. When it is within the high porosity range (>90%) and under the air-saturated environment, the effective thermal conductivity of the structure is more than 10% higher than that under the vacuum environment. At this time, we cannot neglect the contribution of air for heat conduction.
- (2)
- Consider the influence of structural direction on effective thermal conductivity for the random Voronoi structure, when the number of seed points was set as 50 and 70, the difference between the effective thermal conductivity of the various structures is not obvious (<5%), the number of seed points of the structure has no obvious relationship with the effective thermal conductivity when the number of seed points are greater than or equal to 50.
- (3)
- The thermal performance will be affected by the microstructure and orientation of the structure. Because of the heat conduction has different heat transfer paths in different structures and orientations, resulting in slight differences in the effective thermal conductivity. Referring to the RV50 and RV70 structures in an air-saturated environment, within the porosity range studied in this paper, the largest differences in their effective thermal conductivities in different orientations are 3.89% and 2.22%, respectively, showing good isotropic performance, and this performance is proportional to the number of seed points. The RV10 and RV30 structures show anisotropic effective thermal conductivity performance. Therefore, at least 50 seed points are needed to design a random Voronoi structure with isotropic properties. On the other hand, the effective thermal conductivities of KT and KH are more sensitive to the orientation, because the differences in effective thermal conductivities in different orientations are more obvious. The largest differences are 26.67% and 5.66%, respectively. The effective thermal conductivities of the KH and KT structures in the OZ and OY orientations are lower than that of the other five structures in the corresponding orientations.
- (4)
- The porosity has no obvious effect on the temperature distribution. The temperature distribution trends are basically the same for the different structure types. The temperature value decreases from the top surface to the bottom surface in an approximately linear manner. However, in some inconsecutive areas on the KH structure, the temperature values are equal without any temperature gradient.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Structures | PPI | Porosity [%] | Strut Radius [mm] | Volume of the Cellular Structures [mm3] | Surface Area [mm2] |
---|---|---|---|---|---|
RV2 structure | 1.07 | 95.00 | 1.79 | 1351.38 | 2958.81 |
92.02 | 2.31 | 2154.97 | 3624.45 | ||
88.97 | 2.77 | 2977.3 | 4140.52 | ||
85.99 | 3.18 | 3781.43 | 4544.65 | ||
82.97 | 3.57 | 4596.8 | 4886.34 | ||
RV10 structure | 1.82 | 95.05 | 0.93 | 1335.26 | 4063.27 |
92.03 | 1.20 | 2151.78 | 5021.67 | ||
89.01 | 1.43 | 2966.35 | 5747.91 | ||
85.95 | 1.64 | 3793.11 | 6352.50 | ||
82.96 | 1.83 | 4601.27 | 6848.86 | ||
RV30 structure | 2.63 | 94.99 | 0.62 | 1352.08 | 5356.45 |
91.97 | 0.80 | 2169.25 | 6574.01 | ||
89.02 | 0.95 | 2963.36 | 7474.76 | ||
85.98 | 1.09 | 3785.41 | 8234.37 | ||
82.93 | 1.22 | 4609.5 | 8868.72 | ||
RV50 structure | 3.12 | 94.98 | 0.51 | 1355.63 | 6180.35 |
91.97 | 0.66 | 2167.57 | 7558.77 | ||
88.89 | 0.79 | 2999.46 | 8629.87 | ||
86.00 | 0.90 | 3779.25 | 9443.53 | ||
82.89 | 1.01 | 4619.81 | 10,173.77 | ||
RV70 structure | 3.49 | 95.08 | 0.45 | 1329.73 | 6738.12 |
92.12 | 0.58 | 2128.07 | 8247.22 | ||
88.92 | 0.70 | 2992.49 | 9466.01 | ||
85.95 | 0.80 | 3792.67 | 10,363.64 | ||
83.09 | 0.89 | 4566.31 | 11,083.66 | ||
KT structure | - | 94.87 | 0.41 | 1387.01 | 6678.86 |
92.03 | 0.53 | 2237.68 | 8251.04 | ||
88.96 | 0.62 | 2981.27 | 9319.81 | ||
85.91 | 0.71 | 3805.43 | 10,294.41 | ||
83.01 | 0.79 | 4587.59 | 10,984.59 | ||
KH structure | - | 95.01 | 0.41 | 1346.38 | 6363.98 |
91.94 | 0.53 | 2177.02 | 7872.74 | ||
88.92 | 0.63 | 2990.45 | 9005.40 | ||
85.90 | 0.72 | 3805.52 | 9930.22 | ||
83.01 | 0.80 | 4585.99 | 10,676.37 |
Temperature [K] | 273.15 | 293.15 | 313.15 | 333.15 | 353.15 | 373.15 | 393.15 |
---|---|---|---|---|---|---|---|
k [W m−1 K−1] | 7.040 | 7.076 | 7.147 | 7.285 | 7.441 | 7.613 | 7.800 |
Cp [J kg−1 K−1] | 525.117 | 536.041 | 545.973 | 553.497 | 560.723 | 567.660 | 574.316 |
ρ [kg m−3] | 4432.103 | 4429.989 | 4428.525 | 4425.977 | 4423.419 | 4420.850 | 4418.271 |
Structures | PPI |
Porosity [%] | Simulation Data of keff [W m−1 K−1] in Vacuum | Simulation Data of keff [W m−1 K−1] in Air-Saturated | ||||
---|---|---|---|---|---|---|---|---|
OX | OY | OZ | OX | OY | OZ | |||
RV2 structure | 1.07 | 95.00 | 0.144 | 0.141 | 0.143 | 0.175 | 0.171 | 0.174 |
92.02 | 0.240 | 0.238 | 0.241 | 0.271 | 0.269 | 0.268 | ||
88.97 | 0.345 | 0.346 | 0.348 | 0.377 | 0.378 | 0.379 | ||
85.99 | 0.454 | 0.461 | 0.459 | 0.485 | 0.493 | 0.491 | ||
82.97 | 0.569 | 0.586 | 0.579 | 0.600 | 0.618 | 0.611 | ||
RV10 structure | 1.82 | 95.05 | 0.131 | 0.145 | 0.133 | 0.162 | 0.175 | 0.164 |
92.03 | 0.223 | 0.245 | 0.229 | 0.254 | 0.276 | 0.260 | ||
89.01 | 0.321 | 0.352 | 0.333 | 0.354 | 0.383 | 0.365 | ||
85.95 | 0.428 | 0.467 | 0.447 | 0.461 | 0.498 | 0.479 | ||
82.96 | 0.540 | 0.585 | 0.566 | 0.574 | 0.617 | 0.599 | ||
RV30 structure | 2.63 | 94.99 | 0.132 | 0.147 | 0.138 | 0.163 | 0.178 | 0.168 |
91.97 | 0.224 | 0.248 | 0.232 | 0.256 | 0.279 | 0.263 | ||
89.02 | 0.320 | 0.354 | 0.330 | 0.353 | 0.386 | 0.362 | ||
85.98 | 0.426 | 0.470 | 0.438 | 0.459 | 0.503 | 0.470 | ||
82.93 | 0.539 | 0.594 | 0.553 | 0.573 | 0.626 | 0.586 | ||
RV50 structure | 3.12 | 94.98 | 0.138 | 0.136 | 0.135 | 0.169 | 0.167 | 0.166 |
91.97 | 0.236 | 0.233 | 0.23 | 0.268 | 0.265 | 0.262 | ||
88.89 | 0.342 | 0.338 | 0.333 | 0.374 | 0.370 | 0.365 | ||
86.00 | 0.448 | 0.442 | 0.434 | 0.481 | 0.475 | 0.467 | ||
82.89 | 0.570 | 0.562 | 0.551 | 0.603 | 0.595 | 0.585 | ||
RV70 structure | 3.49 | 95.08 | 0.138 | 0.135 | 0.135 | 0.168 | 0.166 | 0.166 |
92.12 | 0.232 | 0.228 | 0.228 | 0.263 | 0.260 | 0.259 | ||
88.92 | 0.343 | 0.336 | 0.336 | 0.375 | 0.368 | 0.368 | ||
85.95 | 0.453 | 0.443 | 0.444 | 0.485 | 0.475 | 0.476 | ||
83.09 | 0.565 | 0.552 | 0.554 | 0.598 | 0.585 | 0.587 | ||
KT structure | - | 94.87 | - | 0.121 | 0.158 | - | 0.150 | 0.19 |
92.03 | - | 0.209 | 0.27 | - | 0.241 | 0.301 | ||
88.96 | - | 0.294 | 0.375 | - | 0.327 | 0.406 | ||
85.91 | - | 0.396 | 0.498 | - | 0.429 | 0.53 | ||
83.01 | - | 0.502 | 0.623 | - | 0.535 | 0.655 | ||
KH structure | - | 95.01 | - | 0.136 | 0.127 | - | 0.168 | 0.159 |
91.94 | - | 0.233 | 0.22 | - | 0.265 | 0.252 | ||
88.92 | - | 0.335 | 0.318 | - | 0.368 | 0.352 | ||
85.90 | - | 0.446 | 0.424 | - | 0.480 | 0.460 | ||
83.01 | - | 0.560 | 0.54 | - | 0.593 | 0.574 |
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Zhang, M.; Shang, J.; Guo, S.; Hur, B.; Yue, X. Numerical Investigation of Effective Thermal Conductivity of Strut-Based Cellular Structures Designed by Spatial Voronoi Tessellation. Materials 2021, 14, 138. https://doi.org/10.3390/ma14010138
Zhang M, Shang J, Guo S, Hur B, Yue X. Numerical Investigation of Effective Thermal Conductivity of Strut-Based Cellular Structures Designed by Spatial Voronoi Tessellation. Materials. 2021; 14(1):138. https://doi.org/10.3390/ma14010138
Chicago/Turabian StyleZhang, Minghao, Junteng Shang, Shiyue Guo, Boyoung Hur, and Xuezheng Yue. 2021. "Numerical Investigation of Effective Thermal Conductivity of Strut-Based Cellular Structures Designed by Spatial Voronoi Tessellation" Materials 14, no. 1: 138. https://doi.org/10.3390/ma14010138