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Porous media are extensively used in the engineering field. The effective thermal conductivity and porosity are very important properties of porous medium materials. It is of great significance to obtain a porous medium material that meets the needs of effective thermal conductivity and porosity. In this paper, a four-parameter random generation method is used to produce a training data set, a conditional generation adversarial network (CGAN) is built, and a predetermined effective thermal conductivity and porosity are used as inputs to generate a porous medium structure that meets the input conditions. In particular, since the pore structure distribution of porous medium has a great influence on the effective thermal conductivity of the material, a local structure loss function is proposed to participate in the network training, so that the network can better learn the relationship between the pore distribution and the thermal conductivity. By using the lattice Boltzmann method to verify the effective thermal conductivity of the porous medium structure generated by the neural network, the results show that the method can quickly and accurately generate the porous medium structure with predetermined parameters.
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Keywords:
- porous media /
- structure generation /
- conditional generation adversarial network /
- effective thermal conductivity
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图 1 不同孔隙分布多孔介质示意图 (a) K1 = 5.52; (b) K2 = 6.37; (c) K2 = 7.32
Figure 1. Schematic diagram of porous media with different pore distributions: (a) K1 = 5.52; (b) K2 = 6.37; (c) K2 = 7.32
图 2 局部结构差异 (a) K1 = 6.0; (b) K2 = 6.4
Figure 2. Local structural differences: (a) K1 = 6.0; (b) K2 = 6.4
图 3 二维多孔介质各方向生成示意图
Figure 3. Schematic diagram of the generation of two-dimensional porous media in all directions.
图 4 四参数随机生成法生成二维多孔介质示例图
Figure 4. An example of two-dimensional porous media generated by the four-parameter random production method.
图 5 生成器网络结构图
Figure 5. Generator network structure diagram.
图 6 判别器网络结构图
Figure 6. Discriminator network structure diagram.
图 7 传统条件生成对抗网络生成的多孔介质
Figure 7. Porous media generated by traditional conditional generation adversarial network.
图 8 局部结构损失结构图
Figure 8. Structure diagram of local structure loss.
图 9 生成多孔介质结构示意图
Figure 9. Schematic diagram of generating porous media.
图 10 生成多孔介质有效导热率验证图
Figure 10. Generate verification chart of effective thermal conductivity of porous media.
图 11 生成多孔介质有效导热率误差图
Figure 11. Error chart of effective thermal conductivity of porous media.
图 12 生成多孔介质有效导热率验证数据集误差汇总图
Figure 12. The error summary of the validation data set for the effective thermal conductivity of porous media.
图 13 生成多孔介质孔隙对比图及误差
Figure 13. The effect diagram and error of generating pores in porous media.
表 1 LBM计算多孔介质导热率与实验值比较
Table 1. Comparison between LBM calculation of thermal conductivity of porous media and experimental values.
Along the foam growing direction Across the foam growing direction Prediction/(W·mK–1) Experiment/(W·mK–1) Deviation/% Prediction/ (W·mK–1) Experiment/(W·mK–1) Deviation/% 0.0253 0.0220 15.0 0.0265 0.0245 8.16 
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表 2 生成多孔介质导热率及孔隙率误差表
Table 2. Generated thermal conductivity and porosity error table of porous media
Porosity 0.45 0.45 0.45 0.55 0.65 Mean error Keff ratio 1∶1000 1∶800 1∶600 1∶1000 1∶1000 Keff error 0.006 0.006 0.008 0.007 0.017 0.009 Porosity error 0.049 0.031 0.039 0.029 0.038 0.037
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[1] Maguire L, Behnia M, Morrison G 2005 Microelectron. Reliab. 45 711
Google Scholar
[2] Moore A L, Shi L 2014 Mater. Today 17 163
Google Scholar
[3] Li T, Song J W, Zhao X P, Yang Z, et al. 2018 Sci. Adv. 4 3724
Google Scholar
[4] Jelle B P 2011 Proceedings of the 9 th Nordic Symposium on Building Physics Tampere, Finland, 2 9
Google Scholar
[5] Mangalgiri P D 1999 Bull. Mater. Sci. 22 657
Google Scholar
[6] 张贝豪, 郑林 2020 69 164401
Google Scholar
Zhang B H, Zheng L 2020 Acta Phys. Sin. 69 164401
Google Scholar
[7] 刘高洁, 郭照立, 施保昌 2016 65 014702
Google Scholar
Liu G J, Guo Z L, Shi B C 2016 Acta Phys. Sin. 65 014702
Google Scholar
[8] Fang W Z, Zhang H, Chen L, Tao W Q 2016 Appl. Therm. Eng. 115 1227
[9] Wang M, Pan N 2008 Int. J. Heat Mass Transfer 51 1325
Google Scholar
[10] Ren S Q, He K M, Girshick R, Sun J 2016 arXiv: 1506.01497 [cs. CV.]
[11] Hochreiter S, Schmidhuber J 1997 Neural Comput. 9 1735
Google Scholar
[12] Han W, Zhao S H, Rong Q Y, Bao H 2018 Int. J. Heat Mass Transfer. 127 908
Google Scholar
[13] Li H, Singh S, Chawla N, Jiao Y 2018 Mater. Charact. 140 265
Google Scholar
[14] Wang Y, Arns J Y, Rahman S S, Arns C H 2018 Phys. Rev. E 98 043310
Google Scholar
[15] Bostanabad R, Zhang Y, Li X, Kearney T, Brinson L C, Apley D W, Liu W K, Chen W 2018 Prog. Mater. Sci. 95 1
[16] Tahmasebi P, Javadpour F, Sahimi M 2015 Transp. Porous Media 110 521
Google Scholar
[17] Yeong C L Y, Torquato S 1998 Phys. Rev. E 57 495
Google Scholar
[18] Yeong C L Y, Torquato S 1998 Phys. Rev. E 28 224
[19] Okabe H, Blunt M J, Petrol J 2005 J. Petrol. Sci. Eng. 46 121
Google Scholar
[20] Gao M L, He X H, Teng Q Z, Zuo C 2015 Phys. Rev. E 91 013308
Google Scholar
[21] Ding K, Teng Q Z, Wang Z Y, He X H 2018 Phys. Rev. E 97 063304
Google Scholar
[22] Mariethoz G, Renard P, Straubhaar J 2010 Water Resour. Res. 4 6
[23] Tahmasebi P, Sahimi M 2012 Phys. Rev. E 85 066709
Google Scholar
[24] Tahmasebi P, Sahimi M 2013 Phys. Rev. Lett. 110 078002
Google Scholar
[25] Tahmasebi P, Sahimi M 2016 Water Resour. Res. 52 2074
Google Scholar
[26] Tahmasebi P, Sahimi M 2016 Water Resour. Res. 52 2099
Google Scholar
[27] Tahmasebi P 2017 Water Resour. Res. 53 5980
Google Scholar
[28] Feng J X, He X H, Teng Q Z, Ren C, Chen H G, Li Y 2019 Phys. Rev. E 100 033308
Google Scholar
[29] Bostanabad R, Chen W, Apley D 2016 J. Microsc. 264 282
Google Scholar
[30] Bostanabad R, Bui A T, Xie W, Apley D W, Chen W 2016 Acta Mater. 103 89
Google Scholar
[31] Feng J X, Teng Q Z, He X H, Wu X 2018 Acta Mater. 159 296
Google Scholar
[32] Chan S, Elsheikh A H 2018 arXiv: 1809.07748 v2 [stat. ML.]
[33] Chan S, Elsheikh A H 2018 arXiv: 1807.05207 v2 [stat. ML.]
[34] Mosser L, Dubrule O, Blunt M J 2017 Phys. Rev. E 96 043309
Google Scholar
[35] Mosser L, Dubrule O, Blunt M J 2018 arXiv: 1802.05622 v1 [stat. ML.]
[36] Mosser L, Dubrule O, Blunt M J 2018 Transp. Porous Media 125 81
Google Scholar
[37] Laloy E, Hrault R, Lee J, Jacques D, Linde N 2017 Adv. Water Resour. 110 387
Google Scholar
[38] Laloy E, Hrault R, Jacques D, Linde N 2018 Water Resour. Res. 54 381
Google Scholar
[39] Wang Y, Arns C H, S S Rahman, Arns J Y 2018 Math. Geosci. 50 781
Google Scholar
[40] Denis V, Ekaterina M, Oleg S, Denis O, Boris B, Vladislav K, Evgeny B, Dmitry K 2019 arXiv: 1901.10233 v3 [cs. CV.]
[41] Wang M, Pan N 2018 Int. J. Heat Mass Transfer 51 1325
[42] Wang M, Wang J K, Pan N, Chen S Y 2007 Phys. Rev. E 75 036702
Google Scholar
[43] He X, Chen S, Doolen G D 1998 J. Comput. Phys. 146 282
Google Scholar
[44] Wang L, Zhao Y, Yang X G, Shi B C, Chai Z H 2019 Appl. Math. Modell. 71 31
Google Scholar
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