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多孔介质在工程领域中的应用非常广泛, 其中有效导热率和孔隙率为多孔介质材料非常重要的性质, 得到一个符合需要的有效导热率和孔隙率的多孔介质材料具有重要意义. 本文使用四参数随机生成方法制作了训练数据集, 搭建了一个条件生成对抗网络(CGAN), 使用预定的有效导热率和孔隙率作为输入, 生成一个满足输入条件的多孔介质结构. 特别地, 由于多孔介质的孔隙结构分布对材料的有效导热率影响巨大, 提出局部结构损失函数参与网络训练, 使得网络更好地学习到孔隙分布与导热率之前的关系. 通过使用格子Boltzmann方法验证神经网络生成的多孔介质结构的有效导热率, 结果表明该方法能够快速且准确地生成预定参数的多孔介质结构.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
Fig. 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
Fig. 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
Fig. 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
Fig. 4. An example of two-dimensional porous media generated by the four-parameter random production method.
图 7 传统条件生成对抗网络生成的多孔介质
Fig. 7. Porous media generated by traditional conditional generation adversarial network.
图 10 生成多孔介质有效导热率验证图
Fig. 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
Fig. 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
Fig. 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
Fig. 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 
下载: 导出CSV
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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