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采用计算流体动力学的方法, 研究了微通道内气体在速度滑移和随机表面粗糙度耦合作用下的流动特性. 其中, 利用二阶速度滑移边界条件描述气体的边界滑移, 利用分形几何学建立随机粗糙表面. 研究发现, 综合考虑二阶速度滑移边界条件和随机表面粗糙度在较大的平均Knudsen数范围内 (0.025-0.59) 得到的计算结果与实验数据符合得很好, 而一阶速度滑移边界条件只在平均Knudsen数较小时(<0.1)符合实验结果. 随机表面粗糙度对气体在边界处的滑移有显著影响, 相对粗糙度越大, 速度滑移系数越小. 并针对计算结果, 给出了滑移系数与相对粗糙度近似满足的关系. 随机粗糙表面对气体流动过程中的压强、速度、Poiseuille数也有显著影响.
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关键词:
- 随机表面粗糙度 /
- 二阶速度滑移边界条件 /
- 分形 /
- 微通道
We have investigated the characteristics of gas flow in microchannels under the coupled effects of random surface roughness and velocity slip by the method of computational fluid dynamics. The random surface roughness is modeled by fractal geometry, and the velocity slip on boundary is described by second-order slip law. Results show that the simulated curves obtained by considering both second-order slip law and random surface roughness are in good agreement with experimental data in a range of averaged Knudsen number from 0.025 to 0.59, while the one gained by using Maxwell slip law are in agreement with experimental data in a range of averaged Knudsen number extending up to 0.1. Random surface roughness has an obvious effect on velocity slip: as relative surface roughness increases, velocity slip coefficients decrease. An approximate relation between relative surface roughness and velocity slip coefficients is given according to the results. Last but not least, random surface roughness has a significant effect on the pressure, velocity and Poiseuille number.-
Keywords:
- random surface roughness /
- second-order slip law /
- fractal /
- microchannel
[1] Barber R W, Emerson D R 2006 Heat. Transfer. Eng. 27 3
[2] Tang G H, Zhang Y H, Emerson D R 2008 Phys. Rev. E 77 046701
[3] Cao B Y, Chen M, Guo Z Y 2006 Inter. J. Eng. Sci. 44 927
[4] Zhang C B, Chen Y P, Deng Z L, Shi M H 2012 Phys. Rev. E 86 016319
[5] Khadem M H, Shams M, Hossainpour S 2009 Int. Commun. Heat. Mass. Transf. 26 69
[6] Lilly T C, Duncan J A, Nothnagel S L, Gimelshein S F, Gimelshein N E, Ketsdever A D, Wysong I J 2007 Phys. Fluid. 19 106101
[7] Zhang C B, Chen Y P, Shi M H, Fu P P, Wu J F 2009 Acta Phys. Sin. 58 7050 (in Chinese) [张程宾, 陈永平, 施明恒, 付盼盼, 吴嘉峰 2009 58 7050]
[8] Hao P F, Yao Z H, He F 2007 Acta Phys. Sin. 56 4728 (in Chinese) [郝鹏飞, 姚朝晖, 何枫 2007 56 4728]
[9] Liu C F, Ni Y S 2008 Chin. Phys. B 17 4554
[10] Zhang W M, Meng G, Wei X Y 2012 Microfluid. Nanofluid. 13 845
[11] Maurer J, Tabeling P, Joseph P, Willaime H 2003 Phys. Fluid. 15 2613
[12] Mandelbrot B B 1983 The Fractal Geometry of Nature (New York: Freeman)
[13] Majumdar A, Tien C L 1990 Wear 136 313
[14] Maxwell J C 1879 Phil. Trans. Roy. Soc. 170 231
[15] Yan J, Kun Y, Chung J N 2006 Int. J. Heat Mass Transf. 49 1329
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[1] Barber R W, Emerson D R 2006 Heat. Transfer. Eng. 27 3
[2] Tang G H, Zhang Y H, Emerson D R 2008 Phys. Rev. E 77 046701
[3] Cao B Y, Chen M, Guo Z Y 2006 Inter. J. Eng. Sci. 44 927
[4] Zhang C B, Chen Y P, Deng Z L, Shi M H 2012 Phys. Rev. E 86 016319
[5] Khadem M H, Shams M, Hossainpour S 2009 Int. Commun. Heat. Mass. Transf. 26 69
[6] Lilly T C, Duncan J A, Nothnagel S L, Gimelshein S F, Gimelshein N E, Ketsdever A D, Wysong I J 2007 Phys. Fluid. 19 106101
[7] Zhang C B, Chen Y P, Shi M H, Fu P P, Wu J F 2009 Acta Phys. Sin. 58 7050 (in Chinese) [张程宾, 陈永平, 施明恒, 付盼盼, 吴嘉峰 2009 58 7050]
[8] Hao P F, Yao Z H, He F 2007 Acta Phys. Sin. 56 4728 (in Chinese) [郝鹏飞, 姚朝晖, 何枫 2007 56 4728]
[9] Liu C F, Ni Y S 2008 Chin. Phys. B 17 4554
[10] Zhang W M, Meng G, Wei X Y 2012 Microfluid. Nanofluid. 13 845
[11] Maurer J, Tabeling P, Joseph P, Willaime H 2003 Phys. Fluid. 15 2613
[12] Mandelbrot B B 1983 The Fractal Geometry of Nature (New York: Freeman)
[13] Majumdar A, Tien C L 1990 Wear 136 313
[14] Maxwell J C 1879 Phil. Trans. Roy. Soc. 170 231
[15] Yan J, Kun Y, Chung J N 2006 Int. J. Heat Mass Transf. 49 1329
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