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针对滑移区复杂气-固边界存在速度滑移现象，提出了一种基于格子Boltzmann方法的非平衡态外推与有限差分相结合的曲边界处理新格式.该格式具有可考虑实际物理边界与网格线偏移量的优势，较传统half-way DBB（diffusive bounce-back）格式更能准确反映实际边界情况，同时还可获取壁面处气体宏观量及其法向梯度等信息.采用本文所提曲边界处理格式模拟分析了滑移区气体平直/倾斜微通道Poiseuille流、微圆柱绕流和同心微圆柱面旋转Couette流问题.研究结果表明，采用曲边界处理新格式所得结果与理论值以及文献结果符合良好，适用于滑移区气体流动的复杂边界处理，且比half-way DBB格式具有更高的精度，较修正DBB格式具有更好的适应性.
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关键词:
- 曲边界 /
- 格子Boltzmann方法 /
- 滑移区 /
- 微气体流动
A new curved boundary treatment in lattice Boltzmann method is developed for micro gas flow in the slip regime. The proposed treatment is a combination of the nonequilibrium extrapolation scheme for curved boundary with no-slip velocity condition and the counter-extrapolation method for the velocity and its normal gradient on the curved boundary. Taking into consideration the effect of the offset between the physical boundary and the closest grid line, the new treatment is proved to be more accurate than the traditional half-way diffusive bounce-back (DBB) scheme. The present treatment is also more applicable than the modified DBB scheme because the specific gas-wall interaction parameters need to be determined to ensure the validation of the modified DBB scheme.The proposed boundary treatment is implemented to simulate the benchmark problems, which include a Poiseuille flow in the aligned/inclined micro-channel, a flow past a microcylinder and a microcylindrical Couette flow. The results and conclusions are summarized as follows.1) The force-driven Poiseuille flow in an aligned microchannel is simulated separately with different values of wall-grid offset qδx (q=0.25, 0.5, 0.75, 1.0). With the consideration of the wall-grid offset, the numerical results with the new boundary treatment show good agreement with the analytical solutions. However, the results obtained by using the half-way DBB scheme only accord well with the analytical solutions under the condition of a fixed wall-grid offset (q=0.5).2) To demonstrate the capability of the present treatment in dealing with gas flow in a more complex geometry, the force-driven Poiseuille flow in a micro-channel is investigated separately with different inclined angles. The present numerical results fit well with the analytical solutions. However, the discrepancy between the results obtained with the half-way DBB scheme and the analytical solutions can be clearly observed near the inclined boundaries.3) The gas flow past a microcylinder is simulated to prove that the present treatment can deal with the curved boundary. The slip velocity profile along the micro cylinder periphery obtained with the present treatment accords well with the available data in the published literature. However, the results obtained with the half-way DBB scheme show lower values than the results from the published work.4) In the simulations of the microcylindrical Couette flow between two coaxial rotating cylinders for different Knudsen numbers the results obtained by using the present treatment show excellent agreement with the analytical solutions. However, the results obtained with the half-way DBB scheme and the modified DBB scheme deviate obviously from the analytical solutions near the inner and outer cylindrical walls, respectively.In summary, the new boundary treatment proposed in this work is capable of dealing with the complex gas-solid boundary in the slip regime. The new treatment has a higher accuracy than the half-way DBB scheme and shows a better applicability than the modified DBB scheme.-
Keywords:
- curved boundary /
- lattice Boltzmann method /
- slip regime /
- micro gas flow
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[21] Nie D M, Lin J Z 2010 Chin. Phys. Lett. 27 104701
[22] Fang H P, Wan R Z, Fan L W 2000 Chin. Phys. 9 515
[23] Szalmas L 2007 Int. J. Mod. Phys. C 18 15
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[25] Guo Z L, Shi B C, Zheng C G 2011 Comput. Math. Appl. 61 3519
[26] Suga K 2013 Fluid Dyn. Res. 45 034501
[27] Yang W L, Li H X, Zhang T J, Elfadel I M 2015 ASME 2015 13th International Conference on Nanochannels, Microchannels, and Minichannels San Francisco, CA, USA, July 6-9, 2015 pV001T04A001
[28] Buick J M, Greated C A 2000 Phys. Rev. E 61 5307
[29] Guo Z L, Zheng C G, Shi B C 2002 Phys. Rev. E 65 046308
[30] Sun Y H, Barber R W, Emerson D R 2005 Phys. Fluids 17 047102
[31] Beskok A, Karniadakis G E 1994 J. Thermophys. Heat Tr. 8 647
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[1] Gad-el-Hak M 1999 ASME J. Fluids Eng. 121 5
[2] Ho C M, Tai Y C 1998 Annu. Rev. Fluid Mech. 30 579
[3] Zhang T T, Jia L, Wang Z C 2008 Chin. Phys. Lett. 25 180
[4] Sun X M, He F, Ding Y T 2003 Chin. Phys. Lett. 20 2199
[5] Liu C F, Ni Y S 2008 Chin. Phys. B 17 4554
[6] Tao S, Wang L, Guo Z L 2014 Acta Phys. Sin. 63 214703 (in Chinese) [陶实, 王亮, 郭照立 2014 63 214703]
[7] Wang Z, Liu Y, Zhang J Z 2016 Acta Phys. Sin. 65 014703 (in Chinese) [王佐, 刘雁, 张家忠 2016 65 014703]
[8] Guo Z L, Zheng C G, Shi B C 2002 Phys. Fluids 14 2007
[9] Mei R W, Luo L S, Shyy W 1999 J. Comput. Phys. 155 307
[10] Ladd A J C 1994 J. Fluid Mech. 271 285
[11] Noble D R, Torczynski J R 1998 Int. J. Mod. Phys. C 9 1189
[12] Yu Z, Yang H, Fan L S 2011 Chem. Eng. Sci. 66 3441
[13] Lee C H, Huang Z H, Chiew Y M 2015 Eng. Appl. Comp. Fluid 9 370
[14] Guo K K, Li L K, Xiao G, AuYeung N A, Mei R W 2015 Int. J. Heat Mass Tran. 88 306
[15] Yin X W, Zhang J F 2012 J. Comput. Phys. 231 4295
[16] Shi D Y, Wang Z K, Zhang A M 2014 Acta Phys. Sin. 63 074703 (in Chinese) [史冬岩, 王志凯, 张阿漫 2014 63 074703]
[17] Le G G, Oulaid O, Zhang J F 2015 Phys. Rev. E 91 033306
[18] Fu S C, Leung W W F, So R M C 2013 Commun. Comput. Phys. 14 126
[19] Gao D Y, Chen Z Q, Chen L H, Zhang D L 2017 Int. J. Heat Mass Tran. 105 673
[20] Izham M, Fukui T, Morinishi K 2011 J. Fluid Sci. Tech. 6 812
[21] Nie D M, Lin J Z 2010 Chin. Phys. Lett. 27 104701
[22] Fang H P, Wan R Z, Fan L W 2000 Chin. Phys. 9 515
[23] Szalmas L 2007 Int. J. Mod. Phys. C 18 15
[24] Tao S, Guo Z L 2015 Phys. Rev. E 91 043305
[25] Guo Z L, Shi B C, Zheng C G 2011 Comput. Math. Appl. 61 3519
[26] Suga K 2013 Fluid Dyn. Res. 45 034501
[27] Yang W L, Li H X, Zhang T J, Elfadel I M 2015 ASME 2015 13th International Conference on Nanochannels, Microchannels, and Minichannels San Francisco, CA, USA, July 6-9, 2015 pV001T04A001
[28] Buick J M, Greated C A 2000 Phys. Rev. E 61 5307
[29] Guo Z L, Zheng C G, Shi B C 2002 Phys. Rev. E 65 046308
[30] Sun Y H, Barber R W, Emerson D R 2005 Phys. Fluids 17 047102
[31] Beskok A, Karniadakis G E 1994 J. Thermophys. Heat Tr. 8 647
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