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In this paper, the microscale non-equilibrium gas flow, and the oscillating Couette and Poiseuille flows, have been investigated by an effective MRT-LBM. The Knudsen layer model is introduced into lattice Boltzmann method (LBM) for the relaxation time correction. In the simulations the plate or external force oscillates in the form of sine curve, and the Couette flow contains a singular oscillation and a double-plate oscillation. It is revealed that the corrected MRT-LBM model can well handle the simulation of microscale non-equilibrium gas flow. For the Couette flow, the wall slip phenomenon is obvious for a larger Kn number, and the streamwise velocity profiles appear to be of a nonliner character when St number increases. When the two plates oscillate, the streamwise velocity profiles almost overlap with each other at small Kn and St. In the Poiseuille flow case, the extent of phase lag decreases as St exceeds a certain value. Compared to the Kn number, St has a bigger impact on the emerging of phase lag in the oscillating Couette and Poiseuille flows.
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Keywords:
- lattice Boltzmann method /
- effective MRT model /
- Knudsen layer /
- oscillating flow
[1] Stone H A, Stroock A D, Ajdari A 2004 Annu. Rev. Fluid Mech. 36 381
[2] [3] Huang Q G, Pan G, Song B W 2014 Acta Phys. Sin. 63 054701 (in Chinese) [黄桥高, 潘光, 宋保维 2014 63 054701]
[4] [5] Guo Y L, Xu H H, Shen S Q, Wei L 2013 Acta Phys. Sin. 62 144704 (in Chinese) [郭亚丽, 徐鹤函, 沈胜强, 魏兰 2013 62 144704]
[6] Harley J C, Huang Y, Bau H H, Zemel J N 1995 J. Fluid Mech. 284 257
[7] [8] Arkilic E B, Breuer K S, Schimidt M A 2001 J. Fluid Mech. 437 29
[9] [10] [11] Guo Z Y, Li Z X 2003 Int. J. Heat and Fluid Flow 24 284
[12] Turner S E, Lam L C, Faghri M, Gregory O J 2004 J. Heat Transfer 126 753
[13] [14] [15] Zhang Y H, Qin R S, Emerson D R 2005 Phys. Rev. E 71 047702
[16] Nie X B, Doolen G D, Chen S Y 2002 J. Stat. Phys. 107 279
[17] [18] [19] Succi S 2002 Phys. Rev. Lett. 89 064502
[20] Ansumali S, Karlin I V 2002 Phys. Rev. E 66 026311
[21] [22] Tang G H, Tao W Q, He Y L 2005 Phys. Fluids 17 058101
[23] [24] Guo Z L, Shi B C, Zheng C G 2007 Europhys. Lett. 80 24001
[25] [26] Guo Z L, Shi B C, Zhao T S, Zheng C G 2007 Phys. Rev. E 76 056704
[27] [28] [29] Guo Z L, Zheng C G, Shi B C 2008 Phys. Rev. E 77 036707
[30] Li Q, He Y L, Tang G H, Tao W Q 2011 Microfluid. Nanofluid. 10 607
[31] [32] [33] Zhang Y H, Gu X J, Barber R W, Emerson D R 2006 Phys. Rev. E 74 046704
[34] Kim S H, Pitsch H, Boyd I D 2008 Phys. Rev. E 77 026704
[35] [36] [37] Tang G H, Gu X J, Barber R W, Emerson D R Zhang Y H 2008 Phys. Rev. E 78 026706
[38] Lallemand P, Luo L S 2000 Phys. Rev. E 61 6546
[39] [40] [41] Qian Y H, D'Humi?res D, Lallemand P 1992 Europhys. Lett. 17 479
[42] [43] Hadjiconstantinou N G 2005 Phys. Fluids 17 100611
[44] Taheri P, Rana A S, Torrilhon M, Struchtrup H 2009 Continuum Mech. Thermodyn. 21 423
[45] [46] Verhaeghe F, Luo L S, Blanpain B 2009 J. Comput. Phys. 228 147
[47] [48] [49] Shen C, Tian D B, Xie C, Fan J 2004 Microscale Thermophys. Eng. 8 405
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[1] Stone H A, Stroock A D, Ajdari A 2004 Annu. Rev. Fluid Mech. 36 381
[2] [3] Huang Q G, Pan G, Song B W 2014 Acta Phys. Sin. 63 054701 (in Chinese) [黄桥高, 潘光, 宋保维 2014 63 054701]
[4] [5] Guo Y L, Xu H H, Shen S Q, Wei L 2013 Acta Phys. Sin. 62 144704 (in Chinese) [郭亚丽, 徐鹤函, 沈胜强, 魏兰 2013 62 144704]
[6] Harley J C, Huang Y, Bau H H, Zemel J N 1995 J. Fluid Mech. 284 257
[7] [8] Arkilic E B, Breuer K S, Schimidt M A 2001 J. Fluid Mech. 437 29
[9] [10] [11] Guo Z Y, Li Z X 2003 Int. J. Heat and Fluid Flow 24 284
[12] Turner S E, Lam L C, Faghri M, Gregory O J 2004 J. Heat Transfer 126 753
[13] [14] [15] Zhang Y H, Qin R S, Emerson D R 2005 Phys. Rev. E 71 047702
[16] Nie X B, Doolen G D, Chen S Y 2002 J. Stat. Phys. 107 279
[17] [18] [19] Succi S 2002 Phys. Rev. Lett. 89 064502
[20] Ansumali S, Karlin I V 2002 Phys. Rev. E 66 026311
[21] [22] Tang G H, Tao W Q, He Y L 2005 Phys. Fluids 17 058101
[23] [24] Guo Z L, Shi B C, Zheng C G 2007 Europhys. Lett. 80 24001
[25] [26] Guo Z L, Shi B C, Zhao T S, Zheng C G 2007 Phys. Rev. E 76 056704
[27] [28] [29] Guo Z L, Zheng C G, Shi B C 2008 Phys. Rev. E 77 036707
[30] Li Q, He Y L, Tang G H, Tao W Q 2011 Microfluid. Nanofluid. 10 607
[31] [32] [33] Zhang Y H, Gu X J, Barber R W, Emerson D R 2006 Phys. Rev. E 74 046704
[34] Kim S H, Pitsch H, Boyd I D 2008 Phys. Rev. E 77 026704
[35] [36] [37] Tang G H, Gu X J, Barber R W, Emerson D R Zhang Y H 2008 Phys. Rev. E 78 026706
[38] Lallemand P, Luo L S 2000 Phys. Rev. E 61 6546
[39] [40] [41] Qian Y H, D'Humi?res D, Lallemand P 1992 Europhys. Lett. 17 479
[42] [43] Hadjiconstantinou N G 2005 Phys. Fluids 17 100611
[44] Taheri P, Rana A S, Torrilhon M, Struchtrup H 2009 Continuum Mech. Thermodyn. 21 423
[45] [46] Verhaeghe F, Luo L S, Blanpain B 2009 J. Comput. Phys. 228 147
[47] [48] [49] Shen C, Tian D B, Xie C, Fan J 2004 Microscale Thermophys. Eng. 8 405
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