微尺度振荡Couette流的格子Boltzmann模拟

陶实; 王亮; 郭照立

doi:10.7498/aps.63.214703

摘要

采用有效多松弛时间-格子Boltzmann方法(Effective MRT-LBM)数值模拟了微尺度条件下的振荡Couette和Poiseuille流动. 在微流动LBM中引入Knudsen边界层模型,对松弛时间进行修正. 模拟时平板或外力以正弦周期振动,Couette流中考虑了单平板振动、上下板同相振动这两类情况. 研究结果表明,修正后的MRT-LBM模型能有效用于这类非平衡的微尺度流动模拟;对于Couette流,随着Kn数的增大,壁面滑移效应变得越明显. St越大,板间速度剖面的非线性特性越剧烈;两板同相振荡时,若Kn,St均较小,板间流体受到平板拖动剪切的影响很小,板间速度几乎重叠在一起;在振荡Poiseuille流动中,St数增大到一定值时,相位滞后现象减弱;相对于Kn数,St数对振荡Couette 和Poiseuille流中不同位置处速度相位差的产生有较大影响.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
华中科技大学, 煤燃烧国家重点实验室, 武汉 430074;

2.
北京计算科学研究中心, 北京 100084

基金项目: 国家自然科学基金(批准号:51125024)资助的课题.

Authors and contacts

1.
State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China;

2.
Beijing Computational Science Research Center, Beijing 100084, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51125024).

参考文献

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施引文献

[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 物理学报 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 物理学报 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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