微尺度下气体在过渡区内流动的格子Boltzmann模拟

刘加利; 张继业; 张卫华

doi:10.3969/j.issn.0258-2724.2013.04.021

微尺度下气体在过渡区内流动的格子Boltzmann模拟

doi: 10.3969/j.issn.0258-2724.2013.04.021

基金项目:

国家自然科学基金资助项目(50823004)

"十一五"国家科技支撑计划资助项目(2009BAG12A01-C12)

铁道部科技研究开发计划资助项目(2008J013)

计量
- 文章访问数: 808
- HTML全文浏览量: 62
- PDF下载量: 327
- 被引次数: 0
出版历程
- 收稿日期: 2011-12-02
- 刊出日期: 2013-08-25

Lattice Boltzmann Simulation of Micro-scale Gas Flows in the Transitional Regime

摘要

摘要: 为研究微尺度下气体在过渡区内的流动特性,基于气体动理学及Knudsen层效应理论,推导了Knudsen数与无量纲松弛时间的关系;应用Succi的边界处理方法和广义二阶滑移边界条件,推导了壁面滑移速度和反弹比例系数的计算公式,建立了适用于过渡区微尺度气体流动的格子Boltzmann模型,并应用该模型对过渡区内微尺度Poiseuille流动进行模拟.结果表明,当稀薄参数取1.64时,计算得到的无量纲速度剖面在整个过渡区与Karniadakis给出的无量纲速度剖面吻合较好,无量纲速度分布在过渡区基本上保持为抛物线形状,边界上的无量纲滑移速度随着Knudsen数的增加而增大,中心线上的无量纲速度随着Knudsen数的增加而减小.
- 微尺度气体流动 /
- 格子Boltzmann模型 /
- Knudsen数 /
- 滑移速度 /
- 过渡区 /
- 稀薄参数
Abstract: In order to study the flow characteristics of micro-scale gas in the transitional regime, the relationship between Knudsen number and dimensionless relaxation time was derived based on the gas kinetic theory and the effect of Knudsen layer. Computational formulas for the slip velocity on the wall and the bounce-back fraction were derived under a generalized second-order slip boundary condition using the boundary treatment method proposed by Succi. Then, a lattice Boltzmann model for micro-scale gas flows in the transitional regime was established, and the micro-scale Poiseuille flows in the transitional regime were simulated. Computational results show that when the rarefaction parameter is equal to 1.64, the computed dimensionless velocity profile is in good agreement with the dimensionless velocity profile given by Karniadakis in the whole transitional regime. The dimensionless velocity profile remains essentially a parabolic shape in the transitional regime. As Knudsen number increases, the dimensionless slip velocity rises in the boundary and falls in the center line.
- micro-scale gas flow /
- lattice Boltzmann model /
- Knudsen number /
- slip velocity /
- transitional regime /
- rarefaction parameter

HTML全文

参考文献(25)

祝兵,宋随弟,谭长建. 三维波浪作用下大直径圆柱绕流的数值模拟[J]. 西南交通大学学报,2012,47(2): 224-229. ZHU Bing, SONG Suidi, TAN Changjian. Numerical simulation for diffraction around large-diameter circular cylinder subjected to three-dimension wave[J]. Journal of Southwest Jiaotong University, 2012, 47(2): 224-229.

OHWADA T, SONE T, AOKI K. Numerical analysis of the Poiseuille and thermal transpiration flows and a rarefied gas between two parallel plates[J]. Physics of Fluids A, 1989, 1(12): 2042-2049.

ABDOU M A. Chapman-enskog-maximum entropy method on time-dependent neutron transport equation[J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 2006, 101(2): 210-225.

KUN X. Numerical hydrodynamics from gas kinetic theory[D]. New York: Columbia University, 1993.

ARKILIC E B, SCHMIDT M A, BREUER K S. Gaseous slip flow in long microchannels[J]. Journal of Microelectromechanical Systems, 1997, 62(2): 167-178.

BESKOK A. Simulation and models for gas flows in microg eometries[D]. Princeton: Princeton University, 1996.

BIRD G A. Recent advances and current challenges for DSMC[J]. Computers and Mathematics with Applications, 1998, 35(1/2): 1-14.

FAN J, SHEN C. Statistical simulation of low-speed rarefied gas flows[J]. Journal of Computational Physics, 2001, 167(2): 393-412.

CAI C P, BOYD I D, FAN J, et al. Direct simulation methods for low-speed micro-channel flows[J]. Journal of Thermophysics and Heat Transfer, 2000, 14(3): 368-378.

NIE X, DOOLEN G D, CHEN S. Lattice-Boltzmann simulations of fluid flows in MEMS[J]. Journal of Statistical Physics, 2002, 107(1): 279-289.

LIM C Y, SHU C, NIU X D, et al. Application of lattice Boltzmann method to simulate microchannel flows[J]. Physics of Fluids, 2002, 14(7): 2299-2308.

SHEN Q, TIAN D B, XIE C, et al. Examination of the LBM in simulation of micro-channel flow in transitional regime[J]. Microscale Thermophysical Engineering, 2004, 8(4): 423-432.

ZHANG Y, QIN R, EMERSON D R. Lattice Boltzmann simulation of rarefied gas flows in microchannels[J]. Physical Review E, 2005, 71(4): 047702-1-047702-5.

LEE T, LIN C L. Rarefaction and compressibility effects of the lattice Boltzmann equation method in a gas microchannel[J]. Physical Review E, 2005, 71(4): 046706-1-046706-10.

GUO Z L, ZHAO T S, SHI Y. Physical symmetry,spatial accuracy,and relaxation timeof the lattice Boltzmann equation for microgas flows[J]. Journal of Applied Physics, 2006, 99(7): 074903-1-074903-8.

ZHANG Y H, GU X J, BARBER R W, et al. Capturing Knudsen layer phenomena usinga lattice Boltzmann model[J]. Physical Review E, 2006, 74(4): 046704-1-046704-4.

ZHANG Y H, GU X J, BARBER R W, et al. Modelling thermal flow in the transitionregime using a lattice Boltzmann approach[J]. Europhysics Letters, 2007, 77(3): 30003-1-30003-5.

GUO Z L, ZHANG C G, SHI B C. Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flows[J]. Physical Review E, 2008, 77(3): 036707-1-036707-12.

QIAN Y H, D'HUMIERES D, LALLEMAND P. Lattice BGK models for Navier-Stokes equation[J]. Europhysis Letters, 1992, 17(6): 479-484.

GUO Z L, ZHENG C G, SHI B C. Discrete lattice effects on the forcing term in the lattice Boltzmann method[J]. Physical Review E, 2002, 65(4): 046308-1-046308-6.

BESKOK A, KARNIADAKIS G E. A model for flows in channels, pipes, and ducts at micro and nano scales[J]. Microscale Thermophys Engineering, 1999, 3(1): 43-77.

VASILIS K, MICHALIS A N, KALARAKIS E D, et al. Rarefaction effects on gas viscosity in the Knudsen transition regime[J]. Microfluid Nanofluid, 2010, 9(4/5): 847-853.

SUCCI S. Mesoscopic modeling of slip motion at fluid-solid interfaces with heterogeneouscatalysis[J]. Physieal Review Letters, 2002, 89(6): 064502-1-064502-4.

GUO Z L, SHI B C, ZHAO T S, et al. Discrete effects on boundary conditions for the lattice Boltzmann equation in simulating mircoscale gas flows[J]. Physical Review E, 2007, 76(5): 056704-1-056704-5.

KARNIADAKIS G E, BESKOK A. Micro flows fundamental and simulation[M]. New York: Springer-Verlag, 2002: 90-110.

施引文献

附加材料(0)

访问统计

点击查看大图

计量

文章访问数: 808
HTML全文浏览量: 62
PDF下载量: 327
被引次数: 0

微尺度下气体在过渡区内流动的格子Boltzmann模拟

doi: 10.3969/j.issn.0258-2724.2013.04.021

计量

出版历程

Lattice Boltzmann Simulation of Micro-scale Gas Flows in the Transitional Regime

计量

出版历程

目录