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微尺度泊肃叶流的高阶连续模型分析

宋诚谦 尹协远 秦丰华

宋诚谦, 尹协远, 秦丰华. 微尺度泊肃叶流的高阶连续模型分析[J]. 力学学报, 2013, 45(3): 314-322. doi: 10.6052/0459-1879-12-294
引用本文: 宋诚谦, 尹协远, 秦丰华. 微尺度泊肃叶流的高阶连续模型分析[J]. 力学学报, 2013, 45(3): 314-322. doi: 10.6052/0459-1879-12-294
Song Chengqian, Yin Xieyuan, Qin Fenghua. THE STUDY BASED ON THE CONTINUUM MODEL FOR THE MICRO-SCALE POISEUILLE FLOW[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3): 314-322. doi: 10.6052/0459-1879-12-294
Citation: Song Chengqian, Yin Xieyuan, Qin Fenghua. THE STUDY BASED ON THE CONTINUUM MODEL FOR THE MICRO-SCALE POISEUILLE FLOW[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3): 314-322. doi: 10.6052/0459-1879-12-294

微尺度泊肃叶流的高阶连续模型分析

doi: 10.6052/0459-1879-12-294
基金项目: 国家自然科学基金委员会与中国工程物理研究院联合基金资助项目(10976029).
详细信息
    通讯作者:

    秦丰华,副教授,主要研究方向:微尺度流体力学、生物流体力学.E-mail:qfh@ustc.edu.cn

  • 中图分类号: O356

THE STUDY BASED ON THE CONTINUUM MODEL FOR THE MICRO-SCALE POISEUILLE FLOW

Funds: The project was supported by the National Natural Science Foundation of China-NSAF (10976029).
  • 摘要: 分别从分子运动论及连续流理论出发,对体积力驱动的微尺度平面泊肃叶(Poiseuille)流的横向分布特征进行了分析. 分子水平模拟采用直接模拟蒙特卡罗(direct simulation Monte Carlo, DSMC)方法;连续流理论则主要考察了伯内特(Burnett)及超伯内特(Super-Burnett)等高阶连续模型,在平行流假设下,获得一组高阶非线性常微分方程,补充完整的边界条件,并应用龙格-库塔(Runge-Kutta)方法求解. 结果表明,即使对于过渡领域流动,高阶连续模型可以给出与DSMC 结果完全相符的压力分布,而速度分布当努森(Knudsen)数约为0.2时即在壁面开始出现偏差;对于温度的横向分布,伯内特模型回复到纳维-斯托克斯(Navier-Stokes)水平,不能得到与DSMC一致的双峰结构,而超伯内特模型在滑移流动领域与DSMC定性相符,在过渡领域却仅能正确预测主流区温度分布,壁面附近差异明显;横向热流与纳维-斯托克斯模型预测接近,但机理上存在本质区别. 本文结果提示选用连续模型时,不仅要根据流动参数来判断,还可以根据所关注的物理量来进行调整,适度扩大连续模型的适用范围. 但即使采用高阶本构关系,连续模型仍然不能完全描述壁面附近区域的非平衡效应(如努森层效应),这是试图扩大连续模型适用范围时必然会遇到的困难.

     

  • 李志信, 罗小兵, 过增元. MEMS技术的现状及发展趋势. 传感器技术, 2001, 20(9): 58-60 (Li Zhixin, Luo Xiaobing, Guo Zengyuan. Present situation and development trend of MEMS technology. Journal of Transducer Technology, 2001, 20(9): 58-60 (in Chinese))
    Arkilic EB, Schmidt MA, Breuer KS. Gaseous slip flow in long microchannels. J Microelectromech S, 1997, 6(2): 167-178  
    樊菁, 沈青. 微尺度气体流动. 力学进展, 2002, 32(3): 321-36 (Fan Jing, Shen Ching. Micro-scale gas flows. Advances In Mechanics, 2002, 32(3): 321-336 (in Chinese))
    Zheng YH, Garcia AL, Alder BJ. Comparison of kinetic theory and hydrodynamics for Poiseuille flow. J Stat Phys, 2002, 109(3-4): 495-505
    Chapman S, Cowling TG. The Mathematical Theory of Non-uniform Gases. Cambridge: Cambridge University Press, 1970
    Shavaliyev MS. Super-burnett corrections to the stress tensor and the heat-flux in a gas of maxwellian molecules. Pmm-J Appl Math Mec+, 1993, 57(3): 573-576  
    Rosenau P. Extending hydrodynamics via the regularization of the chapman-enskog expansion. Phys Rev A, 1989, 40(12): 7193-7196  
    Bobylev AV. The chapman-enskog and grad methods of solution of the boltzmann-equation. Dokl Akad Nauk Sssr+, 1982, 262(1): 71-75
    Zhong XL, Maccormack RW, Chapman DR. Stabilization of the burnett equations and application to hypersonic flows. AIAA Journal, 1993, 31(6): 1036-1043  
    Jin S, Slemrod M. Regularization of the Burnett equations via relaxation. Journal of Statistical Physics, 2001, 103(5-6): 1009-1033
    Bobylev AV. Instabilities in the Chapman-Enskog expansion and hyperbolic Burnett equations. Journal of Statistical Physics, 2006, 124(2-4): 371-399
    Soderholm LH. Hybrid Burnett equations: A new method of stabilizing. Transport Theor Stat, 2007, 36(4-6): 495-512
    Uribe FJ, Garcia AL. Burnett description for plane Poiseuille flow. Phys Rev E, 1999, 60(4): 4063-4078  
    Balakrishnan R, Agarwal RK. Numerical simulation of Bhatnagar-Gross-Krook-Burnett equations for hypersonic flows. J Thermophys Heat Tr, 1997, 11(3): 391-399  
    Xu K. Super-Burnett solutions for Poiseuille flow. Physics of Fluids, 2003, 15(7): 2077-2080  
    Struchtrup H. Failures of the Burnett and super-Burnett equations in steady state processes. 2005, 17: 43-50
    Taheri P, Torrilhon M, Struchtrup H. Couette and Poiseuille microflows: Analytical solutions for regularized 13-moment equations. Physics of Fluids, 2009, 21(1):
    孙江龙, 吕续舰, 郭磊等. 微尺度流动研究的简要综述. 机械强度, 2010, 32(3): 502-508 (Sun Jianglong, Lü Xujian, Guo Lei, et al. Brief summarization of micro-scale flow research. Journal of Mechanical Strength, 2010, 32(3): 502-508 (in Chinese))
    Wang M, Li ZX. Similarity of ideal gas flow at different scales. Science in China Series E-Technological Sciences, 2003, 46(6): 661-670
    Wang M, Lan XD, Li ZX. Analyses of gas flows in micro- and nanochannels. Int J Heat Mass Tran, 2008, 51(13-14): 3630-3641  
    Wang M, Li ZX. Gas mixing in microchannels using the direct simulation Monte Carlo method. Int J Heat Mass Tran, 2006, 49(9-10): 1696-1702
    Lee C. Unique determination of solutions to the Burnett equations. AIAA Journal, 1994, 32: 985-990  
    Zhang J, Fan J, Jiang JZ. Multiple temperature model for the information preservation method and its application to nonequilibrium gas flows. J Comput Phys, 2011, 230(19): 7250-7265  
    Xu K, Guo ZL. Multiple temperature gas dynamic equations for non-equilibrium flows. J Comput Math, 2011, 29(6): 639-660  
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出版历程
  • 收稿日期:  2012-10-26
  • 修回日期:  2012-12-29
  • 刊出日期:  2013-05-18

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