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分离比对混合流体Rayleigh-Bénard对流解的影响

宁利中 王娜 袁喆 李开继 王卓运

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分离比对混合流体Rayleigh-Bénard对流解的影响

宁利中, 王娜, 袁喆, 李开继, 王卓运

Influence of separation ratio on Rayleigh-Bénard convection solutions in a binary fluid mixture

Ning Li-Zhong, Wang Na, Yuan Zhe, Li Kai-Ji, Wang Zhuo-Yun
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  • 混合流体Rayleigh-Bénard对流是研究非平衡对流的非线性动力学特性的典型模型之一. 基于流体力学方程组的数值模拟,首先探讨了矩形腔体中具有强Soret效应(分离比Ψ=-0.60)的混合流体行波对流的分叉特性及斑图演化,沿着分叉曲线的上部分支,随着相对瑞利数的增加,此系统依次出现了局部行波对流、具有缺陷的行波对流、行波对流、摆动行波对流及定常对流5种行波对流解. 然后,研究了分离比Ψ对对流解的影响,与弱Soret效应(Ψ=-0.11)时的对流解相比较,强Soret效应(Ψ=-0.60)时出现的对流解更丰富. 由于有强Soret效应的对流的复杂性,Ψ=-0.60时的对流解与Ψ=-0.20,-0.4 时的对流解不同.
    The Rayleigh-Bénard convection in a binary fluid mixture is one of typical models for studying the nonlinear dynamics of nonequilibrium convection. In this paper, using the numerical simulations of the two-dimensional full equations of hydrodynamics, we study the bifurcation and evolution of patterns in the traveling wave convection in binary fluid mixtures with strong Soret effect (separation ratio Ψ=-0.60) in a rectangular cell. The system exhibits 5 types of traveling wave convection solutions with the increasing of reduced Rayleigh number r along the upper branch of the bifurcation curve. They are localized traveling wave convection, traveling wave convection with defects, traveling wave convection, undulation traveling wave convection, and stationary overturning convection. Second, the influence of separation ratio on convection solutions is investigated. By comparing the convection solutions with strong Soret effect (Ψ=-0.60) with those of weakly Soret effect (Ψ=-0.11), we find that those with strong Soret effect are richer. Because of the complexity in convection with strong Soret effect, the convection solutions at Ψ=-0.60 are different from those at Ψ=-0.20, -0.4.
    • 基金项目: 国家自然科学基金(批准号:10872164)和陕西省重点学科建设专项基金资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10872164) and the Special Foundation of Priority Academic Discipline of Shaanxi Province, China.
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    [2]

    Getling A V 1998 Rayleigh-Bénard Convection (London: World Scientific) pp98-112

    [3]

    Ning L Z 2006 Rayleigh-Bénard Convection in a Binary Fluid Mixture with and without Lateral Flow (Xi'an: Northwest A & F University Press) pp112-134

    [4]

    Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 998

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    Barten W, Lucke M, Kamps M 1991 Phys. Rev. Lett. 66 2621

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    [7]

    Barten W, Lucke M, Kamps M, Schmitz R 1995 Phys. Rev. E 51 5662

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    Yahata H 1989 Prog. Theor. Phys. (Suppl.) 99 493

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    Batiste O, Knobloch E, Alonso A, Mercader I 2006 J. Fluid Mech. 560 149

    [11]

    Batiste O, Knobloch E, Mercader I, Net M 2001 Phys. Rev. E 65 016303

    [12]

    Futterer C 2003 Theor. Comput. Fluid Dyn. 16 467

    [13]

    Ryskin A, Mller H W, Pleiner H 2003 Phys. Rev. E 67 046302

    [14]

    Ning L Z, Zhou Y, Wang S Y, Li G D, Zhang S Y, Zhou Q 2010 Chin. J. Hydrodyn. 25 299 (in Chinese) [宁利中, 周洋, 王思怡, 李国栋, 张淑芸, 周倩 2010 水动力学研究与进展 25 299]

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    Ning L Z, Qi X, Yu L, Zhou Y, Wang S Y, Li G D 2010 J. Basic Sci. Eng. 18 281 (in Chinese) [宁利中, 齐昕, 余荔, 周洋, 王思怡, 李国栋 2010 应用基础和工程科学学报 18 281]

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    Ning L Z, Harada Y, Yahata H 1996 Prog. Theor. Phys. 96 669

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    Ning L Z, Harada Y, Yahata H 1997 Prog. Theor. Phys. 97 831

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    Ning L Z, Harada Y, Yahata H 1997 Prog. Theor. Phys. 98 551

    [19]

    Ning L Z, Harada Y, Yahata H, Li J Z 2001 Prog. Theor. Phys. 106 503

    [20]

    Ning L Z, Harada Y, Yahata H, Li J Z 2001 J. Hydrodyn. 13 65

    [21]

    Ning L Z, Qi X, Harada Y, Yahata H 2006 J. Hydrodyn. 18 199

    [22]

    Ning L Z, Qi X, Zhou Y, Yu L 2009 Acta Phys. Sin. 58 2528 (in Chinese)[宁利中, 齐昕, 周洋, 余荔 2009 物理学报 58 2528]

    [23]

    Ning L Z, Harada Y, Yahata H, Li J Z 2000 J. Hydrodyn. 12 20

    [24]

    Ning L Z, Yu L, Yuan Z, Zhou Y 2009 Sci. China G 39 746 (in Chinese) [宁利中, 余荔, 袁喆, 周洋 2009 中国科学G 39 746]

    [25]

    Ning L Z, Qi X, Yuan Z, Shi F 2008 J. Hydrodyn. 20 567

    [26]

    Jung D, Lucke M 2002 Phys. Rev. Lett. 89 054502

    [27]

    Buchel P, Lucke M 2000 Phys. Rev. E 61 3793

    [28]

    Shen K, Zhang X 2002 Acta Phys. Sin. 51 2702 (in Chinese)[沈柯, 张旭 2002 物理学报 51 2702]

    [29]

    Zhang X, Shen K 2001 Acta Phys. Sin. 50 2116 (in Chinese)[张旭, 沈柯 2001 物理学报 50 2116]

    [30]

    Ni J, Liu H 2002 Physics 31 461 (in Chinese)[倪军, 刘华 2002 物理 31 461]

    [31]

    Taraut A V, Smorodin B L, Lucke M 2012 New J. Phys. 14 093055

    [32]

    Smorodin B L, Lucke M 2010 Phys. Rev. E 82 016310

  • [1]

    Chandrasekhar S 1961 Hydrodynamics and Hydromagnetic Stability (Oxford: Clarendon Press) pp126-146

    [2]

    Getling A V 1998 Rayleigh-Bénard Convection (London: World Scientific) pp98-112

    [3]

    Ning L Z 2006 Rayleigh-Bénard Convection in a Binary Fluid Mixture with and without Lateral Flow (Xi'an: Northwest A & F University Press) pp112-134

    [4]

    Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 998

    [5]

    Barten W, Lucke M, Kamps M 1991 Phys. Rev. Lett. 66 2621

    [6]

    Barten W, Lucke M, Kamps M, Schmitz R 1995 Phys. Rev. E 51 5636

    [7]

    Barten W, Lucke M, Kamps M, Schmitz R 1995 Phys. Rev. E 51 5662

    [8]

    Yahata H 1991 Prog. Theor. Phys. 85 933

    [9]

    Yahata H 1989 Prog. Theor. Phys. (Suppl.) 99 493

    [10]

    Batiste O, Knobloch E, Alonso A, Mercader I 2006 J. Fluid Mech. 560 149

    [11]

    Batiste O, Knobloch E, Mercader I, Net M 2001 Phys. Rev. E 65 016303

    [12]

    Futterer C 2003 Theor. Comput. Fluid Dyn. 16 467

    [13]

    Ryskin A, Mller H W, Pleiner H 2003 Phys. Rev. E 67 046302

    [14]

    Ning L Z, Zhou Y, Wang S Y, Li G D, Zhang S Y, Zhou Q 2010 Chin. J. Hydrodyn. 25 299 (in Chinese) [宁利中, 周洋, 王思怡, 李国栋, 张淑芸, 周倩 2010 水动力学研究与进展 25 299]

    [15]

    Ning L Z, Qi X, Yu L, Zhou Y, Wang S Y, Li G D 2010 J. Basic Sci. Eng. 18 281 (in Chinese) [宁利中, 齐昕, 余荔, 周洋, 王思怡, 李国栋 2010 应用基础和工程科学学报 18 281]

    [16]

    Ning L Z, Harada Y, Yahata H 1996 Prog. Theor. Phys. 96 669

    [17]

    Ning L Z, Harada Y, Yahata H 1997 Prog. Theor. Phys. 97 831

    [18]

    Ning L Z, Harada Y, Yahata H 1997 Prog. Theor. Phys. 98 551

    [19]

    Ning L Z, Harada Y, Yahata H, Li J Z 2001 Prog. Theor. Phys. 106 503

    [20]

    Ning L Z, Harada Y, Yahata H, Li J Z 2001 J. Hydrodyn. 13 65

    [21]

    Ning L Z, Qi X, Harada Y, Yahata H 2006 J. Hydrodyn. 18 199

    [22]

    Ning L Z, Qi X, Zhou Y, Yu L 2009 Acta Phys. Sin. 58 2528 (in Chinese)[宁利中, 齐昕, 周洋, 余荔 2009 物理学报 58 2528]

    [23]

    Ning L Z, Harada Y, Yahata H, Li J Z 2000 J. Hydrodyn. 12 20

    [24]

    Ning L Z, Yu L, Yuan Z, Zhou Y 2009 Sci. China G 39 746 (in Chinese) [宁利中, 余荔, 袁喆, 周洋 2009 中国科学G 39 746]

    [25]

    Ning L Z, Qi X, Yuan Z, Shi F 2008 J. Hydrodyn. 20 567

    [26]

    Jung D, Lucke M 2002 Phys. Rev. Lett. 89 054502

    [27]

    Buchel P, Lucke M 2000 Phys. Rev. E 61 3793

    [28]

    Shen K, Zhang X 2002 Acta Phys. Sin. 51 2702 (in Chinese)[沈柯, 张旭 2002 物理学报 51 2702]

    [29]

    Zhang X, Shen K 2001 Acta Phys. Sin. 50 2116 (in Chinese)[张旭, 沈柯 2001 物理学报 50 2116]

    [30]

    Ni J, Liu H 2002 Physics 31 461 (in Chinese)[倪军, 刘华 2002 物理 31 461]

    [31]

    Taraut A V, Smorodin B L, Lucke M 2012 New J. Phys. 14 093055

    [32]

    Smorodin B L, Lucke M 2010 Phys. Rev. E 82 016310

计量
  • 文章访问数:  1995
  • PDF下载量:  415
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-11-15
  • 修回日期:  2014-02-17
  • 刊出日期:  2014-05-05

分离比对混合流体Rayleigh-Bénard对流解的影响

  • 1. 西安理工大学陕西省西北旱区生态水利工程国家重点实验室, 西安 710048
    基金项目: 

    国家自然科学基金(批准号:10872164)和陕西省重点学科建设专项基金资助的课题.

摘要: 混合流体Rayleigh-Bénard对流是研究非平衡对流的非线性动力学特性的典型模型之一. 基于流体力学方程组的数值模拟,首先探讨了矩形腔体中具有强Soret效应(分离比Ψ=-0.60)的混合流体行波对流的分叉特性及斑图演化,沿着分叉曲线的上部分支,随着相对瑞利数的增加,此系统依次出现了局部行波对流、具有缺陷的行波对流、行波对流、摆动行波对流及定常对流5种行波对流解. 然后,研究了分离比Ψ对对流解的影响,与弱Soret效应(Ψ=-0.11)时的对流解相比较,强Soret效应(Ψ=-0.60)时出现的对流解更丰富. 由于有强Soret效应的对流的复杂性,Ψ=-0.60时的对流解与Ψ=-0.20,-0.4 时的对流解不同.

English Abstract

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