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激波冲击V形界面重气体导致的壁面与旋涡作用及其对湍流混合的影响

李俊涛 孙宇涛 胡晓棉 任玉新

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激波冲击V形界面重气体导致的壁面与旋涡作用及其对湍流混合的影响

李俊涛, 孙宇涛, 胡晓棉, 任玉新

Effect of vortex/wall interaction on turbulent mixing in the Richtmyer-Meshkov instability induced by shocked V shape interface

Li Jun-Tao, Sun Yu-Tao, Hu Xiao-Mian, Ren Yu-Xin
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  • 基于多组分混合物质量分数模型,采用色散最小耗散可控的高分辨率有限体积方法,数值模拟了弱激波冲击V形空气/SF6界面后,界面不稳定性生成的旋涡与固体壁面作用问题.激波冲击V形界面之后,因斜压效应诱导涡量沉积在界面附近,形成沿界面规则排列的多个涡对结构.旋涡的诱导作用使界面不断变形和卷起,同时旋涡之间不断发生相互并对,诱导更多更小尺度的旋涡产生.旋涡诱导作用的叠加效应,使界面尖端处的初始涡对向上下壁面发展.随后,涡结构开始与壁面发生复杂的相互作用.旋涡与壁面作用后沿壁面加速,使得物质界面沿壁面伸展,随后,旋涡从壁面回弹,并诱导二次旋涡产生.旋涡与壁面相互作用的过程,能够明显加剧物质混合.本文从物质混合的角度研究了该过程的机理,分析了旋涡与壁面作用对物质混合的影响.
    An important effect of the interfacial instability occurring at the interfaces of gases is to enhance the mixing of gases. In the present paper, the vortex/wall interactions at the late stage of the evolution of V shaped air/interface accelerated by weak shock wave in a duct is numerically simulated using high-resolution finite volume method with minimized dispersion and controllable dissipation (MDCD) scheme. The objective of the present paper is to study the mechanism of mixing enhancement due to the vortex/wall interactions. Because of the shock impingement, the Richtmyer-Meshkov instability is first developed. As a result, the baroclinic vorticity is deposited near the interface due to the misalignment of the density and pressure gradient right after the interaction of shock wave with V shaped interface, leading to the formation of vortical structures along the interface manifested by the Kelvin-Helmholtz instability. The vortices induce the rolling up and deformation of interface, and multi-scale vortical structures are generated because of the interaction and merging between vortices. This process eventually causes the turbulence mixing transition. The vortex induced velocity field drives the vortices to move to the lower/upper walls of the duct, leading to the complicated interaction between vortex and wall. It is observed in the numerical results that during the vortex/wall interaction, vortex is accelerated along the wall, leading to the stretching of material interface. Then the primary vortex will lift off from the wall and forms a second vortex. These two phenomena are the two main mechanisms of the mixing enhancement. Because of the inherent instability at the interface, the stretching of the interface will spread the area of instability. Furthermore, at the late stage of the interfacial instability, the flow near the interface is turbulent because of the rolling and pairing of the vortices. Therefore, the stretching of the interface will speed up the development of the interfacial turbulence and enhance the mixing. The vortex lifting off from the wall can directly speed up the mixing since it makes the heavy gas move directly into the light gas. To further determine which mechanism is dominant, we study the evolution of the mixing parameter derived from a fictitious fast chemical reaction model. It is shown that during the acceleration of the vortices along the wall and the stretching of the interface, the slope of the mixing parameter increases by a factor of 2, which indicates a significant mixing enhancement. And the vortices lifting off from the wall also shows considerable mixing enhancement but it is not so strong as the first mechanism.
      通信作者: 任玉新, ryx@tsinghua.edu.cn
    • 基金项目: 国家自然科学基金(批准号:U1430235)和国家重点研发计划(批准号:2016YFA0401200)资助的课题.
      Corresponding author: Ren Yu-Xin, ryx@tsinghua.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. U1430235) and the National Basic Research and Development Program of China (Grant No. 2016YFA0401200).
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    Tomkins C, Kumar S, Orlicz G Prestridge K 2006 J. Fluid Mech. 131 150

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    [16]

    Booth E R, Yu Y C 1986 AIAA J. 24 1468

    [17]

    Dee F S, Nicholas O P 1968 British Aeronautical Research Council CP 1065

    [18]

    Harvey J K, Perry F J 1971 AIAA J. 9 1659

    [19]

    Boldes U, Ferreri J C 1973 Phys. Fluids 16 2005

    [20]

    Walker J D A, Smith C R, Cerra A W, Doligalski T L 1987 J. Fluid Mech. 181 99

    [21]

    Orlandi P 1990 Phys. Fluids A 2 1429

    [22]

    Orlandi P, Verzicco R 1993 J. Fluid Mech. 256 615

    [23]

    Wang T, Bai J S, Li P, Tao G, Jiang Y, Zhong M (in Chinese)[王涛, 柏劲松, 李平, 陶钢, 姜洋, 钟敏 2013 高压物理学报 2 18]

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    Shyue K M 1998 J. Comput. Phys. 142 208

    [25]

    Sun Z S, Ren Y X, Larricq C 2011 J. Comput. Phys. 230 4616

    [26]

    Wang Q J, Ren Y X, Sun Z S 2013 Sci. China:Ser. G 56 423

    [27]

    Luo X, Dong P, Si T, Zhai Z G 2016 J. Fluid Mech. 802 186

    [28]

    Su L, Clemens N 2003 J. Fluid Mech. 488 1

    [29]

    Eswaran V, Pope S 1988 Phys. Fluids 31 506

    [30]

    Girimaji S 1992 Phys. Fluids A 4 2529

    [31]

    Rikanati A, Alon U, Shvarts D 2003 Phys. Fluids 15 3776

    [32]

    Si T, Zhai J, Yang J, Luo X 2012 Phys. Fluids 24 054101

    [33]

    Ahmed M N, Manoochehr M K 2004 Phys. Fluids 16 2613

    [34]

    Linden P F, Redondo J M, Youngs D L 1994 J. Fluid Mech. 265 97

    [35]

    Cook A W, Dimotakis P E Youngs D L 1994 Lasers and Particle Beams 12 725

    [36]

    Youngs D L 1994 Lasers and Particle Beams 12 725

  • [1]

    Markstein G H 1957 J. Aerosol Sci. 24 238

    [2]

    Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297

    [3]

    Meshkov E E 1969 Fluid Dyn. 4 101

    [4]

    Arnett W, Bahcall J, Kirshner R, Woosley S 1989 Annu. Rev. Astron. Astrophys. 27 629

    [5]

    Lindl J, McCrory R, Campbell E 1992 Phys. Today 45 32

    [6]

    Yang J, Kubota T, Zukowski E 1993 AIAA J. 31 854

    [7]

    Jacobs J 1992 J. Fluid Mech. 234 629

    [8]

    Zhang S, Zabusky N, Peng G, Gupta S 1992 Phys. Fluids 16 1203

    [9]

    Kumar S, Orlicz G, Tomkins C, Goodenough C, Prestridge K, Vorobieff P Benjamin R 1992 Phys. Fluids 17 082107

    [10]

    Tomkins C, Kumar S, Orlicz G Prestridge K 2006 J. Fluid Mech. 131 150

    [11]

    Li J T, Sun Y T, Pan J H, Ren Y X Acta Phys Sin 65 245202 in Chinese 2016 65 245202 (in Chinese)[李俊涛, 孙宇涛, 潘建华, 任玉新 2016 物理学报 65 245202]

    [12]

    Zheng Z C, Ash R L 1996 AIAA J. 34 580

    [13]

    Tafti D K, Vanka S P 1991 Phys. Fluids A 3 1749

    [14]

    Luton J A, Ragab S A, Telionis D P 1995 Phys. Fluids 7 2757

    [15]

    Koromilas C, Telionis D P 1980 J. Fluid Mech. 97 347

    [16]

    Booth E R, Yu Y C 1986 AIAA J. 24 1468

    [17]

    Dee F S, Nicholas O P 1968 British Aeronautical Research Council CP 1065

    [18]

    Harvey J K, Perry F J 1971 AIAA J. 9 1659

    [19]

    Boldes U, Ferreri J C 1973 Phys. Fluids 16 2005

    [20]

    Walker J D A, Smith C R, Cerra A W, Doligalski T L 1987 J. Fluid Mech. 181 99

    [21]

    Orlandi P 1990 Phys. Fluids A 2 1429

    [22]

    Orlandi P, Verzicco R 1993 J. Fluid Mech. 256 615

    [23]

    Wang T, Bai J S, Li P, Tao G, Jiang Y, Zhong M (in Chinese)[王涛, 柏劲松, 李平, 陶钢, 姜洋, 钟敏 2013 高压物理学报 2 18]

    [24]

    Shyue K M 1998 J. Comput. Phys. 142 208

    [25]

    Sun Z S, Ren Y X, Larricq C 2011 J. Comput. Phys. 230 4616

    [26]

    Wang Q J, Ren Y X, Sun Z S 2013 Sci. China:Ser. G 56 423

    [27]

    Luo X, Dong P, Si T, Zhai Z G 2016 J. Fluid Mech. 802 186

    [28]

    Su L, Clemens N 2003 J. Fluid Mech. 488 1

    [29]

    Eswaran V, Pope S 1988 Phys. Fluids 31 506

    [30]

    Girimaji S 1992 Phys. Fluids A 4 2529

    [31]

    Rikanati A, Alon U, Shvarts D 2003 Phys. Fluids 15 3776

    [32]

    Si T, Zhai J, Yang J, Luo X 2012 Phys. Fluids 24 054101

    [33]

    Ahmed M N, Manoochehr M K 2004 Phys. Fluids 16 2613

    [34]

    Linden P F, Redondo J M, Youngs D L 1994 J. Fluid Mech. 265 97

    [35]

    Cook A W, Dimotakis P E Youngs D L 1994 Lasers and Particle Beams 12 725

    [36]

    Youngs D L 1994 Lasers and Particle Beams 12 725

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  • 收稿日期:  2017-06-18
  • 修回日期:  2017-07-31
  • 刊出日期:  2017-12-05

激波冲击V形界面重气体导致的壁面与旋涡作用及其对湍流混合的影响

  • 1. 中国工程物理研究院研究生院, 北京 100088;
  • 2. 北京应用物理与计算数学研究所, 北京 100094;
  • 3. 清华大学航天航空学院, 北京 100084
  • 通信作者: 任玉新, ryx@tsinghua.edu.cn
    基金项目: 国家自然科学基金(批准号:U1430235)和国家重点研发计划(批准号:2016YFA0401200)资助的课题.

摘要: 基于多组分混合物质量分数模型,采用色散最小耗散可控的高分辨率有限体积方法,数值模拟了弱激波冲击V形空气/SF6界面后,界面不稳定性生成的旋涡与固体壁面作用问题.激波冲击V形界面之后,因斜压效应诱导涡量沉积在界面附近,形成沿界面规则排列的多个涡对结构.旋涡的诱导作用使界面不断变形和卷起,同时旋涡之间不断发生相互并对,诱导更多更小尺度的旋涡产生.旋涡诱导作用的叠加效应,使界面尖端处的初始涡对向上下壁面发展.随后,涡结构开始与壁面发生复杂的相互作用.旋涡与壁面作用后沿壁面加速,使得物质界面沿壁面伸展,随后,旋涡从壁面回弹,并诱导二次旋涡产生.旋涡与壁面相互作用的过程,能够明显加剧物质混合.本文从物质混合的角度研究了该过程的机理,分析了旋涡与壁面作用对物质混合的影响.

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