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在激波与气柱相互作用问题中，压力与密度间断不平行产生的斜压涡量会引起流动的不稳定性，从而促进物质间的混合.本文基于双通量模型，结合五阶加权基本无振荡（WENO）格式，求解多组分二维Navier-Stokes方程，分析激波作用面积相同结构不同的椭圆气柱所致的流动和混合.数值结果清晰地显示了激波诱导Richtmyer-Meshkov不稳定性引起的气柱界面变形和波系演化.同时定量地从界面运动、界面结构参数变化（长度和高度）、气柱体积压缩率、环量及混合率等角度分析激波诱导的流动混合机制，研究椭圆几何构型对氦气混合过程的影响.结果表明，界面及相关参数的演化与气柱初始形状密切相关.当激波沿椭圆长轴作用于气柱时，气柱前端出现空气射流结构，且射流不断增长并渗透到下游界面，致使气柱分离成两个独立涡团，离心率越大，射流发展越快；同时激波作用气柱后在界面处产生不规则反射现象.圆形气柱界面演化与这种作用情形类似.当激波沿椭圆短轴作用于气柱时，界面上游出现类平面结构，随后平面上下缘处产生涡旋，主导流动发展，激波在界面作用产生规则反射，离心率越大，这些现象越明显.界面高度、长度、体积压缩率也因此有所差异.对界面演化、环量和混合率的综合分析表明，激波沿长轴作用于气柱且离心率较大时，流动发展较快，不稳定性导致的流动越复杂，越有利于氦气与环境介质的混合.
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关键词:
- 可压缩流 /
- 激波气泡相互作用 /
- Richtmyer-Meshkov不稳定性 /
- 混合
In shock bubble interaction (SBI), the baroclinic vorticity generated by misalignment of pressure and density gradient will lead to flow instability which promotes the mixing between the bubbles and surrounding gas. A numerical study on the flow and mixing of shock-accelerated elliptic helium cylinder with the surrounding air is presented in this study. To well simulate the SBI, compressible multi-component two-dimensional Navier-Stokes equations are solved by combining with double-flux model and five-order weighted essentially non-oscillatory scheme. Both the wave system evolution and the interface deformation are clearly illustrated by using the present numerical method. Quantitatively, the length scales of distorted interface, compressibility of helium cylinder, circulation, and total mixing rates of helium are measured and compared to investigate the mixing mechanism and structure effect of the helium cylinder. It is found that the evolution of elliptic interface is closely related to its shape. In the case of elliptic gas cylinder shock-accelerated along major axis, the most remarkable feature is the air jet which grows constantly with time and penetrates the downstream interface boundary, forming two independent vortices. The penetration speed of the air jet is found to increase with ellipse eccentricity increasing. In addition, like the case of the circular helium cylinder, typical free-precursor irregular shock wave refraction occurs when incident shock wave passes through the interface. In the case of shock-accelerated elliptic gas cylinder along minor axis, a distinct flat structure appears due to the shock compression during the evolution of interface, and then vorticity concentrates at the two ends of the ellipses, which finally bends the interface severely. Simple regular shock wave refraction occurs in the large frontal area of the helium cylinder. These features also grow intensely with the eccentricity of the initial elliptic interface increasing. The distinct morphologies of these elliptic interfaces also lead to the different behaviors of the interface features including the length and height. The comprehensive analysis shows that for the elliptic helium cylinder, the structure effect not only affects the interface evolution in a length-scale manner but also plays a role in their mixing process. The mixing rate of helium cylinder shocked along the major axis is significantly superior to that along the minor axis.-
Keywords:
- compressible flow /
- shock-bubble interaction /
- Richtmyer-Meshkov instability /
- mixing
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[2] Meshkov E E 1969 Fluid Dyn. 4 101
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[4] Lindl J D, Amendt P, Berger R L 2004 Phys. Plasmas 11 339
[5] Yang J, Kubota T, Zukoski E E 1993 AIAA J. 31 854
[6] Arnett W D, Bahcall J N, Kirshner R P, Woosley S E 1989 Annu. Rev. Astron. Astrophys. 27 629
[7] Haas J F, Sturtevant B 1987 J. Fluid Mech. 181 41
[8] Jacobs J W 1992 J. Fluid Mech. 234 629
[9] Giordano J, Burtschell Y 2006 Phys. Fluids 18 036102
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[13] Sha S, Chen Z H, Xue D W 2013 Acta Phys. Sin. 62 144701 (in Chinese) [沙莎, 陈志华, 薛大文 2013 物理学报 62 144701]
[14] Sha S, Chen Z H, Zhang Q B 2015 Acta Phys. Sin. 64 015201 (in Chinese) [沙莎, 陈志华, 张庆兵 2015 物理学报 64 015201]
[15] Sha S, Chen Z H, Xue D W, Zhang H 2014 Acta Phys. Sin. 63 085205 (in Chinese) [沙莎, 陈志华, 薛大文, 张辉 2014 物理学报 63 085205]
[16] Bai J S, Zou L Y, Wang T, Liu K, Huang W B, Liu J H, Li P, Tang D W, Liu C L 2010 Phys. Rev. E 82 056318
[17] Liao S F, Zou L Y, Huang X L, Liu J H, Zhang K, Wang Y P 2016 Sci. Sin.: Phys. Mech. Astron. 46 034702 (in Chinese) [廖深飞, 邹立勇, 黄熙龙, 刘金宏, 张珂, 王彦平 2016 中国科学: 物理学 力学 天文学 46 034702]
[18] Zhai Z G, Si T, Zou L Y, Luo X S 2013 Acta Mech. Sin. 29 24
[19] Zhai Z G, Dong P, Luo X S 2017 Chin. J. High Pressure Phys. 31 718 (in Chinese) [翟志刚, 董平, 罗喜胜 2017 高压物理学报 31 718]
[20] Fan M R, Zhai Z G, Si T, Luo X S, Zou L Y, Tan D W 2012 Sci. China: Phys. Mech. Astron. 55 284
[21] Wang M, Si T, Luo X 2015 Shock Waves 25 347
[22] Huang X L, Liao S F, Zou L Y, Liu J H, Cao R Y 2017 Explo. Shock Wave 37 829 (in Chinese) [黄熙龙, 廖深飞, 邹立勇, 刘金宏, 曹仁义 2017 爆炸与冲击 37 829]
[23] Abgrall R, Karni S 2001 J. Comput. Phys. 169 594
[24] Ern A, Giovangigli V 1994 Multicomponent Transport Algorithms (Heidelberg: Springer-Verlag) pp329-389
[25] Kee R J, Coltrin M E, Glarborg P 2003 Chemically Reacting Flow Theory and Practice (Hoboken: John Wiley Sons) pp487-530
[26] Svehla R A 1962 Estimated Viscosities and Thermal Conductivities of Gases at High Temperatures (NASA Technical Report R-132) pp20-24
[27] Spiteri R J, Ruuth S J 2003 Siam J. Numer. Anal. 40 469
[28] Verwer J G, Sommeijer B P, Hundsdorfer W 2004 J. Comput. Phys. 201 61
[29] Houim R W, Kuo K K 2011 J. Comput. Phys. 230 8527
[30] Quirk J J, Karni S 1996 J. Fluid Mech. 318 129
[31] Bagabir A, Drikakis D 2001 Shock Waves 11 209
[32] Zhai Z G, Wang M H, Si T, Luo X S 2014 J. Fluid Mech. 757 800
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[1] Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297
[2] Meshkov E E 1969 Fluid Dyn. 4 101
[3] Lindl J D, Mccrory R L, Campbell E M 1992 Phys. Today 45 32
[4] Lindl J D, Amendt P, Berger R L 2004 Phys. Plasmas 11 339
[5] Yang J, Kubota T, Zukoski E E 1993 AIAA J. 31 854
[6] Arnett W D, Bahcall J N, Kirshner R P, Woosley S E 1989 Annu. Rev. Astron. Astrophys. 27 629
[7] Haas J F, Sturtevant B 1987 J. Fluid Mech. 181 41
[8] Jacobs J W 1992 J. Fluid Mech. 234 629
[9] Giordano J, Burtschell Y 2006 Phys. Fluids 18 036102
[10] Ranjan D, Niederhaus J H J, Oakley J G, Anderson M H, Greenough J A, Bonazza R 2008 Phys. Scripta 132 014020
[11] Tomkins C, Kumar S, Orlicz G, Prestridge K 2008 J. Fluid Mech. 611 131
[12] Shankar S K, Kawai S, Lele S K 2011 Phys. Fluids 23 024102
[13] Sha S, Chen Z H, Xue D W 2013 Acta Phys. Sin. 62 144701 (in Chinese) [沙莎, 陈志华, 薛大文 2013 物理学报 62 144701]
[14] Sha S, Chen Z H, Zhang Q B 2015 Acta Phys. Sin. 64 015201 (in Chinese) [沙莎, 陈志华, 张庆兵 2015 物理学报 64 015201]
[15] Sha S, Chen Z H, Xue D W, Zhang H 2014 Acta Phys. Sin. 63 085205 (in Chinese) [沙莎, 陈志华, 薛大文, 张辉 2014 物理学报 63 085205]
[16] Bai J S, Zou L Y, Wang T, Liu K, Huang W B, Liu J H, Li P, Tang D W, Liu C L 2010 Phys. Rev. E 82 056318
[17] Liao S F, Zou L Y, Huang X L, Liu J H, Zhang K, Wang Y P 2016 Sci. Sin.: Phys. Mech. Astron. 46 034702 (in Chinese) [廖深飞, 邹立勇, 黄熙龙, 刘金宏, 张珂, 王彦平 2016 中国科学: 物理学 力学 天文学 46 034702]
[18] Zhai Z G, Si T, Zou L Y, Luo X S 2013 Acta Mech. Sin. 29 24
[19] Zhai Z G, Dong P, Luo X S 2017 Chin. J. High Pressure Phys. 31 718 (in Chinese) [翟志刚, 董平, 罗喜胜 2017 高压物理学报 31 718]
[20] Fan M R, Zhai Z G, Si T, Luo X S, Zou L Y, Tan D W 2012 Sci. China: Phys. Mech. Astron. 55 284
[21] Wang M, Si T, Luo X 2015 Shock Waves 25 347
[22] Huang X L, Liao S F, Zou L Y, Liu J H, Cao R Y 2017 Explo. Shock Wave 37 829 (in Chinese) [黄熙龙, 廖深飞, 邹立勇, 刘金宏, 曹仁义 2017 爆炸与冲击 37 829]
[23] Abgrall R, Karni S 2001 J. Comput. Phys. 169 594
[24] Ern A, Giovangigli V 1994 Multicomponent Transport Algorithms (Heidelberg: Springer-Verlag) pp329-389
[25] Kee R J, Coltrin M E, Glarborg P 2003 Chemically Reacting Flow Theory and Practice (Hoboken: John Wiley Sons) pp487-530
[26] Svehla R A 1962 Estimated Viscosities and Thermal Conductivities of Gases at High Temperatures (NASA Technical Report R-132) pp20-24
[27] Spiteri R J, Ruuth S J 2003 Siam J. Numer. Anal. 40 469
[28] Verwer J G, Sommeijer B P, Hundsdorfer W 2004 J. Comput. Phys. 201 61
[29] Houim R W, Kuo K K 2011 J. Comput. Phys. 230 8527
[30] Quirk J J, Karni S 1996 J. Fluid Mech. 318 129
[31] Bagabir A, Drikakis D 2001 Shock Waves 11 209
[32] Zhai Z G, Wang M H, Si T, Luo X S 2014 J. Fluid Mech. 757 800
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