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基于大涡模拟, 结合五阶加权基本无振荡格式与沉浸边界法对激波自左向右与R22重气柱作用过程进行了数值模拟. 数值结果清晰地显示了激波诱导Richtmyer-Meshkov不稳定性所导致的重气柱变形过程, 并与Haas 和 Sturtevant 的实验结果符合. 另外, 结果还揭示了入射激波在气柱内右侧边界发生聚焦并诱导射流的过程, 以及在Kelvin-Helmhotz 次不稳定性作用下两个主涡滑移层形成次级涡的过程, 并分析了气柱变形过程中与周围空气的混合机理. 最后, 通过改变反射距离对反射激波与不同变形阶段的气柱的再次作用过程进行了研究. 结果表明: 当激波反射距离较长时, 反射激波与充分变形后的气柱作用, 使其在流向方向上进一步被压缩; 而当激波反射距离较短时, 反射激波会在气柱内发生马赫反射, 两个三波点附近产生两个高压区, 当其传播至气柱左侧边界时对气柱边界造成冲击加速, 诱导两道向左传播的反向射流.
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关键词:
- Richtmyer-Meshkov不稳定性 /
- R22重气柱 /
- 反射激波 /
- 射流
Based on the large eddy simulation, combined with the 5th order weighted essentially non-oscillatory scheme and the immersed boundary method, the shock wave interacting with an R22 cylinder is numerically simulated. Our numerical results present clearly the deformation of cylinder induced by the Richtmyer-Meshkov instability due to the interaction of shock wave with R22 cylinder, which accords well with previous experimental results of Haas and Sturtevant [Haas J F and Sturtevant B 1987 J. Fluid Mech. 181 41]. In addition, the numerical results reveal the generation process of a jet induced by the refracted shock focusing near the right interface of the inner cylinder, as well as the roll-up of the secondary vortexes along the slip layer of two main vortexes. The mixing mechanism of R22 gas and air is also expatiated. Furthermore, the evolution of R22 cylinder under reshock condition is numerically simulated with two different end wall distances. For the long distance case, the reflected wave interacts with severely distorted R22 volume, making it further compressed on the x-axis. While for the small case, two Mach reflections occur between the reflected shocks during their propagating upstream within the cylinder. The two high pressure areas behind two triple points can accelerate the boundary of the R22 cylinder while they are passing through it and induce two jets.-
Keywords:
- Richtmyer-Meshkov instability /
- R22 cylinder /
- reshock /
- jet
[1] Sha S, Chen Z H, Zhang H H, Jiang X H 2012 Acta Phys. Sin. 61 064702 (in Chinese) [沙莎, 陈志华, 张焕好, 姜孝海 2012 物理学报 61 064702]
[2] Marble F E, Hendrics G J, Zukoski E E 1987 American Insititute of Aeronautics and Astronautics US, AIAA 87 1880
[3] Oran E S, Gamezo V N 2007 Combust Flame 148 4
[4] Lindl J D, McCrory R L, Campbell E M 1992 Phys. Today 45 32
[5] Markstein G H 1957 J. Aerosol. Sci. 24 238
[6] Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297
[7] Meshkov E E 1969 Fluid Dyn. 4 101
[8] Haas J F, Sturtevant B 1987 J. Fluid Mech. 181 41
[9] Tomkins C, Kumar S, Orlicz G, Prestridge K 2008 J. Fluid Mech. 611 131
[10] Shankar S K, Kawai S, Lele S K 2011 Phys. Fluids 23 024102
[11] Zou L Y, Liu C L, Tan D W, Huang W B, Luo X S 2010 J. Vis. 13 347
[12] Fan M R, Zhai Z G, Si T, Luo X S, Zou L Y, Tan D W 2012 Phys. Mech. Astron. 55 284
[13] Zhai Z G, Si T, Luo X S, Yang J M 2011 Phys. Fluids 23 084104
[14] Wang X S, Si T, Luo X S, Yang J M 2012 Chin. J. Theor. Appl. Mech. 44 664 (in Chinese) [王显圣, 司廷, 罗喜胜, 杨基明 2012 力学学报 44 664]
[15] Fu D X, Ma Y W, Li X L 2008 Chin. Phys. Lett. 25 188
[16] Ma Y W, Tian B L, Fu D X 2004 Chin. Phys. Lett. 21 1770
[17] Tan D W, Zhang X 2009 Chin. Phys. Lett. 26 084703
[18] Tao Y S, Wang L F, Ye W H 2012 Acta Phys. Sin. 61 075207 (in Chinese) [陶烨晟, 王立锋, 叶文华 2012 物理学报 61 075207]
[19] Liu X D, Osher S, Chan T 1994 J. Computat. Phys. 115 200
[20] Jiang G, Shu C W 1996 J. Computat. Phys. 126 202
[21] Charendon S 1961 Hydrodynamic and Hydromagnetic Stability (Oxford: Clarendon press) p481
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[1] Sha S, Chen Z H, Zhang H H, Jiang X H 2012 Acta Phys. Sin. 61 064702 (in Chinese) [沙莎, 陈志华, 张焕好, 姜孝海 2012 物理学报 61 064702]
[2] Marble F E, Hendrics G J, Zukoski E E 1987 American Insititute of Aeronautics and Astronautics US, AIAA 87 1880
[3] Oran E S, Gamezo V N 2007 Combust Flame 148 4
[4] Lindl J D, McCrory R L, Campbell E M 1992 Phys. Today 45 32
[5] Markstein G H 1957 J. Aerosol. Sci. 24 238
[6] Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297
[7] Meshkov E E 1969 Fluid Dyn. 4 101
[8] Haas J F, Sturtevant B 1987 J. Fluid Mech. 181 41
[9] Tomkins C, Kumar S, Orlicz G, Prestridge K 2008 J. Fluid Mech. 611 131
[10] Shankar S K, Kawai S, Lele S K 2011 Phys. Fluids 23 024102
[11] Zou L Y, Liu C L, Tan D W, Huang W B, Luo X S 2010 J. Vis. 13 347
[12] Fan M R, Zhai Z G, Si T, Luo X S, Zou L Y, Tan D W 2012 Phys. Mech. Astron. 55 284
[13] Zhai Z G, Si T, Luo X S, Yang J M 2011 Phys. Fluids 23 084104
[14] Wang X S, Si T, Luo X S, Yang J M 2012 Chin. J. Theor. Appl. Mech. 44 664 (in Chinese) [王显圣, 司廷, 罗喜胜, 杨基明 2012 力学学报 44 664]
[15] Fu D X, Ma Y W, Li X L 2008 Chin. Phys. Lett. 25 188
[16] Ma Y W, Tian B L, Fu D X 2004 Chin. Phys. Lett. 21 1770
[17] Tan D W, Zhang X 2009 Chin. Phys. Lett. 26 084703
[18] Tao Y S, Wang L F, Ye W H 2012 Acta Phys. Sin. 61 075207 (in Chinese) [陶烨晟, 王立锋, 叶文华 2012 物理学报 61 075207]
[19] Liu X D, Osher S, Chan T 1994 J. Computat. Phys. 115 200
[20] Jiang G, Shu C W 1996 J. Computat. Phys. 126 202
[21] Charendon S 1961 Hydrodynamic and Hydromagnetic Stability (Oxford: Clarendon press) p481
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