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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.
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Keywords:
- Richtmyer-Meshkov instability /
- V shaped interface /
- vortex/wall interaction /
- turbulent mixing
[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 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 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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[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 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 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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