激波诱导的多层流体界面上的Richtmyer-Meshkov不稳定现象的实验研究
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摘要
两种不同密度的流体界面经激波瞬间加速后,获得一个有限的速度,界面原有的微小初始扰动得到发展放大,最终导致两种互不相溶的流体强烈混合的现象称为Richtmyer-Meshkov(RM)不稳定性。它在惯性约束热核聚变(ICF)、超新星动力学等领域都有着广泛的应用背景和重要的研究价值。本文应用矩形激波管与高速摄影仪对多相流体界面进行了实验研究。
本文实验在竖直的矩形激波管中进行,激波通过高压气体(氮气和氦气)击破不同厚度的铝膜获得,激波方向自上而下。实验中采用了两种多层流体界面,分别为“空气-硅油-水”界面和“空气-酒精-硅油”界面,实现了Atwood数在同一实验中从0到1的跨越。硅油与酒精分别用140蓝的乙酸乙酯溶液和蓝墨水进行染色,以期在用高速摄影仪拍摄时观察到清楚的界面。
本文在各种不同工况下进行实验后得出以下结论:高粘度流体会对界面发展起到阻碍作用,从而使得RM不稳定性后期的湍流混合现象无法或者推迟产生;Atwood数较小的界面比Atwood数较大的界面优先得到发展;本文实验中观察到的尖钉都为单模态结构,不同波长的气泡增长速度相近,没有出现大气泡吞并小气泡的现象;硅油层厚度也是影响RM不稳定性发展的因素之一,对于4~5mm厚度的油层,出现了失稳后油层与水介质分离、并被气流撕断的现象;当Atwood数为1时,气泡深度与时间的1次方成正比,当Atwood数为0时,气泡深度与时间的2次方成正比,尖钉高度与时间的1次方成正比,混合区宽度增长与时间成线性关系;当激波作用方向与粘度梯度方向(小—大)一致时,混合更加强烈。此外,本文还单独比较了“空气-硅油”界面与“空气-水”界面的RM不稳定性现象。
When two fluid interfaces with different Density were instantaneous accelerated by shock wave, they will get a limited speed, in the course of this a small initial disturbance will get developed and enlarged which will lead to Richtmyer-Meshkov (RM) instabilityin the end, that is a strong mixing phenomenon caused by two totally immiscible fluids. It has widely application background and important research value for Inertial confinement thermonuclear fusion (ICF), Supernova dynamics and so on. This article try to do research on Multiphase fluid interface through Rectangular shock tube and High Speed Photography
The experiment mentioned in text will be organized inside Rectangular shock tube, shock wave will be gained through impact from High-pressure gas to aluminum film and it has a top-down direction. Two Multiphase fluid interface are used in the experiment which are“air- Silicone oil-water”and“air-alcohol-silicone oil”, so that the Atwood-Number realized in the same experiment from 0 to 1. silicone oil and alcohol are colored with Ethyl acetate solution with No.140 blue and blue ink, in order to get clear interface by High-speed photography.
The following conclusions can be made: High-viscosity liquids will block the development of interface, so that the phenomenon of turbulent mixing of RM is not going to appear or it will be delayed; the interface with smaller Atwood-No. will have a priority by development compared with interface with bigger Atwood-No.The spike which has been observed is Single-mode structure, the bubble with different wavelength have similar growing speed, and there are no annex from bigger bubbles to the smaller. The thickness of the silicone-oil is also one of the factors which will influence the unstable development of RM. For oil interface which has thickness between 4-5mm will separate from water media and could be mangled by airflow when it is unstable.If the Atwood-No. is 1, the depth of bubble is in direct ratio to the time, if Atwood-No. is 0, the depth of bubble is in direct ratio to the quadric of time, and the height of spike is in direct ratio of time, and there is a linear relationship between Mixing zone width and time; the mixture goes more fiercely when function direction of shock wave consistent with the Gradient direction of the Viscosity. Besides this text has compared the unstable RM phenomenon between“air-silicone oil”and“air-water”.
本文实验在竖直的矩形激波管中进行,激波通过高压气体(氮气和氦气)击破不同厚度的铝膜获得,激波方向自上而下。实验中采用了两种多层流体界面,分别为“空气-硅油-水”界面和“空气-酒精-硅油”界面,实现了Atwood数在同一实验中从0到1的跨越。硅油与酒精分别用140蓝的乙酸乙酯溶液和蓝墨水进行染色,以期在用高速摄影仪拍摄时观察到清楚的界面。
本文在各种不同工况下进行实验后得出以下结论:高粘度流体会对界面发展起到阻碍作用,从而使得RM不稳定性后期的湍流混合现象无法或者推迟产生;Atwood数较小的界面比Atwood数较大的界面优先得到发展;本文实验中观察到的尖钉都为单模态结构,不同波长的气泡增长速度相近,没有出现大气泡吞并小气泡的现象;硅油层厚度也是影响RM不稳定性发展的因素之一,对于4~5mm厚度的油层,出现了失稳后油层与水介质分离、并被气流撕断的现象;当Atwood数为1时,气泡深度与时间的1次方成正比,当Atwood数为0时,气泡深度与时间的2次方成正比,尖钉高度与时间的1次方成正比,混合区宽度增长与时间成线性关系;当激波作用方向与粘度梯度方向(小—大)一致时,混合更加强烈。此外,本文还单独比较了“空气-硅油”界面与“空气-水”界面的RM不稳定性现象。
When two fluid interfaces with different Density were instantaneous accelerated by shock wave, they will get a limited speed, in the course of this a small initial disturbance will get developed and enlarged which will lead to Richtmyer-Meshkov (RM) instabilityin the end, that is a strong mixing phenomenon caused by two totally immiscible fluids. It has widely application background and important research value for Inertial confinement thermonuclear fusion (ICF), Supernova dynamics and so on. This article try to do research on Multiphase fluid interface through Rectangular shock tube and High Speed Photography
The experiment mentioned in text will be organized inside Rectangular shock tube, shock wave will be gained through impact from High-pressure gas to aluminum film and it has a top-down direction. Two Multiphase fluid interface are used in the experiment which are“air- Silicone oil-water”and“air-alcohol-silicone oil”, so that the Atwood-Number realized in the same experiment from 0 to 1. silicone oil and alcohol are colored with Ethyl acetate solution with No.140 blue and blue ink, in order to get clear interface by High-speed photography.
The following conclusions can be made: High-viscosity liquids will block the development of interface, so that the phenomenon of turbulent mixing of RM is not going to appear or it will be delayed; the interface with smaller Atwood-No. will have a priority by development compared with interface with bigger Atwood-No.The spike which has been observed is Single-mode structure, the bubble with different wavelength have similar growing speed, and there are no annex from bigger bubbles to the smaller. The thickness of the silicone-oil is also one of the factors which will influence the unstable development of RM. For oil interface which has thickness between 4-5mm will separate from water media and could be mangled by airflow when it is unstable.If the Atwood-No. is 1, the depth of bubble is in direct ratio to the time, if Atwood-No. is 0, the depth of bubble is in direct ratio to the quadric of time, and the height of spike is in direct ratio of time, and there is a linear relationship between Mixing zone width and time; the mixture goes more fiercely when function direction of shock wave consistent with the Gradient direction of the Viscosity. Besides this text has compared the unstable RM phenomenon between“air-silicone oil”and“air-water”.
引文
[1] Richtmyer RD.Taylor instability in shock acceleration of compressible fluids [J]. Commun Pure Appl Math, 1960, 13:297-3l9
[2] Meshkov EE.Instability of the interface of two gases accelerated by a shock wave[J].Fluid Dynamics, 1969, 4: 101-104
[3] Sharp D H.An Overview of Rayleigh—Taylor Instability.Physica D,1984,12:3-12.
[4] Lindl JD, McCrory RL, Campbell EM. Progress toward ignition and burn Propagation in inertial confinement fusion [J]. Phys. Fluids, 1992, 45:32-40
[5] Anderson M H ,Puranik B P,Oakley J G,et a1.Shock Tube Investigation of Hydrodynamic Issues Related to Inertial Confinement Fusion[J].Shock Waves,2000,1 3:377-387.
[6] Zhou Y, Remington BA, Robey HF et al, Progress in understanding turbulent mixing induced by Rayleigh-Taylor and Richtmyer-Meshkov instabilities[J], Phys. Plasmas, 2003,10:1883-1896
[7] R.H. Cohen, W.P.Dannevik, A .M. Dimits, D.E.Eliason, A.A. Mirin and Y Zhou, Three-dimensional simulation of a Richtmyer-Meshkov instability with a two-scale initial perturbation[J], Phys.Fluids,2003,14:3692-3709
[8] Zhang Q, Sohn S-I, An analytical nonlinear theory of Richtmyer-Meshkov Instability [J], Phys. Rev.Lett. A 1996, 212:149-155
[9] Velikovich AL, Domonte G, Nonlinear perturbation theory of the incompressible Richtmyer-Meshkov instability[J], Phys. Rev.Lett,1996, 76, 3 :112-3115
[10] Sadot O, Erez L, Alon U, et al. Study of nonlinear evolution of single-mode and two-bubble interaction under Richtmyer-Meshkov instability[J], Phys. Rev.Lett.,1998, 80:1654-1657
[11] Barenblatt GI. Self-similar turbulence propagation from an instantaneous plane source [J]. Nonlinear Dynamics and Turbulence, ed.GI Barenblatt,GIooss, DDJoseph, 1983, pp. 48-60. Boston: Pitman
[12] Mikaelian KO. Turbulent mixing generated by Rayleigh-Taylor and Richtmyer-Meshkov instabilities [J]. Physica D. 1989.36:343-357
[13] Alon U, Hecht J, Ofer D, Shvarts D. Power laws and similarity of Rayleigh-Taylor and Richtmyer-Meshkov mixing fronts at all density ratios[J]. Phys. Rev. Lett. 1995.74:534-537
[14] K.A. Meyer, P.J. Blewet, Numerical investigation of the stability of a shock-accelerated interface between two fluids[J], Phys. Fluids,1972,15:7-53
[15] L.D.Cloutman and M.F. Weimer, Numerical simulation of Richtmyer-Meshkov Instabilities[J], Phys. Fluid A, 1993, 4:18-21
[16] Richard L. Holmes, John W. Grove and David H. Sharp, Numerical investigation of Richtmyre-Meshkov instability using front tracking [J]. Fluid Mech., 1995, 301:51
[17] R .L. Holmes, G Dimonte, B .Fryxell, M.L. Gittings, D.H. Sharp, M .S chnerder, R.P. Weaver and Q .Zhang, Richtmyer-Meshkov instability growth: experiment, simulation and theory [J]. Fluid Mech., 1999, 389:95
[18] Zhang Q, A numerical study of Richtmyre-Meshkov instability driven by Cylindrical shocks [J], Phys. Fluids, 1998, 10:74-92.
[19] SNEZHANA I. ABARZHI, NON-LINEAR DYNAMICS OF THE RICHTM–MESHKOVINSTABILITY IN SUPERNOVAE[J],Astrophysics and space science,2005,298:379-383.
[20]田保林.Richtmyer-Meshkov的数值模拟及其特征分析[D].中国科学院力学研究所,2004.
[21]程军波,唐维军.利用Ghost Fluid方法模拟与柱形界面的相互作用[J].计算物理,2003,20(3):219-225.
[22] Benjamin RF, Experimental observations of shock stability and shock-induced turbulence, In Advances in Compressible Turbulent Mixing[J], 1992, ed. WP Dannevik, AC Buckingham, CE Leith, pp.341-48.Springfield. VA: Natl. Tech. Inf Serv.
[23] Erez L, Sadot O, Oron D, Erez G, Levin LA, et al. Study of membrane effecton turbulent mixing measurements in shock tubes [J]. Shock Waves,2000, 10:241–251
[24] Brouillette M, Experiments on the Richtmyer-Meshkov instability: single-scale perturbations on a continuous interface [J].Fluid Mech., 1994, 263:271
[25] Jones MA, Jacobs JW. A membrane less experiment for the study of Richtmyer-Meshkov instability of a shock-accelerated gas interface [J]. Phys. Fluids .1997.9:3078-3085
[26] Jacobs JW, Collins BD. Experimental study of the Richtmyer-Meshkov study of a diffuse interface [J]. Proc. Intl. Symp. Shock Waves, 22nd 2000, pp: 79-84.London: Imperial College
[27] R.Aure and J.W.Jacobs. Particle image velocimetry study of shock-inducedsingle mode Richtmyer-Meshkov instability[J]. Shock Waves,2009, 18:1205-1210
[28] V.V. Krivets, C.C. Long. Shock tube experiments and numerical simulation of the single mode three-dimensional Richtmyer-Meshkov instability [J]. Shock Waves,2009,18:1205-1210
[29] G. Fontaine, C. Mariani. An attempt to reduce the membrane effectsin Richtmyer– Meshkov instability shock tube experiments[J].Shock Waves,2009,19:285-289
[30] Farley D R, Logory LM. Single-mode nonlinear mix experiments at high Mach number using Nova. AP [J].Suppl.2000, 127:311-316
[31] Sasoh, K.Mori and T. Ohtani. Richtmyer-Meshkov instability in laser plasma-shock wave interaction[J].Shock Waves.2009,18:1199-1203
[32] M. Vetter, B. Sturtevant. Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface[J].Shock Waves, 1995, 4:247-252
[33] L. Houas, E.E. Meshkov. Overview of diagnostic methods used in shock-tube investigationsof mixing induced by Richtmyer-Meshkov instability[J]. Shock Waves, 1999, 9:249-257
[34]施红辉、岸本薰实,瞬态加速液柱时的流体力学问题的研究[J].爆炸与冲击,2003,23(5): 391-397
[35]施红辉、卓启威,Richtmyer-Meshkov不稳定性流体混合区发展的实验研究[J].力学学报,2007,29(3):417-421
[36]卓启威、施红辉,气液界面上Richtmyer-Meshkov不稳定性的实验研究[J].实验流体力学,2007,21(1):25-30
[37] Shi H H, Zhang G, Du K, Jia H X, Experimental Study of the Mechanism of Richtmyer-Meshkov Instability at a Gas/Liquid Interface[J], Journal of Hydrodynamics Ser. B, 2009, 21(3): 423-428.
[38]黄甲,贾洪印,罗喜胜,激波与氦气泡相互作用的实验与数值研究[J].实验流体力学,2010,24(2):10-14
[39]邹立勇、刘金洪,一个用于界面不稳定性实验研究的竖直激波管[J],高压物理学报,2008,22(2):197-201
[40]张鸣远,景思睿,李国君.高等工程流体力学[M].西安交通大学出版社. 2006
[41]王继海,二维非定常流和激波[M].北京:科学出版社,1994
[42] Zhou Y. A scaling analysis of turbulent flows driven by Rayleigh-Taylor and Richtmyer-Meshkov instabilities[J].Phys Fluids,2001.13(2):538—543
[43] Ramshaw JD. 1998. Simple model for linear and nonlinear mixing at unstable fluid interfaces with variable acceleration. Phys. Rev.E 58:5834–40
[2] Meshkov EE.Instability of the interface of two gases accelerated by a shock wave[J].Fluid Dynamics, 1969, 4: 101-104
[3] Sharp D H.An Overview of Rayleigh—Taylor Instability.Physica D,1984,12:3-12.
[4] Lindl JD, McCrory RL, Campbell EM. Progress toward ignition and burn Propagation in inertial confinement fusion [J]. Phys. Fluids, 1992, 45:32-40
[5] Anderson M H ,Puranik B P,Oakley J G,et a1.Shock Tube Investigation of Hydrodynamic Issues Related to Inertial Confinement Fusion[J].Shock Waves,2000,1 3:377-387.
[6] Zhou Y, Remington BA, Robey HF et al, Progress in understanding turbulent mixing induced by Rayleigh-Taylor and Richtmyer-Meshkov instabilities[J], Phys. Plasmas, 2003,10:1883-1896
[7] R.H. Cohen, W.P.Dannevik, A .M. Dimits, D.E.Eliason, A.A. Mirin and Y Zhou, Three-dimensional simulation of a Richtmyer-Meshkov instability with a two-scale initial perturbation[J], Phys.Fluids,2003,14:3692-3709
[8] Zhang Q, Sohn S-I, An analytical nonlinear theory of Richtmyer-Meshkov Instability [J], Phys. Rev.Lett. A 1996, 212:149-155
[9] Velikovich AL, Domonte G, Nonlinear perturbation theory of the incompressible Richtmyer-Meshkov instability[J], Phys. Rev.Lett,1996, 76, 3 :112-3115
[10] Sadot O, Erez L, Alon U, et al. Study of nonlinear evolution of single-mode and two-bubble interaction under Richtmyer-Meshkov instability[J], Phys. Rev.Lett.,1998, 80:1654-1657
[11] Barenblatt GI. Self-similar turbulence propagation from an instantaneous plane source [J]. Nonlinear Dynamics and Turbulence, ed.GI Barenblatt,GIooss, DDJoseph, 1983, pp. 48-60. Boston: Pitman
[12] Mikaelian KO. Turbulent mixing generated by Rayleigh-Taylor and Richtmyer-Meshkov instabilities [J]. Physica D. 1989.36:343-357
[13] Alon U, Hecht J, Ofer D, Shvarts D. Power laws and similarity of Rayleigh-Taylor and Richtmyer-Meshkov mixing fronts at all density ratios[J]. Phys. Rev. Lett. 1995.74:534-537
[14] K.A. Meyer, P.J. Blewet, Numerical investigation of the stability of a shock-accelerated interface between two fluids[J], Phys. Fluids,1972,15:7-53
[15] L.D.Cloutman and M.F. Weimer, Numerical simulation of Richtmyer-Meshkov Instabilities[J], Phys. Fluid A, 1993, 4:18-21
[16] Richard L. Holmes, John W. Grove and David H. Sharp, Numerical investigation of Richtmyre-Meshkov instability using front tracking [J]. Fluid Mech., 1995, 301:51
[17] R .L. Holmes, G Dimonte, B .Fryxell, M.L. Gittings, D.H. Sharp, M .S chnerder, R.P. Weaver and Q .Zhang, Richtmyer-Meshkov instability growth: experiment, simulation and theory [J]. Fluid Mech., 1999, 389:95
[18] Zhang Q, A numerical study of Richtmyre-Meshkov instability driven by Cylindrical shocks [J], Phys. Fluids, 1998, 10:74-92.
[19] SNEZHANA I. ABARZHI, NON-LINEAR DYNAMICS OF THE RICHTM–MESHKOVINSTABILITY IN SUPERNOVAE[J],Astrophysics and space science,2005,298:379-383.
[20]田保林.Richtmyer-Meshkov的数值模拟及其特征分析[D].中国科学院力学研究所,2004.
[21]程军波,唐维军.利用Ghost Fluid方法模拟与柱形界面的相互作用[J].计算物理,2003,20(3):219-225.
[22] Benjamin RF, Experimental observations of shock stability and shock-induced turbulence, In Advances in Compressible Turbulent Mixing[J], 1992, ed. WP Dannevik, AC Buckingham, CE Leith, pp.341-48.Springfield. VA: Natl. Tech. Inf Serv.
[23] Erez L, Sadot O, Oron D, Erez G, Levin LA, et al. Study of membrane effecton turbulent mixing measurements in shock tubes [J]. Shock Waves,2000, 10:241–251
[24] Brouillette M, Experiments on the Richtmyer-Meshkov instability: single-scale perturbations on a continuous interface [J].Fluid Mech., 1994, 263:271
[25] Jones MA, Jacobs JW. A membrane less experiment for the study of Richtmyer-Meshkov instability of a shock-accelerated gas interface [J]. Phys. Fluids .1997.9:3078-3085
[26] Jacobs JW, Collins BD. Experimental study of the Richtmyer-Meshkov study of a diffuse interface [J]. Proc. Intl. Symp. Shock Waves, 22nd 2000, pp: 79-84.London: Imperial College
[27] R.Aure and J.W.Jacobs. Particle image velocimetry study of shock-inducedsingle mode Richtmyer-Meshkov instability[J]. Shock Waves,2009, 18:1205-1210
[28] V.V. Krivets, C.C. Long. Shock tube experiments and numerical simulation of the single mode three-dimensional Richtmyer-Meshkov instability [J]. Shock Waves,2009,18:1205-1210
[29] G. Fontaine, C. Mariani. An attempt to reduce the membrane effectsin Richtmyer– Meshkov instability shock tube experiments[J].Shock Waves,2009,19:285-289
[30] Farley D R, Logory LM. Single-mode nonlinear mix experiments at high Mach number using Nova. AP [J].Suppl.2000, 127:311-316
[31] Sasoh, K.Mori and T. Ohtani. Richtmyer-Meshkov instability in laser plasma-shock wave interaction[J].Shock Waves.2009,18:1199-1203
[32] M. Vetter, B. Sturtevant. Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface[J].Shock Waves, 1995, 4:247-252
[33] L. Houas, E.E. Meshkov. Overview of diagnostic methods used in shock-tube investigationsof mixing induced by Richtmyer-Meshkov instability[J]. Shock Waves, 1999, 9:249-257
[34]施红辉、岸本薰实,瞬态加速液柱时的流体力学问题的研究[J].爆炸与冲击,2003,23(5): 391-397
[35]施红辉、卓启威,Richtmyer-Meshkov不稳定性流体混合区发展的实验研究[J].力学学报,2007,29(3):417-421
[36]卓启威、施红辉,气液界面上Richtmyer-Meshkov不稳定性的实验研究[J].实验流体力学,2007,21(1):25-30
[37] Shi H H, Zhang G, Du K, Jia H X, Experimental Study of the Mechanism of Richtmyer-Meshkov Instability at a Gas/Liquid Interface[J], Journal of Hydrodynamics Ser. B, 2009, 21(3): 423-428.
[38]黄甲,贾洪印,罗喜胜,激波与氦气泡相互作用的实验与数值研究[J].实验流体力学,2010,24(2):10-14
[39]邹立勇、刘金洪,一个用于界面不稳定性实验研究的竖直激波管[J],高压物理学报,2008,22(2):197-201
[40]张鸣远,景思睿,李国君.高等工程流体力学[M].西安交通大学出版社. 2006
[41]王继海,二维非定常流和激波[M].北京:科学出版社,1994
[42] Zhou Y. A scaling analysis of turbulent flows driven by Rayleigh-Taylor and Richtmyer-Meshkov instabilities[J].Phys Fluids,2001.13(2):538—543
[43] Ramshaw JD. 1998. Simple model for linear and nonlinear mixing at unstable fluid interfaces with variable acceleration. Phys. Rev.E 58:5834–40