Richtmyer-Meshkov不稳定性扰动增长率冲击模型的微尺度效应
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摘要
本文通过考虑流体介质输运性质对激波理论的影响,针对微型激波管中的RichtmyerMeshkov(RM)不稳定性,分析了微尺度效应对三种冲击模型扰动增长率的影响。一维气体动力学计算结果表明:流动尺度对于Richtmyer模型、Meyer-Blewett(M-B)模型和Vandenboomgaerde-Mügler-Gauthier(V-M-G)模型中的线性扰动增长率有显著影响。当流动尺度由宏观状态逐渐减小至微尺度时,三种模型的扰动增长率均会经历从少量增长到明显下降,然后迅速上升的过程。微尺度条件下,V-M-G模型的扰动增长率相比宏观尺度有显著提高。与其他两种模型相比,修正后的V-M-G模型更合理地描述了微尺度效应对于线性扰动增长率的影响。此外,对于修正后的V-M-G模型,当入射激波马赫数较低时,扰动增长率受微尺度效应的影响更为明显。
In this paper,taking into account the effect of fluid transport properties on shock wave theory,the influence of microscale effect on perturbation growth rate of three impulsive models is analyzed in view of Richtmyer-Meshkov instability in micro shock tube.Results of one dimensional gas dynamics calculation show that the flow scale has a significant influence on the linear growth rate of the perturbation in the Richtmyer model,the Meyer-Blewett(M-B) model and the Vandenboomgaerde-Mügler-Gauthier(V-M-G)model.As the flow scales decrease from macroscale to microscale,the amplitude growth rates of these three models will undergo a process of littile growth,evident decrease and rapid increase.Compared with the situation in macroscale,there has been a notable rise in the amplitude growth rate of V-M-G model in microscale.By contrast,this fixed model describes the effect of microscale on linear amplitude growth rate of Richtmyer-Meshkov instability more reasonably.In addition,as the Mach number of the incident shock is smaller,the influence of the microscale on the amplitude growth rate is more remarkable in the fixed V-M-G model.
In this paper,taking into account the effect of fluid transport properties on shock wave theory,the influence of microscale effect on perturbation growth rate of three impulsive models is analyzed in view of Richtmyer-Meshkov instability in micro shock tube.Results of one dimensional gas dynamics calculation show that the flow scale has a significant influence on the linear growth rate of the perturbation in the Richtmyer model,the Meyer-Blewett(M-B) model and the Vandenboomgaerde-Mügler-Gauthier(V-M-G)model.As the flow scales decrease from macroscale to microscale,the amplitude growth rates of these three models will undergo a process of littile growth,evident decrease and rapid increase.Compared with the situation in macroscale,there has been a notable rise in the amplitude growth rate of V-M-G model in microscale.By contrast,this fixed model describes the effect of microscale on linear amplitude growth rate of Richtmyer-Meshkov instability more reasonably.In addition,as the Mach number of the incident shock is smaller,the influence of the microscale on the amplitude growth rate is more remarkable in the fixed V-M-G model.
引文
[1] Richtmyer R D.Taylor instability in shock acceleration of compressible fluids[J].Commun Pure Appl Math,1960,13(2):297-319.
[2] Meshkov E E.Instability of the interface of two gases accelerated by a shock wave[J].Fluid Dyn,1969,4(5):101-104.
[3] Lindl J,Landen O,Edwards J,et al.Review of the national ignition campaign 2009-2012[J].Phys Plasmas,2014,21:020501.
[4] Klein R I,Budil K S,Perry T S,et al.Interaction of supernova remnants with interstellar clouds:from the NOVA laser to the galaxy[J].Astrophys J Suppl,2000,127:379-383.
[5] Yang J,Kubota T,Zukoski E E,et al.A model for characterization of a vortex pair formed by shock passage over a light-gas inhomogeneity[J].J Fluid Mech,1994,258:217-244.
[6] Meyer K A,Blewett P J.Numerical investigation of the stability of a shock-accelerated interface between two fluids[J].Phys Fluids,1972,15:753-759.
[7] Vandenboomgaerde M,Mügler C,Gauthier S,et al.Impulsive model for the Richtmyer-Meshkov instability[J].Phys Rev E,1998,58(2):1874-1882.
[8] Holmes R L,Dimonte G,Fryxell B,et al.Richtmyer-Meshkov instability growth:experiment,simulation and theory[J].J Fluid Mech,1999,389:55-79.
[9] Zou Liyong,Liu Jinhong,Liao Shenfei,et al.Richtmyer-Meshkov instability of a flat interface subjected to a rippled shock wave[J].Phys Rev E,2017,95:013107.
[10] Fraley G.Rayleigh-Taylor stability for a normal shock wave-density discontinuity interaction[J].Phys Fluids,1986,29:376-386.
[11] Yang Yumin,Zhang Qiang,Sharp D H.Small amplitude theory of Richtmyer-Meshkov instability[J].Phys Fluids,1994,6:1856-1873.
[12] Goncharov V N.Analytical model of nonlinear,single-mode,classical Rayleigh-Taylor instability at arbitrary Atwood numbers[J].Phys Rev Lett,2002,88(13):134502.
[13] Mikaelian K O.Reshocks,rarefactions,and the generalized Layzer model for hydrodynamic instabilities[J].Phys Fluids,2009,21:024103.
[14] Sohn S I.Simple potential-flow model of Rayleigh-Taylor and Richtmyer-Meshkov instabilities for all density ratios[J].Phys Rev E,2003,67:026301.
[15] Zhang Qiang,Sohn S I.Nonlinear theory of unstable fluid mixing driven by shock wave[J].Phys Fluids,1997,9:1106-1124.
[16] Zhang Qiang.Analytical solutions of Layzer-type approach to unstable interfacial fluid mixing[J].Phys Rev Lett,1998,81(16):3391-3394.
[17] Zhang Qiang,Guo Wenxuan.Universality of finger growth in two-dimensional Rayleigh-Taylor and RichtmyerMeshkov instabilities with all density ratios[J].J Fluid Mech,2016,786:47-61.
[18] Busquet M,Barroso P,Melse T,et al.Miniature shock tube for laser driven shocks[J].Rev Sci Instrum,2010,81:023502.
[19] Mirshekari G,Brouillette M.Microscale shock tube[J].J Microelectromech Syst,2012,21(3):739-748.
[20] Mirshekari G,Brouillette M,Giordano J,et al.Shock waves in microchannels[J].J Fluid Mech,2013,724:259-283.
[21] Brouillette M.Shock waves at microscales[J].Shock waves,2003,13:3-12.
[22]童秉纲,孔祥言,邓国华.气体动力学(2版)[M].北京:高等教育出版社,2012:292-306(TONG Binggang,KONG Xiangyan,DENG Guohua.Gas dynamics(Second Edition)[M].Beijing:High Education Press,2012:292-306(in Chinese))
[23]Udagawa S,Garen W,Meyerer B,et al.Interferometric detection of dispersed shock waves in small scale diaphragm-less shock tube of 1mm diameter[C].Gold Coast,Springer,2007:201-210.
[24] Carlès P,Popinet S.Viscous nonlinear theory of Richtmyer-Meshkov instability[J].Phys Fluids,2001,13:1833-1836.
[25] Sohn S I.Effects of surface tension and viscosity on the growth rates of Rayleigh-Taylor and Richtmyer-Meshkov instabilities[J].Phys Rev E,2009,80:055302(R).
[26] Mikaelian K O.Shock-induced interface instability in viscous fluids and metals[J].Phys Rev E,2013,87:031003(R).
[27] Mirshekari G,Brouillette M.One-dimensional model for microscale shock tube flow[J].Shock Waves,2009,19:25-38.
[28] Parisse J D,Giordano J,Perrier P,et al.Numerical investigation of micro shock waves generation[J].Microfluid Nanofluid,2009,6:699-709.
[29] Zeitoun D E,Burtschell Y.Navier-Stokes computations in micro shock tubes[J].Shock Waves,2006,15:241-246.
[2] Meshkov E E.Instability of the interface of two gases accelerated by a shock wave[J].Fluid Dyn,1969,4(5):101-104.
[3] Lindl J,Landen O,Edwards J,et al.Review of the national ignition campaign 2009-2012[J].Phys Plasmas,2014,21:020501.
[4] Klein R I,Budil K S,Perry T S,et al.Interaction of supernova remnants with interstellar clouds:from the NOVA laser to the galaxy[J].Astrophys J Suppl,2000,127:379-383.
[5] Yang J,Kubota T,Zukoski E E,et al.A model for characterization of a vortex pair formed by shock passage over a light-gas inhomogeneity[J].J Fluid Mech,1994,258:217-244.
[6] Meyer K A,Blewett P J.Numerical investigation of the stability of a shock-accelerated interface between two fluids[J].Phys Fluids,1972,15:753-759.
[7] Vandenboomgaerde M,Mügler C,Gauthier S,et al.Impulsive model for the Richtmyer-Meshkov instability[J].Phys Rev E,1998,58(2):1874-1882.
[8] Holmes R L,Dimonte G,Fryxell B,et al.Richtmyer-Meshkov instability growth:experiment,simulation and theory[J].J Fluid Mech,1999,389:55-79.
[9] Zou Liyong,Liu Jinhong,Liao Shenfei,et al.Richtmyer-Meshkov instability of a flat interface subjected to a rippled shock wave[J].Phys Rev E,2017,95:013107.
[10] Fraley G.Rayleigh-Taylor stability for a normal shock wave-density discontinuity interaction[J].Phys Fluids,1986,29:376-386.
[11] Yang Yumin,Zhang Qiang,Sharp D H.Small amplitude theory of Richtmyer-Meshkov instability[J].Phys Fluids,1994,6:1856-1873.
[12] Goncharov V N.Analytical model of nonlinear,single-mode,classical Rayleigh-Taylor instability at arbitrary Atwood numbers[J].Phys Rev Lett,2002,88(13):134502.
[13] Mikaelian K O.Reshocks,rarefactions,and the generalized Layzer model for hydrodynamic instabilities[J].Phys Fluids,2009,21:024103.
[14] Sohn S I.Simple potential-flow model of Rayleigh-Taylor and Richtmyer-Meshkov instabilities for all density ratios[J].Phys Rev E,2003,67:026301.
[15] Zhang Qiang,Sohn S I.Nonlinear theory of unstable fluid mixing driven by shock wave[J].Phys Fluids,1997,9:1106-1124.
[16] Zhang Qiang.Analytical solutions of Layzer-type approach to unstable interfacial fluid mixing[J].Phys Rev Lett,1998,81(16):3391-3394.
[17] Zhang Qiang,Guo Wenxuan.Universality of finger growth in two-dimensional Rayleigh-Taylor and RichtmyerMeshkov instabilities with all density ratios[J].J Fluid Mech,2016,786:47-61.
[18] Busquet M,Barroso P,Melse T,et al.Miniature shock tube for laser driven shocks[J].Rev Sci Instrum,2010,81:023502.
[19] Mirshekari G,Brouillette M.Microscale shock tube[J].J Microelectromech Syst,2012,21(3):739-748.
[20] Mirshekari G,Brouillette M,Giordano J,et al.Shock waves in microchannels[J].J Fluid Mech,2013,724:259-283.
[21] Brouillette M.Shock waves at microscales[J].Shock waves,2003,13:3-12.
[22]童秉纲,孔祥言,邓国华.气体动力学(2版)[M].北京:高等教育出版社,2012:292-306(TONG Binggang,KONG Xiangyan,DENG Guohua.Gas dynamics(Second Edition)[M].Beijing:High Education Press,2012:292-306(in Chinese))
[23]Udagawa S,Garen W,Meyerer B,et al.Interferometric detection of dispersed shock waves in small scale diaphragm-less shock tube of 1mm diameter[C].Gold Coast,Springer,2007:201-210.
[24] Carlès P,Popinet S.Viscous nonlinear theory of Richtmyer-Meshkov instability[J].Phys Fluids,2001,13:1833-1836.
[25] Sohn S I.Effects of surface tension and viscosity on the growth rates of Rayleigh-Taylor and Richtmyer-Meshkov instabilities[J].Phys Rev E,2009,80:055302(R).
[26] Mikaelian K O.Shock-induced interface instability in viscous fluids and metals[J].Phys Rev E,2013,87:031003(R).
[27] Mirshekari G,Brouillette M.One-dimensional model for microscale shock tube flow[J].Shock Waves,2009,19:25-38.
[28] Parisse J D,Giordano J,Perrier P,et al.Numerical investigation of micro shock waves generation[J].Microfluid Nanofluid,2009,6:699-709.
[29] Zeitoun D E,Burtschell Y.Navier-Stokes computations in micro shock tubes[J].Shock Waves,2006,15:241-246.