Hostname: page-component-7c8c6479df-r7xzm Total loading time: 0 Render date: 2024-03-29T00:08:20.878Z Has data issue: false hasContentIssue false

The Richtmyer–Meshkov instability of a three-dimensional air/SF6 interface with a minimum-surface feature

Published online by Cambridge University Press:  04 April 2013

Xisheng Luo*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Xiansheng Wang
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Ting Si
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
*
Email address for correspondence: xluo@ustc.edu.cn

Abstract

A novel method to create a discontinuous gaseous interface with a minimum-surface feature by the soap film technique is developed for three-dimensional (3D) Richtmyer–Meshkov instability (RMI) studies. The interface formed is free of supporting mesh and the initial condition can be well controlled. Five air/SF6 interfaces with different amplitude are realized in shock-tube experiments. Time-resolved schlieren and planar Mie-scattering photography are employed to capture the motion of the shocked interface. It is found that the instability at the linear stage in the symmetry plane grows much slower than the predictions of previous two-dimensional (2D) impulsive models, which is ascribed to the opposite principal curvatures of the minimum surface. The 2D impulsive model is extended to describe the general 3D RMI. A quantitative analysis reveals a good agreement between experiments and the extended linear model for all the configurations including both the 2D and 3D RMIs at their early stages. An empirical model that combines the early linear growth with the late-time nonlinear growth is also proposed for the whole evolution process of the present configuration.

Type
Rapids
Copyright
©2013 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abarzhi, S. I. 2001 Asymptotic behaviour of three-dimensional bubbles in the Richtmyer–Meshkov instability. Phys. Fluids 13, 28662875.Google Scholar
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445468.CrossRefGoogle Scholar
Chapman, P. R. & Jacobs, J. W. 2006 Experiments on the three-dimensional incompressible Richtmyer–Meshkov instability. Phys. Fluids 18, 074101.Google Scholar
Collins, B. D. & Jacobs, J. W. 2002 PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an interface. J. Fluid Mech. 464, 113136.Google Scholar
Haas, J. F. & Sturtevant, B. 1987 Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J. Fluid Mech. 181, 4176.Google Scholar
Isenberg, C. 1992 The Science of Soap Films and Soap Bubbles. Dover.Google Scholar
Krechetnikov, R. 2009 Rayleigh–Taylor and Richtmyer–Meshkov instabilities of flat and curved interfaces. J. Fluid Mech. 625, 387410.CrossRefGoogle Scholar
Layes, G., Jourdan, G. & Houas, L. 2009 Experimental study on a plane shock wave accelerating a gas bubble. Phys. Fluids 21, 074102.CrossRefGoogle Scholar
Leinov, E., Malamud, G., Elbaz, Y., Levin, L. A., Ben-Dor, G., Shvarts, D. & Sadot, O. 2009 Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions. J. Fluid Mech. 626, 449475.Google Scholar
Long, C. C., Krivets, V. V., Greenough, J. A. & Jacobs, J. W. 2009 Shock tube experiments and numerical simulation of the single-mode, three-dimensional Richtmyer–Meshkov instability. Phys. Fluids 21, 114104.Google Scholar
Mariani, C., Vandenboomgaerde, M., Jourdan, G., Souffland, D. & Houas, L. 2008 Investigation of the Richtmyer–Meshkov instability with stereolithographed interfaces. Phys. Rev. Lett. 100, 254503.Google Scholar
Meshkov, E. E. 1969 Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101104.Google Scholar
Mikaelian, K. O. 2003 Explicit expressions for the evolution of single-mode Rayleigh–Taylor and Richtmyer–Meshkov instabilities at arbitrary Atwood numbers. Phys. Rev. E 67, 026319.Google Scholar
Mikaelian, K. O. 2005 Richtmyer–Meshkov instability of arbitrary shapes. Phys. Fluids 17, 034101.Google Scholar
Niederhaus, C. E. & Jacobs, J. W. 2003 Experimental study of the Richtmyer–Meshkov instability of incompressible fluids. J. Fluid Mech. 485, 243277.CrossRefGoogle Scholar
Oron, D., Arazi, L., Kartoon, D., Rikanati, A., Alon, U. & Shvarts, D. 2001 Dimensionality dependence of the Rayleigh–Taylor and Richtmyer–Meshkov instability late-time scaling laws. Phys. Plasmas 8, 28832889.Google Scholar
Ranjan, D., Oakley, J. & Bonazza, R. 2011 Shock-bubble interactions. Annu. Rev. Fluid Mech. 43, 117140.CrossRefGoogle Scholar
Richtmyer, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297319.CrossRefGoogle Scholar
Rikanati, A., Oron, D., Sadot, O. & Shvarts, D. 2003 High initial amplitude and high Mach number effects on the evolution of the single-mode Richtmyer–Meshkov instability. Phys. Rev. E 67, 026307.Google Scholar
Sadot, O., Erez, L., Alon, U., Oron, D., Levin, L. A., Erez, G., Ben-Dor, G. & Shvarts, D. 1998 Study of nonlinear evolution of single-mode and two-bubble interaction under Richtmyer–Meshkov instability. Phys. Rev. Lett. 80, 16541657.Google Scholar
Si, T., Zhai, Z., Yang, J. & Luo, X. 2012 Experimental investigation of reshocked spherical gas interfaces. Phys. Fluids 24, 054101.Google Scholar
Wang, M., Si, T. & Luo, X. 2013 Generation of polygonal gas interfaces by soap film for Richtmyer–Meshkov instability study. Exp. Fluids 54, 1427.Google Scholar
Yosef-Hai, A., Sadot, O., Kartoon, D., Oron, D., Levin, L. A., Sarid, E., Elbaz, Y., Ben-Dor, G. & Shvarts, D. 2003 Late-time growth of the Richtmyer–Meshkov instability for different Atwood numbers and different dimensionalities. Laser Part. Beams 21, 363368.Google Scholar
Zabusky, N. J. 1999 Vortex paradigm for accelerated inhomogeneous flows: visiometrics for the Rayleigh–Taylor and Richtmyer–Meshkov environments. Annu. Rev. Fluid Mech. 31, 495536.CrossRefGoogle Scholar
Zhai, Z., Si, T., Luo, X. & Yang, J. 2011 On the evolution of spherical gas interfaces accelerated by a planar shock wave. Phys. Fluids 23, 084104.CrossRefGoogle Scholar
Zhang, Q. & Sohn, S. I. 1999 Quantitative theory of Richtmyer–Meshkov instability in three dimensions. Z. Angew. Math. Phys. 50, 146.Google Scholar