Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T14:34:30.107Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental study on a sinusoidal air/SF$_{6}$ interface accelerated by a cylindrically converging shock

Published online by Cambridge University Press:  15 August 2017

Fan Lei ,
Juchun Ding ,
Ting Si Open the ORCID record for Ting Si [Opens in a new window] ,
Zhigang Zhai Open the ORCID record for Zhigang Zhai [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Fan Lei
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Juchun Ding
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
Zhigang Zhai
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Xisheng Luo*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Ritchmyer–Meshkov instability on an air/SF$_{6}$ interface is experimentally studied in a coaxial converging shock tube by a high-speed laser sheet imaging technique. An unperturbed case is first examined to obtain the characteristics of the converging shock and the shocked interface. For sinusoidal interfaces, the wave pattern and the interface morphology of the whole process are clearly observed. It is quantitatively found that the perturbation amplitude first decreases due to the shock compression, then experiences a rapid growth to a maximum value and finally drops quickly before the reshock. The reduction of growth rate is ascribed to the Rayleigh–Taylor stabilization caused by the interface deceleration motion that is present in the converging circumstance. It is noted that the influence of the wavenumber on the amplitude growth is very little before the reshock, but becomes significant after the reshock.

JFM classification

Compressible Flows: Compressible Flows Instability: Instability Mixing: Mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 826 , 10 September 2017 , pp. 819 - 829
Check for updates
Copyright
© 2017 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

Bell, G. I.1951 Taylor instability on cylinders and spheres in the small amplitude approximation. Tech. Rep. LA-1321. Los Alamos Scientific Laboratory.Google Scholar
Biamino, L., Jourdan, G., Mariani, C., Houas, L., Vandenboomgaerde, M. & Souffland, D. 2015 On the possibility of studying the converging Richtmyer–Meshkov instability in a conventional shock tube. Exp. Fluids 56 (2), 1–5.CrossRefGoogle Scholar
Dimotakis, P. E. & Samtaney, R. 2006 Planar shock cylindrical focusing by a perfect-gas lens. Phys. Fluids 18, 031705.Google Scholar
Ding, J., Si, T., Yang, J., Lu, X., Zhai, Z. & Luo, X. 2017 Shock tube experiments on converging Richtmyer–Meshkov instability. Phys. Rev. Lett. 119, 014501.Google Scholar
Fincke, J. R., Lanier, N. E., Batha, S. H., Hueckstaedt, R. M., Magelssen, G. R., Rothman, S. D., Parker, K. W. & Horsfield, C. J. 2004 Postponement of saturation of the Richtmyer–Meshkov instability in a convergent geometry. Phys. Rev. Lett. 93, 115003.Google Scholar
Guderley, G. 1942 Starke kugelige und zylindrische Verdichtungsstö𝛽e in der Nähe des Kugelmittelpunktes bzw. der Zylinderachse. Luftfahrtforschung 19, 302–312.Google Scholar
Hosseini, S. H. R., Ondera, O. & Takayama, K. 2000 Characteristics of an annular vertical diaphragmless shock tube. Shock Waves 10, 151–158.Google Scholar
Hosseini, S. H. R. & Takayama, K. 2005 Experimental study of Richtmyer–Meshkov instability induced by cylindrical shock waves. Phys. Fluids 17, 084101.Google Scholar
Kjellander, M., Tillmark, N. & Apazidis, N. 2011 Experimental determination of self-similarity constant for converging cylindrical shocks. Phys. Fluids 23 (11), 116103.CrossRefGoogle Scholar
Lanier, N. E., Barnes, C. W., Batha, S. H., Day, R. D., Magelssen, G. R., Scott, J. M., Dunne, A. M., Parker, K. W. & Rothman, S. D. 2003 Multimode seeded Richtmyer–Meshkov mixing in a convergent, compressible, miscible plasma system. Phys. Plasmas 10, 1816–1821.Google Scholar
Lindl, J., Landen, O., Edwards, J., Moses, E. & Team, N. 2014 Review of the national ignition campaign 2009–2012. Phys. Plasmas 21, 020501.CrossRefGoogle Scholar
Lombardini, M., Pullin, D. I. & Meiron, D. I. 2014 Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth. J. Fluid Mech. 748, 85–112.Google Scholar
Luo, X., Ding, J., Wang, M., Zhai, Z. & Si, T. 2015 A semi-annular shock tube for studying cylindrically converging Richtmyer–Meshkov instability. Phys. Fluids 27 (9), 091702.Google Scholar
Meshkov, E. E. 1969 Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101–104.CrossRefGoogle Scholar
Mikaelian, K. O. 2005 Rayleigh–Taylor and Richtmyer–Meshkov instabilities and mixing in stratified cylindrical shells. Phys. Fluids 17, 094105.CrossRefGoogle Scholar
Perry, R. W. & Kantrowitz, A. 1951 The production and stability of converging shock waves. J. Appl. Phys. 22, 878–886.Google Scholar
Plesset, M. S. 1954 On the stability of fluid flows with spherical symmetry. J. Appl. Phys. 25, 96–98.Google Scholar
Ponchaut, N. F., Hornung, H. G., Pullin, D. I. & Mouton, C. A. 2006 On imploding cylindrical and spherical shock waves in a perfect gas. J. Fluid Mech. 560, 103–122.Google Scholar
Remington, B. A., Kane, J., Drake, R. P., Glendinning, S. G., Estabrook, K., London, R., Castor, J., Wallace, R. J., Arnett, D., Liang, E. et al. 1997 Supernova hydrodynamics experiments on the Nova laser. Phys. Plasmas 4 (5), 1994–2003.Google Scholar
Richtmyer, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297–319.Google Scholar
Si, T., Long, T., Zhai, Z. & Luo, X. 2015 Experimental investigation of cylindrical converging shock waves interacting with a polygonal heavy gas cylinder. J. Fluid Mech. 784, 225–251.Google Scholar
Si, T., Zhai, Z. & Luo, X. 2014 Experimental study of Richtmyer–Meshkov instability in a cylindrical converging shock tube. Laser Part. Beams 32 (3), 343–351.Google Scholar
Takayama, K., Kleine, H. & Groenig, H. 1987 An experimental investigation of the stability of converging cylindrical shock waves in air. Exp. Fluids 5 (5), 315–322.Google Scholar
Wang, X., Yang, D., Wu, J. & Luo, X. 2015 Interaction of a weak shock wave with a discontinuous heavy-gas cylinder. Phys. Fluids 27, 064104.CrossRefGoogle Scholar
Zhai, Z., Liu, C., Qin, F., Yang, J. & Luo, X. 2010 Generation of cylindrical converging shock waves based on shock dynamics theory. Phys. Fluids 22, 041701.Google Scholar