Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-19T10:41:41.108Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental study of Richtmyer-Meshkov instability in a cylindrical converging shock tube

Published online by Cambridge University Press:  06 June 2014

Ting Si ,
Zhigang Zhai  and
Xisheng Luo
Ting Si
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei, China
Zhigang Zhai
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei, China
Xisheng Luo*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei, China
*
Address correspondence and reprint requests to: Xisheng Luo, Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei, China. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The interaction of a cylindrical converging shock wave with an initially perturbed gaseous interface is studied experimentally. The cylindrical converging shock is generated in an ordinary shock tube but with a specially designed test section, in which the incident planar shock wave is directly converted into a cylindrical one. Two kinds of typical initial interfaces involving gas bubble and gas cylinder are employed. A high-speed video camera combined with schlieren or planar Mie scattering photography is utilized to capture the evolution process of flow structures. The distribution of baroclinic vorticity on the interface induced by the cylindrical shock and the reflected shock from the center of convergence results in distinct phenomena. In the gas bubble case, the shock focusing and the jet formation are observed and the turbulent mixing of two fluids is promoted because of the gradually changed shock strength and complex shock structures in the converging part. In the gas cylinder case, a counter-rotating vortex pair is formed after the impact of the converging shock and its rotating direction may be changed when interacting with the reflected shock for a relatively long reflection distance. The variations of the interface displacements and structural dimensions with time are further measured. It is found that these quantities are different from those in the planar counterpart because of the shock curvature, the Mach number effect and the complex shock reflection within the converging shock tube test section. Therefore, the experiments reported here exhibit the great potential of this experimental method in study of the Richtmyer-Meshkov instability induced by converging shock waves.

Keywords

Converging shockGaseous interfaceRichtmyer-Meshkov instability
Type
Research Article
Information
Laser and Particle Beams , Volume 32 , Issue 3 , September 2014 , pp. 343 - 351
Copyright
Copyright © Cambridge University Press 2014 

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

REFERENCES

Apazidis, N. & Lesser, M. B. (1996). On generation and convergence of polygonal-waves. J. Fluid mech. 309, 301–319.CrossRefGoogle Scholar
Apazidis, N., Lesser, M. B., Tillmark, N. & Johansson, B. (2002). An experimental study of converging polygonal shock waves. Shock Waves 12, 39–58.CrossRefGoogle Scholar
Arnett, W. D., Bahcall, J. N., Kirshner, R. P. & Woosley, S. E. (1989). Supernova 1987a. Annu. Rev. Astron. Astrophys. 27, 629–700.CrossRefGoogle Scholar
Balasubramanian, S., Orlicz, G. C., Balakumar, B. J. C. & Prestridge, K. P. (2012). Experimental study of initial condition dependence on Richtmyer-Meshkov instability in the presence of reshock. Phys. Fluids 24, 031403.CrossRefGoogle Scholar
Bates, K. R. & Nikiforakisb, N. (2007). Richtmyer-MeShkov instability induced by the interaction of a shock wave with a rectangular block of SF6. Phys. Fluids 19, 036101.CrossRefGoogle Scholar
Brouillette, M. (2002). Richtmyer-Meshkov instability. Annu. Rev. Fluid Meeh. 34, 445–468.CrossRefGoogle Scholar
Dimotakis, P. E. & Samtaney, R. (2005). Planar shock cylindrical focusing by a perfect-gas lens. Phys. Fluids 18, 031705.CrossRefGoogle 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. (2005). Effect of convergence on growth of the Richtmyer-Meshkov instability. Laser Part. Beams 23, 2125.CrossRefGoogle Scholar
Glimm, J., Grove, J., Zhang, Y. & Dutta, S. (2002). Numerical study of axisymmetric Richtmyer-Meshkov instability and azimuthal effect on spherical mixing. J. Stat. Phys. 107, 241–260.CrossRefGoogle Scholar
Haas, J. F. & Sturtevant, B. (1987). Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J. Fluid Meeh. 181, 41–76.CrossRefGoogle Scholar
Hosseini, S. H. R., Onodera, O. & Takayama, K. (2000). Characteristics of an annular vertical diaphragm less shock tube. Shock Waves 10, 151–158.CrossRefGoogle Scholar
Hosseini, S. H. R. & Takayama, K. (2005 a). Experimental study of Richtmyer-Meshkov instability induced by cylindrical shock waves. Phys. Fluids 17, 084101.CrossRefGoogle Scholar
Hosseini, S. H. R. & Takayama, K. (2005 b). Implosion of a spherical shock wave reflected from a spherical wall. J. Fluid Meeh. 530, 223–239.CrossRefGoogle Scholar
Jacobs, J. W. (1993). The dynamics of shock accelerated light and heavy gas cylinders. Phys. Fluids A 5, 2239–2247.CrossRefGoogle Scholar
Jacobs, J. W., Klein, D. L., Jenkins, D. G. & Benjamin, R. F. (1992). Instability growth patterns of a shock-accelerated thin fluid layer. Phys. Rev. Lett. 70, 583–589.CrossRefGoogle Scholar
Jacobs, J. W. & Krivets, V. V. (2005). Experiments on the late-time development of single mode Richtmyer-Meshkov instability. Phys. Fluids 17, 034105.CrossRefGoogle Scholar
Jones, M. A. & Jacobs, J. W. (1997). A membraneless experiment for the study of Richtmyer-Meshkov instability of a shock-accelerated gas interface. Phys. Fluids 9, 3078–3085.CrossRefGoogle Scholar
Kjellander, M., Tillmark, N. & Apazidis, N. (2011). Experimental determination of selfsimilarity constant for converging cylindrical shocks. Phys. Fluids 23, 0116103.CrossRefGoogle Scholar
Lanier, N. E., Barnes, C. W., Batha, S. H., Dar, R. D., Magelssen, G. R., Scott, J. M., Dunne, A. M., Parker, K. W. & Rothman, S. D. (2003). Multimode seeded RichtmyerMeshkov mixing in a convergent, compressible, miscible plasma system. Phys. Plas. 10, 1816–1821.CrossRefGoogle Scholar
Layes, G., Jourdan, G. & Houas, L. (2009). Experimental study on a planeshock wave accelerating a gas bubble. Phys. Fluids 21, 074102.CrossRefGoogle Scholar
Lindl, J. D., Mccrory, R. L. & Campbell, E. M. (1992). Progress toward ignition and burn propagation in inertial confinement fusion. Phys. Today. 45, 32–40.CrossRefGoogle 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.CrossRefGoogle Scholar
Luo, X., Si, T., Yang, J. & Zhai, Z. (2014). A Cylindrical converging shock tube for shock interface studies. Rev. Sci. Instrum. 85, 015107.CrossRefGoogle ScholarPubMed
Luo, X., Wang, X. & Si, T. (2013). The Richtmyer-Meshkov instability of a three-dimensional air/SF6 interface with a minimum-surface feature. J. Fluid Mech. 722, 1–11.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
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. (1995). RayleighTaylor and RichtmyerMeshkov instabilities in finite-thickness fluid layers. Phys. Fluids 7, 888890.CrossRefGoogle Scholar
Orlicz, G. C., Balakumar, B. J. C. & Prestridge, K. P. (2013). Incident shock Mach number effects on Richtmyer-Meshkov mixing in a heavy gas layer. Phys. Fluids 25, 114101CrossRefGoogle Scholar
Orlicz, G. C., Balakumar, B. J. C., Tomkins, C. D. & Prestridge, K. P (2009). A mach number study of the Richtmyer-Meshkov instability in a varicose, heavy-gas curtain. Phys. Fluids 21, 064102.CrossRefGoogle Scholar
Perry, R. W. & Kantrowitz, A. (1951). The production and stability of converging shock waves. J. Appl. Phys. 22, 878–886.CrossRefGoogle Scholar
Prestridge, K. P., Rightley, P. M., Vorobieff, P., Benjamin, R. F. & Kurnit, N. A. (2000). Simultaneous density-field visualization and PlV of a shock-accelerated gas curtain. Exp. Fluids 29, 339–346.CrossRefGoogle Scholar
Puranik, P. B., Oakley, J. G., Anderson, M. H. & Bonazza, R. (2004). Experimental study of the Richtmyer-Meshkov instability induced by a Mach 3 shock wave. Shock Waves 13, 413–429.CrossRefGoogle Scholar
Ranjan, D., Anderson, M., Oakley, J. & Bonazza, R. (2005). Experimental investigation of a strongly shocked gas bubble. Phys. Rev. Lett. 94, 184507.CrossRefGoogle ScholarPubMed
Ranjan, D., Oakley, J. & Bonazza, R. (2011). Shock-bubble interactions. Annu. Rev. Fluid Meeh. 43, 117–140.CrossRefGoogle Scholar
Richtmyer, R. D. (1960). Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math. 13, 297–319.CrossRefGoogle Scholar
Sheeley, J. M. & Jacobs, J. W. (1995). Experimental study of incompressible Richtrnyer- Meshkov instability. Phys. Fluids 8, 405–415.Google Scholar
Si, T., Zhai, Z., Luo, X. & Yang, J. (2012). Experimental studies of reshocked spherical gas interfaces. Phys. Fluids 24, 054101.CrossRefGoogle Scholar
Si, T., Zhai, Z., Luo, X. & Yang, J. (2014). Experimental study on a heavy-gas cylinder accelerated by cylindrical converging shock waves. Shoek Waves 24, 3–9.CrossRefGoogle Scholar
Takayama, K., Kleine, H. & Gronig, H. (1987). An experimental investigation of the stability of converging cylindrical shock waves in air. Exps. Fluids 5, 315–322.CrossRefGoogle Scholar
Tomkins, C. D., Kumar, S., Orlicz, G. C. & Prestridge, K. P. (2008). An experimental investigation of mixing mechanisms in shock-accelerated flow. J. Fluid Mech. 611, 131–150.CrossRefGoogle Scholar
Wang, M., Si, T. & Luo, X. (2013). Generation of polygonal gas interfaces by soap film for Richtrnyer-Meshkov instability. Exp. Fluids 54, 1427.CrossRefGoogle Scholar
Yang, J., Kubota, T. & Zukoski, E. E. (1993). Applications of shock-induced mixing to supersonic combustion. AIAA J. 35, 854–862.CrossRefGoogle Scholar
Zabusky, N. (1999). Vortex paradigm for accelerated inhomogeneous flows: visiometrics for the Rayleigh-Taylor and Richtmyer-Meshkov environments. Annu. Rev. Fluid Meeh. 31, 495–536.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.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
Zhai, Z., Si, T., Luo, X., Yang, J., Liu, C., Tan, D. & Zou, L. (2012). Parametric study of cylindrical converging shock waves generated based on shock dynamics theory. Phys. Fluids 24, 026101.CrossRefGoogle Scholar
Zhang, Q. & Graham, M. J. (1998). A numerical study of RichtmyerMeshkov instability driven by cylindrical shocks. Phys. Fluids 10, 974–992.CrossRefGoogle Scholar
Zou, L., Liu, C., Tan, D., Huang, W. & Luo, X. (2010). On interaction of shock wave with elliptic gas cylinder. J. Visual. 13, 347–353.CrossRefGoogle Scholar