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On the interaction of a planar shock with a three-dimensional light gas cylinder

  • Juchun Ding (a1), Ting Si (a1), Mojun Chen (a1), Zhigang Zhai (a1), Xiyun Lu (a1) and Xisheng Luo (a1)...

Abstract

Experimental and numerical investigations on the interaction of a planar shock wave with two-dimensional (2-D) and three-dimensional (3-D) light gas cylinders are performed. The effects of initial interface curvature on flow morphology, wave pattern, vorticity distribution and interface movement are emphasized. In experiments, a wire-restriction method based on the soap film technique is employed to generate N $_{2}$ cylinders surrounded by SF $_{6}$ with well-characterized shapes, including a convex cylinder, a concave cylinder with a minimum-surface feature and a 2-D cylinder. The high-speed schlieren pictures demonstrate that fewer disturbance waves exist in the flow field and the evolving interfaces develop in a more symmetrical way relative to previous studies. By combining the high-order weighted essentially non-oscillatory construction with the double-flux scheme, numerical simulation is conducted to explore the detailed 3-D flow structures. It is indicated that the shape and the size of 3-D gas cylinders in different planes along the vertical direction change gradually due to the existence of both horizontal and vertical velocities of the flow. At very early stages, pressure oscillations in the vicinity of evolving interfaces induced by complex waves contribute much to the deformation of the 3-D gas cylinders. As time proceeds, the development of the shocked volume would be dominated by the baroclinic vorticity deposited on the interface. In comparison with the 2-D case, the oppositely (or identically) signed principal curvatures of the concave (or convex) SF $_{6}$ /N $_{2}$ boundary cause complex high pressure zones and additional vorticity deposition, and the upstream interface from the symmetric slice of the concave (or convex) N $_{2}$ cylinder moves with an inhibition (or a promotion). Finally, a generalized 3-D theoretical model is proposed for predicting the upstream interface movements of different gas cylinders and the present experimental and numerical findings are well predicted.

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Corresponding author

Email address for correspondence: tsi@ustc.edu.cn

References

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Abgrall, R. 1996 How to prevent pressure oscillations in multicomponent flow calculations: a quasi conservative approach. J. Comput. Phys. 125, 150160.
Abgrall, R. & Karni, S. 2001 Computations of compressible multifluids. J. Comput. Phys. 169, 594623.
Arnett, W. D., Bahcall, J. N., Kirshner, R. P. & Woosley, S. E. 1989 Supernova 1987A. Annu. Rev. Astron. Astrophys. 27, 629700.
Balakumar, B. J., Orlicz, G. C., Ristorcelli, J. R., Balasubramanian, S., Prestridge, K. P. & Tomkins, C. D. 2012 Turbulent mixing in a Richtmyer–Meshkov fluid layer after reshock: velocity and density statistics. J. Fluid Mech. 696, 6793.
Balasubramanian, S., Orlicz, G. C., Prestridge, K. P. & Balakumar, B. J. 2012 Experimental study of initial condition dependence on Richtmyer–Meshkov instability in the presence of reshock. Phys. Fluids 24, 034103.
Bonazza, R. & Sturtevant, B. 1996 X-ray measurements of growth rates at a gas interface accelerated by shock waves. Phys. Fluids 8, 24962512.
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445468.
Brouillette, M. & Sturtevant, B. 1993 Experiments on the Richtmyer–Meshkov instability: small-scale perturbations on a plane interface. Phys. Fluids A 5, 916930.
Chapman, P. R. & Jacobs, J. W. 2006 Experiments on the three-dimensional incompressible Richtmyer–Meshkov instability. Phys. Fluids 18, 074101.
Haas, J. F. & Sturtevant, B. 1987 Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J. Fluid Mech. 181, 4176.
Jacobs, J. W. 1992 Shock-induced mixing of a light-gas cylinder. J. Fluid Mech. 234, 629649.
Jenny, P., Müller, B. & Thomann, H. 1997 Correction of conservative Euler solvers for gas mixtures. J. Comput. Phys. 132, 91107.
Jiang, G. S. & Shu, C. W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202228.
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, 30783085.
Karni, S. 1994 Multicomponent flow calculations by a consistent primitive algorithm. J. Comput. Phys. 112, 3143.
Kumar, S., Orlicz, G., Tomkins, C., Goodenough, C., Prestridge, K., Vorobieff, P. & Benjamin, R. 2005 Stretching of material lines in shock-accelerated gaseous flows. Phys. Fluids 17, 082107.
Layes, G., Jourdan, G. & Houas, L. 2009 Experimental study on a plane shock wave accelerating a gas bubble. Phys. Fluids 21, 074102.
Lindl, J., Landen, O., Edwards, J., Moses, E. & Team, N. 2014 Review of the national ignition campaign 2009–2012. Phys. Plasmas 21, 020501.
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.
Luo, X., Dong, P., Si, T. & Zhai, Z. 2016a The Richtmyer–Meshkov instability of a ‘V’ shaped air/SF6 interface. J. Fluid Mech. 802, 186202.
Luo, X., Guan, B., Si, T., Zhai, Z. & Wang, X. 2016b Richtmyer–Meshkov instability of a three-dimensional SF6 –air interface with a minimum-surface feature. Phys. Rev. E 93, 013101.
Luo, X., Guan, B., Zhai, Z. & Si, T. 2016c Principal curvature effects on the early evolution of three-dimensional single-mode Richtmyer–Meshkov instabilities. Phys. Rev. E 93, 023110.
Luo, X., Wang, M., Si, T. & Zhai, Z. 2015 On the interaction of a planar shock with an SF6 polygon. J. Fluid Mech. 773, 366394.
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, R2.
Luo, X., Zhai, Z., Si, T. & Yang, J. 2014 Experimental study on the interfacial instability induced by shock waves. Adv. Mech. 44, 260290.
Mariani, C., Vanderboomgaerde, M., Jourdan, G., Souffland, D. & Houas, L. 2008 Investigation of the Richtmyer–Meshkov instability with stereolithographed interfaces. Phys. Rev. Lett. 100, 254503.
Meshkov, E. E. 1969 Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101104.
Niederhaus, C. E. & Jacobs, J. W. 2003 Experimental study of the Richtmyer–Meshkov instability of incompressible fluids.. J. Fluid Mech. 485, 243277.
Niederhaus, J. H. J., Greenough, J. A., Oakley, J. G., Ranjan, D., Andeson, M. H. & Bonazza, R. 2008 A computational parameter study for the three-dimensional shock–bubble interaction. J. Fluid Mech. 594, 85124.
Picone, J. M. & Boris, J. P. 1988 Vorticity generation by shock propagation through bubbles in a gas. J. Fluid Mech. 189, 2351.
Prasad, J. K., Rasheed, A., Kumar, S. & Sturtevant, B. 2000 The late-time development of the Richtmyer–Meshkov instability. Phys. Fluids 12, 21082115.
Quirk, J. J. & Karni, S. 1996 On the dynamics of a shock–bubble interaction. J. Fluid Mech. 318, 129163.
Ranjan, D., Niederhaus, J., Motl, B., Anderson, M., Oakley, J. & Bonazza, R. 2007 Experimental investigation of primary and secondary features in high-Mach-number shock–bubble interaction. Phys. Rev. Lett. 98 (2), 024502.
Ranjan, D., Niederhaus, J. H. J., Oakley, J., Anderson, M. H., Bonazza, R. & Greenough, J. A. 2008 Shock–bubble interactions: features of divergent shock-refraction geometry observed in experiments and simulations. Phys. Fluids 20, 036101.
Ranjan, D., Oakley, J. & Bonazza, R. 2011 Shock–bubble interactions. Annu. Rev. Fluid Mech. 43, 117140.
Richtmyer, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297319.
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.
Rudinger, G. & Somers, L. M. 1960 Behaviour of small regions of different gases carried in accelerated gas flows. J. Fluid Mech. 7, 161176.
Si, T., Zhai, Z., Yang, J. & Luo, X. 2012 Experimental investigation of reshocked spherical gas interfaces. Phys. Fluids 24, 054101.
Tomkins, C., Kumar, S., Orlicz, G. & Prestridge, K. P. 2008 An experimental investigation of mixing mechanisms in shock-accelerated flow. J. Fluid Mech. 611, 131150.
Tomkins, C. D., Balakumar, B. J., Orlicz, G., Prestridge, K. P. & Ristorcelli, J. R. 2013 Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence. J. Fluid Mech. 735, 288306.
Wang, M., Si, T. & Luo, X. 2013 Generation of polygonal gas interfaces by soap film for Richtmyer–Meshkov instability study. Exp. Fluids 54, 1427.
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.
Weirs, V. G., Dupont, T. & Plewa, T. 2008 Three-dimensional effects in shock–cylinder interactions. Phys. Fluids 20, 044102.
Yang, J., Kubota, T. & Zukoski, E. E. 1993 Application of shock-induced mixing to supersonic combustion. AIAA J. 31, 854862.
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.
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.
Zhai, Z., Wang, M., Si, T. & Luo, X. 2014a On the interaction of a planar shock with a light polygonal interface. J. Fluid Mech. 757, 800816.
Zhai, Z., Zhang, F., Si, T. & Luo, X. 2014b Evolution of heavy gas cylinder under reshock conditions. J. Vis. 17, 123129.
Zoldi, C.2002 A numerical and experimental study of a shock-accelerated heavy gas cylinder. PhD thesis, State University of New York at Stony Brook.
Zou, L., Liu, C., Tan, D., Huang, W. & Luo, X. 2010 On interaction of shock wave with elliptic gas cylinder. J. Vis. 13, 347353.
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