Hostname: page-component-6b989bf9dc-pmhlf Total loading time: 0 Render date: 2024-04-15T00:56:24.979Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  04 September 2017

Juchun Ding ,
Ting Si Open the ORCID record for Ting Si [Opens in a new window] ,
Mojun Chen ,
Zhigang Zhai Open the ORCID record for Zhigang Zhai [Opens in a new window] ,
Xiyun Lu Open the ORCID record for Xiyun Lu [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Juchun Ding
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Ting Si*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Mojun Chen
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Zhigang Zhai
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Xiyun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Xisheng Luo
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
*
†Email address for correspondence: tsi@ustc.edu.cn
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Compressible Flows: Compressible Flows Aerodynamics: High-speed flow Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 289 - 317
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

Abgrall, R. 1996 How to prevent pressure oscillations in multicomponent flow calculations: a quasi conservative approach. J. Comput. Phys. 125, 150–160.CrossRefGoogle Scholar
Abgrall, R. & Karni, S. 2001 Computations of compressible multifluids. J. Comput. Phys. 169, 594–623.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
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, 67–93.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Bonazza, R. & Sturtevant, B. 1996 X-ray measurements of growth rates at a gas interface accelerated by shock waves. Phys. Fluids 8, 2496–2512.CrossRefGoogle Scholar
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34, 445–468.CrossRefGoogle Scholar
Brouillette, M. & Sturtevant, B. 1993 Experiments on the Richtmyer–Meshkov instability: small-scale perturbations on a plane interface. Phys. Fluids A 5, 916–930.CrossRefGoogle Scholar
Chapman, P. R. & Jacobs, J. W. 2006 Experiments on the three-dimensional incompressible Richtmyer–Meshkov instability. Phys. Fluids 18, 074101.Google Scholar
Haas, J. F. & Sturtevant, B. 1987 Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J. Fluid Mech. 181, 41–76.CrossRefGoogle Scholar
Jacobs, J. W. 1992 Shock-induced mixing of a light-gas cylinder. J. Fluid Mech. 234, 629–649.CrossRefGoogle Scholar
Jenny, P., Müller, B. & Thomann, H. 1997 Correction of conservative Euler solvers for gas mixtures. J. Comput. Phys. 132, 91–107.CrossRefGoogle Scholar
Jiang, G. S. & Shu, C. W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228.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
Karni, S. 1994 Multicomponent flow calculations by a consistent primitive algorithm. J. Comput. Phys. 112, 31–43.CrossRefGoogle Scholar
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.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
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
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., Dong, P., Si, T. & Zhai, Z. 2016a The Richtmyer–Meshkov instability of a ‘V’ shaped air/SF6 interface. J. Fluid Mech. 802, 186–202.CrossRefGoogle Scholar
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.Google Scholar
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.Google ScholarPubMed
Luo, X., Wang, M., Si, T. & Zhai, Z. 2015 On the interaction of a planar shock with an SF6 polygon. J. Fluid Mech. 773, 366–394.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Luo, X., Zhai, Z., Si, T. & Yang, J. 2014 Experimental study on the interfacial instability induced by shock waves. Adv. Mech. 44, 260–290.Google Scholar
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.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
Niederhaus, C. E. & Jacobs, J. W. 2003 Experimental study of the Richtmyer–Meshkov instability of incompressible fluids.. J. Fluid Mech. 485, 243–277.CrossRefGoogle Scholar
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, 85–124.CrossRefGoogle Scholar
Picone, J. M. & Boris, J. P. 1988 Vorticity generation by shock propagation through bubbles in a gas. J. Fluid Mech. 189, 23–51.CrossRefGoogle Scholar
Prasad, J. K., Rasheed, A., Kumar, S. & Sturtevant, B. 2000 The late-time development of the Richtmyer–Meshkov instability. Phys. Fluids 12, 2108–2115.CrossRefGoogle Scholar
Quirk, J. J. & Karni, S. 1996 On the dynamics of a shock–bubble interaction. J. Fluid Mech. 318, 129–163.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Ranjan, D., Oakley, J. & Bonazza, R. 2011 Shock–bubble interactions. Annu. Rev. Fluid Mech. 43, 117–140.CrossRefGoogle Scholar
Richtmyer, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297–319.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 ScholarPubMed
Rudinger, G. & Somers, L. M. 1960 Behaviour of small regions of different gases carried in accelerated gas flows. J. Fluid Mech. 7, 161–176.CrossRefGoogle Scholar
Si, T., Zhai, Z., Yang, J. & Luo, X. 2012 Experimental investigation of reshocked spherical gas interfaces. Phys. Fluids 24, 054101.CrossRefGoogle Scholar
Tomkins, C., Kumar, S., Orlicz, G. & Prestridge, K. P. 2008 An experimental investigation of mixing mechanisms in shock-accelerated flow. J. Fluid Mech. 611, 131–150.CrossRefGoogle Scholar
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, 288–306.CrossRefGoogle 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.CrossRefGoogle 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
Weirs, V. G., Dupont, T. & Plewa, T. 2008 Three-dimensional effects in shock–cylinder interactions. Phys. Fluids 20, 044102.CrossRefGoogle Scholar
Yang, J., Kubota, T. & Zukoski, E. E. 1993 Application of shock-induced mixing to supersonic combustion. AIAA J. 31, 854–862.CrossRefGoogle 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, 495–536.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., Wang, M., Si, T. & Luo, X. 2014a On the interaction of a planar shock with a light polygonal interface. J. Fluid Mech. 757, 800–816.CrossRefGoogle Scholar
Zhai, Z., Zhang, F., Si, T. & Luo, X. 2014b Evolution of heavy gas cylinder under reshock conditions. J. Vis. 17, 123–129.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Zou, L., Liu, C., Tan, D., Huang, W. & Luo, X. 2010 On interaction of shock wave with elliptic gas cylinder. J. Vis. 13, 347–353.CrossRefGoogle Scholar

Ding et al. supplementary movie 1

High-speed schlieren imaging of a shocked 2D N2 cylinder surrounded by SF6 in experiments (top) and numerical simulations (bottom).

Download Ding et al. supplementary movie 1(Video)
Video 4.1 MB

Ding et al. supplementary movie 2

High-speed schlieren imaging of a shocked concave N2cylinder surrounded by SF6 in experiments (top) and numerical simulations (bottom).

Download Ding et al. supplementary movie 2(Video)
Video 5.7 MB

Ding et al. supplementary movie 3

High-speed schlieren imaging of a shocked convex N2cylinder surrounded by SF6 in experiments (top) and numerical simulations (bottom).

Download Ding et al. supplementary movie 3(Video)
Video 6.2 MB