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Shock focusing in a planar convergent geometry: experiment and simulation

Published online by Cambridge University Press:  16 November 2009

C. BOND ,
D. J. HILL ,
D. I. MEIRON  and
P. E. DIMOTAKIS
C. BOND
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
D. J. HILL*
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
D. I. MEIRON
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
P. E. DIMOTAKIS
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: dh@galcit.caltech.edu
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Abstract

The behaviour of an initially planar shock wave propagating into a linearly convergent wedge is investigated experimentally and numerically. In the experiment, a 25° internal wedge is mounted asymmetrically in a pressure-driven shock tube. Shock waves with incident Mach numbers in the ranges of 1.4–1.6 and 2.4–2.6 are generated in nitrogen and carbon dioxide. During each run, the full pressure history is recorded at fourteen locations along the wedge faces and schlieren images are produced. Numerical simulations performed based on the compressible Euler equations are validated against the experiment. The simulations are then used as an additional tool in the investigation.

The linearly convergent geometry strengthens the incoming shock repeatedly, as waves reflected from the wedge faces cross the interior of the wedge. This investigation shows that aspects of this structure persist through multiple reflections and influence the nature of the shock-wave focusing. The shock focusing resulting from the distributed reflected waves of the Mach 1.5 case is distinctly different from the stepwise focusing at the higher incoming shock Mach number. Further experiments using CO2 instead of N2 elucidate some relevant real-gas effects and suggest that the presence or absence of a weak leading shock on the distributed reflections is not a controlling factor for focusing.

JFM classification

Compressible Flows: Gas dynamics Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 297 - 333
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Apazidis, N., Lesser, M. B., Tillmark, N. & Johansson, B. 2002 An experimental and theoretical study of converging polygonal shock waves. Shock Waves 12, 39–58.CrossRefGoogle Scholar
Ben-Dor, G. 2006 A state-of-the-knowledge review on pseudo-steady shock-wave reflections and their transition criteria. Shock Waves 15, 277–294.CrossRefGoogle Scholar
Ben-Dor, G. 2007 Shock Wave Reflection Phenomena. Springer.Google Scholar
Colella, P. & Henderson, L. F. 1990 The von Neumann paradox for the diffraction of weak shock-waves. J. Fluid Mech. 213, 71–94.Google Scholar
Deiterding, R., Radovitzky, R., Mauch, S., Noels, L., Cummings, J. & Meiron, D. 2006 A virtual test facility for the efficient simulation of solid material response under strong shock and detonation wave loading. Engng Comput. 22, 325–347.CrossRefGoogle Scholar
Dimotakis, P. E. & Samtaney, R. 2006 Planar shock cylindrical focusing by a perfect-gas lens. Phys. Fluids 18.CrossRefGoogle Scholar
Eliasson, V., Apazidis, N., Tillmark, N. & Lesser, M. B. 2006 Focusing of strong shocks in an annular shock tube. Shock Waves 15, 205–217.CrossRefGoogle Scholar
Evans, A. K. 1996 Instability of converging shock waves and sonoluminescence. Phys. Rev. E 54, 5004–5011.CrossRefGoogle ScholarPubMed
Gottlieb, S., Shu, C. W. & Tadmor, E. 2001 Strong stability-preserving high-order time discretization methods. SIAM Rev. 43, 89–112.Google Scholar
Griffith, W. & Kenney, A. 1957 Fully-dispersed shock waves in carbon dioxide. J. Fluid Mech. 3, 286–288.CrossRefGoogle Scholar
Guderley, G. 1942 Starke kugelige und zylindrische verdichtungsstösse in der nähe des kugelmittelpunktes bzw der zylinderachse. Luftfahrtforschung 19, 302–312.Google Scholar
Henderson, L., Vasilev, E., Ben-Dor, G. & Elperin, T. 2003 The wall-jetting effect in Mach reflection: theoretical consideration and numerical investigation. J. Fluid Mech. 479, 259–286.CrossRefGoogle Scholar
Hill, D. J. & Pullin, D. I. 2004 Hybrid tuned centre-difference-WENO method for large eddy simulations in the presence of strong shocks. J. Comput. Phys. 194, 435–450.CrossRefGoogle Scholar
Hosseini, S. H. R. & Takayama, K. 2005 Experimental study of Richtmyer–Meshkov instability induced by cylindrical shock waves. Phys. Fluids 17.CrossRefGoogle Scholar
Inoue, O., Imuta, S., Milton, B. E. & Takayama, K. 1995 Computational study of shock-wave focusing in a log-spiral duct. Shock Waves 5, 183–188.CrossRefGoogle Scholar
Inoue, O., Takahashi, N. & Takayama, K. 1993 Shock-wave focusing in a log-spiral duct. AIAA J. 31, 1150–1152.CrossRefGoogle Scholar
Johannesen, N., Zienkiewicz, H., Blythe, P. & Gerrard, J. 1962 Experimental and theoretical analysis of vibrational relaxation regions in carbon dioxide. J. Fluid Mech. 13, 213–224.CrossRefGoogle Scholar
Kumar, S., Hornung, H. & Sturtevant, B. 2003 Growth of shocked gaseous interfaces in a conical geometry. Phys. Fluids 15, 3194–3208.CrossRefGoogle Scholar
Liepmann, H. W., Coles, D., Roshko, A. & Sturtevant, B. 1962 17-inch diameter shock tube for studies in rarefied gas dynamics. Rev. Sci. Instrum. 33, 625–631.CrossRefGoogle Scholar
Olim, M. & Dewey, J. 1992 A revised three-shock solution for the Mach reflection of weak shocks. Shock Waves 2, 167–176.CrossRefGoogle Scholar
Pantano, C., Deiterding, R., Hill, D. J. & Pullin, D. I. 2007 A low numerical dissipation patch-based adaptive mesh refinement method for large-eddy simulation of compressible flows. J. Comput. Phys. 221, 63–87.CrossRefGoogle Scholar
Perry, R. W. & Kantrowitz, A. 1951 The production and stability of converging shock waves. J. Appl. Phys. 22, 878–886.CrossRefGoogle Scholar
Sandeman, R. J. 2000 A simple physical theory of weak mach reflection ever plane surfaces. Shock Waves 10, 103–112.CrossRefGoogle Scholar
Sasoh, A. & Takayama, K. 1994 Characterization of disturbance propagation in weak shock-wave reflections. J. Fluid Mech. 277, 331–345.CrossRefGoogle Scholar
Schwendeman, D. W. & Whitham, G. B. 1987 On converging shock-waves. Proc. R. Soc. London A–Math. Phys. Engng Sci. 413, 297–311.Google Scholar
Setchell, R. E., Storm, E. & Sturtevant, B. 1972 Investigation of shock strengthening in a conical convergent channel. J. Fluid Mech. 56, 505–522.CrossRefGoogle Scholar
Skews, B. W. & Ashworth, J. T. 2005 The physical nature of weak shock wave reflection. J. Fluid Mech. 542, 105–114.CrossRefGoogle Scholar
Takayama, K., Kleine, H. & Gronig, H. 1987 An experimental investigation of the stability of converging cylindrical shock waves in air. Exp. Fluids 5, 315–322.CrossRefGoogle Scholar
Vasilev, E., Ben-Dor, G., Elperin, T. & Henderson, L. 2004 The wall-jetting effect in Mach reflection: Navier–Stokes simulations. J. Fluid Mech. 511, 363–379.CrossRefGoogle Scholar
Vasilev, E. I., Elperin, T. & Ben-Dor, G. 2008 Analytical reconsideration of the von Neumann paradox in the reflection of a shock wave over a wedge. Phys. Fluids 20 (4), 046101.Google Scholar
Vincenti, W. & Kruger, C. 1965 Introduction to Physical Gas Dynamics. Wiley.Google Scholar
Watanabe, M. & Takayama, K. 1992 Stability of converging cylindrical shock-waves. JSME Intl J. II–Fluid Engng Heat 35, 218–227.Google Scholar
Whitham, G. B. 1957 A new approach to problems of shock dynamics. 1. 2-dimensional problems. J. Fluid Mech. 2, 145–171.Google Scholar
Zel’dovich, Y. B. & Raizer, Y. P. 2002 Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Dover.Google Scholar