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On the refraction of shock waves at a slow–fast gas interface

Published online by Cambridge University Press:  26 April 2006

L. F. Henderson ,
P. Colella  and
E. G. Puckett
L. F. Henderson
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Permanent address: The Institute of Space and Astronautical Science, 3–1–1 Yoshinodai, Sagamihara, Kanagawa, 229, Japan.
P. Colella
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Permanent address: Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA.
E. G. Puckett
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Permanent address: Department of Mathematics, University of California, Davis, CA 95615, USA.
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Abstract

We present the results of numerical computations of the refraction of a plane shock wave at a CO2/CH4 gas interface. The numerical method was an operator split version of a second-order Godunov method, with adaptive grid refinement. We solved the unsteady, two-dimensional, compressible, Euler equations numerically, assuming perfect gas equations of state, and compared our results with the experiments of Abd-El-Fattah & Henderson. Good agreement was usually obtained, especially when the contamination of the CH4 by the CO2 was taken into account. Remaining discrepancies were ascribed to the uncertainties in measuring certain wave angles, due to sharp curvature, poor definition, or short length of the waves at large angles of incidence. All the main features of the regular and irregular refractions were resolved numerically for shock strengths that were weak, intermediate, or strong. These include free precursor shock waves in the intermediate and strong cases, evanescent (smeared out) compressions in the weak case, and the appearance of an extra expansion wave in the bound precursor refraction (BPR). The structure of a BPR was elucidated for the first time.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 224 , March 1991 , pp. 1 - 27
Copyright
© 1991 Cambridge University Press

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References

Abd-El-Fattah, A. M. & Henderson, L. F. 1978a J. Fluid Mech. 86, 15.
Abd-El-Fattah, A. M. & Henderson, L. F. 1978b J. Fluid Mech. 89, 79.
Abd-El-Fattah, A. M., Henderson, L. F. & Lozzi, A., 1976 J. Fluid Mech. 76, 157.
Bergeb, M. J. & Colella, P., 1989 J. Comput. Phys. 82, 64.
Bitondo, D.: 1950 Inst. Aerophys., University of Toronto, UTIA Rep. 7.
Catherasoo, C. J. & Sturtevant, B., 1983 J. Fluid Mech. 127, 539.
Colella, P., Ferguson, R. & Glaz, H. M., 1990 Multifluid algorithms for Eulerian finite difference methods. Preprint in preparation.
Colella, P. & Glaz, H. M., 1985 J. Comput. Phys. 59, 264.
Colella, P. & Woodward, P., 1984 J. Comput. Phys. 54, 174.
Glaz, H. M., Colella, P., Glass, I. I. & Deschambault, R. L., 1985 Proc. R. Soc. Lond. A 398, 117.
Haas, J. F. & Sturtevant, B., 1987 J. Fluid Mech. 181, 41.
Henderson, L. F.: 1989 J. Fluid Mech. 198, 365.
Hornung, H. G. & Taylor, J. R., 1982 J. Fluid Mech. 123, 143.
Jahn, R. G.: 1956 J. Fluid Mech. 1, 457.
van Leer, R. G.: 1979 J. Comput. Phys. 32, 101.
von Neumann, J.: 1943 In Collected Works vol. 6, p. 1963. Pergamon.
Noh, W. F. & Woodward, P., 1976 UCRL Preprint No. 77651.
Schwendeman, D. W.: 1988 J. Fluid Mech. 188, 383.
Smith, W. R.: 1959 Phys. Fluids 2, 533.
Whitham, G. B.: 1958 J. Fluid Mech. 4, 337.
Whitham, G. B.: 1959 J. Fluid Mech. 5, 369.