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Physics of Fluids / Volume 24 / Issue 2 / ARTICLES / Compressible Flows

Phys. Fluids 24, 026101 (2012); http://dx.doi.org/10.1063/1.3682376 (13 pages)

Parametric study of cylindrical converging shock waves generated based on shock dynamics theory

Zhigang Zhai1, Ting Si1, Xisheng Luo1, Jiming Yang1, Cangli Liu2, Duowang Tan2, and Liyong Zou2

1Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, People's Republic of China
2National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, CAEP, Mianyang 621900, People's Republic of China

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(Received 29 September 2011; accepted 9 January 2012; published online 8 February 2012)

In our previous work, the technique of generating cylindrical converging shock waves based on shock dynamics theory was proposed. In the present work, a further study is carried out to assess the influence of several parameters including the converging angle θ0, the incident planar shock Mach number M0, and the shock tube height h on the wall profile and the converging shock wave. Combining the high-speed schlieren photography and the numerical simulation with the shock dynamics theory, the characteristics of wall profiles, cylindrical converging shock waves, and thermodynamic properties for different controllable parameters are analyzed. It is found that these parameters have great effects on shapes of the wall profile and experimental investigation favors large values of M0 and h and moderate θ0. The experimental sequences of schlieren images indicate that the shocks moving in the converging part are of circular shapes, which further verifies the method in our previous work. In addition, the changes of the shock Mach number, pressure, temperature, and density are obtained quantitatively. The results show that higher pressure and temperature can be reached in the converging part at the same distance to the center of convergence for larger incident shock Mach numbers, larger shock tube heights, or smaller converging angles. All the database will be useful for understanding the shock focusing and further investigating the Richtmyer-Meshkov instability induced by the converging shock waves.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THEORETICAL, EXPERIMENTAL AND NUMERICAL METHODS
    1. Theoretical analysis
    2. Experimental method
    3. Numerical simulation
  3. RESULTS AND DISCUSSION
    1. Characteristics of the wall profiles
    2. Characteristics of the cylindrical converging shock waves
    3. Characteristics of the thermodynamic properties
  4. CONCLUSION

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KEYWORDS and PACS

Keywords

Mach number, numerical analysis, pipe flow, shock waves

PACS

  • 47.40.Nm

    Shock wave interactions and shock effects

  • 02.60.Cb

    Numerical simulation; solution of equations

  • 47.60.Dx

    Flows in ducts and channels

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3682376

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
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    R. W. Perry, and A. Kantrowitz, “The production and stability of converging shock waves,” J. Appl. Phys. 22, 878 (1951)JAPIAU000022000007000878000001.

    S. H. R. Hosseini, and K. Takayama, “Experimental study of Richtmyer-Meshkov instability induced by cylindrical shock waves,” Phys. Fluids 17, 084101 (2005)PHFLE6000017000008084101000001.

    P. E. Dimotakis, and R. Samtaney, “Planar shock cylindrical focusing by a perfect-gas lens,” Phys. Fluids 18, 031705 (2006)PHFLE6000018000003031705000001.

    M. Vandenboomgaerde, and C. Aymard, “Analytical theory for planar shock focusing through perfect gas lens and shock tube experiment designs,” Phys. Fluids 23, 016101 (2011)PHFLE6000023000001016101000001.

    Z. G. Zhai, C. L. Liu, F. H. Qin, J. M. Yang, and X. S. Luo, “Generation of cylindrical converging shock waves based on shock dynamics theory,” Phys. Fluids 22, 041701 (2010)PHFLE6000022000004041701000001.

    Z. G. Zhai, T. Si, X. S. Luo, and J. M. Yang, “On the evolution of spherical gas interfaces accelerated by a planar shock wave,” Phys. Fluids 23, 084104 (2011)PHFLE6000023000008084104000001.


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