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A study of slipstreams in triple shock wave configurations

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Abstract

A shock wave appearing in supersonic gas flow reflects in different ways depending on flow conditions. It can take the form of regular or irregular reflection. For the irregular reflection configuration of three shock waves and a slipstream arises. Mathematical investigations of the development of parameters across slipstream in triple shock configuration have been made with variation of the angle of incidence of the shock wave, the shock wave Mach number and the adiabatic index of the gas. It has been shown that the characteristic mixing parameters of the slipstream increase with the increase of Mach number of the flow and the decrease of the heat capacity ratio. This leads to an increase of vortex formation and an increase of the angular spread of the slipstream. It also has been shown that the angle between the reflected wave and the slipstream diminishes with the decrease in heat capacity ratio so that the value may become of the same order as the spread angle. This may lead to quantitative changes in the whole reflection pattern near the triple point. The evident dependence of slipstream instability magnitude on the physical and chemical transformation intensity in the fluid was previously experimentally observed. The results of an analytical investigation appeared to be in good agreement with the experimental data.

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Abbreviations

\(M_0\) :

Mach number of incident shock wave

\(M_1\) :

Mach number of gas flow

\(a\) :

Speed of sound

\(u\) :

Normal component of gas velocity relative to the shock wave

\(V\) :

Absolute velocity of gas flow

\(P\) :

Pressure

\(T\) :

Temperature

\(h\) :

Enthalpy

\(\rho \) :

Density

\(R\) :

Universal gas constant

\(\mu \) :

Molecular weight

\(\gamma \) :

Adiabatic index or ratio of specific heats

\(\chi \) :

Angle between triple point path and the wedge surface

\(\alpha _0\) :

Wedge angle

\(\omega _1\) :

Incidence wave angle

\(\omega _2\) :

Reflected wave angle

\(\phi \) :

Inclination angle

\(\omega _{RT}\) :

Angle between reflected wave and the slipstream

\(\delta \) :

Slipstream spread angle

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Acknowledgments

The present study is supported in part by the Russian Research Foundation for the Fundamental Sciences Grant 12-01-31362 and 14-08-01070. The authors gratefully thank Prof. Beric Skews for his insightful help in preparing this paper. Thanks are also due to the reviewers for their astute and helpful comments.

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Authors and Affiliations

  1. Joint Institute for High Temperatures of the Russian Academy of Sciences (JIHT RAS) 125412, Izhorskaya st. 13 Bd. 2, Moscow, Russia

    L. Gvozdeva, S. Gavrenkov & A. Nesterov

Authors
  1. L. Gvozdeva
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  2. S. Gavrenkov
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  3. A. Nesterov
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Corresponding author

Correspondence to L. Gvozdeva.

Additional information

Communicated by G. Ciccarelli.

This paper is based on work that was presented at the 24th International Colloquium on the Dynamics of Explosions and Reactive Systems, Taipei, Taiwan, July 28–August 2, 2013.

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Gvozdeva, L., Gavrenkov, S. & Nesterov, A. A study of slipstreams in triple shock wave configurations. Shock Waves 25, 283–291 (2015). https://doi.org/10.1007/s00193-015-0568-1

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