Thermodynamic theory of the shock wave structure in a rarefied polyatomic gas: beyond the Bethe-Teller theory.

The structure of a shock wave in a rarefied polyatomic gas is studied on the basis of the theory of extended thermodynamics. Three types of the shock wave structure observed in experiments, that is, the nearly symmetric shock wave structure (type A, small Mach number), the asymmetric structure (type B, moderate Mach number), and the structure composed of thin and thick layers (type C, large Mach number), are explained by the theory in a unified way. The theoretical prediction of the profile of the mass density agrees well with the experimental data. The well-known Bethe-Teller theory of the shock wave structure in a polyatomic gas is reexamined in the light of the present theory.

[1]  F. J. McCormack Kinetic Moment Equations for a Gas of Polyatomic Molecules with Many Internal Degrees of Freedom , 1970 .

[2]  J. Meixner,et al.  Absorption und Dispersion des Schalles in Gasen mit chemisch reagierenden und anregbaren Komponenten. I. Teil , 1943 .

[3]  D. Gilbarg,et al.  The Structure of Shock Waves in the Continuum Theory of Fluids , 1953 .

[4]  H. Grad On the kinetic theory of rarefied gases , 1949 .

[5]  T. Ruggeri,et al.  Galilean invariance and entropy principle for systems of balance laws , 1989 .

[6]  Takashi Arima,et al.  Extended thermodynamics of real gases with dynamic pressure: An extension of Meixnerʼs theory , 2012 .

[7]  P. Le Tallec,et al.  Microreversible collisions for polyatomic gases and Boltzmann's theorem , 1994 .

[8]  Z. I. Slawsky,et al.  Measurement of the Vibrational Relaxation Effect in CO2 by Means of Shock Tube Interferograms , 1952 .

[9]  T. Ruggeri,et al.  Extended thermodynamics of dense gases , 2012 .

[10]  W. Dreyer,et al.  Maximisation of the entropy in non-equilibrium , 1987 .

[11]  W. Griffith,et al.  On fully-dispersed shock waves in carbon dioxide , 1957, Journal of Fluid Mechanics.

[12]  Takashi Arima,et al.  Dispersion relation for sound in rarefied polyatomic gases based on extended thermodynamics , 2013 .

[13]  P. Lax Hyperbolic systems of conservation laws II , 1957 .

[14]  Tommaso Ruggeri,et al.  On the shock structure problem for hyperbolic system of balance laws and convex entropy , 1998 .

[15]  E. F. Smiley,et al.  Shock‐Tube Measurements of Vibrational Relaxation , 1954 .

[16]  W. Griffith,et al.  STRUCTURE OF SHOCK WAVES IN POLYATOMIC GASES , 1956 .

[17]  P. Blythe,et al.  Experimental and theoretical analysis of vibrational relaxation regions in carbon dioxide , 1962, Journal of Fluid Mechanics.

[18]  W. Bleakney,et al.  Shock Waves in Gases , 1954 .

[19]  Francis J. McCormack,et al.  Kinetic Equations for Polyatomic Gases: The 17‐Moment Approximation , 1968 .

[20]  Takashi Arima,et al.  Effect of the dynamic pressure on the shock wave structure in a rarefied polyatomic gas , 2014 .

[21]  Claus Borgnakke,et al.  Statistical collision model for Monte Carlo simulation of polyatomic gas mixture , 1975 .

[22]  H. Alsmeyer,et al.  Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam , 1976, Journal of Fluid Mechanics.

[23]  Weiss Continuous shock structure in extended thermodynamics. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.