TY - JOUR
T1 - A Kinetic Model for a Polyatomic Gas with Temperature-Dependent Specific Heats and Its Application to Shock-Wave Structure
AU - Kosuge, Shingo
AU - Kuo, Hung Wen
AU - Aoki, Kazuo
N1 - Funding Information:
The authors thank Professor Masaru Sugiyama for valuable comments and professor Shigeru Taniguchi for providing an original figure of his paper. One of the authors (K.A.) thanks Department of Mathematics, National Cheng Kung University and National Center for Theoretical Sciences, National Taiwan University for their support and hospitality.
Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/10/1
Y1 - 2019/10/1
N2 - The ellipsoidal statistical (ES) model of the Boltzmann equation for a polyatomic gas with constant specific heats (calorically perfect gas), proposed by Andries et al. (Eur J Mech B Fluids 19:813, 2000), is extended to a polyatomic gas with temperature-dependent specific heats (thermally perfect gas). Then, the new model equation is applied to investigate the structure of a plane shock wave with special interest in CO 2 gas, which is known to have a very large bulk viscosity, and in the case of relatively strong shock waves. A numerical analysis, as well as an asymptotic analysis for large bulk viscosity, is performed in parallel to the previous paper by two of the present authors (Kosuge and Aoki, in: Phys Rev Fluids 3:023401, 2018), where the structure of a shock wave in CO 2 gas was investigated using the ES model for a polyatomic gas with constant specific heats. From the numerical and analytical results, the effect of temperature-dependent specific heats on the structure of a shock wave is clarified.
AB - The ellipsoidal statistical (ES) model of the Boltzmann equation for a polyatomic gas with constant specific heats (calorically perfect gas), proposed by Andries et al. (Eur J Mech B Fluids 19:813, 2000), is extended to a polyatomic gas with temperature-dependent specific heats (thermally perfect gas). Then, the new model equation is applied to investigate the structure of a plane shock wave with special interest in CO 2 gas, which is known to have a very large bulk viscosity, and in the case of relatively strong shock waves. A numerical analysis, as well as an asymptotic analysis for large bulk viscosity, is performed in parallel to the previous paper by two of the present authors (Kosuge and Aoki, in: Phys Rev Fluids 3:023401, 2018), where the structure of a shock wave in CO 2 gas was investigated using the ES model for a polyatomic gas with constant specific heats. From the numerical and analytical results, the effect of temperature-dependent specific heats on the structure of a shock wave is clarified.
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U2 - 10.1007/s10955-019-02366-5
DO - 10.1007/s10955-019-02366-5
M3 - Article
AN - SCOPUS:85071674208
SN - 0022-4715
VL - 177
SP - 209
EP - 251
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 2
ER -