Boltzmann-based second-order constitutive models of diatomic and polyatomic gases including the vibrational mode

Abstract

Describing diatomic and polyatomic gases at high temperatures requires a deep understanding of the excitation of molecules to a higher vibrational level. We developed new second-order constitutive models for diatomic and polyatomic gases with vibrational degrees of freedom, starting from the modified Boltzmann–Curtiss kinetic equation. The closing-last balanced closure and cumulant expansion of the calortropy production associated with the Boltzmann collision term are key to the derivation of the second-order models, compatible with the second law of thermodynamics. The topology of the constitutive models showed the presence of highly nonlinear and coupled protruding or sunken regions in the compression branch. It was also shown that the vibrational mode reduces the level of nonlinearity in the topology. In addition, analysis of a strong shock structure highlighted the interplay between the second-order effects in the constitutive relations and the vibrational–translational relaxation. Finally, the analysis showed that the results of the second-order models were in better agreement with the direct simulation Monte Carlo data, when compared with the results of the first-order models, especially in the profiles and slopes of density, velocity, and vibrational temperatures.