Non-equilibrium polyatomic gas flows: Nonlinear coupled constitutive relations and topological study of three-temperature relaxation

초록

Non-equilibrium gaseous phenomena at high temperatures may activate additional degrees of freedom that remain dormant at lower temperatures, such as vibrational modes. An accurate prediction of the forces and heat flux acting on a body in such an environment requires detailed information on the energy distribution among rotational and vibrational degrees of freedom. The present study aims to analyze non-equilibrium flows by carefully accounting for the relaxation processes among various degrees of freedom. As higher-order constitutive equations, the nonlinear coupled constitutive relations (NCCR) were employed to obtain more accurate approximations of the stress and heat flux terms by extending the two-temperature formulation proposed by Srivastava et al. [Phys. Fluids 37, 036154 (2025)] to a three-temperature relaxation case. The present study further examined various relaxation models for internal energy to evaluate their effectiveness and accuracy. In addition to the standard energy exchange that considers only translational and other modes, the energy exchange between rotational and vibrational degrees of freedom was investigated. A topological study was further incorporated to observe the changes in the solution space within the second-order NCCR formulation relative to the first-order constitutive relations, i.e., the Navier-Stokes-Fourier formulation. Finally, the new set of equations derived from the three-temperature relaxation model was used to investigate shock wave structures in polyatomic gases.

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