Thermal non-equilibrium nonlinear coupled constitutive relations for hypersonic rarefied diatomic gas flows

Abstract

The generalized hydrodynamic theory and its derived nonlinear coupled constitutive relations (NCCR) model have proven effective in simulating a range of typical hypersonic rarefied non-equilibrium flows, particularly in regimes where traditional Navier-Stokes (NS) equations are inadequate. However, the treatment of bulk viscosity has been limited, serving primarily as an approximation for rotational non-equilibrium effects, and lacking an explicit framework for energy exchange between different modes within the NCCR model. To address this limitation, this study introduces a thermal non-equilibrium NCCR model that operates without bulk viscosity, incorporating the Landau-Teller-Jeans relaxation model to facilitate explicit energy exchange between translational and rotational modes. The model's accuracy has been rigorously validated through a series of classical numerical cases, including analyzing nitrogen shock structures, supersonic flow over a flat plate, and hypersonic flows past blunt and flat-headed cylinders. The results demonstrate a significant improvement in alignment with experimental data and direct simulation Monte Carlo (DSMC) solutions compared to those derived from the NS equations and the original NCCR model lacking bulk viscosity. Furthermore, the proposed model enhances the predictive capability over the original NCCR framework and elucidates the mechanisms of non-equilibrium energy exchange between modes. These findings underscore the potential of the thermal non-equilibrium NCCR model as a robust and accurate tool for the simulation of hypersonic rarefied diatomic gas flows.