Extended continuum models for shock waves in CO2

Three continuum models extending the conventional Navier-Stokes-Fourier approach for modeling the shock wave structure in carbon dioxide are developed using the generalized Chapman-Enskog method. Multi-temperature models are based on splitting multiple vibrational relaxation mechanisms into fast and slow processes and introducing vibrational temperatures of various CO2 modes. The one-temperature model takes into account relaxation processes through bulk viscosity and internal thermal conductivity. All developed models are free of limitations introduced by the assumptions of a calorically perfect gas and constant Prandtl number; thermodynamic properties and all transport coefficients are calculated rigorously in each cell of the grid. Simulations are carried out for Mach numbers 3-7; the results are compared with solutions obtained in the frame of other approaches: multi-temperature Euler equations, model kinetic equations, and models with constant Prandtl numbers. The influence of bulk viscosity and Prandtl number on the fluid-dynamic variables, viscous stress, heat flux, and total enthalpy is studied. Bulk viscosity plays an important role in sufficiently rarefied gases under weak deviations from equilibrium; in multi-temperature models, non-equilibrium effects are associated with slow relaxation processes rather than with bulk viscosity. Using a constant Prandtl number yields over-predicted values of the heat flux. Contributions of various energy modes to the total heat flux are evaluated, with emphasis on the compensation of translational-rotational and vibrational energy fluxes.