Shock wave structure in binary mixtures of CO2 with noble gases

A mathematical model is developed that describes the shock wave structure in a viscous flow of a mixture containing carbon dioxide and noble gases, particularly argon, neon, and helium. The proposed three-temperature model takes into account several mechanisms of vibrational relaxation in polyatomic gases, diffusion, heat conductivity associated with different vibrational modes, shear, and bulk viscosity. A continuum approach based on the generalized Chapman–Enskog method is applied to derive a self-consistently closed set of extended Navier–Stokes–Fourier equations. The peculiarity of the model is that we use neither phenomenological approaches when deriving constitutive relations for the transport fluxes nor widely known approximations for thermodynamic and transport properties; the energy and specific heats for various vibrational modes are calculated explicitly; the transport coefficients are found as solutions of corresponding transport linear systems; and the expression for the diffusion velocity is free of common limitations of the Fick law. The model is implemented to the in-house finite-volume flow solver. The effects of free-stream thermal nonequilibrium, mixture composition, diffusion, and bulk viscosity on the shock structure are discussed. While in the CO2–Ar mixture diffusion is negligible, it is dominating in the CO2–He mixture. The contribution of bulk viscosity is generally weak compared to other effects. In CO2–Ar mixture, there is a compensation effect between the heat fluxes due to diffusion and vibrational relaxation; these contributions are, however, small compared to the flux of translational–rotational energy. In CO2–He, the heat flux due to diffusion is significant, making more than a half of the total heat flux.