TY - JOUR

T1 - Modeling of Nonequilibrium Processes behind a Shock Wave in a Mixture of Carbon Dioxide and Argon

AU - Batalov, S. A.

AU - Kustova, E. V.

PY - 2023

Y1 - 2023

N2 - A closed self-consistent model of a nonequilibrium flow of a mixture of carbon dioxide andargon behind the front of a plane shock wave is developed. The generalized Chapman–Enskogmethod in the three-temperature approach, which takes into account different channels of vibrationalrelaxation in a carbon-dioxide molecule, is used. An extended system of Navier–Stokes–Fourierequations consisting of mass-, momentum-, and energy-conservation equations supplemented by diffusion equations for the mixture components and relaxation equations for vibrational modes of theCO2 molecule are written. Constitutive relations for the stress tensor, diffusion velocity, heat flux, andvibrational energy fluxes are obtained. An algorithm for calculating the coefficients of shear and bulkviscosity, the thermal conductivity of different degrees of freedom, diffusion and thermal diffusion aredeveloped and implemented. The model is validated by comparing calculated transport coefficientswith experimental data for the viscosity and thermal conductivity of carbon dioxide and argon and forthe binary diffusion coefficient. Good agreement with the experiment is obtained. The dependence oftransport coefficients on the gas temperature, vibrational-mode temperatures, and mixture composition is analyzed. The developed model is ready for use in the numerical simulation of shock waves ina CO2–Ar mixture

AB - A closed self-consistent model of a nonequilibrium flow of a mixture of carbon dioxide andargon behind the front of a plane shock wave is developed. The generalized Chapman–Enskogmethod in the three-temperature approach, which takes into account different channels of vibrationalrelaxation in a carbon-dioxide molecule, is used. An extended system of Navier–Stokes–Fourierequations consisting of mass-, momentum-, and energy-conservation equations supplemented by diffusion equations for the mixture components and relaxation equations for vibrational modes of theCO2 molecule are written. Constitutive relations for the stress tensor, diffusion velocity, heat flux, andvibrational energy fluxes are obtained. An algorithm for calculating the coefficients of shear and bulkviscosity, the thermal conductivity of different degrees of freedom, diffusion and thermal diffusion aredeveloped and implemented. The model is validated by comparing calculated transport coefficientswith experimental data for the viscosity and thermal conductivity of carbon dioxide and argon and forthe binary diffusion coefficient. Good agreement with the experiment is obtained. The dependence oftransport coefficients on the gas temperature, vibrational-mode temperatures, and mixture composition is analyzed. The developed model is ready for use in the numerical simulation of shock waves ina CO2–Ar mixture

KW - transport coefficients

KW - three-temperature model

KW - shock wave

KW - carbon dioxide

KW - argon

M3 - Article

VL - 56

SP - 203

EP - 211

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -