TY - JOUR

T1 - Extended continuum models for shock waves in CO2

AU - Алексеев, Илья Владимирович

AU - Кустова, Елена Владимировна

N1 - Publisher Copyright: © 2021 Author(s).

PY - 2021/9/1

Y1 - 2021/9/1

N2 - 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 CO 2 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.

AB - 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 CO 2 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.

KW - STATE-TO-STATE

KW - VIBRATIONAL-RELAXATION

KW - CARBON-DIOXIDE

KW - BULK VISCOSITY

KW - KINETIC-MODEL

KW - FLOWS

KW - SIMULATIONS

KW - MOLECULES

KW - DIFFUSION

UR - https://aip.scitation.org/doi/10.1063/5.0062504

UR - http://www.scopus.com/inward/record.url?scp=85114494180&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/3c7fc8e1-84bd-3256-b609-2c460562c100/

U2 - 10.1063/5.0062504

DO - 10.1063/5.0062504

M3 - Article

VL - 33

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 9

M1 - 096101

ER -