A Note on the Steady Navier–Stokes Equations Derived from an ES–BGK Model for a Polyatomic Gas

Aoki, Kazuo; Bisi, Marzia; Groppi, Maria; Kosuge, Shingo

doi:10.3390/fluids6010032

Fluids

2021

DOI: 10.3390/fluids6010032

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A Note on the Steady Navier–Stokes Equations Derived from an ES–BGK Model for a Polyatomic Gas

Kazuo Aoki

Marzia Bisi

Maria Groppi

et al.

Abstract: The two-temperature Navier–Stokes equations derived from an ellipsoidal Bhatnagar-Gross-Krook (ES-BGK) model for a polyatomic gas (Phys. Rev. E102, 023104 (2020)) are considered in regimes where bulk viscosity is much greater than the shear viscosity. Possible existence of a shock-wave solution for the steady version of these hydrodynamic equations is investigated resorting to the qualitative theory of dynamical systems. Stability properties of upstream and downstream equilibria are discussed for varying param… Show more

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Cited by 3 publications

References 51 publications

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Shock-wave structure in non-polar diatomic and polyatomic dense gases under rotation and vibration

Khapra

Patel

2022

Physics of Fluids

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This study investigates the effect of rotation and vibration on the structure of shock waves in moderately dense diatomic and polyatomic non-polar gases using the one-temperature Navier-Stokes-Fourier approach. The modified Enskog equation of state of the gas is taken to include the denseness and shielding effects. The specific heat at constant volume has been taken to be temperature-dependent. The shear viscosity, the bulk viscosity, and the thermal conductivity have been assumed to follow the temperature-dependent power-law model. Nitrogen and oxygen gas have been taken as the test cases for diatomic gases while carbon dioxide for the polyatomic gases. The implicit system of equations is derived and solved numerically for density and temperature. The inclusion of denseness, rotational and vibrational modes of molecular motion have a significant effect on the density and temperature profiles, the inverse shock thickness, the bulk to shear viscosity ratio, and the molar specific heat at constant pressure. The gas having a low characteristic vibrational temperature has been found to have a high value of inverse shock thickness. The inverse shock thickness, the bulk to shear viscosity ratio, and the molar specific heat at constant pressure for nitrogen and carbon dioxide are found to be in good agreement with the experimental values.

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Shock-wave structure in non-polar diatomic and polyatomic dense gases under rotation and vibration

Khapra

Patel

2022

Physics of Fluids

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H -theorem and boundary conditions for two-temperature model: Application to wave propagation and heat transfer in polyatomic gases

Kumar,

Rana

2023

Phys. Rev. E

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Boundary conditions for two-temperature Navier-Stokes equations for a polyatomic gas

et al. 2021

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A Note on the Steady Navier–Stokes Equations Derived from an ES–BGK Model for a Polyatomic Gas

Cited by 3 publications

References 51 publications

Shock-wave structure in non-polar diatomic and polyatomic dense gases under rotation and vibration

Shock-wave structure in non-polar diatomic and polyatomic dense gases under rotation and vibration

H -theorem and boundary conditions for two-temperature model: Application to wave propagation and heat transfer in polyatomic gases

Boundary conditions for two-temperature Navier-Stokes equations for a polyatomic gas

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