Abstract
AbstractA kinetic model of the Boltzmann equation for non-vibrating polyatomic gases is proposed, based on the Rykov model for diatomic gases. We adopt two velocity distribution functions (VDFs) to describe the system state; inelastic collisions are the same as in the Rykov model, but elastic collisions are modelled by the Boltzmann collision operator (BCO) for monatomic gases, so that the overall kinetic model equation reduces to the Boltzmann equation for monatomic gases in the limit of no translational–rotational energy exchange. The free parameters in the model are determined by comparing the transport coefficients, obtained by a Chapman–Enskog expansion, to values from experiment and kinetic theory. The kinetic model equations are solved numerically using the fast spectral method for elastic collision operators and the discrete velocity method for inelastic ones. The numerical results for normal shock waves and planar Fourier/Couette flows are in good agreement with both conventional direct simulation Monte Carlo (DSMC) results and experimental data. Poiseuille and thermal creep flows of polyatomic gases between two parallel plates are also investigated. Finally, we find that the spectra of both spontaneous and coherent Rayleigh–Brillouin scattering (RBS) compare well with DSMC results, and the computational speed of our model is approximately 300 times faster. Compared to the Rykov model, our model greatly improves prediction accuracy, and reveals the significant influence of molecular models. For coherent RBS, we find that the Rykov model could overpredict the bulk viscosity by a factor of two.
Highlights
The Boltzmann equation is the fundamental equation describing the collective motion of gas molecules from the continuum-fluid to the free-molecular flow regimes (Chapman & Cowling 1970; Cercignani 1990)
We present a new kinetic model for non-vibrating polyatomic gases, in which elastic collisions are modelled by the Boltzmann collision operator (BCO) for a monatomic gas, while inelastic collisions are the same as those in the Rykov model (Rykov 1975)
We have proposed a kinetic model for the Boltzmann equation for non-vibrating polyatomic gases, based on the Rykov model for diatomic gases with a Jeans’ relaxation model for the translational–rotational energy exchange
Summary
The Boltzmann equation is the fundamental equation describing the collective motion of gas molecules from the continuum-fluid to the free-molecular flow regimes (Chapman & Cowling 1970; Cercignani 1990). A kinetic model for non-vibrating polyatomic gases The Rykov kinetic model has been applied to normal shock wave problems (Larina & Rykov 2010; Liu et al 2014) It predicts density profiles in nitrogen with a viscosity index of 0.74; the translational temperature profiles are not in good agreement with DSMC results, especially at large Mach numbers (Liu et al 2014). Note that the early rising of the translational temperature in normal shock waves has been observed when using the Shakhov kinetic model for monatomic gas simulations (Xu & Huang 2011) The reason for this is the use of a single relaxation time τ , while in the Boltzmann equation the relaxation time depends on the molecular velocity. One may choose ω0 and ω1 to make the Eucken factor, as defined by (A 8), equal to experimentally measured values
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