Kinetic model of the Boltzmann equation for a diatomic gas with rotational degrees of freedom

Larina, I. N.; Рыков, В. А.

doi:10.1134/s0965542510120134

Cited by 32 publications

(26 citation statements)

References 3 publications

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“…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; however, the translational temperature profiles are not in good agreement with DSMC results, especially at large Mach numbers (Liu et al 2014).…”

Section: A Kinetic Model For Non-vibrating Polyatomic Gasesmentioning

confidence: 99%

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A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases

White

Scanlon

et al. 2014

J. Fluid Mech.

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A 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.

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Section: A Kinetic Model For Non-vibrating Polyatomic Gasesmentioning

confidence: 99%

“…Kinetic model equations are therefore needed to simplify the complicated BCO. In the following, we first introduce the Rykov kinetic model (Rykov 1975) for diatomic gases because it can predict density profiles in normal shock waves (Larina & Rykov 2010;Liu et al 2014). We then extend the Rykov model to model polyatomic gases.…”

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confidence: 99%

A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases

White

Scanlon

et al. 2014

J. Fluid Mech.

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“…The effort of solving the Boltzmann equation is significantly reduced by substituting the complicated collision term with reliable kinetic models. The Holway kinetic model [26] has been applied with considerable success in rarefied polyatomic gas flows and heat transfer configurations [27,10,12,14] providing good agreement with experimental results. The H-theorem can be proved in a straightforward manner for the Holway model following the arguments leading to analogous proof for the BGK model [12,14].…”

Section: The Holway Kinetic Modelmentioning

confidence: 87%

“…The literature survey on this topic is very extensive and therefore only some indicative works related to the present heat transfer configuration are cited [1][2][3][4][5][6]. Corresponding work in polyatomic gases is quite limited and the existing one ignores the effect of the vibrational degrees of freedom [7][8][9][10][11][12][13][14]. It is known however, that vibrational excitation must be included when the reference temperature of the heat flow setup exceeds about 30% of the lower gas characteristic vibrational temperature which significantly varies for each gas.…”

Section: Introductionmentioning

confidence: 99%

Effect of vibrational degrees of freedom on the heat transfer in polyatomic gases confined between parallel plates

Tantos

Ghiroldi

Valougeorgis

et al. 2016

International Journal of Heat and Mass Transfer

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Conductive stationary heat transfer through rarefied nonpolar polyatomic gases, confined between parallel plates maintained at different temperatures, is investigated. It is assumed that gas molecules possess both rotational and vibrational degrees of freedom, described by the classical rigid rotator and quantum harmonic oscillator models, respectively. The flow structure is computed by the Holway kinetic model and the Direct Simulation Monte Carlo method. In both approaches the total collision frequency is computed according to the Inverse Power Law intermolecular potential. Inelastic collisions in DSMC simulations are based on the quantum version of the Borgnakke–Larsen collision model. Results are presented for N2, O2, CO2, CH4 and SF6 representing diatomic as well as linear and nonlinear polyatomic molecules with 1 up to 15 vibrational modes. The translational, rotational, vibrational and total temperatures and heat fluxes are computed in a wide range of the rarefaction parameter and for various ratios of the hot over the cold plate temperatures. Very good agreement, between the Holway and DSMC results is observed as well as with experiments. The effect of the vibrational degrees of freedom is demonstrated. In diatomic gases the vibrational heat flux varies from 5% up to 25% of the total one. Corresponding results in polyatomic gases with a higher number of vibrational modes show that even at low reference temperatures the contribution of the vibrational heat flux may be considerably higher. For example in the case of SF6 at 300 K and 500 K the vibrational heat flux is about 67% and 76% respectively of the total heat flux. Furthermore, it is numerically proved that the computed solutions are in agreement with the Chapman–Enskog approximation in a central strip of the computational domain even at moderately large values of the rarefaction parameter, as found in previous investigations. This property has been used to compute the gas thermal conductivity predicted by the adopted models

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“…In [38] The dimensionless macroscopic quantities can be obtained from F 0 and F 1 by means of the following formulae:…”

Section: Nondimensional Rykov Modelmentioning

confidence: 99%

A gas kinetic scheme for hybrid simulation of partially rarefied flows

Colonia

Steijl

Barakos

2017

Progress in Flight Physics

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Approaches to predict §ow ¦elds that display rarefaction e¨ects incur a cost in computational time and memory considerably higher than methods commonly employed for continuum §ows. For this reason, to simulate §ow ¦elds where continuum and rare¦ed regimes coexist, hybrid techniques have been introduced. In the present work, analytically de¦ned gas-kinetic schemes based on the Shakhov and Rykov models for monoatomic and diatomic gas §ows, respectively, are proposed and evaluated with the aim to be used in the context of hybrid simulations. This should reduce the region where more expensive methods are needed by extending the validity of the continuum formulation. Moreover, since for high-speed rare¦ed gas §ows it is necessary to take into account the nonequilibrium among the internal degrees of freedom, the extension of the approach to employ diatomic gas models including rotational relaxation process is a mandatory ¦rst step towards realistic simulations. Compared to previous works of Xu and coworkers, the presented scheme is de¦ned directly on the basis of kinetic models which involve a Prandtl number correction. Moreover, the methods are de¦ned fully analytically instead of making use of Taylor expansion for the evaluation of the required derivatives. The scheme has been tested for various test cases and Mach numbers proving to produce reliable predictions in agreement with other approaches for near-continuum §ows. Finally, the performance of the scheme, in terms of memory and computational time, compared to discrete velocity methods makes it a compelling alternative in place of more complex methods for hybrid simulations of weakly rare¦ed §ows.

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Kinetic model of the Boltzmann equation for a diatomic gas with rotational degrees of freedom

Cited by 32 publications

References 3 publications

A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases

A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases

Effect of vibrational degrees of freedom on the heat transfer in polyatomic gases confined between parallel plates

A gas kinetic scheme for hybrid simulation of partially rarefied flows

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