Macroscopic description of the motions of a gas with rotational degrees of freedom

Рыков, В. А.; Skobelkin, V. N.

doi:10.1007/bf01094479

Cited by 23 publications

(15 citation statements)

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“…Similarly, the heat fluxes q t and q r , which are related to the transfer of translational and rotational energies, are given by (A 8) For diatomic gases, the transport coefficients are the same as those found by Rykov & Skobelkin (1978).…”

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confidence: 90%

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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confidence: 90%

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

White

Scanlon

et al. 2014

J. Fluid Mech.

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“…For most of the molecular gases, the second condition is satisfied for usual temperatures, since, in this case, the distance between the rotational levels 2 /2I 0 is small as compared with kT , where is the Plank constant and I 0 is the moment of inertia of the molecule (see [137,168,169,212]). Such a description is correct if the gas temperature is not very high (oscillatory degrees of freedom are not excited) and is not very small (rotational degrees of freedom can be considered classically).…”

Section: Quasi-gas-dynamic Equations For Nonequilibrium Gas Flowsmentioning

confidence: 99%

“…Such a representation of the distribution function is correct in the case where the gas temperature is not very high and, therefore, the oscillatory degrees of freedom are not excited, but it is not very small, i.e., the rotational degrees of freedom of the molecule can be considered in the classical approximation (see [137,168,169,212]). 8.2).…”

Section: Molecular Models and Distribution Functionsmentioning

confidence: 99%

Quasi-Gas Dynamic Equations

Елизарова

2009

Computational Fluid and Solid Mechanics

173

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The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, BerlinPrinted on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) PrefaceThe monograph is devoted to modern mathematical models and numerical methods for solving gas-and fluid-dynamic problems based on them. Two interconnected mathematical models generalizing the Navier-Stokes system are presented; they differ from the Navier-Stokes system by additional dissipative terms with a small parameter as a coefficient. The new models are called the quasi-gas-dynamic and quasi-hydrodynamic equations. Based on these equations, effective finite-difference algorithms for calculating viscous nonstationary flows are constructed and examples of numerical computations are presented. The universality, the efficiency, and the exactness of the algorithms constructed are ensured by the fulfillment of integral conservation laws and the theorem on entropy balance for them.The book is a course of lectures and is intended for scientists and engineers who deal with constructing numerical algorithms and performing practical calculations of gas and fluid flows and also for students and postgraduate students who specialize in numerical gas and fluid dynamics. Moscow Tatiana Elizarova December 2008 v Contents

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“…The well-known Rykov model for diatomic gases with rotational degrees of freedom is originally obtained by Rykov [9,10]. Recently, Wu et al [11] has generalized this model to polyatomic gases.…”

Section: The Rykov Modelmentioning

confidence: 99%

“…By applying the Chapman-Enskog expansion to the Boltzmann equation with the BGK collision operator, the NSF system can be recovered, but with a unit Prandtl number which does not obey the physical reality. Hence, some improved models have been developed to overcome this limitation from different physical considerations, such as the Shakhov (SH) model [5], the ellipsoidal statistical (ES) model [6], the internal energy double-distribution-function (IEDDF) model [7], the total energy double-distribution-function (TEDDF) model [8], and the Rykov (R) model [9,10,11]. Further, we notice that, for example, the ratio between the bulk to shear viscosity in SH model is always less than 2/D, where D is the dimension of the hydrodynamic velocity space.…”

Section: Introductionmentioning

confidence: 99%

A general framework for the inverse design of mesoscopic models based on the Boltzmann equation

Chen¹,

Wang²,

Lai³

et al. 2020

Preprint

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In this paper, we present a general framework for the inverse-design of mesoscopic models based on the Boltzmann equation. Starting from the single-relaxation-time Boltzmann equation with an additional source term, two model Boltzmann equations for two reduced distribution functions are obtained, each then also having an additional undetermined source term. Under this general framework and using Navier-Stokes-Fourier (NSF) equations as constraints, the structures of the distribution functions are obtained by the leading-order Chapman-Enskog analysis. Next, five basic constraints for the design of the two source terms are obtained in order to recover the Navier-Stokes-Fourier system in the continuum limit. These constraints allow for adjustable bulk-to-shear viscosity ratio, Prandtl number as well as a thermal energy source. The specific forms of the two source terms can be determined through proper physical considerations and numerical implementation requirements. By employing the truncated Hermite expansion, one design for the two source terms is proposed. Moreover, three well-known mesoscopic models in the literature are shown to be compatible with these five constraints. In addition, the consistent implementation of boundary conditions is also explored by using the Chapman-Enskog expansion at the NSF order. Finally, based on the higher-order Chapman-Enskog expansion of the distribution functions, we derive the complete analytical expressions for the viscous stress tensor and the heat flux. Some underlying physics can be further explored under this framework.

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Macroscopic description of the motions of a gas with rotational degrees of freedom

Cited by 23 publications

References 1 publication

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

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

Quasi-Gas Dynamic Equations

A general framework for the inverse design of mesoscopic models based on the Boltzmann equation

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