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

Wu, Lei; White, Craig; Scanlon, Thomas; Reese, Jason M.; Zhang, Yonghao

doi:10.1017/jfm.2014.632

Cited by 73 publications

(94 citation statements)

References 52 publications

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“…For instances, in the free-molecular flow regime, even when the density, temperature, and shear viscosity of the two molecular models are exactly the same, the HS model has a mass flow rate (MFR) 16% higher than that of the Lennard-Jones potential for Xenon in the Poiseuille flow between two parallel plates, while in thermal transpiration the HS model has a MFR 24% higher (Sharipov & Bertoldo 2009b;Wu et al 2015a). Moreover, in the coherent Rayleigh-Brillouin scattering of light by rarefied gases, it has been shown that the extraction of gas bulk viscosity could have an relative error of about 100% when inappropriate intermolecular potentials are used (Wu et al 2015b).…”

Section: Introductionmentioning

confidence: 99%

Assessment and development of the gas kinetic boundary condition for the Boltzmann equation

Struchtrup

2017

J. Fluid Mech.

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Gas-surface interactions play important roles in internal rarefied gas flows, especially in micro-electro-mechanical systems with large surface area to volume ratios. Although great progresses have been made to solve the Boltzmann equation, the gas kinetic bound- ary condition (BC) has not been well studied. Here we assess the accuracy the Maxwell, Epstein, and Cercignani-Lampis BCs, by comparing numerical results of the Boltzmann equation for the Lennard-Jones potential to experimental data on Poiseuille and thermal transpiration flows. The four experiments considered are: Ewart et al. [J. Fluid Mech. 584, 337-356 (2007)], Rojas-C ́ardenas et al. [Phys. Fluids, 25, 072002 (2013)], and Yam- aguchi et al. [J. Fluid Mech. 744, 169-182 (2014); 795, 690-707 (2016)], where the mass flow rates in Poiseuille and thermal transpiration flows are measured. This requires the BC has the ability to tune the effective viscous and thermal slip coefficients to match the experimental data. Among the three BCs, the Epstein BC has more flexibility to adjust the two slip coefficients, and hence in most of the time it gives good agreement with the experimental measurement. However, like the Maxwell BC, the viscous slip coefficient in the Epstein BC cannot be smaller than unity but the Cercignani-Lampis BC can. Therefore, we propose to combine the Epstein and Cercignani-Lampis BCs to describe gas-surface interaction. Although the new BC contains six free parameters, our approxi- mate analytical expressions for the viscous and thermal slip coefficients provide a useful guidance to choose these parameters

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Section: Introductionmentioning

confidence: 99%

Assessment and development of the gas kinetic boundary condition for the Boltzmann equation

Struchtrup

2017

J. Fluid Mech.

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“…When Kn lies in the regime 0.001 Kn 0.1   contributions from the central Rayleigh part and the Brillouin side part become mixed and then the widths of both parts broaden due to the increased dissipation in sound propagation. Further increase of Kn results in vanishing contribution of the Brillouin part and the whole spectrum becomes nearly Gaussian [26][27][28]66]. In the typical spectra of the coherent RBS, one can notice the presence of Brillouin peaks only when the gas flow is in the hydrodynamic regime (Kn0.001).…”

Section: Results and Interpretationmentioning

confidence: 99%

“…In the typical spectra of the coherent RBS, one can notice the presence of Brillouin peaks only when the gas flow is in the hydrodynamic regime (Kn0.001). As Kn increases further, both peaks (the central Rayleigh and the two Brillouin side peaks) are present and the relative intensity of these peaks becomes large and later on the whole spectrum becomes Gaussian [26][27][28].…”

Section: Results and Interpretationmentioning

confidence: 99%

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Recasting Navier–Stokes equations

et al. 2019

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Classical Navier-Stokes equations fail to describe some flows in both the compressible and incompressible configurations. In this article, we propose a new methodology based on transforming the fluid mass velocity vector field to obtain a new class of continuum models. We uncover a class of continuum models which we call the re-casted Navier-Stokes. They naturally exhibit the physics of previously proposed models by different authors to substitute the original Navier-Stokes equations. The new models unlike the conventional Navier-Stokes appear as more complete forms of mass diffusion type continuum flow equations. They also form systematically a class of thermomechanically consistent hydrodynamic equations via the original equations. The plane wave analysis is performed to check their linear stability under small perturbations, which confirms that all re-casted models are spatially and temporally stable like their classical counterpart. We then use the Rayleigh-Brillouin scattering experiments to demonstrate that the re-casted equations may be better suited for explaining some of the experimental data where original Navier-Stokes equations fail.Öttinger [11] also proposed earlier a substitute for the classical Navier-Stokes in his phenomenological GENERIC formalism. In the GENERIC formulation, Öttinger [11] demonstrated that by assuming the row and the column, which are associated with the mass density in the friction matrix to be identically zero, leads to the conventional Navier-Stokes equations. A more general form of friction matrix that includes the basic fact that particles operate diffusive motions, leads to a revised set of transport equations that contain two velocities, which are very similar in nature to the volume and mass velocities. Durst et al [12] based their arguments on that the absence of mass diffusion terms in the continuity equation contradicts constitutive relations for momentum and heat diffusion: when the fluid properties changes spatially in the presence of momentum and heat diffusions, there should also be present the mass diffusion. They later derived the Extended Navier-Stokes equations [12,13,17] based on the mass-diffusion controlled formalism. A late suggestion to substitute the Navier-Stokes is given by Svärd [18].Generally, there are a number of experimental data that standard Navier-Stokes fail to predict. Shock wave structure predictions are a ubiquitous example of Navier-Stokes failure [4,6,19,20]. Experimental data of water flows in carbon nanotubes or confined pores is another research topic showing large deviations from the classical Hagen-Poiseuille equation [21,22]. A convincing theoretical interpretation of this data is still lacking. Leaving aside non-linear configurations, conventional Navier-Stokes equations also fail to describe some of the linear flow problems accurately. For example, it is unsuccessful in describing the actual spectrum shapes in the Rayleigh-Brillouin scattering problem [23][24][25][26][27][28].In the current work, we provide new insights into the ...

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

Cited by 73 publications

References 52 publications

Assessment and development of the gas kinetic boundary condition for the Boltzmann equation

Assessment and development of the gas kinetic boundary condition for the Boltzmann equation

Recasting Navier–Stokes equations

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

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