Modeling Nonequilibrium Gas Flow Based on Moment Equations

Torrilhon, Manuel

doi:10.1146/annurev-fluid-122414-034259

Cited by 177 publications

(160 citation statements)

References 131 publications

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“…Besides the Boltzmann equation, rarefaction effects that are beyond the resolution of the NSF system can be predicted by extended macroscopic moment equations (Struchtrup 2005;Gu & Emerson 2009), which were the subject of a recent article in the Annual Review of Fluid Mechanics (Torrilhon 2016). The moment equations form a set of partial differential equations describing the evolution of macroscopic quantities, such as mass density, temperature, velocity, heat flux, stress tensor and so on, defined as moments of the distribution function.…”

Section: Introductionmentioning

confidence: 99%

Evaporation-driven vapour microflows: analytical solutions from moment methods

2018

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Macroscopic models based on moment equations are developed to describe the transport of mass and energy near the phase boundary between a liquid and its rarefied vapour due to evaporation and hence, in this study, condensation. For evaporation from a spherical droplet, analytic solutions are obtained to the linearised equations from the Navier-Stokes-Fourier, regularised 13-moment and regularised 26-moment frameworks. Results are shown to approach computational solutions to the Boltzmann equation as the number of moments are increased, with good agreement for Knudsen number 1, whilst providing clear insight into non-equilibrium phenomena occurring adjacent to the interface.

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Section: Introductionmentioning

confidence: 99%

Evaporation-driven vapour microflows: analytical solutions from moment methods

2018

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“…we retrieve the perfect gas law for heavy species 45) where m h is the mean heavy-species molar mass, given by …”

Section: Heavy-species Thermalizationmentioning

confidence: 99%

Kinetic theory of two-temperature polyatomic plasmas

Orlac’h

Giovangigli

Novikova

et al. 2018

Physica A: Statistical Mechanics and its Applications

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We investigate the kinetic theory of two-temperature plasmas for reactive polyatomic gas mixtures. The Knudsen number is taken proportional to the square root of the mass ratio between electrons and heavy-species, and thermal non-equilibrium between electrons and heavy species is allowed. The kinetic non-equilibrium framework also requires a weak coupling between electrons and internal energy modes of heavy species. The zeroth-order and first-order fluid equations are derived by using a generalized Chapman-Enskog method. Expressions for transport fluxes are obtained in terms of macroscopic variable gradients and the corresponding transport coefficients are expressed as bracket products of species perturbed distribution functions. The theory derived in this paper provides a consistent fluid model for non-thermal multicomponent plasmas.

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“…Here, it is worthwhile to note that while it is an important validity test for moment equations to compute the precise form of the transport coefficients, it is well-known that these coefficients have only a little relevance in non-equilibrium situations when a linear relation between fluxes and gradients does not hold anymore. Instead, it has been shown (for elastic gases) that moment equations allow for cross effects like thermal stresses and non-gradient heat fluxes (Torrilhon 2016) that are expected to also have a systematic influence in granular flows. The actual goal of moment equations is not only to match the transport coefficients but also to go beyond these classical theories and provide an enhanced fluid dynamic theory for granular gases.…”

Section: Comparison With Existing Theories and Computer Simulationsmentioning

confidence: 99%

Higher-order moment theories for dilute granular gases of smooth hard spheres

2017

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Grad's method of moments is employed to develop higher-order Grad moment equations-up to first 26-moments-for dilute granular gases within the framework of the (inelastic) Boltzmann equation. The homogeneous cooling state of a freely cooling granular gas is investigated with the Grad 26-moment equations in a semi-linearized setting and it is shown that the granular temperature in the homogeneous cooling state still decays according to Haff's law while the other higher-order moments decay on a faster time scale. The nonlinear terms of fully contracted fourth moment are also considered and, by exploiting the stability analysis of fixed points, it is shown that these nonlinear terms have negligible effect on Haff's law. Furthermore, an even larger Grad moment system which includes the fully contracted sixth moment is also scrutinized and the stability analysis of fixed points is again exploited to conclude that even the inclusion of scalar sixth order moment into the Grad moment system has negligible effect on Haff's law. The constitutive relations for the stress and heat flux (i.e., the Navier-Stokes and Fourier relations) are derived through the Grad 26-moment equations and compared with those obtained via CE expansion and via computer simulations. The linear stability of the homogeneous cooling state is analyzed through the Grad 26-moment system and various sub-systems by decomposing them into longitudinal and transverse systems. It is found that one eigenmode in both longitudinal and transverse systems in the case of inelastic gases is unstable. By comparing the eigenmodes from various theories, it is established that the 13-moment eigenmode theory predicts that the unstable heat mode of the longitudinal system remains unstable for all wavenumbers below a certain coefficient of restitution while any other higher-order moment theory shows that this mode becomes stable above some critical wavenumber for all values of the coefficient of restitution. In particular, the Grad 26-moment theory leads to a smooth profile for the critical wavenumber in contrast to the other considered theories. Furthermore, the critical system size obtained through the Grad 26-moment and existing theories are also in excellent agreement.

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Modeling Nonequilibrium Gas Flow Based on Moment Equations

Cited by 177 publications

References 131 publications

Evaporation-driven vapour microflows: analytical solutions from moment methods

Evaporation-driven vapour microflows: analytical solutions from moment methods

Kinetic theory of two-temperature polyatomic plasmas

Higher-order moment theories for dilute granular gases of smooth hard spheres

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