Topic
Knudsen number
About: Knudsen number is a research topic. Over the lifetime, 5052 publications have been published within this topic receiving 104278 citations.
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TL;DR: Numerical results demonstrate that accurate solutions in both continuum and rarefied flow regimes can be obtained from the current DUGKS.
Abstract: Based on the Boltzmann-BGK (Bhatnagar-Gross-Krook) equation, in this paper a discrete unified gas kinetic scheme (DUGKS) is developed for low-speed isothermal flows. The DUGKS is a finite-volume scheme with the discretization of particle velocity space. After the introduction of two auxiliary distribution functions with the inclusion of collision effect, the DUGKS becomes a fully explicit scheme for the update of distribution function. Furthermore, the scheme is an asymptotic preserving method, where the time step is only determined by the Courant-Friedricks-Lewy condition in the continuum limit. Numerical results demonstrate that accurate solutions in both continuum and rarefied flow regimes can be obtained from the current DUGKS. The comparison between the DUGKS and the well-defined lattice Boltzmann equation method (D2Q9) is presented as well.
316 citations
01 Jan 1969
TL;DR: In this paper, rarefied gas dynamics is concerned with flows at such low density that the molecular mean free path is not negligible, and important modifications in aerodynamic and heat transfer characteristics are ascribable to the basic molecular structure of the gas.
Abstract: Rarefied gas dynamics is concerned with flows at such low density that the molecular mean free path is not negligible. Under these conditions, the gas no longer behaves as a continuum. Important modifications in aerodynamic and heat transfer characteristics occur which are ascribable to the basic molecular structure of the gas.
311 citations
TL;DR: In this article, a model for the diffusion of gases in porous media in the absence of pressure gradients is presented, in which the porous medium is visualized as a collection of uniformly distributed ''dust'' particles which are constrained to be stationary.
Abstract: A model is presented for the diffusion of gases in porous media in the absence of pressure gradients, in which the porous medium is visualized as a collection of uniformly distributed ``dust'' particles which are constrained to be stationary. By formally considering the dust particles as giant molecules, it is possible to derive all the desired results very simply from rigorous kinetic theory as special cases of multicomponent mixtures. By formally varying the mole fractions of the real gas molecules, the entire pressure range from the Knudsen region to the normal diffusion region can be covered. This model permits the first satisfactory theoretical derivation of the experimentally discovered fact that the flux ratio for binary mixtures is equal to (m2/m1)½ at all pressures (not just in the Knudsen region). It also permits a rigorous theoretical treatment of the entire transition region for the first time, from which is obtained the usual Bosanquet interpolation formula and a differential equation for diffusion which covers the entire range (and appears to be new). The model gives no quantitative a priori characterization of the porous medium itself, but if one gas mixture is measured in a given medium, then the behavior of other gas mixtures in the same medium can be predicted.
308 citations
TL;DR: Numerical results are presented which demonstrate convergence to the hydrodynamic limit and theknudsen layer in the Kramers' problem is reproduced correctly for small Knudsen numbers.
Abstract: Derivation of the lattice Boltzmann method from the continuous kinetic theory [X. He and L. S. Luo, Phys. Rev. E 55, R6333 (1997); X. Shan and X. He, Phys. Rev. Lett. 80, 65 (1998)] is extended in order to obtain boundary conditions for the method. For the model of a diffusively reflecting moving solid wall, the boundary condition for the discrete set of velocities is derived, and the error of the discretization is estimated. Numerical results are presented which demonstrate convergence to the hydrodynamic limit. In particular, the Knudsen layer in the Kramers' problem is reproduced correctly for small Knudsen numbers.
306 citations
TL;DR: In this paper, the tangential momentum accommodation coefficient (TMAC) for several gases in contact with single-crystal silicon was found to be less than unity, ranging from 0.75 to 0.85.
Abstract: High-precision experimental results are reported showing the tangential momentum accommodation coefficient (TMAC) for several gases in contact with single-crystal silicon to be less than unity. A precise and robust experimental platform is demonstrated for measurement of mass flows through silicon micromachined channels due to an imposed pressure gradient. Analytic expressions for isothermal Maxwellian slip flows through long channels are used to determine the TMAC at a variety of Knudsen numbers. Results from experiments using nitrogen, argon and carbon dioxide are presented. For all three gases the TMAC is found to be lower than one, ranging from 0.75 to 0.85.
296 citations