Knudsen number

About: Knudsen number is a research topic. Over the lifetime, 5052 publications have been published within this topic receiving 104278 citations.

Statistical Simulation of the Transition between Regular and Mach Reflection in Steady Flows

Abstract: The transition of planar shock waves over straight wedges in steady flows between regular and Mach reflection was numerically studied by the DSMC method for small Knudsen numbers. The hysteresis effect was observed at increasing and decreasing shock wave angle. Stability of regular and Mach reflection configurations to perturbations was examined and a possibility of transforming one configuration to the other by means of the perturbations was shown. The effect of starting conditions in the dual solution domain was clarified.

On the apparent permeability of porous media in rarefied gas flows

Abstract: The apparent gas permeability of the porous medium is an important parameter in the prediction of unconventional gas production, which was first investigated systematically by Klinkenberg in 1941 and found to increase with the reciprocal mean gas pressure (or equivalently, the Knudsen number). Although the underlying rarefaction effects are well-known, the reason that the correction factor in Klinkenberg's famous equation decreases when the Knudsen number increases has not been fully understood. Most of the studies idealize the porous medium as a bundle of straight cylindrical tubes, however, according to the gas kinetic theory, this only results in an increase of the correction factor with the Knudsen number, which clearly contradicts Klinkenberg's experimental observations. Here, by solving the Bhatnagar-Gross-Krook equation in simplified (but not simple) porous media, we identify, for the first time, two key factors that can explain Klinkenberg's experimental results: the tortuous flow path and the non-unitary tangential momentum accommodation coefficient for the gas-surface interaction. Moreover, we find that Klinkenberg's results can only be observed when the ratio between the apparent and intrinsic permeabilities is $\lesssim30$; at large ratios (or Knudsen numbers) the correction factor increases with the Knudsen number. Our numerical results could also serve as benchmarking cases to assess the accuracy of macroscopic models and/or numerical schemes for the modeling/simulation of rarefied gas flows in complex geometries over a wide range of gas rarefaction. Specifically, we point out that the Navier-Stokes equations with the first-order velocity-slip boundary condition are often misused to predict the apparent gas permeability of the porous media; that is, any nonlinear dependence of the apparent gas permeability with the Knudsen number, predicted from the Navier-Stokes equations, is not reliable. Worse still, for some type of gas-surface interactions, even the ``filtered'' linear dependence of the apparent gas permeability with the Knudsen number is of no practical use since, compared to the numerical solution of the Bhatnagar-Gross-Krook equation, it is only accurate when the ratio between the apparent and intrinsic permeabilities is $\lesssim1.5$.

Monte Carlo study of Knudsen layers in evaporation from elemental and binary media

Abstract: By Monte Carlo simulation the Knudsen layer in front of a surface from which atoms evaporate is studied. Evaporation into a vacuum is simulated by means of an evaporation–condensation geometry. Hard sphere interaction cross sections are employed. With the help of the present simulation data, the Knudsen layer is defined as that region adjacent to the evaporating surface, where the temperature of the flow parallel and perpendicular to the flow direction deviate by at least a given resolution δ. Taking δ=1%, it is found that the Knudsen layer is established after 800 mean‐free flight times; it has an extension of 20 mean‐free paths. It takes 60 monolayers to desorb before a Knudsen layer is formed. The data are generally in good agreement with predictions of analytical theory, where available. The differences observed in the case of evaporation from a binary target are discussed.