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: In this article, the development of continuum models to describe processes in gases in which the particle collisions cannot maintain thermal equilibrium is discussed, and typical results are reviewed for channel flow, cavity flow, and flow past a sphere in the low-Mach number setting for which both evolution equations and boundary conditions are well established.
Abstract: This article discusses the development of continuum models to describe processes in gases in which the particle collisions cannot maintain thermal equilibrium. Such a situation typically is present in rarefied or diluted gases, for flows in microscopic settings, or in general whenever the Knudsen number—the ratio between the mean free path of the particles and a macroscopic length scale—becomes significant. The continuum models are based on the stochastic description of the gas by Boltzmann's equation in kinetic gas theory. With moment approximations, extended fluid dynamic equations can be derived, such as the regularized 13-moment equations. Moment equations are introduced in detail, and typical results are reviewed for channel flow, cavity flow, and flow past a sphere in the low–Mach number setting for which both evolution equations and boundary conditions are well established. Conversely, nonlinear, high-speed processes require special closures that are still under development. Current approaches are ...
157 citations
TL;DR: In this paper, a new way to implement solid obstacles in lattice Boltzmann models is presented, where unknown populations at the boundary nodes are derived from the locally known populations with the help of a second-order Chapman-Enskog expansion and Dirichlet boundary conditions with a given momentum.
Abstract: A new way to implement solid obstacles in lattice Boltzmann models is presented. The unknown populations at the boundary nodes are derived from the locally known populations with the help of a second-order Chapman-Enskog expansion and Dirichlet boundary conditions with a given momentum. Steady flows near a flat wall, arbitrarily inclined with respect to the lattice links, are then obtained with a third-order error. In particular, Couette and Poiseuille flows are exactly recovered without the Knudsen layers produced for inclined walls by the bounce back condition.
156 citations
TL;DR: In this article, a systematic approximation for the moment equations of kinetic theory which describe source flow expansion was constructed for small source Knudsen number, and the moments are expanded and solutions are obtained near the source.
Abstract: A systematic approximation has been constructed for the moment equations of kinetic theory which describe source flow expansion. For small source Knudsen number, the moments are expanded and solutions are obtained near the source. These solutions are nonuniformly valid far from the source, breaking down when transition flow is encountered. To analyze the rarefied regime, the equations are rescaled taking account that the flow is hypersonic in the transition regime. This allows us to apply a hypersonic approximation to the moment equations in the rarefied regime and subsequently match this to the inviscid solution. For spherical expansion we resolve the problem to a relaxation process with two translation temperatures, one along streamlines T ∥, and the other transverse to streamlines T ⊥. We obtain expressions for the terminal Mach number in terms of source Knudsen number and intermolecular force law, and a simple rarefaction criteria is found which states that transition flow is encountered when T ∥ − T ⊥ ≅ T isentropic.
156 citations
TL;DR: In this paper, the effects of both magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel are studied analytically and numerically.
155 citations
TL;DR: In this paper, a mathematical formulation of kinetic boundary conditions for Lattice Boltzmann schemes in terms of reflection, slip, and accommodation coefficients is presented, and it is shown that, in the presence of a non-zero slip coefficient, the flow develops a physical slip flow component at the wall, and the slip coefficient can be tuned to recover quantitative agreement with analytical and experimental results up to second order in the Knudsen number.
Abstract: We present a mathematical formulation of kinetic boundary conditions for Lattice Boltzmann schemes in terms of reflection, slip, and accommodation coefficients. It is analytically and numerically shown that, in the presence of a non-zero slip coefficient, the Lattice Boltzmann flow develops a physical slip flow component at the wall. Moreover, it is shown that the slip coefficient can be tuned in such a way to recover quantitative agreement with analytical and experimental results up to second order in the Knudsen number.
155 citations