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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 paper, it was shown that all limit points of sequences of renormalized solutions of the Boltzmann equation in the limit of small, asymptotically equivalent Mach and Knudsen numbers are governed by Leray solutions of Navier-Stokes equations.
Abstract: The present paper proves that all limit points of sequences of renormalized solutions of the Boltzmann equation in the limit of small, asymptotically equivalent Mach and Knudsen numbers are governed by Leray solutions of the Navier-Stokes equations. This convergence result holds for hard cutoff potentials in the sense of H. Grad, and therefore completes earlier results by the same authors [Invent. Math. 155, 81-161(2004)] for Maxwell molecules.

77 citations

Journal ArticleDOI
TL;DR: An efficient and accurate parallel coupled DSMC-NS method using three-dimensional unstructured grid topology is proposed and verified for the simulation of high-speed gas flows involving continuum and rarefied regimes and predicts the results more accurately than the "one-shot" coupled method.

77 citations

Journal ArticleDOI
TL;DR: Clear evidence of the transition from hydrodynamiclike to strongly kinetic shock-driven implosions is revealed and quantitatively assessed, and a reduced ion kinetic (RIK) model that includes gradient-diffusion and loss-term approximations to several transport processes reproduce the observed yield trends.
Abstract: Clear evidence of the transition from hydrodynamiclike to strongly kinetic shock-driven implosions is, for the first time, revealed and quantitatively assessed. Implosions with a range of initial equimolar D 3 He gas densities show that as the density is decreased, hydrodynamic simulations strongly diverge from and increasingly overpredict the observed nuclear yields, from a factor of ∼2 at 3.1 mg=cm 3 to a factor of 100 at 0.14 mg=cm 3 . (The corresponding Knudsen number, the ratio of ion mean-free path to minimum shell radius, varied from 0.3 to 9; similarly, the ratio of fusion burn duration to ion diffusion time, another figure of merit of kinetic effects, varied from 0.3 to 14.) This result is shown to be unrelated to the effects of hydrodynamic mix. As a first step to garner insight into this transition, a reduced ion kinetic (RIK) model that includes gradient-diffusion and loss-term approximations to several transport processes was implemented within the framework of a one-dimensional radiation-transport code. After empirical calibration, the RIK simulations reproduce the observed yield trends, largely as a result of ion diffusion and the depletion of the reacting tail ions.

77 citations

Journal ArticleDOI
TL;DR: In this paper, an analytic solution on fully developed forced convection, in parallel plates porous micro-channels is accomplished in Local Thermal Non-Equilibrium (LTNE) condition, and the analysis is realized in steady state regime for rarefied gaseous slip flows between two parallel plates with assigned heat flux.

77 citations

Journal ArticleDOI
TL;DR: In this paper, a purely continuum theory for the thermophoretic velocity of aerosol and hydrosol particles in the zero Knudsen number, near continuum limit, valid for both gases and liquids, is proposed.
Abstract: A purely continuum theory for the thermophoretic velocity of aerosol and hydrosol particles in the zero Knudsen number, near continuum limit, Kn = 0 + , valid for both gases and liquids, is proposed. This theoretical result is based upon a fundamentally modified version of the traditional equations governing continuum fluid motion, one which accounts for an intrinsic difference in a fluid's barycentric (mass-based) velocity and its kinematic velocity of volume, this difference arising during molecular transport processes in fluids within which a mass density gradient exists. Our continuum-scale approach contains no free parameters, nor does it rely upon any sub-continuum, molecular concepts, such as Maxwell's thermally-induced velocity-slip condition. The resulting expression for the thermophoretic velocity of a non-Brownian, spherical particle agrees both constitutively and phenomenologically with available correlations of such velocity data in gases, as well as with the more limited data for liquids. Furthermore, the effect of shape and orientation is discussed for the case of non-spherical particles, with specific results furnished for effectively non-conducting particles. Agreement of the theory with the data furnishes explicit experimental support of the non-traditional fluid-mechanical equations utilized herein.

76 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023112
2022236
2021168
2020163
2019190
2018172