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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: The manner in which the Navier-Stokes equations of fluid mechanics break down under conditions of low-density, hypersonic flow is investigated numerically in this paper through careful and detailed comparisons of solutions obtained with continuum and Monte Carlo simulation techniques.
Abstract: The manner in which the Navier–Stokes equations of fluid mechanics break down under conditions of low‐density, hypersonic flow is investigated numerically. This is performed through careful and detailed comparisons of solutions obtained with continuum and Monte Carlo simulation techniques. The objective of the study is to predict conditions under which the continuum approach may be expected to fail. Both normal shock waves and bow shocks formed by flow over a sphere are considered for argon and nitrogen. It is found that a Knudsen number based on local flow conditions and gradients is a convenient and accurate criterion for indicating breakdown of the continuum flow equations. Failure of the Navier–Stokes equations in hypersonic transitional flows occurs both in the shock front and in the region immediately adjacent to the body surface.

286 citations

Journal ArticleDOI
TL;DR: In this paper, a double expansion in the Knudsen number and the degree of inelasticity is used to derive constitutive relations for granular flows in three dimensions.
Abstract: The Chapman–Enskog expansion is generalized in order to derive constitutive relations for flows of inelastically colliding spheres in three dimensions – to Burnett order. To this end, the pertinent (nonlinear) Boltzmann equation is perturbatively solved by performing a (double) expansion in the Knudsen number and the degree of inelasticity. One of the results is that the normal stress differences and the ‘temperature anisotropy’, characterizing granular fluids, are Burnett effects. The constitutive relations derived in this work differ, both qualitatively and quantitatively, from those obtained in previous studies. In particular, the Navier–Stokes (order) terms have a different dependence on the degree of inelasticity and the number density than in previously derived constitutive relations; for instance, the expression for the heat flux contains a term which is proportional to e∇ log n, where e is a measure of the degree of inelasticity and n denotes the number density. This contribution to the heat flux is of zeroth order in the density; a similar term, i.e. one that is proportional to e∇n, has been previously obtained by using the Enskog correction but this term is O(n) and it vanishes in the Boltzmann limit. These discrepancies are resolved by an analysis of the Chapman–Enskog and Grad expansions, pertaining to granular flows, which reveals that the quasi-microscopic rate of decay of the temperature, which has not been taken into account heretofore, provides an important scale that affects the constitutive relations. Some (minor) quantitative differences between our results and previous ones exist as well. These are due to the fact that we take into account an isotropic correction to the leading Maxwellian distribution, which has not been considered before, and also because we consider the full dependence of the corrections to the Maxwellian distribution on the (fluctuating) speed.

282 citations

Journal ArticleDOI
TL;DR: It is found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales.
Abstract: Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.

282 citations

Journal ArticleDOI
TL;DR: In this article, the problem of liquid and gas flow in micro-channels under conditions of a small Knudsen and Mach numbers, that correspond to a continuum model, is considered.

281 citations

Journal ArticleDOI
TL;DR: In this article, the effects of turbulent fluctuations have a striking resemblance to those of microscale (thermal) fluctuations in laminar flows, even to higher order in the Knudsen number.
Abstract: We demonstrate that the effects of turbulent fluctuations have a striking resemblance to those of microscale (thermal) fluctuations in laminar flows, even to higher order in the Knudsen number. This suggests that there may be a good basis for understanding turbulence in terms of Boltzmann kinetic theory. If so, turbulence may be better described in terms of ‘mixing times’ rather than the more classical ‘mixing lengths’. Comparisons are made to Reynolds-stress turbulence models.

280 citations


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