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 creeping equations of motion with slip boundary conditions were used to calculate the hydrodynamic force resisting the approach of a sphere toward a wall, and the results indicate that the force increases as the gap is reduced, but becomes significantly less pronounced as the Knudsen number is increased.
39 citations
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TL;DR: The new concept of multiscale multi-efficiency preserving (MMP) method is introduced, and the UGKWP method is shown to be an MMP scheme, which is specially efficient for hypersonic flow simulation in all regimes in comparison with the wave-type discrete ordinate methods.
Abstract: The unified gas-kinetic scheme (UGKS) provides a framework for simulating multiscale transport with the updates of both gas distribution function and macroscopic flow variables on the cell size and time step scales. The multiscale dynamics in UGKS is achieved through the coupled particle transport and collision in the particle evolution process within a time step. In this paper, under the UGKS framework, we propose an efficient multiscale unified gas-kinetic wave-particle (UGKWP) method. The gas dynamics in UGKWP method is described by the individual particle movement coupled with the evolution of the probability density function (PDF). During a time step, the trajectories of simulation particles are tracked until collision happens, and the post-collision particles are evolved collectively through the evolution of the corresponding distribution function. The evolution of simulation particles and distribution function is guided by evolution of macroscopic variables. The two descriptions on a gas particle, i.e. wave and particle, switch dynamically with time. A new concept of multiscale multi-efficiency preserving (MMP) method is introduced, and the UGKWP method is shown to be an MMP scheme. The UGKWP method is specially efficient for hypersonic flow simulation in all regimes in comparison with the wave-type discrete ordinate methods, and presents a much lower stochastic noise in the continuum flow regime in comparison with the particle-based Monte Carlo methods. Numerical tests for flows over a wide range of Mach and Knudsen numbers are presented. The examples include mainly the hypersonic flow passing a circular cylinder at Mach numbers $20$ and $30$ and Knudsen numbers $1$ and $10^{-4}$, low speed lid-driven cavity flow, and laminar boundary layer. These results validate the accuracy, efficiency, and multiscale property of UGKWP method.
39 citations
39 citations
TL;DR: In this article, a review is constructed with three parts: flow mechanism, reservoir models and numerical approaches, and it is found that gas adsorption process can be concluded into different isotherm models for various reservoir basins.
Abstract: The past two decades have borne remarkable progress in our understanding of flow mechanisms and numerical simulation approaches of shale gas reservoir, with much larger number of publications in recent 5 years compared to that before year 2012. In this paper, a review is constructed with three parts: flow mechanism, reservoir models and numerical approaches. In mechanism, it is found that gas adsorption process can be concluded into different isotherm models for various reservoir basins. Multi-component adsorption mechanisms are taken into account in recent years. Flow mechanism and equations vary with different Knudsen numbers, which could be figured out in two ways: molecular dynamics (MD) and lattice Boltzmann method (LBM). MD has been successfully applied in the study of adsorption, diffusion, displacement and other mechanisms. LBM has been introduced in the study of slippage, Knudsen diffusion and apparent permeability correction. The apparent permeability corrections are introduced to improve classic Darcy’s model in matrix with low velocities and fractures with high velocities. At reservoir-scale simulation, gas flow models are presented with multiple porosity classified into organic matrix with nanopores, organic matrix with micropores, inorganic matrix and natural fractures. A popular trend is to incorporate geomechanism with flow model in order to better understand the shale gas production. Finally, to solve the new models based on enhanced flow mechanisms, improved macroscopic numerical approaches, including the finite difference method and finite element method, are commonly used in this area. Other approaches like finite volume method and fast matching method are also developed in recent years.
39 citations
TL;DR: In this article, a rarefied gas flow through a thin slit caused by a small pressure difference is studied on the basis of the kinetic equation, and the Bhatnagar-Gross-Krook model equation is solved numerically by the optimized discrete velocity method.
Abstract: A rarefied gas flow through a thin slit caused by a small pressure difference is studied on the basis of the kinetic equation. The Bhatnagar–Gross–Krook model equation is solved numerically by the optimized discrete velocity method. The gas–surface interaction is assumed diffuse‐specular. It is shown that the dependence of the mass flow rate on the gas–surface interaction law is negligibly small at any Knudsen number. Analytical formulas for the flow rate embracing the whole range of the Knudsen number are obtained.
39 citations