Apparent permeability of flow through periodic arrays of spheres with first-order slip

Wang, Lei; Yin, Xiaolong

doi:10.1016/j.powtec.2017.01.072

Cited by 6 publications

(7 citation statements)

References 73 publications

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“…) 𝜕 2 q j q term, as denoted in the parabolic closure relation of Equation (41). As the problem physics are governed by Kn = 𝜆∕D h , when varying the grid resolution, that is, D h ∼ N Δx ∼ 1 𝜖 , then 𝜆 varies according to the scaling 𝜆 = Kn∕𝜖 ∼ (𝜖 −1 ).…”

Section: Linear Schemesmentioning

confidence: 99%

“…To the best of the authors' knowledge, those MR slip schemes 21,22 are the only existing pathway in LBM to reproduce Equation (1) within a parabolic level of accuracy, for any arbitrary shaped walls. Alternative LBM slip strategies either support the parabolic accuracy limited to lattice‐aligned surfaces 34,36‐39 or, otherwise, exhibit a degraded accuracy (lowering from second‐ to first‐order) when applied to nonmesh aligned walls 40‐44 . Still, despite the superior accuracy of the MR‐based slip boundary schemes, 21,22 they carry a few points worthwhile improvement, namely: (i) nonlocality of implementation, for example, requiring at least two nodes to accommodate arbitrarily rotated parabolic solutions; (ii) inadequacy of the scheme to operate on edge/corner nodes due to the lack of neighboring nodes; and (iii) inherent difficulty to independently prescribe normal/tangential conditions in a linkwise manner.…”

Section: Introductionmentioning

confidence: 99%

“…As application domain, we focus on the simulation of microchannel slip flows. While in the LBM context this benchmark has been largely studied for 2D channel geometries, 21,[36][37][38][39][40][41]44 its extension to 3D ducts has received considerable less attention, apart from a few exceptions that modeled the slip condition on circular tubes 43 and rectangular ducts. 43,49 Unlike for no-slip walls, the assessment of convergence rates and other accuracy measures have been scarcely reported for slip-flow problems, particularly when the wall does not align with the LBM uniform Cartesian mesh, 21,41,42 much seldom in 3D domains.…”

Section: Introductionmentioning

confidence: 99%

“…While in the LBM context this benchmark has been largely studied for 2D channel geometries, 21,[36][37][38][39][40][41]44 its extension to 3D ducts has received considerable less attention, apart from a few exceptions that modeled the slip condition on circular tubes 43 and rectangular ducts. 43,49 Unlike for no-slip walls, the assessment of convergence rates and other accuracy measures have been scarcely reported for slip-flow problems, particularly when the wall does not align with the LBM uniform Cartesian mesh, 21,41,42 much seldom in 3D domains. We address this question here by considering the discretization of distinct channel cross-sections with rectangular, triangular, circular and annular shapes.…”

Section: Introductionmentioning

confidence: 99%

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Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Silva

Ginzburg

2022

Numerical Methods in Fluids

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Slip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no-slip Dirichlet condition, the case of slip formulates as a Robin-type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcription. The present work concerns with this topic, addressing the modeling of the slip velocity boundary condition in the lattice Boltzmann method (LBM) applied to steady slow viscous flows inside ducts of nontrivial shapes. As novelty, we extend the newly revised local second-order boundary (LSOB) Dirichlet fluid flow method [Philos. Trans. R. Soc. A 378, 20190404 (2020)] to implement the slip velocity condition within the two-relaxation-time (TRT) framework. The LSOB follows an in-node philosophy where its operation principle seeks to explicitly reconstruct the unknown boundary populations in the form of a third-order accurate Chapman-Enskog expansion, where the wall slip condition is built-in as a normal Taylor-type condition. The key point of this approach is that the required first-and second-order momentum derivatives, rather than computed through nonlocal finite difference approximations, are locally determined through a simple local linear algebra procedure, whose formulation is particularly aided by the TRT symmetry argument. To express the obtained derivatives, two approaches are considered, called Lnode and Lwall, which operate with node and wall variables, respectively. These two formulations are developed to prescribe the physical slip condition over plane and curved walls, including the corners. Their consistency and accuracy characteristics are examined against alternative linkwise strategies to impose the wall slip velocity, such as the kinetic-based diffusive bounce-back scheme, the central linear interpolation slip scheme, and the multireflection slip scheme. The several slip schemes are tested over different 3D microchannel configurations, with walls not conforming with the LBM uniform mesh. Numerical tests confirm the advanced accuracy characteristics of the proposed LSOB slip boundary scheme, revealing the added challenge of the wall slip modeling, and that parabolic accuracy is a necessary requirement to reach second-order accuracy within this problem class.

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Section: Linear Schemesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Silva

Ginzburg

2022

Numerical Methods in Fluids

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“…26,27 Javadpour 28 proposed a permeability model in straight tubes accounting for slip flow and Knudsen diffusion based on Maxwell's first-order boundary slip condition. Wang et al 29 derived a lattice Boltzmann bounce-back scheme that can simulate the first-order slip boundary condition at a fluid-solid interface. Pang et al 30 introduced a second-order gas slippage velocity model in rectangular nanopores by using the Naiver-Stokes (N-S) equations.…”

Section: Introductionmentioning

confidence: 99%

Assessment of extended Derjaguin–Landau–Verwey–Overbeek‐based water film on multiphase transport behavior in shale microfractures

Wang

Chen

et al. 2021

AIChE Journal

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This study presents a novel model to predict gas-water two-phase transport behaviors in shale microfractures by incorporating a mobile water film with varying thickness according to the extended Derjaguin-Landau-Verwey-Overbeek theory as well as multiple fluid transport mechanisms (i.e., real gas transport controlled by the Knudsen number and water slippage). This model is implemented in real shale microfractures via digital-core imaging. A gas-water displacement process is modeled by the invasion percolation theory, while a local multiphase distribution is determined by combining disjoining pressure with capillary force. Key findings reveal that gas relative permeability decreases by 17% and water RP enhances by 33.5%, when the mean aperture decreases from 1.67 to 0.0418 μm. Neglecting water film brings a decrease in water RP and an overestimation of gas transport ability. Moreover, two critical microfracture apertures are determined, which enhances an understanding of the water film impact on gas-water transport properties in application.

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Slip boundary condition for lattice Boltzmann modeling of liquid flows

et al. 2018

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Apparent permeability of flow through periodic arrays of spheres with first-order slip

Cited by 6 publications

References 73 publications

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Assessment of extended Derjaguin–Landau–Verwey–Overbeek‐based water film on multiphase transport behavior in shale microfractures

Slip boundary condition for lattice Boltzmann modeling of liquid flows

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