High temperature permeability of fibrous materials using direct simulation Monte Carlo

Borner, Arnaud; Panerai, Francesco; Mansour, Nagi N.

doi:10.1016/j.ijheatmasstransfer.2016.10.113

Cited by 78 publications

(41 citation statements)

References 30 publications

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“…It is seen that both the discrete velocity method on the "stair-case" geometry and the unified gas kinetic scheme on the curvilinear mesh have the same results. Also, although we use the linearized BGK model, our numerical results are quite close to those from the DSMC simulation (Borner et al 2017). Note that in the DSMC simulation, the Knudsen number and AGP are normalized by the radius and radius square of the disc, respectively, so the data should be re-normalized.…”

Section: The Accuracy Of the Nses And Fvbcsupporting

confidence: 55%

“…In this section, we first present analytical/numerical solutions of the NSEs with FVBC, the linearized BGK equation, the R20 equation, as well as the direct simulation Monte Carlo (DSMC) method (Borner et al 2017), for rarefied gas flows through porous media, to show the accuracy of the NSEs with FVBC. Then we give a possible explanation to understand Klinkenberg's experimental results.…”

Section: Numerical Methods and Resultsmentioning

confidence: 99%

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On the apparent permeability of porous media in rarefied gas flows

Germanou

et al. 2017

J. Fluid Mech.

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The apparent gas permeability of a porous medium is an important parameter in the prediction of unconventional gas production, which was first investigated systematically by Klinkenberg in 1941 and found to increase with the reciprocal mean gas pressure (or equivalently, the Knudsen number). Although the underlying rarefaction effects are well known, the reason that the correction factor in Klinkenberg's famous equation decreases when the Knudsen number increases has not been fully understood. Most of the studies idealize the porous medium as a bundle of straight cylindrical tubes; however, according to the gas kinetic theory, this only results in an increase of the correction factor with the Knudsen number, which clearly contradicts Klinkenberg's experimental observations. Here, by solving the Bhatnagar-Gross-Krook equation in simplified (but not simple) porous media, we identify, for the first time, two key factors that can explain Klinkenberg's experimental results: the tortuous flow path and the non-unitary tangential momentum accommodation coefficient for the gas-surface interaction. Moreover, we find that Klinkenberg's results can only be observed when the ratio between the apparent and intrinsic permeabilities is 30; at large ratios (or Knudsen numbers) the correction factor increases with the Knudsen number. Our numerical results could also serve as benchmarking cases to assess the accuracy of macroscopic models and/or numerical schemes for the modelling/simulation of rarefied gas flows in complex geometries over a wide range of gas rarefaction. Specifically, we point out that the Navier-Stokes equations with the first-order velocity-slip boundary condition are often misused to predict the apparent gas permeability of the porous medium; that is, any nonlinear dependence of the apparent gas permeability with the Knudsen number, predicted from the Navier-Stokes equations, is not reliable. Worse still, for some types of gas-surface interactions, even the 'filtered' linear dependence of the apparent gas permeability with the Knudsen number is of no practical use since, compared to the numerical solution of the Bhatnagar-Gross-Krook equation, it is only accurate when the ratio between the apparent and intrinsic permeabilities is 1.5. † Email address for correspondence: lei.wu.100@strath.ac.uk

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Section: The Accuracy Of the Nses And Fvbcsupporting

confidence: 55%

Section: Numerical Methods and Resultsmentioning

confidence: 99%

On the apparent permeability of porous media in rarefied gas flows

Germanou

et al. 2017

J. Fluid Mech.

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“…It can be inferred from Eqs. (1), (14), and (15), that C, τ, and ε depend only on pore structures and the flow direction.…”

Section: Knudsen Number and Effective Pore Sizementioning

confidence: 98%

“…Christou and Dadzie [13] performed a DSMC study for Berea sandstone for a pressure driven flow of CH 4 at different Knudsen numbers, and Kn was found to play an important role for the velocity profiles. Borner et al [14] computed the permeability of several fibrous substrates to high-temperature gases. The actual porous geometry of the materials was digitized using X-ray microtomography and the range of the porosity was 0.8 to 0.9.…”

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confidence: 99%

Investigation of the Klinkenberg effect in a micro/nanoporous medium by direct simulation Monte Carlo method

Yang

2018

Phys. Rev. Fluids

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The pressure-driven gas transport characteristics through a porous medium consisting of arrays of discrete elements is investigated by using the direct simulation Monte Carlo (DSMC) method. Different porous structures are considered, accounting for both two-and three-dimensional arrangements of basic microscale and nanoscale elements. The pore scale flow patterns in the porous medium are obtained, and the Knudsen diffusion in the pores is studied in detail for slip and transition flow regimes. A new effective pore size of the porous medium is defined, which is a function of the porosity, the tortuosity, the contraction factor, and the intrinsic permeability of the porous medium. It is found that the Klinkenberg effect in different porous structures can be fully described by the Knudsen number characterized by the effective pore size. The accuracies of some widely used Klinkenberg correlations are evaluated by the present DSMC results. It is also found that the available correlations for apparent permeability, most of which are derived from simple pipe or channel flows, can still be applicative for more complex porous media flows, by using the effective pore size defined in this study.

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“…37 The method has been well validated by comparing the numerical simulation either with the experimental permeability 38 or the established analytical solution. 39 DSMC has been widely applied to the permeability study for Knudsen gas flows in various structures such as fibrous materials, 39,40 channels filled with packed spheres 41,42 and ablative materials. 38 Previous application of the DSMC method on a 3D nano-particle model claimed that the empirical equation for the estimation of the tortuosity factor t = (e 1/3 ) À1 43 could cause aberrations in concentration distribution.…”

Section: Introductionmentioning

confidence: 99%

The application of hierarchical structures in energy devices: new insights into the design of solid oxide fuel cells with enhanced mass transport

Bertei

et al. 2018

Energy Environ. Sci.

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a Mass transport can significantly limit the rate of reaction and lead to concentration polarisation in electrochemical devices, especially under the conditions of high operating current density. In this study we investigate hierarchically structured micro-tubular solid oxide fuel cells (MT-SOFC) fabricated by a phase inversion technique and quantitatively assess the mass transport and electrochemical performance improvement compared to a conventional tubular SOFC. We present pioneering work to characterise the effective mass transport parameters for the hierarchically porous microstructures by an integrated computed fluid dynamics simulation, assisted by multi-length scale 3D X-ray tomography. This has been historically challenging because either imaging resolution or field of view has to be sacrificed to compensate for the wide pore size distribution, which supports different transport mechanisms, especially Knudsen flow. Results show that the incorporation of radially-grown micro-channels helps to decrease the tortuosity factor by approximately 50% compared to the conventional design consisting of a spongelike structure, and the permeability is also improved by two orders of magnitude. When accounting for the influence of Knudsen diffusion, the molecule/wall collisions yield an increase of the tortuosity factor from 11.5 (continuum flow) to 23.4 (Knudsen flow), but the addition of micro-channels helps to reduce it down to 5.3. Electrochemical performance simulations using the measured microstructural and mass transport parameters show good agreement with the experimental results at elevated temperatures. The MT-SOFC anode displays 70% lower concentration overpotential, 60% higher power density (0.98 vs. 0.61 W cm À2 ) and wider current density window for maximum power density than the conventional design. Broader contextHierarchical materials are a popular choice not only for electrochemical energy devices such as fuel cells and batteries, but also for a range of functional materials including catalysts, diffusion media and membranes for waste processing. This study qualitatively and quantitatively illustrates the effectiveness of hierarchically structured pores in reducing gas transport resistance, providing new insights into advanced microstructure optimisation. Moreover, it is a common mistake in the modelling of hierarchical materials to assume the flow to be governed by continuum physics irrespective of the length scale, whereas in the region of finest structure, the molecule/wall collisions become dominant, which cannot be addressed by continuum physics. It is also impossible to define a relevant average pore size to describe the mass transport in these materials due to the wide pore size distribution. The integrated computed fluid dynamics (I-CFD) technique proposed by us for the first time herein, aims to overcome this problem and accurately characterise the effective mass transport in these complex hierarchical structures. The concept and techniques used in this study are believed to be of wide inter...

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High temperature permeability of fibrous materials using direct simulation Monte Carlo

Cited by 78 publications

References 30 publications

On the apparent permeability of porous media in rarefied gas flows

On the apparent permeability of porous media in rarefied gas flows

Investigation of the Klinkenberg effect in a micro/nanoporous medium by direct simulation Monte Carlo method

The application of hierarchical structures in energy devices: new insights into the design of solid oxide fuel cells with enhanced mass transport

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