On the existence of the derivative of the volume average

Mls, J.

doi:10.1007/bf00192158

Cited by 9 publications

(5 citation statements)

References 6 publications

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“…This is a classical behavior when averaged values are built from the DNS results by averaging over a single unit cell. This kind of averaging is not sufficient to produce a completely regularized average field as pointed out by Marle (1965;1982), Mls (1987) and Prat (1989). It has been discussed at length in Quintard andWhitaker (1993, 1994a, b, c).…”

Section: Validation Against Dns Resultsmentioning

confidence: 99%

Upscaling for Adiabatic Solid–Fluid Reactions in Porous Medium Using a Volume Averaging Theory

2015

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In this paper, an upscaling study of solid-fluid combustion in porous medium with homogeneous and heterogeneous heat sources is carried out using a volume averaging theory. For the sake of simplicity, the reaction rate is assumed to be of first-order Arrhenius type and convection is not taken into account. Local thermal non-equilibrium is considered between the solid and fluid phases. During the resolution of closure problems, periodic boundary condition is utilized in order to determine the effective coefficients in the upscaled model.The obtained macroscale theory is validated against direct numerical simulation results for two typical porous medium geometries made of simple unit cells, namely unconsolidated and consolidated porous media. The comparisons between the present upscaled and microscale results are conducted for various Damköhler numbers for both homogeneous and heterogeneous reaction cases. It has been found that, for the low Damköhler number cases, the temperature profiles generated from the derived upscaled model are in accordance with that of the microscale model. For the high Damköhler number cases, however, the macroscale model fails to predict the combustion front and temperature profile, which evidently suggests that the effects of neglected terms during the upscaling process should be reexamined carefully in further investigations.

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Section: Validation Against Dns Resultsmentioning

confidence: 99%

Upscaling for Adiabatic Solid–Fluid Reactions in Porous Medium Using a Volume Averaging Theory

2015

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“…( 2). This point is not discussed in this paper and the reader is referred to Marle (1965), Mls (1987), Marle (1982) and the series of paper Quintard and Whitaker (1994e,d,c,b,a) for a better understanding of the problem. A macro-scale equation could be obtained from averaging of the pore-scale equation, and this would lead to…”

Section: 1mentioning

confidence: 99%

Transfers in Porous Media

Quintard

2015

Special Topics Rev Porous Media

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Modeling heat transfer in porous media requires to take into account multiple-scale aspects inherent to porous media structures. Several methodologies have been developed to upscale the equations at a lower-scale and to obtain upper-scale models as it is outlined in a brief review based on a simple heat conduction example proposed in the rst part of this paper. The more general and classical problem of heat transfer in porous media is reviewed in this paper with the emphasis on the fact that dierent behaviors and hence dierent models emerge at a given macro-scale, depending on the interplay of the various characteristic times and lengths characterizing the problem. Various classes of models are discussed and their relationships outlined. Extensions to more complicated problems of heat transfer in porous media are discussed: coupling with mass diusion, eect of heat sources, radiation, boiling, etc.

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“…The theory of volume averaging (2) of the flows in porous media was developed in large detail and applied to several important processes (Hassanizadeh and Gray, 1980;Quintard and Whitaker, 1994d;Bennethum and Cushman, 2002a,b;Kechagia et al, 2002;Coutelieris et al, 2006;Valdez-Parada et al, 2007;Valdez-Parada and Alvarez-Ramirez, 2011;Soulaine et al, 2011;Yang et al, 2015;De Los Santos-Sánchez et al, 2016;Qiu et al, 2017). The fundamental theorems have been proven and extensively discussed (Tosun and Willis, 1982;Gray, 1982;Cushman, 1983Cushman, , 1985Howes and Whitaker, 1985;Mls, 1987;Whitaker, 1999;Wood, 2013;Gray and Miller, 2014). The methods for the closure of the systems of governing equations of the macroscale were developed (Narasimhan, 1980;Crapiste et al, 1986;Hassanizadeh and Gray, 1990;Whitaker, 1999), and the coefficients in these equations were expressed in terms of the averaged fluctuation characteristics of the microscale.…”

Section: Introduction 11 Statement Of the Problemmentioning

confidence: 99%