Two-Phase Flow Models: The Closure Issue

Bouré, J. A.

doi:10.1615/multscientechn.v3.i1-4.10

Cited by 19 publications

(20 citation statements)

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“…Although the boundary conditions in single-phase turbulent flow and boiling processes are quite different, the interpretation of both the phenomena in the boundary layers simply in terms of time and space scales related by a characteristic velocity is common to both approaches. This property is also closely related to the closure issue for both turbulent flows [32] and multiphase flows [10,33,34]. In the context of multiphase flows and averaging however, the vapor fraction, interfacial area density flux and their evolution have been identified relevant to achieve closure and to restore the lost information due to averaging.…”

Section: Correlation Of Boiling Heat Flux With Interfacial Area Densitymentioning

confidence: 99%

Identification of unifying heat transfer mechanisms along the entire boiling curve

Lüttich¹,

Marquardt²,

Buchholz³

et al. 2006

International Journal of Thermal Sciences

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Section: Correlation Of Boiling Heat Flux With Interfacial Area Densitymentioning

confidence: 99%

Identification of unifying heat transfer mechanisms along the entire boiling curve

Lüttich¹,

Marquardt²,

Buchholz³

et al. 2006

International Journal of Thermal Sciences

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“…The application of volume averaging entails a loss of information as it smoothes out details of the flow structure [38,73]. Topological closure relations are required to restore the lost information.…”

Section: Topological Closure Relationsmentioning

confidence: 99%

Homogeneous equilibrium model for geomechanical multi-material flow with compressible constituents

Aubram

2016

Journal of Non-Newtonian Fluid Mechanics

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Multi-material flow generally describes a situation where several distinct materials separated by sharp material interfaces undergo large deformations.In order to model such flow situations in the context of geomechanics and geotechnical engineering, a theoretical framework is presented which introduces a possible two-phase coupled saturated granular material behavior among the different materials. This is achieved by extending the technique of local volume averaging to a hierarchy of three spatial scales, based on a product of two indicator functions. A homogeneous equilibrium mixture model is subsequently derived for an example flow consisting of bulk solid, bulk fluid, and undrained granular material with compressible constituents.The closure relations are provided at the macroscale, including those describing granular behavior covering the full frictional-collisional flow regime and bulk material volume fraction evolution. The paper discusses the advantages and restrictions of the proposed mixture model and addresses its application and full-scale numerical implementation. *

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“…This is known as the closure problem. It has been discussed by Bouré [1987] and by Bowen [1980], among others. The solution of Bowen is to postulate

\frac{D^{s P} ε^{K}}{D t}

as a dependent variable, thereby removing

ε^{K}

from the list of unknowns.…”

Section: Entropy Inequality and Constitutive Theory For The Six‐phasementioning

confidence: 99%

The role of connectivity in the theory of saturated/unsaturated flow through swelling media

Kleinfelter-Domelle¹,

Cushman²

2012

Water Resources Research

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[1] A thermodynamically consistent model for multiphase flow which allows for connected and disconnected phases in a swelling medium is developed using hybrid mixture theory with three spatial scales. The mesoscale of the medium consists of swelling particles and two bulk phases, such as liquid water and vapor. The particles are a combination of a vicinal liquid and a solid, which may swell or shrink as a result of interaction with the other bulk phases; an example is a mixture of montmorillonite platelets and water. The theory defines connected and disconnected bulk phases of liquid and vapor at the mesoscale to create a dual-porosity type model at the macroscale. The disconnected vapor phase consists of either buoyant bubbles or confined vapor packets. The incorporation of disconnected and connected phases is useful for modeling unsaturated swelling systems. The macroscale solid phase volume fraction is refined from previous hybrid mixture approaches for two-phase multiscale problems and is fully utilized in the field equations and the constitutive theory. Macroscale equations for each of the six phases are presented with bulk regions separated into connected and disconnected domains. A constitutive theory is derived by exploiting the entropy inequality for the mixture. Generalized Darcy's laws and the final set of field equations for the system are presented and compared with previous hybrid mixture theoretic results. Classical parallel flow models only consider disconnected bulk regions and therefore are only appropriate for drainage; the current system can be useful for both imbibition and drainage, including extremely dry systems.Citation: Kleinfelter-Domelle, N., and J. H. Cushman (2012), The role of connectivity in the theory of saturated/unsaturated flow through swelling media, Water Resour. Res., 48, W01543,

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Two-Phase Flow Models: The Closure Issue

Cited by 19 publications

References 0 publications

Identification of unifying heat transfer mechanisms along the entire boiling curve

Identification of unifying heat transfer mechanisms along the entire boiling curve

Homogeneous equilibrium model for geomechanical multi-material flow with compressible constituents

The role of connectivity in the theory of saturated/unsaturated flow through swelling media

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