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多孔介质期刊
影响因子: 1.49 5年影响因子: 1.159 SJR: 0.504 SNIP: 0.671 CiteScore™: 1.58

ISSN 打印: 1091-028X
ISSN 在线: 1934-0508

多孔介质期刊

DOI: 10.1615/JPorMedia.v12.i4.40
pages 327-344

A Deviation from Darcy's Law due to Unsaturated Flow in Dual-Scale Porous Media

Murthy S. Munagavalasa
S. C. Johnson & Son Inc., Racine, WI 53403, USA
Krishna Pillai
Mechanical Engineering Department EMS Building, 3200 N. Cramer Street, Room 945 College of Engineering and Applied Science University of Wisconsin, Milwaukee,WI 53211

ABSTRACT

The unsaturated flow encountered in the fibrous dual-scale porous media found in the liquid composite molding processes during the manufacture of polymer composites is the object of study here. The delayed absorption of fiber bundles in such media leads to the formation of a sink term in the continuity equation. A rapidly varying sink term near a moving macroscopic front in the dual-scale porous medium gives rise to two extra force terms in the volume-averaged momentum balance equation: a Brinkman term and an interfacial kinetic effect term. In this numerical work, the relative importance of these two terms in the gap-averaged momentum balance equation is studied. A finite element-based numerical method is used to model the 2-D isothermal flow between two parallel liquid-absorbing surfaces representing resin flow in the interbundle regions of a dual-scale porous medium during the unsaturated flow. It is observed that the Brinkman and the interfacial kinetic effect force terms become significant in a small region with rapidly varying sink term behind the moving flow front. The Beavers-Joseph slip-velocity boundary condition imposed at the gap-tow interfacial surfaces does not have any notable impact on the results. However, the correction factors tend to become less significant with an increase in the local Reynolds number. But the overall results suggest that a modified form of Darcy's law with the Brinkman and interfacial kinetic effect correction terms needs to be used near the flow front during liquid composite modeling mold-filling simulation in a dual-scale fiber mat.


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