Estimation of the Permeability Tensor of the Microvasculature of the Liver Through Fabric Tensors

The complete prediction of the second order permeability tensor for a three dimensional multi-axial preform is critical if we are to model and design the manufacturing process for composites by considering resin flow through a multi-axial fiber structure. In this study, the in-plane and transverse permeabilities for a woven fabric were predicted numerically by the coupled flow model, which combines microscopic and macroscopic flows. The microscopic and macroscopic flows were calculated by using 3-D CVFEM(control volume finite element method) for micro and macro unit cells. To avoid a checkerboard pressure field and improve the efficiency of numerical computation, a new interpolation function for velocity is proposed on the basis of analytical solutions. The permeability of a plain woven fabric was measured by means of an unidirectional flow experiment and compared with the permeability calculated numerically. Reverse and simple stacking of plain woven fabrics were taken into account and the relationship between the permeability and the structures of the preform such as the fiber volume fraction and stacking order is identified. Unlike other studies, the current study was based on a more realistic three dimensional unit cell. It was observed that in-plane flow is more dominant than transverse flow within the woven perform, and the effect of the stacking order of a multi-layered preform was negligible.

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Numerical Calculation of Equivalent Permeability Tensor for Fractured Vuggy Porous Media Based on Homogenization Theory

Communications in Computational Physics ◽

10.4208/cicp.150709.130410a ◽

2011 ◽

Vol 9 (1) ◽

pp. 180-204 ◽

Cited By ~ 29

Author(s):

Zhaoqin Huang ◽

Jun Yao ◽

Yajun Li ◽

Chenchen Wang ◽

Xinrui Lv

Keyword(s):

Porous Media ◽

Network Model ◽

Darcy's Law ◽

Permeability Tensor ◽

Homogenization Theory ◽

Fine Scale ◽

Porous Rock ◽

Coarse Scale ◽

Equivalent Permeability ◽

Discrete Fracture

AbstractA numerical procedure for the evaluation of equivalent permeability tensor for fractured vuggy porous media is presented. At first we proposed a new conceptual model, i.e., discrete fracture-vug network model, to model the realistic fluid flow in fractured vuggy porous medium on fine scale. This new model consists of three systems: rock matrix system, fractures system, and vugs system. The fractures and vugs are embedded in porous rock, and the isolated vugs could be connected via discrete fracture network. The flow in porous rock and fractures follows Darcy’s law, and the vugs system is free fluid region. Based on two-scale homogenization theory, we obtained an equivalent macroscopic Darcy’s law on coarse scale from fine-scale discrete fracture-vug network model. A finite element numerical formulation for homogenization equations is developed. The method is verified through application to a periodic model problem and then is applied to the calculation of equivalent permeability tensor of porous media with complex fracture-vug networks. The applicability and validity of the method for these more general fractured vuggy systems are assessed through a simple test of the coarse-scale model.

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The Microwave Permeability of a Ferrite-Filled Parallel-Plate Transmission Structure

Canadian Journal of Physics ◽

10.1139/p73-326 ◽

1973 ◽

Vol 51 (23) ◽

pp. 2495-2497

Author(s):

C. K. Campbell

Keyword(s):

Parallel Plate ◽

Effective Permeability ◽

Phase Shifter ◽

Permeability Tensor ◽

Ferrite Phase ◽

Circularly Polarized ◽

Polarized Waves ◽

Transmission Structure ◽

Microwave Permeability

With the aid of a phasor diagram it is shown that the scalar effective permeability μe = (μ2 − K2)/μ of a parallel-plate longitudinally magnetized microwave ferrite phase shifter may be simply obtained in terms of four circularly polarized waves relating to the permeability tensor eigenvalues μ + K and μ − K.

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