Fluid flow analyses for porous media are of great importance in a wide range of industrial applications including, but not limited to, resin transfer moulding, filter analysis, transport of underground water and pollutants, and hydrocarbon recovery. Permeability is perhaps the most important property that characterizes porous media; however, its determination for different types of porous media is challenging due its complex dependence on the pore-level structure of the media. In the present work, fluid flow in three-dimensional random fibrous media is simulated using the lattice Boltzmann method. We determine the permeability of the medium using the Darcy law across a wide range of void fractions (0.08 ⩽ ϕ ⩽ 0.99) and find that the values for the permeability that we obtain are consistent with available experimental data. We use our numerical data to develop a semi-empirical constitutive model for the permeability of fibrous media as a function of their porosity and of the fibre diameter. The model, which is underpinned by the theoretical analysis of flow through cylinder arrays presented by [Gebart BR. Permeability of unidirectional reinforcements for RTM. J Compos Mater 1992; 26(8): 1100–33], gives an excellent fit to these data across the range of ϕ. We perform further simulations to determine the impact of the curvature and aspect ratio of the fibres on the permeability. We find that curvature has a negligible effect, and that aspect ratio is only important for fibres with aspect ratio smaller than 6:1, in which case the permeability increases with increasing aspect ratio. Finally, we calculate the permeability tensor for the fibrous media studied and confirm numerically that, for an isotropic medium, the permeability tensor reduces to a scalar value.

A general model for the permeability of fibrous porous media based on fluid flow simulations using the lattice Boltzmann method

A novel fractal solution for permeability and Kozeny-Carman constant of fibrous porous media made up of solid particles and porous fibers

A new finite-element scheme to solve the Stokes–Brinkman equation for flow analyses in dual scale porous media is presented and has been applied to predict the effective permeability of dual scale fibrous media. Both continuous and discontinuous stress conditions at the interface between a porous media and a surrounding fluid are explored by introducing an equivalent momentum equation for the Brinkman equation. The proposed scheme uses a uniform structured regular rectangular mesh to discretize the domain and employs the level-set method to describe the porous media allowing for inclusion of complex geometrical features easily. Biperiodic boundary conditions have been applied to conduct the flow analysis in a representative volume of mesoscale porous structures. Numerical solutions in a parallel channel flow over a porous media are presented and compared with analytic solutions to assess the accuracy of the proposed scheme. The scheme is then applied to flow past two regular periodic geometries of ellipti...

Numerical simulations of Stokes–Brinkman equations for permeability prediction of dual scale fibrous porous media

Application of X-ray computed tomography for the virtual permeability prediction of fiber reinforcements for liquid composite molding processes: A review

The lattice Boltzmann method (LBM) is used to investigate the dual-scale problem of fluid flow through three-dimensional multifilament woven fabrics. Such fabrics are characterized by two distinct length scales: the thickness of a single filament and the thickness of a bundle of filaments, known as yarn. The yarn’s thickness is typically two orders of magnitude greater than that of a single filament. The inter-yarn and intra-yarn spaces, through which fluid may flow, are also of two distinct length scales. The direct simulation of fluid flow in multifilament woven fabrics involves the simultaneous resolution of the flow field in the inter-yarn and intra-yarn pores; the LBM is well-suited to modelling such geometrically-complex fluid flow. The methodology is first validated against published analytical results for two-dimensional transverse fluid flow through hexagonal arrays of cylinders; the agreement is excellent. Fluid flow in two-dimensional representations of multifilament woven fabrics is also simulated, and the results are compared against those obtained following Papathanasiou’s approach (2001, Int. J. Multiphase Flow, 27: 1451–1461); the agreement is very good. The model is then used to determine the through-thickness permeability of three-dimensional woven fabrics by direct simulation of the fluid flow. The geometry used for the three-dimensional simulations resembles bi-axial, plain woven fabrics. The inter-yarn porosity (‘weave porosity’, ϕw) and the intra-yarn porosity (‘yarn porosity’, ϕy) are systematically varied in the range 0.3 ⩽ ϕ w ⩽ 0.65 and 0 ⩽ ϕ y ⩽ 0.80 , respectively. These parameters control the weave and yarn permeabilities (Kw and Ky). The influence of these parameters on the effective permeability of the fabric, Kp, is quantified and discussed in terms of the fabric structure. Our results are analyzed following the approach developed by Papathanasiou (2001, Int. J. Multiphase Flow, 27: 1451–1461) for two-dimensional structures. The semi-empirical relationship between the fabric permeability and the weave and yarn permeabilities proposed in that study provides an excellent fit to the data produced by our three-dimensional simulations, with only minor adjustment to the fitting parameters. The parameterized relationship we obtain allows the through-thickness permeability of a three-dimensional woven fabric to be predicted if the weave and yarn permeabilities are known.

Through-thickness permeability prediction of three-dimensional multifilament woven fabrics

A finite-element scheme is presented to investigate the permeability of fibrous porous medium in a bi-periodic domain such that a single cell problem with a small number of fiber filaments may represent a large number of repeated structures. Based on the fictitious domain method and the rigid-ring description, we use a fixed regular mesh for the entire domain, including the interior of fibers, and the fiber is described by its boundary only. A formal bi-periodicity has been implemented with the mortar-element method and fibers split by the domain boundary have been treated in a relatively easy way. To demonstrate the feasibility, examples of the regular fiber packing, the random fiber distribution and the fiber bundle problems have been investigated using the bi-periodic domain and compared with the literature.

Permeability Prediction of Fibrous Porous Media in a Bi-Periodic Domain:

This work is an extension of our previous work [Wang JF and Hwang WR. Permeability prediction of fibrous porous media in a bi-periodic domain. J Compos Mater 2007; 42: 909—929], in which a finite-e...

Transverse mobility prediction of non-Newtonian fluids across fibrous porous media

An electrostatic atomizer of twin-fluid atomization with combined needle and annular electrode was developed, from which a relatively high speed electrostatic spray was obtained. The flow field of charged droplets of the electrostatic spray under different charging voltages was measured by the PIV technique. The characteristics of atomization and motion of droplets of uncharged and charged spray were investigated systematically and analyzed by PIV and PDA systems. The flow field of the twin-fluid jet of electrostatic spray and droplet size distribution was visualized by PIV and PDA measurement techniques. The results indicate that the flow field of spray is clearly affected by the electrical field. The velocity in the spray center becomes higher and the flow field around the spray shows a change of fluctuation with the increase of charging voltage. The diameter of spray droplets on the centerline increases when the spray is charged and keeps the trend of gradual increase from the center point to the edge ...

Experimental investigation of electrostatic spray of twin-fluid atomization

In this work, we present flow simulations of viscoelastic (Oldroyd-B and Leonov) fluids in the unidirectional fibrous porous media to investigate effects of the elasticity on the flow resistance Extensive numerical simulations were carried out for the Oldroyd-B and Leonov fluids to investigate the flow resistance in some typical geometries of unidirectional fibrous porous media: square, hexagonal, as well as randomly aligned arrays of unidirectional fibers To the best knowledge of the authors, we report for the first time the stiff increase of flow resistance through numerical simulations above a certain Weissenberg number Considerable growth in the flow resistance has turned out to be closely associated with microstructure of porous media through the extensional stretch of polymers For the hexagonal and randomly aligned fibers, where there are enough spaces behind fibers, significant amount of polymer stretch is observed along with substantial growth of the corresponding flow resistance On the other hand, only minor change in flow resistance and negligible polymer stretch are observed in case of square-packing porous media

Flow resistance of viscoelastic flows in fibrous porous media

The middle‐size electrostatic spray generated by pressure‐swirl atomizer and annular electrode, which could be applied in inside‐room disinfections, was investigated through PIV experiment. PIV was applied to measure the flow of charged atomized particles. The flow field of uncharged and charged spray was compared and the change of spray flow filed was analyzed under different charging voltage. The experiment results indicate that the spray angular of charged spray increased and the particles disperse apparently compared with conventional spray. The velocity of charged particles in spray core become higher and the motion of particles in the domain around the electrode appears almost different change law when the spray was charged. The flow description of the charged particles spray under different charging voltage was presented in this paper. The measurement and analyses presented a research base for the application of electrostatic spray of the pressuer‐swirl atomizer with an annular electrode.

PIV Experimental Study On Electrostatic Spray Of Pressure-swirl Atomizer With Annular Electrode

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