Principal Permeability Values Research Articles

Modelling the permeability of random discontinuous carbon fibre preforms

A force-directed algorithm was developed to create representative geometrical models of fibre distributions in directed carbon fibre preforms. Local permeability values were calculated for the preform models depending on the local fibre orientation, distribution and volume fraction. The effect of binder content was incorporated by adjusting the principal permeability values of the meso-scale discontinuous fibre bundles, using corresponding experimental data obtained for unidirectional non-crimp fabrics. The model provides an upper boundary for the permeability of directed carbon fibre preform architectures, where predictions are within one standard deviation of the experimental mean for all architectures studied.

Estimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations

In this paper, a comprehensive framework is proposed to estimate the anisotropic permeability matrix in trabecular bone specimens based on micro-computed tomography (microCT) imaging combined with pore-scale fluid dynamics simulations. Two essential steps in the proposed methodology are the selection of (i) a representative volume element (RVE) for calculation of trabecular bone permeability and (ii) a converged mesh for accurate calculation of pore fluid flow properties. Accurate estimates of trabecular bone porosities are obtained using a microCT image resolution of approximately 10μm. We show that a trabecular bone RVE in the order of 2×2×2mm3 is most suitable. Mesh convergence studies show that accurate fluid flow properties are obtained for a mesh size above 125,000 elements. Volume averaging of the pore-scale fluid flow properties allows calculation of the apparent permeability matrix of trabecular bone specimens.For the four specimens chosen, our numerical results show that the so obtained permeability coefficients are in excellent agreement with previously reported experimental data for both human and bovine trabecular bone samples. We also identified that bone samples taken from long bones generally exhibit a larger permeability in the longitudinal direction. The fact that all coefficients of the permeability matrix were different from zero indicates that bone samples are generally not harvested in the principal flow directions. The full permeability matrix was diagonalized by calculating the eigenvalues, while the eigenvectors showed how strongly the bone sample's orientations deviated from the principal flow directions. Porosity values of the four bone specimens range from 0.83 to 0.86, with a low standard deviation of ± 0.016, principal permeability values range from 0.22 to 1.45 ⋅ 10−8m2, with a high standard deviation of ± 0.33. Also, the anisotropic ratio ranged from 0.27 to 0.83, with high standard deviation. These results indicate that while the four specimens are quite similar in terms of average porosity, large variability exists with respect to permeability and specimen anisotropy. The utilized computational approach compares well with semi-analytical models based on homogenization theory. This methodology can be applied in bone tissue engineering applications for generating accurate pore morphologies of bone replacement materials and to consistently select similar bone specimens in bone bioreactor studies.

Permeability characterization of sheared carbon fiber textile preform

Fabric deformation alters its local permeability characteristics which, in turn, influences the resin infusion process. This work investigates the radial permeability test method of sheared carbon fiber textile reinforcement materials for the purposes of infusion modeling. A novel experimental approach is described, which utilizes a customized Matlab video processing code to track fluid flow and calculate permeability using data from the complete flow field. Results show principal permeability values, and , to increase and decrease, respectively, from a near isotropic state as the fabric shear angle increases, yielding a / ratio of 3.74 at the maximum measured shear angle of 40°. Detailed statistical analysis revealed significant error for cases where fewer than 16 measurement directions were used for the permeability calculation, particularly in highly anisotropic samples. POLYM. COMPOS., 39:2287–2298, 2018. © 2016 Society of Plastics Engineers

Effect of specimen history on structure and in-plane permeability of woven fabrics

Before being processed into composites, reinforcement fabrics may undergo repeated involuntary deformation, the complete sequence of which is here referred to as specimen history. To mimic its effect, fabric specimens were subjected to sequences of defined shear operations. For single fabric layers with unconstrained thickness, quantitative evaluation of photographic image data indicated that repeated shear deformation results in a residual increase in inter-yarn gap width. This translates into an increase in measured fabric permeabilities in multi-layer lay-ups at given compaction levels. The extent of both interrelated effects increases with increasing yarn density in the fabric and with increasing maximum angle in the shear history. Additional numerical permeability predictions indicated that the increase in permeability may be partially reversed by through-thickness fabric compression. The observations suggest that the effect of involuntary deformation of the fabric structure can result in variations in the principal permeability values by factors of up to 2.

Experimental determination of the permeability of textiles: A benchmark exercise

In this international permeability benchmark exercise, in-plane permeability data for two reinforcement fabrics, obtained using a total of 16 different experimental procedures, were compared. Although, for each procedure, the results appear consistent, different procedures result in a scatter of up to one order of magnitude in principal permeability values for each fabric at any given fibre volume fraction. The ratio of the principal permeability values varies by factors of up to 2. While experimental uncertainties and variability of the specimens affect the scatter in results for any single series of experiments, it is suspected that the main source of scatter in results from different procedures is related to human factors. Aiming at standardisation of measurement methods and interchangeability of results, “good practice” guidelines will be formulated in order to eliminate sources of scatter.

Recent Patents on In-Plane Permeability Measurement of LCM Composite Reinforcements

Optimization of Liquid Composite Molding (LCM) processes using Darcy flow numerical simulation requires inputting accurate reinforcement permeability data. Historically introduced by its author to describe infiltration phenomenon, permeability coming from Darcys law is usually used in LCM processes as a rheological parameter in order to predict the macroscopic resin motion during the filling stage. Resulting from the flow through a complex fibrous architecture, its measurement is very sensitive to the test conditions due to the high filaments flexibility and mesostructure heterogeneity. Reinforcements are currently anisotropic fibrous media and their in-plane permeability measurement requires specific facilities. Measurements can be performed in transient or steady state conditions, and in one-, two- or three-dimensional configurations. This paper describes the different existing experimental configurations, identification procedures and instrumentation techniques. Advantages and drawbacks of each method are discussed, in the particular case of 2D transient measurements, which are the most representative of Resin Transfer Molding process. Two recent patents using different instrumentation techniques are detailed. They are focused on the simultaneous identification of the in-plane principal permeability values in an anisotropic fibrous reinforcement. Some perspectives are suggested to improve the repeatability of such measurement results. Keywords: Permeability measurement, fibrous reinforcement, liquid composite molding, anisotropic porous media

Effect of differential compression on in-plane permeability tensor of heterogeneous multilayer carbon fibre preforms

The in-plane permeability at various fibre volume fractions and the compressibility were determined experimentally for heterogeneous multi-layer preforms and the individual material components, a unidirectional (UD) carbon fibre fabric and a 5-harness satin weave carbon fibre fabric. The compressibility of the UD fabric does not depend on the number of layers. It is lower than for the woven fabric and mainly determines the compressibility of the multi-layer preform. For both the UD fabric and the satin weave fabric, the permeability was approximated by Kozeny–Carman type relations with different constants for both principal material directions. The principal permeability values of the multi-layer preform, predicted by thickness-weighted averaging of the component permeabilities, tend to overestimate the measured values. The observed maximum in K1/K2 as a function of the fibre volume fraction is caused by changes in the preform void structure with increasing compression. The predicted ratio shows an increasingly steep decay with increasing fibre volume fraction, implying that the preform properties become less anisotropic. While K1 of the multi-layer preform is determined mainly by the permeability of the UD layers, the influence of the permeability of the woven layers increases with increasing compression. For K2, the influence of the woven fabric is dominant at fibre volume fractions higher than 0⋅77.

Influence of the fabric architecture on the variations in experimentally determined in-plane permeability values

Fabric non-uniformities can be described by the geometric parameters R p / a 0, which refers to the average ratio of in-plane dimension of fibre tows R p and fibre tow spacing a 0 and characterises the fibre-void distribution in the fabric, and the standard deviation of the inter-fibre-angle σ α . For three different woven fabrics and a stitch-bonded non-crimp fabric, it was found that in general the higher R p / a 0, the lower is σ α , with an approximately linear relation between R p / a 0 and σ α . Woven fabrics show mainly macro-scale non-uniformities determined by the fibre tow mobility, which is limited by the void space between the tows. The mainly mesoscopic non-uniformities in non-crimp fabrics are imposed by the stitching pattern, which again determines the values of R p / a 0 and σ α . The principal values and the orientation of the principal axes for the global in-plane permeabilities were determined based on series of experiments that were evaluated statistically. All relative variations (standard deviations/mean values) of the principal permeability values were found to be in the range between 9.1% and 29.3%. The variation in the angle describing the orientation of the principal permeability axes increases with increasing relative permeability variations. Analysis of the relation between permeability variations and geometrical fabric parameters suggests that the more homogeneous the fibre-void distribution in the fabric, i.e., the higher R p / a 0 and the lower σ α , respectively, the lower the local permeability variations and the more similar the flow front shape to a perfect ellipse. The global permeability variations, on the other hand, increase with the local variations until they reach a maximum and then decrease again. Quantitative comparison of measured permeability variations and the results of stochastic simulations indicates that, while the results are in the same order of magnitude, the stochastic model is not detailed enough for quantitatively accurate prediction of permeability variations.

Anisotropic Variation Law of Rock Permeability with the Burial Depth of Limestone

Abstract Permeability tensors of both macrofracture and microfracture systems were measured progressively along the depth of limestone formations at severed sites. It was found that the principal permeability values Kx, Ky and Kz in these permeability tensors all decrease simultaneously and logarithmically with depth. However, the limestone aquifers are composed of an upper region where the larger permeability ellipsoid is upright or prolate and characterized by KzKx and Kz>Ky, a transitional zone, and a lower zone whose smaller permeability ellipsoid is horizontal or oblate and characterized by Kz<Kx and Kz<Ky. The inversion of the permeability ellipsoids in direction indicates that the anisotropy of rock permeability with the depth of limestone formations has evidently changed. The anisotropic variation law of permeability tensors in a macrofracture system displays a similar pattern with that in a microfracture system. It is next to impossible to examine the rock permeability tensor of the aquifer just by measuring the hydraulic parameters of macrofracture system directly, unless the limestone aquifer is exposed on or near the earth's surface. Therefore, the permeability tensors of a macrofracture system at any depth may be indirectly and roughly determined from the gaugeable permeability tensors of the microfracture system by conversion. This anisotropic variation law of rock permeability with depth is of great significance in the study of three‐dimensional fracture water flow the huge carbonate formations and in the research on the conditions of karst development and karst distribution.

New set-up for measurement of permeability properties of fibrous reinforcements for RTM

Resin transfer molding (RTM) is becoming increasingly important as a production technique for FRPs. However, the design of molds that assures the production of parts with acceptable quality remains a difficult task. Simulation codes developed for design need reliable input data such as reinforcement permeability. The measurement of this material parameter is still not standardized and thus many different set-ups have been proposed. In this paper a new method will be presented that is much faster and much less operator-dependant than other set-ups. It is a 2D central injection set-up, based on the automatic detection of the flow front position as a function of time. For this purpose, simple electrical sensors were designed and an automated calculation procedure was programmed on a PC-based system. As will be shown, the elements of the permeability tensor are not single valued at a particular fiber volume fraction. Rather, each element displays a broad distribution. More importantly, the variations in the principal permeability values are not correlated since their ratio, the anisotropy, also displays a broad distribution.

Discontinuous flow of fracture water: a new technique of karst collapse prevention

A unique regime of groundwater flow in large limestone aquifers in China is presented in the context of variation of anisotropy of permeability tensors with depth. The limestone aquifers are composed of an upper region where the permeability ellipsoid is upright or prolate and characterized by Kz>Kx and Kz>Ky, a transitional zone, and a lower zone whose permeability ellipsoid is horizontal or oblate and characterized by Kz<Kx and Kz<Ky. The transitional zone partitions the whole limestone into these two upper and lower parts. The principal permeability values Kx, Ky, and Kz in these permeability tensors all decrease simultaneously and logarithmically with depth. When groundwater is discharged out of both the upper part and the lower part of the limestone aquifer by permanent mine drainage at a high yield, an initial regional drawdown cone of groundwater is formed in the aquifer domain. Thus the karst collapse may occur catastrophically. However, a special discontinuous flow environment in this permeable continuum, which we refer to as "double water table flow", could appear in a large limestone aquifer if groundwater is further abstracted out of the lower part of the aquifer through mine drainage even at small yields. Under this condition – where a second water table appears beneath the upper high stage water table due to mine drainage activity at the lower level of the aquifer – the previous regional drawdown cone disappears and the initial groundwater table reappears. Consequently, the high stage of water table is re-established in the upper part of the aquifer, and the karst collapses come to a stop. During the process of tapping the lower aquifer zone, a local drawdown cone, separated from the original groundwater table, gradually takes shape in the lower part of the aquifer. This lower water table migrates downwards with depth as controlled by mine drainage. In this case, the total yield of mine drainage does not increase with depth and approaches a constant value. Although the flow rate of groundwater is uninterrupted between these two parts of the aquifer, an unsaturated region of water cuts off the static pressure in the middle portion of the aquifer. Such an unusual phenomenon can be regarded as a special discontinuous flow condition in a permeable continuum. "Double water table flow" or DWTF is proposed as a new concept in applied hydrogeology and can also be developed into a new technique for karst collapse prevention. It is completely different from some partial discontinuous appearances of groundwater pressure or separations of flow systems that result from a stratiform aquifer combination on groundwater discharge. As the mine drainage changes from the upper part to the lower part in a large limestone aquifer, the original continuous flow (a single water table flow) of fracture water can finally evolve into a discontinuous flow (a double water table flow). The occurrence mechanism of DWTF has been fully demonstrated by the hydraulic simulation of fracture water in an infiltration tank. The prerequisite to the evolution of DWTF in a large limestone aquifer is that the permeability ellipsoid of the lower part of the limestone aquifer must be horizontal or oblate. The economic and environmental benefits of the discontinuous fracture water flow are also briefly pointed out.

The Measurement Of In-plane Permeability For Sheared Preforms

Computer simulations of composites manufacturing processes such as liquid moulding require accurate permeability data. Increasingly sophisticated models have been proposed for the prediction of the permeability of fibrous reinforcements; however these analytical tools are not yet able to account for the actual structure of the preforms. Parameters such as the textile structure or the level of imposed deformation in compaction and shear are known to modify the principal permeability values, as well as the orientation of the inplane permeability tensor. If such parameters are to be considered within the simulations, their effects must be known with a level of accuracy that allows them to be separated from the natural variability observed with permeability data. In this paper, a method for the analysis of permeability measurements obtained from a planar apparatus instrumented along three axes is described. The principal permeabilities, as well as the values for the anisotropy ratio and orientation of the in-plane permeability tensor, are obtained without making any assumption relating the warp and weft directions of the materials to the orientation of the tensor. A metal cavity is used, allowing tests to be performed at high fibre volume fractions. Using this method, values can be obtained in a fraction of the time required for an equivalent work to be done using rectilinear measurements. Typical experimental data is presented to illustrate the potential of the method, and simplifying hypothesis used in other published methods are commented. Transactions on Engineering Sciences vol 21, © 1998 WIT Press, www.witpress.com, ISSN 1743-3533

Variation of the permeability tensor ellipsoid in homogeneous anisotropic soils

The flow of water through a homogeneous anisotropic soil is governed by Darcy's equation in which the velocity is proportional to the imposed hydraulic gradient. The constant of proportionality (coefficient of permeability) is a symmetric tensor of second rank, reducing to a scalar only in the case of isotropic soils. It is shown that for determining the velocity vector from a known hydraulic gradient the permeability tensor ellipsoid should be constructed with semiaxes equal to the inverse of the square root of the permeability values. For determining the hydraulic gradient from a known velocity, the permeability tensor ellipsoid should have semiaxes equal to the square root of the principal permeability values. The fact that two different tensor ellipsoids can be constructed for a given anisotropic soil may produce confusion and give rise to a significant error. Special attention should therefore be given in evaluating the appropriate permeability value to be used in Darey's equation. It is recommended that the ellipsoid used always be the one with semiaxes equal to the inverse square root of the principal permeability values. Permeability tests were conducted on anisotropic sandstone. Cylindrical cores were taken at various directions with respect to a fixed coordinate system, and permeability values were determined in a constant‐head permeameter. The values obtained when plotted on polar coordinate paper result in a two‐dimensional permeability ellipse. The necessary graphical constructions for determining the direction of the velocity or the direction of the hydraulic gradient from the corresponding tensor ellipses are also given.