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Darcy's Law (darcy + law)
Selected AbstractsA finite element algorithm for parameter identification of material models for fluid saturated porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2001R. Mahnken Abstract In this contribution an algorithm for parameter identification of geometrically linear Terzaghi,Biot-type fluid-saturated porous media is proposed, in which non-uniform distributions of the state variables such as stresses, strains and fluid pore pressure are taken into account. To this end a least-squares functional consisting of experimental data and simulated data is minimized, whereby the latter are obtained with the finite element method. This strategy allows parameter identification based on in situ experiments. In order to improve the efficiency of the minimization process, a gradient-based optimization algorithm is applied, and therefore the corresponding sensitivity analysis for the coupled two-phase problem is described in a systematic manner. For illustrative purpose, the performance of the algorithm is demonstrated for a slope stability problem, in which a quadratic Drucker,Prager plasticity model for the solid and a linear Darcy law for the fluid are combined. Copyright © 2001 John Wiley & Sons, Ltd. [source] Numerical simulation of the microscale impregnation in commingled thermoplastic composite yarnsADVANCES IN POLYMER TECHNOLOGY, Issue 2 2010R. Gennaro Abstract The impregnation of a glass woven fabric with an amorphous polyethylene terephthalate copolymer (PET- g) matrix was investigated using a finite element (FE) model for interbundle and intrabundle flow of the matrix. Micrographs of samples obtained by film stacking of PET- g to impregnate the glass fabric have confirmed the occurrence of interbundle and intrabundle flow, taking place as separate steps. On the basis of this evidence, two different mechanisms for the fiber impregnation were postulated. The first flow process is associated with a macroscale interbundle impregnation, whereas the second is associated with microscale intrabundle impregnation. Two different FE models were developed to simulate the microscopic and macroscopic flow of the matrix, considering a large number of different random fiber arrangements. Both models could account for the non-Newtonian rheological behavior of the thermoplastic matrix. The microscale impregnation of fibers was simulated by using randomly spaced and nonoverlapping unidirectional filaments. The effect of the number of filaments and the number of random distributions necessary to achieve an adequate accuracy of the method was assessed. The results obtained from the simulation showed that at low pressures, the polymer melt exhibits Newtonian behavior, which makes it possible to predict the tow permeability by the Darcy law. A more difficult situation arises at high pressures because of the non-Newtonian behavior of the melt. This requires the introduction of a value for the permeability that is also dependent on the rheological properties of the melt. The same non-Newtonian behavior of the matrix was observed for macroscale impregnation of bundles. © 2010 Wiley Periodicals, Inc. Adv Polym Techn 29:122,130, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/adv.20179 [source] A simulation of the non-isothermal resin transfer molding processPOLYMER ENGINEERING & SCIENCE, Issue 12 2000Vincenza Antonucci A simulation of the non-isothermal resin transfer molding manufacturing process accounting for both the filling and the consolidation stage has been developed. The flow of an exothermally reactive resin through a porous medium has been analyzed with reference to the Darcy law, allowing for the chemorheological properties of the reacting resin. Thermal profile calculations have been extended to a three phase domain, namely the mold, the dry preform and the filled preform. The mold has been included in order to evaluate the thermal inertial effects. The energy balance equation includes the reaction term together with the conductive and convective terms, and particular attention has been devoted to setting the thermal boundary condition at the flow front surface. The moving boundary condition has been derived by a jump equation. The simulation performance has been tested by comparing the predicted temperature profiles with experimental data from literature. Further numerical analysis assessed the relevance of using the jump equation at the flow front position for both filling time and thermal profile determination. [source] Hybrid Simulation of Miscible Mixing with Viscous FingeringCOMPUTER GRAPHICS FORUM, Issue 2 2010Seung-Ho Shiny Abstract By modeling mass transfer phenomena, we simulate solids and liquids dissolving or changing to other substances. We also deal with the very small-scale phenomena that occur when a fluid spreads out at the interface of another fluid. We model the pressure at the interfaces between fluids with Darcy's Law and represent the viscous fingering phenomenon in which a fluid interface spreads out with a fractal-like shape. We use hybrid grid-based simulation and smoothed particle hydrodynamics (SPH) to simulate intermolecular diffusion and attraction using particles at a computable scale. We have produced animations showing fluids mixing and objects dissolving. [source] Transpiration and stomatal conductance across a steep climate gradient in the southern Rocky MountainsECOHYDROLOGY, Issue 3 2008Nate G. McDowell Abstract Transpiration (E) is regulated over short time periods by stomatal conductance (Gs) and over multi-year periods by tree- and stand-structural factors such as leaf area, height and density, with upper limits ultimately set by climate. We tested the hypothesis that tree structure, stand structure and Gs together regulate E per ground area (Eg) within climatic limits using three sites located across a steep climatic gradient: a low-elevation Juniperus woodland, a mid-elevation Pinus forest and a high-elevation Picea forest. We measured leaf area : sapwood area ratio (Al : As), height and ecosystem sapwood area : ground area ratio (As : Ag) to assess long-term structural adjustments, tree-ring carbon isotope ratios (,13C) to assess seasonal gas exchange, and whole-tree E and Gs to assess short-term regulation. We used a hydraulic model based on Darcy's law to interpret the interactive regulation of Gs and Eg. Common allometric dependencies were found only in the relationship of sapwood area to diameter for pine and spruce; there were strong site differences for allometric relationships of sapwood area to basal area, Al : As and As : Ag. On a sapwood area basis, E decreased with increasing elevation, but this pattern was reversed when E was scaled to the crown using Al : As. Eg was controlled largely by As : Ag, and both Eg and Gs declined from high- to low-elevation sites. Observation-model comparisons of Eg, Gs and ,13C were strongest using the hydraulic model parameterized with precipitation, vapour pressure deficit, Al : As, height, and As : Ag, supporting the concept that climate, Gs, tree- and stand-structure interact to regulate Eg. Copyright © 2008 John Wiley & Sons, Ltd. [source] Scaling of water flow through porous media and soilsEUROPEAN JOURNAL OF SOIL SCIENCE, Issue 1 2008K. Roth Summary Scaling of fluid flow in general is outlined and contrasted to the scaling of water flow in porous media. It is then applied to deduce Darcy's law, thereby demonstrating that stationarity of the flow field at the scale of the representative elementary volume (REV) is a critical prerequisite. The focus is on the implications of the requirement of stationarity, or local equilibrium, in particular on the validity of the Richards equation for the description of water movement through soils. Failure to satisfy this essential requirement may occur at the scale of the REV or, particularly in numerical simulations, at the scale of the model discretization. The latter can be alleviated by allocation of more computational resources and by working on a finer-grained representation. In contrast, the former is fundamental and leads to an irrevocable failure of the Richards equation as is observed with infiltration instabilities that lead to fingered flow. [source] Natural-gradient tracer experiments in epikarst: a test study in the Acqua dei Faggi experimental site, southern ItalyGEOFLUIDS (ELECTRONIC), Issue 3 2008E. PETRELLA Abstract Two natural-gradient tracer experiments were carried out using borehole fluorometers in order to characterize the internal structure of epikarstic horizons and analyze subsurface flow within these high-conductivity layers. The experiments were carried out in a test site in southern Italy where the epikarst is made up of an upper part with pervasive karstification and a lower part without pervasive karstification. Injection and observation boreholes were 6.9 m apart. An initial experiment demonstrated that wider (conduits) and narrower (fractures and bedding planes) openings coexist in a well-connected network within the lower epikarst. The adjusted aperture of the opening network (105 ,m) suggests that conduits are subordinately developed. The lower epikarstic horizon is hydraulically similar to granular porous media and Darcy's law can be applied to describe groundwater flow. A small value of longitudinal dispersivity (0.13 m) shows that variations in the velocity field in the direction of flow are less significant than those typical of carbonate systems at the same experiment scale. A second experiment demonstrated that longitudinal dispersivity (2.42 m) in the upper epikarst is in agreement with findings in other carbonates at the same experiment scale. However, despite the higher dispersivity and more pervasive karstification, the mean tracer velocity (3.7 m day,1) in the upper epikarst is slightly lower than the velocity in the lower epikarst (13.6 m day,1). [source] About Darcy's law in non-Galilean frameINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2004C. Geindreau Abstract This paper is aimed towards investigating the filtration law of an incompressible viscous Newtonian fluid through a rigid non-inertial porous medium (e.g. a porous medium placed in a centrifuge basket). The filtration law is obtained by upscaling the flow equations at the pore scale. The upscaling technique is the homogenization method of multiple scale expansions which rigorously gives the macroscopic behaviour and the effective properties without any prerequisite on the form of the macroscopic equations. The derived filtration law is similar to Darcy's law, but the tensor of permeability presents the following remarkable properties: it depends upon the angular velocity of the porous matrix, it verifies Hall,Onsager's relationship and it is a non-symmetric tensor. We thus deduce that, under rotation, an isotropic porous medium leads to a non-isotropic effective permeability. In this paper, we present the results of numerical simulations of the flow through rotating porous media. This allows us to highlight the deviations of the flow due to Coriolis effects at both the microscopic scale (i.e. the pore scale), and the macroscopic scale (i.e. the sample scale). The above results confirm that for an isotropic medium, phenomenological laws already proposed in the literature fails at reproducing three-dimensional Coriolis effects in all types of pores geometry. We show that Coriolis effects may lead to significant variations of the permeability measured during centrifuge tests when the inverse Ekman number Ek,1 is ,,(1). These variations are estimated to be less than 5% if Ek,1<0.2, which is the case of classical geotechnical centrifuge tests. We finally conclude by showing that available experimental data from tests carried out in centrifuges are not sufficient to determining the effective tensor of permeability of rotating porous media. Copyright © 2004 John Wiley & Sons, Ltd. [source] Accuracy of Galerkin finite elements for groundwater flow simulations in two and three-dimensional triangulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2001Christian Cordes Abstract In standard finite element simulations of groundwater flow the correspondence between hydraulic head gradients and groundwater fluxes is represented by the stiffness matrix. In two-dimensional problems the use of linear triangular elements on Delaunay triangulations guarantees a stiffness matrix of type M. This implies that the local numerical fluxes are physically consistent with Darcy's law. This condition is fundamental to avoid the occurrence of local maxima or minima, and is of crucial importance when the calculated flow field is used in contaminant transport simulations or pathline evaluation. In three spatial dimensions, the linear Galerkin approach on tetrahedra does not lead to M -matrices even on Delaunay meshes. By interpretation of the Galerkin approach as a subdomain collocation scheme, we develop a new approach (OSC, orthogonal subdomain collocation) that is shown to produce M -matrices in three-dimensional Delaunay triangulations. In case of heterogeneous and anisotropic coefficients, extra mesh properties required for M -stiffness matrices will also be discussed. Copyright © 2001 John Wiley & Sons, Ltd. [source] A finite volume method for multicomponent gas transport in a porous fuel cell electrodeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2003John M. Stockie Abstract We present a mathematical model for multicomponent gas transport in an anisotropic fuel cell electrode. The model couples the Maxwell,Stefan equations for multicomponent diffusion along with Darcy's law for flow in a porous medium. The equations are discretized using a finite volume approach with the method of lines, and the resulting non-linear system of differential equations is integrated in time using a stiff ODE solver. Numerical simulations are performed to validate the model and to investigate the effect of various parameters on fuel cell performance. Copyright © 2003 John Wiley & Sons, Ltd. [source] A parametric study of multi-phase and multi-species transport in the cathode of PEM fuel cellsINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 8 2008Nada Zamel Abstract In this study, a mathematical model is developed for the cathode of PEM fuel cells, including multi-phase and multi-species transport and electrochemical reaction under the isothermal and steady-state conditions. The conservation equations for mass, momentum, species and charge are solved using the commercial software COMSOL Multiphysics. The catalyst layer is modeled as a finite domain and assumed to be composed of a uniform distribution of supported catalyst, liquid water, electrolyte and void space. The Stefan,Maxwell equation is used to model the multi-species diffusion in the gas diffusion and catalyst layers. Owing to the low relative species' velocity, Darcy's law is used to describe the transport of gas and liquid phases in the gas diffusion and catalyst layers. A serpentine flow field is considered to distribute the oxidant over the active cathode electrode surface, with pressure loss in the flow direction along the channel. The dependency of the capillary pressure on the saturation is modeled using the Leverette function and the Brooks and Corey relation. A parametric study is carried out to investigate the effects of pressure drop in the flow channel, permeability, inlet relative humidity and shoulder/channel width ratio on the performance of the cell and the transport of liquid water. An inlet relative humidity of 90 and 80% leads to the highest performance in the cathode. Owing to liquid water evaporation, the relative humidity in the catalyst layer reaches 100% with an inlet relative humidity of 90 and 80%, resulting in a high electrolyte conductivity. The electrolyte conductivity plays a significant role in determining the overall performance up to a point. Further, the catalyst layer is found to be important in controlling the water concentration in the cell. The cross-flow phenomenon is shown to enhance the removal of liquid water from the cell. Moreover, a shoulder/channel width ratio of 1:2 is found to be an optimal ratio. A decrease in the shoulder/channel ratio results in an increase in performance and an increase in cross flow. Finally, the Leverette function leads to lower liquid water saturations in the backing and catalyst layers than the Brooks and Corey relation. The overall trend, however, is similar for both functions. Copyright © 2007 John Wiley & Sons, Ltd. [source] Darcy's law-based model for wicking in paper-like swelling porous mediaAICHE JOURNAL, Issue 9 2010Reza Masoodi Abstract The wicking of liquid into a paper-like swelling porous medium made from cellulose and superabsorbent fibers was modeled using Darcy's law. The work is built on a previous study in which the Washburn equation, modified to account for swelling, was used to predict wicking in a composite of cellulose and superabsorbent fibers. In a new wicking model proposed here, Darcy's law for flow in porous media is coupled with the mass conservation equation containing an added sink or source term to account for matrix swelling and liquid absorption. The wicking-rate predicted by the new model compares well with the previous experimental data, as well as the modified Washburn equation predictions. The effectiveness of various permeability models used with the new wicking model is also investigated. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source] Theoretical analysis of the effects of asymmetric membrane structure on fouling during microfiltrationAICHE JOURNAL, Issue 6 2009Weiyi Li Abstract There is a growing interest in the use of both asymmetric and composite membranes for microfiltration and ultrafiltration processes. This includes particle removal applications in the semiconductor industry and virus clearance in biopharmaceutical applications. Filter fouling plays an important role in these processes. Although flux decline models have been developed for homogeneous membranes, the effects of asymmetric membrane structure on flux decline behavior remain poorly understood on a fundamental level. Here, we develop a theoretical model to describe the effects of asymmetric membrane structure on flux decline. The asymmetric structure was described by the spatial variation in Darcy permeability in the directions normal to and parallel to the membrane surface. The velocity profile and flux decline because of pore blockage were described using Darcy's law and a pore blockage and cake filtration model. Flux decline data were obtained using pseudocomposite membranes with highly interconnected polyvinylidene fluoride membranes (PVDF) and straight through pore polycarbonate track-etched membranes (PCTE). Model composite membranes were formed by layering PCTE or PVDF membranes with different pore sizes on top of each other. Flux decline data for the composite membrane were in good agreement with model calculations. The results provide important insights into the effects of asymmetric membrane pore structures on flux decline. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Unified finite element discretizations of coupled Darcy,Stokes flowNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2009Trygve Karper Abstract In this article, we discuss some new finite element methods for flows which are governed by the linear stationary Stokes system on one part of the domain and by a second order elliptic equation derived from Darcy's law in the rest of the domain, and where the solutions in the two domains are coupled by proper interface conditions. All the methods proposed here utilize the same finite element spaces on the entire domain. In particular, we show how the coupled problem can be solved by using standard Stokes elements like the MINI element or the Taylor,Hood element in the entire domain. Furthermore, for all the methods the handling of the interface conditions are straightforward. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] Fast liquid composite molding simulation of unsaturated flow in dual-scale fiber mats using the imbibition characteristics of a fabric-based unit cellPOLYMER COMPOSITES, Issue 10 2010Hua Tan The use of the dual-scale fiber mats in liquid composite molding (LCM) process for making composites parts gives rise to the unsaturated flow during the mold-filling process. The usual approaches for modeling such flows involve using a sink term in the mass balance equation along with the Darcy's law. Sink functions involving complex microflows inside tows with realistic tow geometries have not been attempted in the past because of the problem of high computational costs arising from the coupling of the macroscopic gap flows with the microscopic tow flows. In this study, a new "lumped" sink function is proposed for the isothermal flow simulation, which is a function of the gap pressure, capillary pressure, and tow saturation, and which is estimated without solving for the microscopic tow simulations at each node of the FE mesh in the finite element/control volume algorithm. The sink function is calibrated with the help of the tow microflow simulation in a stand-alone unit cell of the dual-scale fiber mat. This new approach, which does not use any fitting parameters, achieved a good validation against a previous published result on the 1D unsaturated flow in a biaxial stitched mat,satisfactory comparisons of the inlet-pressure history as well as the saturation distributions were achieved. Finally, the unsaturated flow is studied in a car hood-type LCM mold geometry using the code PORE-FLOW© based on the proposed algorithm. POLYM. COMPOS., 31:1790,1807, 2010. © 2010 Society of Plastics Engineers. [source] | |||||||||||||||||||