An analytical model for the transverse permeability of gas diffusion layer with electrical double layer effects in proton exchange membrane fuel cells

An analytical model is presented for the transverse permeability of gas diffusion layer (GDL) based on an ordered array of parallel charged circular cylinders at the steady state. The formula of calculating the permeability of the transverse direction is given by solving the fluid momentum equation in a unit cell. In the present approach, the proposed model is explicitly related to the porosity and fiber radius of fibrous porous media, the zeta potential, and the physical properties of the electrolyte solution. Besides, the effects of these parameters (the porosity, unit cell aspect ratio, fiber radius, and molar concentration) on the transverse permeability are discussed detailedly. The model predictions are compared with the previous studies in the available literature, and good agreement is found.     

Analytical Monte Carlo Ray Tracing simulation of radiative heat transfer through bimodal fibrous insulations with translucent fibers

In this study, a Monte Carlo Ray Tracing (MCRT) simulation technique is developed to study steady-state radiative heat transfer through fibrous insulation materials. The simulations are conducted in 3-D disordered virtual fibrous media with unimodal and/or bimodal fiber diameter distributions consisting of fibers whose surfaces are specularly reflective, and are translucent to Infrared (IR) radiation. Scattering within the realm of geometric optics is incorporated into our MCRT simulations using Snell’s Law for ray refraction. Fibers’ optical properties are obtained from Fresnel’s law and Beer’s law based on the refractive index of the material. Two different treatments of “high” and “low” conductivities are considered for the fibers and their effects are discussed. Our results indicate that heat flux through a fibrous medium with translucent fibers decreases with increasing packing fraction of the fibers. It was observed that IR transmittance through the media increases with increasing through-plane orientation of the fibers, but is independent of their in-plane orientations. It was also found that fiber orientation has generally a negligible effect on the temperature profile across the media’s thickness. However, for the case of high-conductivity fibers, increasing fibers’ through-plane orientation tends to flatten the temperature profile. The results obtained from simulating bimodal fibrous structures indicate that increasing the fiber-diameter dissimilarity, or the mass fraction of the coarse fibers, slightly increases the radiation transmittance through the media, and accordingly reduces the temperature gradient across the thickness. Our simulation results are compared with those from the two-flux model and good agreement is observed.     

Modeling of gas diffusion layers with curved fibers using a genetic algorithm

This paper presents a methodology for modeling microstructures of fibrous porous media with curved fibers. The developed methodology utilizes implicit periodic surface model coupled with the genetic algorithm (GA) optimization to construct the porous microstructures. The fibers profile is represented by the periodic implicit surfaces and their orientation and curvature are determined by GA optimization. To reconstruct the microstructures with higher resemblance to the actual porous media GA is utilized to minimize the fibers stored strain energy and their intersection volumes. Coupling the image processing techniques to the geometry construction procedure the morphological and transport properties of the constructed microstructures are also determined. To verify the feasibility and the accuracy of the proposed methodology the microstructure of Freudenberg H2315 GDL is constructed and characterized. The presented methodology enables a parametric design approach. Thus, the effects of the microstructure's properties e.g., fibers diameter, fibers orientation and porosity of the porous structure on the transport properties of the fibrous media are investigated.     

Modeling fluid spread in thin fibrous sheets: Effects of fiber orientation

In this paper, a dual-scale model is developed to simulate the radial spreading of liquids in thin fibrous sheets. Using 3-D microscale simulations, the required constitutive equations, capillary pressure and relative permeability, have been determined at each saturation level and used in a macroscale model developed based on the Richards’ equation of two-phase flow in porous media. The dual-scale approach allowed us to include the partially-saturated region of a porous medium in calculations. Simulating different fibrous sheets with identical parameters but different in-plane fiber orientations, it is revealed that the rate of fluid spread increases with increasing the in-plane alignment of the fibers. Our simulations are discussed with respect to existing studies in the literature.     

Analytical determination of permeability of porous fibrous media with consideration of electrokinetic phenomena

Flow behavior in porous fibrous media with consideration of electrokinetic phenomena is investigated based on a linearized Poisson–Boltzmann equation and Navier–Stokes equation. An analytical solution of effective permeability of porous fibrous media as functions of porosity, dimensionless local averaging net charge density and dimensionless electric resistance number is derived in this paper. The influences of the electrokinetic phenomena can be measured by the dimensionless electric resistance number, which is proportional to the square of the liquid dielectric constant, the solid surface Zeta potential and inversely proportional to the liquid dynamic viscosity, electric conductivity and the square of the maximum pore radius. The analytical results show that when the dimensionless electric resistance number is small and the porosity is large, the dimensionless total flow rate shows a nearly uniform distribution. When the dimensionless electric resistance number is large, the resistant effects of the electrical double layer (EDL) become so significant that the superficial velocity decreases. The effective permeability of the porous fibrous media decreases correspondingly. Furthermore, the theoretical predicted effective permeability values are compared with experimental data, and good agreement is observed between the two. It shows that the mathematical model for the effective permeability of porous fibrous media with consideration of electrokinetic phenomena is satisfactory.     

A fractal model for the coupled heat and mass transfer in porous fibrous media

This paper developed a mathematical model for the coupled heat and mass transfer in porous media based on the fractal characters of the pore size distribution. According to Darcy’s law and Hagen–Poiseuille’s law for liquid flows, the diffusion coefficient of the liquid water, a function of fractal dimension, is obtained theoretically. The liquid flow affected by the surface tension and the gravity, the water vapor sorption/desorption by fibers, the diffusion of the water vapor and the phase changes are all taken into account in this model. With specification of initial and boundary conditions, distributions of water vapor concentration in void spaces, volume fraction of liquid water, distribution of water molecular content in fibers and temperature changes in porous fibrous media are obtained numerically. Effects of porosity of porous fibrous media on heat and mass transfer are analyzed. The theoretical predictions are compared with experimental data and good agreement is observed between the two, indicating that the fractal model is satisfactory.     

Investigation of the 3D model of coupled heat and liquid moisture transfer in hygroscopic porous fibrous media

This paper focuses on the investigation of the 3D mathematical model to simulate the coupled heat and liquid moisture transfer in hygroscopic porous fibrous media. The flow of the liquid moisture, the water vapor sorption/desorption by fibers and the diffusion of the water vapor are taken into account in this 3D model. Prediction-corrector method is used to solve the 3D governing equations. A series of computational results of the coupled heat and moisture transfer are obtained with the specific initial conditions and boundary conditions. The distribution of the water vapor concentration in the void spaces, the volume fraction of the liquid water in the void spaces, the distribution of the water content in fibers and the changes of the temperature in porous fibrous media are computed. It is shown that the effects of the gravity and capillary actions are significant in hygroscopic porous fibrous media. The comparison with the experimental measurements shows the reasonable agreement between the two. The results illustrate that the 3D model of the coupled heat and liquid moisture transfer in hygroscopic porous fibrous media is satisfactory.     

CONSOLIDATION AROUND A VOLUMIC SPHERICAL DECAYING HEAT SOURCE

A general solution, scheme is developed for one-dimensional and nonisothermal consolidation problems for fluid-saturated, porous, thermoelastic media. Two fundamental parameters necessary to quantify the coupling effects between thermal, hydraulic, and mechanical behaviors are identified: The ratio thermal diffusivity / hydraulic diffusivity and drained/ undrained limiting cases. An application of this solution scheme to nuclear waste disposal is given: The problem of a volumic spherical decaying heat source buried in a deep thermoporoelastic medium. Numerical applications show that coupling effects are maxima for low-permeability and high-porosity saturated media such as deep compressible clays. This corresponds to a low value of the ratio of hydraulic diffusivity over thermal diffusivity and a high value of the ratio “undrained behavior” over “drained behavior.”     

Numerical modeling of high-temperature shell-and-tube heat exchanger and chemical decomposer for hydrogen production

Numerical simulations of shell-and-tube heat exchanger and chemical decomposer with straight tube configuration and porous media were performed using FLUENT6.2.16 to examine the percentage decomposition of sulfur trioxide. The decomposition process can be a part of sulfur–iodine (S–I) thermochemical water splitting cycle, which is one of the most studied cycles for hydrogen production. A steady-state, laminar, two-dimensional axisymmetric shell-and-tube model with counter flow and parallel flow arrangements and simple uniform cubical packing was developed using porous medium approach to investigate the fluid flow, heat transfer and chemical reactions in the decomposer. As per the investigation, the decomposition percentage of sulfur trioxide for counter flow arrangement was found to be 93% and that of parallel flow was 92%. Also, a high pressure drop was observed in counter flow arrangement compared to parallel flow. The effects of inlet velocity, temperature and the porous medium properties on the pressure drop across the porous medium were studied. The influence of geometric parameters mainly the diameter of the tube, diameter of the shell and the length of the porous zone on the percentage decomposition of sulfur trioxide in the tube was investigated as well. A preliminary parametric study of the mentioned configuration is conducted to explore effects of varying parameters on the decomposition of sulfur trioxide. From the performed calculations, it was found that the Reynolds number played a significant role in affecting the sulfur trioxide decomposition. The percentage decomposition decreases with an increase in Reynolds number. Surface-to-volume area ratio and activation energy were also the important parameters that influenced the decomposition percentage.     

Two-Phase Heat Sinks with Microporous Coating

To minimize flow boiling instabilities in two-phase heat sinks, two different types of microporous coatings were developed and applied on mini- and small-channel heat sinks and tested using degassed R245fa refrigerant. The first coating was epoxy based and was sprayed on heat sink channels, while the second coating was formed by sintering copper particles on heat sink channels. Minichannel heat sinks had overall dimensions 25.4 mm × 25.4 mm × 6.4 mm and 12 rectangular channels with a hydraulic diameter 1.7 mm and a channel aspect ratio of 2.7. Small-channel heat sinks had the same overall dimensions, but only three rectangular channels with hydraulic diameter 4.1 mm and channel aspect ratio 0.6. The microporous coatings were found to minimize parallel channel instabilities for minichannel heat sinks and to reduce the amplitude of heat sink base temperature oscillations from ～6°C to slightly more than 1°C. No increase in pressure drop or pumping power due to the microporous coating was measured. The minichannel heat sinks with porous coating had on average 1.5 times higher heat transfer coefficient than uncoated heat sinks. Also, the small-channel heat sinks with the “best” porous coating had on average 2.5 times higher heat transfer coefficient and the critical heat flux was 1.5 to 2 times higher compared with the uncoated heat sinks.     

Modeling the role of microstructural parameters in radiative heat transfer through disordered fibrous media

Understanding the influence of microstructural parameters on the rate of heat transfer through a disordered fibrous medium is important for the design and development of heat insulation materials. In this work, by generating virtual 3-D geometries that resemble the internal microstructure of fibrous insulation materials, we simulated the influence of diameter, orientation, and emissivity of the fibers, as well as the media’s porosity and thickness on the radiative heat transmittance. Our simulations are based on a Monte Carlo ray tracing algorithm that we have developed for studying radiative heat flow in 3-D disordered media. The media were assumed to be made up of cylindrical opaque fibers with specular surface. The advantage of our modeling approach is that it does not require any empirical input values, and can directly be used to isolate and study the role of individual microstructural parameters of the media. The major limitation of the model is that it is accurate as long as the fibers can be considered large relative to the wavelength of the incoming rays. Our results indicate that heat flux through a fibrous medium decreases by increasing the packing fraction of the fibers when the thickness and fiber diameter are kept constant. Increasing the fibers’ absorptivity (or emissivity) was observed to decrease the radiation transmittance through the media. Our simulations also revealed that for constant porosity and thickness, the heat flux transmitted across the medium can be reduced by using finer fibers. The steady state temperature profiles across the thicknesses of media with different properties were obtained and found to be independent of the fibers’ emissivity.     

Hydraulic permeability of fibrous porous media

In this study, the hydraulic permeability for viscous flow through fibrous media of high porosity is investigated theoretically. Fibrous media in one-dimensional (1D), two-dimensional (2D) or three-dimensional (3D) structure are approximated as consisting of repetitive unit cells based on Voronoi Tessellation approximation and volume averaging method. In the new model, the hydraulic permeability of fibrous media is described as a function of porosity and fiber radius as well as geometrical formation factors including the degree of randomness (viz. randomness of fiber distribution) and fiber orientation. In particular, the slip effect for flow through superfine fibrous media is analytically studied. The prediction of the new model for fibrous media with porosity greater than 0.7 is highly consistent with the analytical, experimental and numerical results found in the literature. It is further demonstrated that randomly packed fibrous media have larger permeability than regular ones, the hydraulic permeability of fibrous media increases with increasing of through-plane orientation, but is less dependent on in-plane fiber orientation, and the slip effect on the longitudinal hydraulic permeability is greater than the perpendicular one.     

A fractal permeability model for bi-dispersed porous media

In this paper a fractal permeability model for bi-dispersed porous media is developed based on the fractal characteristics of pores in the media. The fractal permeability model is found to be a function of the tortuosity fractal dimension, pore area fractal dimension, sizes of particles and clusters, micro-porosity inside clusters, and the effective porosity of a medium. An analytical expression for the pore area fractal dimension is presented by approximating the unit cell by the Sierpinski-type gasket. The pore area fractal dimension and the tortuosity fractal dimension of the porous samples are determined by the box counting method. This fractal model for permeability does not contain any empirical constants. To verify the validity of the model, the predicted permeability data based on the present fractal model are compared with those of measurements. A good agreement between the fractal model prediction of permeability and experimental data is found. This verifies the validity of the present fractal permeability model for bi-dispersed porous media.     

In-plane gas permeability of proton exchange membrane fuel cell gas diffusion layers

A new analytical approach is proposed for evaluating the in-plane permeability of gas diffusion layers (GDLs) of proton exchange membrane fuel cells. In this approach, the microstructure of carbon papers is modeled as a combination of equally-sized, equally-spaced fibers parallel and perpendicular to the flow direction. The permeability of the carbon paper is then estimated by a blend of the permeability of the two groups. Several blending techniques are investigated to find an optimum blend through comparisons with experimental data for GDLs. The proposed model captures the trends of experimental data over the entire range of GDL porosity. In addition, a compact relationship is reported that predicts the in-plane permeability of GDL as a function of porosity and the fiber diameter. A blending technique is also successfully adopted to report a closed-form relationship for in-plane permeability of three-directional fibrous materials.     

Permeability of fractal porous media by Monte Carlo simulations

The permeability of the fractal porous media is simulated by Monte Carlo technique in this work. Based on the fractal character of pore size distribution in porous media, the probability models for pore diameter and for permeability are derived. Taking the bi-dispersed fractal porous media as examples, the permeability calculations are performed by the present Monte Carlo method. The results show that the present simulations present a good agreement compared with the existing fractal analytical solution in the general interested porosity range. The proposed simulation method may have the potential in prediction of other transport properties (such as thermal conductivity, dispersion conductivity and electrical conductivity) in fractal porous media, both saturated and unsaturated.     

Analysis of seepage characters in fractal porous media

In this paper, the plane-radial and plane-parallel flows for Newtonian fluid in fractal porous media are analyzed. Based on the assumption that the porous medium consists of a bundle/set of tortuous streamlines/capillaries and on the fractal characteristics of pore size distribution in porous media, the expressions for porosity, flow rate, velocity and permeability for both radial and parallel flows are developed. The obtained expressions are the functions of tortuosity, fractal dimension, maximum and minimum pore diameters, and there are no empirical constant and every parameter has clear physical meaning in the expressions. The pressure distribution equations for plane-radial and plane-parallel flows in fractal porous media are also derived. The pressure and velocity distributions in plane-radial reservoirs are calculated and discussed.     

Analytic determination of the effective thermal conductivity of PEM fuel cell gas diffusion layers

Accurate information on the temperature field and associated heat transfer rates are particularly important in devising appropriate heat and water management strategies in proton exchange membrane (PEM) fuel cells. An important parameter in fuel cell performance analysis is the effective thermal conductivity of the gas diffusion layer (GDL). Estimation of the effective thermal conductivity is complicated because of the random nature of the GDL micro structure. In the present study, a compact analytical model for evaluating the effective thermal conductivity of fibrous GDLs is developed. The model accounts for conduction in both the solid fibrous matrix and in the gas phase; the spreading resistance associated with the contact area between overlapping fibers; gas rarefaction effects in microgaps; and salient geometric and mechanical features including fiber orientation and compressive forces due to cell/stack clamping. The model predictions are in good agreement with existing experimental data over a wide range of porosities. Parametric studies are performed using the proposed model to investigate the effect of bipolar plate pressure, aspect ratio, fiber diameter, fiber angle, and operating temperature.     

Modeling of composite fibrous porous diffusion media

To engineer the desired properties of fibrous porous media, a parametric modeling approach is needed to support the rational design of the materials before the fabrication. In this study, we propose a methodology that enables the accurate representation of three-dimensional (3D) microstructures of fibrous porous media and prediction of their transport properties. Toray TGP-H-060 gas diffusion layer (GDL) is selected as an example to demonstrate the feasibility of the suggested design methodology. The detailed microstructure of the GDL with the inclusion of locally distributed binder is constructed using an extended periodic surface (PS) modeling technique. A 3D morphological approach is taken to create the binder distribution within the fibrous microstructure. Transport properties including permeability, relative diffusivity, and tortuosity and local structure characteristics of the generated microstructure, under different binder loading are calculated. It is shown that the detailed model of the fiber-binder composite has a strong influence on the predicted properties.     

Analysis of effective thermal conductivity for circular tubes made with porous media based on fractal theory

Accurately evaluating the relation between heat transfer performance and the complex structure of porous media is still a difficult task. Most previous fractal models of effective thermal conductivity (ETC) are developed to describe the heat-conducting characteristics of a unit cell or a representative elementary volume in porous media, and few models have paid attentions to the ETC for practical circular tubes made with a porous structure based on fractal theory. This paper proposes a new ETC model for a circular tube made with porous media based on fractals, and the validity of the present model is proved by previous models and testing data in the literature, then the effects of intrinsic thermo-physical properties of each component and pore structures on the ETC are discussed. The analysis results indicate that a circular tube made with porous media can improve its heat-insulating performance by about 25% compared with a common parallel circular tube. This can supply an alternative scheme for pipe insulation design in cold/hot fluid supplying systems or air conditioning systems.     

Enhancing heat transfer in the core flow by using porous medium insert in a tube

According to the concept of heat transfer enhancement in the core flow, porous media with a slightly smaller diameter to a tube are developed and inserted in the core of the tube under the constant and uniform heat flux condition. The flow resistance and heat transfer characteristics of the air flow for laminar to fully turbulent ranges of Reynolds numbers are investigated experimentally and numerically. There are three different porous media used in the experiments with porosity of 0.951, 0.966 and 0.975, respectively. The effect of porous radius ratio on the heat transfer performance is studied in numerical simulation. Both numerical and experimental results show that the convective heat transfer is considerably enhanced by the porous inserts of an approximate diameter with the tube and the corresponding flow resistance increases in a reasonable extent especially in laminar flow. It shows that the core flow enhancement is an efficacious method for enhancing heat transfer.