Direct Pore-level Simulations Research Articles

Direct pore-level simulation of hydrogen flame anchoring mechanisms in an inert porous media

This work addresses the stabilization of hydrogen flames inside porous media. Hydrogen is a peculiar fuel with a large molecular diffusivity, triggering preferential diffusion and other effects related to non-unity Lewis numbers. Consequently, the macro-scale behavior of hydrogen flames is highly influenced by the flame-wall interactions at the pore-scale. In this study, direct pore-level simulations are used for the investigation of anchoring mechanisms and burning-rate enhancement for lean hydrogen flames embedded in inert porous media. It is observed that preferential diffusion greatly enhances flame anchoring, in the wake of the struts, leading to a high increase in flame surface. Also, the local heat release rate is enhanced not only by the higher gas temperature resulting from the heat recirculation but also by the higher local equivalence ratio resulting from preferential diffusion. Furthermore, most of the heat produced by a hydrogen flame is released by the hydroperoxyl reactions, effective at low temperatures but necessitating radicals, mostly H. These radicals are produced by the shuffle reactions, effective at higher gas temperatures. The coupling between those two reaction groups is very dependent on the transport of radicals, which can be impacted by the pore scale velocity gradient, leading to hydrodynamic dispersion and flame wrinkling. Consequently, it is shown that the burning-rate enhancement observed within porous burners fueled with hydrogen is not only due to heat recirculation but also to increased transports of radicals and preferential diffusion effects, which should be accounted for in macroscopic models.

A numerical investigation to determine longitudinal dispersion coefficient in ideal and randomized reticulated porous structures using transient direct pore level simulation

The purpose of this numerical investigation is to characterize the longitudinal dispersion coefficients in open-cell reticulated porous structures. Open-cell foams are modelled using idealized Kelvin cell structures. Using the conventional Navier–Stokes equation, airflow has been calculated through various porous structures. Along with the flow, the dispersion of a tracer fluid is traced across the structures and analyzed in terms of the effective dispersion coefficient. Using direct pore level simulations (DPLS), a parametric study is performed to understand the influence of geometrical parameters on the dispersion in porous media. To evaluate the longitudinal dispersion coefficient (LDC), the analytic solution gradients were fitted into the simulated gradients. From the results, a new characteristic length correlation is proposed to calculate the Peclet number, and it is compared with experimental and numerical data that are available in the literature.

3D direct pore level simulations of radiant porous burners

Inside porous burners, chemical combustion reactions coincide with complex interaction between thermo-physical transport processes that occur within solid and gaseous phase and across phase boundary. Fluid flow, heat release and resulting heat flows influence each other. The numerical model used in this work considers gaseous and solid phases, includes fluid flow, enthalpy transport, conjugate heat transfer, and radiative heat transfer between solid surfaces, as well as combustion kinetics according to a skeletal chemical reaction mechanism, fully resolved on the pore scale in three-dimensional space (Direct Pore Level Simulation, DPLS). The calculations are performed based on the finite volume method using standard applications implemented in the OpenFOAM library. The present study presents simulations of three different structures, each at four settings of specific thermal power. Results indicate that specific surface area of the porous structure is a major influencing parameter for increasing radiation efficiency, whereas no correlation of the orientation of an anisotropic structure on radiation efficiency was observed.

Conductive Heat Transfer in Partially Saturated Gas Diffusion Layers with Evaporative Cooling

Heat transport is an important, though often neglected function of gas diffusion layers (GDLs) of polymer electrolyte membrane fuel cells. Thermal conductivity is a key property, especially in partially water saturated GDLs and when the phase change of water is considered, such as required for evaporative cooling applications. Continuum models require effective transport properties as input, which in this work were determined for different types of dry and partially saturated commercial GDLs (Toray 060 and 120, Freudenberg H23). Three-dimensional microstructures and phase distributions were recorded using X-ray tomographic microscopy, digitalized and used in direct pore-level simulations. The governing energy conservation equation was solved in the three phases (gas, liquid, solid) with interfacial heat transfer between the phases to determine the effective thermal conductivity. Correlations for through-plane effective thermal conductivity in the different GDL types as a function of saturation are provided. An energy sink term, accounting for the evaporation of water, was added, enabling a quantification of the effective conductive heat transfer in GDLs with evaporative cooling. The water distribution (clustered or layered) in the GDLs was found to be a key factor for the thermal conduction and evaporative cooling ability.

A proposal for a correlation to calculate pressure drop in reticulated porous media with the help of numerical investigation of pressure drop in ideal & randomized reticulated structures

This paper presents a numerical investigation to estimate pressure drop in fluid flow through reticulated ideal and randomized porous structures. The 3D open-cell foam geometries are constructed using an in-house code along with the use of visualization tool kit (VTK) libraries. In this study, the ideal and randomized Kelvin structures with different porosities and pore densities are generated. These structures have been used to perform direct pore level simulations (DPLS) with the aid of a commercial CFD software. The simulation results are used to acquire the pressure drop across the structures. The pressure drop variation with respect to pore density, porosity, specific surface area, and randomization are analyzed and a pressure drop correlation for reticulated structures with new values of viscous and inertial coefficients is proposed. The validity of the proposed correlation is compared against the experimental and numerical data of the real structures that are available in the literature.

Numerical determination of permeability and Forchheimer coefficient in dual-scale porous media

Fluid flow in dual-scale porous media is numerically investigated at the pore level. The dual-scale porous media consist of packed beds of porous spherical particles. The void space between the spherical particles represents the large-scale pores. The spherical particles have internal structures of three-dimensionally ordered macroporous (3DOM) media featuring interconnected small pores. To perform direct pore-level simulation (DPLS), mass and momentum conservation equations for a fluid flowing through the medium are solved. The simulation results are then used to calculate the permeability and Forchheimer coefficient of the dual-scale porous media. The permeability and Forchheimer coefficient of the 3DOM structures forming the spherical particles are implemented in the Darcy-level simulations, in which the volume-averaged and traditional conservation equations are respectively solved for the small-scale pores inside the spherical particles and the large-scale pores between the particles. Finally, the results of the Darcy-level simulations are compared with those of the DPLS. It is observed that the Darcy-level simulations—with the effective permeability and Forchheimer coefficient of the 3DOM particles—overestimate the pressure drop in the dual-scale porous media as compared to the direct pore-level simulations, in particular for higher values of 3DOM structure porosity.

Morphological and effective transport properties of fixed beds of wood chips: Toward realistic modeling of low-temperature pyrolysis

A detailed understanding of heat transfer and flow is critically important for the pyrolysis of carbonaceous feedstock in fixed bed reactors. In this paper, multimode transport phenomena are simulated by direct pore level simulation on representative digitized samples to retrieve the heat-transfer and pressure-drop properties of highly porous fixed beds of oak-wood chips, which exhibit anisotropic solid-phase tortuosity. A comparison of the direct pore level simulation and simple models of porous media with simple morphologies shows that simple models cannot be used to determine the transport properties of a material with a complex morphology, such as fixed beds of wood chips. Because of drying and devolatilization, the effective thermal conductivity of wood chips decreases with increasing temperature. Heat conduction passes preferentially through the fluid because wood chips have very low thermal conductivity. This study also shows that the shrinking and cracking phenomena resulting from pyrolysis lead to a decrease in the porosity and solid-phase tortuosity and an increase in the specific area. At a high Reynolds number, the pyrolysis also diminishes the permeability but increases the inertial resistance to flow and the interfacial heat transfer.

Transport characteristics of saturated gas diffusion layers treated with hydrophobic coatings

Water flooding of cathodic gas diffusion layers (GDLs) in proton-exchange membrane fuel cells at high current densities or low temperatures limits efficient operation due to disturbed transport of reactants to the catalytic sites or products away into the channels. We utilize tomography-based direct pore-level simulations to provide quantitative insights into the transport characteristics of partially saturated GDLs with and without hydrophobic surface treatment to eventually guide the design of better GDLs. High-resolution (voxel size of 1.3 μm) computed tomography images of two different types commercial Toray TGP-H-120 GDLs, one of them untreated and the other treated by hydrophobic coatings, at different water saturation levels were taken. These images were then digitally processed to precisely segment the gas, water, and fiber phases. The digitalized phase information was used in direct pore-level numerical flow simulations to determine effective relative diffusivity of the gas phase, relative permeability of the gas and liquid water phases, and tortuosity in the gas phase. Mathematical morphology operations were used to calculate size distributions of the liquid water phase and the gas phase at different saturation levels for a better understanding of the pore occupation by water at different capillary pressure. Percolation simulations were used to provide information on the connectivity of the gas and liquid phases. The results were validated with reported experimental data and semi-empirical correlations. Power law expressions provide a good level of accuracy for curve fitting. The hydrophobic coating does not affect the relative permeability and effective realtive diffusivity of air; however, it improves the water permeability significantly. The quantitative results presented provide insights and guidance for designing GDLs with better transport behavior.

Reticulated porous ceria undergoing thermochemical reduction with high-flux irradiation

A numerical and experimental analysis is performed on the solar-driven thermochemical reduction of ceria as part of a H2O/CO2-splitting redox cycle. A transient heat and mass transfer model is developed to simulate reticulated porous ceramic (RPC) foam-type structures, made of ceria, exposed to concentrated solar radiation. The RPC features dual-scale porosity in the mm-range and μm-range within its struts for enhanced transport. The numerical model solves the volume-averaged conservation equations for the porous fluid and solid domains using the effective transport properties for conductive, convective and radiative heat transfer. These in turn are determined by direct pore-level simulations and Monte-Carlo ray tracing on the exact 3D digital geometry of the RPC obtained from tomography scans. Experimental validation is accomplished in terms of temporal temperature and oxygen concentration measurements for RPC samples directly irradiated in a high-flux solar simulator with a peak flux of 1200 suns and heated to up to 1940K. Effective volumetric absorption of solar radiation was obtained for moderate optically thick structures, leading to a more uniform temperature distribution and a higher specific oxygen yield. The effect of changing structural parameters such as mean pore diameter and porosity is investigated.

A study of pressure drop in reticulated ceramic sponges using direct pore level simulation

New values for the viscous and inertial coefficients of the Ergun equation to calculate the pressure drop within open cell ceramic sponges made of alumina and silicon infiltrated silicon carbide (SiSiC) are provided based on the direct pore level simulations (DPLS) results. The fluid flow through ceramic structures of different cell densities and porosities are simulated using standard Navier–Stokes equation without any simplification. The computational grid data are reconstructed from three-dimensional computer tomography scans of different reticulated porous media. Influence of tortuosity on the pressure drop is included in a Ergun equation based pressure drop correlation. The new correlation is dependent on the sponge properties such as, cell diameter, specific surface area and flow tortuosity.

Experimental study, 1D volume-averaged calculations and 3D direct pore level simulations of the flame stabilization in porous inert media at elevated pressure

This work is a comprehensive study of combustion in porous inert media (PIM) with focus on the effects of pressure and air/fuel equivalence ratio. Experiments on lean flame stability limits, flame stabilization and temperature profiles in porous inert media burners of different geometry have been carried out at nearly adiabatic conditions. The experiments were complemented by numerical simulations of combustion in porous inert media, employing a volume-averaged 1D model and 3D direct pore level simulation (3D DPLS) on real geometries of sponge like structures. A definition of the burning velocity is proposed to compare the geometrically different burners investigated. The numerically obtained macroscopic thermal flame thicknesses and the burning velocities are compared with that of free flames. The results show a non-monotonic dependence of the burning velocity on pressure considerably affected by the air/fuel equivalence ratio, which is well depicted by the models used in this work with some identified limitations. By performing a parametric study with the 1D model, dispersion of heat and mass has been identified as the major responsible mechanism of increasing of burning velocity with pressure. The DPLS results showed considerable temperature variations along the space coordinate, which were not considered up to now in 1D models when calculating reaction rates and which could be the reason of the observed limitations.

Morphological Characterization and Effective Thermal Conductivity of Dual-Scale Reticulated Porous Structures.

Reticulated porous ceramic (RPC) made of ceria are promising structures used in solar thermochemical redox cycles for splitting CO2 and H2O. They feature dual-scale porosity with mm-size pores for effective radiative heat transfer during reduction and µm-size pores within its struts for enhanced kinetics during oxidation. In this work, the detailed 3D digital representation of the complex dual-scale RPC is obtained using synchrotron submicrometer tomography and X-ray microtomography. Total and open porosity, pore size distribution, mean pore diameter, and specific surface area are extracted from the computer tomography (CT) scans. The 3D digital geometry is then applied in direct pore level simulations (DPLS) of Fourier’s law within the solid and the fluid phases for the accurate determination of the effective thermal conductivity at each porosity scale and combined, and for fluid-to-solid thermal conductivity from 10−5 to 1. Results are compared to predictions by analytical models for structures with a wide range of porosities 0.09–0.9 in both the strut’s µm-scale and bulk’s mm-scale. The morphological properties and effective thermal conductivity determined in this work serve as an input to volume-averaged models for the design and optimization of solar chemical reactors.

Micro-Computed Tomography Based Computational Fluid Dynamics for the Determination of Shear Stresses in Scaffolds Within a Perfusion Bioreactor

Perfusion bioreactors are known to exert shear stresses on cultured cells, leading to cell differentiation and enhanced extracellular matrix deposition on scaffolds. The influence of the scaffold's porous microstructure is investigated for a polycaprolactone (PCL) scaffold with a regular microarchitecture and a silk fibroin (SF) scaffold with an irregular network of interconnected pores. Their complex 3D geometries are imaged by micro-computed tomography and used in direct pore-level simulations of the entire scaffold-bioreactor system to numerically solve the governing mass and momentum conservation equations for fluid flow through porous media. The velocity field and wall shear stress distribution are determined for both scaffolds. The PCL scaffold exhibited an asymmetric distribution with peak and plateau, while the SF scaffold exhibited a homogenous distribution and conditioned the flow more efficiently than the PCL scaffold. The methodology guides the design and optimization of the scaffold geometry.

Tomography-based determination of porosity, specific area and permeability of snow and comparison with measurements

Micro-computed tomography (μ-CT) of snow replicas is used to characterize 34 snow samples by determining their specific surface area, porosity, effective permeability, anisotropy, and tortuosity. Their 3D geometrical representation obtained by μ-CT is used in direct pore-level simulations (DPLS) to numerically solve the governing mass and momentum conservation equations for fluid flow through porous media. It is found that inertial effects, given by a second and third order correction in Darcy's law, influence the air flow even at low Reynolds numbers. Correlations are derived for permeability, the Dupuit–Forchheimer coefficient and the third order coefficient of Darcy's law as a function of density and grain size. Comparison with the experimentally measured data yields good agreement and confirms the applicability of DPLS for determining the transport properties of snow.

Evaluation of longitudinal dispersion coefficient in open-cell foams using transient direct pore level simulation

A new method to analyze fluid flow in open-cell foams is given by the rise in computational speed, which makes it possible to calculate the heat and mass transport within these structures even with conventional CFD methods. In the present study, air flow through several structures has been explicitly calculated using the standard Navier–Stokes equations. Together with the flow, the dispersion of an initial tracer jump is tracked through the structures and analyzed with respect to effective diffusivity coefficients. The structures comprises a broad range of open-cell ceramic foams which were reconstructed from tomographic data obtained by means of MRI and μ-CT scans.

Tomography-based determination of permeability and Dupuit–Forchheimer coefficient of characteristic snow samples

AbstractA tomography-based methodology for the mass transport characterization of snow is presented. Five samples, characteristic for a wide range of seasonal snow, are considered. Their three-dimensional (3-D) geometrical representations are obtained by micro-computed tomography and used in direct pore-level simulations to numerically solve the governing mass and momentum conservation equations, allowing for the determination of their effective permeability and Dupuit–Forchheimer coefficient. The extension to the Dupuit–coefficient is useful near the snow surface, where Reynolds numbers higher than unity can appear. Simplified semi-empirical models of porous media are also examined. The methodology presented allows for the determination of snow’s effective mass transport properties, which are strongly dependent on the snow microstructure and morphology. These effective properties can, in turn, readily be used in snowpack volume-averaged (continuum) models such as strongly layered samples with macroscopically anisotropic properties.

Tomography-Based Analysis of Radiative Transfer in Reacting Packed Beds Undergoing a Solid-Gas Thermochemical Transformation

A reacting packed-bed undergoing a high-temperature thermochemical solid-gas transformation is considered. The steam- and dry-gasification of carbonaceous materials to syngas is selected as the model reaction. The exact 3D digital geometrical representation of the packed-bed is obtained by computer tomography and used in direct pore-level simulations to characterize its morphological and radiative transport properties as a function of the reaction extent. Two-point correlation functions and mathematical morphology operations are applied to calculate porosities, specific surfaces, particle-size distributions, and representative elementary volumes. The collision-based Monte Carlo method is applied to determine the probability distribution of attenuation path length and direction of incidence at the solid-fluid boundary, which are linked to the extinction coefficient, scattering phase function, and scattering albedo. These effective properties can be then incorporated in continuum models of the reacting packed-bed.

Tomography-Based Heat and Mass Transfer Characterization of Reticulate Porous Ceramics for High-Temperature Processing

Reticulate porous ceramics employed in high-temperature processes are characterized for heat and mass transfer. The exact 3D digital geometry of their complex porous structure is obtained by computer tomography and used in direct pore-level simulations to numerically calculate their effective transport properties. Two-point correlation functions and mathematical morphology operations are applied for the geometrical characterization that includes the determination of porosity, specific surface area, representative elementary volume edge size, and mean pore size. Finite volume techniques are applied for conductive/convective heat transfer and flow characterization, which includes the determination of the thermal conductivity, interfacial heat transfer coefficient, permeability, Dupuit–Forchheimer coefficient, residence time, tortuosity, and diffusion tensor. Collision-based Monte Carlo method is applied for the radiative heat transfer characterization, which includes the determination of the extinction coefficient and scattering phase function.