In this paper, a multi-dimensional dynamic model of vanadium Redox Flow Batteries (RFB) is employed to predict battery performance and internal operating condition during charge and discharge. The model consists of a set of partial differential equations of mass, momentum, species, charges, and energy conservation, in conjunction with the electrode’s electrochemical reaction kinetics. After validated against experimental data for a vanadium RFB, flow field, temperature distribution, and reactant evolution are presented. The developed numerical tool is extremely useful in optimizing RFB design and control.

Hydrogen is a resource that provides energy and forms water only after reacting with oxygen. Because there are no emissions such as greenhouse gases when hydrogen is converted to produce energy, it is considered one of the most important energy resources for addressing the problems of global warming and air pollution. Additionally, hydrogen can be useful for constructing “smart grid” infrastructure because electrical energy from other renewable energy sources can be stored in the form of chemical energy by electrolyzing water, creating hydrogen. Among the many hydrogen generation systems, solid oxide electrolysis cells (SOECs) have attracted considerable attention as advanced water electrolysis systems because of their high energy conversion efficiency and low use of electrical energy. To find the relationship between operating conditions and the performance of SOECs, research has been conducted both experimentally, using actual SOEC cells, and numerically, using computational fluid dynamics (CFD). In this investigation, we developed a 3-D simulation model to analyze the relationship between the operating conditions and the overall behavior of SOECs due to different contributions to the over-potential. All SOECs involve the transfer of mass, momentum, species, and energy, and these properties are correlated. Furthermore, all of these properties have a direct influence on the concentration of the gases in the electrodes, the pressure, the temperature and the current density. Therefore, the conservation equations for mass, momentum, species, and energy should be included in the simulation model to calculate all terms in the transfer of mass, heat and fluid. In this simulation model, the transient term was neglected because the steady state was assumed. All governing equations were calculated using Star-CD (CD Adapco, U.S). The source terms in the governing equations were calculated with in-house code, i.e., user defined functions (UDF), written in FORTRAN 77, and these were linked to the Star-CD solver to calculate the transfer processes. Simulations were performed with various cathode inlet gas compositions, anode inlet gas compositions, cathode thickness, and electrode porosity to identify the main parameters related to performance.

Two computational fluid dynamics models have been developed to predict the performance of a solid oxide fuel cell stack, a detailed and a simplified model. In the detailed model, the three dimensional momentum, heat, and species transport equations are coupled with electrochemistry. In the simplified model, the diffusion terms in the transport equations are selectively replaced by rate terms within the core region of the stack. This allows much coarser meshes to be employed at a fraction of the computational cost. Following the mathematical description of the problem, results for a single cell and multi-cell stack are presented. Comparisons of local current density, temperature, and cell voltage indicate that good agreement is obtained between the detailed and simplified models, confirming the validity of the latter as a practical option in stack design.

Management of liquid water formed by the electrochemical fuel cell reaction is a key factor in PEMFC performance and durability. For practical stack applications, an important consideration is the transport of liquid water at the transition between the ends of the bipolar plate channels and the manifolds, where excess reactant flows from all the individual cells are combined and directed to the stack exhaust. In this region, gas-phase momentum can be very low, especially on the anode, where there is little driving force to remove liquid water that may accumulate as a result of geometrical or surface energy variations, or due to relatively low temperatures that exist outside of the fuel cell active area. This study seeks to characterize the water accumulated within the active area and at the channel-to-manifold transition regions at both the anode and cathode outlets, as a function of cell operating temperature and current density. The neutron imaging method was applied to directly measure the water volumes within the transition regions, and provide a comparison to simultaneously measured water volume within the cell active area. Transition-region water was found to be weakly dependent on current density, suggesting that once water forms in this area, little driving force exists to extract it entirely by means of gas momentum. Moreover, it was found that the active area water volume is strongly dependent on cell temperature, and temperature variation of as little as 0.5 °C can produce a significant change in water accumulation which is reflected in the cell voltage.

Management of liquid water formed by the electrochemical reaction has received considerable attention and is considered a key factor in proton exchange membrane fuel cell (PEMFC) performance and durability. For practical stack applications, an aspect of the water management problem that is often overlooked is the transport of liquid water at the transition between the ends of the bipolar plate channels and the manifolds, where excess reactant flows from all the individual cells are combined and directed to the stack exhaust. In the bipolar plate exit region, gas-phase momentum can be very low, especially on the anode, and thus there is little driving force to remove liquid water. This study seeks to first quantify the characteristics of channel-to-manifold water transport by analysis of in-situ neutron radiography images, and correlation of the volumes of liquid water in the active and non-active regions to the relevant fuel cell operating conditions: temperature, pressure, relative humidity, current density and stoichiometric ratio. This analysis is complimented by new ex-situ experiments that directly control the flow of channel-level water and quantify the attendant increase in two-phase pressure drop in the non-active fuel cell region. The ex-situ apparatus has the additional feature of a simultaneous cross-flow channel at the exit plane of the bipolar plate, which enables simulation of two-phase flow dynamics of a fuel cell positioned anywhere in a stack, from zero cross-flow at the capped end of the stack to maximum cross-flow at the gas connected end of the stack.

A three-dimensional, multi-component, two-fluid model developed in the commercial CFD package CFX 13 (ANSYS inc.), is used to investigate the effect of porous media compression on transport phenomenon of a PEM Fuel cell (PEMFC). The PEMFC model only consist of the cathode channel, gas diffusion layer, micro-porous layer and catalyst layer, excluding the membrane and anode. In the porous media liquid water transport is described by the capillary pressure gradient, momentum loss via the Darcy-Forchheimer equation and mass transfer between phases by a non-equilibrium phase change model. Furthermore, the presence of irreducible liquid water is taken into account. In order to account for compression, porous media morphology variations are specified based on the GDL throughplane strain and intrusion which are stated as a function of compression. These morphology variations affect gas and liquid water transport, and hence liquid water distribution and the risk of blocking active sites. Hence, water transport is studied under GDL compression, in order to investigate the qualitative effects. Two simulation cases are compared; one with and one without compression.

Temperature distribution in a fuel cell significantly affects the performance and efficiency of the fuel cell system. Particularly, in low temperature fuel cells, improvement of the system requires addressing the heat management issues, which reveals the importance of developing thermal models. In this study, a 3D numerical thermal model is presented to analyze heat transfer and predict the temperature distribution in air-cooled proton exchange membrane fuel cells (PEMFC). In the modeled fuel cell stack, forced air flow supplies oxidant as well as cooling. Conservation equations of mass, momentum, and energy are solved in the oxidant channel, whereas energy equation is solved in the entire domain, including the gas diffusion layers (GDLs) and separator plates, which play a significant role in heat transfer. A parametric study is done to investigate the effect of various operating conditions on maximum cell temperature. The results are further validated with experiment. This model provides a theoretical foundation for thermal analysis of air-cooled stacks, where temperature non-uniformity is high and thermal management and stack cooling is a significant engineering challenge.

A computational fluid dynamics model is developed to study the effect of cationic contamination on the performance of a polymer electrolyte fuel cell (PEFC). The fuel cell model incorporates mass, species, momentum and heat balances along with the ionic and electronic charge conservations. To model the transport of the cationic species, Nernst-Planck equations are used while taking into consideration of local electroneutrality in the ionomer phase. The diffusive fluxes of the cations are implemented in the Nernst-Planck equations such that they take into account adsorption of the species. A steady-state analysis is carried out to address the effects of contamination on the operating fuel cell performance. It is observed that contamination significantly reduces the output power density of the PEFC by occupying the available charge sites inside the ionomer.

In this study, a three-dimensional computational method was developed to predict convective heat transfer combined with water phase change/two-phase flow in a PEMFC cathode duct. Momentum, heat transport and species equations have been solved by coupled source terms and thermo-physical properties of the multi-component mixture. Advanced boundary conditions are applied at the cathode duct external walls in the analysis, i.e., combined thermal boundary conditions of heat flux on the active surface and thermal insulation on the remaining solid walls. Moreover, effects of mass consumption and generation appearing on the active surface are implemented. The calculated results reveal that the thermal conditions at the interfaces vary along the main stream, and a big permeability of the porous layer promotes the bulk gas transport and the generated liquid water removal via the bottom interface between the flow duct and the porous layer, and a big convective heat transfer coefficient as well.

A simplified quasi-3-dimensional model of a solid oxide fuel cell (SOFC) is developed to investigate the dynamics of internal reformation in an SOFC. The dynamic model solves dynamic equations that govern relevant physical and chemical processes in a simplified geometric representation of a planar SOFC. This makes the model complex enough to resolve major performance characteristics and simple enough to be used in dynamic analyses and controls development at the system level. The model solves dynamic mass, momentum and energy conservation equations to provide local temperature, species concentrations, and current density distributions. These distributions are resolved in two dimensions across the cell, but each 2-D distribution resolves 5 separate control volumes through the nodal unit cell: the PEN; anode and cathode gas compartments; and interconnects. Internal reforming chemical kinetic expressions are included in the model formulation. Simulations show that extent of internal reformation impacts the dynamic temperature difference across the cell. Steady state maximum temperature differential across the cell can be reduced to about 100 K with 100% internal reformation and a cross-flow configuration. A full hydrogen co-production system was then modeled by integrating the SOFC model with heat exchangers, combustor, blower, and hydrogen collector. For conditions of a constant cathode exhaust temperature of 1273 K and lower fuel utilization (60%–70%), the dominant thermal influence on the cell temperature was cooling by the endothermic reformation reactions. But at higher fuel utilization conditions, the dominant thermal influence was the convective cooling of the cathode gases. System simulations showed no tradeoff between power and H 2 production if the cathode exhaust temperature is held constant at 1273 K. High power and high H 2 production conditions were found to be synergistic: high hydrogen production leads to high electrochemical efficiency and lower air flow rate leading to fewer parasitic losses. Dynamic SOFC responses to manipulation of fuel flow rate within the range of fuel utilization between 60 and 85% indicate that the system can be adequately controlled to produce various amounts of hydrogen and electricity.

A computational fluid dynamics model is developed to study the effects of operational parameters on the performance of a micro-tubular SOFC. Coupled partial differential equations for heat, momentum, species and charge balances are solved with a commercial software using finite element method. Effect of temperature on the power characteristics of the system is addressed. Current density distributions for different temperatures are compared with the inclusion of electronic leakage currents in the electrolyte. Current density profiles for different conditions are examined thoroughly and related to the transport properties.

This paper describes the fundamental theory, algorithm and computation methods to predict the performance of proton exchange membrane fuel cells (PEMFC) and direct methanol fuel cells (DMFC) using a simplified computational fluid dynamics (CFD) approach. Based on the common transport phenomenon inside both fuel cells, the mass, momentum, energy and species equations were derived. Darcy laws were employed to simplify the momentum equation and also to linearize the species equation. The mathematical model was solved in various flow channel designs and some membrane electrode assembly (MEA) options. The major concern is mainly on the cathode side, in the PEMFC case, that dominates the performance deterioration due to potential loss in the flow field. In the case of DMFCs, both anode and cathode sides are simulated. The methanol crossover effect is also included. This virtual performance test bench plays an important role in the prototype fuel cell design. The computer aided design tool is proved to be useful in configuration designs. Additionally, it provides the detailed transport phenomenon inside the fuel cell stack.

In this study, a fully three-dimensional calculation method has been further developed to simulate and analyze various processes in a thick anode duct. The composite duct consists of a porous layer, the flow duct and solid current connector. The analysis takes the electrochemical reactions into account. Momentum and heat transport together with gas species equations have been solved by coupled source terms and variable thermo-physical properties (such as density, viscosity, specific heat, etc.) of the fuel gases mixture. The unique fuel cell conditions such as the combined thermal boundary conditions on solid walls, mass transfer (generation and consumption) associated with the electrochemical reaction and gas permeation to / from the porous electrode are applied in the analysis. Results from this study are presented for various governing parameters in order to identify the important factors on the fuel cell performance. It is found that gas species convection has a significant contribution to the gas species transport from / to the active reaction site; consequently characteristics of both gas flow and heat transfer vary widely due to big permeation to the porous layer in the entrance region and species mass concentration related diffusion after a certain distance downstream the inlet.

A numerical model for analyzing a tubular-type Indirect Internal Reforming Solid Oxide Fuel Cell (IIR-SOFC), which is expected to become one of the most important power generators in the near future, was developed. The model simultaneously treats momentum, heat and mass transfer, fuel reforming, electrochemical phenomena and an electric circuit. Calculations for the gas flow fields inside and outside the cell tube are conducted with a two-dimensional cylindrical coordinate system adopting the axisymmetric assumption. At the same time, the electric current field in the cell tube is calculated with a quasi three-dimensional coordinate system in order to consider the ohmic loss properly. Activation overpotential is also considered using a temperature dependent model. As a consequence of the calculations, details of conditions in the cell and its power generation characteristics were revealed. Serious temperature gradients were generated in the cell under circumstances where the catalyst for reforming was distributed uniformly inside the feed tube. Complicated electric current fields that varied in both the axial and circumferential direction of the cell were observed. In addition, it became obvious that the temperature dependency of the activation overpotential could be the most significant factor governing the power generation characteristics.

In this study, a three-dimensional calculation method has been developed to simulate and analyze steam reforming of natural gas, and the effects on various transport processes in a duct from a compact steam reformer. The reformer conditions such as the combined thermal boundary conditions on solid walls, mass balances associated with the reforming reactions and gas permeation to/from the porous catalyst layer are applied in the analysis. Momentum and heat transport together with fuel gas species equations have been solved by coupled source terms and variable thermo-physical properties (such as density, viscosity, specific heat, etc.) of the fuel gas mixture. The predicted results are presented and discussed for a composite duct consisting of a porous catalyst reaction area, the flow duct and solid layers. Parametric studies are conducted and the results show that the variables, such as fuel reformer temperatures and duct configuration, have significant effects on the transport processes and reformer performance.

This paper focuses on a new systematic configuration of micro-channel fuel processors, particularly designed for portable applications. An alternative integration method of the micro-channel fuel processors is attempted to overcome the serious thermal unbalance and to minimize the system volume by introducing the direct contact method of the sub-components. An integrated micro-channel methanol processor was developed by assembling unit reactors, which were fabricated by stacking and bounding micro-channel patterned stainless steel plates, including fuel vaporizer, catalytic combustor and steam reformer. Commercially available Cu/ZnO/Al 2 O 3 catalyst (ICI Synetix 33-5) was coated inside micro-channel of the unit reactor for steam reforming. The steam reforming reaction was conducted in the temperature range of 200°C to 260°C in the basis of reformer side end-plate and the temperature was controlled by varying methanol feeding into the combustor. More than 99% of methanol was converted at 240°C of reformer side temperature. A mechanism-based numerical model aimed at enhancing physical understanding and optimizing designs has been developed for improved micro-channel fuel processors. A two-dimensional numerical model in the reformer section created to model the phenomena of species transport and reaction occurring at the catalyst surface. The mass, momentum, and species equations were employed with kinetic equations that describe the chemical reaction characteristics to solve flow-field, methanol conversion rate, and species concentration variations along the micro-channel. This mechanism-based model was validated against the experimental data from the literature and then applied to various layouts of the micro-channel fuel processors targeted for the optimal catalyst loading and fuel reforming purpose. The computer-aided models developed in this study can be greatly utilized for the design of advanced fast-paced micro-channel fuel processors research.

Recently, there has been considerable interest in the internal reforming reactions of solid oxide fuel cells (SOFCs) using methane or natural gas via. The internal reforming and electrochemical reactions appear in the porous anode layer, and may lead to inhomogeneous temperature and gas species distributions according to the reaction kinetics. A three-dimensional calculation method has been further developed to simulate and analyze the internal reforming and the electrochemical reactions, and the effects on various transport processes in a thick anode duct. In this study, the composite duct consists of a porous anode, fuel flow duct and solid current connector. Momentum, heat transport and gas species equations have been solved by coupled source terms and variable physical properties (density, viscosity, specific heat, etc.) of the fuel gas mixture. The combined thermal boundary conditions on solid walls, mass balances (generation and consumption) associated with the various reactions and gas permeation to/from the porous electrode are applied in the analysis. Simulation results show that the internal reforming and the electrochemical reactions, and operating conditions are significant for fuel gas transport and heat transfer in the anode.

Fundamental performance and the transient characteristics of a small tubular SOFC were numerically investigated. The model simultaneously treats momentum, heat and mass transfer, electrochemical phenomena and an electric circuit. Transient characteristics of a cell upon a sudden change of the cell terminal voltage or the air flow rate were examined. During its process, a steady simulation was first conducted and its result was used as the initial condition for the transient calculation. The transient calculation continued until a steady state under the new boundary condition was obtained. Discussions on the time response of the cell performance and thermal field were made in order to find the key factors mainly affecting the transient characteristics. To confirm what factors affect on the transient behavior, calculations were conducted for two different cell geometries, which have different cell diameters, but have same ratios of cell heat capacity to the heat generating area. As a result, it was found that the transient characteristics of a cell are primarily governed by the balance between the heat capacity of a cell and the heat generation by electrochemical reactions. The large heat capacity of the cell is one of the key problems affecting the transient behavior, limiting its quick response. A numerical demonstration is shown in which a rapid cell status change was achieved by controlling its operation conditions.

The present work considers a two-fluid mathematical model for the gas-liquid flow in PEM fuel cells. One fluid represents the continuous gas phase flow through the layers of the fuel cell. For this fluid, the governing equations of momentum, energy, mass continuity and species mass fractions, are considered with additional inter-fluid exchange source terms. The second fluid represents the dispersed liquid phase that is formed from the condensed water vapor inside the layers of the PEM fuel cell. For this fluid only the momentum and mass continuity equations need to be included, as no electrochemical reactions are essentially possible. The dispersed fluid is made up of small droplets in the gas channel. The mean droplet diameter can be computed from a balance equation of the forces acting on the emerging liquid water from the pores of the GDL into the gas channels. The droplet diameters are found to range between 150 and 170 microns for the present PEM fuel cell at 0.8 V. In the present work, the full momentum conservation equations are invoked, in the layers of the fuel cell, for the two fluids. The resulting governing equations for u, v, T and species mass fractions together with the electric potential and mass continuity equations are solved iteratively, using a modified SIMPLE algorithm, for the two fluids. One solution domain is superimposed over all the layers of the fuel cell. Special care is devoted to the electric potential, ‘Poisson-type’, equation boundary condition to prevent any escape of protons through the two gas diffusion layers and simultaneously insuring a non-singular matrix of finite-difference coefficients. The obtained two-fluid and single-phase numerical simulations are compared with the corresponding experimental and numerical data available in the literature. The 2-fluid model shows that the blocking effect of the liquid phase starts to dominate, for cell voltage less than 0.65 V; in this case, the flowing 2-phase flow produces faster drop in cell voltage as the loading electric current increases. This phenomenon was partially hindered by previous LHF model results and essentially completely bypassed by the single-phase simulations.

This paper discusses numerical analysis of heat and mass transfer characteristics in autothermal fuel reformer. Assuming local thermal equilibrium between bulk gas and surface of catalyst, one medium approach for energy equation is incorporated. Also, mass transfer between concentrations of bulk gas and near the surface of catalyst is neglected due to relatively low gas mixture velocity. For surface chemical reaction Langmuir-Hinshelwood reaction is incorporated when methane (CH 4 ) is reformed to hydrogen-rich gases by autothermal reforming (ATR) reaction. Complete combustion, steam reforming, water gas shift and direct methane steam reforming reactions are included in the chemical reaction model. Under two operating conditions (O/C and S/C), ATR reactions are estimated from the numerical calculations. Mass, momentum, and energy equations are simultaneously calculated with chemical reactions. From the predicted results, we can estimate optimum operating conditions for high hydrogen yield.