1D and 3D numerical simulations in PEM fuel cells

The potential of fuel cells for clean and efficient energy conversion is generally recognized.The proton-exchange membrane (PEM) fuel cells are one of the most promising types of fuel cells. Models play an important role in fuel cell development since they enable the understanding of the influence of different parameters on the cell performance allowing a systematic simulation, design and optimization of fuel cells systems. In the present work, one-dimensional and three-dimensional numerical simulations were performed and compared with experimental data obtained in a PEM fuel cell. The 1D model, coupling heat and mass transfer effects, was previously developed and validated by the same authors [1] and [2]. The 3D numerical simulations were obtained using the commercial code FLUENT - PEMFC module.The results show that 1D and 3D model simulations considering just one phase for the water flow are similar, with a slightly better accordance for the 1D model exhibiting a substantially lower CPU time. However both numerical results over predict the fuel cell performance while the 3D simulations reproduce very well the experimental data. The effect of the relative humidity of gases and operation temperature on fuel cell performance was also studied both through the comparison of the polarization curves for the 1D and 3D simulations and experimental data and through the analysis of relevant physical parameters such as the water membrane content and the proton conductivity. A polarization curve with the 1D model is obtained with a CPU time around 5 min, while the 3D computing time is around 24 h. The results show that the 1D model can be used to predict optimal operating conditions in PEMFCs and the general trends of the impact on fuel cell performance of several important physical parameters (such as those related to the water management). The use of the 3D numerical simulations is indicated if more detailed predictions are needed namely the spatial distribution and visualization of various relevant parameters.An important conclusion of this work is the demonstration that a simpler model using low CPU has potential to be used in real-time PEMFC simulations.     

0D, 1D and 2D nanomaterials for visible photoelectrochemical water splitting. A Review

Global energy problems of the 21st century have led to the search for alternative energy sources, among which is hydrogen produced via photoelectrochemical solar water splitting. Photo-electrochemical water splitting using semiconductor nanostructured materials is a progressive method for producing hydrogen. The unique electronic, mechanical, surface and optical properties of nanomaterials make it possible to create photocatalysts with complex structures of energy zones, allowing the use of a wide range of sunlight and exerting a positive effect on absorption and scattering of sunlight. This review contains a detailed analysis of current studies aimed at improving the efficiency of photocatalytic systems by using 0D, 1D and 2D nanostructures. Special attention is paid to the mechanisms of photocatalytic water splitting to produce hydrogen with the help of various nanostructures.     

Stackelberg-Nash Controllability for a Quasi-linear Parabolic Equation in Dimension 1D, 2D,or 3D

This paper deals with the application of Stackelberg-Nash strategies to the control to quasi-linear parabolic equations in dimensions 1D, 2D, or 3D. We consider two followers, intended to solve a Nash multi-objective equilibrium; and one leader satisfying the controllability to the trajectories.

     

Singularity analysis for 2D and 3D thermoelastic media containing V-notches

The stress field and heat flux singularities at the vertex of two-dimensional (2D) and three-dimensional (3D) V-notches are, respectively, investigated. By introducing typical terms in the series asymptotic expansions of displacement and temperature fields near the notch tip, the thermoelastic governing equations and radial boundary conditions of a V-notched structure are transformed into characteristic ordinary differential equations with respect to the singular order. These equations can be solved by the interpolating matrix method developed earlier by part of the authors. The singular orders related to the stress field and heat flux can be derived simultaneously and can be specified by the corresponding characteristic angular functions in the present method. The singularities are compared between 2D and 3D thermoelastic specimen containing V-notches. It is found that one singular order will be discarded if a 3D medium is simplified into a 2D one.     

A Novel Boundary-Integral Based Finite Element Method for 2D and 3D Thermo-Elasticity Problems

In this article a new hybrid boundary integral-based (HBI) finite element method (FEM) is presented for analyzing two-dimensional (2D) and three-dimensional (3D) thermoelastic problems with arbitrary distribution of body force and temperature changes. The method of particular solution is used to decompose the displacement field into homogeneous part and particular part. The homogeneous solution is obtained by using the HBI-FEM with fundamental solutions, yet the particular solution related to the body force and temperature change is approximated by radial basis function (RBF). The detailed formulation for both 2D and 3D HBI-FEM for thermoelastic problems are given, and two different approaches for treating the inhomogenous terms are presented and compared. Five numerical examples are presented to demonstrate the accuracy and performance of the proposed method. When compared with the existing analytical solutions or ABAQUS results, it is found that the proposed method works well for thermoelastic problems and also when using a very coarse mesh, results with satisfactory accuracy can be obtained.     

Comparison of a small-scale 3D PCM thermal control model with a validated 2D PCM thermal control model

A three-dimensional (3D) numerical model was developed to simulate the use of a phase change material linked to a photovoltaic (PV) system to control the temperature rise of the PV cells. The model can be used to predict temperatures, velocity fields and vortex formation within the system. The 3D predictions have been compared with those from a previously developed experimental validated two-dimensional (2D) finite-volume heat transfer model conjugated hydro-dynamically to solve the Navier–Stokes and energy equations. It was found that for the systems simulated with appropriate boundary conditions, the 2D model predictions compare well with those of the 3D model. The 3D model was used to predict the temperature distributions when the heat transfer to the phase change material was enhanced by high thermal conductivity pin fins.     

Energy R&D A UK perspective

Energy R & D is essential for countries wishing to lessen their dependence on imported oil and to widen their long-term options for energy policy. Accepting that energy R & D must be viewed in an international context, Mr Surrey and Mr Walker review the UK coal, gas, oil, nuclear and electricity supply industries' programmes, examine the role of government and suggest guidelines for a national strategy. They call for more positive direction of energy R & D by the Government in order to balance the interests of the nationalised fuel industries where they conflict or overlap, and to ensure consistency of energy R & D policy with industrial policies.     

3D thermoelastic analysis of rotating disks having arbitrary profile based on a variable kinematic 1D finite element method

A variable kinematic 1D finite element (FE) method is presented for 3D thermoelastic analysis of rotating disks with variable thickness. The principle of minimum potential energy is used to derive general governing equations of the disks subjected to body forces, surface forces, concentrated forces, and thermal loads. To solve the equations, the 1D Carrera unified formulation (CUF), which enables to go beyond the kinematic assumptions of classical beam theories, is employed. Based on the 1D CUF, the disk is considered as a beam, which can be discretized into a finite number of 1D elements along its axis. The displacement field over the beam’s cross section is approximated by Lagrange expansions. This methodology leads to an FE formulation that is invariant with respect to the order of expansions used over the cross sections, and thus the 3D problem reduces to a 1D problem. The effect of the cross section discretization on displacement and stress fields is investigated. Results obtained from this method are in good agreement with the reference analytical and finite difference solutions. The proposed innovative method can be very effective in the thermoelastic analysis of rotating disks.     

Flow channel design in a proton exchange membrane fuel cell: From 2D to 3D

Flow channel design has attracted more and more attention with the evolution of fuel cell technology. Compared with conventional 2D flow channel, 3D flow channel has been proved to improve the performance of proton exchange membrane fuel cell with great enhancement of reactant transport in many researches. In this paper, flow fields of parallel 2D, simplified 3D and 3D with inclination are presented to study the transport and distribution characteristics of reactant and water inside a fuel cell, and efficiency evaluation criterion is proposed to evaluate the superiority of the flow channel design. It is found that 3D flow fields are superior compared with parallel 2D flow channel, with improved capacity of mass transfer, uniform water distribution and advanced water removal ability. The performance improvements of both 3D flow channel designs become significant at elevated current density, with the output voltage increasing to 4.4% at 1.6 A cm^?2 and up to 10% at 2 A cm^?2. Compared with 3D flow channel with inclination, simplified 3D flow channel shows smaller pressure drop, and it has better performance than that of 2D flow channel. Considering both the performance and flow resistance, simplified 3D flow channel performs the best with high efficiency and easy-processing, thus it is the future direction of flow design.     

Exact 2D Solution and Assessment of a 1D Zigzag Theory for Vibration of Thermally Stressed Hybrid Beams

ABSTRACT

A benchmark two-dimensional (2D) piezothermoelasticity solution is presented for buckling and free vibration of simply supported symmetrically laminated hybrid piezoelectric beams under initial stresses due to thermoelectric load. The solution, based second Piola stress tensor and nonlinear Lagrangian strains, accounts for the effect of initial transverse normal strain and the two-way piezoelectric coupling. Benchmark results are presented for the buckling temperature, natural frequencies under initial thermal stresses and modal distributions of displacements and stresses across the thickness, against which the accuracy of 1D beam theories for hybrid beams can be assessed. A recently developed coupled 1D zigzag theory for hybrid beams is extended for vibration under initial thermal stresses. The theory uses a piecewise linear approximation for the thermal and potential fields across sublayers, an approximation for the deflection, which explicitly accounts for the transverse normal strain due to thermal and electric fields and a layerwise (zigzag) variation for the axial displacement. The transverse shear continuity conditions at the layer interfaces and the shear traction-free conditions at the top and bottom are enforced to reduce the number of primary displacement variables to three. The new 1D theory is assessed in comparison with the exact 2D solution for the natural frequencies and mode shapes of beams and panels under initial thermoelectric load. The zigzag theory results show excellent agreement with the 2D results when the initial transverse normal strain is neglected.     

Unsteady 2D PEM fuel cell modeling for a stack emphasizing thermal effects

Models currently used for analyses of thermal and water behavior of a PEM fuel cell are based 3D computational fluid dynamics (CFD). However, the analyses are limited to a single cell with static behavior. Thus, these models cannot be used for analyses of dynamic behavior of a stack that continuously varies according to operating conditions. The model proposed describes dynamic behavior of a stack with two adjoining cells and endplate assembly, and work as a current controlled voltage source that can be used for optimization of BOPs and the associated controls. Simulations have been conducted to analyze start-up behaviors and the performance of the stack. Our analyses deliver following results: (1) dynamic temperature distribution in both the through-plane direction and the along channel direction of the fuel cell stack, (2) effects influencing the source terms of current density, and (3) dynamic oxygen concentration distribution. The temperature profile and its variation propensity are comparable to the previous results [Y. Shan, S.Y. Choe, J. Power Sources, 145 (1) (2005) 30–39; Y. Shan, S.Y. Choe, J. Power Sources, in press].     

Impulse Turbine with 3D Guide Vanes for Wave Energy Conversion

In this study, in order to achieve further improvement of the performance of an impulse turbine with fixed guide vanes for wave energy conversion, the effect of guide vane shape on the performance was investigated by experiment. The investigation was performed by model testing under steady flow condition. As a result, it was found that the efficiency of the turbine with 3D guide vanes are slightly superior to that of the turbine with 2D guide vanes because of the increase of torque by means of 3D guide vane, though pressure drop across the turbine for the 3D case is slightly higher than that for the 2D case.     

On the simulation of laminar strained flames in stagnation flows: 1D and 2D approaches versus experiments

The present work is essentially devoted to the simulation of a laminar strained flame using two approaches: 2D realistic and 1D simplified. The studied case corresponds to a laminar burner that creates an upward-oriented round jet of stoichiometric methane–air mixture impacting on a horizontal metal disk. 2D numerical simulations have been performed using the Fluent® 6.3 software in the axisymmetric configuration. Detailed thermochemical and transport models are applied. Results of the 2D and 1D simulations are analyzed and compared with experimental data on flow velocity obtained by particle image velocimetry (PIV). Limitations of the classical 1D approach are identified and further commented on. Measurement errors due to the particle slip are evaluated by simulating the particle motion with inclusion of the gravity, Stokes drag, and thermophoretic forces.     

3D isotropic approximation for solar diffuse irradiance on tilted surfaces

A well known 2D approach of Liu and Jordan allows computing isotropic solar diffuse irradiance on a tilted surface. It is a 2D theory as the position of a sky element is characterized by a single (zenith) angle. A more realistic 3D model (that uses both zenith and azimuth angles to describe sky element's position) is developed in this paper for both isotropic diffuse irradiance and ground reflected irradiance incident on an arbitrary oriented surface. The 3D formula predicts a lower diffuse irradiance than the 2D relationship while the ground reflected irradiance is higher in case of the 3D model than in case of the 2D approach. In case of a small tilt angle, the 2D and 3D approximations predict comparable values, higher than the mean of the results obtained with a (reference) non-isotropic model. However, the 3D model is slightly more precise. When a larger tilt angle is considered, the 3D model predicts a few percent larger value than the mean of the values estimated by the reference model while the 2D model gives a significantly higher value.     

2D/2D Cu-tetrahydroxyquinone MOF/N-doped graphene heterojunction as photocatalyst for overall water splitting

A novel 2D/2D heterojunction (CuTHQ/NG) has been prepared by in situ growth of the 2D CuTHQ MOF on defective N-doped graphene (NG), and its photocatalytic activity for overall water splitting studied in detail. CuTHQ/NG heterojunction has demonstrated better photocatalytic activity (480 μmol/g) than the individual components (257 and 65 μmol/g for CuTHQ and NG, respectively) for H₂ evolution. Furthermore, unlike the individual components, the as-prepared 2D/2D CuTHQ/NG heterojunction promotes overall water splitting under simulated sunlight (164 μmol of H₂/g and 80 μmol of O₂/g). We have also studied the photo-induced charge separation and recombination reactions. Photocurrent measurements and emission quenching experiments have confirmed improved charge separation in the CuTHQ/NG heterojunction. Moreover, the charge recombination kinetics have been investigated with transient absorption spectroscopy. Electron/hole recombination in the heterojunction has been determined more than one order of magnitude slower (8.9 μs) than the mechanical mixture of CuTHQ and NG (0.35 μs). Finally, the photochemical stability of the 2D/2D heterojunction has been investigated performing a long-term (96 h) experiment, demonstrating near linear H₂ evolution along the irradiation time.     

Adaptive phase field simulation of dendritic crystal growth in a forced flow: 2D vs 3D morphologies

Two- and three-dimensional (3D) adaptive phase field simulations of dendritic crystal growth in a forced flow are presented. The simulations are based on an adaptive finite volume mesh for a better resolution on the dendrite morphology. It also allows the simulation in a large domain without much additional computing cost, so that the boundary effect can be neglected for the comparison with classic solutions. With the efficient simulations, the effect of forced convection on the growth behavior at high undercooling is discussed, and the results agree well with Oseen–Ivantsov solution and the reported results. For the case of low undercooling, the simulated tip radius and speed are also consistent with the experimental ones. As compared with 2D morphologies, side branches are easily induced in 3D dendrites, and the dramatic difference can be explained through the simulated flow structures and temperature fields. The effect of the flow on the side branching for different undercoolings is also illustrated.     

3D risk management for hydrogen installations

This paper introduces the 3D risk management (3DRM) concept, with particular emphasis on hydrogen installations (Hy3DRM). The 3DRM framework entails an integrated solution for risk management that combines a detailed site-specific 3D geometry model, a computational fluid dynamics (CFD) tool for simulating flow-related accident scenarios, methodology for frequency analysis and quantitative risk assessment (QRA), and state-of-the-art visualization techniques for risk communication and decision support. In order to reduce calculation time, and to cover escalating accident scenarios involving structural collapse and projectiles, the CFD-based consequence analysis can be complemented with empirical engineering models, reduced order models, or finite element analysis (FEA). The paper outlines the background for 3DRM and presents a proof-of-concept risk assessment for a hypothetical hydrogen filling station. The prototype focuses on dispersion, fire and explosion scenarios resulting from loss of containment of gaseous hydrogen. The approach adopted here combines consequence assessments obtained with the CFD tool FLACS-Hydrogen from Gexcon, and event frequencies estimated with the Hydrogen Risk Assessment Models (HyRAM) tool from Sandia, to generate 3D risk contours for explosion pressure and radiation loads. For a given population density and set of harm criteria, it is straightforward to extend the analysis to include personnel risk, as well as risk-based design such as detector optimization. The discussion outlines main challenges and inherent limitations of the 3DRM concept, as well as prospects for further development towards a fully integrated framework for risk management in organizations.     

Comparison between 1D and 2D numerical models of a multi-tubular packed-bed reactor for methanol steam reforming

The hydrogen-rich gas produced in-situ by methanol steam reforming (MSR) reactions significantly affects the performance and endurance of the high-temperature polymer electrolyte membrane (HT-PEM) fuel cell stack. A numerical study of MSR reactions over a commercial CuO/ZnO/Al₂O₃ catalyst coupling with the heat and mass transfer phenomena in a co-current packed-bed reactor is conducted. The simulation results of a 1D and a 2D pseudo-homogeneous reactor model are compared, which indicates the importance of radial gradients in the catalyst bed. The effects of geometry and operating parameters on the steady-state performance of the reactor are investigated. The simulation results show that the increases in the inlet temperature of burner gas and the tube diameter significantly increase the non-uniformity of radial temperature distributions in reformer tubes. Hot spots are formed near the tube wall in the entrance region. The hot-spot temperature in the catalyst bed rises with the increase in the inlet temperature of burner gas. Moreover, the difference in simulation results between the 1D and 2D models is shown to be primarily influenced by the tube diameter. With a methanol conversion approaching 100% or a relatively small tube diameter, the simplified 1D model can be used instead of the 2D model to estimate the reactor performance.     

Neutron radiography measurements of in-situ PEMFC liquid water saturation in 2D & 3D morphology gas diffusion layers

This work uses neutron radiography to examine the through-plane liquid water distribution of an operating polymer electrolyte membrane fuel cell (PEMFC) with a Sigracet SGL 25BC, a 235 μm thick, 2D straight fiber Gas Diffusion Layer (GDL). This work is performed for interdigitated flow fields at several cross flow rates, and a parallel flow field for comparison. The effect on pressure drop, effective permeability and liquid water saturation is determined. These results are compared to the previously studied Sigracet SGL 10BC, a 420 μm thick, 3D “spaghetti” fiber GDL, for comparable cross flow rates. The SGL 25BC has a higher permeability than the SGL 10BC. The 25BC has a relatively constant saturation within the GDL, from 8% to 10%, which is higher than the 10BC saturation level, between 4 and 8%. This may indicate that 2D GDLs may be better suited to low pumping power situations, while 3D GDLs may be better suited to low liquid water situations.     

Overview of Gas Research Institute R&D program

Gas Research Institute (GRI) plans, manages and develops financing for a cooperative research and development (R&D) program in supply, transport, storage and end-use of gaseous fuels for the mutual benefit of the gas industry and its present and future customers. Developing new and improved technologies which maximize the value of gas energy services while minimizing the cost of supplying and delivering gaseous fuels is the most effective way to serve the mutual interests of both the industry and its customers. These mutual benefits can only be realized if the results of R&D are used; consequently, GRI makes the prospects for application of developments arising from its R&D program a critical element in pursuing projects beyond proof-of-concept stage. GRI implements its mission through both planning and managing contractor-performed R&D and in-house analyses and communications activities. The R&D program is divided into Supply Options, End Use, Gas Operations and Crosscutting Research. The R&D budget increased from about $137.8 million in 1986 to $171.0 million in 1989. This paper summarizes the objectives and strategies for the GRI R&D program.