Steven Beale

Computer methods for performance prediction in fuel cells

Several transport models for fuel cells have been developed. The models are compared and tested for single fuel cells and multi-cell stacks of planar solid-oxide fuel cells, the three main approaches considered are (a) a detailed numerical model (DNM) of flow, heat and mass transfer and electrochemistry, (b) a flow-based methodology based on a distributed resistance analogy (DRA), and (c) a presumed-flow methodology (PFM). The results from each of the above approaches are compared in detail, and merits and drawbacks discussed. It is shown that, under certain circumstances, the simpler approaches have the potential to supplant or complement the direct numerical method in the analysis of fuel cells.

Effective transport properties of the porous electrodes in solid oxide fuel cells

This article presents a numerical framework for the computation of the effective transport properties of solid oxide fuel cells (SOFCs) porous electrodes from three-dimensional (3D) constructions of the microstructure. Realistic models of the 3D microstructure of porous electrodes are first constructed from measured parameters such as porosity and particle size distribution. Then each phase in the model geometries is tessellated with a computational grid. Three different types of grids are considered: Cartesian, octree, and body-fitted/cut-cell with successive levels of surface refinement. Finally, a finite volume method is used to compute the effective transport properties in the three phases (pore, electron, and ion) of the electrode. To validate the numerical approach, results obtained with the finite volume method are compared to those calculated with a random walk simulation for the case of a body-centred cubic lattice of spheres. Then, the influence of the sample size is investigated for random geometries with monosized particle distributions. Finally, effective transport properties are calculated for model geometries with polydisperse particle size distributions similar to those observed in actual SOFC electrodes.

Use of streamwise periodic boundary conditions for problems in heat and mass transfer

Fully developed periodic boundary conditions have frequently been employed to effect performance calculations for heat and mass exchange devices. In this paper a method is proposed, which is based on the use of primitive variables combined with the prescription of slip values. Either pressure difference or mass flow rate may be equivalently prescribed. Both constant wall temperature (Dirichlet) and constant heat flux (Neumann) conditions may be considered, as well as the intermediate linear (Robin) boundary condition. The example of an offset-fin plate-fin heat exchanger is used to illustrate the application of the procedure. The mathematical basis by which the method may be extended to the consideration of mass transfer problems with arbitrary boundary conditions, and associated continuity, momentum, and species sources and sinks is discussed.

Open-source computational model of a solid oxide fuel cell

The solid oxide fuel cell is an electro-chemical device which converts chemical energy into electricity and heat. To compete in todays market, design improvements, in terms of performance and life cycle, are required. Numerical prototypes can accelerate design and development progress. In this programme of research, a three- dimensional solid oxide fuel cell prototype, openFuelCell, based on open-source computational fluid dynamics software was developed and applied to a single cell. Transport phenomena, combined with the solution to the local Nernst equation for the open-circuit potential, as well as the Kirchhoff-Ohm relationship for the local current density, allow local electro-chemistry, fluid flow, multi-component species transport, and multi-region thermal analysis to be considered. The underlying physicochemical hydrodynamics, including porous- electrode and electro-chemical effects are described in detail. The openFuelCell program is developed in an object-oriented open- source C++ library. The code is available at http://openfuelcell.sourceforge.net/. The paper also describes domain decomposition techniques considered in the context of highly efficient parallel programming

Benchmark Studies for the Generalized Streamwise Periodic Heat Transfer Problem

This is a comparison of calculations performed with a scheme for handling streamwise-periodic boundary conditions with known solutions to the common problem of fully developed heat transfer in a plane duct. Constant value, constant flux, mixed boundary conditions, and linear wall flux (conjugate heat transfer) are all considered. Agreement is, in every case, near exact showing that the methodology may be applied with confidence to complex engineering problems with a variety of thermal wall boundary conditions.

A Simple, Effective Viscosity Formulation for Turbulent Flow and Heat Transfer in Compact Heat Exchangers

A simple algebraic methodology for computing turbulent stresses and fluxes in arrays of heat exchanger elements is proposed. An effective Reynolds number is computed from the back-projection of the friction or heat transfer factor onto the low-Reynolds-number profile. This is then used to obtain the turbulent viscosity for fluid friction, or turbulent Prandtl number, for heat transfer. It is shown that under certain circumstances, the resulting mathematical expression is consistent with the Brinkman–Forchheimer modified form of Darcys law and also with the Reynolds quadratic form for frictional/heat transfer resistance. The model is critically appraised in comparison to empirical data for compact and tube bank heat exchangers. The circumstances where it renders a good predictive measure are highlighted and discussed critically.

Numerical and Experimental Analysis of a Solid Oxide Fuel Cell Stack

A numerical simulation of the Julich F-design solid oxide fuel cell stack is conducted by means of an original mathematical model. The model is implemented in the open source toolbox, OpenFOAM. This cell/stack level model is a key component of a programme to develop a fully integrated multi-scale fuel cell modelling capability, from nano-scale through to system level. It is intended to share the resulting software with other parties openly. Substantial experimental data is available for the Julich F-design; Stack configuration, flow conditions, interconnector geometries and porous electrode properties prescribed in the numerical model are based on field experiments. The numerical model generates distributions of fluid flow, species concentrations, current density and temperature. The results of the simulations are compared against experimental data obtained from short stacks.

Stability Issues for Fuel Cell Models in the Activation and Concentration Regimes

Code stability is a matter of concern for three-dimensional (3D) fuel cell models operating both at high current density and at high cell voltage. An idealized mathematical model of a fuel cell should converge for all potentiostatic or galvanostatic boundary conditions ranging from open circuit to closed circuit. Many fail to do so, due to (i) fuel or oxygen starvation causing divergence as local partial pressures and mass fractions of fuel or oxidant fall to near zero and (ii) nonlinearities in the Nernst and Butler-Volmer equations near open-circuit conditions. This paper describes in detail, specific numerical methods used to improve the stability of a previously existing fuel cell performance calculation procedure, at both low and high current densities. Four specific techniques are identified. A straight channel operating as a (i) solid oxide and (ii) polymer electrolyte membrane fuel cell is used to illustrate the efficacy of the modifications. (Less)

On the Implementation of Stream-Wise Periodic Boundary Conditions

Fully-developed periodic boundary conditions have frequently been employed to perform calculations on the performance of typical elements of heat exchangers. Many such calculations have been achieved by transforming the equations of motion to obtain a new set of state variables which are cyclic in the stream-wise direction. In others, primitive variables, based on substitution schemes are employed. In this paper; a review of existing procedures is provided, and a new method is proposed. The method is based on the use of primitive variables with periodic boundary conditions combined with the use of slip values. Either pressure difference or mass flow rate may be prescribed, and both constant wall temperature and constant heat flux wall conditions may be considered. The example of an offset-fin plate-fin heat exchanger is used to illustrate the application of the procedure. The scope and limitations of the method are discussed in detail, and the mathematical basis by which the method may be extended to the consideration of problems involving mass transfer, with associated continuity, momentum, and species source/sinks is proposed.Copyright

Inlet and Wall Effects on Fluid Flow in Doubly-Periodic Arrays of Spacer-Filled Passages

A numerical investigation has been carried out to study the effect of the sidewalls and the number of cells in arrays of spacer-filled channels on the local flow distribution, for Reynolds number, Re = 100, for a spacer-configuration typically employed in process industries. It was found that the channel sidewalls have a significant effect on the velocity profile near the walls. Numerically calculated values of velocity are compared with those measured experimentally, with good agreement being obtained; a maximum deviation of 4.5% was observed. Particle traces emitted from a cell at the channel entrance revealed that, unexpectedly, the flow moves parallel to the spacer filaments within each channel layer and changes 90° direction mostly at the cell adjacent to the channel side walls. The effects of the number of cells and the type of boundary condition imposed on the channel transverse sidewalls on the pressure drop and friction factor are considered.Copyright