Electrochemical Cell Calculations with OpenFOAM

The transition from fossil to regenerative energy sources is bringing about technological innovations, as well as societal changes. This leads us from a technological paradigm based on crude oil, natural gas, coal, and nuclear energy to one based on renewable energy generation as provided by wind turbines, solar cells, and hydroelectric power plants, with hydrogen playing a dominant role as an energy carrier in the future. In this context, fuel cells and electrolysers will become increasingly important. Even if they appear simple at first glance, fuel cells and electrolysers pose highly complex scientific and technical challenges. This applies not least to the area of modelling and simulation. In addition to a general introduction, the role of the necessary parameters in the simulation of fuel cells at cell and stack level is dealt with using the example of electrochemistry and media transport in porous media.

A case corresponding to the simplest possible electrochemical cell, namely a single oxygen electrode for a polymer electrolyte electrochemical cell, with constant properties, is presented herein. The target audience is one that is familiar with the computer code Open Source Field Operation and Manipulation (OpenFOAM), with little or no knowledge of electrochemistry, who wish to enter the field, as well as those with some knowledge of electrochemistry who wish to build their first mathematical model using OpenFOAM. The simpleFuelCell model has been deliberately kept basic in order to introduce simple electrochemical concepts, such as the stoichiometric ratio and reaction order, in comparison to subsequent chapters of this book, where much more complex algorithms are developed. The simpleFuelCell case is readily built-up from the base case for incompressible laminar flow of Newtonian fluids (icoFoam), by adding terms for the electrochemical reaction and species continuity (mass transfer). Full details are provided. The model may also be run bypassing the solution for the continuity and pressure-corrected momentum equations by fixing the stream-wise velocity to a constant value. The results are compared to an exact analytical solution and show near perfect agreement. The case can be used in-class, for university teaching purposes, e.g., in a first course on electrochemical modelling. If desired, the user may subsequently relax the model assumptions to investigate the impact on model accuracy or computational performance.

As a clean and quiet device, polymer-electrolyte fuel cells (PEFCs), also known as proton exchange membrane fuel cells (PEMFCs), have attracted increasing attention over the past decade.

Many categories of fuel cells (FCs) were developed over the past decade, based on different electrolytes and operating temperature. One promising type of FC is high-temperature polymer.

Solid oxide fuel cells (SOFCs) are an electrochemical device that converts the chemical energy stored in a variety of fuels directly into electricity and produces heat as its by-product. SOFCs typically operate in high temperature range (600–1000 °C) to achieve a good ionic conductivity of solid electrolyte.

Multiple electrochemical cells are arranged into stacks to increase power density. Electrochemical performance of stacks is significantly affected by the design of manifolds that carry reactants to, and reaction products from, each cell in the stack. Flow, pressure, and heat mal-distributions may occur, which leads to variations in the local current density, overall reductions in stack power output and, in some cases, localized damage or degradation effects which are not captured by single cell or purely hydrodynamic models. The modeling of large-scale stacks, necessary for detailed analyses and design, requires the making of assumptions in transport equations in localized regions to resolve phenomena of flow, species and heat transport within reasonable computation times. In this chapter, a distributed resistance analogy (DRA) is described in which the transport equations are averaged by using a first-order rate term to replace the second-order diffusion term in the Navier–Stokes, heat transfer, and species transport equations, using a friction factor, Nusselt number heat transfer resistance, and Sherwood number species transport resistance, respectively. The technique reduces the computational mesh required and so also the required computation time by up to two orders of magnitude. The implementation of the DRA techniques in OpenFOAM are described in detail for modelling real solid oxide fuel cell stacks and high-temperature polymer electrolyte fuel cell stacks. Numerical verification and experimental validation are systematically conducted with good agreement, providing confidence in the accuracy of the model and its implementation in OpenFOAM.

Porous media are an integral part of electrochemical energy conversion and storage devices, including fuel cells, electrolyzers, redox flow batteries and lithium-ion batteries, among others. The calculation of effective transport properties is required for designing more efficient components and for closing the formulation of macroscopic continuum models at the cell/stack level. In this chapter, OpenFOAM is used to determine the effective transport properties of virtually-generated fibrous gas diffusion layers. The analysis focuses on effective properties that rely on the fluid phase, diffusivity and permeability, which are determined by solving Laplace and Navier-Stokes equations at the pore scale, respectively. The model implementation (geometry generation, meshing, solver settings and postprocessing) is described, accompanied by a discussion of the main results. The dependence of orthotropic effective transport properties on porosity is examined and compared with traditional correlations.

This chapter establishes that OpenFOAM is applicable for analyzing the electrolyte flow in a vanadium redox flow battery (VFB) and the transport phenomena in these systems. The local porosity was controlled by inserting an extra layer of electrode at the inlet and outlet. The variations in electrochemical characteristics and energy conversion efficiency with porosity were obtained through VFB single cell experiments. Numerical analysis of the electrolyte flow and pressure distribution provided a theoretical explanation for the physical phenomenon, which depending on the local porosities. When the current density was 50 mA/cm², the electrode with uniform porosity (UP) showed the best energy performance. However, at a high current density of 150 mA/cm², the partial porosity-lowered electrode at inlet (designated as LPI) showed better efficiency than the UP electrode since the rate of electrochemical reaction increases, and the mass transfer of the reactant is enhanced accordingly. OpenFOAM is expected to contribute significantly to the optimization of this flow battery system. In the near future, it will also aid in achieving carbon neutrality by the virtue of collective intelligence.

Liquid metal batteries (LMBs) are introduced as future candidates for grid scale electricity storage. Their completely liquid cell interior entails a prominent role of fluid mechanics to understand and model their behaviour. We describe the equations used to compute electrochemical reactions, heat and mass transfer, electromagnetic fields, and fluid flow and explain the simplifications that can be made in the case of LMBs. The implementation of solution algorithms in OpenFOAM pertaining to domain coupling, multiphase simulations, mesh mapping, and operator discretisation are discussed in detail and accompanied by example code.