Multiphysics Modelling of Lithium-Ion Batteries

Abstract

Batteries, made up of repeating units of anode-electrolyte-cathode sandwiches, are complex structures involving a large number of coupled physical processes at a wide range of length scales. Atomic- and continuum-scale computational models have contributed to our understanding of the underlying physics as well as to the design and development of batteries. However, current continuum laboratory-scale models have limitations which arise from the assumptions and simplifications made when the governing system of equations were originally derived. In this thesis a physically-founded continuum-scale mathematical model for batteries has been derived using multi-component transport theory to ensure that the resulting model is thermodynamically consistent. The generic transport theory equations are applied to a lithium-ion battery, for which an equation of state and a number of transport laws is required. This allows the system of equations to be closed and physical variables such as temperature and pressure to be determined. This derivation is founded on the principle of introducing assumptions individually and only where they can be justified on physical or computational grounds. To this end, a scaling analysis was performed in order to critically examine the sizes of terms coupling different thermodynamic variables. This model can be shown to reduce to existing models, which are extensively reviewed in this thesis, if their additional assumptions are applied. The differences in approach and assumptions are discussed and justified. This mathematical model has been used to create a computational finite volume model of a battery at the electrode scale using the open-source framework AMReX. Computational methods currently used in the simulation of electrolytes were implemented in AMReX and shown to be capable of replicating and improving on existing simulations of electrolytes, in particular for the electrolysis of copper. These methods were then extended, using embedded boundary and ghost fluid methods, to the simulation of a battery. Once fully validated, the computational model was used to compare three different mathematical models of a battery, including the most widely used existing model from the literature. To do this a set of representative geometries and simulation parameters were designed in order to provide a consistent framework for comparison of the mathematical models under a range of operating conditions in 1D and 2D. From these models the effect of operating conditions on internal properties and variables, as well as the terminal voltage, can be assessed. Through the comparison of the results of the simulations using both the newly derived model and existing models, this thesis demonstrates the significant effect which the equation of state has on the internal properties even when the predicted terminal voltage and average temperature are similar. Furthermore, simulation results show that three different models, including the new multi-component transport theory model of this thesis, make significantly different predictions of internal and external properties of a battery at both high charge rates and low temperatures. These simulations also justify the use in the literature of an averaged thermal model and the neglecting of the Dufour effect.