Review of parameterisation and a novel database (LiionDB) for continuum Li-ion battery models

The Doyle–Fuller–Newman (DFN) framework is the most popular physics-based continuum-level description of the chemical and dynamical internal processes within operating lithium-ion-battery cells. With sufficient flexibility to model a wide range of battery designs and chemistries, the framework provides an effective balance between detail, needed to capture key microscopic mechanisms, and simplicity, needed to solve the governing equations at a relatively modest computational expense. Nevertheless, implementation requires values of numerous model parameters, whose ranges of applicability, estimation, and validation pose challenges. This article provides a critical review of the methods to measure or infer parameters for use within the isothermal DFN framework, discusses their advantages or disadvantages, and clarifies limitations attached to their practical application. Accompanying this discussion we provide a searchable database, available at www.liiondb.com, which aggregates many parameters and state functions for the standard DFN model that have been reported in the literature

Extended Stefan problem for solidification of binary alloys in a finite planar domain

We consider the extended Stefan problem for the solidification of a binary alloy in a finite one-dimensional domain accounting for constitutional supercooling. In this problem, solidification fronts start from each boundary and move inward toward one another. We perform an asymptotic analysis of the problem in the limit of large Lewis number, which allows us to identify four important temporal regimes corresponding to distinct behaviors in the solidification process. We find that, for small time, the two solidification fronts are initially far from one another, and move in a self-similar manner toward the interior of the domain. However, when the fronts are sufficiently close, expelled impurities (which diffuse into, and build up within, the liquid phase between the two fronts) increase in concentration, inducing supercooling and thereby slowing the motion of the fronts. For large time, the system tends to its minimum temperature (corresponding to the boundary of the finite domain), with the concentration of impurities following in thermodynamic equilibrium. Asymptotic solutions in each spatiotemporal region are obtained and then matched to neighboring temporal regimes and spatial layers, and by matching we obtain global asymptotic solutions to the extended Stefan problem. We compare our asymptotic solutions to numerical simulations of the full problem obtained by a finite volume method, and the respective solutions show excellent agreement. We also compare our asymptotic solutions to real experimental data arising from the casting process for molten metallurgical grade silicon, with our analysis highlighting the role of supercooling in the solidification of binary alloys appearing in such applications. Read More: https://epubs.siam.org/doi/10.1137/18M118699

Instability in the self-similar motion of a planar solidification front

Understanding the solidification process of a binary alloy is important if one is to control the microstructure obtained during the casting of metals. While much work has been done on the steady state solidification problem, despite their relevance to metallurgical applications, there is less known about non-steady solidification problems and their stability. In the paper we shall consider the non-steady solidification problem in which the planar solidification front moves in a self-similar manner, in both infinite and semi-infinite planar one-dimensional geometries. For each geometry exact solutions are known for the resulting Stefan problem. We direct our attention to the stability of each solution, demonstrating that while the concentration and thermal solutions remain stable, the interface corresponding to the solidification front can develop instabilities. For each geometry, we find that there are always unstable perturbations, although we observe qualitative differences in the form of the unstable perturbations for each case. These results generalize and extend several existing studies in the literature, and throw light on the instability inherent in the non-steady solidification process

Instability in the self-similar motion of a planar solidification front

Understanding the solidification process of a binary alloy is important if one is to control the microstructure obtained during the casting of metals. While much work has been done on the steady state solidification problem, despite their relevance to metallurgical applications, there is less known about non-steady solidification problems and their stability. In the paper we shall consider the non-steady solidification problem in which the planar solidification front moves in a self-similar manner, in both infinite and semi-infinite planar one-dimensional geometries. For each geometry exact solutions are known for the resulting Stefan problem. We direct our attention to the stability of each solution, demonstrating that while the concentration and thermal solutions remain stable, the interface corresponding to the solidification front can develop instabilities. For each geometry, we find that there are always unstable perturbations, although we observe qualitative differences in the form of the unstable perturbations for each case. These results generalize and extend several existing studies in the literature, and throw light on the instability inherent in the non-steady solidification process

Review of parameterisation and a novel database (LiionDB) for continuum Li-ion battery models

The Doyle–Fuller–Newman (DFN) framework is the most popular physics-based continuum-level description of the chemical and dynamical internal processes within operating lithium-ion-battery cells. With sufficient flexibility to model a wide range of battery designs and chemistries, the framework provides an effective balance between detail, needed to capture key microscopic mechanisms, and simplicity, needed to solve the governing equations at a relatively modest computational expense. Nevertheless, implementation requires values of numerous model parameters, whose ranges of applicability, estimation, and validation pose challenges. This article provides a critical review of the methods to measure or infer parameters for use within the isothermal DFN framework, discusses their advantages or disadvantages, and clarifies limitations attached to their practical application. Accompanying this discussion we provide a searchable database, available at www.liiondb.com, which aggregates many parameters and state functions for the standard DFN model that have been reported in the literature

A continuum of physics-based lithium-ion battery models reviewed

Physics-based electrochemical battery models derived from porous electrode theory are a very powerful tool for understanding lithium-ion batteries, as well as for improving their design and management. Different model fidelity, and thus model complexity, is needed for different applications. For example, in battery design we can afford longer computational times and the use of powerful computers, while for real-time battery control (e.g. in electric vehicles) we need to perform very fast calculations using simple devices. For this reason, simplified models that retain most of the features at a lower computational cost are widely used. Even though in the literature we often find these simplified models posed independently, leading to inconsistencies between models, they can actually be derived from more complicated models using a unified and systematic framework. In this review, we showcase this reductive framework, starting from a high-fidelity microscale model and reducing it all the way down to the single particle model, deriving in the process other common models, such as the Doyle–Fuller–Newman model. We also provide a critical discussion on the advantages and shortcomings of each of the models, which can aid model selection for a particular application. Finally, we provide an overview of possible extensions to the models, with a special focus on thermal models. Any of these extensions could be incorporated into the microscale model and the reductive framework re-applied to lead to a new generation of simplified, multi-physics models

Review—"Knees" in lithium-ion battery aging trajectories

Lithium-ion batteries can last many years but sometimes exhibit rapid, nonlinear degradation that severely limits battery lifetime. In this work, we review prior work on "knees" in lithium-ion battery aging trajectories. We first review definitions for knees and three classes of "internal state trajectories" (termed snowball, hidden, and threshold trajectories) that can cause a knee. We then discuss six knee "pathways", including lithium plating, electrode saturation, resistance growth, electrolyte and additive depletion, percolation-limited connectivity, and mechanical deformation—some of which have internal state trajectories with signals that are electrochemically undetectable. We also identify key design and usage sensitivities for knees. Finally, we discuss challenges and opportunities for knee modeling and prediction. Our findings illustrate the complexity and subtlety of lithium-ion battery degradation and can aid both academic and industrial efforts to improve battery lifetime