Efficient Conservative Numerical Schemes for 1D Nonlinear Spherical Diffusion Equations with Applications in Battery Modeling

Zeng, Yi; Albertus, Paul; Klein, Reinhardt; Chaturvedi, N.A.; Kojić, Aleksandar; Bazant, Martin Z.; Christensen, Jake

doi:10.1149/2.102309jes

Cited by 52 publications

(65 citation statements)

References 25 publications

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“…When the current is small,Ĩ 1, diffusion is fast, and the ions remain uniformly distributed inside the particle during intercalation dynamics, as shown in Figure 1. At high currents,Ĩ 1 (not considered here), diffusion becomes rate limiting, and concentration gradients form, as in prior models of spherical nonlinear diffusion [31,65,79]. Given the Butler-Volmer symmetry factor, α = 0.5, and assuming uniform composition, the total voltage drop between anode and particle surface is given by…”

Section: Repulsive Forcesmentioning

confidence: 95%

“…In order to avoid such extrapolation, we propose a numerical scheme that can immediately provide information on the particle surface and still keep the benefits of the finite volume method in conservation and shock toleration, which is inspired by our numerical method for solving the one-dimensional nonlinear spherical diffusion problem [79]. Similar to the finite volume method, our numerical scheme indeed handles the integral form of the original PDE system.…”

Section: Numerical Schemementioning

confidence: 99%

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Phase Separation Dynamics in Isotropic Ion-Intercalation Particles

Zeng¹,

Bazant²

2014

SIAM J. Appl. Math.

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Lithium-ion batteries exhibit complex nonlinear dynamics, resulting from diffusion and phase transformations coupled to ion-intercalation reactions. Using the recently developed Cahn-Hilliard reaction (CHR) theory, we investigate a simple mathematical model of ion intercalation in a spherical solid nanoparticle, which predicts transitions from solid-solution radial diffusion to two-phase shrinking-core dynamics. This general approach extends previous lithium-ion battery models, which either neglect phase separation or postulate a spherical shrinking-core phase boundary, by predicting phase separation only under appropriate circumstances. The effect of the applied current is captured by generalized Butler-Volmer kinetics, formulated in terms of diffusional chemical potentials, and the model consistently links the evolving concentration profile to the battery voltage. We examine sources of charge/discharge asymmetry, such as asymmetric charge transfer and surface "wetting" by ions within the solid, which can lead to three distinct phase regions. In order to solve the fourth-order nonlinear CHR initial-boundary-value problem, a control-volume discretization is developed in spherical coordinates. The basic physics are illustrated by simulating many representative cases, including a simple model of the popular cathode material, lithium iron phosphate (neglecting crystal anisotropy and coherency strain). Analytical approximations are also derived for the voltage plateau as a function of the applied current.

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Section: Repulsive Forcesmentioning

confidence: 95%

Section: Numerical Schemementioning

confidence: 99%

Phase Separation Dynamics in Isotropic Ion-Intercalation Particles

Zeng¹,

Bazant²

2014

SIAM J. Appl. Math.

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“…Efforts in numerical methods have been summarized by Ramadesigan et al [53] and Zeng et al [54]. Although we know that D s varies with concentration and temperature by experiments, an effective mathematical method is still needed to treat variable D s approximately and obtain simulation results in acceptable accuracy.…”

Section: Superposition Integral and Variable D Smentioning

confidence: 99%

Simulation of temperature rise in Li-ion cells at very high currents

Mao

Tiedemann²,

Newman

2014

Journal of Power Sources

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h i g h l i g h t sA radial mass-transport coefficient is used to modify the thermal-electrochemical Dualfoil model. Simulation of current and temperature under very-high-current discharge is achieved. Mass-transport limitation decreased by high cell temperature causes a rapid temperature rise. Effective heat transfer outside the cell center is critical. a b s t r a c tThe Dualfoil model is used to simulate the electrochemical behavior and temperature rise for MCMB/ LiCoO 2 Li-ion cells under a small constant-resistance load, approaching a short-circuit condition. Radial mass transport of lithium from the center of the pore to the pore wall has been added to the model to describe better current limitations at very high discharge currents. Electrolyte and solid-surfaceconcentration profiles of lithium ions across the cell at various times are developed and analyzed to explain the lithium-ion transport limitations. Sensitivity tests are conducted by changing solution and solid-state diffusion coefficients, and the heat-transfer coefficient. Because diffusion coefficients increase at high temperature, calculated discharge curves can show currents dropping initially but then rising to a second peak, with most of the available capacity being consumed in the second peak. Conditions which lead to such a second peak are explored.Published by Elsevier B.V.

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“…Several researchers have used different discretization schemes to eliminate the radial dependence and reduce the dimensionality by one. 3,39,[43][44][45][46] Attempts to simplify the primary dimension have also been done to reduce the computational cost. For example, proper orthogonal decomposition (POD) can reduce the total number of states simulated, but the system must be recreated if parameters or operating conditions are changed.…”

Section: Governing Equationsmentioning

confidence: 99%

Efficient Simulation and Model Reformulation of Two-Dimensional Electrochemical Thermal Behavior of Lithium-Ion Batteries

Northrop

Pathak

Rife

et al. 2015

J. Electrochem. Soc.

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Lithium-ion batteries are an important technology to facilitate efficient energy storage and enable a shift from petroleum based energy to more environmentally benign sources. Such systems can be utilized most efficiently if good understanding of performance can be achieved for a range of operating conditions. Mathematical models can be useful to predict battery behavior to allow for optimization of design and control. An analytical solution is ideally preferred to solve the equations of a mathematical model, as it eliminates the error that arises when using numerical techniques and is usually computationally cheap. An analytical solution provides insight into the behavior of the system and also explicitly shows the effects of different parameters on the behavior. However, most engineering models, including the majority of battery models, cannot be solved analytically due to non-linearities in the equations and state dependent transport and kinetic parameters. The numerical method used to solve the system of equations describing a battery operation can have a significant impact on the computational cost of the simulation. In this paper, a model reformulation of the porous electrode pseudo three dimensional (P3D) which significantly reduces the computational cost of lithium ion battery simulation, while maintaining high accuracy, is discussed. This reformulation enables the use of the P3D model into applications that would otherwise be too computationally expensive to justify its use, such as online control, optimization, and parameter estimation. Furthermore, the P3D model has proven to be robust enough to allow for the inclusion of additional physical phenomena as understanding improves. In this paper, the reformulated model is used to allow for more complicated physical phenomena to be considered for study, including thermal effects. There is an increasing societal pressure to utilize alternative energy sources to supplant the high use of fossil fuels. As energy and power demand is continually increasing, both in terms of grid usage and for transportation, there has been more interest in developing renewable energy sources. One problem with renewable energy sources is the intermittent nature and short-term unpredictability of supply of sources such as wind and solar. Thus, in order to match supply and demand, some form of energy storage is required, and lithium-ion battery technologies are one possible solution. Furthermore, electric vehicles are increasing in popularity as the price of liquid fuels generally increase. Lithium-ion batteries are a popular choice for electric vehicles because of their high energy and power density compared to other battery chemistries.The performance of lithium-ion batteries is highly dependent on the conditions at which they are exposed as well as the state of the internal variables. This has led to the development of several mathematical models to simulate battery behavior, ranging from simple empirical-based models or circuit based models 1,2 to computationally expensive mole...

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Efficient Conservative Numerical Schemes for 1D Nonlinear Spherical Diffusion Equations with Applications in Battery Modeling

Cited by 52 publications

References 25 publications

Phase Separation Dynamics in Isotropic Ion-Intercalation Particles

Phase Separation Dynamics in Isotropic Ion-Intercalation Particles

Simulation of temperature rise in Li-ion cells at very high currents

Efficient Simulation and Model Reformulation of Two-Dimensional Electrochemical Thermal Behavior of Lithium-Ion Batteries

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