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Author: Landstorfer, Manuel × Subject: non-equilibrium thermodynamics ×

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Now showing 1 - 3 of 3
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    A discussion of the reaction rate and the cell voltage of an intercalation electrode during discharge
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Landstorfer, Manuel
    In this work we discuss the modeling procedure and validation of a non-porous intercalation half-cell during galvanostatic discharge. The modeling is based on continuum thermodynamics with non-equilibrium processes in the active intercalation particle, the electrolyte, and the common interface where the intercalation reaction occurs. This yields balance equations for the transport of charge and intercalated lithium in the intercalation compound, a surface reaction rate at the interface, and transport equations in the electrolyte for the concentration of lithium ions and the electrostatic potential. An expression for the measured cell voltage is then rigorously derived for a half cell with metallic lithium as counter electrode. The model is then in detail investigated and discussed in terms of scalings of the non-equilibrium parameters, i.e. the diffusion coefficients of the active phase and the electrolyte, conductivity of both phases, and the exchange current density, with numerical solutions of the underlying PDE system. The current density as well as all non-equilibrium parameters are scaled with respect to the 1-C current density of the intercalation electrode and the C-rate of discharge. Further we derive an expression for the capacity of the intercalation cell, which allows us to compute numerically the cell voltage as function of the capacity and the C-rate. Within a hierarchy of approximations of the non-equilibrium processes we provide computations of the cell voltage for various values of the diffusion coefficients, the conductivities and the exchange current density. For the later we provide finally a discussion for possible concentration dependencies and (surface) thermodynamic consistency.
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    Homogenization of a porous intercalation electrode with phase separation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Heida, Martin; Landstorfer, Manuel; Liero, Matthias
    In this work, we derive a new model framework for a porous intercalation electrode with a phase separating active material upon lithium intercalation. We start from a microscopic model consisting of transport equations for lithium ions in an electrolyte phase and intercalated lithium in a solid active phase. Both are coupled through a Neumann--boundary condition modeling the lithium intercalation reaction. The active material phase is considered to be phase separating upon lithium intercalation. We assume that the porous material is a given periodic microstructure and perform analytical homogenization. Effectively, the microscopic model consists of a diffusion and a Cahn--Hilliard equation, whereas the limit model consists of a diffusion and an Allen--Cahn equation. Thus we observe a Cahn--Hilliard to Allen--Cahn transition during the upscaling process. In the sense of gradient flows, the transition goes in hand with a change in the underlying metric structure of the PDE system.
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    A modeling framework for efficient reduced order simulations of parametrized lithium-ion battery cells
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Landstorfer, Manuel; Ohlberger, Mario; Rave, Stephan; Tacke, Marie
    In this contribution we present a new modeling and simulation framework for parametrized Lithium-ion battery cells. We first derive a new continuum model for a rather general intercalation battery cell on the basis of non-equilibrium thermodynamics. In order to efficiently evaluate the resulting parameterized non-linear system of partial differential equations the reduced basis method is employed. The reduced basis method is a model order reduction technique on the basis of an incremental hierarchical approximate proper orthogonal decomposition approach and empirical operator interpolation. The modeling framework is particularly well suited to investigate and quantify degradation effects of battery cells. Several numerical experiments are given to demonstrate the scope and efficiency of the modeling framework.