Mathematical modeling of transport phenomena in lithium ion batteries

MATHEMATICAL MODELING OF TRANSPORT PHENOMENA IN LITHIUM-ION BATTERIES TONG WEI A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2014 Acknowledgements This work would not have been possible to be achieved without the help of many people I would like to express my deepest gratitude to my supervisors, Professor Arun S Mujumdar, Assistant Professor Erik Birgersson and Associate Professor Christopher Yap for their excellent and tireless guidance for the work done in this thesis It has been a great honor and pleasure to work with them during the past four years Prof Mujumdar paved the way for me as a PhD student to pursue my research in National University of Singapore (NUS) He is a nice and thoughtful mentor and always provides rich knowledge and experience Prof Erik Birgersson opened the door for me to the world of an exciting research area - mathematical modeling of electrochemical energy storage system Prof Erik Birgersson always helped me to build my con…dence His dedication and enthusiasm for research and work impress me very much and set a positive example for me during my four-year study Prof Yap, although only having a short time working with him, helped me a lot The discussion with him, especially in how to strategically organize research papers and the thesis, has been crucial to the completion of my research work In addition, I would like to thank all my colleagues and friends for their assistance which has facilitated the completion of this work I would thank our group members: Dr Agus Pulung Sasmito, Dr Jundika Candra Kurnia for the discussion with them Specially, I would like to thank Dr Karthik Somasundaram for his kind help in developing the mathematical modeling Furthermore, I extend my gratitude to the China Scholarship Council and National University of Singapore for their …nancial support Last but not least, I dedicate this thesis to my parents for their endless love, support and i encouragement during the past 29 years of my life Without them, I de…nitely could not have reached where I am today ii Contents Acknowledgements i Summary ix Preface xii List of Tables xiv List of Figures xv List of Symbols xx Introduction 1.1 Overview of lithium-ion batteries 1.1.1 Structure and operation principles of a lithium-ion battery cell 1.1.2 Types and applications 1.1.3 Heat generation 1.1.4 Capacity fade 1.2 Mathematical modeling of lithium-ion batteries 10 v 1.3 Objectives 10 1.4 Challenges 12 1.5 Outline of the thesis 12 Literature review 15 2.1 Theories of mathematical modeling 15 2.1.1 Porous electrode theory 16 2.1.2 Concentrated solution theory 17 2.1.3 Electrode kinetics 17 2.1.4 Solid phase diÔusion 18 2.2 Review of mathematical models 19 2.2.1 Coupled electrochemical-thermal models 19 2.2.2 Capacity fade models 21 2.2.3 Models for thermal management systems 24 Mathematical formulation 27 3.1 Governing equations 29 3.2 Constitutive relations 33 3.3 Boundary and initial conditions 38 Numerical methodology 41 4.1 COMSOL Multiphysics 42 4.2 Finite element method 43 A Monte Carlo simulation of a lithium-ion battery model - Correlating the uncertainties of system parameters with safety issues vi 46 5.1 Introduction 46 5.2 Mathematical formulation of lithium-ion battery model 49 5.3 Monte Carlo simulation 51 5.4 Numerics 57 5.5 Results and discussion 58 5.5.1 Sample selection 58 5.5.2 Sensitivity analysis 58 5.5.3 Final cell temperature distribution 65 Analysis of capacity fade distribution of a cylindrical lithium-ion battery 69 6.1 Introduction 69 6.2 Mathematical formulation 71 6.3 Numerics 77 6.4 Results and discussion 79 6.4.1 Validation 79 6.4.2 Global behavior 80 6.4.3 Distribution of capacity fade 81 Numerical investigation of air cooling for a lithium-ion battery module 89 7.1 Introduction 89 7.2 Mathematical formulation 90 7.2.1 Governing equations 91 7.2.2 Boundary and initial conditions 95 7.3 Numerics 97 7.4 Results and discussion 98 vii 7.4.1 Discharge curves and current density 99 7.4.2 EÔect of air inlet velocity 101 7.4.3 EÔect of cell arrangement 104 7.4.4 EÔect of cell distance 105 7.4.5 Reversal ‡ ow 106 Numerical investigation of water cooling for a lithium-ion bipolar battery pack 111 8.1 Introduction 111 8.2 Mathematical formulation 113 8.3 Numerics 119 8.4 Results and discussion 119 8.4.1 Limiting cases 120 8.4.2 Thermal management with water cooling 126 Concluding remarks 136 9.1 Summary and conclusions 136 9.2 Contributions of this study 139 9.3 Recommendations for future work 141 viii Summary Worldwide energy shortage and environment problems have necessitated more e¢ cient, reliable and sustainable techniques for energy transfer and storage Electricity, which could produce electrical energy, must be reliably and continuously available for many applications Therefore, electricity storage devices are critical for the eÔective utilization of these energy sources The lithium-ion battery is an electrochemical energy storage system that has attracted increasing attention in recent years because of many advantages over competing technologies These include high operating voltage, high energy density, no memory eÔect and low self-discharge rate However, the performance of lithium-ion batteries is closely associated with thermal and degradation eÔects The identication and quantication of the relationship of battery system properties and operation conditions with the thermal issues as well as how does the degradation develop inside the battery cell are therefore critical for the eÔective and safe utilization of lithium-ion batteries Furthermore, better understanding of the parameters and mechanisms involved will enable the improvement in design of battery thermal management systems In tandem with experimental investigations of lithium-ion battery systems, computational study has become an eÔective tool for identifying the salient features that can be found in lithium-ion battery systems Mathematical modelling not only captures the transport phenomena occurring inside the battery cells which are generally di¢ cult to quantify experimentally, but also saves time and cost in experimental setup Generally, the transport phenomena occurring inside lithium-ion batteries are modelled Transient conservation of species, charge and energy in both solid and liquid phases is based on the porous electrode theory In this thesis, the following work has been undertaken using the lithium-ion battery model Firstly, safety issues arising from a lithium-ion battery during operation can be attributed to the variation of its temperature which is, in turn, associated with the uncertainties in the parameters such as system properties and operating conditions Hence, a Monte Carlo simulation (MCS) of a lithium-ion battery model is conducted to capture the probabilistic nature of uncertainties in the parameters and their relative importance to the temperature of a lithium-ion battery cell Sensitivity analysis is statistically performed and the varied parameters are ranked according to their contributions to the variation of the battery temperature Besides studying thermal eÔects, a simulation is conducted that aims to determine if non-uniform distributions of capacity fade will develop during the cycling of a cylindrical lithium-ion battery It is observed that locally non-uniform distributions of capacity fade will develop across the surface of a single electrode during cycling while the average capacity fade among electrodes of diÔerent wounds is uniform As part of the applied research, the lithium-ion battery model is used to evaluate thermal management systems for lithium-ion batteries at a module or pack level DiÔerent active thermal management systems-forced air or liquid cooling are evaluated for two designs (cylindrical batteries and cells with bipolar con…gurations) of lithium-ion batterx BIBLIOGRAPHY [8] W Wu, X Xiao, and X Huang Modeling heat 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MODELING OF LITHIUM- ION BATTERIES 1.2 Mathematical modeling of lithium- ion batteries Mathematical modeling and computational analysis are extensively employed in. .. transition metal employed for the positive electrode (1.3) 1.1 OVERVIEW OF LITHIUM- ION BATTERIES Figure 1.2: Schematic of a lithium- ion battery operation principle 1.1 OVERVIEW OF LITHIUM- ION BATTERIES. .. OVERVIEW OF LITHIUM- ION BATTERIES 1.1.1 Structure and operation principles of a lithium- ion battery cell A basic lithium- ion battery cell consists of several functional layers: a current collector of