Lattice Boltzmann simulation of ion and electron transport in lithium ion battery porous electrode during discharge process
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1 Available online at ScienceDirect Energy Procedia 88 (2016 ) CUE2015-Applied Energy Symposium and Summit 2015: Low carbon cities and urban energy systems Lattice Boltzmann simulation of ion and electron transport in lithium ion battery porous electrode during discharge process Zhiyuan Jiang a, Zhiguo Qu a, * a Key Laboratory of Thermo-Fluid Science and Engineering of Ministry of Education, School of Energy and Power Engineering, Xi an Jiaotong University, 28# XianNing Road, Xi an , China Abstract A two dimensional lattice Boltzmann simulation of ion and electron transport within lithium ion battery porous electrode was presented in this study. In the simulation, a LiyC6 LixMn2O4 rocking-chair rechargeable battery structure was employed and the electrode was composed of irregular particles. The effects of electrode microstructure on the local lithium concentration distribution, electric potential and macroscopic discharge performance were investigated. Results show that smaller particles were lithiated and delithiated at a higher rate during the discharge process. The lithium depletion in anode and the lithium accumulation in cathode were enhanced in the edges and corners for large irregular particles. The particles with lower lithium concentration produced higher local electric potential in the anode. For discharge performance, the porosity of the electrode had significant influence on the achievable capacity The The Authors. Authors. Published Published by Elsevier by Elsevier Ltd. This Ltd. is an open access article under the CC BY-NC-ND license ( Selection and/or peer-review under responsibility of CUE Peer-review under responsibility of the organizing committee of CUE 2015 Keywords: Lithium ion battery; Electrode micro-structure; Lattice Boltzmann method; Discharge process 1. Introduction In the last two decades, Lithium ion battery (LIB) has become one of the most important power sources for portable devices, electric vehicles and power grid. Due to the increasing demand for environmentally friendly and fuel economy vehicles, automotive companies are paying a lot of effort on electric vehicles and hybrid electric vehicles (HEVs). These vehicles would enable meeting the demands * Corresponding author. Tel.: ; fax: address: zgqu@mail.xjtu.edu.cn The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility of the organizing committee of CUE 2015 doi: /j.egypro
2 Zhiyuan Jiang and Zhiguo Qu / Energy Procedia 88 ( 2016 ) for electrical power due to the increasing use of the electronic features to improve vehicle performance, fuel economy, emissions, passenger comfort, and safety. As a result, it is important to have a firm understanding of working process and conductive mechanisms in LIB. Many experimental studies have reported linkages between morphology of constituent electrode and battery performance [1-3]. Investigations on the effect of electrode with 2D or 3D micro-structure were reported in literature [4-6]. LBM is a good approach to solve the diffusion-reaction problems within complex geometry [7, 8]. In this study, we develop a two dimensional framework for LBM simulation of ion and electron transport in the LIB porous electrode. A Li y C 6 Li x Mn 2 O 4 rocking-chair rechargeable battery structure is employed in our study. The battery electrode is comprised of active cathode and anode particles and electrode with different particle shape and porosity is considered. The effects of the electrode micro-structure on lithium concentration and electric potential distribution and the battery performance are investigated. 2. Theory and Modeling 2.1. Theoretical model In the electrolyte phase, the transport of lithium ion and electron are given by a set of partial difference uations which derive from a Nernst-Plank model. DLi zfcli CLi 0 (1) CLi DLi zfcli DLiCLi 0 t (2) where is the electric potential, κ is the electrical conductivity. C Li is the lithium ion concentration, D Li is the diffusivity of lithium ion. Within the electrode particles, Eq. (1) and Eq. (2) can be reduced to classic diffusion and charge continuity uation by setting z= Lattice Boltzmann method LBM is utilized to solve the governing uations of the transport of ion and electron. Within the electrolyte phase, the following evolution uations are used to describe the ion transport and the electron conduction [9]. 1 zf ci u gik, xcit, ttgik, x, t gik, x, tgik, x, t gik, x, t (3) Dk, 1 FzDCLi hixcit, tthix, t hix, thi x, ti (4) h where gik, and h i are the distribution functions of specie concentration and electric potential, g ik, and hi are the corresponding uilibrium functions, respectively. Within the electrode particles, Eq. (3) and Eq. (4) can be reduced to classic evolution uations by setting z=0. 3. Results and discussion From the LBM calculation, the microscopic distribution of lithium ion and electric potential in the electrode and the macroscopic cell voltage can be obtained. Simulation results of Fig.1 show the time evolutions of the lithium concentration in the battery electrode with irregular geometry. As depicted in
3 644 Zhiyuan Jiang and Zhiguo Qu / Energy Procedia 88 ( 2016 ) Fig. 1, the lithium concentration decreases in negative area and increases in positive area during the discharge process. In the negative electrode, the decrease of lithium concentration in smaller graphite particles is faster than that in large graphite particles. The concentration gradient is more obvious in large particles than that in small particles. Similar phenomena of lithium concentration distribution variation were reported by a previous numerical study which employed true battery structure and finite element method [4]. After time step, some small graphite particles are completely depleted of lithium which shown as the black parts. Moreover, local lithium depletion is enhanced in the edges and corners for large particles in negative electrode area, because lithium moves much faster in these areas. Similarly, local lithium accumulation is improved in the edges and corners for large particles in positive electrode area. Fig. 2 shows the local variation in lithium concentration. Similarly, the lithium accumulation in small electrode fragment is fast than that in big fragment. The concentration gradient can be observed in large particles. The electrode microstructure has influences on the electrolyte lithium concentration distribution. The lithium concentration is lower in the part where more particles aggregate. Fig. 1. Contour maps of lithium concentration in solid phase and electrolyte phase at different time step for electrode with irregular particle geometry. Fig. 2. Local variation in lithium concentration for a small segment of a cathode at time step.
4 Zhiyuan Jiang and Zhiguo Qu / Energy Procedia 88 ( 2016 ) Fig. 3 shows the solid phase lithium concentration distribution and the corresponding solid electric potential distribution at three different time steps. As shown in Fig. 3, the electric potential increases in negative area and decreases in positive area. This microscopic potential change accounts for the macroscopic cell voltage drop during the discharge process. A more detailed description of the distribution of lithium concentration and electric potential is shown in Fig. 4. The significant local variations in lithium concentration and electric potential can be observed. As illustrated in the zoom section 2, the parts with lower lithium concentration produce higher local electric potential. The local electric potential variations cause local variations in charge transfer kinetics. Fig. 3. Contour maps of solid phase Lithium concentration and the corresponding electric potential at different time step for irregular electrode geometry. Fig. 4. Local variation in lithium concentration and electric potential of the anode at time step. 4. Conclusions
5 646 Zhiyuan Jiang and Zhiguo Qu / Energy Procedia 88 ( 2016 ) In this study, we developed a two dimensional LBM simulation of species and charge transport within lithium ion battery porous electrode. The time evolution of lithium concentration and electric potential within irregular electrode particles were obtained. The electrode micro-structure had significant influence on the distribution of lithium concentration and electric potential. For discharge performance, the porosity of the electrode had significant influence on the achievable capacity. Implementations of simulations at the particle scale have the potential to improve battery design, since reliable designs can be achieved with proper incorporation of the physical mechanisms and the true, processing-determined electrode structure at a microstructural level. Acknowledgements This work was financially sponsored by the National Natural Science Foundation of China (No ). References [1] Cho J, Park B. Preparation and electrochemical/thermal properties of LiNi0.74Co0.26O2 cathode material. J Power Sources. 2001;92:35 9. [2] Guerfi A, Charest P, Kinoshita K, Perrier M, Zaghib K. Nano electronically conductive titanium-spinel as lithium ion storage negative electrode. J Power Sources. 2004;126: [3] Zaghib K, Nadeau G, Kinoshita K. Effect of Graphite Particle Size on Irreversible Capacity Loss. J Electrochem Soc. 1999;147: [4] Smith M, Garc'Ia RE, Horn QC. The Effect of Microstructure on the Galvanostatic Discharge of Graphite Anode Electrodes in LiCoO2-Based Rocking-Chair Rechargeable Batteries. J Electrochem Soc. 2008;156:A896-A904. [5] Wang CW, Sastry AM. Mesoscale Modeling of a Li-Ion Polymer Cell. J. Electrochem. Soc. 2007;154:A1035-A47. [6] Wiedemann AH, Goldin GM, Barnett SA, Zhu H, Kee RJ. Effects of three-dimensional cathode microstructure on the performance of lithium-ion battery cathodes. Electrochimica Acta. 2013;88: [7] Qiu G, Joshi AS, Dennison CR, Knehr KW, Kumbur EC, Sun Y. 3-D pore-scale resolved model for coupled species/charge/fluid transport in a vanadium redox flow battery. Electrochim Acta. 2012;64: [8] Li C, Feng YL, Song CX, Lei C, He YL, Tao WQ. Multi-scale modeling of proton exchange membrane fuel cell by coupling finite volume method and lattice Boltzmann method. Int J Heat Mass Tran. 2013;63: [9] He X, Li N. Lattice Boltzmann simulation of electrochemical systems. Comput Phys Commun. 2000;129:
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