Simulating Electrochemical Behaviour of Lithium-Ion Cylindrical Cells Using Two-Dimensional Physics-Based Model
Authors: Mehta Rohit , Gupta Amit 
Published: May 2020

High energy storage density and energy conversion efficiency, rechargeability and zero tailpipe emissions of lithium-ion batteries make them an attractive choice for powering automobiles. However, significant research and improvement are still required to make these batteries comparable with the convenience associated with the use of fossil fuels. One of the major concerns associated with batteries in electric vehicles (EVs) is of safety due to the high current requirements. In this regard, battery pack designs can benefit tremendously by simulating adverse thermo-electrochemical scenarios. Due to the coupled nature of the electrochemical behaviour of the cell on its temperature distribution, the knowledge of temperature distribution and heat generation in constituting cells is required to predict the cell charge-discharge behaviour, local hot-spots formed within the cell and their influence on thermal runaways during pack operation. Though many attempts were made in the past towards this goal, however, several assumptions were used to simplify the model for cylindrical cells. Lumped thermal models with constant temperature were used to determine the cell temperature directly using experimental data [1] or using pseudo-2D model [2,3] on unwounded cells [4]. Heat generation was homogenized in the energy balance [5] and used along with experimental data for computation [6]. The lack of spatial-dependence in such models is not a good representation of physics expected in large format cylindrical cells due to their low effective transport and thermal properties, and the highly non-homogeneous material used to fabricate these cells.
Some models that consider spatial dependence of physics employ this either in one-dimensional radial direction [7], two-dimensional in transverse section [8], or three-dimensional approximation using two-dimensional resistor circuits for current collectors with non-linear one-dimensional resistors between adjacent current collector nodes [9]. For a proper understanding of local heat generation, the three-dimensional, highly local, and coupled nature of thermo-electrochemical behaviour needs to be taken into account in the model. In a step towards this goal, the present work aims at developing a two-dimensional physics-based thermo-electrochemical model for cylindrical cells. The differential-algebraic governing equations have been solved implicitly with the non-linear term in each linearized for one variable at a time using the Taylor series expansion. This approximation method ensures second-order accuracy for the linearized variable being computed while the non-linearity is retained for the other unknown variables. A variable time step solver based on the stability of the output voltage profile enables improved computational speed. A second-order differencing in space and backward differencing in time have been implemented for discretizing the partial differential equations into algebraic equations. The Gauss-Seidel method is employed to iterate for the variables at each time step. This discretization technique has been validated (Fig.1a) over a range of C-rates (up to 6C) against an available solver [10]. Subsequently, the method is adapted for polar coordinates to simulate the two-dimensional cross-section of cylindrical cells. The discretization of the geometry, as shown in Fig.1b, has been done ensuring nodes on all the boundaries separating various domains along the windings. The different domains within the coil have been discretized using Archimedean spirals with nodes at uniformly distributed angular coordinate. The simulation results will be validated using data obtained from cycling of Samsung INR18650-29E lithium-ion cells on a high-current cell cycler in controlled temperature environment. In the future, the coupling of the electrochemical and thermal models for the cylindrical cell geometry will also be attempted.

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Figure 1