In this study, a gradient-based optimization algorithm is used for the computational design and optimization of a non-aqueous lithium-O₂ battery. The sensitivity analysis and numerical optimization capabilities are appended to the multiscale framework previously developed at LRCS for the discharge behavior of this type of batteries. The transport of oxygen in the porous cathode is modeled using Fick’s law at the continuum scale, by assuming isothermal conditions. A micro-scale model predicting the discharge product morphology is coupled to the continuum one. The final discharge product is assumed to form, through both the surface limited thin film growth mechanism and the solution phase reaction mechanism. The cathode microstructure in the model is based on experimentally measured PSD (pore size distribution). A detailed reaction mechanism considering the microstructural properties of the cathode, the surface limited reaction, surface thin film growth and solution phase reaction is used. The sensitivity analysis for the Lithium-O₂ cell is performed using the finite difference approach. Sensitivity derivatives are used to identify the variables that have the most significant impact on design performance of the battery. This information is helpful prior to an optimization study as it can be used to remove design parameters that do not strongly influence. Design variables investigated are the O₂diffusion coefficient, the cathode porosity, temperature, separator porosity and the cathode thickness. The cell performance is optimized and improved using a quasi-Newton algorithm. In the quasi-Newton algorithm, sensitivity derivatives are utilized in determining a search direction that maximizes a cost function representing the cell capacity. This work provides a comprehensive receipt on the implementation of efficient algorithms devoted to the predictions of optimized cell designs. Design guidelines arising from the computational results are discussed from an engineering perspective.

References:

[1] Kan-Hao Xue, Trong-Khoa Nguyen, and Alejandro A. Franco, “Impact of the Cathode Microstructure on the Discharge Performance of Lithium Air Batteries: A Multiscale Model”, J. Electrochem. Soc. 2014 volume 161, issue 8, E3028-E3035.

[2] Kan-Hao Xue, Euan McTurk, Lee Johnson, Peter G. Bruce, and Alejandro A. Franco, “A Comprehensive Model for Non-Aqueous Lithium Air Batteries Involving Different Reaction Mechanisms”, J. Electrochem. Soc. 2015 volume 162, issue 4, A614-A621.