Scale analysis of electrochemical and thermal behaviour of a cylindrical spiral-wound lithium-ion battery

Design and sizing of lithium-ion battery is a challenging task because of inherent multiphysical and multiscale nature of this battery type. Detailed mechanistic models have been developed to resolve the design effects on physico-chemical processes taking place inside the battery and in turn, on battery performance. However, such models are hold back by their mathematically complexity and associated computational cost. In this paper, we come up with efficient design guidelines for Li-ion battery while addressing these model complexities. In essence, we carry out scale analysis of electrochemical and thermal behaviour of a cylindrical spiral wound Li-ion battery. We secure non-dimensional numbers and scales for the leading-order phenomena of charge, energy and species transport as well as associated heat generation and electrochemical reactions. The scales, in particular, provide quick quantification of variables such as temperature increase, potential losses and state of charge during charge/discharge. We verify reliability of the derived scales by comparing their predictions with the results from numerical simulations of an electrochemical-thermal model of battery. Overall, good agreement between the predictions from scales and simulations is obtained. The non-dimensional numbers and scales – which characterize the cell both thermally and electrochemically – are also discussed from the viewpoint of battery design.