Immersion cooling, where cooling fluid flows in direct contact with the Li-ion cell, provides superior temperature control compared to other battery thermal management systems (BTMSs). Although the temperature rise during charging/discharging is low for immersion cooling, the inherent complexity of the cooling approach makes it difficult to predict and control performance. In general, numerical approaches are required to design and analyze immersion cooled BTMS configurations. For accurate results, models must fully couple the electrochemical and thermal-fluid physics solvers. However, such a numerical approach is computationally expensive and may not be feasible, in particular, for large BTMS systems. In the present study, we develop a computationally-efficient approach with coupled electrochemical and thermo-fluid physics to study immersion cooling based BTMSs. The core strategy is to use either analytical expressions or combination of analytical and numerical solutions for all the governing physics. Depending on the discharge rate and on the final design objective, different levels of simplification are leveraged to analyze the thermal and electrochemical response of the system.

For the present analysis, we consider discharging of a cylindrical nickel manganese cobalt oxide (NCM) 18650 cell that is immersed in a cooling fluid stream. Different combinations of mass flow rates and fluids (deionized water, mineral oil, and air) are considered to evaluate performance. For every configuration, we first analyze the system with a fully-coupled fully numerical model and this data serves as the reference to judge the accuracy of the newly developed models. Note that the parameters used in the electrochemical models (such as electrolyte and electrode properties, as well as the reaction rates) are the same for the fully-numerical and the quasi-analytical models allowing direct comparison of the results. To isolate the impact of using the simplified models for the electrochemical aspects, a second set of comparison data is generated using the analytical electrochemical model in conjunction with the full-scale numerical thermo-fluid model. The analytical models rely on calculating a heat transfer coefficient to include the impact of the fluid flow and the heat transfer coefficient can be estimated from correlations or from the fully-coupled fully-numerical models. In general, for air-cooled configuration, the thermal and electrochemical performance (i.e., trend and magnitude of temperature rise and cell potential) of the quasi-analytical models matches the fully-coupled full-scale numerical model. But for other fluids, the results deviate from the baseline fully-coupled fully-numerical models unless the numerical fluid models are used to estimate the evolution of heat transfer coefficient throughout the discharging process. Specifically, a small number of fully-coupled fully-numerical simulations are leveraged to train the quasi-analytical model (based on a particular geometry) for rapid analysis and optimization of the BTMS. In summary, the newly developed models including the numerical data-driven learning provide an efficient trade-off between computation cost and accuracy.