A three‐dimensional thermal‐electrochemical‐mechanical‐porous flow multiscale formulation for battery cells

• Published in: International journal for numerical methods in engineering 2024-07, Vol.125 (13), p.n/a
• Main Authors: Kulathu, Sandeep, Hurtado, Juan A., Bose, Kingshuk, Hahn, Youngwon, Bouzinov, Pavel A., Taylor, Robert L., Oancea, Victor
• Format: Article
• Language: English
• Subjects: electrochemical‐mechanical; Electrodes; electrolyte flow; Electrolytic cells; Industrial applications; Inventions; Lithium-ion batteries; Mathematical analysis; Numerical models; porosity; porous electrode theory; Rechargeable batteries; rechargeable battery; Spherical coordinates; Storage batteries; Swelling; Time integration
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.7464

Several decades after the invention of the rechargeable Li‐ion battery, countless innovations from both the research and industry communities have led to placing the secondary battery at the heart of the electrification revolution in recent years. Mathematical and numerical models have been trusted companions in advancing the technology to help guide design improvements or to gain insight when physical measurements are impossible to perform. Starting with the breakthrough porous electrode theory (PET) model proposed by Newman and co‐workers in 1975 (Newman and Tiedemann, AIChE Journal, 1975, 21, 25–41), many authors have improved the formulation from a variety of perspectives. The novel aspects of the model we propose in this paper expand on this long stream of PET formulations and aim to address modeling needs that, to the authors' knowledge, have not been yet considered. The proposed formulation is characterized by the following concurrent features: (1) a full 3D description of the macroscale behavior and 1D microscale in spherical coordinates (Pseudo 4D formulation [P4D]) accounting for geometric details of the cell architecture such as imperfect spiral jellyrolls in cylindrical cells; (2) multiple concurrent particle chemistries to model the microscale lithiation/delithiation behavior at every macroscale element integration point, leading to a multiscale (FE2$$ {\mathrm{FE}}^2 $$) approach; (3) a fully coupled thermal‐electrochemical‐mechanical stress interaction due to lithiation/delithiation induced swelling and external confinement; (4) spatially‐dependent porosity evolutions due to swelling of the particles in the porous electrodes; (5) electrolyte flow in the porous regions and overfill spaces via Darcy‐based flow including partial saturation of the active regions; (6) detailed descriptions of individual battery components such as the electrodes, separator, and current collectors with the possibility of “connecting” the different components through contact definitions; (7) fully linearized macro‐microscale coupling behavior allowing for large time increments in an implicit time integration scheme for a scalable and computationally effective numerical solution. A number of numerical examples including validation against experimental data are performed to demonstrate the predictive power of the proposed model and its efficiency for industrial applications.