Due to the ever-increasing interest in solid state batteries, there is a significant amount of ongoing research on developing novel fabrication approaches for creating a variety of solid electrolyte architectures. These architectures must be designed to meet multiple design requirements, including mechanical, ion transport, and electrochemical, and overcoming fundamental challenges associated with solid electrolytes. One key challenge for the solid electrolyte is to meet the conflicting requirements of being rigid enough to resist dendrite formation while also being able to deform in order to accommodate volume expansion of the cathode active material particles during lithium intercalation to prevent these particles from cracking. One of the proposed solutions to meet these conflicting requirements is to use a soft catholyte in conjunction with a hard ceramic solid electrolyte separator [1]. However, the thin solid electrolyte separator is fragile and can break relatively easily. This can be addressed by fabricating a bilayer structure consisting of a thin dense layer acting as separator supported by a porous scaffold layer [2]. The porous scaffold layer can be filled with a mixture of soft catholyte and active material particles. Such hybrid electrolyte system help meet the aforementioned conflicting mechanical design requirements. In addition to the mechanical requirements, the electrolyte system needs to provide effective ion conduction without adversely affecting gravimetric energy density. Further, the electrolyte must have wide electrochemical and chemical stability windows to ensure battery longevity. Multiscale modeling connecting atom scale behavior to system level performance can be key to designing complex hybrid electrolyte architectures and identifying electrolyte compositions, specifically in the case of catholyte, to meet these multiple design requirements. In the present work, we study computer-generated composite cathode architectures consisting of three material phases (1) lithium lanthanum zirconium oxide (LLZO) solid electrolyte as the scaffold structure and the dense separator (2) Succinonitrile (SN) based solid catholyte [2,3,4] as the soft, compliant electrolyte (3) Nickel-rich nickel-manganese-cobalt (NMC) cathode primary and secondary particles. The type of computer-generated microstructures to be studied will be restricted based on their manufacturability using the state-of-the-art fabrication techniques [2,3]. The design parameters of the computer-generated architecture (e.g., pore size, shape, surface features, and LLZO and catholyte volume fractions) will be systematically studied to explore the complex design space and understand the tradeoffs concerning key design requirements such as gravimetric energy density, rate capability, and mechanical properties. We will use molecular simulations to obtain key physicochemical properties of potential catholytes composed of SN and lithium salts, which are essential inputs to the continuum scale microstructure modeling. These properties include electrochemical stability windows obtained from density functional theory (DFT) calculations, as well as transport properties, such as self-diffusivity, ionic conductivity, and transference number, determined via molecular dynamics (MD) simulations. Catholytes with suitable properties will be considered in the continuum scale microstructure simulations. References [1] W. Go, M. C. Tucker, and M. M. Doeff, Journal of The Electrochemical Society , 171, 020524 (2024). [2] H. Shen, E. Yi, S. Heywood, D. Y. Parkinson, G. Chen, N. Tamura, S. Sofie, K. Chen, and M. M. Doeff, ACS Appl Mater & Interfaces , 12 , 3494 (2020). [3] F. Y. Shen, R. A. Jonson, D. Y. Parkinson, and M. C. Tucker, J Am Ceram Soc , 105 (1) , 90-98 (2022). [4] D. Han, P. Wang, P. Li, J. Shi, J. Liu, P. Chen, L. Zhai, L. Mi, Y. Fu, ACS Applied Materials & Interfaces 13 , no. 44, 52688-52696 (2021).

Li-ion batteries are used in a wide variety of applications, ranging from consumer electronics to electric vehicles (EVs) and large-scale energy storage. There are also ongoing efforts to electrify air transportation. The system level issues such as safety, thermal effects, and cell balancing need to be addressed as use of batteries become widespread in the transportation sector. These issues can be studied experimentally, however, extensive experimental testing at system level involving large battery packs is impractical. Additionally, experimental testing alone cannot provide insights into these issues. This makes experimental characterization studies necessary as well, which are not feasible beyond the lab scale. Appropriate use of modeling and simulation can provide an attractive alternative to gain insights into the system level issues. Presently, simplified equivalent circuit and empirical models are typically used at pack level. Since these models do not capture various physical phenomena and electrochemical processes, they cannot provide necessary insights into these issues. There are many simulation studies on thermal management of battery packs, but these studies are limited to studying heat transfer and fluid flow without capturing their effect on the life and performance of batteries. At the scale of a single li-ion cell, there are physics-based models incorporating various processes, including transport processes, reaction kinetics, thermal effect, and degradation mechanisms. However, these models are typically not used to study battery packs. One such attempt reported in literature involved the use of thermal single-particle battery model at the pack level, but this study considered simplified thermal boundary conditions representing natural convection type heat transfer, a rather simplistic treatment for the heat leaving the batteries1. There have been other similar studies as well2-4. Since thermal management systems presently used in EVs and new designs developed by researchers involve far more complex heat transfer processes, a model capturing heat transfer processes in these thermal management systems in an accurate manner is necessary. Using an accurate physics-based electrochemical-thermal model at the battery pack level and combing it with a heat transfer model for battery thermal management system can enable studying battery performance, aging, and safety characteristics at the pack level. However, this type of simulation would be computationally prohibitively expensive, especially for large battery packs, like the ones used in EVs. In the present work, we first develop volume averaged heat transfer models for two different battery pack designs, one involving prismatic/pouch cells, and other involving cylindrical cells, like the Tesla EV battery pack. These volume averaged models are informed by full-order steady-state computational fluid dynamics (CFD) simulations, and later validated against full-order transient CFD simulations for a wide variety of operating conditions. The simulations conducted using volume averaged heat transfer models are at least two orders of magnitude faster than conventional simulations while maintaining the same level of accuracy. Next, the volume averaged heat transfer model for one of these battery pack designs and the recently reported volume averaged thermal tank-in-series battery model are used to develop a modeling framework for multiple cells connected in series to form a module, and multiple such modules connected in parallel forming a battery pack. This modeling framework enables fast simulation of large battery packs while considering complex battery physics in each individual battery and heat transfer in the thermal management system. This proposed approach can be used for any battery pack design and configuration. Using this modeling framework, we perform detailed analysis on the battery pack, including studying electrochemical and thermal behavior of individual batteries in the pack as well as pack level characteristics under different operating conditions. Finally, we also study effect of cell-cell to variations due to possible manufacturing variations and variations in the state of charge (SOC) of batteries across the battery pack. References: Guo, M.; White, R. E., Thermal Model for Lithium Ion Battery Pack with Mixed Parallel and Series Configuration. J Electrochem Soc 2011, 158 (10), A1166-A1176. Huang, H. H.; Chen, H. Y.; Liao, K. C.; Young, H. T.; Lee, C. F.; Tien, J. Y., Thermal-electrochemical coupled simulations for cell-to-cell imbalances in lithium-iron-phosphate based battery packs. Appl Therm Eng 2017, 123, 584-591. Schindler, M.; Durdel, A.; Sturm, J.; Jocher, P.; Jossen, A., On the Impact of Internal Cross-Linking and Connection Properties on the Current Distribution in Lithium-Ion Battery Modules. J Electrochem Soc 2020, 167 (12). Wang, B.; Ji, C. W.; Wang, S. F.; Sun, J. J.; Pan, S.; Wang, D.; Liang, C., Study of non-uniform temperature and discharging distribution for lithium ion battery modules in series and parallel connection. Appl Therm Eng 2020, 168.

With the widespread use of Lithium-ion (Li-ion) batteries in multiple industries, the design space for the electrochemical cells has increased drastically. Li-ion batteries’ design parameters and material properties, such as porosity, electrode thickness, active material loading, and solid phase diffusivities, typically vary substantially due to different design goals and variation in the manufacturing process. Due to the difficulty in obtaining these and other battery cell parameters, many battery management systems used to control and monitor Li-ion batteries opt for the simplified resistor-capacitor circuit-based battery cell representation over using physics-based battery models. However, if these parameters become obtainable, scientists could implement advanced battery management systems using physics-based battery models to capture precisely how the battery performs and degrades in a wide variety of applications. Multiple methods, such as genetic algorithms, statistics, and machine learning, have been attempted for the parametrization and characterization of battery cells to enable accurate battery simulations using physics-based models [1, 2]. However, there are inherent limitations to the type and number of parameters that can be estimated using these methods if only the standard battery cell cycling data is utilized for this purpose. The present work elucidates and quantifies these limitations specifically in the case of machine learning based approach and provides deeper insights into these limitations that may help develop more robust cell characterization protocols. In the present work, model parameters are varied in a continuum-level physics-based model and simulations are performed for: (1) constant current-constant voltage (CC-CV) charging and constant current discharge at different C-rates, and (2) electrochemical impedance spectroscopy (EIS) in the relevant frequency range at multiple states of charge (SOCs). The Single Particle Model (SPM) is used for performing these simulations due to its relative simplicity and small number of parameters. At first, the charge and discharge data are input as training data in a long short-term memory neural network (LSTM NN), and EIS data is input as training data in a convolutional neural network (CNN). Once trained, the machine learning (ML) model uses charge, discharge, and EIS data withheld from the original training data set to predict SPM parameters. The estimated parameters are compared with the true parameters used for SPM charge, discharge, and EIS simulations, and the error in parameter estimation is quantified. A rigorous grid convergence analysis is performed to highlight the importance of ensuring that the spatial discretization error of the model does not influence the parameter estimation accuracy. For the first error quantification, all parameters are varied concurrently to obtain the parameter estimation error that arises from a large, undetermined parameter set. Parameters are then analyzed individually and in clusters related to diffusion, kinetics, and stoichiometric limitations. Further analysis is performed on parameters that could not be estimated with sufficient accuracy, including theoretical explanations for the incurred error and the effect of this error on the internal state predictions. References: Dawson-Elli, N., et al., On the creation of a chess-ai-inspired problem-specific optimizer for the pseudo two-dimensional battery model using neural networks. Journal of The Electrochemical Society, 2019. 166 (6): p. A886. Berliner, M.D., et al., Nonlinear identifiability analysis of the porous electrode theory model of lithium-ion batteries. Journal of The Electrochemical Society, 2021. 168 (9): p. 090546.

One the biggest challenges in achieving net-zero in the aviation sector through electrification of electric aircraft is the limitation of current battery systems in terms of simultaneously providing high gravimetric energy density and power density combined with suboptimal performance and safety issues at extreme temperatures. Much of the current literature related to electric aircraft focuses on aircraft design and optimization with overly simplified battery analysis such as linear voltage profile approximation or the use of equivalent circuit models which do not help understand and quantify material limitations of battery systems in electric aircraft application1-3. This is particularly relevant due to the fact that battery cells used in both fixed-wing electric aircraft and eVTOLs (electric vertical take-off and landing aircraft) see unique operating requirements that are often significantly more demanding than those seen in electric vehicles (EVs)4. Recently, there have been a few studies analyzing battery performance in more detail 5-7. However, there is a lack of investigations on the effect of battery design parameters and material properties on battery performance under real-world operating conditions, such as dynamically varying power demand, and the resulting effect on electric aircraft performance characterized by range, speed, and endurance. This type of study is necessary in guiding design of batteries and battery materials tailored to electric aircraft applications, particularly in dealing with the highly dynamic nature of such an application. In the present work, we perform coupled simulation studies of longitudinal flight dynamics and battery dynamics using high fidelity electrochemical battery models. First, we study the effect of model fidelity on the prediction of battery dynamics and key battery states, particularly in the context of studying the effect of battery design parameters. This results in the identification of an appropriate battery model for an in-depth analysis on the effect of battery design parameters and material properties on battery dynamics and the resulting effect on aircraft performance. Additionally, we consider the effect of dynamically changing battery temperature obtained from experimental testing under simulated flight conditions. This is particularly important due to the significant battery temperature variation expected during a typical flight and its implications on battery performance and safety. Overall, this work provides detailed analysis on the effect of battery design on its electrochemical performance and the overall system level performance considering real-world operating conditions. References M. Kaptsov and L. Rodrigues, Journal of Guidance, Control, and Dynamics, 41, 288 (2018). N. Biju and H. Fang, Applied Energy, 339, 120905 (2023). L. Kiesewetter, K. H. Shakib, P. Singh, M. Rahman, B. Khandelwal, S. Kumar and K. Shah, Progress in Aerospace Sciences, 142, 100949 (2023). X.-G. Yang, T. Liu, S. Ge, E. Rountree and C.-Y. Wang, Joule, 5, 1644 (2021). A. Ayyaswamy, B. S. Vishnugopi and P. P. Mukherjee, Joule, 7, 2016 (2023). Dixit, M., Bisht, A., Essehli, R., Amin, R., Kweon, C. B. M. and Belharouak, I., ACS Energy Letters, 9, 934-940 (2024). M. Wang, S. Kolluri, K. Shah, V. R. Subramanian and M. Mesbahi, IEEE Transactions on Aerospace and Electronic Systems, 59, 1084 (2022).

In traditional Li-ion batteries with liquid electrolyte, the transport of lithium ions in the electrolyte and lithium in the active material within a porous electrode are studied extensively. The continuum-scale modeling of these transport phenomena considers a homogenized simulation domain consisting of liquid electrolyte and solid active material with effective transport properties accounting for the heterogeneity [1]. There have been fewer studies that consider digitized versions of the experimentally imaged microstructure in continuum-scale modeling studies, particularly to study mechanics [2]. Despite of the computational challenges, there are inherent advantages in using fully resolved microstructure modeling to improve fundamental understanding of the relevant physical and chemical phenomena in porous electrodes, such as localized degradation and stress concentration. In the case of solid electrolytes, specifically scaffold-type LLZO solid electrolytes, microstructure modeling is of even more relevance, particularly to study anisotropic transport, localized degradation phenomena, stress and deformation leading to loss of contact, and chemo-mechanics. Thus far, microstructure modeling studies on experimentally obtained microstructure consisting of solid electrolyte and active material have been quite limited [3]. The studies that have explored this realm have employed voxel-based mesh to discretize the computation domain [3]. While these methods are sufficient proof of concept, the lack of precision in defining the interface separating active material and electrolyte when using voxel-based mesh provides a source of potentially significant numerical error. Without a highly resolved interface mesh, the total interfacial area increases artificially which leads to inaccuracies in calculations of local reaction rate and overpotential. A highly resolved, smooth interface is also necessary when simulating mechanical deformation and stress field in the microstructure. In the present investigation, we model mass transport and charge transport in the active material/electrolyte microstructure to simulate concentration and potential fields with varying mesh types in order to compare their effectiveness and characterize the error that can be attributed to the mesh type chosen, particularly in the case of voxel-based meshes. Additionally, we study the effect of microstructure domain length chosen in the two directions perpendicular to the shortest length (electrode thickness) as well as boundary condition formulation on the boundaries in these axes on the simulation results. The microstructures studied in this work are derived from the image stacks of the bi/trilayer LLZO solid electrolyte fabricated using freeze-tape-casting method [4]. Overall, the present work aims to develop a better understanding of the best practices in microstructure modeling, particularly when using microstructure image stacks obtained from fabricated samples. References [1] M. Doyle, T.F. Fuller, J. Newman, J. Electrochem. Soc. , 140 , 1526 (1993). [2] H. Mendoza, S.A. Roberts, V.E. Brunini, A.M. Grillet, Electrochim. Acta , 190 , 1 (2016). [3] M. Alabdali, F.M. Zanotto, V. Viallet, V. Seznec, A.A. Franco, Curr Opin Electrochem , 36 , 101127 (2022). [4] Hao Shen, Eongyu Yi, Stephen Heywood, Dilworth Y. Parkinson, Guoying Chen, Nobumichi Tamura, Stephen Sofie, Kai Chen, and Marca M. Doeff, ACS Appl Mater & Interfaces , 12 , 3494 (2020).

Several studies have contributed to the current understanding of the temperature-dependent behavior of solid-electrolyte interphase (SEI) formation in lithium-ion batteries and its impact on battery capacity and lifespan. Liu et al. developed a thermal-electrochemical model that revealed the complex interplay between diffusivity, reaction kinetics, and temperature on SEI growth 1 . Leng et al. presented an electrochemistry-based electrical model to examine the temperature's effect on battery aging 2 . Alipour et al. reviewed temperature-dependent electrochemical properties 3 , while Lubhani Mishra et al. provided a detailed physics-based analysis of battery degradation and temperature inhomogeneities 4 . These studies collectively indicate higher temperatures accelerating and promoting growth of compact and less permeable SEI structures leading to an increase in capacity loss and cell resistance, and lower temperatures resulting in slow ionic transport through the SEI also causing higher ohmic loss. In the present work, we study SEI growth and resulting effect on battery capacity fade using continuum scale modeling under the assumption of constant battery cell temperature as well as considering actual dynamically changing temperature data from experiments. SEI growth under these two considerations is compared and the comparison is used in determining scenarios where considering dynamically varying temperature is crucial for accuracy. The detailed analysis of the internal states from the simulation results contributes to the understanding of the effect of the thermal dynamics on battery cell degradation due to SEI growth. To achieve these objectives, a physics-based model, specifically the Single Particle Model (SPM), is utilized. The model uses temporal temperature data obtained from past experimental studies as well as temperature dependent properties of SEI provided in the literature as inputs for this investigation. The ultimate aim of this study is to better understand how temperature influences SEI characteristics, thereby contributing to improved battery performance and longevity across diverse thermal environments. References Liu, L., Park, J., Lin, X., Sastry, A. M., & Lu, W. (2014). A thermal-electrochemical model that gives spatial-dependent growth of solid electrolyte interphase in a Li-ion battery. Journal of power sources, 268, 482-490. Leng, F., Tan, C. M., & Pecht, M. (2015). Effect of temperature on the aging rate of Li-ion battery operating above room temperature. Scientific reports, 5(1), 12967. Alipour, M., Ziebert, C., Conte, F. V., & Kizilel, R. (2020). A review on temperature-dependent electrochemical properties, aging, and performance of lithium-ion cells. Batteries, 6(3), 35. Mishra, L., Subramaniam, A., Jang, T., Garrick, T. R., & Subramanian, V. R. (2022, October). Model Development for Temperature-Dependent Degradation in Large Format Lithium-Ion Batteries. In Electrochemical Society Meeting Abstracts 242 (No. 28, pp. 1075-1075). The Electrochemical Society, Inc.

Due to the ever-increasing interest in solid state batteries, there is a significant amount of ongoing research on developing novel fabrication approaches for creating a variety of solid electrolyte microstructures. This is done with the goal of meeting the multiple design requirements and overcoming fundamental challenges associated with solid electrolytes. Microstructure modeling can be a powerful tool to study and analyze electrolyte microstructures and guide design of improved microstructures. There have been a limited number of studies that have developed and utilized microstructure models to analyze solid electrolytes and solid-state batteries [1, 2]. These studies are typically limited to analyzing experimentally fabricated microstructures by using experimental imagery for generating the computational domain. While this is necessary for validating microstructure models against experimental data, this is not useful for discovering improved microstructures. There have been some past studies in the case of both traditional lithium-ion batteries and solid-state batteries where computer-generated microstructures are considered to inform architecture design [3, 4]. However, these studies typically assume highly idealized porous electrode structures that are not representative of the microstructures that can be fabricated using existing fabrication methods. In the present work, we study computer-generated lithium lanthanum zirconium oxide (LLZO) solid electrolyte microstructures informed by the microstructures that have been fabricated by scalable fabrication methods [4,5]. Although computer-generated microstructures being analyzed may lack some of the finer features of the fabricated microstructures, the type of computer-generated microstructures to be studied will be restricted based on their manufacturability using the state-of-the-art fabrication techniques [4,5]. The design parameters of the computer-generated microstructures (e.g., pore size, shape, and surface features) will be varied to explore the solid electrolyte design space to study tradeoffs associated with key design requirements such as gravimetric and volumetric energy density, rate capability, and mechanical properties. In the future, we will be fabricating microstructures informed by this analysis to validate the model predicted performance characteristics. References [1] M. Finsterbusch, T. Danner, C. L. Tsai, S. Uhlenbruck, A. Latz, O. Guillon, ACS Appl Mater Interfaces, 10, 22329 (2018). [2] A. Neumann, S. Randau, K. Becker-Steinberger, T. Danner, S. Hein, Z. Ning, J. Marrow, F.H. Richter, J. Janek, A. Latz, ACS Appl Mater Interfaces, 12, 9277 (2020). [3] A. Bielefeld, D. A. Weber, J. Janek, ACS Appl Mater Interfaces, 12, 12821 (2020). [4] J. S. Lopata, T. R. Garrick, F. Wang, H. Zhang, Y. Zeng, and S. Shimpalee, J Electrochem Soc, 170(2), 020530 (2023). [5] H. Shen, E. Yi, S. Heywood, D. Y. Parkinson, G. Chen, N. Tamura, S. Sofie, K. Chen, and M. M. Doeff, ACS Appl Mater & Interfaces, 12, 3494 (2020). [6] F. Y. Shen, R. A. Jonson, D. Y. Parkinson, and M. C. Tucker, J Am Ceram Soc, 105 (1), 90-98 (2022).

Phase change material (PCM) based cooling load reduction analysis commonly incorporates thermal energy storage (TES) on the building interior. Such systems are constrained by the limited overlap in suitable exterior temperatures for TES recharging with acceptable indoor comfort temperatures. In the current paper, this constraint is removed by moving the TES to the exterior and optimizing the TES system design for a certain climate, including PCM size and operating temperature window. The goal of this optimization will be reducing the ambient air temperature before the condensing heat exchanger in typical HVAC equipment for cooling applications to improve its coefficient of performance (COP) and minimize the annual cost. Utilization of organic fatty acid mixtures as the PCM will allow for selecting a solidification temperature appropriate to a given climate. This analysis attempts to minimize the annual cost of cooling structures by appropriately sizing TES systems with suitable eutectic or near-eutectic mixtures of fatty acids for a given climate. For a targeted climate, by analyzing the solidification temperature of a fatty acid mixture and the temperature at which the TES cools the ambient air, energy usage is reduced at times of peak cooling demands to optimize the efficiency of the combined TES and HVAC system and maximize energy cost savings.

Electric aviation has been a major focus of research in recent years as the aviation industry has seen significant growth in electric aircraft development. Most of the current literature related to electric aircraft modeling focuses on aircraft design and optimization with less focus given to battery analysis. Many studies utilize battery simplifications such as linear voltage profiles 1 or the use of equivalent circuit models 2 . Similarly, in the emerging field of electric vertical takeoff and landing (eVTOL) aircraft, battery analysis is often reduced to considering just weight and empirical power parameters, failing to capture physical and electrochemical battery behavior and its effect on battery performance characteristics 3 . These simplifications can often lead to inaccurate battery state estimations and performance prediction. Moreover, the battery packs used for both electric conventional take-off and landing (eCTOL) aircraft and eVTOLs see unique operating requirements that are often significantly more demanding than those seen in electric vehicles (EVs) 4 . This suggests the need to analyze aircraft battery pack performance limitations in greater detail. However, only a few such studies have been reported in the literature 5-6 . In this work, we perform coupled simulation studies of longitudinal flight dynamics and physics-based battery dynamics. For modeling battery dynamics, we use the well-known single particle model 7 . This coupling enables more reliable estimation of battery states and can better inform battery pack design for electric aircraft. The simulations are performed to understand the interplay between battery cell dynamics governed by its design parameters and parameters associated with fixed-wing flight dynamics, such as cruise altitude, flight path angle, and velocity. Additionally, the simulations show how varying these parameters and operating temperature effects the range and endurance of electric aircraft which can be used to determine the optimal aircraft operating parameters for a desired mission profile. Results from this simulation study are compared against an equivalent circuit battery model to highlight the importance of detailed battery analysis in electric aviation. This work will be extended to develop similar coupled physics-based battery models with the state-of-the-art aircraft configurations emerging in the eVTOL field. References M. Kaptsov and L. Rodrigues, Journal of Guidance, Control, and Dynamics , 41 , 288 (2018). N. Biju and H. Fang, Applied Energy , 339 , 120905 (2023). L. Kiesewetter, K. H. Shakib, P. Singh, M. Rahman, B. Khandelwal, S. Kumar and K. Shah, Progress in Aerospace Sciences , 142 , 100949 (2023). X.-G. Yang, T. Liu, S. Ge, E. Rountree and C.-Y. Wang, Joule , 5 , 1644 (2021). A. Ayyaswamy, B. S. Vishnugopi and P. P. Mukherjee, Joule , 7 , 2016 (2023). M. Wang, S. Kolluri, K. Shah, V. R. Subramanian and M. Mesbahi, IEEE Transactions on Aerospace and Electronic Systems , 59 , 1084 (2022). S. Santhanagopalan, Q. Guo, P. Ramadass and R. E. White, Journal of power sources , 156 , 620 (2006).

In this article, we develop an integrated approach to energy optimization for an all-electric aircraft. Our approach involves the formulation of the aircraft energy optimization as a set of optimal control problems (OCPs)—integrating battery and flight dynamics—for the cruise and climb phases, as well as the complete flight profile. The corresponding OCPs are then examined in the context of Pontryagin's minimum principle, providing necessary optimality conditions for the proposed integrated approach. Our analysis is then followed by utilizing the numerical solver Tomlab to devise computational solutions for the energy optimization OCPs. We then proceed to characterize the performance of the energy-optimal solutions for distinct models of the battery. In particular, we show that the choice of the battery model does not alter the form of optimal control for the flight system; however, the current profiles for the battery pack and the total operating costs are affected by the adopted models used for optimization. Finally, we develop a Simulink model built around physics-based battery dynamics to further characterize the interplay between aircraft energy operating costs and the underlying battery dynamics.

One of the contributing factors to the aging of lithium-ion batteries is the growth of the solid-electrolyte interphase (SEI) layer. The growth of the SEI layer leads to the irreversible loss of lithium available for cycling and increases the resistance of the battery. Physics-based models in literature model the kinetically limited or solvent diffusion-limited growth. In such models, the interface resistance is a constant, and the contribution to the overpotential of the intercalation reaction from the SEI layer is considered to be ohmic. In this study, we propose a model that describes the growth of the SEI layer on the electrode surface as a moving interface. The transport of lithium ions and the solvent in the electrolyte are affected by this moving interface. The equations that govern the species transport and the potential drop across the SEI layer are derived from dilute solution theory and solved by transforming the coordinates of the moving boundary. The ion transport induces changes in the conductivity across the SEI layer, which affects the potential drop that arises due to its growth. The effects of this potential on capacity fade are studied over cycling the battery.

Lithium-ion batteries’ performance, degradation, and safety are highly sensitive to their operating temperature [1-3]. Depending upon the form-factor, construction, and thermal boundary conditions, large temperature variations may be present within a battery in more than one direction. Physics-based battery models, such as single-particle model (SPM), enhanced single-particle model (ESPM), tank-in-series model, and the widely used pseudo-two-dimensional (p2D) model, ignore the effect of temperature variations in one or more directions [4]. Specifically, p2D model can resolve temperature variation within anode, cathode, and separator of a single stack but this is often not useful as the temperature variation within a single stack will be negligible due to the small length scale. Also, a commercial-scale Li-ion battery is a multi-stack system with possibly significant temperature variation across the stacks as compared to within a single stack. The recently developed thermal tank-in-series battery model accounts for temperature variation across a multi-stack battery system but does not account for temperature variation in the direction parallel to the current collector [5]. In the case of large-format batteries, significant temperature variations are also expected along the directions corresponding to the longer dimensions. This would typically involve temperature variations in the directions parallel to the current collector. Multi-scale multi-domain (MSMD) models have been developed in the past to extend the single-stack level physics-based models to account for temperature nonuniformity in these directions [6-8]. However, temperature variation in the direction corresponding to the shortest dimension may also be appreciable due to the anisotropic/orthotropic nature of heat transfer in the battery system at the macroscale [9,10]. This is because the heat transfer in this direction may be severely impeded by the multi-stack construct leading to poor thermal conductivity in that direction. This in turn may lead to a large temperature gradient even along the direction corresponding to the shortest dimension of the large-format battery system. This suggests the need for careful formulation of MSMD battery models considering the construction, design parameters, and external thermal conditions of a particular battery system. In the present work, we propose a general three-dimensional modeling framework that accounts for the effect of the three-dimensional temperature field on the local variations in thermodynamics, transport processes, and reaction kinetics in the battery system. This type of battery modeling framework can be used to study nonuniform temperature distribution driven spatially uneven degradation, particularly in large-format batteries. Additionally, this modeling framework can help design physics-aware battery-specific thermal management systems to improve performance and reduce degradation. This will be a drastic departure from the present approach of designing battery thermal management system which treats the battery in a rather simplistic manner. References [1] J. Shim, et al, J. Power Sour. 112, 222-230, 2002. [2] S.S. Zhang, et al, J. Power Sour. 115, 137-140, 2003. [3] X. Feng, et al, Energy Storage Mater. 10, 246-267, 2018. [4] V. Ramadesigan, et al, J. Electrochem. Soc. 159, 31-45, 2012. [5] A. Subramaniam, et al, J. Electrochem. Soc. 167, 113506, 2020. [6] G. Fan, et al, J. Electrochem. Soc. 164, A252, 2017. [7] A. Schmidt, et al, Electrochim. Acta. 393, p.139046, 2021. [8] A. Awarke, et al, J. Electrochem. Soc. 160, A172, 2013. [9] K. Shah, et al, J. Power Sour. 271, 262-268, 2014. [10] S.J. Drake, et al, J. Power Sour. 252, 298-304, 2014.

Lithium-ion batteries degrade as they are cycled due to different phenomena that occur inside the cell that lead to the loss of their capacity. One of the dominant mechanisms that leads to capacity fade is the growth of the solid-electrolyte interphase (SEI) layer due to the reduction of the electrolyte solvent on the electrode surface 1. This passive layer ideally prevents the electrolyte from interacting with the electrode, preventing further reduction of the electrolyte. However, the growth of the SEI layer during cycling leads to the irreversible loss of lithium available for cycling and increases the resistance of the battery. Physics-based models to study the growth of the SEI layer for predicting capacity fade are reported in the literature.2 -8 Adding the SEI layer growth mechanism to battery models can help predict the capacity fade of a cell under different charging protocols and drive cycles for EV and PHEV batteries 2. The different models that exist in literature consider the growth to be kinetic-limited 3 , 4 , diffusion-limited 5, or a combination of both 6 , 7 , 8. In previous studies, the relationship between the growth of the SEI layer and the interface resistance is assumed to be linear and the contribution of the same to the overpotential of the intercalation reaction is assumed to be ohmic. This is because the transport of lithium ions through the SEI layer is not included in these models. In this work, we propose a model that describes the growth of the SEI layer on the graphite anode as a moving interface. The mass transport of both lithium ions and the solvent in the electrolyte are modeled which are affected by this moving interface. The transport during kinetic-limited and diffusion-limited growth are analyzed for different C-rates as the battery is cycled. The ion transport also induces changes in the conductivity across the SEI layer which affects the potential that arises due to its growth. This important effect and its influence on capacity fade is studied by simulating battery cycling using the proposed model. These studies help improve the fundamental understanding of the impact of different battery design parameters and operating conditions on capacity loss and cell lifetime. Acknowledgement This work at the University of Texas at Austin was supported by U.S. DOE Office of Electricity award DEAC05-76RL01830 through PNNL subcontract 475525. References P. Arora, R. E. White, and M. Doyle, J. Electrochem. Soc., 145, 3647–3667 (1998). M. T. Lawder, P. W. C. Northrop, and V. R. Subramanian, J. Electrochem. Soc., 161, A2099–A2108 (2014). P. Ramadass, B. Haran, R. White, and B. N. Popov, J. Power Sources, 123, 230–240 (2003). G. Ning and B. N. Popov, J. Electrochem. Soc., 151, 1584–1591 (2004). H. J. Ploehn, P. Ramadass, and R. E. White, J. Electrochem. Soc., 151, 456–462 (2004). M. Safari, M. Morcrette, A. Teyssot, and C. Delacourt, J. Electrochem. Soc., 156, 145–153 (2009). X. G. Yang, Y. Leng, G. Zhang, S. Ge, and C. Y. Wang, J. Power Sources, 360, 28–40 (2017). N. Kamyab, J. W. Weidner, and R. E. White, J. Electrochem. Soc., 166, A334–A341 (2019).

Understanding the nature of onset and propagation of thermal runaway in a Li-ion battery pack is critical for ensuring safety and reliability. This paper presents thermal runaway simulations to understand the impact of radiative heat transfer on thermal runaway onset and propagation in a pack of cylindrical Li-ion cells during transportation/storage. It is shown that radiative properties of the internal partition walls between cells commonly found in battery packs for transportation/storage play a key role in determining whether thermal runaway propagation occurs or not. Surface emissivity of the internal partitions is shown to drive a key balance between radiative heat absorbed from the trigger cell and emitted to neighboring cells. It is shown that a high thermal conductivity partition may greatly help dissipate the radiatively absorbed heat, and therefore prevent onset and propagation. Therefore, choosing an appropriate emissivity of the internal partitions may offer an effective thermal management mechanism to minimize thermal runaway. Emissivity of the cells is also shown to play a key role in radiative heat transfer within the battery pack. This work contributes towards the fundamental understanding of heat transfer during thermal runaway in a battery pack, and offers practical design guidelines for improved safety and reliability.

a Materials Science and Engineering Program, Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA b Walker Department of Mechanical Engineering, Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA c Department of Chemical Engineering, University of Washington, Seattle, WA 98195, USA d Thermal/Fluid Component Sciences Department, Engineering Sciences Center, Sandia National Laboratories, Albuquerque, NM 87123, USA

Electrochemical models at different scales and varying levels of complexity have been used in the literature to study the evolution of the anode surface in lithium metal batteries. This includes continuum, mesoscale (phase-field approaches), and multiscale models. In this paper, using a motivating example of a moving boundary model in one dimension, we show how battery models need proper formulation for mass conservation, especially when simulated over multiple charge and discharge cycles. The article concludes with some thoughts on mass conservation and proper formulation for multiscale models. (C) 2021 The Electrochemical Society ("ECS"). Published on behalf of ECS by IOP Publishing Limited.

Parameter estimation is critical for efficient Battery Management System (BMS) performance. The accuracy and predictability of a model depends on the precision of its parameters. Moreover, model parameters tend to change with battery aging. Efficient BMS performance requires accurate tracking and updating of relevant parameters as the battery ages. Estimating parameters for electrochemical models is challenging due to the complexity of the governing equations, and the possibility of degeneracy, with multiple sets of parameter values that give the same accuracy for fitting charge/discharge data. Parameter estimation of various lithium-ion battery systems has been attempted with different model types, including equivalent circuit model2, single particle model3 and pseudo 2D (P2D) model.4,5 Estimation approaches reported in literature, such as, GA6, heuristic algorithms7, etc., are difficult to implement in real-time due to computational complexity. In the past, we proposed and implemented reformulated p2D models for real-time parameter estimation.8,9 While the reformulated models are computationally inexpensive, the large set of parameters and resulting likelihood of degeneracy introduce substantial complexity. Recently, we proposed lithium-ion Tanks-in-Series battery model10. This model is generated by systematic volume-averaging of the p2D model that enables efficient and real-time simulation with reduced set of parameters. In this presentation, we propose to estimate non-dimensional grouped parameters using non-dimensional Tanks-in-Series battery model. The grouping of parameters further reduces the number of parameters that needs to be estimated. This also reduces the computational effort required to perform optimization. The non-dimensional model captures resistances offered due to transport, reaction kinetics, and ohmic drop in electrolyte based on the non-dimensional grouped parameters that absorb constitutive expressions and parameters, such as electrolyte diffusivity, ionic conductivity, reaction rate constants and solid phase diffusivity. The estimation is performed on experimental charge/discharge data obtained from cylindrical cells having NCA and NMC cathode chemistries. The accuracy of the estimated parameters is validated using experimental cycling data obtained at different c-rates by calculating the error in voltage-time curves between the model prediction using estimated parameters and the experimental data. Acknowledgements The authors acknowledge funding from the U.S. Department of Energy Office of Electricity Energy Storage Program through Sandia National Laboratories, under the guidance of Dr. Imre Gyuk, and the Texas Materials Institute at The University of Texas at Austin. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy National Nuclear Security Administration under contract DE-NA-0003525. SAND2020-14131 A References V. Ramadesigan, P. W. C. Northrop, S. De, S. Santhanagopalan, R. D. Braatz, and V. R. Subramanian, J. Electrochem. Soc., 159, R31–R45 (2012). Y. Hu, S. Yurkovich, Y. Guezennec, and B. J. Yurkovich, Control Eng. Pract., 17, 1190–1201 (2009). A. P. Schmidt, M. Bitzer, Á. W. Imre, and L. Guzzella, IFAC Proc. Vol., 43, 198–203 (2010). J. C. Forman, S. J. Moura, J. L. Stein, and H. K. Fathy, in 5th Annual Dynamic Systems and Control Conference,, p. 1–8 (2012). S. Santhanagopalan, Q. Guo, and R. E. White, J. Electrochem. Soc., 154, 198–206 (2007). A. Jokar, B. Rajabloo, M. Désilets, and M. Lacroix, J. Electrochem. Soc., 163, A2876–A2886 (2016). J. Li, L. Zou, F. Tian, X. Dong, Z. Zou, and H. Yang, J. Electrochem. Soc., 163, A1646–A1652 (2016). V. Boovaragavan, S. Harinipriya, and V. R. Subramanian, J. Power Sources, 183, 361–365 (2008). V. Ramadesigan, K. Chen, N. A. Burns, V. Boovaragavan, R. D. Braatz, and V. R. Subramanian, J. Electrochem. Soc., 158, A1048–A1054 (2011). A. Subramaniam, S. Kolluri, C. D. Parke, M. Pathak, S. Santhanagopalan, and V. R. Subramanian, J. Electrochem. Soc., 167, 013534-013534–18 (2020).

The lithium-metal battery is drawing a lot of attention being among the top candidates for the next-generation batteries. This is due to the possibility of achieving high redox potential and specific capacity. While lithium plating is the key to the high specific capacity, the surface morphology deteriorates over cycles due to evolution of dendrites and dead lithium1. This results in capacity loss as well as safety risk due to the possibility of internal short-circuit caused by dendrites piercing through the separator2. Unfortunately, there is still a lack of understanding of the conditions that lead to such undesired interfacial phenomena. To understand and minimize these phenomena, it is crucial to have detailed physics-based 2D model and ability to perform robust simulations. Recently, we have provided well-defined 2D models relevant for lithium metal battery and elucidated the significance of rigorous convergence analysis3. In the present work, we will discuss the morphological evolution over cycles as predicted by the proposed 2D moving boundary model using experimentally relevant parameters and conditions. One of the goals of this work is to find experimentally relevant conditions that lead to dendritic growth and gain insights into changes in surface morphology as the cell is cycled. The model equations are obtained through rigorous mathematical formulation of the relevant physical phenomena, and lithium seed, which is observed at the early stage of lithium deposition, is considered in the initial geometry for the simulation. The geometrical parameters used are based on experimental measurements reported in the literature4. In addition to the robust simulation with in-house moving boundary model codes, COMSOL Multiphysics, a commonly used commercial solver for battery simulations, is also used and results are compared. In particular, both phase field and moving mesh methods will be compared. Effect of parameters, and the choice of algorithms will be critically analyzed. Acknowledgments This research was supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the US Department of Energy (DoE) through the Advanced Battery Materials Research Program (Battery500 Consortium). Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. References K. N. Wood, E. Kazyak, A. F. Chadwick, K. H. Chen, J. G. Zhang, K. Thornton, and N. P. Dasgupta, ACS Cent. Sci., 2, 790-801 (2016). J. Liu, Z. Bao, Y. Cui, E. Dufek, J. B. Goodenough, P. Khalifah, Q. Li, B. Liaw, P. Liu, A. Manthiram, Y. S. Meng, V. R. Subramanian, M. F. Toney, V. V. Viswanathan, M. S. Whittingham, J. Xiao, W. Xu, J. Yang, X. Yang, and J. Zhang, Nat. Energy, 14 180-186 (2019). K. Shah, A. Subramaniam, L. Mishra, T. Jang, M. Z. Bazant, R. D. Braatz, and V. R. Subramanian, J. Electrochem. Soc., 167, 133501 (2020). A. Pei, G. Zheng, F. Shi, Y. Li, and Y. Cui., Nano Lett., 17, 1132-1139 (2017).

Interdigitated Eutectic Alloy anode (IdEA) is a promising new candidate for next generation batteries due to its high specific capacity (250-300 mAh/g) [1]. Multiscale modeling approaches are essential to study such new battery chemistries. They help examine the underlying electrochemical properties and phase transitions, including the transport, kinetics and reaction schemes. In this study, we present a multiscale modeling analysis, of a Li-ion cell with a ZTB (Zn-Sn-Bi) IdEA, consisting of DFT simulation and continuum level electrochemical engineering modeling aided by experimental measurements. The DFT simulation is conducted to obtain diffusivity of the alloy anode undergoing phase changes. The electrochemical engineering model is developed based on a 1D reaction-diffusion equation and it models the kinetics and transport in the alloy anode-based battery system. Using this 1D model, a moving phase front has been observed when the eutectic alloy undergoes phase transition during charge/discharge. The cell level voltage response obtained from this model is validated with the experimental data. The practical relevance can be maximized by formulating a techno-economic model. Heligman, B.T., Kreder III, K.J. and Manthiram, A., 2019. Zn-Sn interdigitated eutectic alloy anodes with high volumetric capacity for lithium-ion batteries. Joule, 3(4), pp.1051-1063.