A Critical Review on the 3D Modeling and Mitigation Strategies in the Thermal Runaway of Single-Cell and Modular Lithium-Ion Battery Architectures

Abstract

As the adaptation of lithium (Li) ion batteries (LIBs) in energy storage systems is becoming more prevalent by the day, the issue of safe and environmentally responsible design, installation, and operation of these batteries is posing a rapidly growing challenge. It is imperative to develop realistic multi-physics and multi-scale models that are useful not only for analyzing the thermal runaway (TR) events at the single-cell level but also for modular LIB designs. This needs to be accompanied by the development of easier-to-follow empirical rules and straightforward analytical models as our knowledge of TR events grows over time. The unpredictable nature of TR events and the grave fire and explosion dangers that are particularly associated with violent TR events at the modular level require employing large-scale real-time evaluation of these events as well. Although more innovative battery health indicators are being developed and employed, it is still very challenging to arrest catastrophic TR events in time. The review herein seeks to explore advanced modeling and experimental approaches holistically. The challenges and possibilities of different active and passive thermal management strategies are also critically elaborated for LIB modular designs.

1. Introduction

In the wake of two notable thermal runaway (TR) episodes, the initial event at Boston’s Logan Airport in January 2013, where a vacant Japan Airlines 787 ignited, followed by a similar incident 9 days later in Japan, the Federal Aviation Administration (FAA) took the step of grounding the entire Dreamliner fleet. The FAA sought to ensure necessary rectifications or remedies were put in place [1]. Over the past quarter-century, lithium-ion batteries (LIBs) have emerged as the predominant choice for storing energy, finding widespread use in electric vehicles, handheld electronics, and renewable energy setups [2]. Their exceptional energy density, compact size, and scalability make them a preferred choice in modern technological advancements. As the demand for higher energy density and larger storage capacities grows, the number of individual cells within LIBs increases, leading to more complex battery systems. However, these advancements increase the risks associated with electrical, mechanical, thermal, electrochemical, or mixed-mode damages or failures in these batteries, emphasizing the critical importance of battery safety.

LIBs’ substantial energy density renders them prone to adverse conditions like elevated temperatures, mechanical impacts, overcharging, discharging, and internal short circuits. Moreover, the combustible nature of LIB structural components, comprising the outer casing, separator, and electrolyte, heightens their susceptibility. Currently, commercial LIB operation involves the migration of lithium ions between the cathode (consisting of lithium alloy and metal oxide) and the anode (comprising graphite), a process that generates heat. While this heat is typically dissipated effectively under low-rate operation, rapid charging, and discharging can lead to heat production rates surpassing dissipation rates, resulting in excessive heat accumulation and potential thermal runaway (TR), with the risk of combustion or explosions [3]. Furthermore, battery cycling contributes to capacity and performance degradation, influenced by factors like active material properties, electrolyte composition, and the solid electrolyte interface, directly influencing TR phenomena and their propagation [4, 5].

Gradually, this series of events unfolds, releasing heat in a manner that self-perpetuates and escalates beyond control. The initial release of heat is linked to the breakdown of the solid electrolyte interface (SEI), a phenomenon commonly observed at temperatures near 100°C [6]. The decomposition and regeneration of the SEI result in a continuous release of heat, elevating the internal temperature of the battery—a phase termed heat generation. Following this, the separator, typically composed of polypropylene or polyethylene, liquefies as the battery’s temperature climbs to 120–130°C. According to Joule’s law, the absence of insulation between the anode and cathode causes a short circuit, producing further heat—a phase known as heat spread. Meanwhile, the electrolyte solvent breaks down into hydrogen and hydroxide radicals, potentially initiating the electrolyte combustion process [7]. Moreover, as the cathode material deteriorates, it emits oxygen, intensifying the combustion reaction. Throughout these successive events, both temperature and internal pressure escalate due to the gas generation. Upon reaching a critical threshold, the venting cap ruptures, facilitating the release of gases and preventing case rupture and potential catastrophic events [8].

The mentioned events can vary depending on the specific chemistry of the battery. An experiment was conducted by Lei et al. [9] by using an accelerating rate calorimeter (ARC) to investigate the thermal abuse conditions of various cathode chemistries. The experiment results revealed that the onset temperature was similar across all the chemistries tested, which is around 90°C. Nonetheless, variations existed in the peak temperature, rate of temperature increase, and heat production among the batteries. Notably, the lithium-nickel-cobalt-manganese-oxide (NMC) chemistry exhibited the highest values for these parameters, followed by lithium manganese oxide (LMO) and lithium-iron-phosphate (LFP) batteries. It is essential to recognize that additional factors like state of charge (SOC), state of health (SOH), and triggers for thermal runaway (TR), such as short circuits or external heating, can also influence and alter the progression and characteristics of TR [10].

TR studies have remained oblivious to the influence of battery aging for the most part. While many studies focus on new battery chemistries or designs aiming at higher energy densities, it is also essential to understand that the safety behavior of cells can change over time. Waldmann and Mehrens conducted a study [11] on battery aging at 0°C to examine the impact of increased lithium plating and assess safety concerns using an ARC (accelerating rate calorimeter). The research outcomes highlighted that battery aging was responsible for diminished capacity and contributed to early occurrences of thermal runaway (TR), along with intensified decomposition, culminating in the ejection of the jelly roll from the cell casing. The impact of aging on TR proves intricate, as various studies have presented conflicting observations. While some researchers have documented a decline in specific safety attributes with aging, others have observed enhancements [12]. It is widely acknowledged that the processes of aging bring about changes in the characteristics of materials present within lithium-ion battery (LIB) cells [13]. Therefore, considering the influence of battery aging is crucial for a comprehensive understanding of TR behavior.

Renowned for their cylindrical design spanning 18 mm (roughly 0.71 inches) in diameter and 65 mm (approximately 2.56 inches) in length, 18,650 cells are extensively utilized across diverse sectors, including electric vehicle technology and aerospace endeavors [14]. The capacity of 18,650 cells has been progressively growing over time, with current commercially available cells achieving capacities as high as 3 Ah. However, along with increased capacity comes heightened heat and gas generation during cell failure. One particular issue revolves around the buildup of gas within the rigid casing of an 18,650 cell, essentially converting it into a pressurized container. Failure to relieve internal pressure in a controlled manner can result in violent rupture, potentially culminating in explosion. More innovative engineering solutions are necessary to address these risks and mitigate the potential for catastrophic failure [15]. Various integrated safety devices have been developed to address the potential issues related to gas buildup and pressure within 18,650 cells [16]. Among these tools are pressure relief vents, positive temperature coefficients (PTC), current-limiting switches, and current interrupt devices (CIDs). They are designed to thwart gas accumulation and, when required, effectively regulate pressure release in a secure manner.

By tradition, when evaluating the safety of LIB cells, the experimental approach is seen as the most accurate method. This means that conducting real-world tests and experiments on the batteries has been the primary way to assess their safety. It has been the go-to approach because it allows researchers to observe and measure the battery’s performance under different conditions, such as temperature extremes or high loads. However, a limited number of experiments can be done as it is expensive and time-consuming. Additionally, estimating the performance of large battery packs in a statistically sound manner poses significant challenges. Moreover, the variation in size and capacity of batteries across different applications introduces complexities in scaling up the battery systems, as certain physical phenomena become more prominent at larger scales, which are less significant in single or small battery systems [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27].

TR is a well-documented phenomenon in LIBs, which is not only equivalent to irreversible severe damage or complete failure of a LIB but also accompanied by dangerous fire risks and even explosions. It is safer to assume TR is inevitable at some point in time or under certain conditions, and all efforts must be made to ensure the battery design is not susceptible to catastrophic TR events. On top of that, TR of one cell can lead to a cascading runaway effect on neighboring cells and cause thermal or electrical damage in those cells. Even though the heat released by a single cell can be anywhere between 50 and 500 kJ, the entire energy of a pack could be one thousand times greater, and consequently, the propagation of a single point failure to the rest of the system is a daunting outcome that cannot be overlooked [28]. Capacities of modern 18,650 cells are well over 3 Ah, and it only takes ∼2 s for them to generate >6 L of an essentially flammable gas mixture during a typical TR event [29]. This is also accompanied by the release of almost 70 kJ of energy. At the same time, the surface temperature can exceed 600°C. Inadequate cooling provisions or the absence of effective pressure relief mechanisms during a thermal runaway (TR) incident can escalate the likelihood of side-wall breaches. These breaches occur when thermal melting or pressure-induced splits lead to ruptures in the casings of cells. Side-wall breaches are regarded as the most severe type of breach for the sturdy casings typically utilized in standard 18,650 cells. Breaches with flares may exert enough force to surpass heat-sink materials and disrupt or collide with neighboring cells, consequently facilitating the spread of TR from cell to cell [30, 31].

Cascading failure can be due to the propagation of a premixed flame at the single-cell level. While an insignificant reactant diffusion is expected at this level, single-cell instabilities are usually linked to thermally induced diffusion. On the other hand, the interference of gaps between the cells makes the cell-to-cell propagation unsteady, and subsequent damage initiation in other cells resembles that of ignition under external heat flux. Thermal management systems should mitigate the effects of TR and simultaneously prevent cell-to-cell propagation when batteries are stacked or packed together. Specific considerations are of paramount importance when it comes to battery design and implementation of battery thermal management systems: randomness of TR events widens the range of possible outcomes. It can be arduous to determine or predict the onset, acceleration, trigger, trigger cell peak, and neighbor cell peak temperatures. Calculating the total amount of energy released through the sides and top of the battery cell is also tricky. It is also challenging to predict the exact location of such failures (e.g., top vs. side), analyze the pressure increase, identify the type of evolving gases, and the type/trajectory of ejecta material. Different active and passive cooling systems and countermeasures against damage propagation have been developed and tested. For instance, utilizing Al and Cu barriers is a simple approach for passive thermal management, which also decreases or eliminates the risk of cascading failures. Although this phenomenon has been a subject of intense scientific scrutiny, there is still plenty of room to propose novel, safer individual cells and battery pack designs. Intelligent battery management systems (BMS), battery thermal management systems (BTMS), software controls, and modular designs are becoming more focused on the safety concerns related to TR. Although LIB is not the only type of energy storage system prone to thermal runaway, its lower runaway temperature underscores the importance of thermal management or even the implementation of fire suppression systems [32]. As energy density, size, and the number of individual cells in currently used LIBs and future designs increase, so do the magnitude and probability of risks associated with electrical, mechanical, thermal, electrochemical, or mixed-mode permanent damages or failures in these batteries.

Since the inception of the Doyle, Fuller, and Newman (DFN) pseudo-2D (P2D) model in 1994, battery simulation techniques have undergone rapid advancement. MATLAB/Simulink emerges as a predominant commercially available simulation software tool in today’s market, especially for vehicle system simulation. Prominent examples such as ADVISOR and Autonomie are developed on the MATLAB/Simulink platform. Additionally, Simcenter Amesim and GT-Suite are either utilized independently or provide specialized modules for co-simulation with MATLAB/Simulink, particularly for electronic vehicle (EV)-specific LIBs [33]. Battery Management Systems (BMSs) find widespread application across aerospace, EVs, and consumer electronics industries, equipped to handle intricate geometries and fluid dynamics aspects of heat transfer media like air or liquid cooling agents. Various computer-aided engineering (CAE) software packages such as Simcenter STAR-CCM+ and Fluent are employed to address computational fluid dynamics (CFD) challenges, particularly in BMS design, leveraging conjugate heat transfer (CHT). Multi-physics packages like Simcenter STAR-CCM+ enable complex geometry meshing and the application of diverse physics principles, including fluid dynamics/mechanics and electromagnetism, to generate high-fidelity simulations. A non-exhaustive list of frequently used commercial products for LIB design and simulation includes SIMENS, ANSYS, DASSAULT systems, Gama Technologies, COMSOL, MATLAB, LS-DYNA, Altair, Thermoanalytics, Materials Design, and OpenFOAM.

This short review has the following four main objectives: (1) bring some of the most challenging issues and overlooked phenomena that are faced in TR propagation simulation into light. (2) Pinpoint the most promising experimental and modeling strategies. (3) Compare the efficacy and suitability of recent successful simulations. (4) Shed light on the prospects of advanced TMSs as it is applicable to LIB modules. The exceptional capabilities of National Aeronautics and Space Administration’s (NASA) state-of-the-art FTRC are explained in detail. Contrary to common belief, it is hard to understand how and why a more considerable portion of the generated heat is carried by ejecta material. Some of the most important mitigation strategies in view of structural design are also covered in this work.

2. Thermal runaway at the single-cell level

Utilizing a multi-physics and multi-scale model is essential for comprehensively understanding the intricate dynamics of battery performance. Xu and Hendricks [34] developed a model of a lithium-ion battery (LIB) to investigate both its electrochemical and thermal-mechanical processes. The model’s accuracy was confirmed through comparison with experimental data obtained from large-format battery cells subjected to diverse load and boundary conditions [35]. The simulation model configuration progresses through several stages:

1. The geometry and mesh of the multi-physics models are defined.

2. The multi-physics model is formulated considering the complex interactions between different physical phenomena. Simulation conditions are then identified to replicate experiments conducted on batteries. Validation of the model takes place in the third phase, where its predictions are cross-referenced with data obtained from experiments involving overcharging and oven heating [36].

3. The model incorporates the four exothermic reactions to simulate TR events accurately.

The multi-physics model is simulated by solving a series of individual physics consecutively, and the obtained results will be passed on to the next module to account for the coupling effect. This is done to ensure that the interdependencies and interactions between different physical phenomena within the battery are appropriately accounted for. This physics focuses on different areas such as fluid dynamics, heat transfer, and solid mechanics to individually address heat generation, thermal expansion, and structural deformation.

Figure 1(a) showcases the outcome of the overcharging simulation, providing insights into the temperature distribution within the lithium-ion battery (LIB). By the end of the time-dependent simulation, specifically at 3960 seconds, the highest temperature is localized at the core of the cell, gradually diminishing toward the outer circumference.

Figure 1.

(a) Temperature distribution of the LIB in the overcharging simulation at 3960 s; (b) stress distribution and structural deformation of the LIB in the overcharging simulation at 3960 s; (c) temperature distribution of the LIB in the oven heating test without exothermic reaction at 8560 s; (d) stress distribution and structural deformation of the LIB in the oven heating test without exothermic reactions at 8550 s.

Figure 1(b) presents the simulation results under overcharging conditions, delineating the structural deformation and stress distribution within the LIB cell. At 3960 seconds, signifying the conclusion of the time-dependent simulation, stress concentration emerges along the junction between the upper and side walls of the cell, attaining its maximum intensity. Moreover, Figure 1 highlights that the upper portion of the LIB cell experiences the most pronounced deformation, in line with empirical observations. Additionally, the simulation indicates that the entire battery cell expands due to heightened internal pressure, as depicted in Figure 1.

Figure 1(c) exhibits the outcome illustrating the temperature distribution within the LIB cell, with a focus on the overheating test simulation where exothermic reactions are disregarded. At the end of the time-dependent simulation (8560 seconds), the highest temperature is observed on the outer surface of the cell, gradually decreasing toward the center. This observation aligns with the current simulation condition, wherein the external heat input originates from a heater or heat flux.

It is pertinent to acknowledge that the maximum surface temperature achieved in this simulation is 122°C, significantly lower than the experimental temperature value of 176°C. This variance is expected due to the exclusion of internal exothermic reactions in the simulation. The absence of these reactions elucidates the lower temperature recorded in the simulation compared to the empirical values.

Figure 1(d) illustrates the implications of the simulation conducted under an overheating test scenario, focusing on the structural deformation and stress distribution within the LIB cell. As illustrated, stress concentration becomes apparent along the cell wall at the conclusion of the time-dependent simulation (8550 seconds). This stress concentration likely arises from the thermal expansion of the active battery material due to the heightened temperature. In summary, the simulation suggests that increased temperature induces thermal expansion, resulting in stress concentration along the cell wall. The observations in Figure 1 indicate that elevated temperature conditions can significantly impact the structural integrity of the LIB cell.

As the temperature increases within a battery cell, it can trigger several exothermic chemical reactions. These reactions generate additional heat that accumulates inside the cell. If the heat generation rate surpasses the rate at which heat dissipates to the surroundings, TR may become inevitable once the cell reaches a critical temperature.

As thermal runaway (TR) ensues, heightened internal temperatures accelerate chemical reactions among cell components, giving rise to potential hazards including leakage, smoke emission, gas venting, and the initiation or propagation of flames. The unchecked progression of TR ultimately threatens the integrity of battery cells. Thus, it is imperative to comprehend and address the risks inherent in TR to uphold the secure functioning of battery systems. This study considered four specific exothermic reactions [37].

1. Solid Electrolyte Interface (SEI) decomposition reaction: The SEI layer, which forms on the surface of electrodes, is known to be metastable. At temperatures ranging from 90 to 120°C, the SEI layer can undergo an exothermic decomposition reaction.

2. Negative-Solvent reaction (NS): Involving the interaction between intercalated lithium within the negative electrode and the electrolyte, this reaction unfolds at temperatures above 120°C.

3. Positive-Solvent reaction (PS): At even higher temperatures, typically above 170°C, the positive active material in the battery can undergo a chemical reduction reaction with the electrolyte. This reaction is referred to as the positive-solvent reaction.

4. Electrolyte Decomposition reaction (ELE): The exothermic decomposition of electrolyte unfolds when the temperature goes beyond 200°C.

By considering these four exothermic reactions, the study aimed to understand their impact on the thermal behavior and potential for TR in the battery system [38] (Table 1).

x ɛ {SEI, NS, PS, ELE}, y ɛ {c, p, e}	Reaction Heat Hx/[J/kg]	Frequency Factor Ax/[l/s]	Activation Energy EA/[J/mol]	Volume Content Wy/[kg/m^3]
SEI reaction	2.57*10^5	1.667*10^15	1.3508*10^5	1.39*10^3
NS reaction	1.714*10^6	2.5*10^13	1.3508*10^5	1.39*10^3
PS reaction	3.14*10^5	6.667*10^13	1.396*10^5	1.3*10^3
ELE reaction	1.55*10^5	5.14*10^13	2.74*10^5	5*10^2

Table 1.

Presents the parameters used to calculate the reactions [38].

The temperature distribution is depicted in Figure 2, considering the exothermic reactions within the LIB. As a result of the increased internal temperature, these exothermic reactions are triggered. Consequently, the temperature profile displayed in Figure 2 shows a distinct and noteworthy pattern that differs significantly from that observed in Figure 2. Exothermic reactions notably impact the temperature distribution within the battery cell.

Figure 2.

Temperature distribution in the oven heating test (with exothermic reactions) of the LIB.

Figure 3 represents the surface temperature change over time, showing significant insights. Initially, the surface temperature gradually increases due to ohmic heating during charging and discharging cycles. However, a distinct change occurs around 7500 s, when the temperature curve rises sharply, reaching approximately 90°C. This temperature rise indicates the onset of self-heating.

Figure 3.

Surface temperature of the LIB cell with time and TR occurrence.

As the temperature exceeds 120°C, the temperature increase becomes exponential, indicating the existence of TR. Notably, the simulation results agree with the findings from destructive tests, where self-heating was observed around 110°C, and the surface temperature reached values of 170–180°C. These results also align well with experimental measurements, precisely with the recorded temperature of 176°C. Additionally, the simulation captures the time trend observed in the experimental results.

Leveraging advanced modeling tools and methodologies, their research has effectively encapsulated the electrochemical and thermal-mechanical intricacies of large-scale LIBs. These numerical simulations have deepened the understanding of failure mechanisms, empowered thorough risk assessment, and facilitated the formulation of robust safety measures for LIBs. The adoption of such modeling tools stands as a cornerstone in fortifying battery safety protocols and preemptively addressing potential risks.

3. Thermal runaway at the modular level

A survey of pertinent literature shows most of the previous studies were dedicated to the TR behavior of various single-cell designs with different chemistries [39, 40]. As mentioned, TR at this level includes events such as the evolution of battery gases or fumes, ejection of cell contents, abnormally high-temperature rise, and occasionally self-ignition of the cell or ejecta material. In contrast, damage propagation in more extensive complex systems has not received the same level of attention. Although TR-related failure of a single cell may not affect the overall safety or performance of a battery module in some cases, violent thermal and electrical behavior of one cell may affect the neighboring cells, resulting in a cascading TR effect. This can potentially lead to a domino effect in the thermal failure propagation, which continues to propagate until it engulfs the entire battery pack. A rapid catastrophic release of energy within the confines of a battery module under this worst-case scenario situation may give rise to substantial damage and pose severe threats to the operator or consumer. According to Spotnitz et al. [41], the likelihood of such failures in a modular design is influenced not only by an individual cell’s abuse response but also by the overall cell-to-cell insulation strategy within the battery module. They pointed out that insufficient or lack of insulation between adjacent cells increases the likelihood of thermal failure propagation. On the other hand, the electrical configuration of the battery module may also play a crucial role in how these failures propagate. Offer et al. [42] analyzed how the local temperature of individual cells is affected by the fluctuation of ohmic resistances between them. Blocks and discharge diodes are usually utilized to avoid self-discharge of the entire module through a shorted cell [43, 44]. Thermal isolation between cells is usually inadequate from the failure prevention perspective. Prismatic and pouch cells are typically stacked next to each other either with no gap or separated by cooling thin plates [45]. Electrical connections can also act as additional heat transfer pathways between cells [38]. Most existing fault detection and damage prevention strategies are based on electrical diagnosis and countermeasures. Innovative fault detection methods and battery health indicators must go beyond the traditional cell temperature and voltage monitoring. There is usually a noticeable lag between these traditional battery health indicators and TR initiation, which will not allow us to arrest an ongoing TR event soon enough. Various failure propagation testing methods have been developed to induce failure deliberately, and these will impart varying levels of energy. Among the most important ones are nail penetration testing, single-cell thermal ramp, single-cell overcharge, and TR initiation under high-intensity laser or light beams.

In their study, Xu and Hendricks constructed two distinct 3D multi-physics models using COMSOL Multi-physics, specifically tailored for an 18,650 lithium-ion battery (LIB) affixed to a G10 board [34]. One model was established as the benchmark dataset to validate experimental observations. Conversely, the second model introduced a setup with two identical batteries positioned side by side, with one cell housing a heater atop. The former model facilitated a comprehensive parametric analysis spanning various heating power inputs, aiming to discern the relationship between heating power and thermal runaway (TR). Meanwhile, the latter model was deployed to explore the repercussions of a TR event in one cell on its adjacent counterpart. They extended the second model to include thermal radiation heat transfer and investigated its effect in a battery module. They assumed the heater output changes linearly with temperature (0 to 50 W over 3000 s). Regarding boundary and ambient conditions, the entire setup was subject to natural convection with an average heat transfer coefficient of 5 W/m² K. Their models included four commonly observed types of exothermic reactions, namely SEI decomposition reaction (at 90–120°C), NS reaction (>120°C), PS reaction (> 170°C), and ELE reaction (> 200°C). To account for the generated heat through exothermic reactions, they relied on the following governing equations for the concentration gradient while assuming Arrhenius-law is applicable for the computation of exothermic heat sources:

$$\frac{\partial c_i}{\partial t}\left(x,t\right)=d_i\mathrm{\Delta }{c}_i\left(x,t\right)+{\gamma }_i{R}_i\left(x,t\right)$$E1

$$c_i\left(x,0\right)=c_{i,0}\left(x,0\right),\forall x\in {\mathrm{\Omega }}_i$$E2

$$c_i\left(x,t\right)=0,\forall x\in \partial {\mathrm{\Omega }}_i$$E3

$$Q_i\left(x,t\right)=q_{i}R\left(x,t\right)$$E4

$$R_i\left(x,t\right)=A_i{c}_i\left(x,t\right)exp\left(-\frac{E_{a,i}}{\mathit{RT}\left(x,t\right)}\right)$$E5

where $i\in \left\{\mathrm{SEI},\mathrm{NS},\mathrm{PS},\mathrm{ELE}\right\}$, $c_{i,0}\left(x\right)$ denotes the initial concentration, $d_i$ for the diffusion coefficient, ${\gamma }_i$ for the stochiometric coefficient, $q_i$ for reaction enthalpy in J/g, $A_i$ for the frequency factor in 1/s, $E_{a,i}$ for the activation energy in J/mol, and R for the universal gas constant. While the simulation results based on the first model accord well with the experimental results at the single-cell level, the simulation results in the second model point to an even more important conclusion. They reported that including the radiation heat transfer effect drastically changes the results at the end of the simulation. As illustrated in Figure 4(a), the region with the greatest temperature is observed in close proximity to the heater and the battery it is connected to, with the neighboring cell also experiencing heightened temperatures. They noticed that surface temperature increases gradually over time when the model takes the radiation effect into account (Figure 4(b)), while there is an abrupt temperature rise when this effect is neglected (Figure 4(d)). This was attributed to the exponential increase of radiation with temperature, which is at the order of 4 according to Boltzmann’s equation. While the LIB cell temperature exceeds 500°C at 3800 s without radiation (Figure 4(a)), it almost takes 4400 s for the LIB cell temperature to exceed the same temperature with radiation (Figure 4(c)). Of crucial importance is that now the G10 board and the surrounding areas also experience a more elevated temperature with the inclusion of the radiation effect (Figure 4(c) vs. Figure 4(a)). This seems to be a more realistic simulation and beneficial to risk assessment and mitigation in the safety management of modular battery designs.

Figure 4.

(a) Temperature profile of the battery module at t = 3682 s disregarding the effect of radiation, (b) evolution of the surface temperature of the battery over time in the second model with radiation, and (c) 3D temperature profile of the battery module at t = 4400 s with [35].

The National Aeronautics and Space Administration (NASA) Johnson Space Center (JSC) has set forth Crewed Space Vehicle Battery Requirements (JSC-20793-RevD), as is relevant to human space exploration, to ensure TR severity and cell-to-cell propagation tendencies are meticulously evaluated. One of the most pressing issues is maintaining a reasonable trade-off between rigorous requirements (as in JSC-20793-RevD) and the ever-expanding need for compact, high-energy-density modular designs [46]. Researchers have been relying on copper slug calorimetry (CSC) [47, 48, 49], bomb calorimetry [50], and accelerating rate calorimetry (ARC) [51, 52, 53] methods to characterize TR events in LIBs. None of these methods can discern the portion of the total energy released through the cell casing from that of the ejected materials. In contrast, NASA’s new calorimeter is meticulously designed to test many cells in a short span of time, which is on the order of 10 tests per day. The rationale behind investing in such a vast undertaking is that no two TR events are the same. Hence, it is critical to characterize enough number of like cells to ensure as many unpredictability factors are considered as possible. NASA’s FTRC is equipped with the following: (1) X-ray imaging and in situ X-ray computed tomography, (2) gas collectors and velocity measurement features, (3) high-flux heater induced thermal runaway, (4) nail penetration testing, and (5) general portability.

Using NASA’s state-of-the-art FTRC analyses, researchers could not only estimate the entire energy released during a TR event but also distinguish between the portion of the total energy released through cell casing and the part that belongs to ejecta material [54]. The following four commercially available LIBs were tested in this study: LG 18650-MJ1, LG 18650 Test Cell, Samsung 18,650-30Q, and MOLiCEL® 18,650-J. The impacts of essential factors such as separator material, bottom venting, internal short-circuiting (ISC), casing thickness, bottom rupture, and mass loss in post-TR conditions were all considered in this work. No similar research was conducted to differentiate between ejected and non-ejected materials contributions in heat generation, or at least not as detailed as a handful of FTRC-related publications from NASA. They found that between 20 and 30% of total energy is released through the casing breaches, whereas the heftier rest is released through ejecta particulates and gases. Most modular LIB designs are engineered regardless of the cells’ susceptibility to eject their content violently and the amount of energy released by these violent ejections. Besides that, modeling community has also been reluctant to bring these aspects to light. From a statistical perspective, one of their significant findings was that variation of total energy release mostly follows a lognormal distribution. Moreover, they noted that high-energy cells are more likely to become unpredictable and exhibit violent ejections. As indicated in Figure 5, the LG 18650-MJ1 exhibited the highest median value predicted at 74.9 kJ and the highest overall value observed at 82.9 kJ. Conversely, the MOLiCEL® 18,650-J, possessing the lowest nominal capacity and electrochemical energy when fully charged, displayed the lowest median values predicted at 35.3 kJ regardless of separator material and 38.7 kJ depending on the separator material, alongside the lowest overall observed value at 31.3 kJ. Even though the total energy release was found to have a strong relationship with the stored electrochemical energy, it was hard to claim it is a perfect linear relationship. Yet another important finding was that bottom venting (BV) may alleviate the severity of TR events and let them behave more predictably. The occurrence of BV not only lowered the heat generation by ∼3.9 KJ but also led to a minor mass loss in post-TR condition (6.5 g). When less material is ejected, less material is also available to burn. Besides that, bottom rupture (BR) was found to have a similar effect on the energy release (∼2.6 KJ less for LG 18650-MJ1 cells with BR), but not quite as large as the BV effect either [55].

Figure 5.

Variations of pre-and post-test cell masses next to the estimated ejected mass (difference between pre-and post-mass) along with the corresponding average total TR energy yield (printed with permission from [54]).

In a research conducted by Hoelle et al. on prismatic LIBs, modeling approaches have further evolved to consider more possible phenomena, such as the formation of a gas layer between roll and surrounding can, which was attributed to the electrolyte vaporization (>60 Ah) [56]. They emphasized that mass loss, can bulging, and electrolyte vaporization phenomena should be accounted for.

4. Thermal management at the modular level

Crafting an effective thermal management system (TMS) capable of upholding lithium-ion battery (LIB) modules within designated safe temperature thresholds is imperative. Modern TMS implementations offer a means to mitigate the hazards linked to catastrophic thermal runaway (TR) incidents. Despite its straightforwardness, the efficacy of air-cooling mechanisms is hindered by air’s low heat capacity and thermal conductivity. This diminishes heat transfer rate from the battery to the air medium. Given air’s limited heat dissipation capabilities, achieving efficient air cooling necessitates substantial airflow volume and mixing rates to counterbalance these inherent limitations. Moreover, specific applications, such as those in space exploration, lack access to air altogether. Consequently, for larger LIB modules operating under high discharge rates, active liquid cooling emerges as a more efficient alternative. Liquid coolants circulate through a thermally conductive metal plate, typically equipped with micro- or macro-channels to augment heat transfer rates. In mitigating the potential hazards associated with liquid cooling, heat pipes are considered a safer option for extracting excess heat from the battery and directing it toward a heat sink [57, 58, 59]. Heat pipes are becoming widely adopted in electronic cooling applications owing to their small form factor and exceptional thermal conductivity. Similarly, phase change material (PCM) has surfaced as a novel solution within today’s thermal management systems (TMSs) [60, 61, 62]. The greatest appeal for implementing PCM is that cell temperature is curbed within a safe, narrow temperature range, which is dictated by the PCM’s melting point temperature. Despite this, the PCM system encounters challenges due to its limited thermal conductivity, hindering the efficient dissipation of stored heat. However, utilizing enhanced PCMs like graphene-infused PCM variants could offer a potential solution to overcome this obstacle [63, 64].

One good example of modeling thermal control is the research led by Basu et al. in which they used the capabilities of STAR-CCM+ [65]. By leveraging lateral water coolant channels and harnessing the exceptional heat conductivity of aluminum components, they not only achieved the requisite structural reinforcement but also ensured effective heat exchange between the coolant and water. As illustrated in Figure 6, their lithium-ion battery (LIB) module comprised 30 Li-NCA/C, 18650-sized cells (6S5P), with the initial row of parallel cells meshed using 400,000 polyhedral cells. Utilizing Battery Design Studio (BDS), they developed a model of the 18,650-sized cell, while the P2D DFN model was deployed for electrochemical aspects and current collector discretization. The CAD design of the cooling system, alongside the geometry generated by BDS, served as inputs for STAR-CCM+. This software facilitated the integration of the electrical mesh, electrochemical elements, and polyhedral mesh. Experimental validation was conducted to assess the model’s accuracy in predicting cell temperature profiles, enabling an analysis of the effects of coolant flow rate, contact resistance between LIB cells and cooling elements, and discharge rate. Their compact thermal management system (TMS) successfully limited temperature elevation to within 7 K under high discharge and low coolant flow rates. This endeavor serves as a proof of concept for reliable simulation of a battery TMS, boasting an efficacy level exceeding 90%. Similar methodologies hold potential for streamlined onboard TMSs, promising reduced sensor reliance and simplified control systems.

Figure 6.

(a) Battery module along with its integrated cooling system, and (b) the mesh generated by STAR-CCM+ (b). (Printed with permission from [65]. Copyright 2016, Elsevier).

Table 2 provides a non-exhaustive list of the existing TR propagation simulation strategies. It is common practice to take advantage of Arrhenius type of equations to at least account for the four common reactions during a TR event. Advanced studies consider additional type of reactions and other additional terms such as the ones associated with the electrochemical heat source and joule heating. The higher the number of these additional reactions or terms, the higher the level of complexity and computational cost. This can be a significant barrier to their suitability for larger modular designs. Implementation of empirical heat source terms is seen as step toward simplification, which can be in the form of time- or temperature-dependent terms or some constants.

Author(s)	Modeling approach				Setup
	Type	# of source terms
		Chemical	Electrochemical	Joule heat (ISC)	Dimensions	Solver	# of cells	Design
Shen et al. [66]	Arrhenius	4	_	_	1D	LEM	6	Prismatic
Feng et al. [67]	Arrhenius	6	_	1	1D	LEM	6	Prismatic
Xu et al. [68]	Arrhenius	1 eq. fitted to ARC data			1D	ROM	4,18&3x18	Prismatic
Feng et al. [67]	Arrhenius	1 eq. fitted to ARC data + Joule heat (ISC)			3D	FEM	6	Prismatic
Citarella et al. [69]	Empirical	Temp. dependent on HRR fitted to ARC data			3D	FVM	2x12	Prismatic
Yuan et al. [70]	Arrhenius	4	_	1	3D	FVM	11	Cylindrical
Vyroubal et al. [71]	Arrhenius	4	_	_	3D	FVM	4x10	Cylindrical
Jia et al. [72]	Arrhenius	4	1	1	1D	LEM	2&9	Cylindrical
Li et al. [73]	Arrhenius	4	_	_	3D	FEM + FVM	192	Cylindrical
Jindal et al. [74]	Arrhenius	4	Full model	_	3D	FVM	10	Cylindrical
Mishra et al. [75]	Arrhenius	4	_	_	3D	FVM	25	Cylindrical
Mishra et al. [76]	Arrhenius	4	_	_	3D	FVM	25	Cylindrical
Mishra et al. [77]	Arrhenius	4	_	_	3D	FVM	25	Cylindrical
Liu et al. [78]	Arrhenius	1 eq. fitted to experimental data			3D	FEM	6	Cylindrical
Qin et al. [79]	Empirical	Temp. dependent heat release rate (ARC data)			3D	FVM	9	Cylindrical
Grimmeisen et al. [80]	Empirical	Const. heat release rate			3D	FVM	7	Cylindrical
Coman et al. [81]	Empirical	Time-dependent function for HRR			2D	FEM	48	Cylindrical
Bugryniec et al. [82]	Arrhenius	4	_	_	2D	FEM	9	Cylindrical
Coman et al. [83]	Arrhenius	3	1	_	2D & 3D	FEM	65	Cylindrical
Yikai et al. [72]	Arrhenius	3	_	1	3D	FEM	2	Cylindrical
Zhang et al. [84]	Arrhenius	4	1	_	3D	FEM	2	Pouch
Chen et al. [85]	Arrhenius	6	_	_	1D	LEM	2	Pouch
Kurzawski et al. [28]	Arrhenius	3	1	_	Quasi 1D	FEM	5	Pouch
Bilyaz et al. [86]	Other	Laminar Propagation Theory with 1 reaction			1D	FDM	5&10	Pouch

Table 2.

A non-exhaustive list of empirical and modeling approaches for the heat release during TR in LIB modules.

*

ISC denotes internal short circuit, ARC is accelerating rate calorimetry, HRR is heat release rate, LEM means lumped element method, FEM means finite element method, FVM means finite volume method, ROM means reduced order model), and FDM means finite difference method.

5. Conclusion

The development of accurate models to simulate thermal runaway (TR) events with minimal computational resources, particularly in modular setups susceptible to cascading TR failures, is still evolving. Current TR simulation methodologies are highly valued for their ability to examine the electro-thermal characteristics of lithium-ion batteries (LIBs) during abusive scenarios, irrespective of TMS implementation. The introduction of faults into the simulation model enables the validation of results using measurements derived from previous testing. Despite numerous efforts in this field, TR assessment is still limited to specific cell designs and chemistries, and overgeneralization of obtained results can be misleading. The exact behavior of ejecta material and the diversity of possible mechanical failure modes during TR propagation are abstruse aspects that merit special attention. It is safer to assume TR is inevitable and has specific design criteria rather than waiting for failure analysis results. Traditional battery health indicators are helpful but not fast enough to arrest catastrophic TR events in time. For larger modules, smart TMSs and even fire suppression systems could be other worthwhile investments in the long run. Nonuniformity of temperature distribution across the single cells and over the module is also another research avenue that deserves to be investigated at greater depth. Metal additive manufacturing can be used to design more efficient active or passive cooling systems with complex geometries and reduced weights. More advanced statistical analyses and predictive models are needed to propose more innovative modular designs.