**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 TRrelated 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 cellto-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 highintensity 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/m<sup>2</sup> 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:

$$\frac{\partial c\_i}{\partial t}(\mathbf{x}, t) = d\_i \Delta c\_i(\mathbf{x}, t) + \chi\_i \mathbf{R}\_i(\mathbf{x}, t) \tag{1}$$

$$c\_{i^\*} (\mathbf{x}, \mathbf{0}) = c\_{i,0} (\mathbf{x}, \mathbf{0}), \forall \mathbf{x} \in \Omega\_i \tag{2}$$

$$c\_i(\mathbf{x}, t) = \mathbf{0}, \forall \mathbf{x} \in \partial \Omega\_i \tag{3}$$

$$Q\_i(\mathbf{x}, t) = q\_i R(\mathbf{x}, t) \tag{4}$$

$$R\_i(\varkappa, t) = A\_i c\_i(\varkappa, t) \exp\left(-\frac{E\_{a,i}}{RT(\varkappa, t)}\right) \tag{5}$$

where *i* ∈f g SEI, NS, PS, ELE , *ci*,0ð Þ *x* denotes the initial concentration, *di* for the diffusion coefficient, *γ<sup>i</sup>* for the stochiometric coefficient, *qi* for reaction enthalpy in J/ g, *Ai* for the frequency factor in 1/s, *Ea*,*<sup>i</sup>* 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

*A Critical Review on the 3D Modeling and Mitigation Strategies in the Thermal Runaway… DOI: http://dx.doi.org/10.5772/intechopen.114319*

#### **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 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.

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, highenergy-density modular designs [46]. Researchers have been relying on copper slug

calorimetry (CSC) [47–49], bomb calorimetry [50], and accelerating rate calorimetry (ARC) [51–53] 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

#### **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]).*

*A Critical Review on the 3D Modeling and Mitigation Strategies in the Thermal Runaway… DOI: http://dx.doi.org/10.5772/intechopen.114319*

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].

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.
