*4.3. E*ff*ect of Penetarting Element Size*

In LIBs, the electrodes are separated by a thin separator. The separator prevents the direct contact of electrodes. The electrodes and electrolytes are tightly packed, as in the case of the LIR2450 coin cell, by positive and negative caps. The generally-used polymer separator has safety issues when combined with high-density and high-capacity LIBs, because, during internal short circuit by penetration or crash, the separator shrinks in volume due to heat, making the direct contact of electrodes possible, which is a dangerous scenario [29]. The effect of different shapes of penetrating element on thermal behavior have been studied previously with ellipsoid, flat, cone, and sphere shapes [6]. In the current study, a cylindrical penetrating element in the battery active material (electrodes and electrolytes) with different sizes were considered. The penetrating element with diameters of 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, and 3.5 mm were considered. During the operation of battery with penetrating element, the electrodes come into contact due to deformation and, subsequently, joule heat is produced at a very high rate. The heat is transferred from the point of penetration to the whole battery by conduction, and then to the outside by convection and radiation. In some cases, the high temperature activates the chemical reactions leading to exothermic behavior, and the cell components, including electrolyte and electrode, explode either from penetrating location or safety valve with flames [5]. The nail penetration tests are characterized by a localized hotspot and the propagation of heat to the whole battery through conduction [30]. Figure 5a shows the effect of the penetrating element size on the maximum coin cell temperature. It is evident from Figure 5a that a large penetrating element produces higher temperatures, and temperature continues increasing as the penetrating element size increases. The maximum temperature of the coin cell increases by 103 ◦C as the penetrating element diameter was increases from 0.5 to 3.5 mm. This thermal behavior, of a large increase in temperature for higher penetrating element size, is associated with a large short-circuit area occurring during internal short circuit, leading to a large cross-sectional area available for the flow of secondary current that developed due to the short circuit (i.e., the short-circuit current is proportional to the square of the penetrating element radius) [6]. In addition, a large penetrating element leads to a considerable reaction force and a high-buckling displacement [6]. The thermal behavior due to accumulated heat with penetrating element is closely related to battery internal resistance and contact resistance, which is a direct function of penetrating element size (i.e., diameter) [31].

The heat generation rate increases rapidly at the start due to the internal short circuit for all the cases of different diameters of penetrating element. The total heat generation rate is comprised of heat due to ohmic source, heat due to electrochemical reaction source, and heat due to short-circuit source. As the diameter of the penetrating element decreases, the heat due to the short circuit decreases, as shown in Figure 5b. As the diameter of the penetrating element increases, the contribution of heat due to the short circuit increases. The maximum total volumetric heat generation rate of 636,744.6 W/m<sup>3</sup> is recorded for the penetrating element with diameter of 3.5 mm, whereas the maximum total heat generation rate of 57,784.6 W/m<sup>3</sup> is recorded for diameter of 0.5 mm. Figure 5c shows the voltage response of a coin cell with different penetrating element sizes. It is seen from Figure 5c that as the penetrating diameter increases, from 0.5 to 3.5 mm, the time to attain the discharge cutoff voltage of 2.75 V reduces. The coin cell with the penetrating element of 0.5 mm diameter attained a discharge cut-off voltage of 2.75 V in 3270 s, whereas, for the penetrating element diameter of 3.5 mm only 780 s was needed. The results of maximum temperature, heat generation rate, and voltage profiles of the coin cell for different penetrating element diameters show that penetrating element size has a substantial effect on the thermal behavior of a coin cell.

(**a**)

**Figure 5.** *Cont.*

**Figure 5.** (**a**) Temperature profiles of the coin cell for different penetrating element sizes. (**b**) Heat generation rate profiles of the coin cell for different penetrating element sizes. (**c**) Voltage profiles of the coin cell for different penetrating element sizes. **Figure 5.** (**a**) Temperature profiles of the coin cell for different penetrating element sizes. (**b**) Heat generation rate profiles of the coin cell for different penetrating element sizes. (**c**) Voltage profiles of the coin cell for different penetrating element sizes.

(**c**)

#### *4.4. Effect of Initial State of Charge 4.4. E*ff*ect of Initial State of Charge*

The state of charge is an indicator of usable energy available compared to maximum rated usable energy. Figure 6a shows the effect of initial state of charge (SOC) on the maximum temperature of the coin cell. The maximum temperature of the coin cell increased with the increase in the initial SOC of the coin cell. Although temperature increased continuously for all SOC levels, the cases with high initial SOC levels showed high temperatures owing to stable high currents for sufficiently long periods [6]. Moreover, the rate of increase of temperature is slightly higher for low SOC level, because the available energy depleted quickly in the case of low SOC levels. The maximum and minimum temperatures of 113.5 and 67.7 °C are observed for 100% and 40% SOC levels, respectively. Similarly, the continuous heat generation rate is maintained for long periods with higher SOCs leading to higher temperatures, as shown in Figure 6b. The characteristic rapid rise of the heat generation rate at the start is observed for all cases of SOCs. The maximum and minimum total heat generation rates of 472707.2 and 340656.4 W/m3 are observed for 100% and 40% SOC levels, respectively. The results of various SOCs show that the thermal runaway temperature attainment is strongly dependent on the SOC level. The results support the findings of Cai et al., which showed that chances of partiallycharged LIBs (at 50% SOC or lower) to attain thermal runaway temperatures are rare during mechanical abuse [32]. The maximum temperature decreases as the SOC decreases. On the other hand, more energy is produced for higher SOC levels, as visible for the area below the heat generation curve shown in Figure 6a [31]. The thermal stability of LIB components is strongly dependent on SOC levels [33]. LIBs operate based on the intercalation–deintercalation phenomenon, in which lithiumion occupies porous structures of cathodes or anodes during charging–discharging. As the level of lithiation in negative electrodes increases, more lithium-ions are available for reactions that are exothermic in nature [34]. The exothermic reactions involving cathodes and electrolytes increase heat generation linearly with the increase in the SOC level, which indicates that SOC levels can play an The state of charge is an indicator of usable energy available compared to maximum rated usable energy. Figure 6a shows the effect of initial state of charge (SOC) on the maximum temperature of the coin cell. The maximum temperature of the coin cell increased with the increase in the initial SOC of the coin cell. Although temperature increased continuously for all SOC levels, the cases with high initial SOC levels showed high temperatures owing to stable high currents for sufficiently long periods [6]. Moreover, the rate of increase of temperature is slightly higher for low SOC level, because the available energy depleted quickly in the case of low SOC levels. The maximum and minimum temperatures of 113.5 and 67.7 ◦C are observed for 100% and 40% SOC levels, respectively. Similarly, the continuous heat generation rate is maintained for long periods with higher SOCs leading to higher temperatures, as shown in Figure 6b. The characteristic rapid rise of the heat generation rate at the start is observed for all cases of SOCs. The maximum and minimum total heat generation rates of 472,707.2 and 340,656.4 W/m<sup>3</sup> are observed for 100% and 40% SOC levels, respectively. The results of various SOCs show that the thermal runaway temperature attainment is strongly dependent on the SOC level. The results support the findings of Cai et al., which showed that chances of partially-charged LIBs (at 50% SOC or lower) to attain thermal runaway temperatures are rare during mechanical abuse [32]. The maximum temperature decreases as the SOC decreases. On the other hand, more energy is produced for higher SOC levels, as visible for the area below the heat generation curve shown in Figure 6a [31]. The thermal stability of LIB components is strongly dependent on SOC levels [33]. LIBs operate based on the intercalation–deintercalation phenomenon, in which lithium-ion occupies porous structures of cathodes or anodes during charging–discharging. As the level of lithiation in negative electrodes increases, more lithium-ions are available for reactions that are exothermic in nature [34]. The exothermic reactions involving cathodes and electrolytes increase heat generation linearly with the increase in the SOC level, which indicates that SOC levels can play an important role in the event

of thermal runaway. This is experimentally shown by Mao et al., where batteries with 100% SOC were burnt owing to thermal runaway, and low SOC level batteries with 0% and 50% were not burnt [22]. batteries with 100% SOC were burnt owing to thermal runaway, and low SOC level batteries with 0% and 50% were not burnt [22]. Besides this, other parameters, including battery type, battery design, components of active

*Symmetry* **2020**, *12*, x FOR PEER REVIEW 13 of 23

important role in the event of thermal runaway. This is experimentally shown by Mao et al., where

Besides this, other parameters, including battery type, battery design, components of active battery material, battery shape, and size of battery, are key important factors that can affect the thermal behavior of LIBs. Therefore, the SOC level effect with penetrating element on the thermal behavior of LIBs is very specific, and may have different results (with above suggested parameters) for different batteries. In addition, the temperature non-uniformity is dependent on the size of the battery under consideration. In the present study, due to the compact size of the coin cell, the temperature non-uniformity study is not considerably relevant. The initial rise of the heat generation rate is maximum for 100% SOC and decreases as the SOC level decreases. Zao et al. discussed practical ways to prevent thermal runaway, and ruled out the decrease of SOC as a practical option to prevent thermal runaway in the case of nail penetration [31]. However, this strategy can be used for aircraft "cargo-only" transportation of batteries, where SOC should be kept at less than 30% to prevent thermal runaway [35]. Figure 6c shows the voltage response of the coin cell for different SOC levels. For different SOC levels, the initial voltage is different [9]. For low SOC, the capacity depletes soon after the stable current is established, with the attainment of a discharge cut-off voltage of 2.75 V. This results in a relatively less heat generation rate, leading to a comparatively low temperature. The voltage curve trends are the same for all the cases of SOC, as all other parameters are kept constant except SOC. The present model did not consider the discussions on thermal runaway behavior for temperatures exceeding 128 ◦C, as thermal runaway behavior including material decomposition is not included in the present study [6,36]. The results of maximum temperature, heat generation rate, and voltage profile of the coin cell for different SOC levels show that the initial SOC level has a substantial effect on the thermal behavior of the coin cell. battery material, battery shape, and size of battery, are key important factors that can affect the thermal behavior of LIBs. Therefore, the SOC level effect with penetrating element on the thermal behavior of LIBs is very specific, and may have different results (with above suggested parameters) for different batteries. In addition, the temperature non-uniformity is dependent on the size of the battery under consideration. In the present study, due to the compact size of the coin cell, the temperature non-uniformity study is not considerably relevant. The initial rise of the heat generation rate is maximum for 100% SOC and decreases as the SOC level decreases. Zao et al. discussed practical ways to prevent thermal runaway, and ruled out the decrease of SOC as a practical option to prevent thermal runaway in the case of nail penetration [31]. However, this strategy can be used for aircraft "cargo-only" transportation of batteries, where SOC should be kept at less than 30% to prevent thermal runaway [35]. Figure 6c shows the voltage response of the coin cell for different SOC levels. For different SOC levels, the initial voltage is different [9]. For low SOC, the capacity depletes soon after the stable current is established, with the attainment of a discharge cut-off voltage of 2.75 V. This results in a relatively less heat generation rate, leading to a comparatively low temperature. The voltage curve trends are the same for all the cases of SOC, as all other parameters are kept constant except SOC. The present model did not consider the discussions on thermal runaway behavior for temperatures exceeding 128 °C, as thermal runaway behavior including material decomposition is not included in the present study [6,36]. The results of maximum temperature, heat generation rate, and voltage profile of the coin cell for different SOC levels show that the initial SOC level has a substantial effect on the thermal behavior of the coin cell.

**Figure 6.** *Cont.*

**Figure 6.** (**a**) Temperature profiles of the coin cell for different levels of initial state of charge. (**b**) Heat generation rate profiles of the coin cell for different levels of initial state of charge. (**c**) Voltage profiles of the coin cell for different levels of initial state of charge. **Figure 6.** (**a**) Temperature profiles of the coin cell for different levels of initial state of charge. (**b**) Heat generation rate profiles of the coin cell for different levels of initial state of charge. (**c**) Voltage profiles of the coin cell for different levels of initial state of charge.

*4.5. Effect of the Location of the Penetrating Element*

The location of the penetrating element can have different effects on different types of batteries. In case of accidents, it is unpredictable as to how and where the battery will be impacted in terms of
