*4.5. E*ff*ect 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 penetration or crash. As the battery design is different for cylindrical, pouch, or coin cells with different capacities, the penetration or crash during any accident will have varying effects. In the present study, three different locations of the coin cell with penetrating element were considered. These three locations were: Center of the coin cell, middle of the radius, and edge of the coin cell. Figure 7a shows the effect of penetrating element location on the temperature profile of the coin cell. As evident, the temperature increases continuously regardless of penetrating element position. The penetrating element at the center of the coin cell showes slightly higher temperatures than on the middle of the radius and on edge of the coin cell. The results indicate that the penetrating location at the center of the coin cell is the most dangerous, because, with abrupt high heat generation, heat is accumulated at the nail penetration location due to the inability to dissipate heat quickly be means of conduction, convection, or radiation. The location of penetrating element can have varying effects on different types of commercially available LIBs. For example, for the 18650-type cylindrical cell, the penetrating position at the center of the cylinder along the height is the most dangerous case, as thermal runaway can spread to the entire cell. The penetrating element at other locations, than center, may not cover thermal runaway over the entire cell [22]. However, this is dependent on the size, shape, and design of the LIB. For the pouch-type LIB, which has a generally high ampere-hour capacity, the penetrating element at the center of the pouch cell on the flat side is very dangerous as a large amount of heat is accumulated. Additionally, if the penetrating element is near the tabs, that could lead to a large wraparound current source [16]. As in case of the coin cell, due to smaller size and capacity, the position of the penetrating element does not have much differentiating effect, indicating the batteries are prone to thermal runaway or fire hazards, irrespective of the location of the penetrating element. The maximum temperatures of 113.5, 108.7, and 107.5 ◦C are observed at the center of the coin cell, middle of the radius, and on edge of the coin cell, respectively. Figure 7b shows the voltage response of a coin cell with different penetrating element locations. The penetrating effect has minimal effect on voltage profile. The discharge cut-off voltage for all three cases reached 2.75 V at almost the same time of battery operation.

Figure 8 presents the magnitude of current density and temperature of the coin cell on the middle of the height plane and details of three different cases are presented. The vectors of current density at the central plane of the coin cell for three different cases are presented in Figure 8a,c,e. The maximum current density reaches as high as 8200 A/m<sup>2</sup> , which is an extremely high level of current concentrated at the site of penetrating element for a coin cell. The high level of flow of current occurs owing to the low resistance of the penetrating element. The arrow indicates the direction and the color indicates the magnitude of the current density vector at the central plane of the coin cell. The magnitude of the current density decreases with the distance from the penetrating element. Evidently, the temperature also decreases with the distance from the penetrating element. From Figure 8b, it can be seen that the lowest temperature is observed at the edges and this can be attributed to the availability of heat dissipation surface near the edges. The temperature contours for three different cases are presented in Figure 8b,d,f. In addition, the difference between maximum and minimum temperatures for all three cases with penetrating element are below 3.5 ◦C, owing to the compact size of the coin cell and heat spreading to the entire coin cell. Radial symmetry is observed, as shown in Figure 8a,b, for current density pattern and temperature distribution pattern, owing to the uniform temperature gradient between the center of the coin cell and the edge of the coin cell. The highest temperature is observed at the center due to the penetrating element, and the lowest temperature is observed at the edges with uniform convective heat transfer. The results of the maximum temperature profile, voltage profile, and current density profile for the coin cell with different penetrating locations show minimal variation considering the thermal behavior of the coin cell.

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**Figure 7.** (**a**) Temperature profiles for different locations of the penetrating element. (**b**) Voltage profiles for different locations of the penetrating element. **Figure 7.** (**a**) Temperature profiles for different locations of the penetrating element. (**b**) Voltage profiles for different locations of the penetrating element.

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**Figure 8.** Magnitude of current density (**a**,**c**,**e**) and temperature distribution (**b**,**d**,**f**) of the coin cell, with penetrating element diameter of 3 mm and heat transfer coefficient of 10 W/(m<sup>3</sup>K), at a discharge rate of 1C, with initial state of charge (SOC) of 100% at the center of the cell, middle of the radius, and edge of the coin cell. **Figure 8.** Magnitude of current density (**a**,**c**,**e**) and temperature distribution (**b**,**d**,**f**) of the coin cell, with penetrating element diameter of 3 mm and heat transfer coefficient of 10 W/(m3K), at a discharge rate of 1C, with initial state of charge (SOC) of 100% at the center of the cell, middle of the radius, and edge of the coin cell.

#### *4.6. Effect of the Heat Transfer Coefficient 4.6. E*ff*ect of the Heat Transfer Coe*ffi*cient*

Figure 9 shows the effect of the heat transfer co-efficient on the maximum temperature of the coin cell during the internal short circuit. As expected, the heat transfer co-efficient has a consequential effect on the maximum temperature of the coin cell. A cooling convective heat transfer coefficient of 1 W/(m2K) or less represents a condition similar to a battery packed with insulating materials, whereas 200 W/(m2K) or more indicates an effective liquid cooling situation [31]. For the case of the coin cell, the heat transfer coefficients ranging from 5 to 25 W/(m2K) are considered, which Figure 9 shows the effect of the heat transfer co-efficient on the maximum temperature of the coin cell during the internal short circuit. As expected, the heat transfer co-efficient has a consequential effect on the maximum temperature of the coin cell. A cooling convective heat transfer coefficient of 1 W/(m2K) or less represents a condition similar to a battery packed with insulating materials, whereas 200 W/(m2K) or more indicates an effective liquid cooling situation [31]. For the case of the coin cell, the heat transfer coefficients ranging from 5 to 25 W/(m2K) are considered, which are reasonable

are reasonable assumptions for partially-insulated to forced air cooling convection. The heat transfer

assumptions for partially-insulated to forced air cooling convection. The heat transfer coefficient of 10 W/(m2K) can be considered as a natural convection case. The heat dissipation term presented in Equation (7) is dependent on temperature variations of LIBs. The maximum temperature of 165.3 ◦C is observed in the case of a heat transfer coefficient of 5 W/(m2K), whereas the lowest temperature of 59.5 ◦C is observed for a heat transfer coefficient of 25 W/(m2K). The thickness of the battery plays an important role in transferring heat to the surface. For thicker batteries, the heat transfer coefficient is insignificant [31]; however, for thinner batteries, such as LIR2450 coin cells, the heat transfer coefficient has a substantial effect on the maximum temperature of the coin cell. Providing efficient cooling is useful, especially for cases of thermal abuse, as this is an effective tool to prevent thermal runaway or to reduce the effect of propagation of thermal runaway in LIBs, as previously discussed [23]. The results show that the heat transfer coefficient has a substantial effect on the thermal behavior of coin cells. presented in Equation (7) is dependent on temperature variations of LIBs. The maximum temperature of 165.3 °C is observed in the case of a heat transfer coefficient of 5 W/(m2K), whereas the lowest temperature of 59.5 °C is observed for a heat transfer coefficient of 25 W/(m2K). The thickness of the battery plays an important role in transferring heat to the surface. For thicker batteries, the heat transfer coefficient is insignificant [31]; however, for thinner batteries, such as LIR2450 coin cells, the heat transfer coefficient has a substantial effect on the maximum temperature of the coin cell. Providing efficient cooling is useful, especially for cases of thermal abuse, as this is an effective tool to prevent thermal runaway or to reduce the effect of propagation of thermal runaway in LIBs, as previously discussed [23]. The results show that the heat transfer coefficient has a substantial effect on the thermal behavior of coin cells.

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**Figure 9.** Temperature profiles for different heat transfer co-efficients. **Figure 9.** Temperature profiles for different heat transfer co-efficients.

#### *4.7. Effect of Short-Circuit Resistance 4.7. E*ff*ect of Short-Circuit Resistance*

[31].

Figure 10 shows the variation of dimensionless short-circuit heat generation rates with dimensionless internal short-circuit resistance. The dimensionless short-circuit heat generation rate is represented by Equation (14) and the dimensionless internal short resistance is represented by Equation (15). The internal resistance of the coin cell is 400 mΩ. During the internal short circuit, heat is generated due to a short circuit along with heat generation due to electrochemical reaction source and ohmic source. The total heat generation is the sum of the electrochemical heat source, ohmic heat source, and short-circuit heat source. The results from Figure 10 indicate that there is an optimum point at which the heat generation contribution from the short circuit is maximum. A similar trend was presented with the 1 Ah capacity pouch cell by Fang et al., although the values differ as the battery under consideration is different from previously studied [21]. There are few researches which focus on the increase in charge transfer resistance by using thermal runaway retardant (TRR) such as dibenzylamine [18], by using flexible separators, or by using high-viscosity protection films [31]. With decrease of internal resistance, the contribution of heat source from the short circuit increased due to a higher short-circuit current with constant contact resistance (constant size of penetrating element) Figure 10 shows the variation of dimensionless short-circuit heat generation rates with dimensionless internal short-circuit resistance. The dimensionless short-circuit heat generation rate is represented by Equation (14) and the dimensionless internal short resistance is represented by Equation (15). The internal resistance of the coin cell is 400 mΩ. During the internal short circuit, heat is generated due to a short circuit along with heat generation due to electrochemical reaction source and ohmic source. The total heat generation is the sum of the electrochemical heat source, ohmic heat source, and short-circuit heat source. The results from Figure 10 indicate that there is an optimum point at which the heat generation contribution from the short circuit is maximum. A similar trend was presented with the 1 Ah capacity pouch cell by Fang et al., although the values differ as the battery under consideration is different from previously studied [21]. There are few researches which focus on the increase in charge transfer resistance by using thermal runaway retardant (TRR) such as dibenzylamine [18], by using flexible separators, or by using high-viscosity protection films [31]. With decrease of internal resistance, the contribution of heat source from the short circuit increased due to a higher short-circuit current with constant contact resistance (constant size of penetrating element) [31].

$$\text{Dimensionless short circuit heat generation rate} = \frac{q\_{\text{short}}}{q\_{\text{ECh}} + q\_{\text{Olmic}} + q\_{\text{short}}} \tag{14}$$

$$\text{Dimensionless short circuit resistance} = \frac{R\_{\text{short}}}{R\_{\text{cell}}} \tag{15}$$

**Figure 10.** Dimensionless short-circuit heat generation rate variation with dimensionless internal short-circuit resistance. **Figure 10.** Dimensionless short-circuit heat generation rate variation with dimensionless internal short-circuit resistance.

The short-circuit resistance during the penetration can play an important role, as it can affect the extent of damage to the coin cell in the case of thermal abuse leading to thermal runaway. The shortcircuit resistance varies from 0.001 to 0.0000005 Ω and effects on the thermal behavior of coin cell is reported. A high value of short-circuit resistance can contain thermal runaway, whereas a very lowresistance value could facilitate the exothermic reactions leading to thermal runaway. Figure 11a shows the effect of various short-circuit resistances on the maximum coin cell temperature. It is evident from Figure 11a that a lower short-circuit resistance produces a high temperature, and the temperature continues increasing as the short-circuit resistance decreases. The maximum temperature of the coin cell increases to 82.9 °C as the short-circuit resistance decreases from 0.001 to 0.0000005 Ω. This thermal behavior of a large increase in temperature for lower short-circuit resistance is associated with the large flow of a short-circuit current with a low-resistance path. The variation in heat generation rates is considerably large for different short-circuit resistances, as shown in Figure 11b. The low heat generation for higher short-circuit resistance is reported, as the contribution from the short-circuit heat source is very low. In such cases, the electrochemical heat source is a dominating heat source. However, as the short-circuit resistance decreases, the shortcircuit heat source dominates over the electrochemical heat source. This is also supported from the results of Figure 10, which shows that the contribution from the short-circuit heat source to the total heat source is relatively large for low short-circuit resistances. Figure 11c shows the voltage response of a coin cell with penetrating element diameter of 3 mm and different short-circuit resistances. It is seen from the Figure 11c that as the short-circuit resistance decreases, the time to attain the discharge cutoff voltage of 2.75 V reduces. The coin cell with a short-circuit resistance of 0.001 Ω attained a discharge cut-off voltage of 2.75 V in 3420 s, whereas the coin cell with a short-circuit resistance of The short-circuit resistance during the penetration can play an important role, as it can affect the extent of damage to the coin cell in the case of thermal abuse leading to thermal runaway. The short-circuit resistance varies from 0.001 to 0.0000005 Ω and effects on the thermal behavior of coin cell is reported. A high value of short-circuit resistance can contain thermal runaway, whereas a very low-resistance value could facilitate the exothermic reactions leading to thermal runaway. Figure 11a shows the effect of various short-circuit resistances on the maximum coin cell temperature. It is evident from Figure 11a that a lower short-circuit resistance produces a high temperature, and the temperature continues increasing as the short-circuit resistance decreases. The maximum temperature of the coin cell increases to 82.9 ◦C as the short-circuit resistance decreases from 0.001 to 0.0000005 Ω. This thermal behavior of a large increase in temperature for lower short-circuit resistance is associated with the large flow of a short-circuit current with a low-resistance path. The variation in heat generation rates is considerably large for different short-circuit resistances, as shown in Figure 11b. The low heat generation for higher short-circuit resistance is reported, as the contribution from the short-circuit heat source is very low. In such cases, the electrochemical heat source is a dominating heat source. However, as the short-circuit resistance decreases, the short-circuit heat source dominates over the electrochemical heat source. This is also supported from the results of Figure 10, which shows that the contribution from the short-circuit heat source to the total heat source is relatively large for low short-circuit resistances. Figure 11c shows the voltage response of a coin cell with penetrating element diameter of 3 mm and different short-circuit resistances. It is seen from the Figure 11c that as the short-circuit resistance decreases, the time to attain the discharge cutoff voltage of 2.75 V reduces. The coin cell with a short-circuit resistance of 0.001 Ω attained a discharge cut-off voltage of 2.75 V in 3420 s, whereas the coin cell with a short-circuit resistance of 0.0000005 Ω only needed

1200 s. The results of maximum temperature, heat generation rate, and voltage profiles of the coin cell for different short-circuit resistances show that short-circuit resistance has a substantial effect on the thermal behavior of the coin cell. In addition, the findings from the present studies are useful, especially focusing on the thermal-runaway retardant (TRR) of lithium-ion batteries, as heat generation, temperature distribution, and effect of resistance could be used to evaluate the effect of TRR. *Symmetry* **2020**, *12*, x FOR PEER REVIEW 20 of 23 has a substantial effect on the thermal behavior of the coin cell. In addition, the findings from the present studies are useful, especially focusing on the thermal-runaway retardant (TRR) of lithiumion batteries, as heat generation, temperature distribution, and effect of resistance could be used to evaluate the effect of TRR.

**Figure 11.** *Cont.*

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**Figure 11.** (**a**) Temperature profiles of the coin cell for different internal short-circuit resistances. (**b**) Heat generation rate profiles of the coin cell for different internal short-circuit resistances. (**c**) Voltage profiles of the coin cell for different internal short-circuit resistances. **Figure 11.** (**a**) Temperature profiles of the coin cell for different internal short-circuit resistances. (**b**) Heat generation rate profiles of the coin cell for different internal short-circuit resistances. (**c**) Voltage profiles of the coin cell for different internal short-circuit resistances.

#### **5. Conclusions 5. Conclusions**

This study presents the thermal behavior of the LIR2450 micro coin cell battery, with capacity of 120 mAh, with internal short circuit by penetrating element. The numerical model is developed using voltage, temperature, and current characteristics from experimental study and validated within ±5.0%. The effect of the penetrating element size, the location of the penetrating element, initial state of charge, discharge rate, short-circuit resistance, and heat transfer coefficient on the maximum temperature and the heat generation rate of the coin cell are investigated. The maximum temperature and heat generation rate increased with the increase of the penetrating element size and initial state of charge, whereas it decreased with the increase of the heat transfer coefficient. The penetrating element at the center of the coin cell reached the highest temperature and heat generation rate, as compared to the penetrating element at middle of the radius or on the edge of the coin cell. The variation of dimensionless short-circuit heat generation rates with dimensionless short-circuit resistances showed an optimum point. The study provides comprehensive insights on the thermal behavior of lithium-ion cells during thermal abuse condition, with internal short circuit by penetrating element, and can be used for enhancing the design of safe lithium-ion batteries. **Author Contributions:** Conceptualization, M.-Y.L. and M.S.P.; methodology, M.-Y.L.; software, M.S.P.; This study presents the thermal behavior of the LIR2450 micro coin cell battery, with capacity of 120 mAh, with internal short circuit by penetrating element. The numerical model is developed using voltage, temperature, and current characteristics from experimental study and validated within ±5.0%. The effect of the penetrating element size, the location of the penetrating element, initial state of charge, discharge rate, short-circuit resistance, and heat transfer coefficient on the maximum temperature and the heat generation rate of the coin cell are investigated. The maximum temperature and heat generation rate increased with the increase of the penetrating element size and initial state of charge, whereas it decreased with the increase of the heat transfer coefficient. The penetrating element at the center of the coin cell reached the highest temperature and heat generation rate, as compared to the penetrating element at middle of the radius or on the edge of the coin cell. The variation of dimensionless short-circuit heat generation rates with dimensionless short-circuit resistances showed an optimum point. The study provides comprehensive insights on the thermal behavior of lithium-ion cells during thermal abuse condition, with internal short circuit by penetrating element, and can be used for enhancing the design of safe lithium-ion batteries.

M.-Y.L. and M.S.P.; resources, M.-Y.L.; data reduction, M.-Y.L., M.S.P. and J.-H.S.; writing—original draft preparation, M.-Y.L. and M.S.P.; writing—review and editing, M.-Y.L., M.S.P., J.-H.S. and N.K.; visualization, M.S.P.; supervision, M.-Y.L.; project administration, M.-Y.L.; funding acquisition, M.-Y.L. All authors have read and agreed to the published version of the manuscript. **Author Contributions:** Conceptualization, M.-Y.L. and M.S.P.; methodology, M.-Y.L.; software, M.S.P.; validation, M.-Y.L., M.S.P. and N.K.; experimental study, M.-Y.L., M.S.P. and J.-H.S.; numerical investigation, M.-Y.L. and M.S.P.; resources, M.-Y.L.; data reduction, M.-Y.L., M.S.P. and J.-H.S.; writing—original draft preparation, M.-Y.L. and M.S.P.; writing—review and editing, M.-Y.L., M.S.P., J.-H.S. and N.K.; visualization, M.S.P.; supervision, M.-Y.L.; project administration, M.-Y.L.; funding acquisition, M.-Y.L. All authors have read and agreed to the published version of the manuscript.

validation, M.-Y.L., M.S.P. and N.K.; experimental study, M.-Y.L., M.S.P. and J.-H.S.; numerical investigation,

**Funding:** This research received no external funding.

**Acknowledgments:** This work was supported by LG Yonam Foundation (of Korea).

**Conflicts of Interest:** The authors declare no conflict of interest.
