Passive Mitigation of Cascading Propagation in Multi-Cell Lithium Ion Batteries

Propagation through pouch cell stacks is first investigated with a group of cells at 100% SOC without the inclusion of metallic plates to establish a baseline for the heat transfer between cells and to identify an analysis approach for other configurations. Thermocouple measurements between each cell or between outer cells and cement-boards are shown in Fig. 2 along with cell voltages. The results show a rapid propagation of thermal runaway after the initial nail penetration with the entire five cell string consumed within ∼90 s. The thermocouple-measured peak temperatures, when averaged across the thermocouples located between the cells (2–4), is 650 °C. Temperatures measured at the edges of cell 1 and cell 5 are lower than the temperatures across the remainder of the stack, indicating heat losses through the cement board are not negligible. The severity of failure is in line with what has previously been observed in propagation tests.^13–17

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The baseline propagation shown in Fig. 2 is used to develop an analysis approach across various thermal configurations. To simplify the discussion, we will orient the analysis so that the initial nail penetration is on the left side and the thermal runaway evolves from left to right. Thermocouples measure heating from the failed cell and then, if thermal runaway propagates, heating from the right is observed when the next cell undergoes thermal runaway. For example, the thermocouple between cells 1 and 2 (C1-C2) in Fig. 2 shows rapid heating at ∼10 s coming from the nail-induced short circuit in cell 1 followed by rapid heating after 20 s coming from thermal runaway initiating in cell 2.

Time derivatives of thermocouple signals are shown in Fig. 3. Thermocouples that are on the edge of the stack (between a cell and the insulator) exhibit a single peak when thermal runaway reaches the edge of these cells. Thermocouples between two cells exhibit two significant peaks if runaway propagates and a single peak if propagation fails at that point. Figure 3 shows clear separation between these various peaks, and to better understand the propagation we extract "cell-crossing times" by measuring the time between the thermocouple peak on the left and right side of the cell. The cell-crossing time is a measure of the rate of propagation across the cell.

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We also extract "gap-crossing times" by measuring the time between two peaks observed by the same thermocouple. The gap-crossing time shows the delay between heat released by the left cell propagation ending and the start of heat release as the next cell initiates thermal runaway. It is evident in Fig. 3 that gap-crossing times are not trivial relative to the overall evolution of the propagation. For this condition we find that the cell-crossing times and gap-crossing times are of the same magnitude, in the range of ten to fifteen seconds. This will be discussed further after propagation results for other thermal configurations are presented.

It is conventional wisdom that cells with reduced SOC present less thermal hazard.^6,31–34 The active materials are reactive in their charged state, but the discharged state is thermodynamically stable; partially discharging cells reduces the potential energy release. In Figs. 4 and 5 we identify the limits of propagation as a function of SOC for the current cells and configuration.

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Figure 4 shows the voltage and temperature response with SOCs of 50% and 75%. At 50% only minimal cell heating and no further propagation of the failure is observed. It is likely the short-circuited cell was heated more strongly at the nail location, but the transfer of that heat to the thermocouples occurs with some heat dissipation. At this low SOC, the short-circuit heat release and cell reactivity are not sufficient to trigger a substantial thermal runaway and are well away from triggering thermal runaway in neighboring cells. This may vary with resistance of the short circuit, and the result might change in very well-insulated conditions (for example, if cells were buried deep within a high-energy battery system) but from this testing the risk of cascading propagation from single-cell thermal runaway at 50% SOC appears low.

Figure 4 (right) shows the response at 75% SOC, with the short-circuited cell reaching ∼327 °C. This was sufficient to cause cell failure in the second cell of the stack as represented by voltage loss. However, the thermocouple between cells 1 and 2 only reached ∼283 °C and the cascading propagation halted at the second cell.

Figure 5 shows cascading propagation at 80% SOC. For the 80% SOC case, four replicates were carried out. For two cases propagation occurred as shown on the left of Fig. 5, but for two cases propagation failed to occur (right of Fig. 5). With two of four repeated tests giving propagation, this 80% SOC can be considered as the separation between propagation and failure to propagate. The peak temperatures in the propagating cases were observed to be somewhat lower than those at 100% SOC, with maximum temperatures for each internal thermocouple averaging to ∼560 °C. The cell-crossing and gap-crossing times are also extracted from these profiles as described in the previous subsection. Relative to 100% SOC, the 80% SOC measurements show increased cell-crossing times, roughly doubled relative to those at 100% SOC. The gap-crossing times have also increased, but not as significantly. The overall duration of the propagation for 80% SOC is about twice that observed in Fig. 2 for 100% SOC. Detailed cell and gap-crossing times are compiled and analyzed in the discussion section.

Figure 6 through Fig. 10 show the impact of passive thermal management with either copper or aluminum plates between cells. Here we consider the impact of adding simple metallic plates in between cells as a means of mitigating heat transfer between cells during a thermal runaway event by adding thermal capacitance. For these tests, five-cell strings at 100% SOC were constructed using pouch-type cells with varying thicknesses of either aluminum or copper plates between each cell. Metal plates have significant heat capacity and absorb some of the released energy. Heat conduction across thin metal plates is fairly rapid but there might also be some increased contact resistance. The system heat capacity and the parasitic mass of the battery packs are listed in Table II to provide a comparison of the tradeoff between additional mass and reducing the risk of thermal propagation. The parasitic mass of large battery systems is often linked to structural support, and it could be beneficial as it provides opportunities to take advantage of heat capacity. Figures 6 and 7 show the results using 1.6 mm Al and Cu plates. At this thickness, only limited propagation to the nearest neighbor is observed. After the initial cell failure, the second cell in the string failed with a modest temperature rise and voltage loss. However, the kinetics of this failure are muted, and no further propagation is observed beyond the second cell. Thicker plates were shown to completely mitigate the propagation.

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Figures 8 and 9 show the results of fully charged multi-cell packs using 0.8 mm thick aluminum and copper plates, respectively. In both cases complete propagation of thermal runaway was observed. Similar to the testing at 80% SOC, a significant extension of the time for the propagation to occur was observed when compared to the pack at 100% without plates. While the 80% SOC string peaked at ∼560 °C, the string with Al plates peaked at 620 °C, and the string with copper plates peaked at ∼600 °C. In both cases, the final cell failure was observed ∼200 s after the initial cell failure. This is about twice the time required for the unmitigated 100% SOC cell stack to propagate across five cells in Fig. 2. The increased propagation time is fully attributed to the gap-crossing times that are affected by the added copper and aluminum plates. Detailed crossing times are provided and discussed further in the next section.

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For the first cell, nail penetration leads to heat release and reactions focused around the nail. For the remaining cells, thermal runaway is expected and observed to evolve as a propagation front from the first-heated side of the cell. This can be seen as rapid rises in temperature, signaling the presence of the reaction front. Following the crossing-time analysis previously outlined around Fig. 3, the cell-crossing times for the interior cells (2–4) are summarized in Fig. 10 for all conditions where propagation through the stack was unmitigated. The following trends are present in the data:

• As the propagation front moves away from the initiating cell, the cell-crossing time increases (i.e. the propagation velocity slows down).
• An increase in SOC (which is related to the heat release) leads to a faster cell-crossing time, which is expected as more energy is available to drive propagation. Cell-crossing occurs in 10 to 12 s for 100% SOC compared to 12 to 18 s for 80% SOC.
• The addition of plates significantly decreases the cell-crossing time despite the fact that the plates will absorb some of the thermal energy released. With metal plates between cells, the cell-crossing times are generally faster than 10 s indicating that there are aspects of the nearly mitigated case that can be more severe than unmitigated cell stacks. However, the metal plates were not directly thermally linked to the battery structure; results may change if they were, for example, intimately linked to the cell collector plates with a more direct internal heat dissipation path.

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To better understand propagation of thermal runaway in the cell stack, we look to the gap-crossing times presented in Fig. 11. Gap-crossing times are determined as shown in Fig. 3. As noted there, gap-crossing times for a 100% SOC stack with no metal plates are around ten seconds. When propagation at 80% SOC occurs, the gap-crossing times increase significantly, mostly between 20 and 30 s but nearly 50 s in one case. When plates are added, the gap-crossing time increases, typically to more than 30 s. This added delay in gap-crossing occurs because some heat is absorbed by the metal plate, but this also allows for more even preheating of the next cell in the stack as discussed below.

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For the marginal cases (i.e. 80% SOC and 0.8 mm metal plates), gap-crossing times increase because a greater fraction of the heat generated in the previous cell must be transferred to start thermal runaway in the next cell. However, when the gap-crossing times increase, more heat spreads into the next cell while raising its peak temperature towards the critical temperature where thermal runaway begins (also see the later section on Cell heating during gap-crossing). When runaway begins, more thermal energy is present in the cell to drive propagation than the unmitigated 100% SOC case. More energy is associated with faster heat release (Arrhenius reaction rates), thus increasing the velocity of the reaction front.

For the marginal propagation cases, the longer gap-crossing times are more important overall in determining global heat release rates even though the instantaneous heat release rates (energy released per cell-crossing time) are greater during faster cell-crossing in metal-plate mitigated cases. This is observed in the approximate doubling of the time to propagate across the stack of five cells: for the unmitigated 100% SOC case propagation was completed in approximately 90 s (Fig. 2) while propagation across the lower SOC and 0.8 mm metal plate cases took roughly 200 s (Figs. 5, 8, and 9). If we estimate the heat released using the nominal stored energy in each cell, 45 kJ per cell, then the range of heat release rates averaged over the five-cell stack is approximately 2.2 kW at 100% SOC and closer to 1 kW for the 80% SOC and plate-mitigated cases. This estimate is on the low side because additional heat can be released in thermal runaway due to electrolyte venting combustion and burning of other materials like plastic packaging and structural materials, but it provides important order-of-magnitude estimates of cell-to-cell propagation heat-release rates.

In Fig. 3 it was noted that the time between the end of propagation in one cell and the start of propagation of the next cell was significant. Thermal contact resistance between cells can affect the gap-crossing times, and here thermal contact resistance is estimated through a simple analytical heat transfer analysis and a finite volume model taking advantage of the measured gap-crossing times.

The interface between a cell finishing thermal runaway and an adjacent (uncompromised) cell can be analyzed as a semi-infinite solid in the direction of the adjacent cell with a Robin boundary condition representing heat transfer from the cell in runaway to the surface of the adjacent cell through some contact resistance. The analytical solution for the surface temperature (T_s) of the adjacent cell is⁴¹

$$\begin{eqnarray}&&{T}_{s}={T}_{i}+\left({T}_{1}-{T}_{i}\right)\left[1-\exp \left({\eta }^{2}\right)erfc\left(\eta \right)\right]\end{eqnarray} \tag{ 1 }$$

where T_i is the initial temperature of the uncompromised cell, ${T}_{1}$ is the temperature of the cell finishing thermal runaway, and time evolves according to $\eta$ as

$$\begin{eqnarray}&&\eta =\displaystyle \frac{\sqrt{\alpha t}}{R^{\prime\prime} k}\end{eqnarray} \tag{ 2 }$$

The thermal contact resistance $R^{\prime\prime}$ is contained in the expression for $\eta$ along with the thermal diffusivity (α) and thermal conductivity ($k$) of the battery as well as the time (t) from the end of thermal runaway in the initiating cell.

The addition of plates between cells adds a layer of complexity to the contact resistance analysis. We simplify the metal plate (subscript m) as thermally lumped with a finite volume approximation so the plate temperature is approximated using

$$\begin{eqnarray}&&{\rho }_{m}{c}_{p,m}{L}_{m}\displaystyle \frac{d{T}_{m}}{dt}=\displaystyle \frac{\left({T}_{1}-{T}_{m}\right)}{R^{\prime\prime} }-\displaystyle \frac{\left({T}_{m}-{T}_{s}\right)}{R^{\prime\prime} }\end{eqnarray} \tag{ 3 }$$

where the metal plate density, specific heat, and thickness are given by ${\rho }_{m},$ ${c}_{p,m},$ and ${L}_{m}$ respectively. The initial condition is ${T}_{m}={T}_{i}$ at time zero. The temperature in the uncompromised cell of thickness ${L}_{c}$ evolves according to a finite-element discretization of

$$\begin{eqnarray}&&\rho {c}_{p}\displaystyle \frac{\partial T}{\partial t}=k\displaystyle \frac{{\partial }^{2}T}{\partial {x}^{2}}\end{eqnarray} \tag{ 4 }$$

with boundary conditions

$$\begin{eqnarray}&&{\left.-k\displaystyle \frac{dT}{dx}\right|}_{x=0}=\displaystyle \frac{\left({T}_{m}-{T}_{s}\right)}{R^{\prime\prime} }\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{\left.-k\displaystyle \frac{dT}{dx}\right|}_{x={L}_{c}}=0\end{eqnarray} \tag{ 6 }$$

where we seek the value of ${T}_{s}=T(x=0)$ as a function of time. The density and thermal properties of the cells and metal plates are compiled in Table III. The density and specific heat of the cells was estimated from a tear-down of the cells while the thermal conductivity was approximated as a portion of this work and is similar to values given by Ahmed et al.⁴² The thermal properties of the metal plates are taken from Incropera et al.⁴¹ As the metal plates are approximated with a thermally lumped model, the thermal conductivities of these materials are not required for the model.

Table III.  Thermal properties and densities of the cell, aluminum, and copper used in the contact resistance models.

	k (W/m/K)	${c}_{p}$ (J/kg/K)	ρ (kg m−3)	Source
Cell	0.5	778	1816	Current work
Aluminum	237	903	2707	Incropera et al.41
Copper	401	395	8933	Incropera et al.41

We solve both systems (with and without plates) for the contact resistance using experimentally measured values for the driving temperature (${T}_{1}$) and the gap-crossing time (calculated using the method depicted in Fig. 3). Equations (1) and (2) are used for the system without plates, and Eqs. (3)–(6) are used for the system with plates. The driving temperature can be taken as the maximum temperature (T_max) measured at each thermocouple. We must also specify the target surface temperature (T_s) at the onset of thermal runaway in the uncompromised cell. While oven tests suggest initiation of thermal runaway occurs just above 155 °C,⁴⁰ for this analysis we take the higher value of T_s = 200 C based on the shorter time scales and thermocouple measurements (see first paragraphs of this Discussion section). As we are relying on the time to onset of thermal runaway to estimate the contact resistance, this analysis is limited to cases where full propagation occurs.

We solve the inverse problem for the contact resistance that results in T_s = 200 °C at the gap-crossing time for each pair of cells (except for cell 1) in the 100% SOC cases that fully propagated, including those with 0.8 mm aluminum and copper plates. The resulting contact resistances are plotted against T_max in Fig. 12 along with the thermal resistance of 0.2 mm of Mylar (which approximates the resistance of the pouch cell container material and serves as a lower bound for the contact resistance).

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The analytical solution and numerical plate solution effectively estimate the thermal contact resistance for the maximum temperature difference between a cell in thermal runaway and a cell that is being heated. The average values for the cell-to-cell and cell-to-plate contact resistance are 12.3e-3 m² K W⁻¹ and 4.8e-3 m² K W⁻¹ respectively, but there are two cell-to-plate contacts between each cell with metal plates. The equivalent resistance for cell-to-plate-to-cell of 9.6e-3 m² K W⁻¹ (two times cell-to-plate) is on the same order as the cell-to-cell contact resistance. We note that these contact resistances are much greater than the equivalent thermal resistance $\left({L}_{m}/{k}_{m}\right)$ of the plates themselves which are smaller than 1e-5 m² K W⁻¹. Using ${T}_{\max }$ as the constant temperature, T₁, provides an upper bound on the thermal contact resistance, as in the real system, the cell that has completed thermal runaway will be losing heat to the surroundings and adjacent cells/plates. Using a lower value for T_s would tend to reduce the estimated contact resistance. An improved estimate for the thermal contact resistance could be determined by simulating cooling of the failed cell while the adjacent cell heats up and undergoes thermal runaway, but this is beyond the scope of the current work.

The gap-crossing refers to processes occurring after one cell completes thermal runaway but before the next cell in the stack indicates strong thermal runaway. While the runaway cell is heating the next cell during the gap-crossing, this heat spreads into the next cell, preheating it. Using the models from the previous section, we can estimate the total energy transferred to the next cell (and plate if present) during the gap time. This is accomplished by integrating the heat flux into the cell during the gap-crossing time using the simplified models developed in the previous subsection. These models constitute a simple 1-D approach, neglecting external heat losses.

For the 100% SOC case, the average energy absorbed by the next cell during the gap-crossing time was 2.0 kJ. The heating will be concentrated on the left side of cells exposed to a cell runaway on the left side, but over a ten second crossing time the heat spreads a few millimeters into the cell. When the 0.8 mm plates were added, the average energy increased to 2.6 kJ and 2.5 kJ for the aluminum and copper plates, respectively. The addition of the plates decreases the heat flux to the next cell resulting in a longer gap-crossing time required to reach the ignition temperature. However, when the gap-crossing time increases, heat spreads further into the cells and more heat is added before thermal runaway can be initiated at 200 °C. During the gap-crossing the 0.8 mm aluminum and copper plates are estimated to absorb 3.2 kJ and 4.1 kJ, respectively. Thus, the heating of the metal plates is significant relative to the heating of the adjacent cells. The gap-crossing time is further lengthened because the amount of heat that must be transferred from the hot cell to start thermal runaway in the next cell is roughly tripled in the case with metal plates (∼2.5 kJ + 3.2 kJ = 5.7 kJ compared to 2 kJ without plates). The accelerated cell-crossing times observed for propagating cells with metal plates is attributed to the modest added heat (2.5 kJ vs 2 kJ). It is noteworthy that such modest thermal preheating significantly affects the cell-crossing time, but this is typical of Arrhenius rate processes.⁴³

Thermal runaway was mitigated in two ways in these experiments: reducing the state of charge and increasing the total heat capacity of the system. For an adiabatic system with constant heat capacity (${c}_{p}$) and stored energy (Q), the potential temperature rise (${\rm{\Delta }}T$) can be estimated as the energy released per heat capacity

$$\begin{eqnarray}&&{\rm{\Delta }}T=\displaystyle \frac{Q}{m{c}_{p}}\end{eqnarray} \tag{ 7 }$$

where m is the mass of the system. In a real system, heat is lost to the surroundings though convection, conduction, and venting of electrolyte and product gases. Additional heat can be released due to electrolyte combustion and burning of plastics. We estimate the above potential temperature rise in the cells using the energy stored in the cells (45 kJ per cell at full SOC) and total heat capacity of the cells and plates (if present). A summary of the experiments along with ΔT and propagation status is displayed in Table IV. When the experiments are sorted by this stored energy per heat capacity, two transitions in the propagation behavior are apparent: from the 80% SOC to the 1.6 mm Aluminum plates case where propagation is limited to the second cell and from the 1.6 mm Copper plates case to the 3.2 mm Aluminum plates case (at 75% SOC) where thermal runaway is mitigated. The failure of the second cell can be seen in Figs. 4, 6, and 7 as a loss of voltage accompanied by a small heat release that is proportional to the rate at which the voltage drops. We suggest this limiting ${\rm{\Delta }}T$ is specific to the cell type and configuration, but the general alignment of cascading propagation vs mitigation should be well correlated with this potential temperature rise, ${\rm{\Delta }}T.$

Table IV.  Propagation status of each case sorted by potential temperature rise (stored energy in the stack scaled by the total heat capacity).

Name	${\rm{\Delta }}T$ (°C)	Propagation
100% SOC	828	Full
0.8 mm Aluminum	721	Full
0.8 mm Copper	685	Full
80% SOC	663	Full/None
1.6 mm Aluminum	639	Second Cell
75% SOC	621	Second Cell
1.6 mm Copper	584	Second Cell
3.2 mm Aluminum	520	None
3.2 mm Copper	451	None
50% SOC	414	None