Modeling Analysis of Thermal Runaway Propagation and Mitigation in a Large-Format Lithium-Ion Battery Module

Abstract

A thermal abuse model of a single lithium-ion battery, coupling the electric–chemical reaction model and heat transfer model condition, is presented in this work to predict the battery’s thermal response. This model was validated by the experimental results, and it was found that it can predict the battery’s thermal runaway in adiabatic conditions well. It was found that a local hot spot is formed first on the cell nearest the air gap inside the battery. A thermal runaway propagation model was constructed based on this thermal abuse model of a single battery. In addition, the effect of four different modes on the mitigation of thermal runaway propagation is also discussed, including the air gap, cooling plate and insulation layer. The thermal runaway propagation event is successfully prevented when the aerogel is placed between adjacent batteries. However, low-thermal-conductivity insulation material has a negative effect on the heat sink of the battery in thermal runaway, which may aggravate this behavior. This study demonstrates that the model can be used to predict thermal runaway propagation event in battery modules with different prevention measures, and also contributes to the design of safe lithium-ion battery systems.

1. Introduction

As a promising substitute for traditional fuels for driving vehicles, the use of lithium-ion batteries (LIBs) has continued to increase around the world in recent years. Additionally, the energy density and scale of the single LIB are trending to increase to satisfy the market demand. Further, the LIB modules used in electric vehicles (EVs) and power stations are always composed of a large number of single LIBs. As a result, if a single LIB undergoes thermal runaway, it may result in the whole battery module going into thermal runaway and may even cause fire or explosive events for the EVs and power stations [1,2]. Thus, it is important to understand the thermal runaway features of single lithium-ion batteries as well as investigating preventive measures.

Some researchers have shown that lithium-ion batteries will rupture or be ignited when subject to abuse conditions such as overheating, overcharge and mechanical shock [3,4,5,6,7,8]. In addition, many published works have demonstrated that a single LIB in thermal runaway will produce a lot of heat in the battery module [9,10,11,12,13]. Further, the temperature of its neighboring LIBs will continue to increase and eventually result in a thermal runaway propagation event when the rate of heat dissipation from the LIB to its surroundings is lower than its heat-generated rate [11]. Feng et al. [1,4] built a thermal runaway propagation model that consists of six LIBs. The results indicate that the intense heat from the LIB in thermal runaway will increase the temperature of its adjacent batteries to a certain threshold, which will result in thermal runaway propagation between LIBs after a thermal balance stage. Huang et al. [11] investigated the combustion behavior over seven 50 Ah Li(Ni_1/3Mn_1/3Co_1/3)O₂/Li₄Ti₅O₁2 large-format LIBs. A violent combustion event was observed in the presented tests, and they also found that fire impingement resulted in a significant temperature rise in adjacent LIBs in the range between 200 and 900 °C, which could aggravate thermal runaway propagation events. Lamb and Lopez et al. [13,14] also successfully found that thermal runaway will propagate in small-scale lithium-ion battery modules without any protective measures. These published works indicate that thermal runaway between neighboring LIBs in modules can result in catastrophic events if the intense heat from the single LIB in thermal runaway is not dissipated effectively. Thermal runaway propagation is therefore a key issue that needs to be addressed in large-scale applications of lithium-ion batteries.

In order to prevent thermal runaway propagation in lithium-ion battery modules, Larsson [15] adopted a method of inserting firewalls and cooling plates between cells in the module. The result shows that this method may mitigate fire risks, but there is a substantial risk as the firewalls can weaken the heat dissipation of the LIB module. Lopez et al. [14] indicated that intumescent material can prevent thermal runaway propagation in 9P prismatic modules. In addition, Wilke et al. [16] successfully prevented thermal runaway propagation between 18650 lithium-ion battery modules using a phase change composite material. Yan et al. [17] balanced the heat insulation and dissipation capabilities of the lithium-ion battery system using a composite board containing a heat conducting shell, an insulation panel and phase change material (PCM). The result shows that the composite board could enhance the heat dissipation capacity, and was also beneficial for the uniformity of the temperature in the lithium-ion battery module. However, the preventative effect of the composite board on the thermal runaway propagation process has not been investigated in detail. Moreover, the experiments of thermal runaway propagation are hardly conducted due to its high cost and safety risks. The primary objective of this study is to develop a validated electrochemical–thermal coupled model capable of predicting thermal runaway in a single LIB and to evaluate the effectiveness of different mitigation strategies in preventing thermal runaway propagation by this model.

In this work, an electrochemical–thermal coupled model is presented to analyze the thermal behavior of an LIB under thermal abuse conditions. Further, the model is validated by experimental measurements using an extended volume accelerating rate calorimeter (EV-ARC). In addition, a thermal runaway propagation model of a lithium-ion battery module that consists of five LIBs is proposed based on the thermal abuse model of the single LIB. Additionally, the feasibility of four prevention measures on the thermal runaway propagation process is analyzed, including the air gap, cooling plate, and insulation material with different thermal properties. The thermal runaway propagation process is discussed in this study, as well the amount of heat transfer between adjacent LIBs, to compare the effect of the preventative measures.

2. Model Description

2.1. Geometric Construction

The 38 Ah LIB with a LiNi_1/3Co_1/3Mn_1/3O₂/graphite electrode was chosen as the simulation unit in this work. Figure 1a,b illustrate the schematic of the Li-ion battery; each battery is mainly composed of two cells, a shell and current collectors. The thermal–physical properties of the Li-ion battery are summarized in

Table 1. Thermal properties of the components [1].

Component	ρ (kg m−3)	Cp (J g−1 K−1)	k (W m−1 K−1)
Heater	2700	900	160
Cell	2500	1100	kx = ky = 21, kz = 1.1 [1]
Shell	2700	900	160
Positive pole	2700	900	160
Negative pole	8960	385	146

.

2.2. Governing Equations and Boundary Conditions

The energy conservation equation of the LIB can be expressed as follows:

$$\rho C_{\mathrm{p}}{\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }t}}=k\nabla (\nabla T)+{\displaystyle \frac{Q_{\mathrm{gen}}}{V_{\mathrm{bat}}}}$$

(1)

where ρ, C_p, k, Q_gen, and V_bat represent the density, heat capacity, thermal conductivity, heat generation and volume term, respectively.

2.3. Chemical Reactions

The thermal abuse model of the single cell considers the chemical reactions and the stored electric energy as follows:

$$Q_{\mathrm{gen}}=Q_{\mathrm{chem}}+Q_{\mathrm{ec}}$$

(2)

where $Q_{\mathrm{gen}}$ is the total heat source of the LIB in thermal runaway; $Q_{\mathrm{chem}}$ is the heat source of the chemical reactions; and $Q_{\mathrm{ec}}$ is the heat source of the electrochemical reactions.

The phenomenon of temperature rise in batteries due to electrochemical reactions was investigated in this study with reference to the research by Coman et al. [18,19,20]. In addition to the heat source from the chemical reactions, the stored electric energy also contributes to temperature increases when the LIB is subjected to thermal runaway and further accelerates the rates of the chemical reactions. Thus, the heat generation power of the electrochemical reactions can be expressed as an Arrhenius formulation. This method is also used to describe the heat source from the electrochemical reactions in this work.

In previous studies, the micro short-circuit was initiated when the separator started to melt at around 135 °C, resulting in a slight rise in temperature and self-heating rate of the LIB [1]. Therefore, the heat source from the electrochemical reactions was divided into two terms to describe the micro- and large-scale electric energy released event, defined as follows:

$$Q_{\mathrm{ec}}=Q_{\mathrm{ec},1}+Q_{\mathrm{ec},2}=\mathrm{\Delta }{H}_{\mathrm{ec}}\cdot \left({\displaystyle \frac{d{c}_{{\mathrm{SoC}}_1}}{dt}}+{\displaystyle \frac{d{c}_{{\mathrm{SoC}}_2}}{dt}}\right)$$

(3)

$$\mathrm{\Delta }{H}_{\mathrm{ec}}=C\cdot V\cdot 3600\cdot \eta$$

(4)

$${\displaystyle \frac{d{c}_{{\mathrm{SoC}}_1}}{dt}}=-A_{{\mathrm{SoC}}_1}\cdot \exp (-{\displaystyle \frac{E_{{\mathrm{a}, \mathrm{SoC}}_1}}{R\cdot T}})\cdot c_{{\mathrm{SoC}}_1}^{\hspace{1em}\hspace{1em}{m}_{{\mathrm{SoC}}_1}}\cdot {(1-c_{{\mathrm{SoC}}_1})}^{n_{{\mathrm{SoC}}_1}}\cdot {\left[-\ln (1-c_{{\mathrm{SoC}}_1})\right]}^{k_{{\mathrm{SoC}}_1}}$$

(5)

$${\displaystyle \frac{d{c}_{{\mathrm{SoC}}_2}}{dt}}=-A_{{\mathrm{SoC}}_2}\cdot \exp (-{\displaystyle \frac{E_{{\mathrm{a}, \mathrm{SoC}}_2}}{R\cdot T}})\cdot c_{{\mathrm{SoC}}_2}^{\hspace{1em}\hspace{1em}{m}_{{\mathrm{SoC}}_2}}\cdot {(1-c_{{\mathrm{SoC}}_2})}^{n_{{\mathrm{SoC}}_2}}\cdot {\left[-\ln (1-c_{{\mathrm{SoC}}_2})\right]}^{k_{{\mathrm{SoC}}_2}}$$

(6)

where $Q_{\mathrm{ec},1}$ and $Q_{\mathrm{ec},2}$ are the heat sources from the micro- and large-scale electrochemical reactions; $\mathrm{\Delta }{H}_{\mathrm{ec}}$ is the enthalpy of the electro-chemical reaction; C = 38 Ah and V = 4.2 V are the capacity and voltage of the battery, respectively; and η is the conversion efficiency of the electrical energy to thermal energy for micro and large-scale electrochemical reactions, which takes values from 0 to 1 to fit the experimental result.

The exothermic chemical reactions inside the cell will be induced sequentially when the temperature is elevated to various ranges, including the decomposition reaction of the SEI layer, the reaction between the anode and electrolyte, and the decomposition reactions of electrolyte and cathode [1,21].

$$Q_{\mathrm{chem}}={\displaystyle \sum Q_{\mathrm{i}}}=Q_{\mathrm{SEI}}+Q_{\mathrm{anode}}+Q_{\mathrm{electrolyte}}+Q_{\mathrm{cathode},1}+Q_{\mathrm{cathode},2}$$

(7)

where $Q_{\mathrm{i}}$ denotes the heat generation power of one of the specific chemical reactions; $Q_{\mathrm{SEI}}$ denotes the heat generation power of the decomposition reaction of the SEI layer when the temperature is elevated to around 90 °C; $Q_{\mathrm{anode}}$ denotes the heat generation power of the reaction between the intercalated Li and the solvent when the SEI layer begins to decompose; and $Q_{\mathrm{electrolyte}}$ denotes the heat generation power of the decomposition reaction of the electrolyte when the temperature is elevated to around 190 °C. The heat generation power of the decomposition reaction of the cathode material considers two terms, $Q_{\mathrm{cathode},1}$ and $Q_{\mathrm{cathode},2}$, because of the two exothermic peaks [1,10], which will be initiated at 180 and 220 °C, respectively.

For these chemical reactions, the heat source can be determined as follows:

$$Q_{\mathrm{i}}=\mathrm{\Delta }{H}_{\mathrm{i}}\cdot m_{\mathrm{i}}\cdot {\displaystyle \frac{d{c}_{\mathrm{i}}}{dt}}$$

(8)

$${\displaystyle \frac{d{c}_{\mathrm{i}}}{dt}}=-A_{\mathrm{i}}\cdot \exp (-{\displaystyle \frac{E_{\mathrm{a}, \mathrm{i}}}{R\cdot T}})\cdot c_{\mathrm{i}}^{{\mathrm{m}}_{\mathrm{i}}}\cdot {(1-c_{\mathrm{i}})}^{{\mathrm{n}}_{\mathrm{i}}}\cdot {(-\ln (1-c_{\mathrm{i}}))}^{{\mathrm{k}}_{\mathrm{i}}}$$

(9)

where $\mathrm{\Delta }{H}_{\mathrm{i}}$ is the enthalpy of the chemical reaction, $m_{\mathrm{i}}$ is the total mass of the reactants, and $A_{\mathrm{i}}$ and $E_{\mathrm{a},\mathrm{i}}$ are the pre-exponential factor and activation energy of reaction i, respectively.

The rate of the chemical reaction ${\displaystyle \frac{d{c}_{\mathrm{i}}}{dt}}$ can be expressed in Arrhenius form. In addition, the kinetic parameters used in the thermal abuse model of the single Li-ion battery are given in

Table 2. The kinetic parameters used in the thermal abuse model [1,18,19,20,21,22].

i	Ai (s−1)	Ea,i (J mol−1)	∆Hi (J kg−1)	c0,i	mi	ni	ki
SEI	1.667 × 1015	1.3508 × 105 [2]	257	0.15	1	0	0
Anode	2.5 × 1011	1.1756 × 105	1714	1	1	0	0
Electrolyte	3 × 1015	1.5555 × 105	800	1	1	0	0
Cathode1	1.75 × 109	1.1495 × 105	77	0.99	1	1	0.2
Cathode2	1.077 × 1012	1.5888 × 105	84	0.99	1	1	0.2
SoC1	3.37 × 1013	1.1275 × 105	574.56	0.01	1	0	0
SoC2	3.37 × 1013	1.3244 × 105	574.56	0.99	1	1	0.2

.

It should be noted that the kinetic parameters listed in Table 2 are derived from calorimetric experiments and established models of Li(Ni_1/3Co_1/3Mn_1/3)O₂ and graphite cells with conventional organic electrolytes [5,6]. Their direct extrapolation to substantially different cell chemistries or electrolyte systems is not recommended without proper re-parameterization, although these values provide a reliable foundation for modeling the specific 38 Ah square cell with Li(Ni_1/3Co_1/3Mn_1/3)O₂ as the cathode in this study.

2.4. Thermal Runaway Propagation Model of the LIB Module

As shown in Figure 2, the thermal runaway propagation model for the battery module is built and consists of five single LIBs and a heating plate. For convenience, the surface of the “i#” battery nearest the position of the heater is named the “front surface” of the “i#” battery, and its temperature variation is denoted as Tif. Further, the thermal properties of the battery, including the initial temperature, heat transfer coefficient, and emissivity, as well as the thermal resistance between the contact walls of adjacent LIBs, are given in

Table 3. Thermal properties of lithium-ion battery module [1,10].

Condition	Value
Initial temperature	T = 25 °C
Ambient temperature	T = 25 °C
Heat transfer coefficient	h = 5 W m−2 K−1
Emissivity of the battery	ε = 0.8

.

It is worth mentioning that the thermal resistance between the cells is impacted by the contact area and thermal conductivity, and its value was approximately 1.83 × 10⁻³ to 3 × 10⁻³ m²·K·W⁻¹ measured under an adiabatic environment by EV-ARC and a heater film with a constant power [7]. Furthermore, the intense heat from the battery in a thermal runaway event can significantly affect the thermal resistance between cells. The influence of this effect on thermal runaway propagation behavior will be investigated in detail in our next work.

Thermal runaway propagation events are an urgent issue in the large-scale application of lithium-ion batteries. As shown in

Table 4. Simulation conditions.

NO.	Thickness	Material	Description
Case 1	0	--	The batteries were placed without spacing
Case 2	2	Air	Two batteries were placed with an air gap
Case 3	2	Aluminum	Aluminum plate was placed between each two batteries
Case 4	2	Mica	Mica insulation layer was placed between two batteries
Case 5	2	Aerogel	Aerogel insulation layer was placed between two batteries

, five cases are simulated to investigate the effect of several common prevention measures for thermal runaway propagation. “Case 1” represents the LIB module without spacing between batteries. In addition, “Case 2” features an air gap between batteries, as shown in Figure 2, respectively.

In addition, the effects of two materials with different thermal properties on thermal runaway propagation are compared and discussed in this work. The thermal properties of three materials are listed in

Table 5. Thermal properties of aluminum plate and aerogel insulation layers.

Property	Aluminum	Mica	Aerogel
Heat conductivity (k)/W·m−1·K−1	160	0.5	0.02
Density (ρ)/kg·m−3	2700	880	195

. In “Case 3 to 5”, the aluminum plate, mica and aerogel insulation layer, respectively, are placed between each two LIBs to prevent thermal runaway propagation events. Given the limited space inside the LIB module, the air gap and thickness of the insulation layer are set at 2 mm.

3. Results and Discussion

3.1. Model Validation

Figure 3a displays the profiles of the temperature variation with time and temperature rate variation with temperature for the EV-ARC test in Ref. [7]. The progress of the LIB from normal to thermal runaway was divided into four stages, with some special phenomena, such as the micro short-circuit and safety venting, as well material ejection behavior. All of these behaviors contribute to the energy tally when the LIB undergoes thermal runaway. Figure 3b,c show the comparison of the predicted temperature and self-heating rate of the LIB with the measurements in previous studies. It can be seen that the simulation results fit the experimental measurements well for both the temperature– time and temperature rate–temperature curves during the self-heating stage.

It is worth mentioning that a notable difference in temperature rise data exists between experiments and simulations. The safety venting behavior will release some hot gases, which will result in a slight temperature decrease in the LIB, as shown in the enlarged photo in Figure 3a. However, the repeated experiments show that this behavior lacks a clear pattern; this phenomenon was not observed in thermal runaway propagation tests, as the LIB was heated violently in our previous study [7]. In order to reduce the uncertainty and the amount of the computation, the effects of safety venting and ejecta are not considered in detail, but are included in the effective coefficient (η). Therefore, the predicted time of the thermal runaway event is earlier than the experimental result, which is denoted as Δt, as shown in Figure 3b. Furthermore, the simulated temperature rise rate is slightly higher than the experimental result in the ARC test.

In the adiabatic thermal runaway experiments, the peak temperature of the lithium-ion battery during thermal runaway was 522.6 °C, which is lower than the peak temperature of 600–700 °C observed under normal environmental conditions in the thermal runaway propagation process. This discrepancy may result from the severe swelling of the battery, which causes the measured surface temperature to be lower than the actual temperature. Further, the value is set at 0.4 to fit the experimental result in the thermal runaway propagation model to bring the simulated peak temperature closer to the peak temperature observed in the actual experiments.

The temperature distribution of the LIB during the self-heating stage is shown in Figure 4. In the adiabatic environment, the temperature rise of the battery is primarily caused by the exothermic chemical reactions of its internal materials. Therefore, the temperature increased slowly and showed little difference between the internal and external temperatures during the initial stage of self-heating as shown in Figure 4a,b. The maximum temperature gradient across the cell remains below 1 °C. However, the temperature was increased rapidly when the intense heat was released in thermal runaway stage. As shown in Figure 4c, the maximum temperature gradient is around 7 °C with the acceleration of the exothermic chemical reactions inside the battery. And approximately 253 °C temperature gradient was observed between the internal and shell of the LIB as shown in Figure 4d, which was primarily influenced by the thermal conductivity of its material structure and the location of heat sources.

In the thermal runaway propagation event in our previous studies, heated cells indeed exhibit a significant temperature gradient inside the battery due to the presence of two jelly rolls and an air gap. Moreover, approximately 8–10 s was needed to spread thermal runaway from the layer near the front surface to the whole battery. In addition, a 228–437 °C temperature difference was observed between the front and back surface. In this study, a lumped model is constructed to maintain computational efficiency while focusing on heat transfer and barrier analysis. The temperature difference between the front and back surface was around 360 °C as shown in Figure 5a. The results partly support the feasibility of the lumped method.

3.2. Thermal Runaway Propagation in the LIB Module

Figure 5 displays the temperature variation in the front surface of each lithium-ion battery in the simulation work. The result indicates that the thermal runaway has been propagated in the module without any prevention measures. A large amount of heat will be released when the LIB undergoes thermal runaway, and the front surface temperature of its neighbor will rapidly increase to around 430 °C, as shown in Figure 5a. Then, the next LIB will be induced after a heat balance stage. In this simulation, the average propagated time between each two LIBs is 89 s, which is close to the 87 s in the experiment [1]. The internal temperature of the LIB is shown in Figure 5b. It can be seen that the peak temperature inside the LIB can reach approximately 970 °C, which is much higher than its surface temperature.

For a better explanation, the thermal runaway propagation process between 1# and 2# LIBs are discussed and the temperature distribution of the module’s cross section is illustrated in Figure 6. As shown in Figure 5b, the front surface’s temperature increases steeply when 1# LIB undergoes thermal runaway, and there was a significant temperature difference between cells 1 and 2 inside 2# LIB because each LIB consists of two cells. The exothermic chemical reactions of cell 1 were first induced at 412 s and further contribute to its temperature rise, as shown in Figure 6b. After approximately 58 s, the thermal runaway of cell 1 inside 2# LIB was triggered, further resulting in an immediate thermal runaway event of the whole 2# LIB, as shown in Figure 6c.

3.3. Thermal Runaway Mitigation in the LIB Module

Because there are no prevention measures in “Case 1”, the released heat from the LIB in thermal runaway can be directly transferred to its neighbors, resulting in thermal runaway propagation event in the module. According to the simulation result in “Case 1”, measures should be taken to avoid the formation of a local hot spot on the cell inside the LIB. In this study, the effect of four insulation materials was analyzed in “Case 2–5” in Table 4. Figure 7a–d display the temperature variations with time in each LIB in “Case 2–5”, respectively. It can be seen that thermal runaway is prevented in “Case 5” due to the excellent thermal insulation effect of aerogel in the normal condition. In some extreme scenarios, the necessary thickness of the aerogel should in the battery be further investigated. However, thermal runaway is still propagated to the entire LIB module in “Case 2–4”, in which the air gap, aluminum plate and mica insulation layer are placed between the LIBs, respectively. In addition, the propagation time between each adjacent LIB is listed in

Table 6. Thermal runaway propagation time between adjacent LIBs.

NO.	Δt1#–2#	Δt2#–3#	Δt3#–4#	Δt4#–5#
Case 2	416	459	497	458
Case 3	133	156	154	143
Case 4	218	242	233	214
Case 5	--	--	--	--

. In “Case 2”, the average time is around 458 s, which is much higher than the 147 s in “Case 3” and 227 s in “Case 4”. This indicates that the air gap shows a significant effect on the delay of the thermal runaway propagation time due to the change in the dominated heat transfer mode. In “Case 2”, the heat is mainly transferred through convection and radiation, while conduction is the dominant heat transfer mode in “Case 3–5”.

However, Li et al. indicate that heat absorption by the aluminum plate is the key factor in thermal runaway propagation event, and this phenomenon is also observed in this study. Figure 8 shows the temperature distribution of each LIB in thermal runaway in “Case 2–5”. The heat from the LIB in thermal runaway was dissipated rapidly due to the high thermal conductivity of the aluminum plate. Thus, the peak temperature of the back surface of the LIBs in thermal runaway in “Case 3” is around 487 °C, which is much lower than the 730 °C in “Case 2”, with the air gap, and 761 °C in “Case 5”, with the aerogel insulation layer. In addition, the high thermal conductivity of the aluminum plate also contributes to the heat sink, and thus more time is needed to induce thermal runaway of 1# LIB.

Further, thermal runaway was prevented when the 2 mm aerogel insulation layer was placed between each two batteries. However, the peak temperature of the cells in 2# LIB can reach around 120 °C at 3742 s, as shown in the “Case 5” section in Figure 8. This value is high enough to induce the self-heating reactions inside the LIB. Then, the temperature of the 2# LIB starts to decrease, as its total heat generation rate is lower than the heat transfer rate from it to the next ambient LIB.

Moreover, the simulations coupling insulation layer thickness and thermal conductivity was also conducted to assess the applicability limits of thermal insulation materials under extreme conditions.

In practical applications, high energy density requirements for battery systems limit the insulation layer thickness (δ) to within 2 mm (δ = 0.5, 1.0, 1.5, 2.0 mm). And safety levels are assigned according to the propagation time (Δt_i#–(i+1)#) as shown in

Table 7. Safety levels and criteria for thermal runaway propagation in LIB module.

Safety Level	Thermal Runaway Propagation	The Internal Temperature of the Adjacent Battery Reaches the Separator Melting Temperature	Δti#–(i+1)# ≤ 5 min
I	NO	NO	NO
II	NO	YES	NO
III	YES	YES	YES
IV	YES	YES	YES

.

As shown in Figure 9, the results indicated that the internal core temperature of the adjacent battery still approaches the melting temperature of the separator (135 °C) under the effect of the battery undergoing thermal runaway even the thermal conductivity k is reduced to 0.01 W·m⁻¹·K⁻¹ at a thickness of 0.5 mm.

When the thickness of the thermal insulation layer is increased to 1 mm, the thermal insulation material with k < 0.02 W·m⁻¹·K⁻¹ can effectively suppress thermal runaway propagation. The aerogel materials can meet this basic requirement. For insulation layer thicknesses of 1.5–2 mm, the corresponding thermal conductivity can be increased to 0.03 W·m⁻¹·K⁻¹ and 0.05 W·m⁻¹·K⁻¹, respectively, allowing the use of materials such as fiberglass and rock wool board as insulation layers.

3.4. Heat Transfer Between LIBs in the LIB Module

According to the simulation results, the heat transfer rate from an LIB in thermal runaway to the next fresh LIB can determine the thermal runaway propagation event. Figure 9 illustrates the network of heat transfer paths between each two adjacent LIBs in “Cases 3–5”; the thermal resistance consists of the contact resistance (R_t,c) and the conduction resistance (R_t,cond). In addition, there is no conduction between LIBs in “Case 2”, and thus the thermal resistance is replaced by convection resistance (R_t,conv = 1/h) and radiation resistance (R_t,rad = 1/h).

The amount of heat transfer between adjacent LIBs during the thermal runaway propagation event can be calculated as follows [23,24]:

$$Q_{i^{\#}\to {(i+1)}^{\#}}= A_{\mathrm{shell}}\cdot {\displaystyle {\int }_t^{t+\mathrm{\Delta }{t}_{i^{\#}\to {(i+1)}^{\#}}}{q}_{\mathrm{total}}}(t) dt$$

(10)

$$q_{\mathrm{total}}={\displaystyle \frac{\mathrm{\Delta }T}{R_t}}$$

(11)

where $A_{\mathrm{shell}}$ is the contact walls; $q_{\mathrm{total}}$ is the total heat flux from the LIB in thermal runaway to next LIB; $\mathrm{\Delta }{t}_{i^{\#}\to {(i+1)}^{\#}}$ is the thermal runaway propagation time between adjacent LIBs; and $R_t$ is thermal resistance between each two LIBs. Equations (10) and (11) are derived from the thermal resistance network under the following assumptions: (1) heat transfer through the insulation layer and contact interfaces is one-dimensional and at steady state; (2) the thermal contact resistance R_t,c is assumed to be constant with temperature, which is a simplification justified because the intense thermal runaway transient limits the time for meaningful variation; (3) the thermal resistance values in this study are primarily determined by the thermal conductivities of the adjacent materials, as heat conduction is the dominated mode of heat transfer in all cases, as shown in Figure 10.

The amount of heat transfer between each two adjacent LIBs is shown in Figure 11. It can be seen that the lowest amount of heat is required to induce thermal runaway of the next fresh LIB in “Case 2”, at around 53.3 to 53.9 kJ, as the LIB is separated by an air gap. This demonstrates that the heat sink of the insulation material can contribute to the mitigation of thermal runaway propagation event.

According to Figure 10, the thermal conductivity of the insulation material has a negative correlation with the conduction resistance when its thickness remains constant. Thus, the value of the transferred heat between LIBs increased with the decreased thermal conductivity of the insulation material in this study, as shown in Figure 10. For the LIB module with the aluminum plate and mica insulation layer in “Cases 2 and 3”, it takes approximately 64 to 67.8 kJ and 91.5 to 99.5 kJ to propagate thermal runaway between LIBs, respectively. It is worth noting that thermal runaway was mitigated in “Case 5”, and the time from the thermal runaway of 1# LIB to the peak temperature of 2# LIB is considered to be the thermal runaway propagation time. Therefore, the 2# LIB still does not undergo thermal runaway even if a large amount of heat is transferred from 1# LIB to 2# LIB. Furthermore, the thermal resistance in Case 4 is approximately 533 times that in Case 3 in this study, and the results indicate that the average thermal runaway propagation time between adjacent cells in Case 4 is significantly longer than that in Case 3, representing an increase of about 54%. Meanwhile, the amount of heat transferred from the runaway cell to the adjacent cell in Case 4 (91.5–99.5 kJ) is also considerably higher than that in Case 3 (64–67.8 kJ), showing an increase of approximately 40–45%.

The results in this study indicate that insulation materials can contribute to the mitigation of thermal runaway propagation event in the battery module, but they can also weaken the heat dissipation condition and further aggravate the severity of the thermal runaway event. If the total heat transfer rate from an LIB in thermal runaway next to a fresh LIB is higher than the heat sink rate, the temperature of the next LIB will be increased constantly until the occurrence of thermal runaway. Therefore, effective prevention measures should be considered to balance the heat insulation and dissipation conditions in battery modules. It is essential to strike an optimal balance between “rapid heat conduction” for uniform heat source distribution and “effective heat dissipation” for efficient heat removal to the environment in practical engineering. For example, this can be achieved by designing anisotropic composite insulation layers (such as high-thermal-conductivity surface layers combined with low-thermal-conductivity core layers) or employing gradient composite structures between aerogels and aluminum plates. Furthermore, the incorporation of phase change materials alongside thermal insulation materials represents a promising approach to reconciling the competing demands of heat conduction and dissipation. Collectively, these strategies offer a direct quantitative foundation for the passive thermal management design of high-safety lithium-ion battery modules.

It should be emphasized that the quantitative results reported in this work are specific to the 38 Ah NCM square cell. Therefore, the direct extrapolation of the quantitative results should re-parameterize again for the battery module with substantially different capacities, chemistry and form factors, which includes propagation times and critical heat transfer amounts. Nonetheless, the selection method of thermal insulation materials from this study are expected to remain broadly applicable across a wide range of lithium-ion battery modules.

In most existing thermal runaway propagation models, a constant thermal conductivity for the insulation layer is assumed and the temperature-dependent behavior of separator melting was also neglected. Several improvements have also been identified, as follows. Firstly, the present model explicitly incorporates the separator melting temperature (135–150 °C) as a critical threshold for propagation risk and systematically evaluates the combined effect of insulation thickness (δ) and thermal conductivity (k). Moreover, the model quantitatively analyzes the delay times (Δt_i#–(i+1)#) and establishes a four-level safety classification (Levels I–IV), which can offer direct guidance for material selection in practical applications.

More importantly, the model can be applied to engineering scenarios without significant revision. For example, the predicted preventing conditions (δ = 1.0 mm, k < 0.02 W·m⁻¹·K⁻¹) for thermal runaway propagation event were fully consistent with the thermal conductivity of commercial aerogel materials. Similarly, the recommended k values of 0.03 to 0.05 W·m⁻¹·K⁻¹ correspond directly to readily available materials such as fiberglass and rock wool board when the thickness is 1.5 and 2 mm, respectively. These material parameters are directly substituted into the model without any case-specific tuning, demonstrating its ready-to-use nature for battery thermal barrier design.

4. Conclusions

In this work, a thermal abuse model of a single LIB under adiabatic conditions, which couples the electric–chemical reaction model and heat transfer model, is established through COMSOL 5.2 Multiphysics software. This model is then validated by the experimental results from the EV-ARC test. Based on this thermal abuse model of the single LIB, a thermal runaway propagation model was constructed for a lithium-ion battery module with five single batteries, and the effect of four materials with different thermal properties on thermal runaway propagation event was also discussed. The outcomes can be summarized as follows.

(a)

The simulation results of the single LIB under adiabatic conditions indicate that the hot spot on the cell inside the LIB will first form on the section nearest the air gap. However, the heat source is mainly derived from the LIB in thermal runaway in the thermal runaway propagation event. Thus, a local hot spot occurs first on the layer near its front surface, which is heated violently by an LIB in thermal runaway.

(b)

The air gap, cooling plate and the insulation layer all contribute to the mitigation of thermal runaway propagation events. In addition to the case in which the aerogel is inserted between the LIBs, thermal runaway still propagated in the battery module in other cases. This indicates that the thermal runaway propagation event can be prevented by the proper design of thermal insulation measures. Specifically, an air gap can significantly delay the thermal runaway propagation time, but it has a limited effect on the heat sink of an LIB in thermal runaway. Furthermore, the aluminum plate shows a positive effect on the heat sink because of its high thermal conductivity. Thus, a smaller amount of heat is transferred from a battery in thermal runaway to the next fresh battery, even if the thermal runaway propagation time is significantly delayed, as in the battery module with an air gap.

(c)

Thermal resistance is the dominant factor in the heat transfer rate between adjacent lithium-ion batteries. The excellent thermal insulation properties of the aerogel can significantly increase the resistance to thermal conduction between batteries, thereby preventing the formation of a local hot spot on the cells inside the next fresh battery. However, the heat dissipation capability of the battery module is also greatly weakened. Around 3384 s after the thermal runaway of battery 1#, the temperature of LIB 2# began to rise, peaking at around 120 °C.