Advances and challenges in thermal runaway modeling of lithium-ion batteries

Abstract

The broader application of lithium-ion batteries (LIBs) is constrained by safety concerns arising from thermal runaway (TR). Accurate prediction of TR is essential to comprehend its underlying mechanisms, expedite battery design, and enhance safety protocols, thereby significantly promoting the safer use of LIBs. The complex, nonlinear nature of LIB systems presents substantial challenges in TR modeling, stemming from the need to address multiscale simulations, multiphysics coupling, and computing efficiency issues. This paper provides an extensive review and outlook on TR modeling technologies, focusing on recent advances, current challenges, and potential future directions. We begin with an overview of the evolutionary processes and underlying mechanisms of TR from multiscale perspectives, laying the foundation for TR modeling. Following a comprehensive understanding of TR phenomena and mechanisms, we introduce a multiphysics coupling model framework to encapsulate these aspects. Within this framework, we detail four fundamental physics modeling approaches: thermal, electrical, mechanical, and fluid dynamic models, highlighting the primary challenges in developing and integrating these models. To address the intrinsic trade-off between computational accuracy and efficiency, we discuss several promising modeling strategies to accelerate TR simulations and explore the role of AI in advancing next-generation TR models. Last, we discuss challenges related to data availability, model scalability, and safety standards and regulations.

Graphical abstract

Public summary

• •Thermal runaway mechanism is elucidated from multiscale perspectives of electrode, cell, module, and system.
• •Multiphysics modeling framework is introduced based on thermal, electrical, mechanical, and fluid dynamics models.
• •Promising modeling strategies for accelerating thermal runaway simulations are outlined and envisioned.
• •Machine learning can break inherent contradictions between accuracy and efficiency in thermal runaway modeling.
• •Perspectives guide future thermal runaway model development toward higher accuracy, efficiency and scalability.

Introduction

Safety issues of lithium-ion batteries

In response to escalating greenhouse gas emissions and the urgent issue of climate change, nations worldwide have signed the landmark United Nations climate agreement in Paris, committing to limit global warming to less than 1.5°C by 2050.^1,2 The electrification of various types of industrially derived equipment has emerged as a crucial strategy to achieve carbon neutrality and sustainably support human activities. Lithium-ion batteries (LIBs), owing to their high specific energy and long cycle life, play a crucial role in this electrification process, permeating all aspects of modern industry and life, including transportation, energy storage, and portable devices.^3,4,5

Safety is universally recognized as one of the primary concerns for LIBs. Containing substantial active chemical materials and stored electrical energy, LIBs are susceptible to exceeding their normal operating temperature range under abusive conditions.^6,7,8 These conditions can arise from thermal, electrical, and mechanical abuse.⁹ If the generated heat is not effectively dissipated, then it can initiate a sequence of self-sustaining exothermic reactions, eventually resulting in the catastrophic phenomenon known as thermal runaway (TR).¹⁰ TR in a single cell is characterized by drastic heat release, accompanied by intense gas venting and combustion.⁶ This disastrous phenomenon can potentially propagate through the battery pack of electric vehicles (EVs) and energy storage systems (ESSs), leading to fire, explosion, and other severe consequences.^11,12 Despite ongoing efforts, significantly enhancing the safety level of LIBs in the short term remains a challenge, as evidenced by the increasing incidence of fire and explosion accidents associated with TR. Consequently, the safety issue posed by TR remains a challenge in LIBs, hindering the wider adoption of LIB technology.

Why do we need TR models?

Understanding the reaction and degradation mechanisms of LIBs provides insights into the TR process, inspiring innovative strategies to enhance safety performance. Initial research efforts toward addressing LIB safety problems began with experimental approaches, characterizing TR through measurement and attempting to understand the underlying mechanisms. With advancements in computational techniques, simulation-based research has emerged, attempting to reveal multiphysical phenomena and the interactions among different physics by developing TR models. Compared with experiments, simulation models are not constrained by economic costs, time costs, or potential safety risks and can provide detailed distributions and fluxes of physical parameters.¹¹ Such insights are challenging to obtain experimentally and, in some cases, are beyond the reach of existing experimental techniques. Therefore, the TR model is a valuable tool for understanding battery safety issues. In industrial circles, new research and applications based on TR simulation techniques are rapidly emerging, supported by computational techniques and spanning the entire lifespan of LIBs. As illustrated in Figure 1, TR models play a crucial role in different stages of LIBs, covering design, operation, reuse, and accident scenarios.

• (1)Design: TR models can assist in the search for safer materials and structures by establishing a mapping between design properties and the macroscopic thermal behavior of LIBs, contributing to the intrinsic safety and protection design of LIBs.
• (2)Operation: TR models serve as an indispensable link in monitoring and predicting systems, interpreting captured physical signals to identify faults and assess the risk of potential failure, ultimately guiding the battery management system’s response.
• (3)Reuse: TR models can identify risks and hazards associated with improper operation in battery disassembly and recycling. They are also effective in forecasting performance degradation and increasing inconsistency during LIBs’ long-term service, ensuring the safety of battery echelon utilization.^13,14
• (4)Accidents: TR models provide deep insights into the potential evolution and consequences of battery failure, guiding the development of emergency strategies. They can also reconstruct scenarios and processes of a TR accident to infer causation.

Figure 1.

Typical application scenarios of LIBs and the roles of TR models in different stages of design, operation, reuse, and accidents

Given the importance of TR models in battery safety applications, their development remains an active research topic. Recent reviews have focused on TR modeling,^15,16,17 whose focus is limited to thermal and electrical modeling of single cell/module. However, TR modeling is facing new challenges as TR research progresses. First, as insights into the TR process deepen, the simulated ranges of TR models are required to extend from the battery itself to the fluid region, from a small single-cell scale to a large multiscale and from thermal modeling to multiphysics modeling. Second, considering the complex nonlinear systems of LIBs, how to couple different physical models to more accurately capture TR behavior needs to be fully discussed. Finally, reducing the computational cost burden and seeking a balance between accuracy and efficiency remain open questions for the next generation of TR models.

Article organization

This perspective reviews the TR modeling strategies and discusses their future development in response to current questions, providing readers with a macroscopic framework of existing TR models and a roadmap for the next-generation TR models. The paper is organized as follows. Section introduction introduces the background of LIBs and their safety issues, addressing “why do we model TR?” Section understanding thermal runaway process from multiscale perspectives delves into the underlying processes and mechanisms of TR from multiscale perspectives, clarifying “what do we simulate about TR?” Section developing multiphysics coupling model for thermal runaway summarizes four foundational physical models for TR simulation, responding to “how do we model TR?” Section seeking a balance between accuracy and efficiency explores potential optimization strategies to accelerate TR simulation, discussing “how can we predict TR faster?” Section other challenges and directions provides perspectives on the challenges of data availability, model scalability, and safety regulations. Finally, Section conclusion presents the main conclusions of this paper.

Understanding the TR process from multiscale perspectives

A comprehensive understanding of the evolutionary processes and underlying mechanisms of TR is fundamental for TR modeling. To assist in understanding these complex mechanisms and processes, we introduce a time sequence map (TSM) for a typical TR accident, as shown in Figure 2.^11,18,19 The TSM describes the evolution of TR through two crucial aspects: time series and spatial scales. Vertically, the TSM in Figure 2 sequentially summarizes TR performance considering the electrode, cell, pack, and system scales. Horizontally, it elucidates the chemical or physical processes at different levels, where the TR time series at a lower level serves as a link to that at a higher level.

Figure 2.

Evolution and mechanism of TR of LIBs from multiscale perspectives

Electrode scale

The evolution process at the electrode scale focuses on microelectrochemical reactions. When the LIB cell is exposed to various types of abuse, including thermal,²⁰ electric,^21,22,23 and mechanical,^24,25,26 its temperature may exceed the normal range, triggering a series of successive exothermic chain reactions. The solid electrolyte interface (SEI) layer on the graphite anode may initially decompose, releasing CO₂ and C₂H₄.^27,28 Without the SEI layer’s protection, the intercalated lithium in the graphite anode could react with the electrolyte, potentially generating hydrocarbons.²⁹ Contact between the cathode and anode, following separator shrinkage, leads to an internal short circuit (ISC), significantly increasing the battery’s internal temperature and resistance. This broad-scale ISC event can cause the cell temperature to rapidly rise to 300°C or higher, leading to cathode material decomposition and massive oxygen release.^30,31 Subsequently, the electrolyte decomposes exothermically.³² Finally, the binder, maintaining electrode integrity, reacts with reactive lithium leached from the lithiated graphite, producing H₂.³³ Key strategies to prevent TR at the electrode level include improving the thermal stability of electrode materials and interrupting chain reactions. This involves safety modifications to the cathode and anode,³⁴ the use of nonflammable ionic liquids and solid polymer electrolytes,³⁵ electrolyte additives,³⁶ and shutdown separators.³⁷

Cell scale

The aforementioned reactions not only serve as a heat source, accelerating the temperature increase within the LIB cell, but also generate substantial reaction gases that promote pressure buildup inside the cell. Simultaneously, the organic solvents in the electrolyte vaporize at the phase interface between the jelly roll and the cell’s headspace, contributing to partial pressure. As battery temperature increases and reaction rates intensify, rapid gas generation and pressure elevation can lead to cell expansion.³⁸ The jelly roll may deform or even fracture due to the resulting pressure difference between layers.³⁹ Once the cell pressure reaches its designed critical level, the safety valve will activate, releasing gases and initiating the initial venting event. LIB venting involves a typical multiphase process, including the ejection of gas-phase substances (H₂, CO, CO₂, CH₄, C₂H₄, C₂H₆, electrolyte, etc.),^40,41 liquid-phase components (electrolyte droplets), and solid-phase materials (electrode particles, collector fragments, etc.).^42,43 As the reaction progresses, the violent burst of exothermic reactions can eventually lead to TR, along with a secondary gas venting event. The flammable gas mixture can also ignite, resulting in a jet fire. At the cell level, the employment of positive temperature coefficient thermistors, current interrupt devices, safety valves, and protection circuitry represents standard safety strategies to mitigate TR hazards.⁴⁴

Module scale

The TR of a single cell can easily heat adjacent cells, resulting in TR propagation (TRP) and failure of the entire module, the culprit behind serious fire and explosion accidents. Mechanism analysis at the module scale focuses on two questions: how does TRP evolve, and how is heat transferred? As illustrated in Figure 2, when a cell undergoes TR, the generated heat from electrochemical reactions, including chemical crosstalk between electrodes and the ISC,^45,46 will be transferred to neighboring batteries through thermal conduction, leading to horizontal TRP within the module.^{47,48,49,50,51,52} Additionally, a ceiling fire forms when the jet impacts the battery pack’s top ceiling,⁵³ enhancing heat transfer between adjacent batteries and accelerating horizontal TRP.⁵⁴ The batteries in an upper module will heat up due to the flame, causing vertical TRP.^55,56 As combustible gases feed into the air from a battery pack, the fire will spread upwards along the pack’s wall, driven by buoyancy. This flame spread significantly enhances thermal feedback to the upper modules, promoting vertical TRP acceleration. TRP at the module level depends on the single cell’s heat dissipation and absorption capabilities.⁵⁷ Therefore, improving TR tolerance and decreasing TR intensity at the cell level, such as by mitigating crosstalk reactions to reduce heat release and increasing the TR triggering temperature, are effective prevention methods.³⁴ Because the thermal conduction through battery shells dominates the heat transfer, enhancing heat dissipation on noncontact surfaces by using a battery thermal management system (BTMS) and incorporating extra thermally resistant layers to reduce heat flux between adjacent batteries are crucial for inhibiting TRP.⁵⁸

System scale

At the system level, TR initially propagates within one battery module and then between different modules. TR accidents at the system scale typically present two hazard pathways: gas explosion and large-scale fire. Alongside TRP, substantial flammable gases continuously release and disperse within the fluid domains. If these gases accumulate in confined or semiconfined spaces and meet the fire triangle requirements, explosion incidents may occur. Furthermore, a phenomenon known as fire propagation can occur if the released gases ignite successively during TRP. The heat release rates (HRRs) during fire propagation at the system level can rapidly escalate to the MW scale,^59,60 potentially igniting other combustible components and leading to catastrophic fire incidents. Note that explosion and fire are not mutually exclusive but can occur simultaneously during accident evolution. At the system level, TR prevention focuses on effectively suppressing fires and reducing explosion risks. Currently, fire extinguishing agents, including gas, dry powder, water-based, and aerosol extinguishing agents, are the primary technologies for combating LIB fires.^61,62 To prevent gas explosions, effective combustible gas detectors and exhaust ventilation systems are feasible approaches.^63,64

While TR behaviors at the cell and module scales have received extensive investigation, understanding at the microscale and system scale remains limited. At the microscale, despite the development of many battery characterization and monitoring techniques to explore complex reaction processes in LIBs, some reaction mechanisms remain unclear due to the limited time-spatial-elemental resolution of current approaches.⁶⁵ On the other hand, at the system scale and beyond, the considerable economic cost associated with conducting full-scale TRP and fire tests presents a significant barrier. These challenges underscore the advantages of TR modeling in revealing the evolutionary characteristics and underlying mechanisms. In the future, combining experimental characterization and numerical simulation will prove to be an effective approach for gaining a deeper understanding of TR.

Developing a multiphysics coupling model for TR

The phenomena involved in TR encompass mechanics, thermodynamics, electrochemistry, and fluid dynamics. A comprehensive model that incorporates multiple physics fields facilitates the integration of these diverse physical phenomena, yielding more realistic simulations and deeper insights into their interactions. Figure 3 depicts a “tree” of multiphysics TR modeling for LIBs. This tree comprises four fundamental physics modeling approaches: thermal, electrical, mechanical, and fluid dynamics models. These models are interconnected by “tree branches” that represent their coupling relationships. The “tree root” emphasizes modeling the origins of TR, while the “tree crown” focuses on modeling the outcomes of TR. In the context of this TR modeling tree, this section reviews the current state of development for various physical models related to LIB’s TR and discusses potential challenges for future TR modeling.

Figure 3.

“Tree” of multiphysics modeling for TR of LIBs, where the “tree root” presents causation of TR, and the “tree crown” presents consequences of TR

Thermal model

The thermal models are fundamental to LIB TR modeling. They address three basic issues: how to mathematically describe thermal conditions, how to construct the energy balance of batteries, and how to determine the heat generation within batteries.

To describe the thermal conditions of a cell, thermal models may include boundary conditions (BCs), such as applying the Neumann BC on cell surfaces or the coupled BC between cells, heaters, and environments.^66,67,68,69 The integration of thermal BCs and energy balance models can yield an essential heat transfer model, the foundation of any TR model. The modeling approaches for an LIB’s energy balance can be mainly categorized into the lumped model and multidimensional models (see supplemental information for details). In a lumped model, each cell is treated as a node with mass and heat capacity, offering the advantages of simplifying system complexity and reducing modeling and analysis difficulty. As the node temperature represents the average temperature, the lumped model is suitable for cells with lower Biot numbers. Multidimensional models can be implemented using the finite difference method, finite element method, and finite volume method. Compared with the lumped model, multidimensional models can couple multiple physical fields to provide more detailed information about temperature distribution during TR, making them the most comprehensive approach in the field of battery modeling.

Heat generation and reaction kinetics

The primary method to describe heat generation from abuse reactions utilizes the reaction kinetic equations based on the Arrhenius law, as pioneered by Hatchard et al.⁷⁰ Subsequently, this model was extended by researchers to include additional exothermic reactions during TR (see supplemental information for details).^{66,68,71,72,73,74} The accuracy of simulated cell temperature critically depends on the correct estimation of reaction heat and kinetic parameters, typically derived from accelerating rate calorimetry (ARC) and differential scanning calorimetry (DSC) studies. Depending on the fitting methods, reaction kinetic models can be categorized into cell-based and component-based models. Cell-based reaction kinetic models refer to the temperature rise curve of the full cell measured under adiabatic conditions, such as that in ARC, which is utilized to estimate thermal kinetic parameters.^{75,76,77,78,79} In this approach, the entire TR process is divided into several stages based on the temperature rise rate range, and each stage is linearly fitted individually to derive corresponding kinetic parameters for various ranges.⁷⁷ However, this model cannot elucidate the sequence of reactions or the kinetics of electrode materials during TR. Another widely used reaction kinetic model is the component-based model.^{80,81,82,83,84,85} This model determines thermal kinetic parameters at the component level from DSC tests using Kissinger’s and Ozawa’s methods.^80,86 Hence, it aids in understanding the relationship between the heat generation of battery components and TR behavior, highlighting its potential for evaluating the safety performance of modified or new electrode materials and selecting safer battery materials.

However, thermodynamic parameters obtained from calorimetry tests are specific to one chemical system or state, as TR performance is influenced by materials,^87,88 state of charge (SOC),⁸⁹ and state of health (SOH).^90,91 In practical applications, SOC and SOH may vary over time or between cells, including SOC changes during cycling and differing aging degrees due to cell inconsistency. Recently, some modeling strategies have been proposed to identify thermodynamic parameters across the full SOC range, such as interpolating kinetic parameters⁹² and developing thermal-electric coupled models based on dimensionless normalized concentration.⁷⁶ In addition, as next-generation batteries with novel chemical systems, such as all-solid-state and sodium-ion batteries, emerge,^{93,94,95,96,97} there is a continued need to explore universal thermal kinetic models and matching parameters that can comprehensively encompass different chemical systems and cell states. Moreover, the current identification of kinetic parameters generally relies on extensive calorimetry testing to align with experimental results. Hence, developing robust and cost-effective parameter identification methods is urgently needed to improve model development efficiency.

TR propagation

TRP modeling approaches predominantly include the thermal resistance network model (TRNM)^98,99,100 and the three-dimensional (3D) numerical model.^{79,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115} In the TRNM, each cell is represented as an individual node with mass, heat capacity, and a heat source, connected by specific thermal resistances. The modeling procedure of the TRNM generally includes the development of a heat generation model for a single cell node and the subsequent combination of nodes based on energy balance (see supplemental information for details). The 3D numerical models are developed based on energy balance, effectively aggregating a single cell’s TR model through the application of heat transfer laws.¹¹⁶ Compared to 3D models, the TRNM is less suitable for geometrically complex systems and does not provide detailed temperature distribution during TRP. 3D numerical models not only overcome these limitations but also integrate multiphysics simulations to assess the effectiveness of various BTMS designs in preventing TRP.^{103,106,107,117,118,119,120,121}

TR exhibits multiple propagation modes in large-scale systems, including horizontal TRP, vertical TRP, and fire propagation. Current numerical investigations into TRP have primarily focused on horizontal propagation within a single battery module,^{79,101,103,106,107,110,113,115,122} with modeling of vertical TRP and subsequent fire propagation being relatively rare. A key challenge in these models is accurately coupling the TRP and combustion processes to capture their complex interactions. A significant step toward addressing this challenge has been the coupling of computational fluid dynamics (CFD) models with TR models.^108,123,124 However, such models are computationally demanding, and their accuracy heavily depends on the fineness of the geometric models used. This introduces another challenge, related to computational efficiency, in TRP modeling. Looking ahead, an important direction for future development is the creation of practicable TRP modeling strategies for large-scale and complex systems. This involves approximating ideal high-fidelity coupling models while ensuring that computational efficiency remains within acceptable limits.

Electrical model

In TR modeling, the electrical model is coupled with the thermal model through electrical heat generation, resolving electrical parameters such as current and voltage to further determine the electrical HRR, thereby assisting the thermal model in calculating cell temperature. Common electrical models include the electrochemical model and the equivalent circuit models (ECMs).

Comparison between electrochemical model and ECM

The electrochemical model, as a mechanistic model, captures the complex processes within LIBs. The widely used pseudo-two-dimensional model, pioneered by Newman’s group,¹²⁵ applies concentrated solution theory and porous electrode theory, with subsequent simplifications including the porous electrode model with polynomial approximation and the single-particle model (see supplemental information for details).¹²⁶ Electrochemical models provide accurate insights into the electrochemical mechanisms, enhancing understanding of the coupled nature of heat and electricity during TR. However, their complexity limits application in large-scale battery systems. Thus, electrochemical models primarily focus on mechanism analysis in thermoelectric coupling performance under various electrical abuse conditions, such as overcharge/discharge and short circuit, rather than consequence prediction.^127,128

The ECM characterizes electrical parameters using equivalent circuits composed of simple electrical components, such as voltage sources, resistors, and capacitors.^129,130 The commonly used ECMs are divided into two main approaches: the Thévenin model and the impedance model. Thévenin models are comprised of a voltage source, a series resistor-capacitor (RC), and resistors (see supplemental information for details). The impedance models usually incorporate a constant phase element (normally a Warburg element), whose value can be determined by electrochemical impedance spectroscopy. ECM’s advantages include simplified parameters and improved computational efficiency. Furthermore, it can potentially describe the electrical performance of connected battery modules. In practice, multiple batteries are assembled into a module with electrical connections to meet voltage and capacity requirements, with TRP behavior impacted by electricity transfer through these connections.^{50,52,131,132,133} Compared to electrochemical models, ECM is more suited to calculating electricity transfer between connected cells, offering a direct description of series/parallel connections using virtual topology rather than actual geometry. Hence, it can be coupled with TRP models to examine the influence of electrical connections on propagation. However, such coupled TRP models are rare and require further development.

Nevertheless, ECM has several disadvantages. It generally lacks an accurate depiction of LIBs’ local electrical-thermal coupling performance. Although enhancing ECM with additional circuit components, such as more RC pairs, can improve accuracy in replicating LIB electrical parameters, this increases computation time. Additionally, ECM lacks physical meaning, making it difficult to find a mechanism-based law to describe the response of electrical parameters to internal physical states, such as electrode degradation during TR. While parameter identification techniques can determine the values of circuit model components and integrate them into other models,¹³⁴ this relies on extensive preliminary experiments for data extraction. Thus, developing a physics-based ECM that maps internal battery states remains a challenge, necessitating further effort.

ISC

ISC occurs when the cathode and anode come into contact after separator failure, commonly linking mechanical, thermal, and electrical abuse conditions, resulting in TR.^7,22,23 Depending on the failure mechanism, ISC can be primarily categorized into spontaneous ISC and abuse-induced ISC.

Spontaneous ISC typically originates from internal defects during manufacturing.²² Modeling spontaneous ISC can provide references for early warning systems, though it presents significant challenges due to the need for multiscale modeling in both time and space. The development of spontaneous ISC from initial contamination and defects to noticeable heat generation often spans a lengthy incubation period, from days to months, while the subsequent TR may last only seconds or minutes,⁷ necessitating a model capable of considering these disparate time scales. Moreover, the scale of manufacturing defects is usually on the order of microns,¹³⁵ requiring models to resolve heat generation at this scale while considering energy balance at the whole-cell level, making multilength scale resolution crucial yet challenging.

ISC can also be triggered by thermal, electrical, and mechanical abuse. Thermal abuse may cause separator shrinkage and collapse, leading to significant ISC, typically integrated into thermal models based on separator melting points and cell temperature to simulate ISC triggers.^68,74 Electrical abuse, including overcharge and overdischarge, promotes continuous dendrite growth, eventually penetrating the separator.^136,137 This dendrite growth can be modeled using the kinetic Monte Carlo model,^138,139 the phase-field model,^140,141 and the Lagrangian particle-based smoothed particle hydrodynamics method, offering microscopic descriptions. However, linking microscopic dendrite formation to macroscopic TR behavior requires further investigation. Mechanical abuse, such as nail penetration or crushing,^24,142,143 leads to separator deformation and fracture, accounting for ISC.¹⁴⁴ Modeling frameworks for abuse-induced ISC simultaneously incorporate mechanical, electrical, and thermal models.^{25,145,146,147,148,149} In these frameworks, the mechanical and thermal models describe the battery’s mechanical and temperature responses, respectively, with the electrical model acting as a bridge: it couples with the mechanical model through stress states and with the thermal model through joule heat generation.

ISC links all “roots” of TR in most abuse scenarios. Note that ISC may not occur or significantly impact TR behavior in certain cases. For instance, chemical crosstalk between cathode oxygen and anode can directly generate heat, triggering TR without severe ISC.¹⁰ Furthermore, even if ISC is induced, the joule heat from ISC may be limited by sharply increased battery resistance, thus contributing minimally to TR heat generation.¹⁵⁰ The ISC model is a crucial step in early-stage TR modeling that focuses on the incubation mechanisms of TR under various abuse conditions. Looking forward, integrating the ISC model with TR detection and early warning systems is essential to facilitate early TR prevention.

Mechanical model

The mechanical model plays a critical role in developing a multiphysics coupling model for TR, spanning the simulation of the entire accident period of TR. As illustrated in Figure 3, the mechanical model can reveal the underlying process from initial mechanical damage to the occurrence of TR by coupling with the ISC model and thermal model. It also describes the mechanical response to internal pressure changes within the cell during TR by integrating with the fluid dynamic model. The former simulation focuses on modeling the origins of TR, while the latter addresses the consequences of TR.

Deformation under mechanical abuse

The battery structure will deform mechanically when subjected to mechanical abuse, such as crushing and penetration.¹⁵¹ The resulting ISC due to mechanical failure of the separator or electrodes can eventually lead to TR. Therefore, accurately describing the mechanical behavior and characteristics under abuse is crucial. Mechanical behavior is closely linked to the electrothermal behavior of LIBs; given that their coupling relationship in ISC modeling has been discussed, it is not reiterated here. Furthermore, modeling LIB mechanical behaviors involves multiple scales, including the component scale, cell scale, and module/pack scale.^152,153 The constitutive model, which characterizes the mechanical properties of battery components, forms the basis for predicting overall mechanical response.^154,155,156 The cell-level models consist of the homogenized model, the detailed model, and the representative volume element model.^{149,157,158,159} The homogenized model treats the cell as a single material described by an equivalent constitutive equation. In contrast, the detailed model considers each layer of individual components, providing deeper insights into the relationship between battery deformation and TR, although at a higher computational cost. The mechanical model at the module/pack scale primarily examines the overall mechanical behavior of the module and the impact of module structure on this behavior.¹⁶⁰ The considerable mechanical deformation of battery modules inevitably involves TRP; however, modeling TRP behavior considering the deformation of multiple batteries presents a significant challenge. Future research aiming to identify and implement the bidirectional coupling mechanism between deformation, electrochemical reaction, and heat transfer will enhance the precision of modeling at the module or even vehicle scale. This advancement is crucial for designing safer EV structures and determining escape times following an EV collision.

Mechanical response during TR

The mechanical responses of various battery components play a crucial role in the overall behavior of LIB cells and are integral to the safety design of LIBs. Due to pressure changes associated with gas generation and venting, batteries exhibit complex mechanical behaviors, including expansion,³⁸ collapse of the jelly roll,^39,161 and rupture of the safety valve.¹⁶² Current research on LIB mechanical response predominantly utilizes experimental methods. For instance, the evolution of internal structural damage and deformation can be observed in situ using high-speed synchrotron X-ray computed tomography.^39,161 Battery expansion behaviors during TR can be characterized by force sensors and strain gauges.^38,163 Modeling the mechanical response during TR is still relatively nascent. Given the strong coupling between mechanical behavior and fluid dynamics within and outside the battery, the fluid-structure interaction model emerges as a promising simulation strategy at the macroscale. This approach integrates a CFD solver with a structural finite element solver to capture structural responses. The fluid solver resolves the TR and fluid dynamics models and then transfers the pressure data to the mechanical model for strain calculation. At the microscale, the goal is to track the interaction between gas generation, pressure differentials between jelly roll layers, fracture of electrode and separator, and ISC. Coupled continuum and discrete (particle) numerical approaches have the potential to precisely simulate the porous structure formed by electrode particles and explore the thermal-electrical-mechanical coupled behavior during TR at the micrometer scale.

Fluid dynamics model

The TR of LIBs is always accompanied by the generation, emission, and flow of combustible gases, making the fluid dynamic model a critical component of multiphysics modeling for TR. The modeling approach for fluid dynamics in TR typically follows an “inside-to-outside” process, starting with the accurate simulation of gas generation and pressure changes inside the cell. This is essential for successfully depicting jet behavior, which, in turn, allows the CFD model to simulate the subsequent spread, combustion, and explosion behaviors outside the cell. Current fluid dynamic models for TR tend to focus more on the consequences of TR rather than its causation. The contribution from Ouyang’s group, highlighting that generated reductive gases could accelerate TR even during the early self-heating stage, is noteworthy.¹⁶⁴ This insight suggests the need to incorporate the influence of gas generation on the early stages of TR into future models, potentially providing new avenues for battery safety research.

Inside cell: Gas generation and pressure change

Gas generation, including the evaporation of electrolytes and the release of reaction gases, leads to pressure accumulation. Understanding the relationship between gas generation and internal TR progression is necessary for accurately capturing the internal pressure changes within LIBs. Currently, attempts are made to correlate evaporation rates with cell temperature and the generation rates of reaction gases with chemical reaction rates.^{19,165,166,167,168,169} However, accurately describing the quantitative relationship between each gas component’s generation rates and these parameters presents a significant challenge, both through mechanism analysis and experimental measurement. Firs, quantifying TR progression and reaction degree over time is difficult with existing experimental methods, and identifying experiment-based intermediary variables that can couple the easily measured heat and gas generation is urgent. Additionally, measuring each gas component’s yield in real time is challenging in the closed system of a battery before venting. Thus, analyzing vented gases after TR has become the standard method for investigating gas production.^{40,170,171,172,173,174} To overcome these challenges, current research often relies on simplifications and assumptions, such as presuming that gas generation rates are proportional to reaction rates^{19,123,166,167,168} and parameterizing coupling relationships mainly using gas analysis results after TR instead of real-time gas data.^{12,167,175,176,177} While these approaches may approximate pressure evolution to a certain extent, their accuracy remains a concern.

Outside the cell: Venting, combustion, and explosion

Coupling the internal pressure state inside LIBs with the highly transient flow field outside is a critical issue in modeling the cell venting and subsequent events. A commendable strategy is to construct a unified computing domain for both the battery and the external fluid, then simulate the flow process from the cell interior to the exterior using the CFD model.¹⁶⁷ However, this method faces difficulty in addressing the high-speed flow as gases pass through the safety valve, potentially reaching supersonic speeds. Our group has proposed a modeling framework based on conjugate heat transfer, adopting dynamic BCs at the vents to connect the cell interior and exterior (see supplemental information for details).⁶⁸ Initially, jet velocity is predicted based on internal pressure using a series of ordinary differential equations (ODEs) describing isentropic flow. Subsequently, the calculated jet dynamic parameters are applied to the coupled boundary on the safety valve to reflect the internal TR state. This framework has been widely adopted in subsequent numerical studies for its practicality in capturing both jet dynamics and heat transfer.^{123,168,176,177}

If the vented gas ignites immediately, a jet fire occurs; if not, the gas diffuses, posing an explosion risk. Early investigations of battery fires focused on calculating combustion properties using combustion kinetics models.^178,179,180 Recently, CFD models for LIB fires have emerged,^{78,124,167,175,176,177,181,182} enabling reliable predictions of physical field distributions outside LIBs. Nonetheless, challenges remain, such as explaining the generation mechanism of multiphase materials involved in the typical multiphase process of LIB venting and fire, which includes emissions of gases, electrode particles, and electrolyte droplets.¹⁸³

Concerning explosion hazards from gas release, two main questions arise: will an explosion occur, and what are the consequences? Calculating the lower explosive limit based on gas identification enables assessing the explosion possibility;^{41,184,185,186,187,188} however, integrating this with actual scenarios is challenging. Recent advancements include explosion behavior analysis through gas diffusion simulation,^12,168,189 aiding in dynamic risk assessment. Explosion consequences are generally assessed using premixed (or partly premixed) gas explosion models based on CFD.^190,191,192 Note that venting is a dynamic, continuous process in battery modules and broader TRP, implying that the probability and consequences of an explosion also vary dynamically. Thus, simulations based on specific states are not comprehensive. Therefore, developing a multiscale model that spans the entire “venting-TRP-diffusion-explosion” phenomenon chain is recommended, offering a valuable tool for the detection, early warning, and consequence assessment of TR.

Seeking a balance between accuracy and efficiency

The principal aim of developing multiphysics coupling models for TR is to comprehensively represent the emergence of TR from initial conditions. Given the computational cost limitations, a significant challenge is to extend the model across multiple scales—from microscopic particles to the cell level, module level, and even the entire system level—while integrating the coupled responses from various physical fields. Therefore, identifying ways to reduce the computational burden and achieve an optimal balance between accuracy and efficiency is another critical aspect of model development. In this section, we discuss promising modeling strategies to enhance calculation efficiency, focusing on the optimization of numerical and computational methods, model order reduction, and data-driven approaches, as depicted in Figure 4.

Figure 4.

Schematic of strategies to accelerate TR simulation

Optimization of numerical and calculation methods

The numerical simulation of TR involves solving a series of ODEs and partial differential equations governing the conservation of various physical parameters through time and space discretization. Due to their highly nonlinear and coupled nature, solving these equations typically incurs high computational costs. Optimizing numerical and calculation methods is considered the most fundamental strategy to accelerate the numerical solution of TR, focusing on the following aspects.

• (1)Mesh. Constructing high-quality mesh models is fundamental for accurate TR simulations. In a high-quality mesh, the sparsity and density should align with the parameter changes in physical fields, employing dense, body-fitted meshes for boundary layers.¹⁹³ Although using more mesh elements can yield more realistic results, the computational cost increases significantly with finer meshes across the entire domain. Adaptive mesh refinement offers an effective solution to balance calculation accuracy and efficiency by dynamically adjusting fine grids in regions with high gradients while employing coarser grids in less critical areas.
• (2)Discretization scheme. This involves both spatial and temporal discretization. Considering the stiff nature of the TR model, especially regarding chemical reaction source terms, selecting an appropriate discretization scheme is crucial. Parhizi et al. compared several time discretization schemes for a lumped TR model, finding that explicit methods can achieve accuracies similar to that of implicit methods but with reduced time costs, maintaining stability even in stiff TR scenarios.¹⁹⁴ The selection of discretization schemes for higher spatial dimensions and more complex physical fields requires further investigation.
• (3)Parallel computing. This technique decomposes the TR calculations into multiple subprocesses, which are then independently solved on different processors. The results from each processor are coordinated through communication, achieving acceleration through parallel computing.
• (4)Cloud computing. As a form of distributed computing, cloud computing enables the operation of developed TR models and data storage over the Internet.^195,196 It can address the storage and computing capacity limitations of edge devices during battery operation, facilitating rapid TR behavior prediction using the high-performance computing hardware available on cloud servers.¹⁹⁵

Model order reduction

The reduced-order model (ROM) is an approximation of the full-order model (FOM), designed to rapidly capture essential features, fundamentally transforming a large-scale complex system model into a smaller-scale approximate model through dimension reduction or parameter/model simplification. In battery TR modeling, ROMs, such as the TRNM, have been successfully applied to TRP in battery packs. Table 1 outlines the advantages, limitations, and applications of the ROM compared to the FOM. Advantages of the ROM include the following.

• (1)High computational efficiency. ROMs significantly reduce computation nodes, offering advantages in quick predictions and TRP simulation in large-scale ESSs.
• (2)Convenient parameterization. ROMs typically rely on fewer model parameters, simplifying TR modeling and calibration.
• (3)Reduced storage requirements. The extensive data from TR simulations generally demand substantial storage capacity on the battery system’s onboard hardware. ROMs, retaining only a limited number of state parameters of LIBs, require less storage space.

Table 1.

Comparison of advantages, limitations, and applications between the ROM and FOM

Model type	Advantages	Limitations	Applications
ROM	•high computational efficiency •convenient parameterization •reduced storage requirements	•limited accuracy •limited scalability	•large-scale ESSs •quick prediction and real-time control
FOM	•detailed information on physical processes and parameter distribution •capability to couple multiphysics simulation	•limited computational efficiency •simulation accuracy depends on mesh fineness	•high-fidelity simulations •mechanism research on TR

However, the pursuit of high computational efficiency in ROMs comes at the expense of fidelity, making it challenging for ROMs to capture detailed and complex physical processes during TR. Moreover, ROMs are specific to certain systems and operating conditions, complicating their direct application across different scenarios. Overall, both FOM and ROM have shortcomings in addressing TR simulation in LIBs; FOMs are computationally intensive, whereas ROMs may oversimplify the complex interactions between different physical phenomena. Thus, integrating FOM and ROM into hybrid models emerges as a promising solution, combining the strengths of both to ensure acceptable accuracy and efficiency.

Data-driven approach

The advancement of super time-sensitive technologies for LIBs, such as real-time monitoring and digital twins (DTs),^197,198 necessitates higher computational efficiency, with the simulation clock time required to be at least equal to the central processing unit time. Traditional optimization strategies often face significant delays when addressing the highly transient processes of TR, including the onset of TR, jet fire, and gas explosion. With the rapid development of AI technologies in recent years,¹⁹⁹ machine learning (ML) is being applied to battery modeling and real-time predictions, including online state estimation and diagnostics.^200,201,202 The incorporation of ML in LIB TR modeling is still emerging. We explore three potential modeling strategies that integrate TR forecasts with ML, as illustrated in Figure 5, aiming to inspire and guide the next generation of LIB TR modeling.

• (1)Parameter-based ML. This approach establishes a direct mapping relationship between the physical information of the battery system and TR feature parameters using artificial neural networks (ANNs) or other intelligent algorithms,²⁰³ effectively a “parameter-to-parameter” mapping. This model’s simplicity and intuitiveness are advantageous, with no practical constraints on dataset generation, as all test conditions can be labeled specifically. Thus, data from any TR test can be included in a unified dataset, provided it encompasses broadly applicable input features. Notably, data cleaning methods are required to eliminate abnormal data and enhance data quality, as not all experimentally collected battery data are of high quality.²⁰⁴ Establishing a standardized database and big-data platform is promising for efficient data storage, management, and analysis, facilitating the development of parameter-based ML models by reducing dataset creation costs and promoting data sharing.
• (2)Physical field-based ML. This model uses 2D and 3D engine data, such as simulation result images, as inputs or outputs for ML models to analyze and predict TR behavior, treating these image data similarly to physical field data. This approach, either “parameter-to-field” or “field-to-field” mapping, involves several steps, including data generation, feature engineering, data reduction, data regression, and data reconstruction.²⁰⁵ Data generation involves the systematic creation of physical field data from numerical models to serve as training data for the ML model and testing data to evaluate its performance. Feature engineering is a critical stage where key features influencing the TR simulation results, such as geometry, BCs, and initial conditions, are identified, selected, and then extracted, transformed, or combined. Data reduction involves the progressive downsampling of image size through convolutional blocks or layers. This process extracts large-scale and abstract information until it culminates in a single data point with several features. Data reconstruction utilizes symmetric layers to accurately reconstruct the target functions in the appropriate dimensions. The physical field-based ML model requires geometry, BCs, and initial conditions as inputs to output physical fields for the entire domain. Therefore, it can accelerate multiphysics simulations, presenting significant application prospects in the design and operation stages of LIBs. First, this method increases the optimization efficiency of battery safety design, as it can assess the risks and hazards of TR for several designs in a short time, accelerating optimization. In addition, it can reconstruct high-fidelity data from sparse sensor measurements in ESSs or EVs, aiding the development of real-time monitoring and DT technologies.
• (3)Physics-informed ML. Purely data-driven methods may fail to predict behaviors outside the training data range²⁰⁶ and occasionally produce unphysical predictions due to neglecting underlying physical mechanisms. Integrating physical governing equations into the data-driven framework can address these issues. Raissi et al. introduced a physics-informed neural network (PINN) that incorporates physics governing equations, initial conditions, and BCs as training constraints to ensure the predicted results satisfy physics rules.²⁰⁷ Compared to the ANN, this approach is more tolerant to the reductions in the number of sample points, indicating that the distributed data matrix measured by experiments can be used for training.²⁰⁸ Besides, the PINN is a meshless approach, particularly suited to simulations involving large deformation and high-speed jets that require high-quality meshes. These advantages make the PINN promising for practical applications in TR multiphysics modeling.

Figure 5.

Flowchart of three types of ML for TR modeling

While ML’s expansion continues to significantly impact LIB modeling, its integration with TR simulation is not without challenges. ML’s reliance on high-fidelity data, substantial training data requirements, and lack of interpretability as a black-box model are key constraints. Therefore, ML should be viewed as complementary to traditional multiphysics coupling models for TR rather than as a complete replacement.

Other challenges and directions

Data and code availability and accessibility

TR modeling necessitates extensive data, encompassing input data for model parameterization, experimental data for model validation, and datasets for ML training. The safety risks and economic costs associated with TR experiments pose significant challenges in acquiring reliable and informative data. Precise input data, such as battery physical property parameters and reaction kinetic parameters, form the foundation for establishing a reliable TR model, usually obtained through extensive testing and meticulous calibration or fitting. An AI-driven approach may offer a novel method to extract model input parameters directly from macroscopic TR behavior in the future. Validation data currently lack in situ experimental evidence at the electrode level and comprehensive data from full-scale TR tests at the system level and beyond. Furthermore, existing experimental data primarily focus on cell temperature, voltage, and HRR, with scarce data on cell internal pressure, transient rates of gas generation, jet velocity, etc. ML datasets require a large volume of data to ensure sufficient training iterations and statistical accuracy. Establishing a standardized database for free and easy access and sharing is advocated, demanding ongoing efforts from the TR research community.

Model universality and scalability

The continuous evolution of battery designs and increasingly complex application scenarios underscore the necessity for ongoing model updates, highlighting the need for improved universality and scalability in TR models. Model parameterization should allow easy adaptation to LIBs of varying sizes, geometries, materials, and operating conditions by adjusting relevant input parameters. At the code level, a modular modeling architecture is considered a strategic approach to enhance TR model scalability. Modularization involves decomposing a comprehensive model structure into smaller, independent sub-models, each with its defined interface for inputs and outputs, capable of operating independently or in combination with other modules. This building-block architecture facilitates the addition of governing equations by integrating new simulation modules without requiring recompilation or source code modifications. It enables practitioners to focus on developing advanced TR models by utilizing existing modules with minimal effort. Advancing the development of modular TR models can be supported in several ways. Open-sourcing of code can aid in understanding, utilizing, and enhancing the model, promoting the sharing and continuous improvement of modular TR models. Data harmonization and normalization are essential to ensure input and output parameter consistency and compatibility across different TR simulation modules. Moreover, TR modeling technology spans multiple disciplines, including physics, chemistry, materials science, and computer science. Interdisciplinary collaboration is vital, merging expertise from various fields to overcome disciplinary barriers and promote the comprehensive advancement of modular TR models.

Safety testing standards and regulations

To ensure the sufficient safety quality of LIBs available on the market, numerous safety requirements have been established by business assessment standards and national compulsory testing regulations, including GB 38031-2020, UL 2580-2020, GTR 20, and UN ECE R100.^{209,210,211,212} For instance, a thermal alarm signal of 5 min is required in EVs before any passenger compartment hazard caused by TRP. Considering the low pressure for air transport, the battery packs shall be stored in a low-pressure environment of 11.6 kPa for at least 6 h according to UN T 38.3. For ESS, the global combustible concentrations have to be limited at or below 25% of the lower flammability limit after TR, required by NFPA 69. These standards and regulations aim to mitigate the risk of TR by mandating a series of tests that a LIB cell, battery module, pack, or system must successfully undergo to achieve certification. In this context, TR modeling may become a requisite part of the certification process to verify that products meet both safety and performance standards, provided that the trustworthiness in TR models has been achieved. Consequently, there is a need to develop an integrated model that incorporates all types of abuse conditions to comply with the diverse approval test categories, parameters, and conditions. Moreover, reliable and extensive experimental data are required for the comprehensive validation of the developed TR model.

Conclusion

The modeling of TR plays a crucial role in comprehending TR behavior and in the development and operation of safer batteries, marking it as a significant area of research for many years. However, with increasingly complex application scenarios and heightened demands for simulation scale, model fidelity, and computational efficiency, TR model development faces significant challenges. This perspective paper reviews current modeling strategies for TR, addressing the challenges and future directions around key questions in TR simulation techniques. It begins by examining the evolutionary processes and underlying mechanisms of TR from multiscale perspectives, introducing a TSM that depicts the complete event chains of TR from the electrode to the system level. This aims to deepen researchers’ understanding of TR and delineate the objectives/processes for simulation. Subsequently, the framework for a multiphysics coupling model to capture these phenomena during TR is presented. The basic models within this framework, including thermal, electrical, mechanical, and fluid dynamics models, and their interconnections are detailed with emphasis. Promising strategies to enhance calculation efficiency, such as optimization of numerical and calculation methods, model order reduction, and data-driven approaches, are discussed. With the advent of super-time-sensitive technologies for prediction, integrating AI with multiphysical modeling emerges as a forward path in TR modeling. Last, the paper outlines challenges related to data availability, model scalability, and adherence to standards and regulations. The purpose of this paper is to assist researchers in addressing unresolved issues in TR modeling and enhancing the understanding of modeling procedures and strategies. This work seeks to provide insights and directions for future scholars dedicated to advancing next-generation TR models.

Published Online: April 8, 2024

Lead contact website

https://cmee.upc.edu.cn/2024/0305/c21432a424369/page.psp.