Heat Pipe Integrated Cooling System of 4680 Lithium–Ion Battery for Electric Vehicles

Abstract

This study investigates a novel heat pipe integrated cooling system designed for thermal management of Tesla’s 4680 cylindrical lithium–ion batteries in electric vehicles (EVs). Through a comprehensive approach combining experimental analysis, 1-D AMESim simulations, and 3-D Computational Fluid Dynamics (CFD) modeling, the thermal performance of various wick structures and working fluid filling ratios was evaluated. The experimental setup utilized a triangular prism chamber housing three surrogate heater blocks to replicate the heat generation of 4680 cells under 1C, 2C, and 3C discharge rates. Results demonstrated that a blended fabric wick with a crown-shaped design (Wick 5) at a 30–40% filling ratio achieved the lowest maximum temperature (T_max of 47.0 °C), minimal surface temperature deviation (ΔT_surface of 2.8 °C), and optimal thermal resistance (R_th of 0.27 °C/W) under 85 W heat input. CFD simulations validated experimental findings, confirming stable evaporation–condensation circulation at a 40% filling ratio, while identifying thermal limits at high heat loads (155 W). The proposed hybrid battery thermal management system (BTMS) offers significant potential for enhancing the performance and safety of high-energy density EV batteries. This research provides a foundation for optimizing thermal management in next-generation electric vehicles.

1. Introduction

The advancement of battery electric vehicles (BEVs) has become central to the transformation of the automotive industry. BEVs offer significant advantages over traditional internal combustion engine (ICE) vehicles, including the elimination of tailpipe greenhouse gas emissions, improved energy conversion efficiency, and a reduced number of mechanical parts, contributing to lower maintenance requirements [1]. Among various energy storage technologies, lithium–ion batteries have emerged as the dominant power source for new energy vehicles. Since their initial commercialization by Sony Corporation in 1990, lithium–ion batteries have played a crucial role in shaping the development of BEVs [2].

Despite the rapid progress in battery technologies, the mass adoption of BEVs is currently experiencing stagnation. This deceleration, often described in terms of the “chasm” phenomenon, has been linked to persistent technical challenges, most notably limited driving range and long charging times [3]. These constraints remain primary concerns for consumers and have hindered broader market penetration. Addressing such challenges necessitates not only improvements in electrochemical performance but also the development of high-power fast-charging capabilities, often exceeding 300 kW. However, increasing energy density and rapid charging rates are directly associated with higher heat generation, thereby intensifying the need for robust BTMS.

Various BTMS technologies have been proposed and implemented to maintain safe and efficient operating temperatures. These include air cooling, direct and indirect liquid cooling, phase change material (PCM)-based methods, and heat pipe-assisted approaches. Each configuration offers distinct advantages and is subject to specific limitations in terms of thermal conductivity, system integration, reliability, and cost.

Parallel to advancements in thermal control technologies, the evolution of battery cell formats has significantly influenced BEV design and performance. The industry has progressed from the 18650 cylindrical format, known for its manufacturing maturity and reliability, to the 2170 format, which provides improved capacity and thermal behavior. More recently, the 4680 cylindrical cell has gained attention due to its increased energy density, tabless internal structure, and reduced internal resistance [4]. While this format offers improved volumetric efficiency and performance, it also introduces substantial thermal management challenges, owing to its larger thermal mass and greater internal heat generation.

Thermal regulation of 4680 format cells has become an increasingly important research topic. In experimental investigations, Li et al. [5] observed that during 1.5 C discharge, the surface temperature of 4680 cells exceeded 70 °C, despite the use of tabless design and top and bottom indirect liquid cooling. This suggests that even with architectural innovations, conventional BTMS strategies are not sufficient to handle the thermal loads of large-format cells. Similarly, Baazouzi et al. [4] reported limited thermal improvements in 4680 cells compared to 2170 cells under high load conditions, based on teardown analysis. To explore possible improvements in cooling strategies, Eze et al. [6] performed a coupled electrochemical–thermal simulation to evaluate the effectiveness of different cooling approaches. Their findings indicated that a combined top and bottom cooling method is more suitable for large-format cylindrical cells. However, they also noted that the analysis was conducted under ideal thermal boundary conditions and lacked experimental validation. Furthermore, practical integration aspects, including module design constraints and coolant routing, remain underexplored.

The aforementioned studies collectively reveal a critical limitation in existing thermal management practices. While the 4680 format improves energy density and enables simplified module design, its substantial internal heat generation and nonuniform thermal distribution pose serious challenges for maintaining thermal stability. In particular, the literature rarely addresses important design factors such as wick structure optimization, thermal interface design, or the effective use of internal chamber geometry. Moreover, experimental validation of BTMS strategies tailored specifically for the 4680 format remains insufficient.

To address these gaps, the present study introduces a novel hybrid BTMS that combines heat pipe-based thermal transport with two-phase immersion cooling. The proposed configuration incorporates a capillary wick structure that actively facilitates liquid return within the heat pipe through capillary action. This mechanism enables efficient two-phase heat transfer using a small volume of working fluid and enhances the thermal uniformity of the system. Unlike conventional immersion cooling systems, which rely solely on natural convection or PCM integration, this approach allows for passive circulation without the need for mechanical pumps. The overall result is improved thermal performance and reduced system weight, which are both essential for high-power density applications such as BEV battery modules.

In this study, the proposed system is evaluated through both experimental investigations and multiphysics simulations. Key parameters analyzed include thermal behavior under high-rate charging conditions, the influence of wick structure configuration, and the effects of varying filling ratios. The integrated approach aims to establish a scalable and reliable solution that addresses the unique thermal demands of large-format cylindrical lithium–ion cells.

Understanding the operational thermal limits of lithium–ion batteries is essential for evaluating the significance of the proposed BTMS design. These batteries typically operate within a functional range of minus 20 to 60 °C and have an optimal temperature window between 15 and 35 °C [7,8]. Exceeding these boundaries can result in reduced charge efficiency, capacity degradation, and, in extreme cases, thermal runaway, a highly dangerous and irreversible failure process [9]. Tesla’s 4680 battery, for example, exhibits an average temperature of 67.77 °C and a thermal gradient of 2.64 °C under a 1.5 C discharge rate with top and bottom cooling. In contrast, the 2170 cell under the same conditions reaches 86.84 °C and exhibits a much steeper thermal gradient of 20.92 °C [5].

These results demonstrate the superior capacity, output performance, and thermal stability of the 4680 battery compared to the commercialized 2170 cell. However, even at a 1.5 C discharge rate, the 4680 cell still exceeds the upper allowable temperature limit of 60 °C. This suggests that during fast charging at rates of 2 C or higher, excessive heat generation may lead not only to reduced charging efficiency and capacity loss but also to an increased risk of thermal runaway [5].

Air cooling, one of the earliest and most widely adopted BTMS methods, is appreciated for its simplicity, light weight, and cost-effectiveness [10]. However, due to the low thermal conductivity and specific heat capacity of air, this approach often results in uneven temperature distribution and insufficient cooling performance [11]. Several enhancements, such as pressure-relieved ventilation [12], parallel airflow design [13], reciprocating flow configurations [14], and specialized heat sink structure [15], have been investigated to improve heat dissipation. Although hybrid air cooling systems combining series and parallel flow paths show potential [16], air cooling still suffers from critical limitations when applied to high-density battery systems. In addition, the ingress of airborne particulates can further degrade cooling performance and increase thermal resistance, as shown by Feng et al. [15].

To overcome these limitations, liquid cooling has been increasingly adopted in modern BTMS designs. Direct liquid cooling offers excellent thermal performance but presents challenges in ensuring uniform coolant distribution and avoiding leakage [12]. Indirect methods, which use cooling plates and low-viscosity fluids to transfer heat without direct contact with battery cells, are more practical for modular integration [17,18,19]. Nevertheless, issues such as thermal contact resistance, increased component weight, and higher installation costs remain [20,21]. The use of nanofluids containing aluminum oxide or titanium dioxide particles has been proposed to improve the thermal conductivity of liquid coolants [22,23], and structural optimizations, such as serpentine cooling channels, have also been explored [24]. For example, Ahmad et al. [15] investigate the performance of a microchannel heat sink enhanced with sidewall ribs to improve heat removal under single-phase liquid cooling, which is a relevant indirect cooling strategy for high-power density systems such as electric vehicle battery packs.

PCM-based BTMS approaches have attracted attention for their ability to regulate temperature passively through latent heat absorption and release during phase transitions [11,25]. However, the inherently low thermal conductivity of PCMs, along with volume changes during melting and solidification, limits their overall effectiveness [26,27,28,29]. To mitigate these issues, composite structures incorporating metal foam or expanded graphite have been proposed, and hybrid PCM–heat pipe systems have been introduced to improve thermal response [30,31].

Heat pipe systems provide high thermal conductivity and passive operation without external energy input. They typically consist of evaporation, adiabatic, and condensation regions, allowing working fluid to circulate through evaporation and condensation cycles. These systems offer promising potential for regulating temperature in battery modules [30,32,33]. Modular implementations have demonstrated reduced peak temperatures [34] and improved thermal uniformity through enhanced surface contact designs [35]. However, heat pipes face limitations related to limited cooling capacity, small contact area, and manufacturing cost, especially when copper materials are used [36].

Two-phase immersion cooling using electrically insulating fluids offers another promising approach. By directly submerging cells in dielectric fluids, this method achieves efficient thermal regulation and reduces the risk of thermal runaway [30]. When combined with heat pipes, immersion cooling further improves thermal performance while eliminating the need for active pumping. For high-energy density batteries such as the 4680 cell, where thermal buildup under fast charging can surpass 70 °C [18], such an integrated solution can play a vital role in maintaining safe and efficient operation.

In consideration of the aforementioned issues, the present study proposes and experimentally validates a hybrid thermal management strategy that integrates heat pipes with two-phase immersion cooling, as depicted in Figure 1. This figure presents the proposed cooling configuration specifically designed for the 4680-format cylindrical battery cell. In this system, the battery pack is vacuum-sealed, and a working fluid is introduced to form a closed-loop structure that operates analogously to a heat pipe with an internal heat source. During the charge and discharge processes, heat generated by the battery is effectively transported to the upper cooling plate through the continuous evaporation and condensation of the working fluid. This mechanism significantly reduces thermal resistance between the battery surface and the cooling interface.

Unlike conventional immersion cooling systems, which rely on mechanical circulation of the coolant to ensure contact across the entire cell surface, the proposed method utilizes a smaller quantity of working fluid while simplifying the internal flow path of the cooling plate. This also reduces the power requirements of auxiliary components such as pumps. Accordingly, the objective of this study is to develop a compact, passively operated, and thermally efficient battery thermal management system that is well-suited for next-generation cylindrical lithium–ion batteries in electric vehicles and other high-power applications.

2. Experiment

2.1. System Description

This study was conducted to experimentally investigate the heat-generation characteristics of 4680 cylindrical battery cells used in EVs under realistic operating conditions and to validate the effectiveness of a proposed thermal management strategy. The experimental setup defined a single module as a triangular cross-sectional chamber capable of housing three cells. By analyzing the thermal behavior at the module level, the feasibility of a modular design approach was assessed.

Due to the inherent risks of thermal runaway and explosion associated with lithium–ion batteries under overheating conditions, direct experimentation using actual battery cells poses significant structural and safety constraints. Therefore, this study employed a surrogate experimental system in which controlled power levels corresponding to 1 C, 2 C, and 3 C discharge rates were applied. A custom-designed metal heater was used to replicate the lower tab region of the cell, where heat generation is most concentrated. This approach enabled safe and quantitative reproduction of the battery’s thermal behavior under realistic operating scenarios.

The experimental testbed was designed in the form of a triangular prism chamber that contains three cylindrical heating blocks that imitate the thermal behavior of the 4680 battery cells. The equilateral triangular layout offers some benefits for the system. First, the layout allows minimizing the dead space within an EV battery pack, therefore maximizing the modular integration efficiency. Moreover, besides its spatial compactness, the layout provides benefits in managing thermal behavior inside the chamber by creating symmetric conduction paths between adjacent cells, whose performance was verified by the study from Liu et al. [37], promoting thermal dissipation and contributing to improved overall energy density.

Each heating block included a 1 mm long lower tab region and was fabricated from stainless steel (SUS304) to simulate the primary heat-generating characteristics of actual 4680 cells. Within the chamber, a clearance of approximately 9 mm was maintained between the heating blocks, the chamber walls, and adjacent blocks to provide sufficient space for the circulation of the working fluid and the placement of wick structures.

Table 1. Experimental component dimensions.

Component	Parameter	Value	Description
Triangular Cooling Chamber	Side length	165.85 mm	Side length of the internal equilateral triangular layout
	Height	83 mm	Internal chamber height
	Wall thickness	2 mm	Wall thickness of the chamber
Cylindrical Heater Block	Diameter	46 mm	Designed based on the geometry of a 4680 cylindrical battery cell
	Height	81 mm	Total length including the actual cell tab
	Quantity	3ea	Arranged in an internal equilateral triangular configuration

presents the dimensions and characteristics of the triangular cooling chamber and cylindrical heater block used in the experiment. As illustrated in Figure 2, a total of three heater blocks were installed in an equilateral configuration, allowing temperature measurement via TC rods and heating through cartridge heaters.

The entire system was hermetically sealed under vacuum to enable efficient operation of the evaporation–condensation mechanism of the working fluid. Thermal performance was quantitatively evaluated based on three key metrics: maximum temperature (T_max), surface temperature deviation (∆T_surface), and thermal resistance (R_th).

According to Ank et al. [38], Tesla’s 4680 cylindrical cell has a reported capacity of approximately 21 Ah and an internal resistance in the range of 5–7 mΩ. Using the conservative values of 21 Ah capacity and 7 mΩ internal resistance with the heat-generation formula Q = I²R, the theoretical heat output per cell was calculated as approximately 3.09 W at 1 C, 12.35 W at 2 C, and 27.78 W at 3 C, corresponding to total module heat loads of 9.26 W, 37.04 W, and 83.35 W, respectively.

The experimental heat input levels were established at 15 W, 50 W, and 85 W based on two primary considerations. First, lithium–ion cell parameters such as internal resistance vary within typical ranges (5–7 mΩ), even among nominally identical cells. When this variability is accounted for, heat generation at each C-rate spans a corresponding range. The selected values represent the upper end of these possible ranges, ensuring test conditions reflect more demanding thermal scenarios and account for worst-case heat load conditions during high-rate operation. Second, heat input was delivered using electrical cartridge heaters controlled by manually adjusting current and voltage on a DC power supply. The rounded values (15 W, 50 W, and 85 W) correspond to easily settable and repeatable power levels under this control scheme, improving experimental accuracy and reproducibility while maintaining thermal loads representative of 1 C–3 C operating conditions.

For experimental convenience and alignment with the testbed’s design constraints, these values were rounded to experimental input levels of 15 W, 50 W, and 85 W, respectively. This heat input configuration was intended to replicate the high-power thermal environment that could arise in actual 4680 cell-based systems, while also enabling a clear evaluation of the cooling system’s performance limits.

Table 2. Material of wick.

Wick 1	Wick 2, 3	Wick 4, 5
Polyurethane	Cellulose	Viscose rayon and polyester-blended non-woven fabric (hereafter referred to as “Blended Fabric”)

provides information on the materials used for the wicks and Figure 3a–f illustrates the geometries and detailed dimensions of the six wick configurations used in this study. The Wickless case, which contains no wick structure, served as the reference condition and provided a baseline without capillary action. Wick 1 was designed to completely fill the interior of the triangular heater block with polyurethane foam, ensuring minimal voids. The wick was in close contact with the heater surface, while maintaining a ~2 mm clearance between the top of the wick and the cooling plate to allow for unobstructed vapor flow. Wick 2 and Wick 3 utilized cellulose-based wick materials, each with a uniform thickness of 3 mm, and were configured to wrap around the cylindrical surface of the heater blocks. Wick 2 enveloped the entire outer surface of each heater block, promoting uniform contact with the working fluid. In contrast, Wick 3 featured a vertical slit starting from the center of the wrapping surface, forming a “crown” structure. This modification aimed to facilitate vapor release and enhance internal circulation. Wick 4 and Wick 5 employed blended fabric instead of cellulose, while mimicking the geometrical designs of Wick 2 and Wick 3, respectively. Thus, Wick 4 corresponds structurally to Wick 2, and Wick 5 replicates the crown-type configuration of Wick 3. These variations enabled a comparative analysis of thermal transport and capillary performance depending on wick material. The differences among these wick designs influence working fluid recovery, vapor release, and heat transfer uniformity. Ultimately, the goal was to evaluate structural optimization strategies for enhancing thermal control under high-heat flux conditions.

Figure 4 presents SEM (scanning electron microscope) images of the surface morphology of the three wick materials used in this study. Image (a) corresponds to the polyurethane foam used in Wick 1, while image (b) shows the cellulose-based fiber material applied in Wick 2 and Wick 3. Image (c) represents the blended fabric used for Wick 4 and Wick 5. Each material exhibits a porous structure capable of inducing capillary action, which, in combination with wick geometry, plays a critical role in influencing heat transfer performance. To estimate the porosity of the PU wick shown in Figure 4a, SEM images were binarized using a MATLAB (R20214b) algorithm to calculate the 2D porosity. Since 2D porosity tends to underestimate 3D porosity, we referred to the work by Guelcher et al. [39], which reported both SEM images and ASTM D3574–01-based 3D porosity values for PU foams. By comparing the SEM-derived 2D porosity of those samples with their corresponding 3D values, we derived a correction factor (1.3), which, when applied to our experimental 2D result (73.8%), yielded a 3D porosity of 95.9%. This value aligns well with both the literature range (89.1–95.8%) and our initial density-based estimate (~98%), supporting the validity of the corrected result. This SEM-based porosity estimation was applied only to the polyurethane sample in Figure 4a, as its material properties were not available from the manufacturer’s catalog. In contrast, both cellulose (Figure 4b) and blended fabric (Figure 4c) had well-documented density and structural information provided by the manufacturers. Therefore, their porosities were calculated using conventional density-based estimation methods. The porosity of the cellulose and blended fabric wicks was estimated to be approximately 90% and 95%, respectively.

2.2. Material Properties

Table 3. Material properties used in the experiment.

Material	Density, kg/m3	Thermal Conductivity, W/m-K	Specific Heat Capacity, J/kg-K
SUS304	8000	16.3	530
Polyurethane	979	0.051	4070
Cellulose	1500	0.57	1209
Blended Fabric	1020	0.50	3970

summarizes the material properties used in the experimental setup. It includes four materials: SUS304, polyurethane, cellulose, and blended fabric. The table lists the density, thermal conductivity, and specific heat capacity of each material, which are critical for evaluating heat transfer behavior.

2.3. Experimental Setup

Figure 5 shows the overall configuration of the experimental apparatus used in this study. Inside the triangular prism-shaped chamber, three heater blocks were arranged in an equilateral triangular layout. A cartridge heater (Seonglim Industry, Daejeon, Republic of Korea) was embedded at the center of each heater block to serve as the heat source. The heaters were connected to an external power supply unit, the Slideax SD-1000 (Daesung Electric, Cheongju, Republic of Korea), which maintained output voltage stability within ±5% under load conditions. Each heater block was instrumented with six K-type thermocouples (Omega Engineering, Norwalk, CT, USA) [40], totaling 18 thermocouples. These were attached to metal rods and inserted at three vertical positions (top, middle, and bottom) to capture detailed temperature distributions. TC numbers 1 and 2 were installed at the inlet and outlet of the chiller, respectively. Thermocouples TC 3 through TC 20 were inserted from the lower external side of the chamber in metallic probe form. The sensors had a measurement accuracy of ±0.75%, and all temperature data were transmitted to an MX-100 data acquisition system (Yokogawa, Tokyo, Japan) [41], where readings were recorded every 500 ms with a ±0.05% accuracy and logged to a connected PC. The cooling system circulated coolant through a top-mounted cooling plate to induce condensation of the working fluid. This system utilized a forced-circulation chiller (Model RBC-9, LAB HOUSE, Pocheon, Republic of Korea) [42], which featured a working temperature range from −10 °C to 90 °C, a temperature control accuracy of ±0.2 °C, and a built-in 1.5 kW heater. The chiller maintained consistent flow rate and temperature, ensuring a stable condensation environment during testing. Prior to each experiment, the chamber was evacuated to a partial vacuum level of approximately 0.1 bar using an air pump. Distilled water was then introduced as the working fluid, and the filling ratio was adjusted accordingly. To ensure accurate measurements, the entire experimental setup was thermally insulated with extruded polystyrene (XPS) boards. This minimized external heat losses and allowed precise evaluation of the internal heat transfer performance within the heater blocks.

2.4. Evaluation Metrics and Calculation Formulas

2.4.1. Filling Ratio

The filling ratio (FR) is one of the key parameters influencing the performance of heat pipe-based cooling systems. It represents the proportion of working fluid filled within the system. In this study, cooling performance was quantitatively evaluated by varying the filling ratio from 30% to 70% in 10% increments, using a configuration that includes a heat source simulating a 4680 cylindrical battery. This experimental range was selected based on previous studies that identified optimal thermal performance in the vicinity of 30–50% FR. Tharayil et al. [43] reported that a 30% filling ratio yielded the lowest thermal resistance and best cooling stability in a miniature loop heat pipe, while both lower (20%) and higher (50%) ratios showed degraded performance due to dry-out and partial flooding, respectively. Similarly, Verma et al. [44] found that a filling ratio of 50% provided the best performance with DI water in a pulsating heat pipe, and that thermal resistance increased when FR exceeded this point. Based on these findings, a range of 30% to 70% was chosen to encompass the commonly reported optimum zone while exploring the effects of moderate over- and underfilling. Ratios below 30% were avoided due to the increased risk of dry-out, and those above 70% were excluded to prevent flooding or vapor flow restriction—both of which can lead to thermal inefficiency. The filling ratio is defined by Equation (1).

$$FR={\displaystyle \frac{V_f}{V_t}},$$

(1)

An appropriate filling ratio is essential to ensure stable evaporation–condensation cycling of the working fluid. This directly contributes to lowering the T_max, minimizing surface temperature deviation ΔT_surface, and reducing thermal resistance R_th. Therefore, validating the optimal filling ratio is critical for enhancing the thermal performance of the system.

In this study, distilled water was selected as the working fluid. Due to its high specific heat capacity and large latent heat of vaporization, distilled water offers excellent heat absorption characteristics under high-power conditions. It is also chemically stable and cost-effective and offers high experimental repeatability and reproducibility, making it an ideal reference fluid for early-stage evaluations.

Given these advantages, this study quantitatively assessed the cooling performance as a function of wick structure and filling ratio using distilled water. For future research, dielectric fluids such as the Novec™ series (3M Korea, Seoul, Republic of Korea), known for their electrical insulation and chemical stability, should be considered. These fluids are suitable for immersion cooling applications and will allow system performance evaluation under more realistic operating conditions.

Moreover, to verify whether the wick structure can fully exhibit capillary action, it is necessary to first examine performance using distilled water before introducing more complex working fluids. Accordingly, the present study focuses on analyzing the thermal behavior under various filling ratios using distilled water, laying the groundwork for extended investigations involving diverse fluids and structural configurations.

2.4.2. Thermal Resistance

In this study, an uncertainty analysis was conducted for the calculation of system thermal resistance (STR). This analysis was essential to evaluate the accuracy of the measured voltage (V), current (I), and the temperatures at the evaporator (T_Evaporator, T_E) and condenser (T_Condenser, T_C). R_th was calculated using Equation (2)

$$R_{th}={\displaystyle \frac{T_{Evaporator}-T_{Condenser}}{Q}},$$

(2)

where Q represents the input heat to the system, determined using Equation (3)

Q = V · I,

(3)

where T_E denotes the average temperature of the evaporator, which corresponds to the mean value of the stabilized temperatures measured inside the test block. T_C refers to the average temperature of the condenser, defined as the inlet temperature of the cooling plate.

The uncertainty of the thermal resistance Ur was calculated using Equation (4)

$$U_r=\sqrt{{\left({\displaystyle \frac{\partial R_{th}}{\partial T}}{U}_T\right)}^2+{\left({\displaystyle \frac{\partial R_{th}}{\partial Q}}{U}_Q\right)}^2,}$$

(4)

where U_T is the uncertainty of thermal couple and U_Q is the uncertainty in heat input Q, primarily influenced by the output stability of the power supply unit (Slideax SD-1000), which is specified as ±5% under load conditions. According to the uncertainty analysis, the maximum relative error in thermal resistance occurred under the condition of Wick 2 at 30% filling ratio and 85 W heat input, yielding approximately 5.00% relative error, which corresponds to an absolute error of 0.0126 °C/W. To minimize the effect of external heat loss, the entire experimental setup was thermally insulated using extruded polystyrene (XPS) boards.

2.4.3. Wick Porosity

The wick, composed of porous material, is a critical component that facilitates capillary-driven circulation of the working fluid and directly affects thermal transfer efficiency. In particular, the pore structure within the wick plays a key role in generating capillary pressure, which in turn sustains continuous evaporation and condensation of the cooling fluid.

$${\epsilon }_{porosity}=1-{\displaystyle \frac{{\rho }_{wick}}{{\rho }_{cellulose}}},$$

(5)

As previously described, the porosity of the polyurethane (PU) wick was obtained through SEM-based 2D image analysis using MATLAB, followed by the application of a correction factor derived from literature-reported 3D porosity values. In contrast, the porosities of the cellulose and blended fabric wicks were calculated using a density-based approach, which involved measuring the bulk density of the sample and comparing it to the theoretical solid density values readily available, as described in Equation (5).

2.4.4. Data Analysis in the Experiment

Each experimental condition was performed once due to the time-intensive nature of the setup and the stability of the measurement system. For each trial, surface temperature data from 18 thermocouples embedded in the heater blocks were continuously recorded. T_max was defined as the highest temperature observed across all measurement points and all-time steps, while ΔT_surface was calculated as the largest temperature difference among the 18 sensors during the measurement period. R_th was computed based on the average temperature difference and input power during the steady-state period, identified through temperature stabilization trends. Although no statistical replicates were conducted, measurement uncertainty was minimized by maintaining identical initial and boundary conditions for all trials. Each experiment began at a controlled ambient temperature of 25 °C, and the entire test setup was thermally insulated using extruded polystyrene (XPS) boards to suppress external heat losses and ensure internal thermal isolation.

2.5. Experimental Results and Discussion

2.5.1. Transient Temperature Variation

Figure 6, the transient thermal response analysis, was conducted under a representative condition of a 30% filling ratio with 85 W of heat input. This condition was selected because it revealed the most distinct performance differences among the wick configurations and provided a suitable baseline for time-dependent thermal behavior comparison.

As shown in Figure 6, each cooling system with a different wick structure exhibited stable thermal responses without abrupt temperature spikes. However, in the wickless thermosyphon system shown in Figure 6a, a noticeable temperature rise and subsequent drop occurred during the initial operation phase. This behavior is attributed to the typical vapor circulation mechanism in wickless systems, involving the formation and collapse of vapor bubbles. A temporary temperature rise of approximately 5 °C was observed during this startup phase.

In the case of Wick 2, composed of cellulose and lacking a dedicated vapor–liquid separation path, a sudden temperature drop of approximately 5 °C was observed around 5000 s, as shown in Figure 6b. This drop was not localized but occurred throughout the battery region. It is presumed that the absence of a segregated vapor channel led to excessive condensed liquid accumulating and suddenly draining, resulting in rapid cooling at that moment.

Among the tested wick configurations, Wick 5 (Figure 6f) exhibited the most stable thermal response, with the smallest temperature variation across the battery region and the least temperature difference between the condensation section and battery core. This indicates the most efficient thermal transfer among the configurations.

Meanwhile, broader comparisons across experimental conditions were performed using more quantitative metrics: T_max, ΔT_surface, and R_th. These indicators allowed for a clear evaluation of the thermal management performance differences between wick structures.

2.5.2. Analysis of Maximum Surface Temperature on the Battery Simulator

Figure 7 presents the T_max observed under various filling ratios (30–70%) and heat inputs (15 W, 50 W, and 85 W) for each wick configuration, including a wickless case, which was extracted as the highest recorded value among the thermocouples over the entire test duration. In this study, the maximum surface T_max was measured under varying heater input powers (15 W, 50 W, and 85 W) and working fluid filling ratios (30% to 70%). These measurements were used to evaluate and compare the thermal performance of wick structures with different geometries and materials. Among the three key indicators assessed in this work—T_max, ΔT_surface, and R_th—T_max was considered the most critical, primarily due to its direct relevance to battery safety under high thermal loads.

While all three indicators provide important insights into thermal behavior, T_max is particularly sensitive to localized overheating and serves as a useful proxy for evaluating the risk of thermal instability. Prior studies, including Aris et al. [45], have reported that lithium–ion cells may initiate exothermic reactions when temperatures exceed approximately 60 °C, potentially escalating into thermal runaway if uncontrolled. From this perspective, keeping T_max below 60 °C is widely regarded as a practical reference point for safe operation. A lower T_max implies more stable evaporative–condensative cycling, effective heat dispersion, and reduced thermal risk.

A particularly notable finding was the contrasting trend in T_max depending on the presence or absence of a wick structure. For the reference system without any wick (Figure 7a, Wickless), T_max decreased as the filling ratio increased. For instance, at 85 W, T_max was 57.7 °C with a 30% filling ratio and dropped to 47.0 °C at 70%, indicating that the increase in working fluid enhanced the cooling capacity. This result is attributed to the increased thermal capacity of the system due to the higher fluid volume. However, when the filling ratio exceeded 40%, a slight performance decline or plateau was observed at 15 W and 50 W, while cooling performance consistently degraded at 85 W. This trend is consistent with previous studies suggesting that the optimal filling ratio for thermosyphon-type heat pipes is around 40% [43] and highlights the influence of thermal capacity and system heat transfer limits on cooling effectiveness. Conversely, when wick structures were present, a lower filling ratio tended to result in a lower T_max. This is likely because excessive fluid within the wick impedes capillary action and partially blocks vapor flow channels, thereby reducing circulation efficiency. This behavior is consistent with previous findings by Ling et al. [46], who reported that overfilling in microchannel separate heat pipes led to liquid accumulation in the condenser region and degraded thermal performance, suggesting that excessive saturation may suppress capillary-driven transport and phase-change effectiveness within the wick structure. Each wick structure showed distinct thermal performance characteristics depending on its material and geometry. Wick 1, made of polyurethane foam, was designed to fill the entire triangular chamber volume. Across all test conditions, it exhibited the highest T_max, with a peak value of 57.4 °C under the 85 W and 30% filling ratio condition. This was attributed to the lack of sufficient vapor channels, which inhibited proper condensate return and led to heat accumulation.

Wick 2 was composed of cellulose material and wrapped around the heater block, allowing for some vapor flow clearance. The T_max values were generally lower than those of Wick 1, with a value of 49.9 °C under the 85 W and 30% filling condition. Although this structure provided improved vapor circulation, its limited evaporation area led to somewhat unstable heat transfer under high-power conditions. Wick 3, a modified crown-type version of Wick 2 with an upper slit, was designed to better facilitate vapor escape. It showed a slightly improved T_max of 48.8 °C under the same conditions, confirming the benefit of an additional vapor pathway. Wick 4 used a blended fabric of viscose rayon and polyester, featuring a porous structure that facilitated both vapor escape and condensate return, while maintaining full surface contact with the heater block—similar to Wick 1 in shape. Under the 85 W, 30% filling condition, it achieved a T_max of 47.6 °C, demonstrating a balanced thermal management performance due to its structural–material synergy. Wick 5, also made from blended fabric, featured a crown-like cutout at the top similar to Wick 3, maximizing the vapor pathway. It allowed smooth fluid circulation even under low filling ratios and recorded the lowest T_max of 47.0 °C at 85 W and 30% filling.

Taken together, the results indicate that Wick 5 offered the most effective thermal control under low filling conditions due to the optimal combination of material properties and geometric design. It demonstrated superior capillary action and vapor management, positioning it as the most effective wick structure in terms of minimizing T_max and enhancing heat transfer stability.

2.5.3. Analysis of the Maximum Surface Temperature Difference on the Battery Simulator

In this study, the surface temperature deviation (ΔT_surface) of the heater blocks—representing battery cells—was measured under varying wick structures and filling ratio conditions to evaluate the thermal uniformity of the cooling system. Figure 8 presents ΔT_surface under various filling ratios (30–70%) and heat inputs (15 W, 50 W, and 85 W) for each wick configuration. ΔT_surface reflects the temperature variation on the surface (measured by thermocouples) of each block; a smaller value denotes more uniform heat dispersion and, consequently, more consistent cooling performance across the system. For each condition, ΔT_surface was extracted as the maximum temperature difference among the thermocouples at any given time point during the test. As described above, each heater block was embedded with three copper rods arranged radially, and each rod was instrumented with three K-type thermocouples at the top, middle, and bottom positions. The ΔT_surface for each block was defined as the difference between the maximum and minimum temperatures among these nine measurement points. Alongside T_max, ΔT_surface serves as a critical indicator in BTMS, particularly for preventing thermal runaway and maintaining intercellular temperature uniformity.

Overall, the Wickless configuration showed improved cooling performance as the filling ratio increased, with ΔT_surface decreasing accordingly. For example, at 85 W, ΔT_surface decreased from 4.9 °C at a 30% filling ratio to 4.6 °C at 70%. In contrast, wick-embedded configurations exhibited the opposite trend, with lower filling ratios yielding lower ΔT_surface values. This phenomenon is likely due to excessive working fluid occupying the wick’s internal pores, impeding vapor flow and reducing capillary effectiveness, thereby increasing the risk of local overheating. Additionally, an increase in heat input was generally correlated with a rise in ΔT_surface across all configurations. This trend reflects the system’s thermal capacity limits, where excessive heat input results in thermal imbalance within the block.

Wick 1, composed of polyurethane and designed to fill the entire internal volume of the triangular chamber, consistently showed the highest ΔT_surface values across all test conditions. Under the 85 W input, the maximum ΔT_surface reached 5.5 °C, with elevated deviation levels observed across all filling ratios. This result is attributed to poor internal vapor circulation due to the absence of dedicated vapor channels. Wick 2, made of cellulose and wrapped only around the surface of the heater block, maintained relatively low ΔT_surface values across the power range. Specifically, at 30% and 40% filling ratios, it recorded 3.6 °C, and under the 85 W condition, it remained limited to a maximum of 5.1 °C, suggesting a stable thermal dispersion performance. Wick 3, a crown-type structure derived from Wick 2 with a cutout at the top to facilitate vapor escape, maintained ΔT_surface values of 3.4 °C at 30% and 4.4 °C at 50% filling. Wick 4, composed of blended synthetic fibers and enveloping the entire heater block, showed excellent thermal dispersion under low filling conditions. Notably, it recorded the lowest ΔT_surface of 3.1 °C at 30% filling under 85 W input, slightly increased to 3.2 °C at 50%, and rose to 4.9 °C at 70%. Wick 5, which shared the same blended fabric as Wick 4 but featured a crown-type design with a top opening, demonstrated the most consistent and stable ΔT_surface results overall. At 30% filling, it achieved the lowest value of 2.8 °C, with 3.9 °C at 50%, and a maximum of only 4.3 °C even at 85 W. These findings indicate that Wick 5 not only outperformed other configurations in terms of T_max reduction but also offered the most uniform thermal dispersion, as evidenced by the lowest ΔT_surface values. It also implies that for wick-embedded systems, low to moderate filling ratios are optimal for achieving stable and efficient thermal management.

2.5.4. Thermal Resistance Analysis

Figure 9 presents the thermal resistance (R_th) values calculated using Equation (2) under various filling ratios (30–70%) and heat inputs (15 W, 50 W, and 85 W) for each wick configuration. R_th was determined during the steady-state period.

In this study, the thermal resistance (R_th) was calculated for each wick structure and filling ratio condition to evaluate the heat transfer efficiency of the cooling system. R_th represents the temperature rise per unit heat input, with lower values indicating more effective thermal dissipation to the external environment.

Overall, R_th tended to decrease as the heat input increased. In the Wickless configuration, increasing the filling ratio resulted in either a slight reduction or stabilization of R_th. Conversely, wick-embedded configurations exhibited lower R_th values at lower filling ratios. This is attributed to the fact that excessive working fluid within the wick can constrict vapor pathways and hinder thermal transport.

Wick 1, made of polyurethane and designed to completely fill the chamber, recorded the highest R_th across all filling ratios. At 70% filling, R_th reached 0.71 °C/W under 50 W input and 0.52 °C/W under 85 W, indicating the poorest performance among all wick designs. This is likely due to inadequate vapor channels within the structure. Wick 2, composed of cellulose and wrapped around the heater block, demonstrated excellent performance under low filling conditions, with the lowest R_th of 0.25 °C/W at 30% filling and 85 W. However, its Rth increased significantly with higher filling ratios, reaching 0.38 °C/W at 70%, suggesting that fluid oversaturation degraded vapor circulation and capillary action. Wick 3, a crown-type modification of Wick 2, showed moderate thermal performance. At 30% filling and 85 W, R_th was 0.28 °C/W. However, a gradual increase in R_th was observed at 50% and 70%, indicating a decline in efficiency with higher fluid volumes. Wick 4, constructed from blended synthetic fibers and encompassing the entire heater block, consistently exhibited low R_th values across the entire power range. At 30% filling and 85 W, it recorded the lowest R_th of 0.24 °C/W, indicating excellent thermal performance. Wick 5, sharing the same material as Wick 4 but featuring a crown-type design, displayed a similar trend. At 30% filling and 85 W, it achieved a R_th of 0.26 °C/W. Although R_th increased to 0.38 °C/W at 70%, the overall performance remained relatively stable.

In the experimental analysis, Wick 5 demonstrated the best thermal performance under low filling ratio and high heat load conditions when considering the three key metrics: T_max, ΔT_surface, and R_th. Specifically, it achieved a T_max of 47 °C, a ΔT_surface of 2.8 °C, and a R_th of 0.26 °C/W.

Notably, the results indicate that the application of a crown structure improves thermal performance regardless of the wick material, as observed in both Wick 3 and Wick 5. The upper part of the crown structure forms multiple open flow channels that enable effective release of working fluid vapor generated under high heat load conditions, thereby facilitating vapor transport. The lower part of the crown structure is fully surrounded by wick, which enables the surface of the heater blocks to be submerged completely, even at lower rate of filling ratio. In addition, while the behavior of condensed working fluid typically occurs along the inner wall surface of the chamber, the upper part of the wicks in the crown structure guides the condensed droplets more directly back to the evaporator region. This enhances the return flow and promotes capillary circulation of the working fluid, thereby improving the overall fluid transport efficiency. These combined mechanisms are interpreted to further enhance the thermal performance of the system.

While the current experimental setup has been designed to ensure overall measurement reliability, there remains room for refinement. Specifically, the power supply employed in this study exhibits an output voltage accuracy of ±5%, which may introduce a degree of variability in the applied heat input. Future work will incorporate higher precision instrumentation to further enhance the accuracy and consistency of thermal loading conditions.

3. 1D Simulation

3.1. Objective and Overview of the Simulation

To systematically compare and analyze the heat transfer performance differences observed experimentally depending on wick structure and working fluid filling ratio, a one-dimensional (1D) simulation model was developed based on the same structural configuration. This model reflects the physical structure of the experimental setup and functionally implements the major components, including the heat source, wick, and working fluid. The primary focus was to predict the temperature response within the heater block under various heat input conditions. Through this approach, quantitative comparison with experimental results becomes feasible, and the thermal behavior trends according to wick design can be assessed via simulation. This provides foundational insight for both structural design and performance evaluation.

3.2. Theoretical Background of 1D Modeling

The simulation was conducted using Siemens Simcenter AMESim (ver. 2310) based on a one-dimensional model. Thermodynamic variables, such as pressure and specific enthalpy, were used in the simulation process, and by inputting these into AMESim, the software automatically calculated the related physical properties and output results [47]. To simplify the analysis and focus on key parameters, several assumptions were adopted in constructing the simulation model [48].

First, the wick structure was assumed to be fully saturated with the working fluid, implying complete contact between the wick and the fluid throughout the entire domain.

Second, the internal flow within the wick was considered to follow Darcy’s law, allowing for simplified treatment of fluid flow through porous media. Third, the concept of effective thermal conductivity was applied to the wick structure to enable more accurate heat transfer analysis.

Lastly, the filling ratio was calculated based on the ratio of the area occupied by the working fluid to the total cross-sectional area of the internal space. The interior of the wick is assumed to be fully saturated with the working fluid, and its internal structure is considered to follow a packed spherical particle model based on SEM images [44].

This full saturation assumption is supported by experimental observations: when the wick was placed in contact with the working fluid, complete saturation occurred over time due to capillary action, as the wick consists of a hydrophilic porous medium. As the wick is a composite structure comprising both solid and fluid phases, directly modeling its microscopic pore structure poses significant challenges. Therefore, it was treated as a homogeneous equivalent material, and the effective thermal conductivity was calculated using the Maxwell–Eucken model.

The thermal properties of the wick structures—such as effective thermal conductivity, effective density, and specific heat—were then determined based on the material properties of the solid and working fluid, as well as the porosity. Appendix A presents all relevant equations, including those used to calculate the volumes of the working fluid and the vapor passage, both of which were derived from cross-sectional area calculations. In addition, the hydraulic diameter was calculated based on the tortuosity values of the wick structures, which were estimated from SEM image analysis. The calculated thermal properties and the hydraulic diameters for each wick structure are summarized in

Table 4. Wick Properties.

Material	Effective Density, kg/m3	Effective Thermal Conductivity, W/m-K	Effective Specific Heat, J/kg-K	Hydraulic Diameter, mm
Wick 1	979	0.051	4070	33.65
Wick 2, 3	1500	0.57	1209	22.91
Wick 4, 5	1020	0.50	3970	23.57

[49,50].

Implementation of Heat Transfer Modeling in AMESim

In this study, a heat transfer model based on heat transfer coefficients and thermal resistance was implemented within the AMESim environment. The built-in thermal–fluid analysis module in AMESim automatically calculates flow states and heat transfer coefficients based on user-defined physical parameters, such as temperature, pressure, and flow rate, and simulates the overall thermal behavior of the system through a thermal resistance network across different regions.

Using Equations (6) and (7), the latent heat $l_v$ of the system can be calculated from the saturated vapor enthalpy $H_v$ and saturated liquid enthalpy $H_f$:

$$l_v=H_v-H_f,$$

(6)

This value is a key factor in determining the fluid flow within the heat pipe, as internal flow is computed using the correlation between mass flow rate $\dot{m}$, supplied heat Q, and latent heat $l_v$:

$$Q=\dot{m}·l_v,$$

(7)

In AMESim, conductive heat transfer between components is governed by predefined theoretical expressions, and the conduction is calculated based on Equation (8) [47]:

$$Q={\displaystyle \frac{\mathit{ln}\left(\frac{diamCt}{diamInt}\right)}{2\pi K_1{l}_e}}+{\displaystyle \frac{\mathit{ln}\left(\frac{diamExt}{diamCt}\right)}{2\pi K_2{l}_e}},$$

(8)

The heat transfer Q within the working fluid is represented by Newton’s law of cooling, as described in Equation (9):

$$Q=hA\left(T_s-T_o\right),$$

(9)

where $T_s$ is the surface temperature, $T_o$ is the ambient temperature, $h$ is the convective heat transfer coefficient, and $A$ is the heat transfer area [51].

The convective heat transfer coefficient $h_c$ is derived from the Nusselt number Nu, which characterizes convective heat transfer performance. Nu is calculated based on Equation (10), incorporating the thermal conductivity k and characteristic length $L_c$. To obtain Nu, dimensionless numbers such as the Reynolds number Re, Prandtl number Pr, and Grashof number Gr are required, which are defined by Equations (11)–(13), respectively. These numbers reflect the effects of flow inertia, viscosity, and buoyancy on the convection process [47]:

$$Nu={\displaystyle \frac{L_c·h_c}{k}},$$

(10)

$$Re={\displaystyle \frac{L_c·V_s·\rho }{\mu }},$$

(11)

$$Pr={\displaystyle \frac{C_p·\mu }{k}},$$

(12)

$$Gr={\displaystyle \frac{g·aǀT_{wall}-T_{fluid}ǀ·{L_c}^3}{k}},$$

(13)

In the single-phase turbulent flow region, the Nusselt number is calculated using the Gnielinski correlation, as shown in Equation (14) [47]:

$$Nu={\displaystyle \frac{\frac{f}{8}\left(Re-1000\right)Pr}{1+12.7\sqrt{\frac{f}{8}}\left({Pr}^{\frac{2}{3}}-1\right)}},$$

(14)

Under two-phase flow conditions, the convective heat transfer coefficient in the condensation region is defined in the simulation based on Equation (15) [47]:

$$H_{TP}=H_{LO}\{{\left(1-x\right)}^{0.8}+\left(3.8·{\displaystyle \frac{x^{0.76}{\left(1-x\right)}^{0.04}}{{\left(\frac{p}{p_{Cr}}\right)}^{0.38}}}\right)\},$$

(15)

where $H_{LO}$ represents the convective heat transfer coefficient for the fully liquid state of the working fluid and is calculated by Equation (16) [47]:

$$H_{LO}=0.023\times {Re}_{LO}^{0.8}\times {Pr}_I^{0.4}\times {\displaystyle \frac{{\lambda }_I}{D_h}},$$

(16)

In the boiling region, the convective heat transfer coefficient is defined by Equations (17) and (18), reflecting the heat transfer characteristics in the liquid–vapor mixture region [47]:

$$H_c=\sqrt[3]{H_{CV}^3+H_{NcB}^3},$$

(17)

$$H_{CV}=H_{LO}·F_{TP},$$

(18)

The terms $H_{NcB}$ and $F_{TP}$, which quantify heat transfer characteristics under two-phase flow conditions, are calculated using Equations (19) and (20) [47]:

$$H_{NcB}=H_{NcB0}·F_{NcB},$$

(19)

$$F_{TP}={\displaystyle \frac{1}{{\left(A_1+A_2\right)}^{0.5}}},$$

(20)

The variables $A_1$ and $A_2$ are calculated using Equations (21) and (22) [47]:

$$A_1={\left[{\left(1-x\right)}^{1.5}+{1.9x}^{0.6}\times {\left(1-x\right)}^{0.01}\times {\left({\displaystyle \frac{p_l}{p_g}}\right)}^{0.35}\right]}^{-2.2},$$

(21)

$$A_2={\left[\right({\displaystyle \frac{H_{VO}}{H_{LO}}})\times x^{0.01}\times [1+{8\left(1-x\right)}^{0.7}\times \left({{\displaystyle \frac{p_l}{p_g}})}^{0.67}\right]}^{-2},$$

(22)

Additionally, $F_{NcB}$ is calculated by Equation (23), and $F_{PF}$ is derived using Equation (24) [47]:

$$F_{NcB}=F_{PF}\times {\left({\displaystyle \frac{\Phi }{{\Phi }_0}}\right)}^{nf}({{\displaystyle \frac{D_h}{D_0}})}^{-0.4}{\left({\displaystyle \frac{R_p}{R_0}}\right)}^{0.133}·F\left(M\right),$$

(23)

$$F_{PF}=2.816·{\left(P_{red}\right)}^{0.45}+[3.4+{\displaystyle \frac{1.7}{1+{\left(P_{red}\right)}^7}}{\left]\right(P_{red})}^{3.7},$$

(24)

The variable $M$ in the function $F\left(M\right)$ in Equation (n) represents the molar mass of the working fluid. Constants such as $F_{PF}$, ${\Phi }_0$, $H_{NcB0}$, $R_{p0}$, and ${\dot{m}}_0$ are determined based on the properties of the working fluid. These parameters are incorporated into the relevant equations used to calculate ${\Phi }_{Cr,PB}$ within the AMESim software environment [47].

Table 5. Initial condition and boundary condition of 1D simulation.

Category	Condition
Material of heat block	SUS304
Material of wick 1	Polyurethane
Material of wick 2, 3	Cellulose fiber
Material of wick 4, 5	Viscose rayon and polyester-blended nonwoven fabric
Porosity of wick 1 (%)	95.9
Porosity of wick 2, 3	89.5
Porosity of wick 4, 5	94.7
Working fluid	Water
Coolant fluid	Water
Initial temperature of heat block (°C)	25
Temperature of coolant (°C)	20
Mass flow rate of coolant (L/min)	0.5
Thickness of wick (mm)	3
Heat input (W)	15–85 with interval in 35 W
Filling ratio (%)	30–70

describes the initial and boundary conditions used to develop the AMESim software model in this study. The material properties of SUS304 were used for the battery, as it matches the material used in both the actual battery and the experimental apparatus, thereby enhancing the reliability of the simulation results. Each porosity value was calculated under the assumption that the internal structure of the wick follows a packed spherical particle configuration, based on SEM images of the wicks used in the experiments [39]. Water was used as the coolant in the cooling plate, with a maintained temperature of 20 °C and a flow rate of 0.5 L/min. Additionally, as in the experiment, filling ratios ranging from 30% to 70% were considered, and heat loads of 15 W, 50 W, and 85 W were applied based on the heat generation rates corresponding to 1 C, 2 C, and 3 C charging rates of the Tesla 4680 battery cells [38].

3.3. Initial Modeling Parameters

Simulation Workflow and Modeling Logic in AMESim

As shown in Figure 10, the simulation system was modeled based on the Wick 2 structure used in the experiment.

The entire system consists of three key components: a heater block, a wick module, and a capillary circulation unit, as detailed in Appendix B [47]. The heater block and wick structure are represented by red and yellow boxes, respectively, and were designed to allow physical interaction within the simulated environment that reflects the experimental setup. The blue box in the center represents the capillary system, which plays a crucial role in sustaining the circulation of the working fluid. The mass flow rate was calculated by converting the average pressure of the vapor and liquid lines using a thermodynamic state converter component. The resulting pressure information was then transformed into specific enthalpy values, which were mapped to the fully evaporated state (x = 1) and the saturated liquid state (x = 0). These calculations were executed according to the flow chart-based system constructed within AMESim to simulate the behavior of the working fluid, as illustrated in Figure 11.

A constant heat input ranging from 15 to 85 W was applied to each of the three heater blocks. Each block was vertically divided into three equal sections to allow for precise measurement of temperature distribution along the height.

As shown in Figure 12, the wick module was constructed by vertically stacking three layers of wick and enclosing them within an outer casing. This configuration ensures that the working fluid is uniformly distributed across the entire wick through a series connection. This modular design was optimized based on the physical characteristics observed in the experiment, while also maintaining high consistency in implementation and analysis within the simulation environment.

In particular, the cylindrical wick structure was tightly wrapped around the inner wall of the circular heater block, allowing for uniform heat transfer from both directions. Additionally, a cooling plate was positioned at the top of the system to extract heat from the working fluid. This plate enables the condensation of vapor-phase fluid through its cooled surface, thereby stabilizing the thermal circulation cycle throughout the system. In other words, the vaporized fluid ascends along the vapor line and condenses at the cooling plate, thus realizing a heat pipe-based thermal exchange mechanism.

This configuration accurately reflects the coupled thermal and fluid behavior observed during the experiment and is well-suited for effectively simulating the actual heat transfer flow within the system.

3.4. Validation of Simulation Model

To evaluate the reliability of the simulation results, the difference between the simulated and experimental maximum surface temperatures of the battery, one of the most critical performance indicators in this study, was analyzed. This temperature difference was defined as $∆T_{AE}=T_{AMESim}-T_{Experiment}$.

To minimize discrepancies between the simulation and experimental results, a correction factor was applied to the heat transfer gain coefficient of the working fluid. Instead of referencing existing literature values, this study directly derived the correction factors based on experimental data [32,33].

First, separate correction factors were obtained independently for wickless and wicked (Wick 1–5) structures. For the wickless structure, which has a single configuration, the correction factor was calculated individually for each filling ratio by minimizing the error between the simulation and experimental results. The final correction factor of 1.014 was determined as the average of these values.

For the wicked structures (Wick 1–5), correction factors were similarly derived for each filling ratio and then averaged for each wick type. To ensure consistency across different wick geometries, the average correction factors of all wicked structures were further averaged, resulting in a unified correction factor of 1.2872, which was commonly applied to all wicked configurations.

By consistently applying these correction factors, the simulation model achieved reliable quantitative comparisons across various wick designs. As shown in Figure 13, the temperature differences between simulation and experiment were mostly within ±10 °C under all conditions, with some cases showing high agreement within ±1 °C.

Such error margins are generally considered acceptable in heat pipe modeling, and the results obtained after applying the correction factors contributed to enhancing the predictive accuracy and reliability of the simulation model. For instance, Lee et al. [32] reported a 6.5% error in their heat pipe modeling study but considered it acceptable due to the physical trend agreement between simulation and experiment. Therefore, the present model can also be considered sufficiently reliable in terms of prediction accuracy.

In the case of the wickless structure, a generally negative $∆T_{AE}$ was observed under the 15 W condition. At 50 W and 85 W, $∆T_{AE}$ gradually transitioned from positive to negative as the filling ratio increased. Particularly at a filling ratio of 70%, large negative $∆T_{AE}$ values were found across all heat load conditions. This is attributed to the fact that in the experiment, the hydrothermal siphon effect is activated around a 60% filling ratio, leading to superior cooling performance. In contrast, the AMESim simulation primarily reflects cooling effects driven by total latent heat rather than detailed evaporation and condensation behavior, resulting in underprediction compared to actual experimental outcomes.

From the comprehensive analysis of simulation results for Wick 1 through 5 structures, the $∆T_{AE}$ at 50% filling ratio generally converged to within ±5 °C across all heat loads. This aligns well with the 40–50% range in which the system showed optimal performance experimentally, indicating that the simulation model can reasonably predict thermal behavior under these conditions. However, some exceptional deviations were observed. For example, Wick 2 and Wick 3 showed abnormally high $∆T_{AE}$ values at 85 W under 40% filling, likely due to limitations in AMESim’s ability to accurately capture the micro-pore geometry and capillary behavior of the actual wick structures. These findings suggest that in wick configurations with complex internal geometries, simulation accuracy cannot be fully ensured using only a generalized correction factor, and structure-specific thermal modeling is required.

As shown in Figure 14, the simulation results with correction factors applied exhibited a consistent trend of decreasing maximum temperature as the filling ratio increased across all conditions. This trend can be explained by the increase in total working fluid mass in the system, which in turn increases the amount of latent heat absorbed during the evaporation–condensation process. This enhanced latent heat buffering effect contributes to limiting the maximum surface temperature rise of the battery under the same heat load conditions. However, when the working fluid volume exceeds the experimentally verified optimal range, the heat pipe fails to operate in a stable manner. Therefore, filling ratios beyond that range should be considered outside the valid operating range.

These results demonstrate that the simulation model can significantly improve its agreement with experimental data through the application of correction factors. In particular, the model was enhanced to a degree that it can reflect the complex micro-pore characteristics of wick structures to some extent. However, in certain conditions, deviations exceeding ±10 °C still occurred. This is likely due to simplifications within the numerical model regarding physical variables such as the internal pore geometry of the wick, working fluid distribution, and initial wetting conditions. Therefore, the adoption of advanced modeling techniques that can more precisely capture these microscopic characteristics is needed in future work. In particular, beyond simply incorporating wick structures based on porosity and tortuosity, it is necessary to introduce advanced submodels that accurately describe the internal structure without simplification, thereby enabling a more precise representation of capillary phenomena.

Additionally, Figure 15 compares the thermal resistance results between the experimental and simulation data under varying filling ratios at a heat input of 85 W. In this study, thermal resistance was calculated based on the transient temperature difference between the coolant and the heat block. According to the experimental results, at 15 W, the variation in thermal resistance with respect to the filling ratio was too small to derive any meaningful trend, while at 50 W, only a relatively linear increase was observed. In contrast, the 85 W condition exhibited the largest variation in thermal resistance across filling ratios, indicating that the heat pipe was operating most actively under this condition. Therefore, the analysis focused on the 85 W condition. Wick 5 was selected as the simulation target structure because it exhibited the best cooling performance in the experimental results. Under the 85 W condition, the AMESim simulation results for Wick 5 showed thermal resistance levels similar to those of the experiment in the 30–50% filling ratio range, suggesting high predictive reliability of the simulation model in this region.

However, in the 60–70% filling ratio range, the trends in thermal resistance between simulation and experiment diverged. This discrepancy aligns with the previously discussed $∆T_{AE}$ analysis and is considered to stem from the tendency of the AMESim model to overestimate the cooling performance enhancement due to increased heat capacity with higher working fluid content, while underestimating the actual degradation in heat pipe operation under high filling conditions.

3.5. One-Dimensional Simulation Results and Discussion

Figure 16 presents a comprehensive summary of the sensitivity analysis and predictive simulations conducted in this study. The purpose of this analysis was to investigate the thermal behavior of the system under conditions constrained by experimental limitations and to predict the system’s performance across different design configurations. By combining sensitivity assessment with predictive simulations of future design scenarios, this study identifies the relative influence of each design variable and provides practical insights for optimizing wick structures and improving cooling system performance.

Among various configurations, the Wick 5 structure with a 30% filling ratio was selected as the baseline for this analysis, as it demonstrated the best cooling performance during experiments. This condition was thus considered the most significant and meaningful for further predictive evaluation.

Figure 16a illustrates the change in the maximum surface temperature of the Wick 5 structure under different coolant temperatures (10 °C, 20 °C, and 30 °C), with all other conditions held constant. As the coolant temperature decreased, the maximum system temperature also declined.

Taking 20 °C as the reference condition, the maximum surface temperature at 85 W was 58.1 °C. When the coolant temperature was lowered to 10 °C, the temperature decreased to 52.5 °C, resulting in a 5.6 °C reduction or approximately 9.6% improvement. Conversely, increasing the coolant temperature to 30 °C led to a rise in maximum temperature to 64.5 °C, representing a 6.4 °C increase or approximately 11.0% degradation compared to the baseline. This trend is attributed to enhanced condensation performance and an increased thermal gradient, which more effectively drives the evaporation and condensation cycle of the working fluid, thereby demonstrating that coolant temperature is a highly sensitive parameter influencing the system’s thermal performance.

Figure 16b shows the effect of wick thickness (2.5 mm, 3.0 mm, and 3.5 mm). As the thickness increased, the maximum temperature gradually decreased. Using the 3.0 mm configuration as the reference, the maximum surface temperature at 85 W was 58.1 °C. When the wick thickness was reduced to 2.5 mm, the temperature increased to 58.7 °C, showing a 0.6 °C rise or approximately 1.0% degradation. Conversely, increasing the wick thickness to 3.5 mm resulted in a temperature of 57.4 °C, indicating a 0.7 °C decrease or approximately 1.2% improvement. This trend can be explained by the increased pore volume in thicker wicks, which allows more working fluid to be stored, thereby enhancing latent heat absorption and promoting more distributed heat dissipation. Overall, the findings suggest that while wick thickness influences thermal behavior, its impact is moderate compared to other design variables.

Initially, simulations were conducted by varying only the porosity of the wick structure. However, this resulted in negligible differences in maximum temperature. Consequently, a more representative parameter of internal structural complexity—tortuosity—was varied to perform additional analysis. Figure 16c presents the effect of tortuosity variation on the maximum surface temperature. As the tortuosity increased from 1.2 to 1.52 and 1.8, the maximum temperature consistently rose. Using 1.52 as the reference, the maximum surface temperature at 85 W was 58.3 °C. When the tortuosity was reduced to 1.2, the temperature slightly decreased to 57.9 °C, indicating a 0.4 °C reduction or approximately 0.7% improvement. In contrast, increasing the tortuosity to 1.8 resulted in a temperature of 58.6 °C, showing a 0.3 °C increase or approximately 0.5% degradation. These results indicate that tortuosity has a measurable but limited impact on thermal performance. The trend is attributed to increased internal flow resistance in more complex structures, which impedes the movement of working fluid and reduces heat transfer efficiency.

Figure 16d presents simulation results for different wick materials (blended fabric, aluminum, and SUS304). Although these materials possess distinct effective thermal conductivity, density, and specific heat, the simulation results showed minimal differences. This implies that, within the AMESim model, cooling performance is more significantly influenced by the behavior of the working fluid circulating through the wick rather than the wick material itself.

This analysis extends beyond a basic sensitivity evaluation by offering predictive insights into operating conditions that are difficult to replicate through experiments. It provides practical direction for optimizing wick structures and improving cooling system performance. Based on the results, the filling ratio of the working fluid and the geometric configuration of the wick emerged as the most critical parameters affecting the system’s thermal response. The simulations also confirmed that coolant temperature is a highly influential factor. Reducing the coolant temperature from 20 °C to 10 °C resulted in a 5.6 °C drop in surface temperature, corresponding to a performance improvement of approximately 9.6%. This indicates that adjusting coolant temperature is the most effective approach among the variables studied. Changes in wick thickness and tortuosity produced improvements of approximately 1.2% and 0.7%, respectively, suggesting that their thermal impact is moderate but meaningful. In contrast, material selection for the wick demonstrated relatively minor influence on the overall thermal performance. These results show that the simulation model can reliably predict system behavior across design variations and can be used to guide future design efforts toward configurations that maximize thermal efficiency under constrained conditions.

4. CFD Simulation

To evaluate the thermal management performance of a 4680 cylindrical battery, a CFD simulation was conducted and analyzed by comparing the results with experimental data. The simulation system is based on the finite volume method and solves governing equations, including the continuity, momentum, and energy equations, while incorporating multiphase flow and phase-change models. In this study, ANSYS Fluent V24.2.0 was employed to numerically analyze the internal thermal–fluid characteristics of a heat pipe integrated cooling system. The analysis was carried out under the following conditions and assumptions to enable comparison between the simulated temperature values and the experimental results [52,53,54].

• The vapor phase was assumed to be turbulent, and the Realizable k–ε model—commonly used in multiphase flow—was applied [55].
• Based on the experimentally observed boiling point, the saturation temperature was back-calculated, and the internal pressure was set to approximately 10,000 Pa. Accordingly, the saturation temperature was set to 318.7 K.
• A low-pressure rarefied air region was assumed to occupy the space not filled by the vapor or liquid phases within the domain.
• The system was assumed to be symmetric with respect to a single cell.
• All components of the system, except for the heating and cooling sections, were assumed to be adiabatic.

4.1. Governing Equations

This section describes the key numerical theories applied in the analysis and explains how these theories are implemented within ANSYS Fluent.

4.1.1. Continuity Equation

The continuity equation is based on the principle of mass conservation, which states that the mass of a fluid remains constant over time and serves as a fundamental basis for all flow analyses. The variations in fluid density and velocity are expressed by Equation (25) [52,53,54]:

$${\displaystyle \frac{\partial \rho }{\partial t}}+ \nabla ·\left(\rho \overrightarrow{v}\right)=S_m,$$

(25)

In cases where there is an additional mass source, $S_m$ is assigned a value greater than 0. However, in this study, no external mass source was assumed; therefore, $S_m$ was set to 0.

4.1.2. Momentum Equation

The momentum equation describes the changes in momentum of a fluid element due to external forces such as pressure, viscous forces, and gravity. It represents the numerical implementation of Newton’s second law of motion, as expressed in Equation (26) [52,53,54]:

$${\displaystyle \frac{\partial \left(\rho \overrightarrow{v}\right)}{\partial t}} + \nabla ·\left(\rho \overrightarrow{v}\overrightarrow{v}\right)= -\nabla p + \nabla ·\stackrel{̿}{\tau } + \rho \overrightarrow{g}+\overrightarrow{F},$$

(26)

4.1.3. Energy Equation

The energy equation is based on the principle of energy conservation within the system and is used to calculate the temperature distribution by accounting for internal energy, thermal conduction, and viscous dissipation in the fluid, as expressed in Equation (27) [52,53]:

$${\displaystyle \frac{\partial \left(\rho E\right)}{\partial t}} + \nabla ·\left(\overrightarrow{v}\left(\rho E+p\right)\right)= \nabla ·\left(k_{eff}\nabla T-\sum _j{h}_j\overrightarrow{J_j}+{\overline{\tau }}_{eff}\cdot \overrightarrow{v}\right)+S_h,$$

(27)

$E$ is defined by Equation (28):

$${E= h-{\displaystyle \frac{p}{\rho }}+{\displaystyle \frac{v}{2}}}^2,$$

(28)

The enthalpy $h$ is given by Equation (29):

$$h=\sum _j{Y}_j{h}_j+{\displaystyle \frac{p}{\rho }},$$

(29)

The species enthalpy $h_j$ is defined by Equation (30):

$$h_j={\int }_{T_{ref}}^T{c}_{p,j}dT,$$

(30)

The reference temperature $T_{ref}$ used in the enthalpy calculation is 298.15 K when using the pressure-based solver. The energy equation is included in the solver by enabling the Energy Equation option in ANSYS Fluent, allowing the calculation of temperature variations due to heat transfer and phase change within the working fluid.

4.1.4. Multiphase Flow Model (VOF)

Since both vapor and liquid phases coexist inside the heat pipe, the Volume of Fluid (VOF) model in ANSYS Fluent was employed in this study. The VOF model solves a single set of momentum equations while tracking the volume fraction of each phase throughout the computational domain, enabling the modeling of two or more immiscible fluids. This model is available only with the pressure-based solver and does not allow void regions where no fluid exists. The VOF algorithm calculates the volume fraction of the q-th phase using Equation (31), after which the volume fractions of all phases are summed within each computational cell [53,54,56]:

$${\displaystyle \frac{\partial {\alpha }_q}{\partial t}} + \nabla ·\left({\alpha }_q\overrightarrow{v}\right)=0, \sum _q{\alpha }_q=1,$$

(31)

Here, ${\alpha }_q$ represents the volume fraction of the q-th phase, and it satisfies one of the following three conditions:

• ${\alpha }_q=0$: The cell contains none of the q-th phase (empty cell).
• ${\alpha }_q=1$: The cell is completely filled with the q-th phase.
• ${0<\alpha }_q<1$: The cell contains the interface between the q-th phase and one or more other phases.

In this study, only the VOF model was employed to simulate the two-phase flow inside the heat pipe. The primary objective of the CFD analysis was to accurately reproduce the interfacial behavior associated with evaporation and condensation.

In ANSYS Fluent, the VOF model is configured through the multiphase model settings, where parameters such as interfacial surface tension and initial volume fractions of each phase can be defined. This enables dynamic tracking of the spatial distribution of liquid and vapor phases within the heat pipe.

The VOF model is particularly well-suited for capturing sharp liquid–vapor interfaces. While the Eulerian–Eulerian model is commonly used for dispersed multiphase flows, it does not distinguish between phases at the interface.

Guerrero et al. [57] compared both models and found that only the VOF model could replicate actual two-phase flow structures, such as slug and bubbly flow, observed in experiments. Based on these considerations, the VOF model was selected as the most appropriate method in this study.

4.1.5. Evaporation–Condensation Model

In the VOF model, the Lee model is employed to simulate interphase mass transfer resulting from evaporation and condensation, as described by Equation (32)–(34) [52,54]:

$${\displaystyle \frac{\partial \left({\alpha }_v{\rho }_v\right)}{\partial t}}+\nabla \cdot \left({\alpha }_v{\rho }_v\overrightarrow{V_v}\right)={\dot{m}}_{lv}-{\dot{m}}_{vl},$$

(32)

If $T_l>T_{sat}$ (evaporation),

$${\dot{m}}_{lv}=coeff\cdot {\alpha }_l{\rho }_l\left({\displaystyle \frac{T_l-T_{sat}}{T_{sat}}}\right),$$

(33)

If $T_v>T_{sat}$ (condensation),

$${\dot{m}}_{vl}=coeff\cdot {\alpha }_v{\rho }_v\left({\displaystyle \frac{{T_{sat}-T}_l}{T_{sat}}}\right),$$

(34)

This model calculates mass transfer such that evaporation occurs when the working fluid temperature is higher than the saturation temperature, and condensation occurs when it is lower.

4.2. CFD Simulation Model

The simulation model in this study consists of a wickless heat pipe (thermosyphon type) integrated cooling system, in which three 4680 cylindrical lithium–ion battery cells are arranged in an equilateral triangular configuration. To improve computational efficiency and reduce simulation time, the domain was simplified to one-third of the full geometry based on its inherent symmetry, as illustrated in Figure 17. The simplified domain represents one-third of the equilateral triangle, corresponding to a single battery cell, and the analysis focuses on the internal flow of the working fluid and the resulting steady-state temperatures under different heat generation conditions.

Water was used as the working fluid, and the filling ratios were set to 30%, 40%, and 50%, based on the internal volume, using the Split Body function in SpaceClaim V 2024.2.0.06032. The simulations were performed using a pressure-based transient solver with the energy equation enabled, the Realizable k-ε turbulence model, and a multiphase VOF model (implicit scheme) incorporating the Lee phase-change model. Each simulation was run with a time step of 0.1 s and continued until the battery temperature reached steady state (flow time of 60 s).

4.2.1. Grid Independence Test

To ensure reliable numerical results, a grid independence test was conducted. The mesh configuration was constructed using unstructured triangular elements. Mesh refinement was applied in the vicinity of wall regions to accurately resolve fluid dynamics and thermal gradients within the simulation domain. While increasing the total number of mesh elements generally improves the precision of the computed results, it also significantly raises the computational cost and may exceed the capacity of available hardware.

To evaluate the influence of mesh resolution on simulation accuracy and identify a practical configuration, four mesh cases were tested under identical boundary conditions. Each case was simulated using a filling ratio of 40%, a heat generation rate of 85 W, and a coolant inlet temperature of 293 K. The simulations were conducted over a physical time duration of 10 s. The results of this assessment are summarized in Figure 18.

Among the four mesh configurations tested in this study, Case C provided the most balanced outcome in terms of numerical accuracy and computational efficiency.

This configuration consisted of 2,140,049 mesh elements, and the simulation resulted in a maximum temperature of 1033.01 K. Case D, which used a finer mesh with 2,856,949 elements, produced a maximum temperature of 1057.94 K. The difference in temperature between Case C and Case D was 2.36%, which was considered minor. However, the computational time required for Case D was significantly longer. Case A was composed of 1,055,264 mesh elements, and the maximum temperature obtained was 852.58 K. Further reduction in mesh density caused numerical instability, and the simulation could not be completed successfully. Case B included 1,342,004 mesh elements and resulted in a maximum temperature of 1002.67 K, which indicated a temperature deviation of approximately 14.9% compared to Case A. These findings are summarized in Figure 18. Based on these results, the mesh configuration used in Case C was selected for all subsequent simulations, as it ensured sufficient numerical precision and computational stability.

The choice of mesh resolution was further guided by practical considerations related to computational resources. The selected mesh ensured convergence and stable operation of the solver while remaining within acceptable limits of memory usage and simulation time.

Although adaptive refinement methods are known to improve spatial accuracy, particularly in regions with steep temperature gradients or near the liquid and vapor interface, such techniques were not employed in the present study. This decision was made due to the high computational cost associated with transient multiphase simulations involving the volume of fluid method in combination with the Lee phase change model. Future research will consider the application of local mesh refinement strategies to improve the resolution of interfacial phenomena and capillary-scale transport mechanisms.

4.2.2. Boundary Conditions

As shown in

Table 6. 3D analysis cases.

No.	Analysis Cases
1	FR 30%—85 W
2	FR 40%—85 W
3	FR 50%—85 W
4	FR 40%—50 W
5	FR 40%—120 W
6	FR 40%—155 W
7	FR 40%—190 W

, a total of seven CFD cases were constructed for this study. CFD Cases 1–4 were designed to implement a digital twin of the heat pipe integrated immersion cooling system, aiming to validate the consistency between the simulation and experimental results. CFD Cases 5–7 were carried out under high heat generation conditions that could not be tested experimentally in order to conduct an extended performance analysis of the system and achieve the intended purpose of the digital twin approach.

In CFD Cases 1–3, the filling ratios were set to 30%, 40%, and 50%, respectively, with a constant heat input of 85 W applied to the battery surface. CFD Cases 4–7 focused on the 40% filling ratio, which showed the best performance in the experiments, and applied heat inputs of 50 W, 120 W, 155 W, and 190 W, respectively. The condenser temperature $T_c$ was set to 293 K, consistent with the experimental setup. The detailed boundary conditions are summarized in

Table 7. Boundary conditions.

Boundary Conditions	Value
Initial Temperature, K	298.15 K
Operating Pressure, Pa	10,000 Pa
Initial Saturation Temperature, K	318.7 K
Heat, W	50, 85, 120, 155, 190
Free Stream Temperature, K	298.15 K
Temperature at Cooling Plate, K	293 K

.

4.3. CFD Simulation Results and Discussion

As expected from the CFD simulation results, condensation occurred along the inner walls of the system. Figure 19 corresponds to the conditions of CFD Case 2 and illustrates the variation in liquid volume fraction near the upper cooling plate between flow times 58.1 and 58.4 s. The evaporated fluid loses heat through the cooling plate, subsequently condenses, and flows downward along the wall due to gravity, returning to the bottom of the system. This process repeats, resulting in continuous circulation of the working fluid.

Figure 20a–c presents the vapor volume fraction distributions within the system at filling ratios of 30%, 40%, and 50%, respectively (corresponding to CFD Cases 1–3), under a heat input of 85 W. The figure illustrates only the vapor phase. Regions with high vapor volume fractions, typically corresponding to localized hotspots, are displayed in red. The remaining blue regions do not represent a complete absence of liquid but instead indicate areas with low vapor concentration, which may contain either liquid or air.

This distinction arises because any region not initially filled with liquid is automatically assigned as rarefied air within the simulation. Due to the difference in density between air and liquid, air tends to accumulate in the upper portion of the system, while the denser liquid phase tends to migrate downward along the walls and settle at the bottom. When comparing the results with the vapor volume fraction scale fixed between 0 and 1, both cases (a) and (b) show vigorous vapor generation and clearly observable evaporation–condensation circulation, with condensed liquid flowing downward along the wall. However, in case (c), vapor initially appears but suddenly disappears, suggesting a breakdown in the circulation pattern. This behavior can be explained by the increased volume of water, which leads to a higher heat capacity and a rapid decrease in system temperature, reducing the time spent above the saturation point. Moreover, the reduced vapor space due to the increased liquid volume may result in rapid pressure buildup within a confined area, leading to abrupt vapor condensation. These conditions deviate from the typical latent heat exchange cycle of a functioning heat pipe, where continuous evaporation and condensation occur.

On the other hand, in the 30% filling condition, nearly all the liquid evaporates, indicating the onset of a dry-out condition. At filling ratios lower than this, proper heat pipe operation may not be achieved. In contrast, at 40% filling, sufficient working fluid remains at the bottom, while vapor generation is observed on both sides around the battery. The rising vapor and the descending condensed liquid clearly demonstrate a stable evaporation–condensation circulation.

Additionally, the average surface temperatures for each filling ratio were extracted from the simulation results. At a filling ratio of 30%, the average temperature was 327.2 K, while it slightly decreased to 325.3 K at a filling ratio of 40%. At a filling ratio of 50%, the average temperature further declined to 316.1 K, indicating a general trend of decreasing temperature with increasing liquid volume. However, at a filling ratio of 30%, the rising temperature suggested a tendency toward dry-out, while at 50%, the rapid temperature drop indicated a breakdown in evaporation–condensation circulation.

Therefore, the optimal filling ratio for this thermosyphon-type heat pipe system is determined to be 40%, which is also supported by experimental results showing the best performance under this condition.

Table 8. Analysis of vapor circulation and operational stability at various filling rate under 85 W heat input.

Filling Ratio, %	CFD Average Temperature, K	Circulation Characteristics
30	327.2 K	Onset of dry-out tendency, Potential operational instability
40	325.3 K	Stable formation of an evaporation–condensation structure
50	316.1 K	Insufficient vapor space, Rapid condensation and pressure rise

summarizes the changes in steady-state temperature and flow characteristics of CFD Cases 1–3.

To implement a digital twin of the heat pipe integrated cooling system, the simulation results from CFD Cases 1 through 4 were compared with the experimental data. Figure 21a presents the simulation result of CFD Case 4, in which the average temperature was 318.5 K, closely matching the experimental average temperature of 316.4 K. Under the low heat generation condition of 50 W, an evaporation–condensation circulation structure was observed; however, due to the reduced vapor generation, the vapor inflow into the condensation region and its recirculation slowed down, resulting in less active circulation compared to higher heat generation conditions.

Figure 21b,c compares the average steady-state surface temperatures of the battery obtained from CFD Cases 1–3 with those from the experiments. The temperature differences between the simulation and experimental results remained within a range of 2–6 K, demonstrating a high level of agreement.

Figure 22 presents the results of CFD Cases 5–7, which were performed under high heat generation conditions that could not be tested experimentally due to safety concerns. These simulations provide an extended analysis of the system’s thermal performance. As the heat input increased, the amount of vapor generated within the system also increased significantly. At 120 W, a stable evaporation–condensation circulation structure was observed, but the amount of vapor exceeded the capacity of the condensation region, leading to near saturation throughout the domain even at the point where condensation occurred. From 155 W onward, delayed recovery of condensed liquid at the condenser was observed, and the vapor volume fraction began to increase abnormally throughout the system. Under the 190 W condition, the system was almost entirely filled with saturated vapor, and the evaporation–condensation circulation collapsed due to insufficient condensation and return flow. These results indicate that, under high heat loads of 155 W or more, excessive vapor saturation, imbalance in condensation and recirculation, internal pressure buildup, and the onset of dry-out conditions prevent the heat pipe from maintaining its normal phase change-driven operation.

The steady-state temperatures under 120 W and 155 W were 327.2 K and 335.9 K, respectively, remaining below the critical temperature threshold for thermal runaway. However, under the 190 W condition, the battery temperature did not converge and instead continued to increase over time. As the heat input increases, the average temperature shows a general upward trend, and when the heat input exceeds 155 W, the heat pipe is no longer able to maintain stable operation based on the phase-change mechanism. As a result, thermal performance may deteriorate, and it becomes necessary to define a heat source limit to ensure system stability.

Table 9. Analysis of vapor circulation and operational stability according to heat input (FR = 40%).

Heat	CFD Average Temperature, K	Circulation Characteristics
50 W (1120.0 W/${\mathrm{m}}^2$)	318.5 K	Weak vapor generation and circulation, Limited vapor production and flow circulation
85 W (1903.5 W/${\mathrm{m}}^2$)	325.3 K	Stable formation of an evaporation–condensation structure
120 W (2687.3 W/${\mathrm{m}}^2$)	327.2 K	Vapor accumulation within the system, Higher risk of flow circulation instability
155 W (3471.1W/${\mathrm{m}}^2$)	335.9 K	Delayed recovery of condensate and increased vapor volume fraction, Unstable phase-change circulation
190 W (4254.9W/${\mathrm{m}}^2)$	Non-converging temperature behavior	Vapor supersaturation and condensation stagnation within the system, Circulation collapse and potential onset of dry-out

summarizes the changes in steady-state temperature and flow characteristics under various heat loads at a 40% filling ratio. Based on this analysis, it can be inferred that 155 W is the upper limit of heat input for maintaining stable evaporation–condensation circulation under the experimentally verified optimal filling ratio of 40%.

5. Conclusions

This study investigated the thermal performance of a heat pipe-based cooling system specifically developed for cylindrical lithium–ion battery cells in the 4680 format. The system was evaluated through experimental testing, one-dimensional simulation using AMESim, and three-dimensional analysis using computational fluid dynamics. All wick configurations, from Wick 1 to Wick 5, showed improved thermal performance at lower filling ratios within the 30 to 70% range. Among them, Wick 5, which employed a blended fabric material with a crown-shaped structure, demonstrated the most favorable performance under an 85 W heat load at a 30% filling ratio. The recorded maximum temperature was 47 °C, the surface temperature difference was 2.8 °C, and the thermal resistance was 0.26 °C/W. Although Wick 4 exhibited a slightly lower thermal resistance of 0.24 °C/W, Wick 5 was identified as the most effective configuration when all performance criteria were considered. The crown-shaped structure was found to improve phase-change efficiency at reduced fluid volumes, contributing to lower system weight and enhanced packaging efficiency, both of which are essential for automotive battery applications.

To confirm the observed trends and extend the analysis to a broader set of conditions, a one-dimensional AMESim model was constructed. Correction factors derived from experimental results were applied to improve consistency between simulation and measurement. The model produced the most accurate predictions within the 30 to 50% filling ratio range, which corresponded to the optimal conditions identified through experimentation. Parametric evaluations revealed that the filling ratio and wick geometry had the most significant influence on thermal response. A reduction in coolant temperature from 20 °C to 10 °C decreased the surface temperature by 5.6 °C, corresponding to an improvement of 9.6%. Variations in wick thickness and tortuosity yielded smaller improvements of 1.2% and 0.7%, respectively. The selection of wick material was found to have limited impact on system performance.

Three-dimensional simulations using ANSYS Fluent were performed to analyze system behavior under high heat input conditions that could not be safely tested in the laboratory. The simulations focused on a wickless thermosyphon configuration within the 30 to 50% filling ratio range, which represented the most thermally active condition observed experimentally. Under an 85 W heat input and a 40% filling ratio, the average temperature was 325.3 K, and stable internal circulation through evaporation and condensation was maintained. Increasing the heat input to 155 W raised the average temperature to 335.9 K and resulted in early signs of internal instability. At 190 W, further temperature increase and loss of convergence indicated the onset of dry-out conditions and system failure. These results indicate the existence of a thermal limit that must be carefully considered during design to ensure operational stability.

To reduce simulation complexity, the CFD model excluded the porous wick domain. However, future simulations will incorporate detailed wick structures to improve alignment with physical conditions. In addition, further development of the one-dimensional simulation framework will include an expanded range of environmental and operational variables. This enhancement will enable more comprehensive assessment of system performance and battery temperature distribution under realistic usage scenarios. Experiments and simulations with electrically insulating working fluids will also be pursued to improve safety and broaden applicability in automotive systems.

The study proposes a novel thermal management strategy specifically optimized for the thermal and structural characteristics of large cylindrical battery cells. Compared to conventional indirect liquid cooling methods, the proposed system reduced thermal resistance and improved temperature uniformity at the battery surface. These improvements are expected to support higher cell packing densities by minimizing local temperature differences and enabling compact module integration. Similar to immersion cooling methods, the proposed system involves direct contact between the coolant and the battery surface, allowing for suppression of flame propagation during thermal runaway events. However, unlike conventional immersion systems, the proposed method uses a smaller volume of coolant, which supports a lighter and more efficient design without compromising cooling effectiveness.

In conclusion, this work presents a practical and experimentally verified cooling configuration that addresses the thermal regulation and structural requirements of next-generation battery modules. The findings may serve as a foundational reference for the continued development and refinement of advanced thermal management systems in high-power electric vehicle applications.