Numerical Simulations for Indirect and Direct Cooling of 54 V LiFePO₄ Battery Pack

Abstract

In this study, three-dimensional thermal simulations for a 54 V Lithium-ion battery pack composed of 18 LiFePO₄ pouch battery cells connected in series were conducted using a multi-scale electrochemical-thermal-fluid model. An equivalent circuit model (ECM) is used as a subscale electrochemical model at each cell node of the battery, which is then combined with the macro-scale thermal and fluid equations to construct a model of the battery and battery pack. With the model, the cooling effects of indirect cooling and direct cooling battery thermal management systems (BTMS) on the battery pack under rapid discharging conditions are explored. It is found that when the battery pack is discharged at 2C, indirect cooling of the bottom plate can effectively dissipate heat and control the temperature of the battery pack. Under the 10C discharging condition, the maximum temperature of the battery pack will exceed 100 °C, and the temperature uniformity will be very poor when using indirect cooling of the bottom plate for the battery pack. Direct air cooling is also unable to meet the cooling requirements of the battery pack at a 10C discharging rate. The possible reason is that the convective heat transfer coefficient of direct air cooling is small, which makes it difficult to meet the heat dissipation requirements at the 10C condition. When single-phase direct cooling with fluorinated liquid is used, the maximum temperature of the battery pack under the 10C discharging condition can be controlled at about 65 °C. Compared with air direct cooling, the pressure drop of fluorinated liquid single-phase direct cooling is smaller, and the obtained battery pack temperature uniformity is better. From the detailed study of fluorinated liquid single-phase direct cooling, it is concluded that increasing the coolant flow rate and reducing the cell spacing in the battery pack can achieve a better cooling effect. Finally, a new cooling method, two-phase immersion cooling, is investigated for cooling the battery pack. The maximum temperature of the battery pack discharged at a 10C rate can be controlled below 35 °C, and good temperature uniformity of the battery pack is also achieved at the same time. This study focuses on fluorinated liquid immersion cooling using numerical simulations, showing that it is a promising cooling method for lithium-ion battery packs and deserves further study. This paper will provide a reference for the design and selection of BTMS for electric vehicles.

1. Introduction

In recent years, environmental issues and the energy crisis have become serious concerns for the transportation industry. Clean energy vehicles, represented by electric vehicles, can effectively reduce air pollution with high energy efficiency. Many countries are paying more and more attention to the development of electric vehicles day by day [1,2]. The breakthrough of power battery-related technology is the key to the wide application of electric vehicles. Due to its high energy density [3], high specific energy [4,5], long cycle life [6], and low memory effect compared with the traditional Ni-Cd and Ni-MH batteries [7,8], lithium-ion batteries have been used as power batteries for electric vehicles and hybrid vehicles [9]. Thermal management and temperature regulation are essential for lithium-ion batteries. The performance, life, and safety of lithium-ion batteries are influenced by their operating and storage temperatures [10]. Lithium-ion batteries generate a lot of heat during discharging, causing an increase in the operating temperature of the battery, which can accelerate the cell capacity fade and lifetime performance loss. Bandhauer et al. [11] summarized a large number of previous research results and concluded that when the battery temperature exceeds 50 °C, its capacity will decay regardless of its discharging rate and electrochemical properties. Väyrynen [12] considered that the tolerable temperature range of lithium-ion batteries is −20 °C to 60 °C. To maintain optimal battery performance, the optimal operating temperature range for lithium-ion batteries is 25 °C to 40 °C, and it is also indicated that the maximum temperature difference between battery cells and battery modules in the battery pack should be less than 5 °C. Motloch et al. [13] showed that for every 1 °C increase in the operating temperature of lithium battery between 30 °C to 40 °C, the lifetime of the battery will be reduced by two months. Besides, when the temperature of a lithium-ion battery exceeds 80 °C, it may trigger thermal runaway and lead to battery combustion, explosion, and even the generation of toxic gases such as CO in the limited vehicle space, which may cause more serious disasters [14,15,16]. Therefore, the battery modules in electric vehicles must be equipped with a suitable battery thermal management system (BTMS) to control the temperature of battery modules within a reasonable range and to improve the temperature uniformity of the battery pack.

Currently, the main cooling methods applied to battery packs in electric vehicles are air cooling and indirect liquid cooling (single-phase fluid and two-phase fluid), etc., which are well developed and widely used [17,18,19]. The air-cooled method embraces the advantages of simple structure and low cost, but due to the low specific heat of air, a battery pack under air-cooled thermal management often has a large temperature difference inside. Most studies on air-cooled approaches for prismatic lithium-ion battery packs have been conducted by optimizing the structural design of air-cooled BTMS to achieve improved cooling effects [20,21,22]. Compared with air cooling, the structure of the liquid cooling method is usually more complicated, but its cooling efficiency is higher and can make the temperature distribution of battery packs more uniform, which is the most widely used thermal management method for lithium-ion batteries. The liquid cooling systems used in prismatic lithium-ion batteries can usually be categorized as indirect cooling and are mainly achieved by using liquid cooling plates. In the corresponding BTMS, the structure and arrangement of the liquid cooling plates have an important influence on the cooling effect [23]. Thus, many related studies have focused on improving the structure and arrangement of liquid cooling plates [24,25,26]. In addition, the cooling effect can be enhanced by increasing the coolant flow rate to meet the cooling requirements of a battery pack under some more severe conditions [27,28]. Refrigerant two-phase cooling mainly uses the latent heat from the phase change of the refrigerant to remove the heat generated by a battery pack, thus realizing efficient temperature control of the battery. However, it is hard to meet the heating needs with a refrigerant two-phase cooling system as the thermal conductivity of the refrigerant is usually poor. Nowadays, most studies for prismatic lithium-ion batteries under refrigerant cooling are based on the indirect contact cooling of microchannel cooling plates [29,30], and there is little research related to the direct immersion of the battery pack by the refrigerant. Fluorinated fluids are non-conductive and non-flammable, making them a good choice for coolants in the immersion cooling method [31,32]. In addition to the above thermal management approaches, many scholars have also investigated novel battery thermal management systems, such as phase-change material based thermal management systems [33,34], heat pipe-based thermal management systems [35], and thermoelectric material-based thermal management systems [36].

To have a deeper understanding of the thermal behavior of lithium-ion batteries, it is helpful to establish a thermal model for the lithium-ion battery and conduct numerical simulation studies based on the model. With the numerical simulation method, it is possible to visualize the internal temperature distribution and temperature variation of lithium-ion batteries that cannot be observed by ordinary experimental methods, which is helpful to the design work of BTMS. Researchers have done a lot of studies on the modeling of lithium-ion batteries and have developed several effective models, including the equivalent circuit model (ECM), the NTGK model, and the physics-based model. These models have been integrated into a variety of numerical simulation platforms and are widely used. The ECM model primarily uses capacitors and resistors to build a circuit that can simulate the electrical behavior of a battery, and it does not take the chemical components and the corresponding chemical reactions inside the battery into account. In past decades, scholars have proposed various ECM models [37]. Chen and Rincόn-Mora [38] established an ECM model that accounts for all the dynamic characteristics of the battery. Their model includes a total of three resistors and two capacitors, whose relative open-circuit voltage, resistance, and capacitance are considered as a function of the state of charge (SOC). This model can accurately predict the I-V characteristic curve of the battery. The NTGK model is a semi-empirical model proposed by Kwon [39]. It considers the volumetric current density source term as a function of the potential difference between the positive and negative electrodes of the battery, and the parameters related to the model can be obtained from the experiment data of the battery. Newman’s P2D model is a physics-based model proposed by the lab of Newman [40] which accurately captures the migration process of lithium ions in a battery. The model is more accurate, but it is also more computationally intensive.

For several years, some scholars have adopted battery models to simulate prismatic batteries [41], pouch battery cells [42], and battery packs [43] in research related to BTMS. At an earlier time, constrained by computer performance at that time, Sun et al. [42] developed a decoupled three-dimensional battery pack thermal model for a pouch battery pack which incorporated a three-dimensional battery sub-model, an equivalent circuit sub-model, a one-dimensional battery pack network sub-model, and a three-dimensional battery cell/module thermal sub-model. On this foundation, they proposed an improvement to the U-type channel battery pack based on liquid cooling by setting the upper duct of the U-type channel to be tapered, and the simulation found that such optimization could improve the maximum temperature variation of the battery pack by approximately 70%. Jiang et al. [41] proposed a cooling system for a single lithium battery cell using both heat pipes and phase change materials and constructed a corresponding thermal model that used a one-dimensional fully coupled electrochemical-thermal model based on physics to simulate the battery’s behavior. Their model was proved by experimental data validation. Based on this model, they simulated the battery at different discharging rates, and the results showed that this cooling system had a good cooling effect. Li et al. [44] conducted a numerical and experimental relevant study to investigate the mitigation effect of a passive thermal management system on the thermal runaway of a pouch battery module. They proposed a three-dimensional integrated multi-physics battery safety model, in which the NTGK model was used as an electrochemical sub-model, and the related parameters in the model were obtained from experimental data. Their study demonstrated that a proper passive thermal management system could prevent the propagation of thermal runaway in battery modules. Similarly, Patil et al. [45] performed multi-scale multi-domain (MSMD) modeling for the pouch battery module by utilizing the NTGK model and found that the non-conductive liquid immersion cooling is effective in stopping the propagation of thermal runaway caused by an internal short circuit in the battery pack. In addition, Li et al. [27] selected the ECM model as a subscale electrochemical sub-model and then developed a three-dimensional thermal model of a 50 V prismatic battery pack and investigated the cooling effect of single-phase liquid cooling under external short circuit conditions. They conclude that the temperature and temperature gradient of the battery pack could be effectively limited to an acceptable level under external short circuit conditions when the flow rate of the liquid-cooled plate is large enough.

Currently, a systematic comparison of various indirect and direct cooling methods for the lithium-ion battery pack cooling by large electrochemical-thermal simulations is still lacking. Specifically, numerical simulation studies of lithium-ion battery packs composed of pouch cells with direct fluorinated liquid cooling (single-phase and two-phase) are still scarce. In this work, three-dimensional thermal simulations of a lithium-ion battery pack using the MSMD model are performed, and the cooling effects of direct and indirect cooling under a 10C fast discharging condition are discussed in detail. For studying indirect cooling, the cooling effect of the indirect cooling system with different heat transfer coefficients at different discharging rates was investigated. As for the direct cooling, the cooling effects of air natural convection, air forced convection, and fluorinated fluid single-phase forced convection of the battery pack under the 10C rapid discharging condition were studied. This work conducted a parametric study on these cooling methods and investigated the influence of cooling methods, cooling fluid velocity, cell spacing, and other conditions on the cell temperature field. Lastly, this study explored the feasibility of a new cooling method for lithium battery pack heat dissipation applications. Fluorinated liquid immersion two-phase cooling using the principle of pool boiling, which is often applied in the field of electronic chip heat dissipation, was proposed for the 54 V lithium-ion battery pack cooling. Its cooling effect on lithium-ion battery packs was investigated by simulations, and it is pointed out that the fluorinated liquid immersion cooling has the potential to control the battery temperature well and reduce the temperature difference in the battery pack. It is a promising cooling method for lithium-ion battery systems. This study will provide a reference for the design and selection of BTMS for electric vehicles.

2. Modeling Method

2.1. Model Building

The battery selected for investigation is the AMP20 LiFePO₄ pouch battery from A123. The nominal voltage of the battery is 3.3 V and the nominal capacity is 20 Ah. The object for simulations is a 54 V battery pack consisting of 18 single cells connected in series. And the content of this study is to investigate the cooling effect under indirect cooling, air natural convection cooling, air forced convection cooling, FC-72 single-phase direct cooling, HFE-7100 single-phase direct cooling, and HFE-7000 two-phase direct cooling through simulation. In addition, the influence of spacing between cells in a battery pack on the cooling effect under HFE-7100 single-phase direct cooling is also investigated. For modeling setup, the battery is divided into three sections: the positive tab domain (colored in red in Figure 1), negative tab domain (colored in orange in Figure 1), and cell domain (colored in cyan in Figure 1), and its geometric model and mesh are shown in Figure 1a,b, respectively. For a single cell, we verified the mesh independence using the maximum cell temperature as the discriminant criterion. A total of five types of meshes were established for simulation comparison, and the numbers of the meshes were 21,060, 94,000, 186,000, 363,420, and 557,100, respectively. Taking the mesh with the number of 557,100 as the base, the relative errors of the calculation results of the first four meshes are 0.168%, 0.200%, 0.133%, and 0.079%, respectively. When the mesh number of elements is 186,000, the calculation results are accurate enough. So, the mesh with the number of 186,000 is selected as the mesh of single battery in this paper. The mesh has a total of 186,000 cells, where the maximum cell volume is 2.023 × 10⁻⁹ m³. The minimum orthogonal quality of the mesh is 0.9939. The geometric parameters and some characteristic parameters of the battery are shown in

Table 1. Parameters of the cell characteristics.

Parameters	Values
Cell length	205.5 mm
Cell width	156.0 mm
Cell thickness	7.1 mm
Nominal voltage	3.3 V
Nominal capacity	20 Ah

.

The method used to conduct the study of indirect cooling is to place a 2 mm thick aluminum plate underneath the battery pack, set the boundary condition on the bottom surface of the plate as a convective heat transfer boundary condition, and then simulate indirect cooling by giving the fluid temperature and convective heat transfer coefficient. To more realistically simulate the indirect cooled thermal management system applied in electric vehicles, a pack of 18 batteries connected in series is divided into 3 groups of 6 batteries each, with each module wrapped in a 1 mm thick aluminum shell. Additionally, a thin layer with a thickness of 0.6 mm and 5 W/(m⋅K) thermal conductivity is added between every two cells to mimic the contact thermal resistance between the cells. The geometric model and mesh are shown in Figure 2a,b, respectively. The mesh has a total of 7,760,298 cells, where the maximum cell volume is 1.043 × 10⁻⁹ m³. The minimum orthogonal quality of the mesh is 0.9862. In Figure 2, the geometry was divided into three parts with different colors, and each part represents a battery module, including six single batteries.

The method used to conduct the study of natural convection cooling of air is to set the boundary condition of the outer wall surface of the cell domain in the battery pack as a convective heat transfer boundary condition, which means assigning the fluid temperature and the convective heat transfer coefficient of natural convection. So, the corresponding geometric model has no fluid domain and contains only the battery pack composed of 18 cells, in which the cell spacing is 4 mm. When conducting the study of HFE-7000 two-phase direct cooling, the same method is used to set the boundary condition of the outer wall surface of the cell domain in the battery pack as the convective heat transfer boundary condition, but the wall convective heat transfer coefficient is a function of the temperature of the wall surface. Therefore, the same as air natural convection cooling, the fluorinated liquid two-phase direct cooling method has no fluid domain either, and their geometric model and mesh are exactly the same, as shown in Figure 3a,b, respectively. The mesh has a total of 1,793,067 cells, where the maximum cell volume is 2.730 × 10⁻⁹ m³. The minimum orthogonal quality of the mesh is 0.9804.

Van Gils et al. [31] experimentally investigated the relationship between the convective heat transfer coefficient h and the wall temperature for an 18,650 lithium-ion battery with a capacity of 1 Ah under HFE-7000 immersion two-phase cooling. They calculated the convective heat transfer coefficient at the battery wall by Equation (1) based on the experimentally obtained data.

$$h=\frac{Q_{in}}{A\left(T_{bat}^{eq}-T_{bulk}^{eq}\right)}$$

(1)

where $A$ is the contact area between the battery and the fluid. $T_{bat}^{eq}$ and $T_{bulk}^{eq}$ denote the temperatures of the battery wall and the fluid at thermal equilibrium, respectively, and $Q_{in}$ is the heat flux from battery to fluid. In the experiment, $Q_{in}$ can be determined by the battery test system, MACCOR system. The fitted HFE-7000 convective heat transfer coefficient as a function of wall temperature is shown in Equation (2). For numerical modeling two-phase immersed cooling of the battery pack with HFE-7000, the battery surface convective heat transfer coefficient is adopted as a function of the battery wall temperature with the following correlation, and the correlation is programmed into the calculation via the UDF function in Fluent.

$$h=\left\{\begin{array}{cc}3.119 (T_w-273.15)+283.43\hfill & \hfill T_w<303.15\\ 117.283 (T_w-273.15)-3139.36 303.15\hfill & \hfill \le T_w<306.65\\ 789.6\hfill & \hfill T_w\ge 306.65\end{array}\right.$$

(2)

To conduct the studies of air forced convection, FC-72 single-phase direct cooling, and HFE-7100 single-phase direct cooling, it is necessary to create fluid a domain around the battery pack. The height of the fluid domain is the same as the height of the cell domain. The thickness of the fluid domain at the side of the battery pack is 10 mm, and the thickness of the fluid domain in front and behind the battery pack is 2 mm. The inlet and outlet lengths are 30 mm. The geometric model and mesh used for these cases are shown in Figure 4a,b, respectively. The mesh has a total of 6,429,900 cells where the maximum cell volume is 2.753 × 10⁻⁹ m³. The minimum orthogonal quality of the mesh is 0.9761.

To investigate the different cell spacing on single-phase direct cooling of the battery pack (HFE-7100 as coolant), besides the model with 4 mm cell spacing, it is also essential to build the battery pack models with cell spacing of 2 mm and 6 mm, respectively, and their geometric models and meshes are similar to those shown in Figure 4.

Since the structure of a pouch battery is a laminated structure of different materials stacked together, it is equivalent to a composite material with a large difference in the thermal conductivity of the battery in different directions. So, the battery needs to apply anisotropic thermal conductivity. In this study, the anisotropic thermal conductivity estimated by Taheri and Bahrami [46] is used, and the thermal conductivities in each direction are:

$$k_1=0.97\mathrm{W}/\left(\mathrm{m}\cdot \mathrm{K}\right),k_2=k_3=26.57\mathrm{W}/\left(\mathrm{m}\cdot \mathrm{K}\right)$$

(3)

where $k_1$ represents the thermal conductivity of the cell domain in the direction perpendicular to its front side (i.e., the battery thickness direction), $k_2$ and $k_3$ represent the thermal conductivity in the cell height and width directions, respectively.

The materials used in all the above geometric models include, in total: cell domain material, positive tab material (aluminum), negative tab material (copper), aluminum plate, aluminum shell, air, FC-72, and HFE-7100. The thermal physical parameters of these materials are shown in

Table 2. The thermal physical parameters of the used materials.

Materials	$\mathit{\rho }\left(\mathbf{kg}/{\mathsf{m}}^3\right)$	$\mathit{c}\left(\mathbf{J}/\left(\mathbf{kg}\cdot \mathbf{K}\right)\right)$	$\mathit{k}\left(\mathbf{W}/\mathbf{m}\cdot \mathbf{K}\right)$	$\mathit{\mu }\left(\mathbf{Pa}\cdot \mathbf{s}\right)$
Cell domain	1871.7	678	-	-
Aluminum	2719	871	202.4	-
Cooper	8978	381	387.6	-
Air	1.225	1006.43	0.0242	1.79 × 10−5
FC-72	1602.2	1101	0.054	4.33 × 10−4
HFE-7100	1370.2	1255	0.062	3.7 × 10−4

. Among them, the parameters of FC-72 and HFE-7100 were obtained from the study of EL-Genk et al. [47].

2.2. Multi-Scale Modeling Principle and Equivalent Circuit Model

In this study, numerical simulation is adopted to study the indirect cooling and direct cooling of a lithium-ion battery pack. Due to its multi-domain and multi-physics nature, it is difficult to model the lithium-ion battery. In order to obtain the temperature distributions of the battery, the transport equations need to be established. In addition, the embedding and de-embedding of lithium ions during charging and discharging takes place between the anode-separator-cathode triple layers. The transport process of lithium ions in the active material occurs at the atomic length scale. Therefore, a multi-scale modeling approach is required for lithium-ion battery modeling. The MSMD model is used to achieve multi-scale electrochemical-thermal-fluid simulation of lithium-ion battery [48]. The equations governing the current flux at battery scale are shown as:

$$\nabla \cdot \left({\sigma }_{+}\nabla {\phi }_{+}\right)=-j$$

(4)

$$\nabla \cdot \left({\sigma }_{-}\nabla {\phi }_{-}\right)=j$$

(5)

where ${\sigma }_{+}$ and ${\sigma }_{-}$ are the effective electric conductivities, both taken 5 × 10⁵ Ω/m in this work. ${\phi }_{+}$ and ${\phi }_{-}$ are phase potentials for the positive and negative electrodes. The equations at different scales are bridged by the volumetric current transfer rate $j$. The volumetric current rate can be calculated in the subscale electrochemical sub-model. The battery scale model and the subscale model interact with each other to derive the current flux, and then the source term in the heat transfer equation (as described in Equation (17)) is generated and the temperature equation can be solved.

The most commonly used electrochemical sub-models include the ECM, NTGK model, and Newman model. The ECM model is selected for lithium-ion battery modeling in this work. In the ECM model, the electric behavior of the battery is described by an electric circuit with the I–V performance relationship as:

$$V=V_{OCV}-V_{tran,s}-V_{tran,l}-R_{series}I\left(t\right)$$

(6)

$$\frac{d{V}_{tran,s}}{dt}=-\frac{1}{R_{tran,s}{C}_{tran,s}}{V}_{tran,s}-\frac{1}{C_{tran,s}}I\left(t\right)$$

(7)

$$\frac{d{V}_{tran,l}}{dt}=-\frac{1}{R_{tran,l}{C}_{tran,l}}{V}_{tran,l}-\frac{1}{C_{tran,l}}I\left(t\right)$$

(8)

$$\frac{d\left(SOC\right)}{dt}=\frac{I\left(t\right)}{3600Q_{ref}}$$

(9)

In these equations, $V_{OCV}$, $V_{tran,s}$, $V_{tran,l}$ and $R_{series}$ are all the functions of SOC. The fitting parameters in those functions are derived from the experimental data by multiple simulations at different discharge rates, as follows:

$$V_{OCV}=3.2+0.08SOC-0.01SO{C}^2+0.05SO{C}^3-0.9\exp \left(-13SOC\right)$$

(10)

$$R_{series}=0.01+0.01\exp \left(-24.37SOC\right)$$

(11)

$$R_{tran,s}=0.01+0.01\exp \left(-29.14SOC\right)$$

(12)

$$C_{tran,s}=703.6-752.9\exp \left(-13.51SOC\right)$$

(13)

$$R_{tran,l}=0.01+0.01\exp \left(-155.2SOC\right)$$

(14)

$$C_{tran,l}=4475-6056\exp \left(-27.12SOC\right)$$

(15)

The I–V performance curves obtained from the model with these parameters at different discharging rates are in fairly good agreement with the experimental data from A123 [49], as shown in Figure 5. In Figure 5, the curves corresponding to 2C, 5C, and 10C represent the voltage curves during the discharge of the single battery at a constant current of 40 A, 100 A, and 200 A, respectively. After constructing the ECM model, the volumetric current flux rate can be derived from the following equation:

$$j=I\frac{Q_{total}}{Q_{ref}{V}_{CV}}$$

(16)

Bernardi et al. [50] developed an equation of general energy balance for battery systems. According to their research, the electrochemical volumetric heat source can be divided into reversible and irreversible heat sources, as described by the following equation:

$$\stackrel{·}{q}=j\left[V_{OCV}-\left({\phi }_{+}-{\phi }_{-}\right)-T\frac{dU}{dT}\right]+{\sigma }_{+}\nabla {\phi }_{+}\cdot \nabla {\phi }_{+}+{\sigma }_{-}\nabla {\phi }_{-}\cdot \nabla {\phi }_{-}$$

(17)

where, $j\left[V_{OCV}-\left({\phi }_{+}-{\phi }_{-}\right)\right]$ is the irreversible heat source term and $-jT\frac{dU}{dT}$ is reversible. The rest is ohmic heat term. The irreversible heat source term and the reversible heat source term together compose the electrochemical reaction heat source term, which is due to electrochemical reactions. The research in this study is carried out on the ANSYS Fluent platform.

3. Results and Discussions

3.1. Cooling of 54 V Battery Pack under Indirect Cooling

This section investigates the temperature responses of the battery pack under 2C and 10C discharging conditions with indirect cooling as the cooling method, respectively. The simulated I-V performance curves of the 54 V LiFePO4 battery pack discharging at 2C and 10C are shown in Figure 6. In Figure 6, the curves corresponding to 2C, and 10C represent the voltage curves during the discharge of the battery pack at a constant current of 40 A and 200 A, respectively. The initial temperature of the battery pack is 30 °C. The convective heat transfer coefficients $h$ of the bottom liquid cooling plate wall are assigned to be $h=100\mathrm{W}/({\mathrm{m}}^2\cdot \mathrm{K})$ and $h=1000\mathrm{W}/({\mathrm{m}}^2\cdot \mathrm{K})$ for investigation, respectively. Those heat transfer coefficients are assumed to test indirect cooling with different heat transfer intensities, and the temperature of the coolant in the plate is 25 °C. The maximum, average, and minimum temperatures of the battery pack and the changes of the temperature contour during the discharging process are analyzed to explore the thermal performance of the battery pack under indirect cooling. The temperature evolution of the battery pack with time for 2C and 10C discharging rates is shown in Figure 7 and Figure 8, respectively.

It can be seen from Figure 7 that the indirect cooling can roughly control the temperature of the battery pack within the optimal operating temperature range (25 °C to 40 °C) under 2C discharging conditions. The maximum temperature difference can be controlled within 5 °C when $h=100\mathrm{W}/({\mathrm{m}}^2\cdot \mathrm{K})$ and nearly 8 °C when $h=1000\mathrm{W}/({\mathrm{m}}^2\cdot \mathrm{K})$. This is due to the fact that the fluid temperature in convective heat transfer is 25 °C, while the initial temperature of the battery pack is 30 °C, so the temperature at the bottom of the battery pack will drop if the heat transfer intensity is greater, which leads to an increase in the maximum temperature difference of the battery pack and a deterioration in the uniformity of temperature. As can be seen in Figure 8, the cooling effect of indirect cooling under a 10C discharging condition is not satisfactory. The maximum temperature in the battery pack is about 100 °C, which exceeds the critical temperature of 80 °C for thermal runaway. When $h=100\mathrm{W}/({\mathrm{m}}^2\cdot \mathrm{K})$, the maximum temperature difference is around 28 °C, and when $h=1000\mathrm{W}/({\mathrm{m}}^2\cdot \mathrm{K})$, the maximum temperature difference is approximately 57 °C, and the temperature uniformity is also very poor. In addition, the maximum temperature of the battery pack is almost the same for both $h=100\mathrm{W}/({\mathrm{m}}^2\cdot \mathrm{K})$ and $h=1000\mathrm{W}/({\mathrm{m}}^2\cdot \mathrm{K})$, and the average temperature is not so different, while the minimum temperature is very different, which means that there is not a large difference in the cooling performance between the two.

Figure 9 and Figure 10 show the temperature contour evolutions of an indirectly cooled battery pack at 60 s, 150 s, 240, and 330 s for $h$, taking $h=100\mathrm{W}/({\mathrm{m}}^2\cdot \mathrm{K})$ and $h=1000\mathrm{W}/({\mathrm{m}}^2\cdot \mathrm{K})$ under a 10C discharging condition, respectively. From these graphs, it can be seen that there is really not much difference in the overall cooling effect of indirect cooling on the battery pack for the two heat transfer intensities. The highest temperature of the battery appears at the location between the two battery tabs, where more joule heat is generated due to the higher current flux density. The maximum temperature of the battery pack is basically the same for both heat transfer intensities, but there is a difference in the minimum temperature. When $h$ is taken as $h=1000\mathrm{W}/({\mathrm{m}}^2\cdot \mathrm{K})$, the minimum temperature appearing at the bottom of the battery pack is obviously much lower than that when $h$ is taken as $h=100\mathrm{W}/({\mathrm{m}}^2\cdot \mathrm{K})$.

In indirect cooling BTMS, the liquid cooling plate is placed at the bottom of the battery pack, and the pack is cooled from the bottom to the top during the discharging. When the discharging rate is slow, the discharging time of the battery pack is longer and the heat generated by the battery has sufficient time to be taken away by the bottom plate (coolant in the case of indirect liquid cooling). When the discharge rate is fast, the discharging time is shorter, and the internal thermal conductivity and thermal resistance of the battery pack are larger, so the heat generated in the top and middle of the battery cannot be taken away in time and will accumulate, causing the rising temperature of the battery pack. Even if the heat transfer intensity of the indirect cooling system is enhanced, the thermal performance of the battery stack cannot be significantly improved. Therefore, it is difficult to effectively cool the lithium-ion battery pack under a 10C discharging rate by indirect cooling.

3.2. 54 V Battery Pack Discharging at High Rate under Single-Phase Direct Cooling

3.2.1. 54 V Battery Pack Discharging at High Rate under Air Cooling

In this section, the temperature responses of a battery pack cooled by natural and forced convection of air under 10C discharging conditions are investigated. The initial temperature and ambient temperature of the battery pack are both 25 °C. The convective heat transfer coefficient h = 10 W/(m² K) for natural convection and the inlet flow velocity of forced convection air are taken as 20 m/s and 100 m/s. The maximum temperature and average temperature on all the cells of the battery pack obtained from the simulation with time are shown in Figure 11.

As can be seen in Figure 11, the forced convection cooling method has a better temperature control performance compared to the natural convection cooling method. As shown in the figure, the flow velocity has a relatively limited improvement in the temperature control performance in this case. When natural convection cooling is used, the average temperature of cells is about 30 °C lower than the maximum temperature, which means that the temperature uniformity of the battery pack is poor. When the discharge process is over, the maximum temperature of the battery pack with forced convection exceeds 95 °C and that with natural convection exceeds 105 °C, both exceeding the normal operating temperature of lithium-ion batteries. For air forced convection cooling, the simulation results show that for the battery pack with a forced convection inlet flow velocity of 20 m/s, the average outlet temperature of air at the end of discharging is 35.08 °C, and the pressure difference between the inlet and outlet is 496.06 Pa, and the required power is 20.34 W. When the flow velocity is 100 m/s, the average outlet temperature at the end of discharging is 27.55 °C, and the pressure difference between the inlet and outlet is 12,024.39 Pa, and the required power is 2065 W. It can be seen that when the flow velocity is large, the fluid temperature difference in the flow channel is smaller, the cooling environment between the cells in the battery pack is closer, and the uniform temperature effect of cooling is better, but a larger pump work is required to be consumed. However, for the cells at a 10C discharging rate, increasing the flow velocity of air cooling does not have a great effect. Due to the limited convective heat transfer coefficient of air forced convection cooling, it is difficult to control the temperature rise of lithium batteries at large heat flux density in the situation involved in the study.

Figure 12 and Figure 13 show the temperature contour evolutions of the natural convection battery pack and forced convection battery pack with inlet flow velocity of 100 m/s at 60 s, 150 s, 240 s, and 330 s under 10C discharging conditions, respectively. Figure 14 shows the streamline diagram of air under the forced convection condition. It can be seen from the figure that the temperature distribution of each cell of the battery pack under natural convection is almost the same because the cooling conditions are almost the same. The lower temperature of the cells near the fluid outlet and the higher temperature of the cells near the inlet in the forced convection battery pack is due to the better flow conditions and heat transfer effect on the cells near the outlet under this flow path design. In addition, the temperature on the side near the outlet channel of each cell is higher because the fluid in the downstream position has absorbed the heat released from the cells upstream, and then the fluid temperature increases, and thus the heat transfer is less effective. The overall temperature of the battery pack under forced convection is lower compared to that under natural convection.

3.2.2. 54 V Battery Pack Discharging at High Rate under Fluorinated Liquid Single-Phase Cooling

This section investigates the temperature responses of the battery pack with FC-72 single-phase direct cooling and HFE-7100 single-phase direct cooling under a 10C discharging condition and the influence of cell spacing on the cooling effect of the battery stack under HFE-7100 single-phase direct cooling. In the study of FC-72 single-phase direct cooling and HFE-7100 single-phase direct cooling, the initial temperature of both the battery pack and the fluorinated fluid is 25 °C, and the fluid inlet velocities are 0.01 m/s, 0.02 m/s, 0.05 m/s, and 0.1 m/s, respectively. The variations of maximum temperature and average temperature with time on all the cells for FC-72 and HFE-7100 single-phase direct cooling battery packs at different flow velocities are shown in Figure 15 and Figure 16, respectively.

From Figure 15 and Figure 16, it can be seen that the use of fluorinated liquid single-phase direct cooling can control the maximum cell temperature below 80 °C, and the overall cell temperature is better controlled. Increasing the flow velocity can significantly improve the cooling effect, but the uniformity of temperature distribution is still not ideal. Since the thermal properties of FC-72 and HFE-7100 are not very different, their cooling effects are similar. The pressure difference between the inlet and outlet of FC-72 and HFE-7100 single-phase direct cooling battery packs is shown in

Table 3. The pressure difference between inlet and outlet of FC-72 and HFE-7100 single-phase direct cooling.

Method	0.01 m/s	0.02 m/s	0.05 m/s	0.1 m/s
FC-72	0.33 Pa	1.03 Pa	5.47 Pa	20.76 Pa
HFE-7100	0.28 Pa	0.88 Pa	4.68 Pa	17.85 Pa

, and the average fluid outlet temperature is shown in

Table 4. The average outlet temperature of FC-72 and HFE-7100 single-phase direct cooling.

Method	0.01 m/s	0.02 m/s	0.05 m/s	0.1 m/s
FC-72	45.43 °C	37.72 °C	30.67 °C	27.80 °C
HFE-7100	46.23 °C	38.24 °C	30.90 °C	27.88 °C

. The average outlet temperature of both is almost the same, and the pressure difference is small, but the pressure difference between the inlet and outlet of FC-72 is slightly larger. Due to the small pressure difference between the two and the slow flow velocity, the power required for both cooling methods is small and can be neglected.

Figure 17 and Figure 18 show the temperature contour evolutions at 60 s, 150 s, 240 s, and 330 s for the battery pack using FC-72 with a flow velocity of 0.01 m/s and 0.1 m/s under 10C discharging conditions, respectively. It can be seen that the temperature distribution of the battery pack is not uniform, and the temperature is higher on the upper right corner, and increasing the inlet flow velocity can improve the uneven temperature distribution.

In the study of the influence of cell spacing on the cooling effect in the HFE-7100 single-phase direct cooling battery pack, the initial temperature of both the battery pack and the fluorinated fluid is 25 °C, and the fluid inlet velocity is 0.1 m/s. Three cell spacings of 2 mm, 4 mm, and 6 mm are taken for comparison. The variation of the maximum temperature and the average temperature of all cells with time on the HFE-7100 single-phase direct cooling battery pack at different cell spacings is shown in Figure 19.

It can be seen from Figure 19 that at the end of discharging, the maximum temperature of the battery pack with 2 mm cell spacing is about 55 °C and the average temperature is about 36 °C. The maximum temperature of the battery pack with 4 mm cell spacing is about 66 °C and the average temperature is about 44 °C. The maximum temperature of the battery pack with 6 mm cell spacing is about 69 °C, and the average temperature is about 50 °C. It can be concluded that the cooling effect of the battery pack with HFE-7100 single-phase direct cooling as the cooling method is better with smaller cell spacing at 10C discharging conditions. This can be explained as follows. In the laminar flow state, the Nusser number $Nu$ of the fully developed fluid is only related to the shape of flow channel cross-section [51]. The cross-section shapes of the flow channels for the 2 mm, 4 mm, and 6 mm models can be regarded as the same for a simplified analysis, so the corresponding $Nu$ is almost the same. According to the equation $Nu=hD/k$, when $Nu$ is equal, the larger $D$ is, the smaller $h$ is. Thus, the cooling effect will be better when the cell spacing is smaller.

The pressure differences between the inlet and outlet of the HFE-7100 single-phase direct cooling battery pack and the average fluid outlet temperature at different cell spacings are shown in

Table 5. The pressure difference between the inlet and outlet and the average fluid outlet temperature of HFE-7100 single-phase direct cooling battery pack at different cell spacings.

Cell Spacing	2 mm	4 mm	6 mm
Pressure difference (Pa)	18.07	17.85	15.80
Average fluid outlet temperature (°C)	28.21	27.88	27.80

. It can be seen that although the pressure differences between the inlet and outlet and the average outlet temperature corresponding to the 2 mm battery pack are slightly larger, the overall gap between the three is not very large, and the power required is small and can be neglected.

Figure 20 and Figure 21 show the temperature contour evolutions of the HFE-7100 single-phase direct cooling battery pack with a flow velocity of 0.1 m/s and cell spacings of 2 mm and 6 mm at 60 s, 150 s, 240 s, and 330 s, respectively, under 10C discharging conditions. It is obvious that the 2 mm pack performs better in terms of temperature control and temperature uniformity.

3.3. 54 V Battery Pack Discharging at High Rate under Fluorinated Fluid Two-Phase Cooling

This section explores the temperature response of the battery pack cooled by HFE-7000 two-phase immersion cooling under a 10C rate discharging condition. Immersion cooling is a kind of cooling method that takes away the heat generated by the object through the pool boiling two-phase heat transfer. Because of the insulating and fireproof nature of fluorinated liquid, it can be applied not only to the cooling and temperature controlling of electronic components, but also to the effective cooling of lithium-ion batteries. The initial temperature of the battery pack is 25 °C. A comparison of maximum temperature and average temperature of the battery pack over time under different cooling methods of single-phase direct cooling above and HFE-7000 two-phase cooling is shown in Figure 22. It can be visually seen that the HFE-7000 two-phase cooling method can effectively control the maximum temperature of the battery pack below 35 °C, which is in the optimal operating temperature range of lithium-ion batteries, and has the best cooling effect compared with the other direct cooling methods.

Figure 23 shows the temperature contour evolutions of the battery pack with HFE-7000 two-phase cooling under 10C discharging conditions at 60 s, 150 s, 240 s, and 330 s. It can be seen from the figure that good uniformity in the temperature distribution of the battery pack is achieved. The local high temperature appears on the cell near the tabs, and the temperature of the tabs is higher than that of the cell domain, which is because the HFE-7000 liquid only submerges the cell domain in this simulation, and the tabs are not submerged. It is conceivable that the temperature uniformity should be better if cell domain and tabs are both submerged in HFE-7000. Under high rate discharging condition, the battery generates a large amount of heat, which in turn causes a large heat flux on battery surface. The large heat flux density triggers the pool boiling heat transfer of HFE-7000 liquid with a low boiling point. Since the phase change process in pool boiling takes away a large amount of latent heat of vaporization, it provides a heat transfer coefficient at the battery surface that is much larger than the forced heat transfer by single-phase flow. As a result, the maximum temperature and average temperature of the battery pack are well limited. It is worth mentioning that continuous 10C discharging is already an extremely fast discharging rate for lithium-ion batteries under normal operating conditions, while fluorinated liquid two-phase cooling is still able to provide effective heat dissipation and precise temperature control for lithium-ion battery packs. Therefore, it can be found through this study that fluorinated fluid two-phase direct cooling is a cooling method for lithium-ion batteries that deserves more research and discussion, and more detailed subsequent experiments and simulation studies are needed.

4. Conclusions

In this study, a multi-scale modeling approach and the ECM model were used to conduct a three-dimensional thermal simulation of lithium-ion batteries. The cooling effect of a 54 V battery pack consisting of 18 LiFePO₄ pouch cells with a capacity of 20 Ah under a 10C discharging condition using indirect cooling and direct cooling thermal management methods is investigated. The key findings are shown as follows.

• It is found that under a 2C discharging condition, the maximum temperature of the battery pack can be controlled below 40 °C and the maximum temperature difference can be controlled within 8 °C with indirect cooling, which can achieve the cooling of the battery pack very well. However, when the discharging rate is 10C, the maximum temperature of the battery pack with indirect cooling can exceed 100 °C, and the maximum temperature difference can reach 28 °C. Due to the low thermal conductivity of the battery and the short discharging time at a 10C rate, even enhancing the cooling performance by significantly increasing the heat transfer intensity of the indirect cooling will have little effect. Therefore, it is difficult to cool the battery pack effectively with indirect cooling under the 10C discharging condition.
• For direct cooling, when natural convection of air is used as the cooling method of the battery pack, the maximum temperature of the battery pack can rise to 105 °C and the average temperature is above 75 °C under the 10C discharging condition. Natural convection also makes it difficult to meet the cooling requirement of the battery pack under the 10C discharging condition. In the same situation, the cooling effect of forced air convection is better than that of natural convection. When the inlet flow velocity is 100 m/s, the average temperature of the battery pack is 70 °C. The pressure drop between the inlet and outlet is 12,024.39 Pa, and the power required is 2065 W. Although the air forced convection cooling is somewhat effective, the pump work consumed is larger and the cooling effect obtained is not very satisfactory.
• When fluorinated fluid single-phase forced convection is selected as the cooling method for the battery pack under a 10C discharging rate, the maximum temperature of the battery pack can be controlled up to 65 °C, and the average temperature can be controlled up to about 45 °C. The pressure drop between the inlet and outlet is about 20 Pa, and the power required is of small magnitude. In addition, when two different fluorinated fluids, FC-72 and HFE-7100, are used as the coolant for single-phase direct cooling, the difference in cooling effect is very small. The fluorinated fluid single-phase forced convection cooling has a significant advantage over air forced convection cooling. Further, the influences of flow velocity and cell spacing on the cooling effect were investigated for fluorinated fluid single-phase forced convection. The study found that increasing the flow velocity could lower the temperature of the battery pack to a certain extent and improve the temperature uniformity of the battery pack. For the same flow velocity, reducing the cell spacing in the battery pack can achieve a better cooling effect.
• Finally, a preliminary numerical simulation study on a new cooling method, fluorinated liquid immersion cooling, is made. It is found that it can help to reduce the average temperature and maximum temperature of the battery, and can control the maximum temperature of the battery pack below 35 °C under a 10C discharging rate, and also can effectively reduce the temperature difference in the battery pack. This is a promising cooling method for lithium-ion battery cooling.

By comparing the conventional air-cooling and indirect liquid-cooling methods, this paper shows that the fluorinated liquid single-phase and two-phase direct cooling methods have good cooling effects for lithium-ion battery packs under a high discharge rate. This study will provide some help to the subsequent research related to direct fluoride liquid cooling and will provide a reference for the design and selection of BTMS for electric vehicles. Due to its excellent temperature control performance, fluorinated liquid immersion cooling will be widely used in the field of electric vehicle battery thermal management. However, it still has some problems to be solved on its development path, such as high cost and difficulties in the design of two-phase cycle systems. It is worthwhile to note that this work is only confined to the simulation study, and subsequent experimental studies are still needed for the matching of fluorinated liquid immersion cooling with a lithium-ion battery system.