Electric vehicles have become a trend in recent years, and the lithium-ion battery pack provides them with high power and energy. The battery thermal system with air cooling was always used to prevent the high temperature of the battery pack to avoid cycle life reduction and safety issues of lithium-ion batteries. This work employed an easily applied optimization method to design a more efficient battery pack with lower temperature and more uniform temperature distribution. The proposed method consisted of four steps: the air-cooling system design, computational fluid dynamics code setups, selection of surrogate models, and optimization of the battery pack. The investigated battery pack contained eight prismatic cells, and the cells were discharged under normal driving conditions. It was shown that the optimized design performs a lower maximum temperature of 2.7 K reduction and a smaller temperature standard deviation of 0.3 K reduction than the original design. This methodology can also be implemented in industries where the battery pack contains more battery cells.

## Introduction

Due to the growing scarcity of oil resources, more and more countries are promoting and popularizing electric vehicles (EVs) instead of fuel-powered vehicles [1]. Countries in Europe, including Britain, France, Germany, The Netherlands, and Norway, and India in Asia have initially said they will stop producing and selling fuel-powered vehicles, giving a rough time frame that the fuel-powered vehicle will be stopped entirely by 2050. Generally, EVs have become a trend. A battery pack is the heart of an EV, and it supports enough power for driving, which requires that a battery pack should comprise hundreds of battery cells [2,3]. Compared with other types of batteries, lithium-ion batteries are the most popular batteries because of high power-volume ratio, high energy-volume ratio, long cycling life, and low-self-discharge rate [4,5].

When an EV works at the normal driving condition, high discharging current will lead to high heat generation power inside the battery pack [6]. It was found that under the normal range of working temperature, the lifespan of lithium-ion batteries will dramatically decline when the temperature rises. Therefore, it is necessary to design a battery thermal management system to avoid overheated situations. Air-cooling, liquid-cooling, and phase-change-materials (PCMs)-based cooling methods were usually used as cooling strategies, and many publications and literature in this field can be found. Wang et al. [7] used a computational fluid dynamics (CFD) method to investigate the thermal performance of air-cooling battery packs with different cell arrangements, and a lumped model of heat generation of a sing cell was applied, and the authors found that the cubic arrangement was the best structure if they concern both the cooling effect and the cost. Yang et al. [8] compared the cooling effect of the aligned cell arrangement with the staggered one, and an optimal combination of parameters was given for the aligned arrangement using qualitative analysis. Zhao et al. [9] established air-cooling numerical models to conduct a parametric investigation on different parameters, and it was found that the airspeed has a nonlinear fluence on the local temperature difference.

Moreover, liquid-cooling systems have a stronger cooling effect while consuming more space and power compared with air-cooling systems. Zhao et al. [10] proposed a minichannel-based liquid-cooling method, and they pointed out that increasing fluid rate has a limited influence on the cooling effect. Panchal et al. [11] built a liquid-cooling system on a prismatic lithium-ion battery cell using experimental and numerical methods, and they succeeded to control the cell temperature at a safe range under high discharge rate. Greco et al. [12] considered a cooling system with heat pipes, and the predicted highest temperature of the lithium-ion battery is 27.6 °C, which was comparably low than the air-cooling system with 51.5 °C.

The PCM-based cooling method is different from the other two cooling methods since it does not consume power to remove heat. Moreover, many of the literature on this method is focusing on the improvement of PCM conductivity. For example, Goli et al. [13] incorporated graphene into PCM to increase conductivity and led to an apparent temperature decrease. Samimi et al. [14] used carbon fiber–PCM composites to improve conductivity and temperature uniformity. Other than these three cooling strategies, some researchers employed the cooling method combining two or three of these strategies [1517].

As shown by the relevant literature, most of the work has succeeded to reduce the high temperature. The temperature difference remains a considerable problem, especially in the most popular air-cooling systems. Also, parametric and quantitative techniques were uncommonly used to analyze the influence of each factor on the cooling effect [18]. Moreover, the method to obtain a combination of parameters with the best temperature distribution was still lacking [19].

This paper aimed to propose a four-step methodology to overcome the shortages and provide a comprehensive way to design a more effective air-cooling battery pack with a lower maximum temperature and a smaller temperature difference. With this motivation, the article was organized as follows: The research problem was described in Sec. 2. Section 3 presented a detailed description of the four-step methodology. Section 4 displayed the results and discussion. The conclusion was given in Sec. 5.

## Statement of Research Problem

The investigated battery pack contained eight prismatic cells, and the cells were charged and discharged using some typical driving cases, which was defined by Fan et al. [20]. The authors in Ref. [20] have found that the uneven gaps between cells can affect the temperature distribution without increasing the maximum temperature, yet they did not apply a quantitative to optimize the temperature distribution. In this article, a battery pack with a similar structure was designed and parameterized (Fig. 1).

According to our descriptions, two objectives were defined in this research: (1) the minimization of the maximum temperature of the battery pack and (2) the minimization of the temperature difference of the eight cells. An all-in-one formulation is given as Eq. (1) to clearly define the problem
$findx=[d1,d2,d3,d4,d5,d6,d7,d8,d9,d10,v]minTmaxminTSDsubjectto3≤d1≤5,3≤d2≤5,3≤d3≤5,3≤d4≤53≤d5≤5,3≤d6≤5,3≤d7≤5,3≤d8≤510≤d9≤30,10≤d10≤30,v=1$
(1)

## Design Optimization Methodology

In this work, we tried to provide a comprehensive way to design a more effective air-cooling battery pack with a lower maximum temperature and a smaller temperature difference. Figure 2 illustrates the methodology to improve the design of the air-cooled battery pack, which can be divided into four steps: First, the lumped air-cooling battery pack model was built using experimental data. Second, CFD methods were used to calculate the temperature distribution of the eight cells by defining the material properties, design variables, and heat generation. Third, CFD experiment samples were created using a central composite design (CCD) [21] method, and the response surface method (RSM) [22] was used to quantitatively evaluate the influence of each factor on the cooling effect, which is also known as sensitivity analysis. Fourth, compared with the original design, the optimized air-cooling structural design was obtained with minimum highest temperature and minimum temperature standard deviation.

### Design of Battery Pack and Computational Fluid Dynamics.

The initial battery pack is built with the dimensions and parameters given in Tables 1 and 2. Surrounding cooling air of the battery pack takes away the generated heat of internal battery reactions. Also, the temperature rise of the battery cell can be defined by Eq. (2). The calorific value of the battery unit varies with the charge–discharge ratio [23]. The higher the charge ratio, the faster the chemical reaction rate and the calorific value of the cell. The heat generation was set as 29,600 W/m3, which was calculated using an equivalent specific heat capacity test. The experimental setup of a single cell battery was shown in Fig. 3(a), and the experimental setup of a battery pack with air cooling was shown in Fig. 3(b).

The other thermophysical parameters were given in Table 3. The flow rate was set as 20.4 m3/h [20]. We assumed that the air passes through nine cooling channels inside the battery box evenly, then the Reynolds number was 328, which means that a laminar model should be chosen for the cooling air. Conversion equations including energy conversion and flow conservation were chosen as Eqs. (3)(6) to model the thermal behavior. The velocity-inlet was defined as the inlet boundary condition, and the pressure-outlet was defined as the outlet boundary. And all the equations were solved using ansys fluent
$ΔT=QρCpΔt$
(2)

$ρbCb∂T∂t=∇⋅(kb∇T)+Q$
(3)

$ρaCa∂Ta∂t+∇⋅(ρacav→Ta)=∇⋅(ka∇Ta)$
(4)

$∇⋅v→=0$
(5)

$ρadv→dt=−∇p+μ∇2v→$
(6)

Q is the battery heat generation rate, ρb and ρa are the mass densities of the battery and the cooling air, Cb and Ca are the specific heats of the battery and the cooling air, ka and kb are the thermal conductivities of the battery and the cooling air, Ta is the temperature of the cooling air, $v→$ is the velocity of the cooling air, p is the static pressure of the cooling air, and µ is the dynamic viscosity of the cooling air.

A three-dimensional model was used, and a grid independence study was carried out, as shown in Fig. 4, and the maximum temperature of a battery pack varies slightly when the element number is between 16,308 and 114,161. Considering the accuracy of simulation results and computing time, the element number was chosen as 114,161.

An experiment was carried out to validate the CFD model. As shown in Fig. 5, the temperature on the surface of the middle part of a battery raised fast under a discharge rate of 1.8 C, and the simulated temperature fitted well with the experimental data.

### Selection of Surrogate Models.

The most common way to design a battery pack was manually specifying hundreds of combinations of values for the design variables and then analyzed the expecting outputs, such as maximum temperature. This method cannot take full account of the interaction of variables. Also, it is inefficient and subjective, which cannot ensure accuracy. Therefore, collecting effective combinations is one of the most important things for this work.

Surrogate modeling was one of the most useful methods to drive the optimization process. Design of experiments (DoE) and construction of surrogate models were the two main parts of the surrogate modeling.

For the approximation of surrogate modeling, the CCD method was used for DoE, which was one of the most familiarly adopted DoE approaches. Also, the design space can be filled well by the training samples. Considering the common battery spacing arrangement [7,9], the range of cell gap spacing (d1d8) was 3–5 mm, and the range of the height of the air inlet and outlet (d9 and d10) was 15–25 mm.

We used the RSM to analyze the influence of each factor on the cooling effect. Although there were a lot of methods for formulating the surrogate model, such as radical basic function (RBF) [24] and Krigin, RSM was the most widely used method, and it guarantees high accuracy for our model. Median absolute deviation, maximum absolute error, and root-mean-square-error were used as the metrics to access the accuracy of the surrogate model. Then, the two objectives of our work, the maximum temperature and standard temperature deviation, can be represented by Eqs. (7) and (8)
$Tmax=f~max(d1,d2,d3,d4,d5,d6,d7,d8,d9,d10,v)$
(7)

$TSD=f~TSD(d1,d2,d3,d4,d5,d6,d7,d8,d9,d10,v)$
(8)

Since the temperature keeps rising when the battery pack discharges at 1 °C, we chose the temperature at the end of the discharge cycle as the temperature index and the objective.

### Multi-Objective Optimization.

A multi-objective optimization model of Eq. (1) was established by using intelligent optimization algorithm based on the surrogate modeling model. One of the most commonly used methods for multi-objective optimization, multi-objective optimization genetic algorithm (MOGA), was used to carry out the multi-objective optimization.

The objective of the optimization model was to obtain a Pareto frontier to find the optimal solution to minimize the maximum temperature and the standard deviation of temperature.

Finally, the original scheme of the air-cooled battery pack was compared with the optimized one.

## Results and Discussion

Two hundred samples were generated randomly using CCD. These 200 samples were divided into three parts: 1–120 was the training set (Set No. 1), 121–160 was the validation set (Set No. 2), and 161–200 (Set No. 3) was the test set. Set No. 1 was used to formulate surrogate models by RBF, Kriging, and RSM methods. Set No. 2 was used to evaluate the surrogate model. Set No. 3 was used to calculate the accuracy of the surrogate models using the defined metrics. A cross-validation method was used to estimate the performance of the models.

Sensitivity analysis can be defined as the research of how uncertainty in the output of a model can be attributed to different sources of uncertainty in the model input [25]. From Fig. 6, the average temperature (T1–7) of battery Nos. 1–7 is mostly affected by the outlet height (d10) of the battery pack. The distance between two sides of the batteries also had a significant influence. For the average temperature of No. 1 battery, the outlet height (d10) was found to be significant (41.8%), followed by the gap on the right side (24.2%) and the gap on the left side (8.4%). The average temperature of No. 8 battery was most affected by its left clearance d8, which reached 32.2%, followed by d10 (24.4%). Based on this analysis, it can be concluded that the sensitivity map can use the form of percentage to clearly show which input parameters have the most significant impact on the specified output parameters. It also provided a clear basis for the selection of optimization parameters.

As shown in Fig. 7, the maximum temperature of battery cell 1, which is nearest to the fan, appears when d10 is minimum and d9 is maximum. The farther the cell away from the inlet, the higher the average temperature is. When the cell is far enough away from the inlet, the influence of d9 becomes inverse; as we can see, the temperature begins decreasing when d9 increases from cell 4 to cell 8, which is just opposite to that in cell 1 and cell 2. Also, the cell temperature becomes more susceptible to d9 and less sensitive to d10 as the distance increases.

From Fig. 8, the sensitivity of the average temperature for each battery cell is similar. The maximum average temperature occurs when the distance between the two sides reaches the minimum value at the same time, and the minimum average temperature occurs when the two sides’ distance gap reaches the maximum. As the distance becomes large, the average temperature of the battery is reduced.

After obtaining the RSM model of the two objectives, the MOGA was applied to the RSM model to obtain the Pareto solution. The initial settings of the MOGA were shown in Table 4. Table 5 shows the selected two candidate solutions of the MOGA along with the current design.

As shown in Table 5 and Fig. 9, candidate design 1 and candidate design 2 had significantly improved the thermal performance of the battery pack. Compared with the current design, the maximum temperature of the battery pack dropped from 311.32 K to 308.89 K and 308.55 K. The standard deviation of the average temperature of each battery was 0.378 K for candidate design 1 and 0.337 K for candidate design 2, respectively. Therefore, candidate design 1 and candidate design 2 with lower maximum temperature and lower temperature difference can be used as the optimized design of parameter combinations.

## Experimental Verification of the Optimized Designs

As shown in Fig. 10, the battery charging and discharging equipment was used to maintain the 1 C discharging rate. The cooling air speed was measured by an electronic wind speed tester. The surface temperature of batteries was measured by a thermal resistor and then collected in the data logger. Temperature measurement points were distributed near the positive pole, negative pole, and middle and bottom of the battery cells. The average temperatures of four measurement points were then used as the experimental results. The computer was used to set discharge parameters. The battery pack was charged and discharged for ten cycles. And experimental results were presented as the average temperatures of the ten cycles with the changing range in Fig. 11. The experimental results fitted well with the calculated results, the temperatures of the battery cells were reduced, and the difference between all the experimental values and the predicted values was less than 0.8 K, which meant that the surrogate model can be used for optimization purposes.

## Conclusion

This article proposed a comprehensive four-step optimization method to design a more efficient air-cooling battery pack with better thermal performance. The main findings from the analysis were as follows:

1. The average temperature was mostly influenced by the height of the inlet and outlet (d9 and d10), and the two neighbor gap spaces of a battery cell also had an essential impact on the average temperature of the cell.

2. The maximum temperature of the battery pack dropped from 311.32 K to 308.89 K and 308.55 K. The standard deviation of the average temperature of each battery was 0.378 K for candidate design 1 and 0.337 K for candidate design 2, respectively.

In this work, the optimization results did not count in the effect of uncertainty. Since uncertainty during the entire cycle life of battery exists and can affect the performance of the battery pack, we are taking consideration of the robust design in our future work.

## Funding Data

• Natural Science Foundation of Hunan Province of China (2017JJ3057).

• Guangdong Natural Science Foundation (2018A030310150).

• Guangdong Science and Technology Innovation Project (Grant No. 2017KQNCX080).

• Shantou University National Fund Cultivation Project (Grant No. NFC17002).

## Nomenclature

• d =

length, mm

•
• k =

thermal conductivity

•
• p =

static pressure

•
• v =

the cooling air speed, m/s

•
• v =

velocity, m/s

•
• T =

temperature, K

•
• Q =

heat generation rate, W/m3

•
• C =

specific heat, J/(kg K)

•
• d1 =

the distance between the left border and cell 1, mm

•
• d9 =

the distance between the bottom border and cells top, mm

•
• d10 =

the distance between the top border and cells bottom, mm

•
• dcon =

the fixed distance between the right border and cell 8, mm

•
• di(i = 2–7) =

the distance between cell i − 1 and cell i, mm

•
• Ti =

the average temperature of cell i(i = 1–8)

•
• Tmax =

the maximum one of Ti

•
• TSD =

temperature standard deviation, K

•
• TSD =

standard deviation of Ti

•
• ρ =

density, kg/m3

• eq =

equation

•
• min =

min

•
• max =

maximum

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