While usually being arranged closely in order to improve the space utilization, batteries will produce a lot of heat in the normal charge and discharge.If the heat can not be removed for a long time, the battery temperature will exceed the normal working range and the battery temperature difference will be too large. These will lead to a great reduction of battery performance, or even an explosion[1-5]. Therefore, the thermal battery structure of the battery pack has great influence on the performance and life of the entire battery pack.

Peng Y[6] used a thermal coupling model to compare the different cooling methods for lithium iron phosphate batteries, and the results showed that high speed air cooling can make the battery pack work within the normal operating temperature range. Yang et al.[7] optimized the heat dissipation scheme of the battery pack, and the results showed that the improvement of the temperature field can be achieved by optimizing the inlet angle, the air flow rate, the inlet form and the local structure of the battery pack. Yuan H[8] designed a structure with inlet and outlet on the same side of liquid cooling, which improved the temperature consistency.Air cooling, liquid cooling, phase-change materials are currently used in the main cooling mode. Air cooling system because of its simple structure, light weight, low cost, etc. are widely used in battery thermal management system[9]. At present the effect of the structure with inlet and outlet on the same side applied to air cooling has not been studied.

Based on the CFD simulation platform, the heat generation and three-dimensional heat transfer models of the battery pack are established in this study. The temperature distributions of difference battery packs at 3C discharge rate are studied and analyzed. The influence of the main cooling structure parameters on the results provides theoretical guidance for the thermal management system design of the battery pack.

1 Battery Thermal Model

The battery used in this study is the square lithium iron phosphate battery developed by a company.Its capacity is 35 A·h, with a size of 110 mm×25 mm×260 mm. The charge and discharge reaction equation and the total reaction equation are as follows.

Positive reaction:

Negative reaction：

是“烟富3号”的早熟株变。2015年通过贵州省品种审定委员会审定。其主要的优良变异体现在成熟期上，在贵州长顺8月中下旬成熟。果实近圆形，果形指数0.87，平均单果重210～250克。果面平滑，稀有果粉，果皮底色淡黄，条红，着色面积85%以上。果肉淡黄，质地硬脆，肉质细，汁液多，风味酸甜，香气浓，品质上等。可溶性固形物14.7%～15.9%。

除此之外，笔者认为还有两篇值得关注的文章，一篇是杨振之先生从哲学角度提出的“诗意栖居说”[27]，另一篇是胡传东先生从进化心理学角度提出的“心理适应说”[28](笔者姑且这样称之)。本文认为，杨振之先生的“诗意地栖居”一定程度上切近了旅游的本质。但由于其切入的路径是哲学的思辨，逻辑上虽有说服力，但比较缺少科学和事实的说服力。本文认为与其说是“诗意地栖居”，不如说是“流动地栖居”“迁移地栖居”更能反映出旅游的动态性特征，也更符合人类发展演化的历史事实。

In order to simplify the analysis and calculation, following assumptions are proposed for the constructed thermal model of the battery: ① The battery material is uniform in texture, and the specific heat capacity and thermal conductivity are constant, which are not affected by the battery SOC and temperature. ② Batteries’ heat radiant is ignored and only the heat conduction and convection are considered in the heat transfer process. ③ Each battery is a stable heat source in the discharge process. ④ The effect of air buoyancy is ignored and air is treated as an incompressible ideal gas.

1.1 Heat generation model

It is difficult to obtain the heat generation rate of the battery accurately by experimental methods. The existing D. Bernardi[10] model is used to estimate the heat generation rate, and it can be expressed as

(1)

where Vb is the battery cell volume; I is the charge or discharge current; E0 is the battery open circuit voltage; U1 is the cell voltage; T is the thermodynamic temperature; dE/dT is the temperature influence coefficient.

1.2 Heat transfer model

The battery inside is a heat source. The density is about 1 958.7 kg/m-3, the thermal conductivity is 0.908/2.732/2.732 W/(m·K)-1, and the specific heat capacity is 733 J/(kg·K-1). The temperature of the air and the environment is 20 ℃. The inlet boundary is set to Velocity; the outlet boundary is set to Outflow in order to avoid reflow; the contact surface of the battery pack with the cooling air is set to Coupled. The computational model is chosen as the energy conservation equation and the turbulence k-ε equation. Second order upwind is used for the momentum equation, energy equation and turbulence dissipation equation.

Heat conduction refers to the direct contact of different objects or the same object which does not occur relative to the part of the movement due to the existence of temperature differences relying on material molecules, atoms and free electrons to occur in the heat transfer and diffusion process[11]. The whole process can be described by the Fourier thermal differential equation as shown in the equation:

Total reaction equation：

(2)

where ρ is the cell density; C is the specific heat capacity of the battery; T is the battery temperature; λx,λy,λz are the thermal conductivity in the x, y, z directions of the battery, respectively.

where q is the heat flux density; hf is the convective heat transfer coefficient; TS is the battery surface temperature, TB is the temperature of the surrounding fluid.

As shown in Fig.1, the simplified model of the battery pack is drawn through the 3D modeling software UG. Then the model is imported into ICEM for meshing. The import and export extends outward for a distance to avoid reflow in the calculation. Fluid and solid domain grid separately and the boundary layer is set near the wall, in order to improve the calculation accuracy. The final generation of about 200 million grid. And grids quality is good.

Based on the structure with inlet and outlet on the same side and inlet angle of 3°, the air outlet angle is set to 0°, 1°, 2°, 3° and 4° respectively. The results are shown in Tab.3. It shows that the effect of the outlet angle on the heat dissipation is not as significant as the inlet angle. When the outlet angle increases from -2° to 4°, the average temperature increases by 0.36 ℃ and the temperature difference increases by 1.4 ℃.

q=hf(TS-TB)

(3)

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采用SPSS20.0软件对本研究数据资料进行统计学分析，其中计数资料采用[n(%)]描述，组间比较采用χ2检验。P＜0.05(双侧检验)为差异有统计学意义。

2 CFD Simulation

2.1 Creating a battery geometry model and dividing the grid

1.2.2 Convective heat transfer

Fig.1 3D model and grid model

2.2 Physical field settings

1.2.1 Heat conduction

3 Thermal Structure Optimization

3.1 Inlet and outlet direction optimization

Tab.1 compares the simulation results of different structures. It is clear that the cooling effect of the battery pack structure with the inlet and outlet on the same side is significantly better than that with the inlet and outlet on the different sides.Both of its average temperature and maximum temperature difference are reduced. By comparing Fig.2a with Fig.3a, it is found that the cooling effect near the inlet is poor and that almost no air flow through the channel in Fig.2a. But in Fig.3c the air flow more evenly through the battery pack. By comparing Fig.2b with Fig.3b, the outlet speed in Fig.3b is also less than the outlet speed in Fig.2b, which indicates that the cooling air stays in the battery pack longer, allowing the air to exert the cooling effect fully.

1.5.1 单因素分析 将血药浓度检测结果定义为“因变量”，对应的“自变量”为性别、年龄、体表面积（BSA）、白蛋白水平、肝功能水平、N-乙酰化酶2（NAT2）*4位点基因型、NAT2*15位点基因型和有无合并基础疾病。对于部分更适合作为分类资料处理的自变量进行赋值量化 （肝功能异常为ALT或AST＞40 U·L-1），量化结果见表 1。使用 SPSS 20.0 软件进行统计分析。

Tab.1 Temperature simulation results comparison of different structures

ModelAverage/℃Maximum/℃Minimum/℃Maximumdifference/℃Inletandoutletonthesameside35.848.024.523.5Inletandoutletonthedifferentsides31.838.524.114.3

Fig.2 Simulation results of the structure with inlet and outlet on the different sides

Fig.3 Simulation results of the structure with inlet and outlet on the same side

Although the cooling effect has been improved greatly, the temperature difference is still large. Based on the structure with inlet and outlet on the same side (Fig.4), the main parameters need to be analyzed and optimized, such as outlet width L, air inlet angle α, air outlet angle β and the inlet air speed, in order to further improve the cooling performance.

Fig.4 Battery pack structure diagram

3.2 Air inlet angle optimization

Based on the structure with inlet and outlet on the same side, the air inlet angle is set to 0°, 1°, 2°, 3° and 4°. The simulation calculation results are shown in Tab.2. It shows that increasing the inlet angle within a certain range has a significant effects on reducing the maximum temperature and the temperature difference of the battery, and the effect become not conspicuous when the inlet angle is greater than 3°. When the inlet angle increases to 3°, the average temperature changes little, but the maximum temperature and maximum temperature difference are reduced by 5 ℃ and 6.6 ℃, thereby increasing the temperature consistency.

Figs.4-8 shows the battery temperature distribution and velocity flow field when the air inlet angle is 4°. It can be seen from Fig.5a and Fig.3a that the air flow more evenly than before. By comparing Fig.5b with Fig.6b, it can be seen that the highest temperature region moves from the left to the right of the pack as the angle changes. The reason is that when the air inlet angle is 4°, the airflow of right channels is too small, resulting in insufficient cooling. It can be concluded that when other factors remain unchanged, the inlet angle in the range of 3° to 4° brings a uniform temperature distribution.

Tab.2 Temperature simulation results comparison of different inlet angles

Inletangle/(°)Average/℃Maximum/℃Minimum/℃Maximumdifference/℃031.8038.524.114.3131.3336.725.611.1231.8634.025.28.8331.7333.425.67.8431.6033.525.87.7

3.3 Air outlet angle optimization

Convective heat transfer is the process by which the fluid flows through the heat generated by the solid surface and the solid[11]. It is a phenomenon of thermal exchange that characterizes the macroscopic motion of fluid. The law of motion can be described by the Newton’s Cooling Law shown as

Fig.7 shows the simulation results when the outlet angle is 4°. The uniformity of the battery temperature field is slightly worse with the increase of the outlet angle, but not obvious. Considering the error, it can be considered that the outlet angle has no effect on results. The final angle is set to 0° in order to facilitate the processing and manufacturing.

3.4 Air outlet width optimization

Based on the structure with inlet and outlet on the same side, inlet angle of 3°, and outlet angle of 0°, the air outlet width is set to 40 mm, 50 mm, 60 mm and 70 mm. The simulation calculation results are shown in Tab.4, and Fig.8 shows the temperature distribution and velocity field with an outlet width of 40 mm. It shows that the width of the outlet has a slight effect on the average temperature, the maximum temperature and the maximum temperature difference. When the width of the outlet increases from 40 mm to 70 mm, the average temperature is only reduced by 0.54 ℃ and the maximum temperature is reduced by 2.5 ℃. But it is worth noting that when the outlet width exceeds 60 mm, the average temperature and temperature changes are not obvious. So 60 mm of the outlet width led to not only saving space but also to maximizing the cooling effect.

Fig.5 Simulation results of the structure with 4° inlet angle

Fig.6 Simulation results of the structure with 3° inlet angle

Fig.7 Simulation results of the structure with 4° outlet angle

Fig.8 Simulation results of the structure with 40 mm outlet width

Tab.3 Temperature simulation results comparison of different outlet angles

Outletangle/(°)Average/℃Maximum/℃Minimum/℃Maximumdifference/℃-231.5833.425.97.5031.6033.525.87.7231.6834.025.28.8431.8534.825.69.2

Tab.4 Temperature simulation results comparison of different outlet widths

Outletwidth/mmAverage/℃Maximum/℃Minimum/℃Maximumdifference/℃4032.0735.125.1105031.7834.225.38.96031.6033.525.87.77031.5333.325.87.5

3.5 Inlet air speed optimization

In the case of keeping the structural parameters unchanged, only the inlet air speed is changed. The inlet air speed is set to 3 m/s, 4 m/s, 5 m/s, 6 m/s and 7 m/s, respectively, and the results are shown in Tab.5. It shows that changing the inlet air speed has a significant effect on the average temperature. As the air speed increases from 3 m/s to 7 m/s, the average temperature decreases by nearly 8 ℃, and the maximum temperature decreases by 9.6 ℃, and the maximum temperature difference decreases from 10.8 ℃ to 5.9 ℃. However, as the speed becomes larger, the gradient of the average temperature change is smaller. Larger inlet speed requires more energy. When the battery temperature is already within normal range, there is no need to set a larger inlet speed. So it is necessary to choose a reasonable inlet air speed.

或许，小伊应该感谢上苍给他一次重塑自己的机会。之后，他就可以像正常人一样平庸地活着。无论是甩掉e还是E，对他来说都是一种解脱。如果仅留下关于e的记忆，他就是最普通不过的少年，每天背着被教科书和草稿纸填充地满满当当的破旧书包穿梭在老城区，睁开眼是城市的喧嚣，入睡时耳边循环着从旧录音机里传来的忽高忽低的英语听力，他实在不知道这刺激大脑皮层的噪音怎么会有利于睡眠。如果选E，那他就更无拘无束了，深冬的田野、凌晨的街道、充斥着尖叫和笑声的酒吧，无论人们怎么评价、诋毁，对他来说都无所谓——作为一个DJ，以一种极端的生活方式活着，已经成为了他的基本职业素养。

Tab.5 Temperature simulation results comparison of different air speeds

Airspeed/(m·s-1)Average/℃Maximum/℃Minimum/℃Maximumdifference/℃337.1039.929.110.8433.5936.027.18.9531.6033.525.87.8629.7731.725.06.7728.8630.324.45.9

4 Conclusion

The simulation results show that the heat dissipation effect of the structure with the inlet and outlet on the same side is better than that on the different sides. The appropriate inlet angle and outlet size can improve the uniformity of temperature field. When the inlet angle is 4°, the maximum temperature difference is reduced by 6.6° compared with the initial 0°. The effect of inlet angle and outlet width on the temperature field of the battery pack is not obvious, but selecting the appropriate outlet width can improve the space utilization and reduce the maximum temperature difference. The inlet angle, the outlet angle and the outlet width do not affect the average temperature of the battery pack, and only the air speed can reduce the average temperature. Inlet air speed could be chosen according to the different heat dissipation rate of the battery so as to achieve the best cooling effect.In the case of a discharge rate of 3C and air speed of 5 m/s, the average temperature after structural optimization is reduced by 4.8 ℃ and the temperature difference is reduced by 15.8 ℃. The cooling effect is significantly improved.

不管峨眉武术在概念上是宏观上的还是微观上的，其在长期的历史变迁中，已然逐渐形成了具有独特风格、文化哲理且注重内外兼修的传承理念。

References:

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②钱忠好:《非农就业是否必然导致农地流转——基于家庭内部分工的理论分析及其对中国农户兼业化的解释》，《中国农村经济》2008年第10期。