# Integration of Computational Fluid Dynamics and Artificial Neural Network for Optimization Design of Battery Thermal Management System

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## Abstract

**:**

## 1. Introduction

_{4}cuboid battery packs and optimize the U-type structure. However, pioneering studies have highlighted the possibility of using ANN for battery thermal problems. These studies include modelling battery spacing, specific format, and some battery performances. The detailed temperature distribution of LIB and battery pack have not been fully investigated. Besides, the ambient temperature and natural ventilation should be considered during the battery working process. Therefore, the combination between ANN analysis and the electro-thermal battery model is proposed to investigate further the battery system’s cooling efficiency and battery fire safety performance. Figure 1 shows the schematic figure of the integrated CFD-ANN model proposed in this study.

- (i)
- Establishment and development of a three-dimensional electro-thermal model capable of considering temperature distribution of battery packs and heat exchange with the ambient environment.
- (ii)
- Utilize the numerical results to comprehensively describe and predict the battery system’s thermal behaviour to improve battery safety during the designing and working stages.
- (iii)
- Coupled the electro-thermal model with the ANN model to optimize the battery system configuration design and enhance the cooling performance of the battery system.

## 2. Numerical Models Applied in the Battery Pack

#### 2.1. Electrochemical Model

_{cell}is calculated by applying time-dependent cell current I

_{cell}. Additionally, the battery open circuit voltage data, named E

_{OCV}, is estimated from SOC.

_{4}/Carbon power battery, considering the physical and electrical conservations, as well as thermal principles and electrochemical kinetics. The electrochemical reactions of common LIBs can be described as the following Equations (1)–(3), where M stands for a metal, which is used as a cathode material such as cobalt or nickel, and C is recognized as the anode materials.

_{IR}due to ohmic and charge transfer processes are given as follows:

_{IR,}

_{1C}represents the potential losses under the 1C current. The 1C current I

_{1C}means that the discharge current will discharge the entire battery in one hour, and it is calculated as:

_{0}is applied for the integrated voltage dissipation accompanied by the charge delivery reactions on the two electrodes’ surfaces, shown as:

_{act}. Derived from diffusion in an idealized particle or by applying a resistor-capacitor combination, concentration overpotential effects can be explained among the lumped battery interfaces. In this model, particle diffusion is calculated. Fickian diffusion of a dimensionless SOC parameter is calculated in this case, using spherical symmetry, according to:

_{shape}equals three for spherical particles in this model. The SOC of the surface, SOC

_{surface}, is identified at the particle surface. The average SOC, named SOC

_{average}, is prescribed by lumping the particle volume, appropriately considering spherical coordinates, and is defined as:

_{conc}and defined as:

_{cell}is defined as:

_{conc}and E

_{cell}is also calculated as:

_{IR},

_{1C}, τ, and J

_{0}is demonstrated using experimental data. This is achieved using the Global Least-Squares Objective node in the optimization interface, combined with the optimization study step using a Levenberg-Marquardt optimization solver. Lastly, cell voltage prediction is performed using the optimized lumped parameter values obtained in the previous parameter estimation study compared with experimental data.

#### 2.2. Thermal Model

_{T,r}, and along the cylinder length direction, k

_{T,ang}, are defined separately as follows:

#### 2.3. ANN Model

_{ij}and bias w

_{bi}, expressed as:

## 3. Results and Discussions

#### 3.1. Electro-Thermal Model Simulation Results

^{−1}achieve 36%, which is the maximum percentage of temperature difference drop compared to other cases in this configuration. It is demonstrated that when the minimum values of maximum temperature and temperature difference are reached, the format set up is the best and optimization results.

#### 3.2. Training and Results Analysis

_{t}represents the heat transfer coefficient, and v is the relative speed between the object exterior and air. This equation is empirical and can be applied to the velocity range from 2 to 20 m s

^{−1}[51].

_{i,network}is the network output and R

_{i,target}is the target output from the simulation data. The number of hidden neurons has been mentioned in Equation (22).

#### 3.3. Optimization Analysis and Discussions

^{−1}. Compared to the original configuration with the same operating conditions, the maximum temperature decreased by 1.9%, and the temperature difference dropped by 4.5%, which means the CFD-ANN model optimization improved both the cooling efficiency and battery performance. The proposed framework demonstrates an efficient way to improve the thermal performance of the battery pack by optimizing the configuration under different operating conditions.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Comparison of numerical results of working voltage (

**a**) and temperature (

**b**) with experimental results [23] during 1C galvanostatic discharge under natural convection conditions.

**Figure 5.**The profile of maximum temperature (

**a**) and temperature difference (

**b**,

**c**) under various operation conditions.

**Figure 8.**(

**a**) Maximum temperature and (

**b**) temperature difference of the battery pack for different input combinations.

**Table 1.**This is a table. Tables should be placed in the main text near to the first time they are cited.

Grid Resolution | Elements Number | Calculation Time | Maximum Electrolyte Temperature |
---|---|---|---|

Finer | 114,273 | 75.6 min | 20.250 °C |

Fine | 43,486 | 30.5 min | 19.829 °C |

Normal | 23,986 | 18.7 min | 19.810 °C |

Coarse | 9708 | 10.6 min | 18.910 °C |

Geometry Parameters | Battery Parameters | ||||
---|---|---|---|---|---|

d_batt | 21 [mm] | Battery diameter | C_rate | 4 | C rate |

Q_cell | 4 [A·h] | Battery cell capacity | |||

r_batt | d_batt/2 | Battery radius | I_1C | Q_cell/1 [h] | 1C current |

kT_batt_ang | 30 [W m^{−1} K^{−1}] | Thermal conductivity, in plane | |||

h_batt | 70 [mm] | Battery height | kT_batt_r | 1 [W m^{−1} K^{−1}] | Thermal conductivity, cross plane |

Ea_eta1C | 24 [kJ mol^{−1}] | Activation energy | |||

h_term | 1 [mm] | Terminal thickness | Ea_J0 | −59 [kJ mol^{−1}] | Activation energy |

Ea_Tau | 24 [kJ mol^{−1}] | Activation energy | |||

r_term | 3 [mm] | Terminal radius | T0 | 20 [°C] | Reference temperature |

J0_0 | 0.85 | J0 at reference temperature | |||

d_sc | 2 [mm] | Serial connector depth | tau_0 | 1000 [s] | tau at reference temperature |

eta_1C | 4.5 [mV] | eta_1C at reference temperature | |||

h_sc | 1 [mm] | Serial connector height | rho_batt | 2000 [kg m^{−3}] | Battery density |

Cp_batt | 1400 [J kg^{−1} K^{−1})] | Battery heat capacity | |||

h_pc | 0.5 [mm] | Parallel connector height | ht | 30 [W m^{−2} K^{−1}] | Heat transfer coefficient |

T_init | 20 [°C] | Initial/external temperature | |||

w_pc | 1 [mm] | Parallel connector width |

Inputs | Outputs | |||||
---|---|---|---|---|---|---|

Parameters | X_Gap | Y_Gap | Air velocity | Ambient temperature | Maximum temperature | Temperature difference |

Units | m | m | m s^{−1} | °C | °C | °C |

Range | 0–0.02 | 0–0.02 | 30–39.96 | 20–30 | - | - |

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**MDPI and ACS Style**

Li, A.; Yuen, A.C.Y.; Wang, W.; Chen, T.B.Y.; Lai, C.S.; Yang, W.; Wu, W.; Chan, Q.N.; Kook, S.; Yeoh, G.H.
Integration of Computational Fluid Dynamics and Artificial Neural Network for Optimization Design of Battery Thermal Management System. *Batteries* **2022**, *8*, 69.
https://doi.org/10.3390/batteries8070069

**AMA Style**

Li A, Yuen ACY, Wang W, Chen TBY, Lai CS, Yang W, Wu W, Chan QN, Kook S, Yeoh GH.
Integration of Computational Fluid Dynamics and Artificial Neural Network for Optimization Design of Battery Thermal Management System. *Batteries*. 2022; 8(7):69.
https://doi.org/10.3390/batteries8070069

**Chicago/Turabian Style**

Li, Ao, Anthony Chun Yin Yuen, Wei Wang, Timothy Bo Yuan Chen, Chun Sing Lai, Wei Yang, Wei Wu, Qing Nian Chan, Sanghoon Kook, and Guan Heng Yeoh.
2022. "Integration of Computational Fluid Dynamics and Artificial Neural Network for Optimization Design of Battery Thermal Management System" *Batteries* 8, no. 7: 69.
https://doi.org/10.3390/batteries8070069