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

^{1}

^{2}

^{3}

^{4}

^{*}

## 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

- Yang, Y.; Bremner, S.; Menictas, C.; Kay, M. Battery energy storage system size determination in renewable energy systems: A review. Renew. Sustain. Energy Rev.
**2018**, 91, 109–125. [Google Scholar] [CrossRef] - Armand, M.; Axmann, P.; Bresser, D.; Copley, M.; Edström, K.; Ekberg, C.; Guyomard, D.; Lestriez, B.; Novák, P.; Petranikova, M. Lithium-ion batteries–Current state of the art and anticipated developments. J. Power Sour.
**2020**, 479, 228708. [Google Scholar] [CrossRef] - Li, Y.; Vilathgamuwa, M.; Xiong, B.; Tang, J.; Su, Y.; Wang, Y. Design of minimum cost degradation-conscious lithium-ion battery energy storage system to achieve renewable power dispatchability. Appl. Energy
**2020**, 260, 114282. [Google Scholar] [CrossRef] - Chen, T.; Jin, Y.; Lv, H.; Yang, A.; Liu, M.; Chen, B.; Xie, Y.; Chen, Q. Applications of lithium-ion batteries in grid-scale energy storage systems. Trans. Tianjin Univ.
**2020**, 26, 208–217. [Google Scholar] [CrossRef][Green Version] - Lai, C.S.; Jia, Y.; Xu, Z.; Lai, L.L.; Li, X.; Cao, J.; McCulloch, M.D. Levelized cost of electricity for photovoltaic/biogas power plant hybrid system with electrical energy storage degradation costs. Energy Convers. Manag.
**2017**, 153, 34–47. [Google Scholar] [CrossRef] - Zhang, C.; Jiang, J.; Gao, Y.; Zhang, W.; Liu, Q.; Hu, X. Charging optimization in lithium-ion batteries based on temperature rise and charge time. Appl. Energy
**2017**, 194, 569–577. [Google Scholar] [CrossRef] - Dong, G.; Wei, J. Determination of the load capability for a lithium-ion battery pack using two time-scale filtering. J. Power Sour.
**2020**, 480, 229056. [Google Scholar] [CrossRef] - Xia, Q.; Wang, Z.; Ren, Y.; Yang, D.; Sun, B.; Feng, Q.; Qian, C. Performance reliability analysis and optimization of lithium-ion battery packs based on multiphysics simulation and response surface methodology. J. Power Sour.
**2021**, 490, 229567. [Google Scholar] [CrossRef] - Feng, X.; Ouyang, M.; Liu, X.; Lu, L.; Xia, Y.; He, X. Thermal runaway mechanism of lithium ion battery for electric vehicles: A review. Energy Storage Mater.
**2018**, 10, 246–267. [Google Scholar] [CrossRef] - Wang, Q.; Mao, B.; Stoliarov, S.I.; Sun, J. A review of lithium ion battery failure mechanisms and fire prevention strategies. Prog. Energy Combust. Sci.
**2019**, 73, 95–131. [Google Scholar] [CrossRef] - Sun, P.; Bisschop, R.; Niu, H.; Huang, X. A review of battery fires in electric vehicles. Fire Technol.
**2020**, 56, 1–50. [Google Scholar] [CrossRef] - Li, A.; Yuen, A.C.Y.; Wang, W.; Cordeiro, I.M.d.; Wang, C.; Chen, T.B.Y.; Zhang, J.; Chan, Q.N.; Yeoh, G.H. A Review on Lithium-Ion Battery Separators towards Enhanced Safety Performances and Modelling Approaches. Molecules
**2021**, 26, 478. [Google Scholar] [CrossRef] [PubMed] - Akinlabi, A.H.; Solyali, D. Configuration, design, and optimization of air-cooled battery thermal management system for electric vehicles: A review. Renew. Sustain. Energy Rev.
**2020**, 125, 109815. [Google Scholar] [CrossRef] - Jiang, Z.; Li, H.; Qu, Z.; Zhang, J. Recent progress in lithium-ion battery thermal management for a wide range of temperature and abuse conditions. Int. J. Hydrog. Energy
**2022**, 47, 9428–9459. [Google Scholar] [CrossRef] - Al-Zareer, M.; Dincer, I.; Rosen, M.A. Novel thermal management system using boiling cooling for high-powered lithium-ion battery packs for hybrid electric vehicles. J. Power Sour.
**2017**, 363, 291–303. [Google Scholar] [CrossRef] - Smith, J.; Singh, R.; Hinterberger, M.; Mochizuki, M. Battery thermal management system for electric vehicle using heat pipes. Int. J. Therm. Sci.
**2018**, 134, 517–529. [Google Scholar] [CrossRef] - Al-Zareer, M.; Dincer, I.; Rosen, M.A. Performance assessment of a new hydrogen cooled prismatic battery pack arrangement for hydrogen hybrid electric vehicles. Energy Convers. Manag.
**2018**, 173, 303–319. [Google Scholar] - Saw, L.H.; Ye, Y.; Tay, A.A.; Chong, W.T.; Kuan, S.H.; Yew, M.C. Computational fluid dynamic and thermal analysis of Lithium-ion battery pack with air cooling. Appl. Energy
**2016**, 177, 783–792. [Google Scholar] - Kirad, K.; Chaudhari, M. Design of cell spacing in lithium-ion battery module for improvement in cooling performance of the battery thermal management system. J. Power Sour.
**2021**, 481, 229016. [Google Scholar] [CrossRef] - Shen, M.; Gao, Q. A review on battery management system from the modeling efforts to its multiapplication and integration. Int. J. Energy Res.
**2019**, 43, 5042–5075. [Google Scholar] [CrossRef] - Deng, J.; Bae, C.; Marcicki, J.; Masias, A.; Miller, T. Safety modelling and testing of lithium-ion batteries in electrified vehicles. Nat. Energy
**2018**, 3, 261–266. [Google Scholar] [CrossRef] - Cordeiro, I.M.D.C.; Liu, H.; Yuen, A.C.Y.; Chen, T.B.Y.; Li, A.; Cao, R.F.; Yeoh, G.H. Numerical investigation of expandable graphite suppression on metal-based fire. Heat Mass Transf.
**2021**, 58, 1–17. [Google Scholar] - Xu, M.; Zhang, Z.; Wang, X.; Jia, L.; Yang, L. Two-dimensional electrochemical–thermal coupled modeling of cylindrical LiFePO4 batteries. J. Power Sour.
**2014**, 256, 233–243. [Google Scholar] [CrossRef] - Larsson, F.; Anderson, J.; Andersson, P.; Mellander, B.-E. Thermal modelling of cell-to-cell fire propagation and cascading thermal runaway failure effects for lithium-ion battery cells and modules using fire walls. J. Electrochem. Soc.
**2016**, 163, A2854. [Google Scholar] [CrossRef] - Jin, X.; Duan, X.; Jiang, W.; Wang, Y.; Zou, Y.; Lei, W.; Sun, L.; Ma, Z. Structural design of a composite board/heat pipe based on the coupled electro-chemical-thermal model in battery thermal management system. Energy
**2021**, 216, 119234. [Google Scholar] [CrossRef] - Wang, Z.; Fan, W.; Liu, P. Simulation of temperature field of lithium battery pack based on computational fluid dynamics. Energy Procedia
**2017**, 105, 3339–3344. [Google Scholar] [CrossRef] - Wilke, S.; Schweitzer, B.; Khateeb, S.; Al-Hallaj, S. Preventing thermal runaway propagation in lithium ion battery packs using a phase change composite material: An experimental study. J. Power Sour.
**2017**, 340, 51–59. [Google Scholar] [CrossRef] - An, Z.; Jia, L.; Li, X.; Ding, Y. Experimental investigation on lithium-ion battery thermal management based on flow boiling in mini-channel. Appl. Therm. Eng.
**2017**, 117, 534–543. [Google Scholar] [CrossRef] - Ouyang, D.; Liu, J.; Chen, M.; Weng, J.; Wang, J. An experimental study on the thermal failure propagation in lithium-ion battery pack. J. Electrochem. Soc.
**2018**, 165, A2184. [Google Scholar] [CrossRef] - Li, H.; Duan, Q.; Zhao, C.; Huang, Z.; Wang, Q. Experimental investigation on the thermal runaway and its propagation in the large format battery module with Li (Ni1/3Co1/3Mn1/3) O2 as cathode. J. Hazard. Mater.
**2019**, 375, 241–254. [Google Scholar] [CrossRef] - Zhang, X.; Wang, Y.; Wu, J.; Chen, Z. A novel method for lithium-ion battery state of energy and state of power estimation based on multi-time-scale filter. Appl. Energy
**2018**, 216, 442–451. [Google Scholar] [CrossRef] - Li, K.; Yan, J.; Chen, H.; Wang, Q. Water cooling based strategy for lithium ion battery pack dynamic cycling for thermal management system. Appl. Therm. Eng.
**2018**, 132, 575–585. [Google Scholar] [CrossRef] - Zhao, R.; Zhang, S.; Liu, J.; Gu, J. A review of thermal performance improving methods of lithium ion battery: Electrode modification and thermal management system. J. Power Sour.
**2015**, 299, 557–577. [Google Scholar] [CrossRef] - Kim, J.; Oh, J.; Lee, H. Review on battery thermal management system for electric vehicles. Appl. Therm. Eng.
**2019**, 149, 192–212. [Google Scholar] [CrossRef] - Patel, J.R.; Rathod, M.K. Recent developments in the passive and hybrid thermal management techniques of lithium-ion batteries. J. Power Sour.
**2020**, 480, 228820. [Google Scholar] [CrossRef] - Fan, L.; Khodadadi, J.; Pesaran, A. A parametric study on thermal management of an air-cooled lithium-ion battery module for plug-in hybrid electric vehicles. J. Power Sour.
**2013**, 238, 301–312. [Google Scholar] [CrossRef] - Wang, T.; Tseng, K.; Zhao, J.; Wei, Z. Thermal investigation of lithium-ion battery module with different cell arrangement structures and forced air-cooling strategies. Appl. Energy
**2014**, 134, 229–238. [Google Scholar] [CrossRef] - Choudhari, V.; Dhoble, A.; Panchal, S. Numerical analysis of different fin structures in phase change material module for battery thermal management system and its optimization. Int. J. Heat Mass Transf.
**2020**, 163, 120434. [Google Scholar] [CrossRef] - Chen, S.; Peng, X.; Bao, N.; Garg, A. A comprehensive analysis and optimization process for an integrated liquid cooling plate for a prismatic lithium-ion battery module. Appl. Therm. Eng.
**2019**, 156, 324–339. [Google Scholar] [CrossRef] - Mitchell, T.M. Machine Learning; McGraw-hill: New York, NY, USA, 1997. [Google Scholar]
- Jaliliantabar, F.; Mamat, R.; Kumarasamy, S. Prediction of lithium-ion battery temperature in different operating conditions equipped with passive battery thermal management system by artificial neural networks. Mater. Today Proc.
**2022**, 48, 1796–1804. [Google Scholar] [CrossRef] - Wu, B.; Han, S.; Shin, K.G.; Lu, W. Application of artificial neural networks in design of lithium-ion batteries. J. Power Sour.
**2018**, 395, 128–136. [Google Scholar] [CrossRef] - Qian, X.; Xuan, D.; Zhao, X.; Shi, Z. Heat dissipation optimization of lithium-ion battery pack based on neural networks. Appl. Therm. Eng.
**2019**, 162, 114289. [Google Scholar] [CrossRef] - Feng, F.; Teng, S.; Liu, K.; Xie, J.; Xie, Y.; Liu, B.; Li, K. Co-estimation of lithium-ion battery state of charge and state of temperature based on a hybrid electrochemical-thermal-neural-network model. J. Power Sour.
**2020**, 455, 227935. [Google Scholar] [CrossRef] - Shi, Y.; Ahmad, S.; Liu, H.; Lau, K.T.; Zhao, J. Optimization of air-cooling technology for LiFePO4 battery pack based on deep learning. J. Power Sour.
**2021**, 497, 229894. [Google Scholar] [CrossRef] - Guo, M.; Sikha, G.; White, R.E. Single-particle model for a lithium-ion cell: Thermal behavior. J. Electrochem. Soc.
**2010**, 158, A122. [Google Scholar] [CrossRef] - Doyle, M.; Newman, J.; Gozdz, A.S.; Schmutz, C.N.; Tarascon, J.M. Comparison of modeling predictions with experimental data from plastic lithium ion cells. J. Electrochem. Soc.
**1996**, 143, 1890. [Google Scholar] [CrossRef] - Chen, S.-C.; Wang, Y.-Y.; Wan, C.-C. Thermal analysis of spirally wound lithium batteries. J. Electrochem. Soc.
**2006**, 153, A637. [Google Scholar] [CrossRef] - Chen, M.; Challita, U.; Saad, W.; Yin, C.; Debbah, M. Artificial neural networks-based machine learning for wireless networks: A tutorial. IEEE Commun. Surv. Tutor.
**2019**, 21, 3039–3071. [Google Scholar] [CrossRef][Green Version] - Hunter, D.; Yu, H.; Pukish, M.S., III; Kolbusz, J.; Wilamowski, B.M. Selection of proper neural network sizes and architectures—A comparative study. IEEE Trans. Ind. Inform.
**2012**, 8, 228–240. [Google Scholar] [CrossRef] - ToolBox, E. Convective Heat Transfer. Available online: https://www.engineeringtoolbox.com/convective-heat-transfer-d_430.html (accessed on 27 July 2021).
- Hagan, M.T.; Menhaj, M.B. Training feedforward networks with the Marquardt algorithm. IEEE Trans. Neural Netw.
**1994**, 5, 989–993. [Google Scholar] [CrossRef] - Levenberg, K. A method for the solution of certain non-linear problems in least squares. Q. Appl. Math.
**1944**, 2, 164–168. [Google Scholar] [CrossRef][Green Version] - Marquardt, D.W. An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math.
**1963**, 11, 431–441. [Google Scholar] [CrossRef] - Yetik, O.; Karakoc, T.H. Estimation of thermal effect of different busbars materials on prismatic Li-ion batteries based on artificial neural networks. J. Energy Storage
**2021**, 38, 102543. [Google Scholar] [CrossRef]

**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 | - | - |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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