An Analytical 2D Formulation for the Combined Cooling of PCM-Covered Cylindrical Battery Cells
Publication: Journal of Energy Engineering
Volume 148, Issue 2
Abstract
Lithium-ion battery packs are being used more and more in high energy, high power applications such as in power devices, drones, and electric or unmanned vehicles. Battery packs require careful heat management to guarantee near-optimal and safe, hazard-free operation. Modern heat management systems include combined air–phase change material (PCM) strategies, the accurate analysis and simulation of which lead to FEM/computational fluid dynamics (CFD) modeling, as is often seen in the literature. In this study, we developed an analytical two-dimensional (2D) formulation for an air–PCM cooling system installed around a cylindrical cell. This approximate formulation enabled us to rapidly investigate the effects of the airflow field and PCM thickness at multiple operating conditions and to estimate the overall thermal resistance and melted volume of PCM. The results were benchmarked with FEM simulations and then compared with the literature. A comprehensive investigation of the airflow effects under various temperature and current rates is presented and discussed in detail. The analytical formulation in this work can be easily programmed and used in fast estimations of performance or for design purposes.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data and source codes are available from the corresponding author upon request.
References
Alawadhi, E. M. 2008. “Thermal analysis of a pipe insulation with a phase change material: Material selection and sizing.” Heat Transfer Eng. 29 (7): 624–631. https://doi.org/10.1080/01457630801922469.
Al Hallaj, S., H. Maleki, J.-S. Hong, and J. R. Selman. 1999. “Thermal modeling and design considerations of lithium-ion batteries.” J. Power Sources 83 (1–2): 1–8. https://doi.org/10.1016/S0378-7753(99)00178-0.
Al-Hallaj, S., and J. R. Selman. 2000. “A novel thermal management system for electric vehicle batteries using phase-change material.” J. Electrochem. Soc. 147 (9): 3231–3236. https://doi.org/10.1149/1.1393888.
Amine, K., J. Liu, and I. Belharouak. 2005. “High-temperature storage and cycling of C-LiFePO4/graphite Li-ion cells.” Electrochem. Commun. 7 (7): 669–673. https://doi.org/10.1016/j.elecom.2005.04.018.
An, Z., X. Chen, L. Zhao, and Z. Gao. 2019. “Numerical investigation on integrated thermal management for a lithium-ion battery module with a composite phase change material and liquid cooling.” Appl. Therm. Eng. 163 (Dec): 114345. https://doi.org/10.1016/j.applthermaleng.2019.114345.
Bamdezh, M., and G. Molaeimanesh. 2020. “Impact of system structure on the performance of a hybrid thermal management system for a Li-ion battery module.” J. Power Sources 457 (May): 227993. https://doi.org/10.1016/j.jpowsour.2020.227993.
Bao, Y., Y. Fan, Y. Chu, C. Ling, X. Tan, and S. Yang. 2019. “Experimental and numerical study on thermal and energy management of a fast-charging lithium-ion battery pack with air cooling.” J. Energy Eng. 145 (6): 04019030. https://doi.org/10.1061/(ASCE)EY.1943-7897.0000631.
Bergman, T. L., F. P. Incropera, D. P. DeWitt, and A. S. Lavine. 2011. Fundamentals of heat and mass transfer. Hoboken, NJ: Wiley.
Caggiano, A., C. Mankel, and E. A. Koenders. 2019. “Reviewing theoretical and numerical models for PCM-embedded cementitious composites.” Buildings 9 (1): 3. https://doi.org/10.3390/buildings9010003.
Chamkha, A., A. Veismoradi, M. Ghalambaz, and P. Talebizadehsardari. 2020. “Phase change heat transfer in an L-shape heatsink occupied with paraffin-copper metal foam.” Appl. Therm. Eng. 177 (Aug): 115493. https://doi.org/10.1016/j.applthermaleng.2020.115493.
Chen, F., R. Huang, C. Wang, X. Yu, H. Liu, Q. Wu, K. Qian, and R. Bhagat. 2020a. “Air and PCM cooling for battery thermal management considering battery cycle life.” Appl. Therm. Eng. 173 (Jun): 115154. https://doi.org/10.1016/j.applthermaleng.2020.115154.
Chen, K., Y. Chen, Y. She, M. Song, S. Wang, and L. Chen. 2020b. “Construction of effective symmetrical air-cooled system for battery thermal management.” Appl. Therm. Eng. 166 (Feb): 114679. https://doi.org/10.1016/j.applthermaleng.2019.114679.
Chen, K., J. Hou, M. Song, S. Wang, W. Wu, and Y. Zhang. 2021. “Design of battery thermal management system based on phase change material and heat pipe.” Appl. Therm. Eng. 188 (Apr): 116665. https://doi.org/10.1016/j.applthermaleng.2021.116665.
Chen, K., W. Wu, F. Yuan, L. Chen, and S. Wang. 2019. “Cooling efficiency improvement of air-cooled battery thermal management system through designing the flow pattern.” Energy 167 (Jan): 781–790. https://doi.org/10.1016/j.energy.2018.11.011.
Chen, S., C. Wan, and Y. Wang. 2005. “Thermal analysis of lithium-ion batteries.” J. Power Resour. 140 (1): 111–124. https://doi.org/10.1016/j.jpowsour.2004.05.064.
Choudhari, V., A. Dhoble, and S. Panchal. 2020. “Numerical analysis of different fin structures in phase change material module for battery thermal management system and its optimization.” Int. J. Heat Mass Transfer 163 (Dec): 120434. https://doi.org/10.1016/j.ijheatmasstransfer.2020.120434.
Churchill, S. W., and M. Bernstein. 1977. “A correlating equation for forced convection from gases and liquids to a circular cylinder in crossflow journal of heat transfer.” J. Heat Transfer 99 (2): 300–306. https://doi.org/10.1115/1.3450685.
Evans, T. I., and R. E. White. 1989. “A thermal analysis of a spirally wound battery using a simple mathematical model.” J. Electrochem. Soc. 136 (8): 2145. https://doi.org/10.1149/1.2097230.
Getling, A. V. 1998. Vol. 11 of Rayleigh-Bé nard convection: Structures and dynamics. Singapore: World Scientific.
Ghalambaz, M., S. M. Hashem Zadeh, S. Mehryan, I. Pop, and D. Wen. 2020. “Analysis of melting behavior of PCMs in a cavity subject to a non-uniform magnetic field using a moving grid technique.” Appl. Math. Modell. 77 (Part 2): 1936–1953. https://doi.org/10.1016/j.apm.2019.09.015.
Ghalambaz, M., and J. Zhang. 2020. “Conjugate solid-liquid phase change heat transfer in heatsink filled with phase change material-metal foam.” Int. J. Heat Mass Transfer 146 (Jan): 118832. https://doi.org/10.1016/j.ijheatmasstransfer.2019.118832.
Gomadam, P. M., R. E. White, and J. W. Weidner. 2003. “Modeling heat conduction in spiral geometries.” J. Electrochem. Soc. 150 (10): A1339. https://doi.org/10.1149/1.1605743.
Heyhat, M. M., S. Mousavi, and M. Siavashi. 2020. “Battery thermal management with thermal energy storage composites of PCM, metal foam, fin and nanoparticle.” J. Storage Mater. 28 (Apr): 101235. https://doi.org/10.1016/j.est.2020.101235.
Hilpert, R. 1933. “Wärmeabgabe von geheizten drähten und rohren im luftstrom.” Forschung auf dem Gebiet des Ingenieurwesens A 4 (5): 215–224. https://doi.org/10.1007/BF02719754.
Javani, N., I. Dincer, G. Naterer, and B. S. Yilbas. 2014. “Heat transfer and thermal management with PCMs in a Li-ion battery cell for electric vehicles.” Int. J. Heat Mass Transfer 72 (May): 690–703. https://doi.org/10.1016/j.ijheatmasstransfer.2013.12.076.
Jiaqiang, E., et al. 2018a. “Orthogonal experimental design of liquid-cooling structure on the cooling effect of a liquid-cooled battery thermal management system.” Appl. Therm. Eng. 132 (Mar): 508–520. https://doi.org/10.1016/j.applthermaleng.2017.12.115.
Jiaqiang, E., M. Yue, J. Chen, H. Zhu, Y. Deng, Y. Zhu, F. Zhang, M. Wen, B. Zhang, and S. Kang. 2018b. “Effects of the different air cooling strategies on cooling performance of a lithium-ion battery module with baffle.” Appl. Therm. Eng. 144 (Nov): 231–241. https://doi.org/10.1016/j.applthermaleng.2018.08.064.
Jilte, R., A. Afzal, and S. Panchal. 2021. “A novel battery thermal management system using nano-enhanced phase change materials.” Energy 219 (Mar): 119564. https://doi.org/10.1016/j.energy.2020.119564.
Jilte, R. D., R. Kumar, M. H. Ahmadi, and L. Chen. 2019a. “Battery thermal management system employing phase change material with cell-to-cell air cooling.” Appl. Therm. Eng. 161 (Oct): 114199. https://doi.org/10.1016/j.applthermaleng.2019.114199.
Jilte, R. D., R. Kumar, and L. Ma. 2019b. “Thermal performance of a novel confined flow Li-ion battery module.” Appl. Therm. Eng. 146 (Jan): 1–11. https://doi.org/10.1016/j.applthermaleng.2018.09.099.
Joulin, A., Z. Younsi, L. Zalewski, D. R. Rousse, and S. Lassue. 2009. “A numerical study of the melting of phase change material heated from a vertical wall of a rectangular enclosure.” Int. J. Comput. Fluid Dyn. 23 (7): 553–566. https://doi.org/10.1080/10618560903203723.
Junior, J. R., R. D. C. Oliveski, L. O. Rocha, and C. Biserni. 2018. “Numerical investigation on phase change materials (PCM): The melting process of erythritol in spheres under different thermal conditions.” Int. J. Mech. Sci. 148 (Nov): 20–30. https://doi.org/10.1016/j.ijmecsci.2018.08.006.
Kamkari, B., H. Shokouhmand, and F. Brunob. 2014. “Experimental investigation of the effect of inclination angle on convection-driven melting of phase change material in a rectangular enclosure.” Int. J. Heat Mass Transfer 72 (2): 186–200. https://doi.org/10.1016/j.ijheatmasstransfer.2014.01.014.
Karami, R., and B. Kamkari. 2019. “Investigation of the effect of inclination angle on the melting enhancement of phase change material in finned latent heat thermal storage units.” Appl. Therm. Eng. 146 (Jan): 45–60. https://doi.org/10.1016/j.applthermaleng.2018.09.105.
Khateeb, S. A., M. M. Farid, J. R. Selman, and S. AlHallaj. 2004. “Design and simulation of a lithium-ion battery with a phase change material thermal management system for an electric scooter.” J. Power Sources 128 (2): 292–307. https://doi.org/10.1016/j.jpowsour.2003.09.070.
Kim, J., J. Oh, and H. Lee. 2019. “Review on battery thermal management system for electric vehicles.” Appl. Therm. Eng. 149 (Feb): 192–212. https://doi.org/10.1016/j.applthermaleng.2018.12.020.
Kizilel, R., A. Lateef, R. Sabbah, M. Farid, J. R. Selman, and S. Al-Hallaj. 2008. “Passive control of temperature excursion and uniformity in high-energy Li-ion battery packs at high current and ambient temperature.” J. Power Sources 183 (1): 370–375. https://doi.org/10.1016/j.jpowsour.2008.04.050.
Kong, D., R. Peng, P. Ping, J. Du, G. Chen, and J. Wen. 2020. “A novel battery thermal management system coupling with PCM and optimized controllable liquid cooling for different ambient temperatures.” Energy Convers. Manage. 204 (Jan): 112280. https://doi.org/10.1016/j.enconman.2019.112280.
Lamberg, P. 2004. “Approximate analytical model for two-phase solidification problem in a finned phase-change material storage.” Appl. Energy 77 (2): 131–152. https://doi.org/10.1016/S0306-2619(03)00106-5.
Lazrak, A., J.-F. Fourmigué, and J.-F. Robin. 2018. “An innovative practical battery thermal management system based on phase change materials: Numerical and experimental investigations.” Appl. Therm. Eng. 128 (Jan): 20–32. https://doi.org/10.1016/j.applthermaleng.2017.08.172.
Li, J., and H. Zhang. 2020. “Thermal characteristics of power battery module with composite phase change material and external liquid cooling.” Int. J. Heat Mass Transfer 156 (Aug): 119820. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119820.
Li, Y., Y. Du, T. Xu, H. Wu, X. Zhou, Z. Ling, and Z. Zhang. 2018. “Optimization of thermal management system for Li-ion batteries using phase change material.” Appl. Therm. Eng. 131 (Feb): 766–778. https://doi.org/10.1016/j.applthermaleng.2017.12.055.
Lin, X., X. Zhang, L. Liu, and M. Yang. 2021. “Optimization investigation on air phase change material based battery thermal management system.” Energy Technol. 9 (7): 2100060. https://doi.org/10.1002/ente.202100060.
Ling, Z., F. Wang, X. Fang, X. Gao, and Z. Zhang. 2015. “A hybrid thermal management system for lithium ion batteries combining phase change materials with forced-air cooling.” Appl. Energy 148 (Jun): 403–409. https://doi.org/10.1016/j.apenergy.2015.03.080.
Liu, H., S. Ahmad, Y. Shi, and J. Zhao. 2021. “A parametric study of a hybrid battery thermal management system that couples PCM/copper foam composite with helical liquid channel cooling.” Energy 231 (Sep): 120869. https://doi.org/10.1016/j.energy.2021.120869.
Liu, H., Z. Wei, W. He, and J. Zhao. 2017. “Thermal issues about Li-ion batteries and recent progress in battery thermal management systems: A review.” Energy Convers. Manage. 150 (Oct): 304–330. https://doi.org/10.1016/j.enconman.2017.08.016.
Lua, Z., X. Mengb, L. Weic, W. Hud, L. Zhangb, and L. Jinb. 2016. “Thermal management of densely-packed EV battery with forced air cooling strategies.” J. Power Sources 88 (Jun): 682–688. https://doi.org/10.1016/j.egypro.2016.06.098.
Lv, Y., G. Liu, G. Zhang, and X. Yang. 2020. “A novel thermal management structure using serpentine phase change material coupled with forced air convection for cylindrical battery modules.” J. Power Sources 468 (Aug): 228398. https://doi.org/10.1016/j.jpowsour.2020.228398.
Mahamud, R., and C. Park. 2011. “Reciprocating air flow for Li-ion battery thermal management to improve temperature uniformity.” SAE Tech. Pap. 196 (13): 5685–5696. https://doi.org/10.1016/j.jpowsour.2011.02.076.
Mehryan, S., K. Ayoubi-Ayoubloo, M. Shahabadi, M. Ghalambaz, P. Talebizadehsardari, and A. Chamkha. 2020a. “Conjugate phase change heat transfer in an inclined compound cavity partially filled with a porous medium: A deformed mesh approach.” Transp. Porous Media 132 (3): 657–681. https://doi.org/10.1007/s11242-020-01407-y.
Mehryan, S., M. Vaezi, M. Sheremet, and M. Ghalambaz. 2020b. “Melting heat transfer of power-law non-Newtonian phase change nano-enhanced n-octadecane-mesoporous silica (mpsio2).” Int. J. Heat Mass Transfer 151 (Apr): 119385. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119385.
Mohammed, H. I., P. Talebizadehsardari, J. M. Mahdi, A. Arshad, A. Sciacovelli, and D. Giddings. 2020. “Improved melting of latent heat storage via porous medium and uniform joule heat generation.” J. Storage Mater. 31 (Oct): 101747. https://doi.org/10.1016/j.est.2020.101747.
Panchal, S., I. Dincer, M. Agelin-Chaab, R. Fraser, and M. Fowler. 2016. “Experimental and theoretical investigation of temperature distributions in a prismatic lithium-ion battery.” Int. J. Therm. Sci. 99 (Jan): 204–212. https://doi.org/10.1016/j.ijthermalsci.2015.08.016.
Park, C., and A. K. Jaura. 2003. Dynamic thermal model of li-ion battery for predictive behavior in hybrid and fuel cell vehicles. Warrendale, PA: Society of Automotive Engineers. https://doi.org/10.4271/2003-01-2286.
Patel, J. R., and M. K. Rathod. 2020. “Recent developments in the passive and hybrid thermal management techniques of lithium-ion batteries.” J. Power Sources 480 (Dec): 228820. https://doi.org/10.1016/j.jpowsour.2020.228820.
Rao, Z., and S. Wang. 2011. “A review of power battery thermal energy management.” Renewable Sustainable Energy Rev. 15 (9): 4554–4571. https://doi.org/10.1016/j.rser.2011.07.096.
Safdari, M., R. Ahmadi, and S. Sadeghzadeh. 2020. “Numerical investigation on PCM encapsulation shape used in the passive-active battery thermal management.” Energy 193 (Feb): 116840. https://doi.org/10.1016/j.energy.2019.116840.
Sardari, P. T., D. Grant, D. Giddings, G. S. Walker, and M. Gillott. 2019. “Composite metal foam/PCM energy store design for dwelling space air heating.” Energy Convers. Manage. 201 (Dec): 112151. https://doi.org/10.1016/j.enconman.2019.112151.
Sheikholeslami, M., A. Arabkoohsar, I. Khan, A. Shafee, and Z. Li. 2019. “Impact of Lorentz forces on -water ferrofluid entropy and exergy treatment within a permeable semi annulus.” J. Cleaner Prod. 221 (Jun): 885–898. https://doi.org/10.1016/j.jclepro.2019.02.075.
Sheng, L., H. Zhang, L. Su, Z. Zhang, H. Zhang, K. Li, Y. Fang, and W. Ye. 2021. “Effect analysis on thermal profile management of a cylindrical lithium-ion battery utilizing a cellular liquid cooling jacket.” Energy 220 (Apr): 119725. https://doi.org/10.1016/j.energy.2020.119725.
Shim, J., R. Kostecki, T. Richardson, X. Song, and K. Striebel. 2002. “Electrochemical analysis for cycle performance and capacity fading of a lithium-ion battery cycled at elevated temperature.” J. Power Sources 112 (1): 222–230. https://doi.org/10.1016/S0378-7753(02)00363-4.
Siddique, A. R. M., S. Mahmud, and B. Van Heyst. 2018. “A comprehensive review on a passive (phase change materials) and an active (thermoelectric cooler) battery thermal management system and their limitations.” J. Power Sources 401 (Oct): 224–237. https://doi.org/10.1016/j.jpowsour.2018.08.094.
Sun, Z., R. Fan, and N. Zheng. 2021. “Thermal management of a simulated battery with the compound use of phase change material and fins: Experimental and numerical investigations.” Int. J. Therm. Sci. 165 (Jul): 106945. https://doi.org/10.1016/j.ijthermalsci.2021.106945.
Tang, Z., X. Min, A. Song, and J. Cheng. 2019. “Thermal management of a cylindrical lithium-ion battery module using a multichannel wavy tube.” J. Energy Eng. 145 (1): 04018072. https://doi.org/10.1061/(ASCE)EY.1943-7897.0000592.
Verma, A., S. Shashidhara, and D. Rakshit. 2019. “A comparative study on battery thermal management using phase change material (PCM).” Therm. Sci. Eng. Prog. 11 (Jun): 74–83. https://doi.org/10.1016/j.tsep.2019.03.003.
Wang, H., T. Tao, J. Xu, X. Mei, X. Liu, and P. Gou. 2020. “Cooling capacity of a novel modular liquid-cooled battery thermal management system for cylindrical lithium ion batteries.” Appl. Therm. Eng. 178 (Sep): 115591. https://doi.org/10.1016/j.applthermaleng.2020.115591.
Wang, Q., B. Jiang, B. Li, and Y. Yan. 2016. “A critical review of thermal management models and solutions of lithium-ion batteries for the development of pure electric vehicles.” Renewable Sustainable Energy Rev. 64 (Oct): 106–128. https://doi.org/10.1016/j.rser.2016.05.033.
Wang, T., K. Tseng, J. Zhao, and Z. Wei. 2014. “Thermal investigation of lithium-ion battery module with different cell arrangement structures and forced air-cooling strategies.” Appl. Energy 134 (Dec): 229–238. https://doi.org/10.1016/j.apenergy.2014.08.013.
Weng, J., X. Yang, G. Zhang, D. Ouyang, M. Chen, and J. Wang. 2019. “Optimization of the detailed factors in a phase-change-material module for battery thermal management.” Int. J. Heat Mass Transfer 138 (Aug): 126–134. https://doi.org/10.1016/j.ijheatmasstransfer.2019.04.050.
Xia, G., L. Cao, and G. Bi. 2017. “A review on battery thermal management in electric vehicle application.” J. Power Sources 367 (Nov): 90–105. https://doi.org/10.1016/j.jpowsour.2017.09.046.
Yang, S. 2019. “A review of lithium-ion battery thermal management system strategies and the evaluate criteria.” Int. J. Electrochem. Sci. 14 (7): 6077–6107. https://doi.org/10.20964/2019.07.06.
Yang, X., Z. Niu, Q. Bai, H. Li, X. Cui, and Y.-L. He. 2019. “Experimental study on the solidification process of fluid saturated in fin-foam composites for cold storage.” Appl. Therm. Eng. 161 (Oct): 114163. https://doi.org/10.1016/j.applthermaleng.2019.114163.
Yang, Y., W. Li, X. Xu, and G. Tong. 2020. “Heat dissipation analysis of different flow path for parallel liquid cooling battery thermal management system.” Int. J. Energy Res. 44 (7): 5165–5176. https://doi.org/10.1002/er.5089.
Zhang, F., A. Lin, P. Wang, and P. Liu. 2021. “Optimization design of a parallel air-cooled battery thermal management system with spoilers.” Appl. Therm. Eng. 182 (Jan): 116062. https://doi.org/10.1016/j.applthermaleng.2020.116062.
Zhao, J., Z. Rao, Y. Huo, X. Liu, and Y. Li. 2015a. “Thermal management of cylindrical power battery module for extending the life of new energy electric vehicles.” Appl. Therm. Eng. 85 (Jun): 33–43. https://doi.org/10.1016/j.applthermaleng.2015.04.012.
Zhao, R., S. Zhang, J. Liu, and J. Gu. 2015b. “A review of thermal performance improving methods of lithium-ion battery: Electrode modification and thermal management system.” J. Power Sources 299 (Dec): 557–577. https://doi.org/10.1016/j.jpowsour.2015.09.001.
Information & Authors
Information
Published In
Journal of Energy Engineering
Volume 148 • Issue 2 • April 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Mar 26, 2021
Accepted: Aug 3, 2021
Published online: Dec 20, 2021
Published in print: Apr 1, 2022
Discussion open until: May 20, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.