Stochastic analysis of time series temperature in battery cooling with ejector bubble generator
Abstract
This study identifies flow patterns in the cooling channels and analyzes temperature during LiFePO4 battery cooling using an ejector bubble generator. The cooling fluids included quiet air, circulating air, and bubbles, with airflow rates ranging from 0.1 to 1.5 lpm. The temperature patterns were analyzed using probability density functions (PDFs), and Sample entropy—PDFs were quantified using mean, variance, skewness, and kurtosis. The results showed the formation of a slug film, an elongated slug film, and clustered bubbles on the bottom wall of the battery pack. There was a 3.75% and 5.98% decrease in the maximum temperature and thermal resistance, respectively, at an airflow rate of Qa = 1.5 lpm. The farther the thermocouple is from the bubble-generator nozzle and the greater the supplied airflow, the lower the PDF's kurtosis. The greater the airflow, the lower the entropy.
Keywords
Slug film; Thermal resistance; Chaotic analysisReferences
- [1] H. S. Hamut, I. Dincer, and G. F. Naterer, “Exergy analysis of a TMS (thermal management system) for range-extended EVs (electric vehicles),” Energy, vol. 46, no. 1, pp. 117–125, Oct. 2012, doi: 10.1016/j.energy.2011.12.041.
- [2] F. S. Hwang et al., “Review of battery thermal management systems in electric vehicles,” Renewable and Sustainable Energy Reviews, vol. 192, no. December 2022, p. 114171, 2024, doi: 10.1016/j.rser.2023.114171.
- [3] K. . Chau and Y. . Wong, “Overview of power management in hybrid electric vehicles,” Energy Conversion and Management, vol. 43, no. 15, pp. 1953–1968, Oct. 2002, doi: 10.1016/S0196-8904(01)00148-0.
- [4] G. Krishna, “Understanding and identifying barriers to electric vehicle adoption through thematic analysis,” Transportation Research Interdisciplinary Perspectives, vol. 10, p. 100364, Jun. 2021, doi: 10.1016/j.trip.2021.100364.
- [5] Q. Huang, X. Li, G. Zhang, J. Zhang, F. He, and Y. Li, “Experimental investigation of the thermal performance of heat pipe assisted phase change material for battery thermal management system,” Applied Thermal Engineering, vol. 141, pp. 1092–1100, Aug. 2018, doi: 10.1016/j.applthermaleng.2018.06.048.
- [6] M. Mahmud et al., “Lithium-ion battery thermal management for electric vehicles using phase change material: A review,” Results in Engineering, vol. 20, no. August, p. 101424, 2023, doi: 10.1016/j.rineng.2023.101424.
- [7] L. Ianniciello, P. H. Biwolé, and P. Achard, “Electric vehicles batteries thermal management systems employing phase change materials,” Journal of Power Sources, vol. 378, pp. 383–403, Feb. 2018, doi: 10.1016/j.jpowsour.2017.12.071.
- [8] Y. Ye, Y. Shi, L. H. Saw, and A. A. O. Tay, “Performance assessment and optimization of a heat pipe thermal management system for fast charging lithium ion battery packs,” International Journal of Heat and Mass Transfer, vol. 92, pp. 893–903, Jan. 2016, doi: 10.1016/j.ijheatmasstransfer.2015.09.052.
- [9] D. M. Weragoda, G. Tian, Q. Cai, T. Zhang, K. Hing Lo, and Y. Gao, “Conceptualization of a novel battery thermal management system based on capillary-driven evaporative cooling,” Thermal Science and Engineering Progress, vol. 47, p. 102320, Jan. 2024, doi: 10.1016/j.tsep.2023.102320.
- [10] G. Shruti, P. B. Salunkhe, and B. S. Shenoy, “Recent progress on passive cooling strategies for Li-ion battery of electric vehicles,” Journal of Energy Storage, vol. 156, p. 121550, Apr. 2026, doi: 10.1016/j.est.2026.121550.
- [11] S. R. Patil, B. R. Lokavarapu, and H. K. Thaliyanveedu, “Optimization of battery cooling system used in electric vehicles,” Journal of Energy Storage, vol. 58, p. 106299, Feb. 2023, doi: 10.1016/j.est.2022.106299.
- [12] X. Wang, R. Yin, and Q. Peng, “Optimizing hybrid cooling strategy for enhanced thermal management of Lithium-ion battery packs at high discharge rates,” Applied Thermal Engineering, vol. 295, p. 130611, May 2026, doi: 10.1016/j.applthermaleng.2026.130611.
- [13] B. Suhendra, N. Alif Indratma, E. Kusrini, N. Putra, and M. Hasanuzzaman, “Thermal performance and temperature uniformity of battery modules using static single phase immersion cooling with multiple dielectric fluids,” Applied Thermal Engineering, vol. 296, p. 130774, Jun. 2026, doi: 10.1016/j.applthermaleng.2026.130774.
- [14] J. Kim, J. Oh, and H. Lee, “Review on battery thermal management system for electric vehicles,” Applied Thermal Engineering, vol. 149, no. September 2018, pp. 192–212, 2019, doi: 10.1016/j.applthermaleng.2018.12.020.
- [15] N. Bianco, A. Fragnito, M. Iasiello, V. Orlanducci, and F. Piccirillo, “Numerical evaluation of different cooling strategies for cylindrical battery packs: from air natural convection to topology-optimized cold plates,” International Journal of Thermal Sciences, vol. 225, p. 110773, Jul. 2026, doi: 10.1016/j.ijthermalsci.2026.110773.
- [16] S. Hekmat and G. R. Molaeimanesh, “Hybrid thermal management of a Li-ion battery module with phase change material and cooling water pipes: An experimental investigation,” Applied Thermal Engineering, vol. 166, p. 114759, Feb. 2020, doi: 10.1016/j.applthermaleng.2019.114759.
- [17] A. A. Pesaran, “Battery Thermal Management in EVs and HEVs: Issues and Solutions,” in Advanced Automotive Battery Conference, 2001.
- [18] C. Roe et al., “Immersion cooling for lithium-ion batteries – A review,” Journal of Power Sources, vol. 525, p. 231094, Mar. 2022, doi: 10.1016/j.jpowsour.2022.231094.
- [19] A. S. Bidwaik, S. S. Bhusnoor, and S. R. Nikam, “Energy-optimized microchannel liquid cooling for 21700 lithium-ion battery packs,” Thermal Science and Engineering Progress, vol. 73, p. 104638, May 2026, doi: 10.1016/j.tsep.2026.104638.
- [20] A. Sharma, S. Sreedhara, M. Khatamifar, and W. Lin, “Comparative investigation of different liquid-cooled battery thermal management systems (LC-BTMS) designs for battery module of electric vehicle,” Applied Thermal Engineering, vol. 292, p. 130436, Apr. 2026, doi: 10.1016/j.applthermaleng.2026.130436.
- [21] J. Weng, D. Ouyang, X. Yang, M. Chen, G. Zhang, and J. Wang, “Optimization of the internal fin in a phase-change-material module for battery thermal management,” Applied Thermal Engineering, vol. 167, p. 114698, Feb. 2020, doi: 10.1016/j.applthermaleng.2019.114698.
- [22] X. Ding, Y. Wang, X. Yuan, D. A. Khan, J. Gu, and Z. Yang, “Design of cold plate structures for energy storage battery cooling and analysis of heat transfer performance,” Thermal Science and Engineering Progress, vol. 72, p. 104612, Apr. 2026, doi: 10.1016/j.tsep.2026.104612.
- [23] J. Smith, R. Singh, M. Hinterberger, and M. Mochizuki, “Battery thermal management system for electric vehicle using heat pipes,” International Journal of Thermal Sciences, vol. 134, pp. 517–529, Dec. 2018, doi: 10.1016/j.ijthermalsci.2018.08.022.
- [24] R. Sukarno et al., “Innovative Pickup Car Cooling System Based on Thermoelectric Coupled With Heat Pipe Sink,” Automotive Experiences, vol. 8, no. 2, pp. 296–309, Sep. 2025, doi: 10.31603/ae.13494.
- [25] R. Sukarno, A. Premono, Y. Gunawan, A. Wiyono, and A. Lubi, “Experimental Investigation of Using Thermoelectric Coolers under Different Cooling Methods as An Alternative Air Conditioning System for Car Cabin,” Automotive Experiences, vol. 7, no. 2, 2024, doi: 10.31603/ae.11485.
- [26] M. F. Jauhari et al., “Experimental Analysis of a Hybrid-Configured Battery Thermal Management System Using Paraffin Oil and Fan,” Automotive Experiences, vol. 8, no. 3, pp. 612–623, 2025, doi: 10.31603/ae.13403.
- [27] A. R. Abrari, T. H. Ariwibowo, D. Pramadihanto, N. R. Arini, E. H. Binugroho, and A. Miyara, “Thermal Performance Enhancement of Serpentine Cooling Design Using Branch Modification for Lithium-Ion Batteries,” Automotive Experiences, vol. 7, no. 3, pp. 552–566, Dec. 2024, doi: 10.31603/ae.12709.
- [28] N. T. Atmoko, A. Jamaldi, and T. W. B. Riyadi, “An Experimental Study of the TEG Performance using Cooling Systems of Waterblock and Heatsink-Fan,” Automotive Experiences, vol. 5, no. 3, pp. 361–367, 2022, doi: 10.31603/ae.6250.
- [29] W. Tong, K. Somasundaram, E. Birgersson, A. S. Mujumdar, and C. Yap, “Thermo-electrochemical model for forced convection air cooling of a lithium-ion battery module,” Applied Thermal Engineering, vol. 99, pp. 672–682, Apr. 2016, doi: 10.1016/j.applthermaleng.2016.01.050.
- [30] A. Kumar Thakur et al., “A state-of-the art review on advancing battery thermal management systems for fast-charging,” Applied Thermal Engineering, vol. 226, p. 120303, May 2023, doi: 10.1016/j.applthermaleng.2023.120303.
- [31] L. Zhao, J. Wang, M. Zheng, and M. Chen, “Design and performance optimization of liquid immersion cooling system for prismatic lithium-ion battery modules,” International Journal of Heat and Fluid Flow, vol. 118, p. 110181, Mar. 2026, doi: 10.1016/j.ijheatfluidflow.2025.110181.
- [32] Z. Jiang et al., “Immersion cooling battery thermal management system design and optimization for high-energy-density battery packs: A comparative study with side cooling plates,” International Journal of Heat and Mass Transfer, vol. 261, p. 128550, Jun. 2026, doi: 10.1016/j.ijheatmasstransfer.2026.128550.
- [33] L. Zhang et al., “Post-venting immersion cooling of over-heated battery: Effect of thermal runaway risk, cell scale, and quenching strategy,” Process Safety and Environmental Protection, vol. 210, p. 108730, Apr. 2026, doi: 10.1016/j.psep.2026.108730.
- [34] Y. Lu, B. Sun, L. Li, F. Huang, and C. Chen, “Numerical investigation of vertical vibration effects on immersion cooling heat transfer for lithium-ion battery at high discharge rate,” Case Studies in Thermal Engineering, vol. 77, p. 107607, Jan. 2026, doi: 10.1016/j.csite.2025.107607.
- [35] C. Mo, A. C. Y. Yuen, Y. Wu, B. Fei, and J. Wang, “Experiments on the effects of immersion cooling on lithium-ion battery module and mitigating battery thermal runaway,” Journal of Energy Storage, vol. 154, p. 121373, Apr. 2026, doi: 10.1016/j.est.2026.121373.
- [36] M. A. Adit, S. Hasan, and N. N. Mustafi, “Performance analysis of a novel battery thermal management system integrating thermoelectric and dielectric immersion cooling in EVs,” Energy Conversion and Management: X, vol. 30, p. 101550, May 2026, doi: 10.1016/j.ecmx.2026.101550.
- [37] T. Ouyang, Z. Wang, G. Huang, Y. Li, and Z. Huang, “An integrated thermoelectric cooling design for preventing thermal runaway propagation in lithium-ion batteries,” Energy Conversion and Management, vol. 356, p. 121327, May 2026, doi: 10.1016/j.enconman.2026.121327.
- [38] S. K. Chung, Y. Jo, S. Baik, S.-W. Kang, and K. Choi, “Enhanced cooling performance of hybrid battery thermal management system with thermoelectric modules and multi-layered phase change materials,” Journal of Energy Storage, vol. 155, p. 121587, Apr. 2026, doi: 10.1016/j.est.2026.121587.
- [39] Z. M. Marouf, M. A. Fouad, and M. A. Hassan, “Experimental investigation of the effect of air bubbles injection on the performance of a plate heat exchanger,” Applied Thermal Engineering, vol. 217, p. 119264, Nov. 2022, doi: 10.1016/j.applthermaleng.2022.119264.
- [40] S. S. Hasan, A. Sh. Baqir, and H. B. Mahood, “The Effect of Injected Air Bubble Size on the Thermal Performance of a Vertical Shell and Helical Coiled Tube Heat Exchanger,” Energy Engineering, vol. 118, no. 6, pp. 1595–1609, 2021, doi: 10.32604/EE.2021.017433.
- [41] Z. M. Marouf and M. A. Fouad, “Combined Energetic and Exergetic Performance Analysis of Air Bubbles Injection into a Plate Heat Exchanger: An Experimental Study,” Energies, vol. 16, no. 3, p. 1164, Jan. 2023, doi: 10.3390/en16031164.
- [42] F. L. Rashid et al., “An Examination of Air-Bubble Injection Mechanisms for Optimising Heat Transfer in Industrial Applications,” International Journal of Heat and Technology, vol. 41, no. 5, pp. 1226–1248, Oct. 2023, doi: 10.18280/ijht.410513.
- [43] H. Liu, C. Shi, C. Liu, and W. Chang, “A Review of Lithium-Ion Battery Thermal Management Based on Liquid Cooling and Its Evaluation Method,” Energies, vol. 18, no. 17, p. 4569, Aug. 2025, doi: 10.3390/en18174569.
- [44] M. U. Z. Priyadi et al., “Systematic review of battery cooling technologies in electric vehicles: Methods, challenges, and recent innovations,” Mechanical Engineering for Society and Industry, vol. 5, no. 2, pp. 434–458, Dec. 2025, doi: 10.31603/mesi.14070.
- [45] I. G. N. B. Catrawedarma, S. Ton, D. D. Pranowo, and F. Surahmanto, “Hydrodynamic characteristics of the microbubble dissolution in water using an ejector-type bubble generator,” Case Studies in Chemical and Environmental Engineering, vol. 11, p. 101043, Jun. 2025, doi: 10.1016/j.cscee.2024.101043.
- [46] I. Catrawedarma, S. Ton, D. D. Pranowo, and F. Surahmanto, “Size Distribution and Mean Diameter of Microbubbles in Different Types of Ejector Bubble Generators,” Journal of Applied Fluid Mechanics, vol. 18, no. 4, Jun. 2025, doi: 10.47176/jafm.18.6.3227.
- [47] E. N. Sari, A. Fiveriati, N. Rusti, J. Rulianto, R. Bhiqman Susanto, and I. G. N. B. Catrawedarma, “Visual and Pressure Signal Investigations on Bubble Produced by Ejector Bubble Generator,” E3S Web of Conferences, vol. 483, p. 03020, Jan. 2024, doi: 10.1051/e3sconf/202448303020.
- [48] I. Catrawedarma, Deendarlianto, and Indarto, “Statistical Characterization of Flow Structure of Air–water Two-phase Flow in Airlift Pump–Bubble Generator System,” International Journal of Multiphase Flow, vol. 138, p. 103596, May 2021, doi: 10.1016/j.ijmultiphaseflow.2021.103596.
- [49] I. Catrawedarma, Deendarlianto, and Indarto, “Hydrodynamic behaviors of air–water two-phase flow during the water lifting in a bubble generator type of airlift pump system,” Heat and Mass Transfer, vol. 58, no. 6, pp. 1005–1026, Jun. 2022, doi: 10.1007/s00231-021-03157-z.
- [50] I. G. N. B. Catrawedarma, F. A. Resnaraditya, Deendarlianto, and Indarto, “Statistical characterization of the flow structure of air-water-solid particles three-phase flow in the airlift pump-bubble generator system,” Flow Measurement and Instrumentation, vol. 82, p. 102062, Dec. 2021, doi: 10.1016/j.flowmeasinst.2021.102062.
- [51] A. Adham, N. Mohd-Ghazali, and R. Ahmad, “Optimization of nanofluid-cooled microchannel heat sink,” Thermal Science, vol. 20, no. 1, pp. 109–118, 2016, doi: 10.2298/TSCI130517163A.
- [52] W. Wu, S. Wang, W. Wu, K. Chen, S. Hong, and Y. Lai, “A critical review of battery thermal performance and liquid based battery thermal management,” Energy Conversion and Management, vol. 182, pp. 262–281, Feb. 2019, doi: 10.1016/j.enconman.2018.12.051.
- [53] S. Pincus, “Approximate entropy (ApEn) as a complexity measure,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 5, no. 1, pp. 110–117, Mar. 1995, doi: 10.1063/1.166092.
- [54] A. Delgado-Bonal and A. Marshak, “Approximate Entropy and Sample Entropy: A Comprehensive Tutorial,” Entropy, vol. 21, no. 6, p. 541, May 2019, doi: 10.3390/e21060541.
- [55] S. Zurek, P. Guzik, S. Pawlak, M. Kosmider, and J. Piskorski, “On the relation between correlation dimension, approximate entropy and sample entropy parameters, and a fast algorithm for their calculation,” Physica A: Statistical Mechanics and its Applications, vol. 391, no. 24, pp. 6601–6610, Dec. 2012, doi: 10.1016/j.physa.2012.07.003.
- [56] P. Grassberger and I. Procaccia, “Estimation of the Kolmogorov entropy from a chaotic signal,” Physical Review A, vol. 28, no. 4, pp. 2591–2593, Oct. 1983, doi: 10.1103/PhysRevA.28.2591.
- [57] V. S. Anishchenko and S. Astakhov, “Relative kolmogorov entropy of a chaotic system in the presence of noise,” International Journal of Bifurcation and Chaos, vol. 18, no. 09, pp. 2851–2855, Sep. 2008, doi: 10.1142/S021812740802210X.
