Statistical characteristics of time series temperature in cooling the electric vehicle controller using the bubble generator
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Keywords:
Water block, thermal resistance, kolmogorov entropy
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Abstract
The present study examines the thermal performance of the cooling system in an electric vehicle controller. This is achieved by injecting bubbles into the water block at various input airflow rates, using quiet-water and circulating-water cooling fluids. The thermal performance of a system is determined by two factors: the maximum temperature at the controller-water block interface and the corresponding thermal resistance. The temperature distribution is analyzed using statistical moments, the Probability Density Function (PDF), and Kolmogorov entropy to determine the irregularity of the temperature signal. The findings indicate that an increase in airflow rate can result in a decrease in maximum temperature and an enhancement in thermal resistance and flatness of the PDF curve. The maximum temperature decreases by 15.5% when the cooling medium is quiet water when compared to bubble injection at an airflow rate of Qa = 1.5 lpm. The bubble-cooling fluid, with an airflow rate of Qa = 1.5 lpm has a relatively uniform entropy across all thermocouple positions. The presence of low Kolmogorov entropy and low PDF flatness indicate a more stable controller response and fewer extreme spikes. In turn, it has an impact on the increasing system reliability and extending the durability of the controller's electronic components.
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IGNB, C., Anggra, F., & Abdul, H. (2026). Statistical characteristics of time series temperature in cooling the electric vehicle controller using the bubble generator. Communications in Science and Technology, 11(1), 42–52. https://doi.org/10.21924/cst.11.1.2026.1858
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References
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33. I. Catrawedarma, S. Ton, D.D. Pranowo, F. Surahmanto, Size Distribution and Mean Diameter of Microbubbles in Different Types of Ejector Bubble Generators, JAFM. 18 (2025).
34. I. Catrawedarma, S. Ton, D.D. Pranowo, F. Surahmanto, Hydrodynamic characteristics of the microbubble dissolution in water using an ejector-type bubble generator, Case Studies in Chemical and Environmental Engineering. 11 (2025) 101043.
35. H. Park, A design of air flow configuration for cooling lithium ion battery in hybrid electric vehicles, Journal of Power Sources. 239 (2013) 30–36.
36. E.N. Sari, A. Fiveriati, N. Rusti, J. Rulianto, R. Bhiqman Susanto, I. Catrawedarma, Visual and Pressure Signal Investigations on Bubble Produced by Ejector Bubble Generator, E3S Web Conf. 483 (2024) 03020.
37. S. Riera, J. Barrau, M. Omri, L.G. Fréchette, J.I. Rosell, Stepwise varying width microchannel cooling device for uniform wall temperature: Experimental and numerical study, Applied Thermal Engineering. 78 (2015) 30–38.
38. I. Catrawedarma, D. Deendarlianto, I. Indarto, Statistical Characterization of Flow Structure of Air–water Two-phase Flow in Airlift Pump–Bubble Generator System, International Journal of Multiphase Flow. 138 (2021).
39. I. Catrawedarma, Deendarlianto, 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. 58 (2022) 1005–1026.
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44. D.B. Donoghue, A. Albadawi, Y.M.C. Delauré, A.J. Robinson, D.B. Murray, Bubble impingement and the mechanisms of heat transfer, International Journal of Heat and Mass Transfer. 71 (2014) 439–450.
45. N.S. Panicker, A. Passalacqua, R.O. Fox, Computational Study of the Effect of Homogeneous and Heterogeneous Bubbly Flows on Bulk Gas–Liquid Heat Transfer, Journal of Fluids Engineering. 142 (2020) 101402.
46. I. Michiyoshi, A. Serizawa, Turbulence in two-phase bubbly flow, Nuclear Engineering and Design. 95 (1986) 253–267.
47. A.H. Astyanto, J.A.E. Pramono, I. Catrawedarma, Deendarlianto, Indarto, Statistical characterization of liquid film fluctuations during gas-liquid two-phase counter-current flow in a 1/30 scaled-down test facility of a pressurized water reactor (PWR) hot leg, Annals of Nuclear Energy. 172 (2022) 109065.
48. U.C. Saxena, A.D.K. Laird, Heat Transfer from a Cylinder Oscillating in a Cross-Flow, Journal of Heat Transfer. 100 (1978) 684–689.
49. J.W.C. De Vries, M.Y. Jansen, W.D. Van Driel, On the difference between thermal cycling and thermal shock testing for board level reliability of soldered interconnections, Microelectronics Reliability. 47 (2007) 444–449.
50. V. Lakshminarayanan, N. Sriraam, The effect of temperature on the reliability of electronic components, in: 2014 IEEE International Conference on Electronics, Computing and Communication Technologies (CONECCT), IEEE, Bangalore, India, 2014: pp. 1–6.
51. S. Moreau, L. Lequeu, R. Jerisian, Comparative study of thermal cycling and thermal shocks tests on 2004, Microelectronics Reliability. 44 (2004) 1343–1347.
2. A.A. Pesaran, Battery Thermal Management in EVs and HEVs: Issues and Solutions, Advanced Automotive Battery Conference. (2001).
3. J. Kim, J. Oh, H. Lee, Review on battery thermal management system for electric vehicles, Applied Thermal Engineering. 149 (2019) 192–212.
4. J.-M. Mottard, C. Hannay, E.L. Winandy, Experimental study of the thermal behavior of a water cooled Ni–Cd battery, Journal of Power Sources. 117 (2003) 212–222.
5. A. Kumar Thakur, R. Sathyamurthy, R. Velraj, R. Saidur, A.K. Pandey, Z. Ma, P. Singh, S.K. Hazra, S. Wafa Sharshir, R. Prabakaran, S.C. Kim, S. Panchal, H.M. Ali, A state-of-the art review on advancing battery thermal management systems for fast-charging, Applied Thermal Engineering. 226 (2023) 120303.
6. Q. Huang, X. Li, G. Zhang, J. Zhang, F. He, Y. Li, Experimental investigation of the thermal performance of heat pipe assisted phase change material for battery thermal management system, Applied Thermal Engineering. 141 (2018) 1092–1100.
7. M. Mahmud, K.S. Rahman, Md. Rokonuzzaman, A.K.M.A. Habib, M.R. Islam, S.M.A. Motakabber, S. Channumsin, S. Chowdhury, Lithium-ion battery thermal management for electric vehicles using phase change material: A review, Results in Engineering. 20 (2023) 101424.
8. L. Ianniciello, P.H. Biwolé, P. Achard, Electric vehicles batteries thermal management systems employing phase change materials, Journal of Power Sources. 378 (2018) 383–403.
9. J. Weng, D. Ouyang, X. Yang, M. Chen, G. Zhang, J. Wang, Optimization of the internal fin in a phase-change-material module for battery thermal management, Applied Thermal Engineering. 167 (2020) 114698.
10. Z. Rao, S. Wang, G. Zhang, Simulation and experiment of thermal energy management with phase change material for ageing LiFePO4 power battery, Energy Conversion and Management. 52 (2011) 3408–3414.
11. S.A. Khateeb, S. Amiruddin, M. Farid, J.R. Selman, S. Al-Hallaj, Thermal management of Li-ion battery with phase change material for electric scooters: experimental validation, Journal of Power Sources. 142 (2005) 345–353.
12. S.A. Khateeb, M.M. Farid, J.R. Selman, S. Al-Hallaj, Design and simulation of a lithium-ion battery with a phase change material thermal management system for an electric scooter, Journal of Power Sources. 128 (2004) 292–307.
13. A. Hussain, Thermal management of lithium ion batteries using graphene coated nickel foam saturated with phase change materials, International Journal of Thermal Sciences. (2018).
14. C. Wang, Heat transfer enhancement of phase change composite material: Copper foam/paraffin, Renewable Energy. (2016).
15. P. Goli, S. Legedza, A. Dhar, R. Salgado, J. Renteria, A.A. Balandin, Graphene-Enhanced Hybrid Phase Change Materials for Thermal Management of Li-Ion Batteries, Journal of Power Sources. (2013).
16. C. Lin, Experiment and simulation of a LiFePO4 battery pack with a passive thermal management system using composite phase change material and graphite sheets, Journal of Power Sources. (2015).
17. Z. Ling, Experimental and numerical investigation of the application of phase change materials in a simulative power batteries thermal management system, Applied Energy. (2014).
18. Z. Ling, Thermal management performance of phase change materials with different thermal conductivities for Li-ion battery packs operated at low temperatures, (2018).
19. F.S. Hwang, T. Confrey, C. Reidy, D. Picovici, D. Callaghan, D. Culliton, C. Nolan, Review of battery thermal management systems in electric vehicles, Renewable and Sustainable Energy Reviews. 192 (2024) 114171.
20. N. Putra, B. Ariantara, R.A. Pamungkas, Experimental investigation on performance of lithium-ion battery thermal management system using flat plate loop heat pipe for electric vehicle application, Applied Thermal Engineering. 99 (2016) 784–789.
21. R. Sukarno, Z. Indasyach Moreno, D. Rio Budi Syaka, Y. Gunawan, N. Gama Yoga, R. Fariz Adzani, A. Putra Mustafit, D. Kurniawati, Experimental investigation of a thermoelectric generator assisted with heat pipe sinks for pickup car exhaust waste heat recovery, CST. 10 (2025) 106–116.
22. Y. Ye, Y. Shi, L.H. Saw, 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. 92 (2016) 893–903.
23. J. Smith, R. Singh, M. Hinterberger, M. Mochizuki, Battery thermal management system for electric vehicle using heat pipes, International Journal of Thermal Sciences. 134 (2018) 517–529.
24. C. Roe, X. Feng, G. White, R. Li, H. Wang, X. Rui, C. Li, F. Zhang, V. Null, M. Parkes, Y. Patel, Y. Wang, H. Wang, M. Ouyang, G. Offer, B. Wu, Immersion cooling for lithium-ion batteries – A review, Journal of Power Sources. 525 (2022) 231094.
25. Z.M. Marouf, M.A. Fouad, M.A. Hassan, Experimental investigation of the effect of air bubbles injection on the performance of a plate heat exchanger, Applied Thermal Engineering. 217 (2022) 119264.
26. S. S. Hasan, A. Sh. Baqir, 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. 118 (2021) 1595–1609.
27. Z.M. Marouf, M.A. Fouad, Combined Energetic and Exergetic Performance Analysis of Air Bubbles Injection into a Plate Heat Exchanger: An Experimental Study, Energies. 16 (2023) 1164.
28. F. Colonius, C. Kawan, Invariance Entropy for Control Systems, SIAM J. Control Optim. 48 (2009) 1701–1721.
29. H. Jin, Y. Guan, L. Yao, Minimum Entropy Active Fault Tolerant Control of the Non-Gaussian Stochastic Distribution System Subjected to Mean Constraint, Entropy. 19 (2017) 218.
30. M. Bröcker, L. Herrmann, Flatness based control and tracking control based on nonlinearity measures, IFAC-PapersOnLine. 50 (2017) 8250–8255.
31. H. Gharsallaoui, M. Ayadi, M. Benrejeb, P. Borne, Flatness-based Control and Conventional RST Polynomial Control of a Thermal Process, INT J COMPUT COMMUN. 4 (2009) 41.
32. S. Scholz, L. Berger, D. Lebiedz, Benchmarking of Flatness-based Control of the Heat Equation, (2023).
33. I. Catrawedarma, S. Ton, D.D. Pranowo, F. Surahmanto, Size Distribution and Mean Diameter of Microbubbles in Different Types of Ejector Bubble Generators, JAFM. 18 (2025).
34. I. Catrawedarma, S. Ton, D.D. Pranowo, F. Surahmanto, Hydrodynamic characteristics of the microbubble dissolution in water using an ejector-type bubble generator, Case Studies in Chemical and Environmental Engineering. 11 (2025) 101043.
35. H. Park, A design of air flow configuration for cooling lithium ion battery in hybrid electric vehicles, Journal of Power Sources. 239 (2013) 30–36.
36. E.N. Sari, A. Fiveriati, N. Rusti, J. Rulianto, R. Bhiqman Susanto, I. Catrawedarma, Visual and Pressure Signal Investigations on Bubble Produced by Ejector Bubble Generator, E3S Web Conf. 483 (2024) 03020.
37. S. Riera, J. Barrau, M. Omri, L.G. Fréchette, J.I. Rosell, Stepwise varying width microchannel cooling device for uniform wall temperature: Experimental and numerical study, Applied Thermal Engineering. 78 (2015) 30–38.
38. I. Catrawedarma, D. Deendarlianto, I. Indarto, Statistical Characterization of Flow Structure of Air–water Two-phase Flow in Airlift Pump–Bubble Generator System, International Journal of Multiphase Flow. 138 (2021).
39. I. Catrawedarma, Deendarlianto, 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. 58 (2022) 1005–1026.
40. C. Roy, P. Venuvanalingam, J.F. Klausner, R. Mei, ON THE MECHANISM OF BUBBLE INDUCED FORCED CONVECTIVE HEAT TRANSFER ENHANCEMENT, Frontiers in Heat and Mass Transfer. 11 (2018).
41. A. Kitagawa, Y. Murai, Natural convection heat transfer from a vertical heated plate in water with microbubble injection, Chemical Engineering Science. 99 (2013) 215–224.
42. D.I. Mawarni, W.E. Juwana, I. Catrawedarma, K.A. Yuana, W. Budhijanto, D. Deendarlianto, I. Indarto, Statistical Characterization of Bubble Breakup Flow Structures in Swirl-Type Bubble Generator Systems, ASEAN J. Chem. Eng. 23 (2023) 62.
43. M. Lopez De Bertodano, R.T. Lahey, O.C. Jones, Phase distribution in bubbly two-phase flow in vertical ducts, International Journal of Multiphase Flow. 20 (1994) 805–818.
44. D.B. Donoghue, A. Albadawi, Y.M.C. Delauré, A.J. Robinson, D.B. Murray, Bubble impingement and the mechanisms of heat transfer, International Journal of Heat and Mass Transfer. 71 (2014) 439–450.
45. N.S. Panicker, A. Passalacqua, R.O. Fox, Computational Study of the Effect of Homogeneous and Heterogeneous Bubbly Flows on Bulk Gas–Liquid Heat Transfer, Journal of Fluids Engineering. 142 (2020) 101402.
46. I. Michiyoshi, A. Serizawa, Turbulence in two-phase bubbly flow, Nuclear Engineering and Design. 95 (1986) 253–267.
47. A.H. Astyanto, J.A.E. Pramono, I. Catrawedarma, Deendarlianto, Indarto, Statistical characterization of liquid film fluctuations during gas-liquid two-phase counter-current flow in a 1/30 scaled-down test facility of a pressurized water reactor (PWR) hot leg, Annals of Nuclear Energy. 172 (2022) 109065.
48. U.C. Saxena, A.D.K. Laird, Heat Transfer from a Cylinder Oscillating in a Cross-Flow, Journal of Heat Transfer. 100 (1978) 684–689.
49. J.W.C. De Vries, M.Y. Jansen, W.D. Van Driel, On the difference between thermal cycling and thermal shock testing for board level reliability of soldered interconnections, Microelectronics Reliability. 47 (2007) 444–449.
50. V. Lakshminarayanan, N. Sriraam, The effect of temperature on the reliability of electronic components, in: 2014 IEEE International Conference on Electronics, Computing and Communication Technologies (CONECCT), IEEE, Bangalore, India, 2014: pp. 1–6.
51. S. Moreau, L. Lequeu, R. Jerisian, Comparative study of thermal cycling and thermal shocks tests on 2004, Microelectronics Reliability. 44 (2004) 1343–1347.