{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T17:33:19Z","timestamp":1775323999952,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,30]],"date-time":"2022-01-30T00:00:00Z","timestamp":1643500800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Transmission Research Association for Mobility Innovation","award":["A3-6-03"],"award-info":[{"award-number":["A3-6-03"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Stator coils of automobiles in operation generate heat and are cooled by coolant poured from above. The flow characteristic of the coolant depends on the coil structure, flow condition, solid\u2013fluid interaction, and fluid property, which has not been clarified due to its complexities. Since straight coils are aligned and layered with an angle at the coolant-touchdown region, the coil structure is simplified to a horizontal square rod array referring to an actual coil size. To obtain the flow and wetting characteristics, two-phase fluid flow simulations are conducted by using the phase-field lattice Boltzmann method. First, the flow onto the single-layered rod array is discussed. The wetting area is affected both by the rod gap and the wettability, which is normalized by the gap and the averaged boundary layer thickness. Then, the flow onto the multi-layered rod arrays is investigated with different rod gaps. The top layer wetting becomes longitudinal due to the reduction of the flow advection by the second layer. The wetting area jumps up at the second layer and increases proportionally to the below layers. These become remarkable at the narrow rod gap case, and finally, the dimensionless wetting area is discussed at each layer.<\/jats:p>","DOI":"10.3390\/e24020219","type":"journal-article","created":{"date-parts":[[2022,1,31]],"date-time":"2022-01-31T01:46:08Z","timestamp":1643593568000},"page":"219","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Coolant Wetting Simulation on Simplified Stator Coil Model by the Phase-Field Lattice Boltzmann Method"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8516-7007","authenticated-orcid":false,"given":"Makoto","family":"Sugimoto","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai 599-8531, Japan"}]},{"given":"Tatsuya","family":"Miyazaki","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai 599-8531, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0740-3641","authenticated-orcid":false,"given":"Masayuki","family":"Kaneda","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai 599-8531, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9313-1816","authenticated-orcid":false,"given":"Kazuhiko","family":"Suga","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai 599-8531, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"734","DOI":"10.1109\/TIA.2003.810635","article-title":"Modeling of iron losses of permanent-magnet synchronous motors","volume":"39","author":"Mi","year":"2003","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_2","unstructured":"Cez\u00e1rio, C.A., Verardi, M., Borges, S.S., Silva, J.C., and Oliveira, A.A.M. (2005, January 6\u201321). Transient Thermal Analysis of an Induction Electric Motor. Proceedings of the 18th International Congress of Mechanical Engineering, Ouro Preto, Brazil."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"113733","DOI":"10.1016\/j.applthermaleng.2019.113733","article-title":"Thermal management of a Formula E electric motor: Analysis and optimization","volume":"157","author":"Cavazzuti","year":"2019","journal-title":"Appl. Therm. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Fujita, H., Itoh, A., and Urano, T. (2019). Newly Developed Motor Cooling Method Using Refrigerant. World Electr. Veh. J., 10.","DOI":"10.3390\/wevj10020038"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/s12206-020-1240-y","article-title":"Cooling effect of oil cooling method on electric vehicle motors with hairpin winding","volume":"35","author":"Ha","year":"2021","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1103\/PhysRevE.53.743","article-title":"Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method","volume":"53","author":"Martys","year":"1996","journal-title":"Phys. Rev. E"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4320","DOI":"10.1103\/PhysRevA.43.4320","article-title":"Lattice Boltzmann model of immiscible fluids","volume":"43","author":"Gunstensen","year":"1991","journal-title":"Phys. Rev. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1815","DOI":"10.1103\/PhysRevE.47.1815","article-title":"Lattice Boltzmann model for simulating flows with multiple phases and components","volume":"47","author":"Shan","year":"1993","journal-title":"Phys. Rev. E"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5041","DOI":"10.1103\/PhysRevE.54.5041","article-title":"Lattice Boltzmann simulations of liquid-gas and binary fluid systems","volume":"54","author":"Swift","year":"1996","journal-title":"Phys. Rev. E"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/s41230-017-7186-8","article-title":"Phase-field-lattice Boltzmann study for lamellar eutectic growth in a natural convection melt","volume":"14","author":"Zhang","year":"2017","journal-title":"China Foundry"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Facci, A.L., Lauricella, M., Succi, S., Villani, V., and Falcucci, G. (2021). Optimized Modeling and Design of a PCM-Enhanced H2 Storage. Energies, 14.","DOI":"10.3390\/en14061554"},{"key":"ref_12","first-page":"20-00014","article-title":"Phase-field lattice Boltzmann simulation of minute droplet onto isotropic porous media","volume":"86","author":"Sugimoto","year":"2020","journal-title":"Trans. JSME"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"033309","DOI":"10.1103\/PhysRevE.97.033309","article-title":"Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows","volume":"97","author":"Liang","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1006\/jcph.1999.6332","article-title":"Calculation of two-phase Navier-Stokes flows using phase-field modeling","volume":"155","author":"Jacqmin","year":"1999","journal-title":"J. Comput. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1103\/PhysRev.94.511","article-title":"A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems","volume":"94","author":"Bhatnagar","year":"1954","journal-title":"Phys. Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.jcp.2017.03.062","article-title":"A weighted multiple-relaxation-time lattice Boltzmann method for multiphase flows and its application to partial coalescence cascades","volume":"341","author":"Fakhari","year":"2017","journal-title":"J. Comput. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"053320","DOI":"10.1103\/PhysRevE.89.053320","article-title":"Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows","volume":"89","author":"Liang","year":"2014","journal-title":"Phys. Rev. E"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"33","DOI":"10.26804\/capi.2019.03.01","article-title":"A brief review of the phase-field-based lattice Boltzmann method for multiphase flows","volume":"2","author":"Wang","year":"2019","journal-title":"Capillarity"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1016\/j.camwa.2015.01.010","article-title":"A D3Q27 multiple-relaxation-time lattice Boltzmann method for turbulent flows","volume":"69","author":"Suga","year":"2015","journal-title":"Comput. Math. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","article-title":"Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations","volume":"79","author":"Osher","year":"1988","journal-title":"J. Comput. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.1142\/S0129183109014710","article-title":"Wall free energy based polynomial boundary conditions for non-ideal gas lattice Boltzmann equation","volume":"20","author":"Liu","year":"2009","journal-title":"Int. J. Mod. Phys. C"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1016\/j.jcp.2017.01.025","article-title":"Diffuse interface modeling of three-phase contact line dynamics on curved boundaries: A lattice Boltzmann model for large density and viscosity ratios","volume":"334","author":"Fakhari","year":"2017","journal-title":"J. Comput. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3452","DOI":"10.1063\/1.1399290","article-title":"Momentum transfer of a Boltzmann-lattice fluid with boundaries","volume":"13","author":"Bouzidi","year":"2001","journal-title":"Phys. Fluids"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/BF01461107","article-title":"Ueber das Zeitgesetz des kapillaren Aufstiegs von Fl\u00fcssigkeiten","volume":"23","author":"Lucas","year":"1918","journal-title":"Kolloid-Zeitschrift"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1103\/PhysRev.17.273","article-title":"The Dynamics of Capillary Flow","volume":"17","author":"Washburn","year":"1921","journal-title":"Phys. Rev."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/2\/219\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:11:33Z","timestamp":1760134293000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/2\/219"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,30]]},"references-count":25,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["e24020219"],"URL":"https:\/\/doi.org\/10.3390\/e24020219","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,30]]}}}