{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T06:34:40Z","timestamp":1772087680330,"version":"3.50.1"},"reference-count":47,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T00:00:00Z","timestamp":1771459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52479084, 52309113"],"award-info":[{"award-number":["52479084, 52309113"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Yunnan Fundamental Research Projects","award":["202501AT070316"],"award-info":[{"award-number":["202501AT070316"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Francis turbines are renowned for their high efficiency and adaptability across a wide range of head and discharge conditions. However, internal mechanical friction losses (IMFLs), resulting from rotational frictional resistance between the rotating runner and the surrounding fluid, remain a significant obstacle to further performance optimisation. This study introduced a CFD-derived integral friction torque framework, validated through theoretical analysis, that enables the spatially resolved quantification of IMFLs in Francis turbine runners. Building on this framework, a comprehensive computational approach was established to quantify IMFLs in a Francis turbine runner using a CFD-derived integral torque method combined with a theoretical verification model. Three runner configurations were analysed: the original runner model (ORM), a modified runner (RM1) with selective exit height reduction, and a modified runner (RM2) with uniform exit height reduction. Transient simulations were conducted at the best efficiency point (BEP) using the shear stress transport (SST) k\u2013\u03c9 turbulence model and a sliding mesh approach. The numerical results were verified using the theoretical model and systematically evaluated to assess IMFL mechanisms and runner performance. The findings demonstrate that variations in runner geometry significantly influence internal frictional resistance and turbine efficiency. Compared with ORM, both RM1 and RM2 reduced the rotational friction torque, with RM2 exhibiting the greatest improvement: a 2.83% reduction in total friction resistance torque, a 14.74% reduction in total power losses, and a 1% absolute increase in efficiency. These improvements are primarily attributed to reduced wall shear stress and a more uniform pressure distribution across the runner surface.<\/jats:p>","DOI":"10.3390\/computation14020053","type":"journal-article","created":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T11:44:27Z","timestamp":1771501467000},"page":"53","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analysis of Internal Mechanical Friction Losses Influence on the Francis-99 Runner Using the Friction Torque Approach"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-2231-921X","authenticated-orcid":false,"given":"Otibh M. M.","family":"Abubkry","sequence":"first","affiliation":[{"name":"Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0537-3960","authenticated-orcid":false,"given":"Yun","family":"Zeng","sequence":"additional","affiliation":[{"name":"Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan","family":"Duan","sequence":"additional","affiliation":[{"name":"Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6472-8138","authenticated-orcid":false,"given":"Altyib Abdallah","family":"Mahmoud Ahmed","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hassan","family":"Babeker","sequence":"additional","affiliation":[{"name":"College of Materials Science and Engineering, Kunming University of Science and Technology, Kunming 650093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9420-9910","authenticated-orcid":false,"given":"Altyeb","family":"Ali Abaker Omer","sequence":"additional","affiliation":[{"name":"School of Tea and Coffee, Puer University, Puer 665000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1016\/j.renene.2019.12.141","article-title":"A review on remedial attempts to counteract the power generation compromise from draft tubes of hydropower plants","volume":"150","author":"Muhirwa","year":"2020","journal-title":"Renew. 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