{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:13:21Z","timestamp":1772252001472,"version":"3.50.1"},"reference-count":57,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T00:00:00Z","timestamp":1755216000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Escuela Polit\u00e9cnica Nacional","award":["PIIF-23-04"],"award-info":[{"award-number":["PIIF-23-04"]}]},{"name":"Escuela Polit\u00e9cnica Nacional","award":["UIDB\/04625\/2025"],"award-info":[{"award-number":["UIDB\/04625\/2025"]}]},{"name":"Escuela Polit\u00e9cnica Nacional","award":["EAPA_0001\/2022"],"award-info":[{"award-number":["EAPA_0001\/2022"]}]},{"name":"Foundation for Science and Technology (FCT)","award":["PIIF-23-04"],"award-info":[{"award-number":["PIIF-23-04"]}]},{"name":"Foundation for Science and Technology (FCT)","award":["UIDB\/04625\/2025"],"award-info":[{"award-number":["UIDB\/04625\/2025"]}]},{"name":"Foundation for Science and Technology (FCT)","award":["EAPA_0001\/2022"],"award-info":[{"award-number":["EAPA_0001\/2022"]}]},{"name":"Interreg Atlantic Area Programme","award":["PIIF-23-04"],"award-info":[{"award-number":["PIIF-23-04"]}]},{"name":"Interreg Atlantic Area Programme","award":["UIDB\/04625\/2025"],"award-info":[{"award-number":["UIDB\/04625\/2025"]}]},{"name":"Interreg Atlantic Area Programme","award":["EAPA_0001\/2022"],"award-info":[{"award-number":["EAPA_0001\/2022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Machines"],"abstract":"<jats:p>Hydraulic erosion from suspended sediment is a major degradation mechanism in Francis turbines of sediment-laden rivers, especially in Andean hydropower plants. This study presents a Python3.9-based computational tool integrating the empirical Oka erosion model within a Lagrangian particle tracking framework, coupled to single-phase CFD in OpenFOAM 10. The novelty lies in a reduced-domain approach that omits the spiral casing and replicates its particle-induced swirl via a custom algorithm, lowering meshing complexity and computational cost while preserving erosion prediction accuracy. The method was applied to a full-scale Francis turbine at the San Francisco hydropower plant in Ecuador (nominal discharge 62.4 m3\/s, rated output 115 MW, rotational speed 34.27 rad\/s), operating under volcanic and erosive sediment loads. Maximum erosion rates reached ~1.2 \u00d7 10\u22124 mm3\/kg, concentrated on runner blade trailing edges and guide vane pressure sides. Impact kinematics showed most collisions at near-normal angles (85\u00b0\u201398\u00b0, peak at 92\u00b0) and 6\u20139 m\/s velocities, with rare 40 m\/s impacts causing over 50\u00d7 more loss than average. The workflow identifies critical wear zones, supports redesign and coating strategies, and offers a transferable, open-source framework for erosion assessment in turbines under diverse sediment-laden conditions.<\/jats:p>","DOI":"10.3390\/machines13080725","type":"journal-article","created":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T16:09:55Z","timestamp":1755274195000},"page":"725","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Lagrangian Simulation of Sediment Erosion in Francis Turbines Using a Computational Tool in Python Coupled with OpenFOAM"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-1360-5354","authenticated-orcid":false,"given":"Mateo","family":"Narv\u00e1ez","sequence":"first","affiliation":[{"name":"Laboratorio de Mec\u00e1nica Inform\u00e1tica, Escuela Polit\u00e9cnica Nacional (EPN), Quito 170517, Ecuador"},{"name":"Departamento de Ingenier\u00eda Mec\u00e1nica, Escuela Polit\u00e9cnica Nacional (EPN), Quito 170517, Ecuador"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-8860-3928","authenticated-orcid":false,"given":"Jeremy","family":"Guam\u00e1n","sequence":"additional","affiliation":[{"name":"Laboratorio de Mec\u00e1nica Inform\u00e1tica, Escuela Polit\u00e9cnica Nacional (EPN), Quito 170517, Ecuador"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4732-2421","authenticated-orcid":false,"given":"V\u00edctor Hugo","family":"Hidalgo","sequence":"additional","affiliation":[{"name":"Laboratorio de Mec\u00e1nica Inform\u00e1tica, Escuela Polit\u00e9cnica Nacional (EPN), Quito 170517, Ecuador"},{"name":"Departamento de Ingenier\u00eda Mec\u00e1nica, Escuela Polit\u00e9cnica Nacional (EPN), Quito 170517, Ecuador"},{"name":"Carrera de Pedagog\u00eda T\u00e9cnica de la Mecatr\u00f3nica, Facultad de Filosof\u00eda, Letras y Ciencias de la Educaci\u00f3n, Universidad Central del Ecuador (UCE), Quito 170129, Ecuador"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8316-7778","authenticated-orcid":false,"given":"Modesto","family":"P\u00e9rez-S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Hydraulic Engineering and Environmental Department, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Valencia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9028-9711","authenticated-orcid":false,"given":"Helena M.","family":"Ramos","sequence":"additional","affiliation":[{"name":"Civil Engineering Research and Innovation for Sustainability (CERIS), Instituto Superior T\u00e9cnico, Department of Civil Engineering, Architecture and Environment, University of Lisbon, 1049-001 Lisbon, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,15]]},"reference":[{"key":"ref_1","unstructured":"Graham, E., Fulghum, N., and Altieri, K. 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