Prediction of the particle’s impact velocity due to the bubble–particle interaction causing synergic wear
Cavitation damage and hard particle erosion are some of the main sources of wear in most hydraulic machines, such as pumps or hydroturbines. However, the synergic effect of these two phenomena leads to a wear phenomenon that is often more severe than the sum of the individual effects of cavitation a...
- Autores:
-
Laín Beatove, Santiago
Terán, Leonel A.
Rodríguez, Sara A.
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2023
- Institución:
- Universidad Autónoma de Occidente
- Repositorio:
- RED: Repositorio Educativo Digital UAO
- Idioma:
- eng
- OAI Identifier:
- oai:red.uao.edu.co:10614/15549
- Acceso en línea:
- https://hdl.handle.net/10614/15549
https://doi.org/10.1016/j.triboint.2023.108261
https://red.uao.edu.co/
- Palabra clave:
- Computational fluid dynamics
Bubble-particle interaction
Cavitation
Hard particle Erosion
Synergy
Particle’s impact velocity
- Rights
- openAccess
- License
- Derechos reservados - Elsevier, 2023
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Prediction of the particle’s impact velocity due to the bubble–particle interaction causing synergic wear |
| title |
Prediction of the particle’s impact velocity due to the bubble–particle interaction causing synergic wear |
| spellingShingle |
Prediction of the particle’s impact velocity due to the bubble–particle interaction causing synergic wear Computational fluid dynamics Bubble-particle interaction Cavitation Hard particle Erosion Synergy Particle’s impact velocity |
| title_short |
Prediction of the particle’s impact velocity due to the bubble–particle interaction causing synergic wear |
| title_full |
Prediction of the particle’s impact velocity due to the bubble–particle interaction causing synergic wear |
| title_fullStr |
Prediction of the particle’s impact velocity due to the bubble–particle interaction causing synergic wear |
| title_full_unstemmed |
Prediction of the particle’s impact velocity due to the bubble–particle interaction causing synergic wear |
| title_sort |
Prediction of the particle’s impact velocity due to the bubble–particle interaction causing synergic wear |
| dc.creator.fl_str_mv |
Laín Beatove, Santiago Terán, Leonel A. Rodríguez, Sara A. |
| dc.contributor.author.none.fl_str_mv |
Laín Beatove, Santiago Terán, Leonel A. Rodríguez, Sara A. |
| dc.subject.proposal.eng.fl_str_mv |
Computational fluid dynamics Bubble-particle interaction Cavitation Hard particle Erosion Synergy Particle’s impact velocity |
| topic |
Computational fluid dynamics Bubble-particle interaction Cavitation Hard particle Erosion Synergy Particle’s impact velocity |
| description |
Cavitation damage and hard particle erosion are some of the main sources of wear in most hydraulic machines, such as pumps or hydroturbines. However, the synergic effect of these two phenomena leads to a wear phenomenon that is often more severe than the sum of the individual effects of cavitation and hard particle erosion and that has been scarcely studied. Therefore, in this work, simplified computational fluid dynamics (CFD) simulations using 2D and 3D approaches were performed to investigate the behaviour of a particle interacting with a cavitation bubble near a solid wall under several conditions of pressure, position, bubble maximum size, and mass of the particle. All the involved variables were combined into three nondimensional variables: the dependent variable includes the impact velocity of the particle normal to the surface, while the other two variables include the particle position relative to the eroded wall and the particle mass. Through this approach, several correlations were identified, and a dimensionless function of two variables and six fitting factors was proposed to comply with those correlations. Then, this function was returned to its dimensional form to obtain an expression to predict the impact velocity of a particle normal to the solid wall due its interaction with a collapsing bubble |
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2023 |
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2023-02 |
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2024-04-19T13:36:40Z |
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2024-04-19T13:36:40Z |
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Laín Beatove, S.; Teran, L. A.; Rodríguez, S. A. (2023). Prediction of the particle’s impact velocity due to the bubble–particle interaction causing synergic wear. Tribology International. volume 180. p.p. 1-12. https://doi.org/10.1016/j.triboint.2023.108261 |
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0301-679X |
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https://hdl.handle.net/10614/15549 |
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https://doi.org/10.1016/j.triboint.2023.108261 |
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Universidad Autónoma de Occidente |
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Respositorio Educativo Digital UAO |
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https://red.uao.edu.co/ |
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Laín Beatove, S.; Teran, L. A.; Rodríguez, S. A. (2023). Prediction of the particle’s impact velocity due to the bubble–particle interaction causing synergic wear. Tribology International. volume 180. p.p. 1-12. https://doi.org/10.1016/j.triboint.2023.108261 0301-679X Universidad Autónoma de Occidente Respositorio Educativo Digital UAO |
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https://hdl.handle.net/10614/15549 https://doi.org/10.1016/j.triboint.2023.108261 https://red.uao.edu.co/ |
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eng |
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180 |
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Tribology International |
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[1] Haosheng C, Jiadao W, Darong C. Cavitation damages on solid surfaces in suspensions containing spherical and irregular microparticles. Wear 2009;266: 345–8. [2] Hu H, Zheng Y. The effect of sand particle concentrations on the vibratory cavitation erosion. Wear 2017;384:95–105. [3] Huang S, Ihara A, Watanabe H, Hashimoto H. Effects of solid particle properties on cavitation erosion in solid-water mixtures. J Fluids Eng 1996;118:749–55. [4] Romero R, Teran L, Coronado J, Ladino J, Rodríguez S. Synergy between cavitation and solid particle erosion in an ultrasonic tribometer. Wear 2019;428:395–403. [5] Yan D, Wang J, Liu F. Inhibition of the ultrasonic microjet-pits on the carbon steel in the particles-water mixtures. AIP Adv 2015;5:077159. [6] Amarendra H, Chaudhari G, Nath S. Synergy of cavitation and slurry erosion in the slurry pot tester. Wear 2012;290:25–31. [7] Amarendra H, Hallalli GB, Madhusudhana G, Mahendra H, Athani MK. Effect of cavitation inducers’ apex angle on erosion [8] Thapa B, Chaudhary P, Dahlhaug OG, Upadhyay P. Study of combined effect of sand erosion and cavitation in hydraulic turbines. Int Conf Small HydropowerHydro Sri Lanka 2007:24. [9] K. Su, D. Xia, Z. Ding, Cavitation damage in particle-laden liquids with considering particle concentration and size, 22nd IAHR-APD Congress, Sapporo, Japan, 2020. [10] Franc J-P, Michel J-M. Fundamentals of cavitation. Springer Science & Business Media,; 2006. [11] Jayaprakash A, Hsiao C-T, Chahine G. Numerical and experimental study of the interaction of a spark-generated bubble and a vertical wall. J Fluids Eng 2012;134: 031301. [12] Kim K-H, Chahine G, Franc J-P, Karimi A. Advanced experimental and numerical techniques for cavitation erosion prediction. Springer,; 2014. [13] Philipp A, Lauterborn W. Cavitation erosion by single laser-produced bubbles. J Fluid Mech 1998;361:75–116. [14] Zhang A, Cui P, Wang Y. Experiments on bubble dynamics between a free surface and a rigid wall. Exp Fluids 2013;54:1602. [15] Soh W, Willis B. A flow visualization study on the movements of solid particles propelled by a collapsing cavitation bubble. Exp Therm Fluid Sci 2003;27:537–44. [16] Arora M, Ohl C-D, Mørch KA. Cavitation inception on microparticles: a selfpropelled particle accelerator. Phys Rev Lett 2004;92:174501. [17] Wu S, Zuo Z, Stone HA, Liu S. Motion of a free-settling spherical particle driven by a laser-induced bubble. Phys Rev Lett 2017;119:084501. [18] Poulain S, Guenoun G, Gart S, Crowe W, Jung S. Particle motion induced by bubble cavitation. Phys Rev Lett 2015;114:214501. [19] Teran LA, Laín S, Jung S, Rodríguez SA. Surface damage caused by the interaction of particles and a spark-generated bubble near a solid wall. Wear 2019;438: 203076. [20] Teran LA, Rodríguez SA, Laín S, Jung S. Interaction of particles with a cavitation bubble near a solid wall. Phys Fluids 2018;30:123304. [21] Plesset MS, Chapman RB. Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary. J Fluid Mech 1971;47:283–90. [22] Chahine GL, Hsiao C-T. Modelling cavitation erosion using fluid–material interaction simulations. Interface Focus 2015;5:20150016. [23] Johnsen E, Colonius T. Numerical simulations of non-spherical bubble collapse. J Fluid Mech 2009;629:231–62. [24] Osterman A, Dular M, Sirok B. Numerical simulation of a near-wall bubble collapse in an ultrasonic field. J Fluid Sci Technol 2009;4:210–21. [25] Schnerr GH, Sauer J. Physical and numerical modeling of unsteady cavitation dynamics. Fourth Int Conf Multiph Flow, ICMF N Orleans 2001. [26] Supponen O, Obreschkow D, Kobel P, Farhat M. Detailed jet dynamics in a collapsing bubble, Journal of Physics. Conf Ser, IOP Publ 2015:012038. [27] Li S. Cavitation enhancement of silt erosion—an envisaged micro model. Wear 2006;260:1145–50. [28] Dunstan P, Li S. Cavitation enhancement of silt erosion: Numerical studies. Wear 2010;268:946–54. [29] Teran LA, Laín S, Rodríguez SA. Synergy effect modelling of cavitation and hard particle erosion: Implementation and validation. Wear 2021;478:203901. [30] Li S, Li L. Computational investigation of baffle influence on windage loss in helical geared transmissions. Tribology Int 2021;156:106852. [31] ANSYS, Fluent Theory Guide, Release 16.1, ANSYS, Inc., Canonsburg, 2015. [32] Brackbill JU, Kothe DB, Zemach C. A continuum method for modeling surface tension. J Comput Phys 1992;100:335–54. [33] Teran LA, Larrahondo FJ, Rodríguez SA. Performance improvement of a 500-kW Francis turbine based on CFD. Renew Energy 2016;96:977–92. [34] ANSYS, Fluent User’s Guide, Release 16.1, ANSYS, Inc., Canonsburg, 2015. [35] Ghobadian A, Vasquez S. A general purpose implicit coupled algorithm for the solution of eulerian multiphase transport equation. Int Conf Multiph Flow, Leipz, Ger 2007. [36] Zambrano O, García D, Rodríguez S, Coronado J. The mild-severe wear transition in erosion wear. Tribology Lett 2018;66:95. [37] Teran L, Roa C, Munoz-Cubillos ˜ J, Aponte R, Valdes J, Larrahondo F, Rodríguez S, Coronado J. Failure analysis of a run-of-the-river hydroelectric power plant. Eng Fail Anal 2016;68:87–100. |
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Laín Beatove, Santiagovirtual::5341-1Terán, Leonel A.Rodríguez, Sara A.2024-04-19T13:36:40Z2024-04-19T13:36:40Z2023-02Laín Beatove, S.; Teran, L. A.; Rodríguez, S. A. (2023). Prediction of the particle’s impact velocity due to the bubble–particle interaction causing synergic wear. Tribology International. volume 180. p.p. 1-12. https://doi.org/10.1016/j.triboint.2023.1082610301-679Xhttps://hdl.handle.net/10614/15549https://doi.org/10.1016/j.triboint.2023.108261Universidad Autónoma de OccidenteRespositorio Educativo Digital UAOhttps://red.uao.edu.co/Cavitation damage and hard particle erosion are some of the main sources of wear in most hydraulic machines, such as pumps or hydroturbines. However, the synergic effect of these two phenomena leads to a wear phenomenon that is often more severe than the sum of the individual effects of cavitation and hard particle erosion and that has been scarcely studied. Therefore, in this work, simplified computational fluid dynamics (CFD) simulations using 2D and 3D approaches were performed to investigate the behaviour of a particle interacting with a cavitation bubble near a solid wall under several conditions of pressure, position, bubble maximum size, and mass of the particle. All the involved variables were combined into three nondimensional variables: the dependent variable includes the impact velocity of the particle normal to the surface, while the other two variables include the particle position relative to the eroded wall and the particle mass. Through this approach, several correlations were identified, and a dimensionless function of two variables and six fitting factors was proposed to comply with those correlations. Then, this function was returned to its dimensional form to obtain an expression to predict the impact velocity of a particle normal to the solid wall due its interaction with a collapsing bubble12 páginasapplication/pdfengElsevierPaíses BajosDerechos reservados - Elsevier, 2023https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)http://purl.org/coar/access_right/c_abf2Prediction of the particle’s impact velocity due to the bubble–particle interaction causing synergic wearArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85121180Tribology International[1] Haosheng C, Jiadao W, Darong C. Cavitation damages on solid surfaces in suspensions containing spherical and irregular microparticles. Wear 2009;266: 345–8.[2] Hu H, Zheng Y. The effect of sand particle concentrations on the vibratory cavitation erosion. Wear 2017;384:95–105.[3] Huang S, Ihara A, Watanabe H, Hashimoto H. Effects of solid particle properties on cavitation erosion in solid-water mixtures. J Fluids Eng 1996;118:749–55.[4] Romero R, Teran L, Coronado J, Ladino J, Rodríguez S. Synergy between cavitation and solid particle erosion in an ultrasonic tribometer. Wear 2019;428:395–403.[5] Yan D, Wang J, Liu F. Inhibition of the ultrasonic microjet-pits on the carbon steel in the particles-water mixtures. AIP Adv 2015;5:077159.[6] Amarendra H, Chaudhari G, Nath S. Synergy of cavitation and slurry erosion in the slurry pot tester. Wear 2012;290:25–31.[7] Amarendra H, Hallalli GB, Madhusudhana G, Mahendra H, Athani MK. Effect of cavitation inducers’ apex angle on erosion[8] Thapa B, Chaudhary P, Dahlhaug OG, Upadhyay P. Study of combined effect of sand erosion and cavitation in hydraulic turbines. Int Conf Small HydropowerHydro Sri Lanka 2007:24.[9] K. Su, D. Xia, Z. Ding, Cavitation damage in particle-laden liquids with considering particle concentration and size, 22nd IAHR-APD Congress, Sapporo, Japan, 2020.[10] Franc J-P, Michel J-M. Fundamentals of cavitation. Springer Science & Business Media,; 2006.[11] Jayaprakash A, Hsiao C-T, Chahine G. Numerical and experimental study of the interaction of a spark-generated bubble and a vertical wall. J Fluids Eng 2012;134: 031301.[12] Kim K-H, Chahine G, Franc J-P, Karimi A. Advanced experimental and numerical techniques for cavitation erosion prediction. Springer,; 2014.[13] Philipp A, Lauterborn W. Cavitation erosion by single laser-produced bubbles. J Fluid Mech 1998;361:75–116.[14] Zhang A, Cui P, Wang Y. Experiments on bubble dynamics between a free surface and a rigid wall. Exp Fluids 2013;54:1602.[15] Soh W, Willis B. A flow visualization study on the movements of solid particles propelled by a collapsing cavitation bubble. Exp Therm Fluid Sci 2003;27:537–44.[16] Arora M, Ohl C-D, Mørch KA. Cavitation inception on microparticles: a selfpropelled particle accelerator. Phys Rev Lett 2004;92:174501.[17] Wu S, Zuo Z, Stone HA, Liu S. Motion of a free-settling spherical particle driven by a laser-induced bubble. Phys Rev Lett 2017;119:084501.[18] Poulain S, Guenoun G, Gart S, Crowe W, Jung S. Particle motion induced by bubble cavitation. Phys Rev Lett 2015;114:214501.[19] Teran LA, Laín S, Jung S, Rodríguez SA. Surface damage caused by the interaction of particles and a spark-generated bubble near a solid wall. Wear 2019;438: 203076.[20] Teran LA, Rodríguez SA, Laín S, Jung S. Interaction of particles with a cavitation bubble near a solid wall. Phys Fluids 2018;30:123304.[21] Plesset MS, Chapman RB. Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary. J Fluid Mech 1971;47:283–90.[22] Chahine GL, Hsiao C-T. Modelling cavitation erosion using fluid–material interaction simulations. Interface Focus 2015;5:20150016.[23] Johnsen E, Colonius T. Numerical simulations of non-spherical bubble collapse. J Fluid Mech 2009;629:231–62.[24] Osterman A, Dular M, Sirok B. Numerical simulation of a near-wall bubble collapse in an ultrasonic field. J Fluid Sci Technol 2009;4:210–21.[25] Schnerr GH, Sauer J. Physical and numerical modeling of unsteady cavitation dynamics. Fourth Int Conf Multiph Flow, ICMF N Orleans 2001.[26] Supponen O, Obreschkow D, Kobel P, Farhat M. Detailed jet dynamics in a collapsing bubble, Journal of Physics. Conf Ser, IOP Publ 2015:012038.[27] Li S. Cavitation enhancement of silt erosion—an envisaged micro model. Wear 2006;260:1145–50.[28] Dunstan P, Li S. Cavitation enhancement of silt erosion: Numerical studies. Wear 2010;268:946–54.[29] Teran LA, Laín S, Rodríguez SA. Synergy effect modelling of cavitation and hard particle erosion: Implementation and validation. Wear 2021;478:203901.[30] Li S, Li L. Computational investigation of baffle influence on windage loss in helical geared transmissions. Tribology Int 2021;156:106852.[31] ANSYS, Fluent Theory Guide, Release 16.1, ANSYS, Inc., Canonsburg, 2015.[32] Brackbill JU, Kothe DB, Zemach C. A continuum method for modeling surface tension. J Comput Phys 1992;100:335–54.[33] Teran LA, Larrahondo FJ, Rodríguez SA. Performance improvement of a 500-kW Francis turbine based on CFD. Renew Energy 2016;96:977–92.[34] ANSYS, Fluent User’s Guide, Release 16.1, ANSYS, Inc., Canonsburg, 2015.[35] Ghobadian A, Vasquez S. A general purpose implicit coupled algorithm for the solution of eulerian multiphase transport equation. Int Conf Multiph Flow, Leipz, Ger 2007.[36] Zambrano O, García D, Rodríguez S, Coronado J. The mild-severe wear transition in erosion wear. Tribology Lett 2018;66:95.[37] Teran L, Roa C, Munoz-Cubillos ˜ J, Aponte R, Valdes J, Larrahondo F, Rodríguez S, Coronado J. Failure analysis of a run-of-the-river hydroelectric power plant. Eng Fail Anal 2016;68:87–100.Computational fluid dynamicsBubble-particle interactionCavitationHard particle ErosionSynergyParticle’s impact velocityComunidad generalPublication082b0926-3385-4188-9c6a-bbbed7484a95virtual::5341-1082b0926-3385-4188-9c6a-bbbed7484a95virtual::5341-1https://scholar.google.com/citations?user=g-iBdUkAAAAJ&hl=esvirtual::5341-10000-0002-0269-2608virtual::5341-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000262129virtual::5341-1ORIGINALLICENSElicense.txtlicense.txttext/plain; charset=utf-81672https://red.uao.edu.co/bitstreams/ec2717a4-10eb-416b-8fae-c81cbff8d8e4/download6987b791264a2b5525252450f99b10d1MD5210614/15549oai:red.uao.edu.co:10614/155492024-10-17 11:22:33.007https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos reservados - Elsevier, 2023metadata.onlyhttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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 |