Simplified mathematical model for computing draining operations in pipelines of undulating profiles with vacuum air valves
The draining operation involves the presence of entrapped air pockets, which are expanded during the phenomenon occurrence generating drops of sub-atmospheric pressure pulses. Vacuum air valves should inject enough air to prevent sub-atmospheric pressure conditions. Recently, this phenomenon has bee...
- Autores:
-
Coronado Hernández, Óscar Enrique
Fuertes Miquel, Vicente S.
Quiñones-Bolaños, Edgar Eduardo
Gatica, Gustavo
Coronado Hernández, Jairo Rafael
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/9554
- Palabra clave:
- Hydraulic transients
Air-water interface;
Air valves
Bernoulli’s equation
Draining
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
| id |
UTB2_f66bd1055a0e087d0d776eeb07171733 |
|---|---|
| oai_identifier_str |
oai:repositorio.utb.edu.co:20.500.12585/9554 |
| network_acronym_str |
UTB2 |
| network_name_str |
Repositorio Institucional UTB |
| repository_id_str |
|
| dc.title.spa.fl_str_mv |
Simplified mathematical model for computing draining operations in pipelines of undulating profiles with vacuum air valves |
| title |
Simplified mathematical model for computing draining operations in pipelines of undulating profiles with vacuum air valves |
| spellingShingle |
Simplified mathematical model for computing draining operations in pipelines of undulating profiles with vacuum air valves Hydraulic transients Air-water interface; Air valves Bernoulli’s equation Draining |
| title_short |
Simplified mathematical model for computing draining operations in pipelines of undulating profiles with vacuum air valves |
| title_full |
Simplified mathematical model for computing draining operations in pipelines of undulating profiles with vacuum air valves |
| title_fullStr |
Simplified mathematical model for computing draining operations in pipelines of undulating profiles with vacuum air valves |
| title_full_unstemmed |
Simplified mathematical model for computing draining operations in pipelines of undulating profiles with vacuum air valves |
| title_sort |
Simplified mathematical model for computing draining operations in pipelines of undulating profiles with vacuum air valves |
| dc.creator.fl_str_mv |
Coronado Hernández, Óscar Enrique Fuertes Miquel, Vicente S. Quiñones-Bolaños, Edgar Eduardo Gatica, Gustavo Coronado Hernández, Jairo Rafael |
| dc.contributor.author.none.fl_str_mv |
Coronado Hernández, Óscar Enrique Fuertes Miquel, Vicente S. Quiñones-Bolaños, Edgar Eduardo Gatica, Gustavo Coronado Hernández, Jairo Rafael |
| dc.subject.keywords.spa.fl_str_mv |
Hydraulic transients Air-water interface; Air valves Bernoulli’s equation Draining |
| topic |
Hydraulic transients Air-water interface; Air valves Bernoulli’s equation Draining |
| description |
The draining operation involves the presence of entrapped air pockets, which are expanded during the phenomenon occurrence generating drops of sub-atmospheric pressure pulses. Vacuum air valves should inject enough air to prevent sub-atmospheric pressure conditions. Recently, this phenomenon has been studied by the authors with an inertial model, obtaining a complex formulation based on a system composed by algebraic-differential equations. This research simplifies this complex formulation by neglecting the inertial term, thus the Bernoulli’s equation can be used. Results show how the inertial model and the simplified mathematical model provide similar results of the evolution of main hydraulic and thermodynamic variables. The simplified mathematical model is also verified using experimental tests of air pocket pressure, water velocity, and position of the water column |
| publishDate |
2020 |
| dc.date.accessioned.none.fl_str_mv |
2020-11-04T21:51:08Z |
| dc.date.available.none.fl_str_mv |
2020-11-04T21:51:08Z |
| dc.date.issued.none.fl_str_mv |
2020-09-11 |
| dc.date.submitted.none.fl_str_mv |
2020-11-04 |
| dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/article |
| dc.type.hasversion.spa.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
| dc.type.spa.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 |
| status_str |
publishedVersion |
| dc.identifier.citation.spa.fl_str_mv |
Coronado-Hernández, Ó.E.; Fuertes-Miquel, V.S.; Quiñones-Bolaños, E.E.; Gatica, G.; Coronado-Hernández, J.R. Simplified Mathematical Model for Computing Draining Operations in Pipelines of Undulating Profiles with Vacuum Air Valves. Water 2020, 12, 2544. |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/9554 |
| dc.identifier.url.none.fl_str_mv |
https://www.mdpi.com/2073-4441/12/9/2544 |
| dc.identifier.doi.none.fl_str_mv |
10.3390/w12092544 |
| dc.identifier.instname.spa.fl_str_mv |
Universidad Tecnológica de Bolívar |
| dc.identifier.reponame.spa.fl_str_mv |
Repositorio Universidad Tecnológica de Bolívar |
| identifier_str_mv |
Coronado-Hernández, Ó.E.; Fuertes-Miquel, V.S.; Quiñones-Bolaños, E.E.; Gatica, G.; Coronado-Hernández, J.R. Simplified Mathematical Model for Computing Draining Operations in Pipelines of Undulating Profiles with Vacuum Air Valves. Water 2020, 12, 2544. 10.3390/w12092544 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
| url |
https://hdl.handle.net/20.500.12585/9554 https://www.mdpi.com/2073-4441/12/9/2544 |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
| dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| dc.rights.uri.*.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| dc.rights.accessrights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
| dc.rights.cc.*.fl_str_mv |
Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
| rights_invalid_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.extent.none.fl_str_mv |
12 páginas |
| dc.format.mimetype.spa.fl_str_mv |
application/pdf |
| dc.publisher.place.spa.fl_str_mv |
Cartagena de Indias |
| dc.source.spa.fl_str_mv |
Water 2020, 12(9), 2544 |
| institution |
Universidad Tecnológica de Bolívar |
| bitstream.url.fl_str_mv |
https://repositorio.utb.edu.co/bitstream/20.500.12585/9554/1/100.pdf https://repositorio.utb.edu.co/bitstream/20.500.12585/9554/2/license_rdf https://repositorio.utb.edu.co/bitstream/20.500.12585/9554/3/license.txt https://repositorio.utb.edu.co/bitstream/20.500.12585/9554/4/100.pdf.txt https://repositorio.utb.edu.co/bitstream/20.500.12585/9554/5/100.pdf.jpg |
| bitstream.checksum.fl_str_mv |
f4db13e419eb6c9ad2e395d8a75a99e9 4460e5956bc1d1639be9ae6146a50347 e20ad307a1c5f3f25af9304a7a7c86b6 b20f84ab1e56a192fec82ab407900c30 ee25eaa8d8082c16c15de5a259f7565b |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 |
| repository.name.fl_str_mv |
Repositorio Institucional UTB |
| repository.mail.fl_str_mv |
repositorioutb@utb.edu.co |
| _version_ |
1814021786495352832 |
| spelling |
Coronado Hernández, Óscar Enriqueb47200b6-5b93-42e3-b9ee-3c619bcec915Fuertes Miquel, Vicente S.f682be4f-81f2-4a2c-b84a-347dbfe6756fQuiñones-Bolaños, Edgar Eduardodb57cb19-1bb7-46d0-8fa9-2e3fd8fc7de7Gatica, Gustavofe6fa1c9-2c41-4f0b-9b8c-8dbc65eb42a0Coronado Hernández, Jairo Rafael86b71d5d-cfcc-464b-9792-545bb0afd5a52020-11-04T21:51:08Z2020-11-04T21:51:08Z2020-09-112020-11-04Coronado-Hernández, Ó.E.; Fuertes-Miquel, V.S.; Quiñones-Bolaños, E.E.; Gatica, G.; Coronado-Hernández, J.R. Simplified Mathematical Model for Computing Draining Operations in Pipelines of Undulating Profiles with Vacuum Air Valves. Water 2020, 12, 2544.https://hdl.handle.net/20.500.12585/9554https://www.mdpi.com/2073-4441/12/9/254410.3390/w12092544Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThe draining operation involves the presence of entrapped air pockets, which are expanded during the phenomenon occurrence generating drops of sub-atmospheric pressure pulses. Vacuum air valves should inject enough air to prevent sub-atmospheric pressure conditions. Recently, this phenomenon has been studied by the authors with an inertial model, obtaining a complex formulation based on a system composed by algebraic-differential equations. This research simplifies this complex formulation by neglecting the inertial term, thus the Bernoulli’s equation can be used. Results show how the inertial model and the simplified mathematical model provide similar results of the evolution of main hydraulic and thermodynamic variables. The simplified mathematical model is also verified using experimental tests of air pocket pressure, water velocity, and position of the water column12 páginasapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Water 2020, 12(9), 2544Simplified mathematical model for computing draining operations in pipelines of undulating profiles with vacuum air valvesinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1Hydraulic transientsAir-water interface;Air valvesBernoulli’s equationDrainingCartagena de IndiasPúblico generalFuertes-Miquel, V.S.; Coronado-Hernández, Ó.E.; Mora-Melia, D.; Iglesias-Rey, P.L. Hydraulic Modeling during Filling and Emptying Processes in Pressurized Pipelines: A Literature Review. Urban Water J. 2019, 16, 299–311.Fuertes-Miquel, V.S.; Coronado-Hernández, Ó.E.; Iglesias-Rey, P.L.; Mora-Melia, D. Transient Phenomena during the Emptying Process of a Single Pipe with Water-Air Interaction. J. Hydraul. Res. 2019, 57, 318–326.Tijsseling, A.; Hou, Q.; Bozkus, Z.; Laanearu, J. Improved One-Dimensional Models for Rapid Emptying and Filling of Pipelines. J. Press. Vessel Technol. 2016, 138, 031301.Coronado-Hernández, Ó.E.; Fuertes-Miquel, V.S.; Besharat, M.; Ramos, H.M. Subatmospheric Pressure in a Water Draining Pipeline with an Air Pocket. Urban Water J. 2018, 15, 346–352.Ramezani, L.; Karney, B.; Malekpour, A. Encouraging Effective Air Management in Water Pipelines: A Critical Review. J. Water Resour. Plan. Manag. 2016, 142, 04016055.Zhou, L.; Liu, D. Experimental Investigation of Entrapped Air Pocket in a Partially Full Water Pipe. J. Hydraul. Res. 2013, 51, 469–474.Carlos, M.; Arregui, F.J.; Cabrera, E.; Palau, C.V. Understanding Air Release through Air Valves. J. Hydraul. Eng. 2011, 137, 461–469.American Water Works Association (AWWA). Manual of Water Supply Practices-M51: Air-Release, Air-Vacuum, and Combination Air Valves, 1st ed.; American Water Works Association: Denver, CO, USA, 2001Bianchi, A.; Mambretti, S.; Pianta, P. Practical Formulas for the Dimensioning of Air Valves. J. Hydraul. Eng. 2007, 133, 1177–1180.Ramezani, L.; Karney, B.; Malekpour, A. The Challenge of Air Valves: A Selective Critical Literature Review. J. Water Resour. Plan. Manag. 2016, 141, 04015017.Coronado-Hernández, Ó.E.; Fuertes-Miquel, V.S.; Besharat, M.; Ramos, H.M. Experimental and Numerical Analysis of a Water Emptying Pipeline Using Different Air Valves. Water 2017, 9, 98.Koppel, T.; Laanearu, J.; Annus, I.; Raidmaa, M. Using Transient Flow Equations for Modelling of Filling and Emptying of Large-Scale Pipeline. In Proceedings of the 12th Annual Conference on Water Distribution Systems Analysis (WDSA), Tucson, AZ, USA, 12–15 September 2010; American Society of Civil Engineers: Reston, VA, USA, 2010.Laanearu, J.; Annus, I.; Koppel, T.; Bergant, A.; Vuˇckoviˇc, S.; Hou, Q.; van’t Westende, J.M.C. Emptying of Large-Scale Pipeline by Pressurized Air. J. Hydraul. Eng. 2012, 138, 1090–1100.Coronado-Hernández, Ó.E.; Fuertes-Miquel, V.S.; Iglesias-Rey, P.L.; Martínez-Solano, F.J. Rigid Water Column Model for Simulating the Emptying Process in a Pipeline Using Pressurized Air. J. Hydraul. Eng. 2018, 144, 06018004.Coronado-Hernández, Ó.E.; Fuertes-Miquel, V.S.; Iglesias-Rey, P.L.; Martínez-Solano, F.J. Closure to “Rigid Water Column Model for Simulating the Emptying Process in a Pipeline Using Pressurized Air”. J. Hydraul. Eng. 2020, 146, 07020002.Coronado-Hernández, Ó.E.; Fuertes-Miquel, V.S.; Besharat, M.; Ramos, H.M. A Parametric Sensitivity Analysis of Numerically Modelled Piston-Type Filling and Emptying of an Inclined Pipeline with an Air Valve. In Proceedings of the 13th International Conference on Pressure Surges, Bordeaux, France, 14–16 November 2018; BHR Group: Bordeaux, France, 2018.Vasconcelos, J.G.; Wright, S.J. Rapid Flow Startup in Filled Horizontal Pipelines. J. Hydraul. Eng. 2008, 134, 984–992.Vasconcelos, J.G.; Klaver, P.R.; Lautenbach, D.J. Flow Regime Transition Simulation Incorporating Entrapped Air Pocket Effects. Urban Water J. 2015, 6, 488–501.Wang, L.; Wang, F.; Lei, X. Investigation on Friction Models for Simulation of Pipeline Filling Transients. J. Hydraul. Res. 2018, 56, 888–895.Malekpour, A.; Karney, B.W.; Nault, J. Physical Understanding of Sudden Pressurization of Pipe Systems with Entrapped Air: Energy Auditing Approach. J. Hydraul. Eng. 2016, 142, 04015044.Coronado-Hernández, Ó.E.; Fuertes-Miquel, V.S.; Mora-Meliá, D.; Salgueiro, Y. Quasi-static Flow Model for Predicting the Extreme Values of Air Pocket Pressure in Draining and Filling Operations in Single Water Installations. Water 2020, 12, 664.Wylie, E.; Streeter, V. Fluid Transients in Systems; Prentice Hall: Englewood Cliffs, NJ, USA, 1993.Chaudhry, M.H. Applied Hydraulic Transients, 3rd ed.; Springer: New York, NY, USA, 2014.Graze, H.R.; Megler, V.; Hartmann, S. Thermodynamic Behaviour of Entrapped Air in an Air Chamber. In Proceedings of the 7th International Conference on Pressure Surges and Fluid Transients in Pipelines and Open Channels, Harrogate, UK, 16–18 April 1996.León, A.; Ghidaoui, M.; Schmidt, A.; García, M. A Robust Two-equation Model for Transient-mixed Flows. J. Hydraul. Res. 2010, 48, 44–56.http://purl.org/coar/resource_type/c_2df8fbb1ORIGINAL100.pdf100.pdfArtículo principalapplication/pdf6215934https://repositorio.utb.edu.co/bitstream/20.500.12585/9554/1/100.pdff4db13e419eb6c9ad2e395d8a75a99e9MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://repositorio.utb.edu.co/bitstream/20.500.12585/9554/2/license_rdf4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83182https://repositorio.utb.edu.co/bitstream/20.500.12585/9554/3/license.txte20ad307a1c5f3f25af9304a7a7c86b6MD53TEXT100.pdf.txt100.pdf.txtExtracted texttext/plain25926https://repositorio.utb.edu.co/bitstream/20.500.12585/9554/4/100.pdf.txtb20f84ab1e56a192fec82ab407900c30MD54THUMBNAIL100.pdf.jpg100.pdf.jpgGenerated Thumbnailimage/jpeg90772https://repositorio.utb.edu.co/bitstream/20.500.12585/9554/5/100.pdf.jpgee25eaa8d8082c16c15de5a259f7565bMD5520.500.12585/9554oai:repositorio.utb.edu.co:20.500.12585/95542023-05-26 09:42:32.955Repositorio Institucional UTBrepositorioutb@utb.edu.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 |