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...

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Autores:
Coronado-Hernández, Oscar E.
Fuertes-Miquel, Vicente S.
Quiñones-Bolaños, Edgar
Gustavo, Gatica
Coronado-Hernandez, Jairo R.
Tipo de recurso:
Article of journal
Fecha de publicación:
2020
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/7326
Acceso en línea:
https://hdl.handle.net/11323/7326
https://repositorio.cuc.edu.co/
Palabra clave:
Hydraulic transients
Air-water interface
Air valves
Bernoulli’s equation
Draining
Rights
openAccess
License
CC0 1.0 Universal
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oai_identifier_str oai:repositorio.cuc.edu.co:11323/7326
network_acronym_str RCUC2
network_name_str REDICUC - Repositorio CUC
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, Oscar E.
Fuertes-Miquel, Vicente S.
Quiñones-Bolaños, Edgar
Gustavo, Gatica
Coronado-Hernandez, Jairo R.
dc.contributor.author.spa.fl_str_mv Coronado-Hernández, Oscar E.
Fuertes-Miquel, Vicente S.
Quiñones-Bolaños, Edgar
Gustavo, Gatica
Coronado-Hernandez, Jairo R.
dc.subject.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 2020-11-18T15:19:16Z
dc.date.available.none.fl_str_mv 2020-11-18T15:19:16Z
dc.date.issued.none.fl_str_mv 2020-09-11
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.doi.spa.fl_str_mv doi:10.3390/w12092544
dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv REDICUC - Repositorio CUC
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identifier_str_mv 2073-4441
doi:10.3390/w12092544
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
url https://hdl.handle.net/11323/7326
https://repositorio.cuc.edu.co/
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.references.spa.fl_str_mv 1. Fuertes-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. [CrossRef]
2. 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. [CrossRef]
3. 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. [CrossRef]
4. 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. [CrossRef]
5. Ramezani, L.; Karney, B.; Malekpour, A. Encouraging Effective Air Management in Water Pipelines: A Critical Review. J. Water Resour. Plan. Manag. 2016, 142, 04016055. [CrossRef]
6. Zhou, L.; Liu, D. Experimental Investigation of Entrapped Air Pocket in a Partially Full Water Pipe. J. Hydraul. Res. 2013, 51, 469–474. [CrossRef]
7. Carlos, M.; Arregui, F.J.; Cabrera, E.; Palau, C.V. Understanding Air Release through Air Valves. J. Hydraul. Eng. 2011, 137, 461–469. [CrossRef]
8. 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, 2001.
9. Bianchi, A.; Mambretti, S.; Pianta, P. Practical Formulas for the Dimensioning of Air Valves. J. Hydraul. Eng. 2007, 133, 1177–1180. [CrossRef]
10. Ramezani, L.; Karney, B.; Malekpour, A. The Challenge of Air Valves: A Selective Critical Literature Review. J. Water Resour. Plan. Manag. 2016, 141, 04015017. [CrossRef]
11. 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. [CrossRef]
12. 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.
13. 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. [CrossRef]
14. 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. [CrossRef]
15. 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.
16. 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.
17. Vasconcelos, J.G.; Wright, S.J. Rapid Flow Startup in Filled Horizontal Pipelines. J. Hydraul. Eng. 2008, 134, 984–992. [CrossRef]
18. 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. [CrossRef]
19. Wang, L.; Wang, F.; Lei, X. Investigation on Friction Models for Simulation of Pipeline Filling Transients. J. Hydraul. Res. 2018, 56, 888–895. [CrossRef]
20. 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. [CrossRef]
21. 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. [CrossRef]
22. Wylie, E.; Streeter, V. Fluid Transients in Systems; Prentice Hall: Englewood Cliffs, NJ, USA, 1993.
23. Chaudhry, M.H. Applied Hydraulic Transients, 3rd ed.; Springer: New York, NY, USA, 2014.
24. 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.
25. León, A.; Ghidaoui, M.; Schmidt, A.; García, M. A Robust Two-equation Model for Transient-mixed Flows. J. Hydraul. Res. 2010, 48, 44–56. [CrossRef]
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spelling Coronado-Hernández, Oscar E.Fuertes-Miquel, Vicente S.Quiñones-Bolaños, EdgarGustavo, GaticaCoronado-Hernandez, Jairo R.2020-11-18T15:19:16Z2020-11-18T15:19:16Z2020-09-112073-4441https://hdl.handle.net/11323/7326doi:10.3390/w12092544Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/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.Coronado-Hernández, Oscar E.-will be generated-orcid-0000-0002-6574-0857-600Fuertes-Miquel, Vicente S.-will be generated-orcid-0000-0003-3524-2555-600Quiñones-Bolaños, Edgar-will be generated-orcid-0000-0002-2833-8455-600Gustavo, Gatica-will be generated-orcid-0000-0002-1816-6856-600Coronado-Hernandez, Jairo R.-will be generated-orcid-0000-0003-4360-6128-600application/pdfengCorporación Universidad de la CostaCC0 1.0 Universalhttp://creativecommons.org/publicdomain/zero/1.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Waterhttps://www.mdpi.com/2073-4441/12/9/2544Hydraulic transientsAir-water interfaceAir valvesBernoulli’s equationDrainingSimplified mathematical model for computing draining operations in pipelines of undulating profiles with vacuum air valvesArtículo 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/acceptedVersion1. Fuertes-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. [CrossRef]2. 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. [CrossRef]3. 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. [CrossRef]4. 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. [CrossRef]5. Ramezani, L.; Karney, B.; Malekpour, A. Encouraging Effective Air Management in Water Pipelines: A Critical Review. J. Water Resour. Plan. Manag. 2016, 142, 04016055. [CrossRef]6. Zhou, L.; Liu, D. Experimental Investigation of Entrapped Air Pocket in a Partially Full Water Pipe. J. Hydraul. Res. 2013, 51, 469–474. [CrossRef]7. Carlos, M.; Arregui, F.J.; Cabrera, E.; Palau, C.V. Understanding Air Release through Air Valves. J. Hydraul. Eng. 2011, 137, 461–469. [CrossRef]8. 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, 2001.9. Bianchi, A.; Mambretti, S.; Pianta, P. Practical Formulas for the Dimensioning of Air Valves. J. Hydraul. Eng. 2007, 133, 1177–1180. [CrossRef]10. Ramezani, L.; Karney, B.; Malekpour, A. The Challenge of Air Valves: A Selective Critical Literature Review. J. Water Resour. Plan. Manag. 2016, 141, 04015017. [CrossRef]11. 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. [CrossRef]12. 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, 2010.13. 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. [CrossRef]14. 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. [CrossRef]15. 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, 07020002.16. 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, 2018.17. Vasconcelos, J.G.; Wright, S.J. Rapid Flow Startup in Filled Horizontal Pipelines. J. Hydraul. Eng. 2008, 134, 984–992. [CrossRef]18. 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. [CrossRef]19. Wang, L.; Wang, F.; Lei, X. Investigation on Friction Models for Simulation of Pipeline Filling Transients. J. Hydraul. Res. 2018, 56, 888–895. [CrossRef]20. 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. [CrossRef]21. 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. [CrossRef]22. Wylie, E.; Streeter, V. Fluid Transients in Systems; Prentice Hall: Englewood Cliffs, NJ, USA, 1993.23. Chaudhry, M.H. Applied Hydraulic Transients, 3rd ed.; Springer: New York, NY, USA, 2014.24. 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 1996.25. León, A.; Ghidaoui, M.; Schmidt, A.; García, M. A Robust Two-equation Model for Transient-mixed Flows. J. Hydraul. Res. 2010, 48, 44–56. 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