Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling
The estimation of thermodynamic behavior during filling processes with entrapped air in water pipelines is a complex task as it requires solving a system of algebraic-differential equations. A lot of different numerical methods have been used for this purpose in literature including the rigid water...
- Autores:
-
Bonilla-Correa, Dalia M.
Coronado-Hernández, Óscar E.
Fuertes-Miquel, Vicente S.
Besharat, Mohsen
Ramos, Helena M.
- Tipo de recurso:
- Fecha de publicación:
- 2023
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/12271
- Palabra clave:
- Air; Geysers;
Emptying
LEMB
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling |
| title |
Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling |
| spellingShingle |
Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling Air; Geysers; Emptying LEMB |
| title_short |
Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling |
| title_full |
Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling |
| title_fullStr |
Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling |
| title_full_unstemmed |
Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling |
| title_sort |
Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling |
| dc.creator.fl_str_mv |
Bonilla-Correa, Dalia M. Coronado-Hernández, Óscar E. Fuertes-Miquel, Vicente S. Besharat, Mohsen Ramos, Helena M. |
| dc.contributor.author.none.fl_str_mv |
Bonilla-Correa, Dalia M. Coronado-Hernández, Óscar E. Fuertes-Miquel, Vicente S. Besharat, Mohsen Ramos, Helena M. |
| dc.subject.keywords.spa.fl_str_mv |
Air; Geysers; Emptying |
| topic |
Air; Geysers; Emptying LEMB |
| dc.subject.armarc.none.fl_str_mv |
LEMB |
| description |
The estimation of thermodynamic behavior during filling processes with entrapped air in water pipelines is a complex task as it requires solving a system of algebraic-differential equations. A lot of different numerical methods have been used for this purpose in literature including the rigid water column (RWC) model. The main advantage of the RWC model is its acceptable accuracy with very low computational load. In that context, this research presents the computation of critical points of the physical equations that describe the phenomenon. These points provide information about the final position of the air–water interface. The Newton–Raphson method was then applied to obtain a unique equation that can be used by engineers to directly compute variables such as air pocket pressure and water column length at the end of the hydraulic event. A case study was analyzed to compare the results of the mathematical model with the obtained equation for computing critical points. Both methods provided the same values for the water column length at the end of the hydraulic event. A sensitivity analysis was conducted to identify dependent and non-dependent parameters for evaluating the critical points. The proposed formulation was validated through an experimental set of data. © 2023 by the authors. |
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2023 |
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2023-07-21T15:39:24Z |
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2023-07-21T15:39:24Z |
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2023 |
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2023 |
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info:eu-repo/semantics/draft |
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Bonilla-Correa, D.M.; Coronado-Hernández, Ó.E.; Fuertes-Miquel, V.S.; Besharat, M.; Ramos, H.M. Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling. Water 2023, 15, 1304. https://doi.org/10.3390/w15071304 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/12271 |
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https://doi.org/10.3390/w15071304 |
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Universidad Tecnológica de Bolívar |
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Repositorio Universidad Tecnológica de Bolívar |
| identifier_str_mv |
Bonilla-Correa, D.M.; Coronado-Hernández, Ó.E.; Fuertes-Miquel, V.S.; Besharat, M.; Ramos, H.M. Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling. Water 2023, 15, 1304. https://doi.org/10.3390/w15071304 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
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https://hdl.handle.net/20.500.12585/12271 https://doi.org/10.3390/w15071304 |
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eng |
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eng |
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
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15 páginas |
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Cartagena de Indias |
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Water (Switzerland) |
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Universidad Tecnológica de Bolívar |
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Bonilla-Correa, Dalia M.db642292-e40e-4d2d-b8b3-620338cccabeCoronado-Hernández, Óscar E.b47200b6-5b93-42e3-b9ee-3c619bcec915Fuertes-Miquel, Vicente S.ee591d7a-dc42-4bff-b9db-a19f976e419bBesharat, Mohsen9bc60135-8166-40cd-9250-625e81504c7dRamos, Helena M.55b0330e-7043-4bb2-8745-c564ce43175a2023-07-21T15:39:24Z2023-07-21T15:39:24Z20232023Bonilla-Correa, D.M.; Coronado-Hernández, Ó.E.; Fuertes-Miquel, V.S.; Besharat, M.; Ramos, H.M. Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling. Water 2023, 15, 1304. https://doi.org/10.3390/w15071304https://hdl.handle.net/20.500.12585/12271https://doi.org/10.3390/w15071304Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThe estimation of thermodynamic behavior during filling processes with entrapped air in water pipelines is a complex task as it requires solving a system of algebraic-differential equations. A lot of different numerical methods have been used for this purpose in literature including the rigid water column (RWC) model. The main advantage of the RWC model is its acceptable accuracy with very low computational load. In that context, this research presents the computation of critical points of the physical equations that describe the phenomenon. These points provide information about the final position of the air–water interface. The Newton–Raphson method was then applied to obtain a unique equation that can be used by engineers to directly compute variables such as air pocket pressure and water column length at the end of the hydraulic event. A case study was analyzed to compare the results of the mathematical model with the obtained equation for computing critical points. Both methods provided the same values for the water column length at the end of the hydraulic event. A sensitivity analysis was conducted to identify dependent and non-dependent parameters for evaluating the critical points. The proposed formulation was validated through an experimental set of data. © 2023 by the authors.15 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 (Switzerland)Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Fillinginfo:eu-repo/semantics/articleinfo:eu-repo/semantics/drafthttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/version/c_b1a7d7d4d402bccehttp://purl.org/coar/resource_type/c_2df8fbb1Air; Geysers;EmptyingLEMBCartagena de IndiasTasca, E., Besharat, M., Ramos, H.M., Luvizotto, E., Karney, B. Contribution of Air Management to the Energy Efficiency of Water Pipelines (2023) Sustainability (Switzerland), 15 (5), art. no. 3875. http://www.mdpi.com/journal/sustainability/ doi: 10.3390/su15053875Martins, N.M.C., Soares, A.K., Ramos, H.M., Covas, D.I.C. CFD modeling of transient flow in pressurized pipes (2016) Computers and Fluids, 126, pp. 129-140. Cited 70 times. doi: 10.1016/j.compfluid.2015.12.002Maddahian, R., Shaygan, F., Bucur, D.M. Developing a 1D-3D model to investigate the effect of entrapped air on pressure surge during the rapid filling of a pipe (2021) IOP Conference Series: Earth and Environmental Science, 774 (1), art. no. 012069. Cited 2 times. https://iopscience.iop.org/journal/1755-1315 doi: 10.1088/1755-1315/774/1/012069Fuertes-Miquel, V.S., Coronado-Hernández, O.E., Mora-Meliá, D., Iglesias-Rey, P.L. Hydraulic modeling during filling and emptying processes in pressurized pipelines: a literature review (2019) Urban Water Journal, 16 (4), pp. 299-311. Cited 27 times. http://www.tandf.co.uk/journals/titles/1573062X.asp doi: 10.1080/1573062X.2019.1669188(2016) Manual of Water Supply Practices M51—Air Valves: Air Release, Air/Vacuum and Combination. Cited 9 times. AWWA, Denver, CO, USAZhou, L., Liu, D. Experimental investigation of entrapped air pocket in a partially full water pipe (2013) Journal of Hydraulic Research, 51 (4), pp. 469-474. Cited 37 times. doi: 10.1080/00221686.2013.785985Tijsseling, A.S., Hou, Q., Bozkuş, Z. Rapid Liquid Filling of a Pipe With Venting Entrapped Gas: Analytical and Numerical Solutions (Open Access) (2019) Journal of Pressure Vessel Technology, Transactions of the ASME, 141 (4), art. no. 041301. Cited 11 times. https://pressurevesseltech.asmedigitalcollection.asme.org/journal.aspx doi: 10.1115/1.4043321Liou, C.P., Hunt, W.A. Filling of pipelines with undulating elevation profiles (1996) Journal of Hydraulic Engineering, 122 (10), pp. 534-539. Cited 83 times. http://ascelibrary.org/journal/jhend8 doi: 10.1061/(ASCE)0733-9429(1996)122:10(534)Izquierdo, J., Fuertes, V.S., Cabrera, E., Iglesias, P.L., García-Serra, J. Pipeline start-up with entrapped air (1999) Journal of Hydraulic Research, 37 (5), pp. 579-590. Cited 91 times. http://www.tandfonline.com/toc/tjhr20/current doi: 10.1080/00221689909498518Wang, H., Zhou, L., Liu, D., Karney, B., Wang, P., Xia, L., Ma, J., (...), Xu, C. CFD approach for column separation in water pipelines (Open Access) (2016) Journal of Hydraulic Engineering, 142 (10), art. no. 04016036. Cited 32 times. http://ascelibrary.org/journal/jhend8 doi: 10.1061/(ASCE)HY.1943-7900.0001171Chan, S.N., Cong, J., Lee, J.H.W. 3D numerical modeling of geyser formation by release of entrapped air from horizontal pipe into vertical shaft (2018) Journal of Hydraulic Engineering, 144 (3), art. no. 04017071. Cited 29 times. http://ascelibrary.org/journal/jhend8 doi: 10.1061/(ASCE)HY.1943-7900.0001416Wang, J., Vasconcelos, J.G. Manhole cover displacement caused by the release of entrapped air pockets (2018) Journal of Water Management Modeling, 2018, art. no. C444. Cited 10 times. https://www.chijournal.org/Journals/PDF/C444 doi: 10.14796/JWMM.C444Martins, N.M.C., Delgado, J.N., Ramos, H.M., Covas, D.I.C. Maximum transient pressures in a rapidly filling pipeline with entrapped air using a CFD model (2017) Journal of Hydraulic Research, 55 (4), pp. 506-519. Cited 33 times. http://www.tandfonline.com/toc/tjhr20/current doi: 10.1080/00221686.2016.1275046Tijsseling, A.S., Hou, Q., Bozkus, Z., Laanearu, J. Improved One-Dimensional Models for Rapid Emptying and Filling of Pipelines (Open Access) (2016) Journal of Pressure Vessel Technology, Transactions of the ASME, 138 (3), art. no. 031301. Cited 35 times. http://asmedl.aip.org/PressureVesselTech doi: 10.1115/1.4031508Zhou, L., Cao, Y., Karney, B., Vasconcelos, J.G., Liu, D., Wang, P. Unsteady friction in transient vertical-pipe flow with trapped air (Open Access) (2021) Journal of Hydraulic Research, 59 (5), pp. 820-834. Cited 4 times. http://www.tandfonline.com/toc/tjhr20/current doi: 10.1080/00221686.2020.1844808Zhou, L., Pan, T., Wang, H., Liu, D., Wang, P. Rapid air expulsion through an orifice in a vertical water pipe (Open Access) (2019) Journal of Hydraulic Research, 57 (3), pp. 307-317. Cited 20 times. http://www.tandfonline.com/toc/tjhr20/current doi: 10.1080/00221686.2018.1475427Zhou, L., Cao, Y., Karney, B., Bergant, A., Tijsseling, A.S., Liu, D., Wang, P. Expulsion of Entrapped Air in a Rapidly Filling Horizontal Pipe (2020) Journal of Hydraulic Engineering, 146 (7), art. no. 04020047. Cited 14 times. http://ascelibrary.org/journal/jhend8 doi: 10.1061/(ASCE)HY.1943-7900.0001773Coronado-Hernández, O.E., Bonilla-Correa, D.M., Lovo, A., Fuertes-Miquel, V.S., Gatica, G., Linfati, R., Coronado-Hernández, J.R. An Implicit Formulation for Calculating Final Conditions in Drainage Maneuvers in Pressurized Water Installations (2022) Water (Switzerland), 14 (21), art. no. 3364. Cited 2 times. http://www.mdpi.com/journal/water doi: 10.3390/w14213364Canelon, D.J. Pivoting strategies in the solution of the saint-venant equations (Open Access) (2009) Journal of Irrigation and Drainage Engineering, 135 (1), pp. 96-101. Cited 3 times. doi: 10.1061/(ASCE)0733-9437(2009)135:1(96)Martin, C.S. Entrapped Air in Pipelines Proceedings of the Second International Conference on Pressure Surges. Cited 148 times. London, UK, 22–24 September 1976Chapra, S., Canale, R. (2015) Numerical Methods for Engineers. 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