{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:22:28Z","timestamp":1760145748345,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,16]],"date-time":"2024-08-16T00:00:00Z","timestamp":1723766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"HY4RES (Hybrid Solutions for Renewable Energy Systems)","award":["EAPA_0001\/2022"],"award-info":[{"award-number":["EAPA_0001\/2022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fluids"],"abstract":"<jats:p>Water utilities are concerned about the issue of pipeline collapses, as service interruptions lead to water shortages. Pipeline collapses can occur during the maintenance phase when water columns compress entrapped air pockets, consequently increasing the pressure head. Analysing entrapped air pockets is complex due to the necessity of numerically solving a system of differential equations. Currently, water utilities need more tools to perform this analysis effectively. This research provides a numerical solution to the problem of entrapped air pockets in pipelines which can be utilised to predict filling operations. The study develops an analytical solution to examine the filling process. A practical application is shown, considering a 600 m long pipeline with an internal diameter of 400 mm. Compared with existing mathematical models, the results of the new analytical equations demonstrate their effectiveness as a new tool for computing the main hydraulic and thermodynamic variables involved in this issue.<\/jats:p>","DOI":"10.3390\/fluids9080185","type":"journal-article","created":{"date-parts":[[2024,8,16]],"date-time":"2024-08-16T09:15:41Z","timestamp":1723799741000},"page":"185","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Proposed Approach for Modelling the Thermodynamic Behaviour of Entrapped Air Pockets in Water Pipeline Start-Up"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2198-8703","authenticated-orcid":false,"given":"Dalia M.","family":"Bonilla-Correa","sequence":"first","affiliation":[{"name":"Facultad de Ciencias Exactas y Naturales, Universidad de Cartagena, Cartagena 131001, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6574-0857","authenticated-orcid":false,"given":"Oscar E.","family":"Coronado-Hern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Instituto de Hidr\u00e1ulica y Saneamiento Ambiental, Universidad de Cartagena, Cartagena 131001, Colombia"}]},{"given":"Alfonso","family":"Arrieta-Pastrana","sequence":"additional","affiliation":[{"name":"Instituto de Hidr\u00e1ulica y Saneamiento Ambiental, Universidad de Cartagena, Cartagena 131001, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8316-7778","authenticated-orcid":false,"given":"Modesto","family":"P\u00e9rez-S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Hidr\u00e1ulica y Medio Ambiente, 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, Architecture and Environment Department, CERIS, Instituto Superior T\u00e9cnico, University of Lisbon, 1049-001 Lisbon, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1080\/00221689909498518","article-title":"Pipeline Start-up with Entrapped Air","volume":"37","author":"Izquierdo","year":"1999","journal-title":"J. Hydraul. Res."},{"key":"ref_2","first-page":"2238853","article-title":"Experiments and Numerical Analysis of the Dynamic Flow Characteristics of a Pump\u2212pipeline System with Entrapped Air during Start-Up","volume":"17","author":"Li","year":"2023","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1080\/1573062X.2019.1669188","article-title":"Hydraulic Modeling during Filling and Emptying Processes in Pressurized Pipelines: A Literature Review","volume":"16","year":"2019","journal-title":"Urban Water J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"547","DOI":"10.3826\/jhr.2009.3390","article-title":"Investigation of Rapid Filling of Poorly Ventilated Stormwater Storage Tunnels","volume":"47","author":"Vasconcelos","year":"2009","journal-title":"J. Hydraul. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1061\/(ASCE)0733-9429(2002)128:6(625)","article-title":"Transient Flow in a Rapidly Filling Horizontal Pipe Containing Trapped Air","volume":"128","author":"Zhou","year":"2002","journal-title":"J. Hydraul. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"031301","DOI":"10.1115\/1.4031508","article-title":"Improved One-Dimensional Models for Rapid Emptying and Filling of Pipelines","volume":"138","author":"Tijsseling","year":"2015","journal-title":"J. Press. Vessel Technol."},{"key":"ref_7","first-page":"127","article-title":"Simulation of Flow Transients in a Water Filling Pipe Containing Entrapped Air Pocket with VOF Model","volume":"5","author":"Zhou","year":"2011","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_8","first-page":"1444","article-title":"Three-Dimensional CFD Analysis of Liquid Slug Acceleration and Impact in a Voided Pipeline with End Orifice","volume":"16","author":"He","year":"2022","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"04015044","DOI":"10.1061\/(ASCE)HY.1943-7900.0001067","article-title":"Physical Understanding of Sudden Pressurization of Pipe Systems with Entrapped Air: Energy Auditing Approach","volume":"142","author":"Malekpour","year":"2016","journal-title":"J. Hydraul. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1154","DOI":"10.1061\/(ASCE)0733-9429(1999)125:11(1154)","article-title":"Flow Modeling in Pressurized Systems Revisited","volume":"125","author":"Abreu","year":"1999","journal-title":"J. Hydraul. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wan, W., Zhang, B., and Chen, X. (2019). Investigation on Water Hammer Control of Centrifugal Pumps in Water Supply Pipeline Systems. Energies, 12.","DOI":"10.3390\/en12010108"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"06020018","DOI":"10.1061\/(ASCE)HY.1943-7900.0001849","article-title":"Rigid-Column Model for Rapid Filling in a Partially Filled Horizontal Pipe","volume":"147","author":"Biao","year":"2021","journal-title":"J. Hydraul. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1080\/1573062X.2024.2346727","article-title":"Attenuation of Pipeline Filling Over-Pressures through Trapped Air","volume":"21","author":"Tasca","year":"2024","journal-title":"Urban Water J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4020022","DOI":"10.1061\/(ASCE)HY.1943-7900.0001726","article-title":"Investigation of Manhole Cover Displacement during Rapid Filling of Stormwater Systems","volume":"146","author":"Wang","year":"2020","journal-title":"J. Hydraul. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Bonilla-Correa, D.M., Coronado-Hern\u00e1ndez, \u00d3.E., Fuertes-Miquel, V.S., Besharat, M., and Ramos, H.M. (2023). Application of Newton\u2013Raphson Method for Computing the Final Air\u2013Water Interface Location in a Pipe Water Filling. Water, 15.","DOI":"10.3390\/w15071304"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1686","DOI":"10.1061\/(ASCE)HY.1943-7900.0000460","article-title":"Influence of Entrapped Air Pockets on Hydraulic Transients in Water Pipelines","volume":"137","author":"Zhou","year":"2011","journal-title":"J. Hydraul. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ferras, D., Manso, P.A., Schleiss, A.J., and Covas, D.I. (2018). One-dimensional fluid\u2013structure interaction models in pressurized fluid-filled pipes: A review. Appl. Sci., 8.","DOI":"10.20944\/preprints201809.0049.v1"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Feng, Y., Yi, H., and Liu, R. (2024). Analytical Solution for Transient Electroosmotic and Pressure-Driven Flows in Microtubes. Fluids, 9.","DOI":"10.3390\/fluids9060140"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"041301","DOI":"10.1115\/1.4043321","article-title":"Rapid Liquid Filling of a Pipe With Venting Entrapped Gas: Analytical and Numerical Solutions","volume":"141","author":"Tijsseling","year":"2019","journal-title":"J. Press. Vessel Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1061\/(ASCE)HY.1943-7900.0000765","article-title":"Phenomenon of White Mist in Pipelines Rapidly Filling with Water with Entrapped Air Pockets","volume":"139","author":"Zhou","year":"2013","journal-title":"J. Hydraul. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Coronado-Hern\u00e1ndez, \u00d3.E., Besharat, M., Fuertes-Miquel, V.S., and Ramos, H.M. (2019). Effect of a Commercial Air Valve on the Rapid Filling of a Single Pipeline: A Numerical and Experimental Analysis. Water, 11.","DOI":"10.3390\/w11091814"},{"key":"ref_22","unstructured":"Martin, C.S. (1977). Entrapped Air in Pipelines."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Budak, H., Hezenci, F., Kara, H., and Sarikaya, M.Z. (2023). Bounds for the Error in Approximating a Fractional Integral by Simpson\u2019s Rule. Mathematics, 11.","DOI":"10.3390\/math11102282"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Huang, B., Fan, M., Liu, J., and Zhu, D.Z. (2021, January 7\u201311). CFD Simulation of Air\u2013Water Interactions in Rapidly Filling Horizontal Pipe with Entrapped Air. Proceedings of the World Environmental and Water Resources Congress, Virtual.","DOI":"10.1061\/9780784483466.045"}],"container-title":["Fluids"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2311-5521\/9\/8\/185\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:37:48Z","timestamp":1760110668000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2311-5521\/9\/8\/185"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,16]]},"references-count":24,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["fluids9080185"],"URL":"https:\/\/doi.org\/10.3390\/fluids9080185","relation":{},"ISSN":["2311-5521"],"issn-type":[{"type":"electronic","value":"2311-5521"}],"subject":[],"published":{"date-parts":[[2024,8,16]]}}}