{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T05:17:16Z","timestamp":1787807836511,"version":"build-2784847793"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T00:00:00Z","timestamp":1787616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The National Key R&D Program of China","award":["2023YFC3206101"],"award-info":[{"award-number":["2023YFC3206101"]}]},{"DOI":"10.13039\/501100001809","name":"The National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["U23A20668"],"award-info":[{"award-number":["U23A20668"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"The National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["52521005"],"award-info":[{"award-number":["52521005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"award":["U23A20668"],"award-info":[{"award-number":["U23A20668"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"award":["52521005"],"award-info":[{"award-number":["52521005"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"name":"The Specialized Research Fund of Nanjing Hydraulic Research Institute","award":["Yy125006"],"award-info":[{"award-number":["Yy125006"]}]},{"award":["Yy125006"],"award-info":[{"award-number":["Yy125006"]}],"id":[{"id":"https:\/\/ror.org\/02403qw73","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The filling-and-emptying valve and downstream shaft are crucial components of navigation-lock systems. Under insufficient downstream submergence, air can be drawn through the shaft and trapped in the post-valve culvert, altering the flow structure and compromising hydraulic stability. A three-dimensional Reynolds-averaged Navier\u2013Stokes\/volume-of-fluid model was developed to investigate shaft aeration and entrapped-air-pocket evolution under varying inlet velocities and downstream-submergence depths. The aeration process comprises three stages: jet establishment, air-pocket formation, and air-pocket breakup and reorganization. Downstream-submergence depth determines whether a continuous air-intake pathway forms, whereas inlet velocity primarily controls aeration intensity and air-pocket persistence once the pathway is established. With decreasing submergence depth, the flow transitions successively from a water-sealed regime to a transition regime, a stable entrapped-air-pocket regime, and a strongly unsteady hydraulic-jump-like regime. For the present geometry and fixed valve opening, the transition from transient to sustained shaft aeration is identified within the downstream-submergence interval of hw = 2\u20135 m. Combined analyses of the air-pocket volume per unit width, pressure response, vortex structures, and shear-layer characteristics indicate that enhanced jet-induced shear is closely associated with shaft aeration and air entrapment, while pressure fluctuations are closely coupled with air-pocket formation, persistence, breakup, and reorganization.<\/jats:p>","DOI":"10.3390\/e28090954","type":"journal-article","created":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T09:04:30Z","timestamp":1787648670000},"page":"954","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Numerical Investigation of Downstream-Shaft Aeration and Air-Pocket Evolution in a Navigation-Lock Valve"],"prefix":"10.3390","volume":"28","author":[{"given":"Tingqiang","family":"Xie","sequence":"first","affiliation":[{"name":"State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China"},{"name":"Hydraulic Engineering Department, Nanjing Hydraulic Research Institute, Nanjing 210029, China"},{"name":"Key Laboratory of Navigation Structures Construction Technology, Nanjing Hydraulic Research Institute, Nanjing 210029, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhonghua","family":"Li","sequence":"additional","affiliation":[{"name":"Hydraulic Engineering Department, Nanjing Hydraulic Research Institute, Nanjing 210029, China"},{"name":"Key Laboratory of Navigation Structures Construction Technology, Nanjing Hydraulic Research Institute, Nanjing 210029, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiujun","family":"Yan","sequence":"additional","affiliation":[{"name":"Hydraulic Engineering Department, Nanjing Hydraulic Research Institute, Nanjing 210029, China"},{"name":"Key Laboratory of Navigation Structures Construction Technology, Nanjing Hydraulic Research Institute, Nanjing 210029, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Deng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-6421-833X","authenticated-orcid":false,"given":"Duo","family":"Xu","sequence":"additional","affiliation":[{"name":"Hydraulic Engineering Department, Nanjing Hydraulic Research Institute, Nanjing 210029, China"},{"name":"Key Laboratory of Navigation Structures Construction Technology, Nanjing Hydraulic Research Institute, Nanjing 210029, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,25]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Hydraulic study of valve with extra long emptying culvert of the Three Gorges Lock\u2019s last chamber (3)\u2014Measures improving the valve working conditions with emergent valve closing","volume":"3","author":"Zhang","year":"2001","journal-title":"Hydro-Sci. 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