Parametric study of flow at circular piano-key inlets over the vertical shaft spillways

References

• Ackers, J., Bennett, F., Scott, T., & Karunaratne, G. (2013). Raising the bellmouth spillway at Black Esk reservoir using Piano Key weirs. In S. Erpicum, F. Laugier, M. Pfister, M. Pirotton, G.-M. Cicero, & A. J. Schleiss (Eds.), Labyrinth Piano Key Weirs II- PKW 2013 (pp. 235–242). Liege: CRC Press.
   Google Scholar
• Ackers, J., Gethin, D., Karunaratne, G., Pryce, S., Scott, T., Tudhope, J., & Wheeler, M. (2014). The design and construction of an enlargement scheme for Black Esk reservoir (Scotland). Proceedings of the 18th Biennial Conference of the British Dam Society: Maintaining the Safety of our Dams and Reservoirs. Belfast, 336–347.
   Google Scholar
• Andersen, A., Bohr, T., Stenum, B., & Rasmussen, J. J. (2006). The bathtub vortex in a rotating container. Journal of Fluid Mechanics, 556, 121–146. doi:10.1017/S0022112006009463
   Web of Science ®Google Scholar
• Anderson, R., & Tullis, B. (2011). Comparison of piano key and rectangular labyrinth weir hydraulics. Journal of Hydraulic Engineering, 138(4), 358–361. doi:10.1061/(ASCE)HY.1943-7900.0000509
   Web of Science ®Google Scholar
• Anwar, H. O., Weller, J. A., & Amphlett, M. B. (1978). Similarity of free vortex at horizontal intake. Journal of Hydraulic Research, 16(2), 95–106. doi:10.1080/00221687809499623
   Web of Science ®Google Scholar
• Aydin, M. C., & Ulu, A. E. (2023). Numerical investigation of labyrinth-shaft spillway. Applied Water Science, 13(89), 1–12.
   Google Scholar
• Barcouda, M., Cazaillet, O., Cochet, P., & Jones, B. A. (2006, June 18–23). Cost effective increase in storage and safety of most dams using fusegates or P.K. weirs. Proceedings of 22nd ICOLD Congress, Barcelona, Catalonia, Spain.
   Google Scholar
• Borghei, S. M., & Kabiri-Samani, A. R. (2010). Effect of anti-vortex plates on critical submergence at a vertical. Sientia Iranica, 17(2), 89–95.
   Web of Science ®Google Scholar
• Chan, S. N., Guo, J., & Lee, J. H. W. (2022). Physical and numerical modeling of swirling flow in a scroll vortex intake. Journal of Hydro-environment Research, 40, 64–76. doi:10.1016/j.jher.2021.11.004
   Web of Science ®Google Scholar
• Chang, E. (1977). Review of literature on drain vortices in cylindrical tanks. BHRA, Cranfield, UK, Report TN1342.
   Google Scholar
• Christodoulou, G., Mavrommatis, A., & Papathanassiadis, T. (2010, May 4–6). Experimental study on the effect of piers and boundary proximity on the discharge capacity of a Morning glory spillway. 1st IAHR European Congress, Edinburgh, Scotland.
   Google Scholar
• Cicero, G. M., Barcouda, M., Luck, M., & Vettori, E. (2011). Study of piano-key Morning glory to increase the spillway capacity of the Bage dam. In S. Erpicum, F. Laugier, M. Pfister, M. Pirotton, G.-M. Cicero, & A. J. Schleiss (Eds.), Labyrinth and Piano Key Weirs (pp. 81–86). Liege: CRC Press.
   Google Scholar
• Crookston, B. M., Erpicum, S., Tullis, B. P., & Laugier, F. (2019, August 27–31). Hydraulic of labyrinth and piano key weirs: 100 years of prototype structures, advancements, and future research needs. Journal of Hydraulic Engineering, 145(12), 02519004-1–02519004-7. doi:10.1061/(ASCE)HY.1943-7900.0001646
   Web of Science ®Google Scholar
• Daggett, L. L., & Keulegan, G. H. (1974). Similitude in free-surface vortex formations. Journal of Hydraulic Division, 100(11), 1565–1581. doi:10.1061/JYCEAJ.0004105
   Google Scholar
• Duinmeijer, A., Oldenziel, G., & Clemens, F. (2020). Experimental study on the 3D-flow field of a free-surface vortex using stereo PIV. Journal of Hydraulic Research, 58(1), 105–119. doi:10.1080/00221686.2018.1555558
   Web of Science ®Google Scholar
• Echavez, G., & McCann, E. (2002). An experimental study on the free-surface vertical vortex. Experiments in Fluids, 33(3), 414–421. doi:10.1007/s00348-002-0463-2
   Web of Science ®Google Scholar
• Falvey, H. T. (1980). Air-water flow in hydraulic structures. Engineering Monograph, 41. Water and Power Resources Service.
   Google Scholar
• Hashid, M., & Ahmad, Z. (2022). Critical submergence for horizontal dual water intakes under perpendicular uniform approach flow. Journal of Hydraulic Engineering, 148(10), https://doi.org/10.1061/(ASCE)HY.1943-7900.0002016
   Web of Science ®Google Scholar
• Hite, E. J., & Mih, W. C. (1994). Velocity of air-core vortices at hydraulic intakes. Journal of Hydraulic Engineering, 120(3), 284–297. doi:10.1061/(ASCE)0733-9429(1994)120:3(284)
   Web of Science ®Google Scholar
• Jain, A. K., Ranga Raju, K. G., & Garde, R. J. (1978). Vortex formation in vertical pipe intakes. Journal of Hydraulic Division, 104(10), 1429–1448. doi:10.1061/JYCEAJ.0005087
   Web of Science ®Google Scholar
• Kabiri-Samani, A. R., & Borghei, S. M. (2013). Effects of anti-vortex plates on air entrainment by free vortex. Scientia Iranica, 20(2), 251–258.
   Web of Science ®Google Scholar
• Kabiri-Samani, A. R., Jafarinasab, N., & Sheikh Khozani, Z. (2023). Relationship between two-phase flow in bottom outlet and air-core vortices at intake. Proceedings of the Institution of Civil Engineers-Water Management. Published Online, https://doi.org/10.1680/jwama.21.00055.
   Google Scholar
• Kabiri-Samani, A. R., & Javaheri, A. (2012). Discharge coefficients for free and submerged flow over piano key weirs. Journal of Hydraulic Research, 50(1), 114–120. doi:10.1080/00221686.2011.647888
   Web of Science ®Google Scholar
• Kabiri-Samani, A. R., & Keihanpour, M. (2021). Hydraulic characteristics of swirling flow at shaft spillways with the marguerite-shaped inlets. Journal of Hydraulic Research, 59(5), 724–738. doi:10.1080/00221686.2020.1818313
   Web of Science ®Google Scholar
• Keihanpour, M., & Kabiri-Samani, A. R. (2021). Effects of modern marguerite-shaped inlets on hydraulic characteristics of swirling flow in shaft spillways. Water Science and Engineering, 14(3), 246–256. doi:10.1016/j.wse.2021.08.005
   Web of Science ®Google Scholar
• Khanarmuei, M., Rahimzadeh, H., & Sarkardeh, H. (2019). Effect of dual intake direction on critical submergence and vortex strength. Journal of Hydraulic Research, 57(2), 272–279. doi:10.1080/00221686.2018.1459896
   Web of Science ®Google Scholar
• Knauss, J. (1987). Swirling flow problems at intakes, 13–38. IAHR Hydraulic Structures Manual 1. Balkema.
   Google Scholar
• Liu, T. (2014). Modelling air-water flows in bottom outlets of dams. KTH Royal Institute of Technology. http://www.diva-portal.org/smash/record.jsf?pid=diva2%3A695501anddswid=-4019
   Google Scholar
• Loisel, P. E., Duval, F., & Chanourdie, S. (2013). Hydraulic scale model of the daisy-shape spillway on the Causse Corrézien dam. In Labyrinth and Piano Key Weirs II, PKW2013 (vol. 55, pp. 177–184). Taylor & Francis Group. doi:10.1201/b15985-25.
   Google Scholar
• Ma, Y., Li, P., Zhu, D. Z., & Khan, A. (2022). Air flow inside a vertical pipe induced by a free-falling water jet. Journal of Hydro-environment Research, 44, 23–34. doi:10.1016/j.jher.2022.07.003
   Web of Science ®Google Scholar
• Machiels, O., Pirotton, M., Pierre, A., Dewals, B., & Erpicum, S. (2014). Experimental parametric study and design of piano key weirs. Journal of Hydraulic Research, 52(3), 326–335. doi:10.1080/00221686.2013.875070
   Web of Science ®Google Scholar
• Mosalman Yazdi, A., Hoseini, S. A., Nazari, S., & Amanian, N. (2020). Effects of weir geometry on scour development in the downstream of Piano Key weirs. Water Supply, 21(1), 289–298. doi:10.2166/ws.2020.272
   Google Scholar
• Nasiri, S., Kabiri-Samani, A. R., Asghari, K., & Bagheri, S. (2022). Numerical modelling of flow field at shaft spillways with circular piano-key inlets. Proceedings of the Institution of Civil Engineers-Water Management, 175(3), 111–122. doi:10.1680/jwama.19.00085
   Web of Science ®Google Scholar
• Novak, P., & Cabelka, J. (1981). Models in hydraulic engineering, physical principles and design applications. Pitman Publication.
   Google Scholar
• Odgaard, A. J. (1986). Free-surface air core vortex. Journal of Hydraulic Engineering, 112(7), 610–620. doi:10.1061/(ASCE)0733-9429(1986)112:7(610)
   Web of Science ®Google Scholar
• Rankine, W. J. M. (1876). Manual of applied mechanics. Griffin.
   Google Scholar
• Ribeiro, M. L., Bieri, M., Boillat, J.-L., Schleiss, A. J., Delorme, F., & Laugier, F. (2009, August 27–31). Hydraulic capacity improvement of existing spillways: Design of piano key weirs. Proceedings of 23rd ICOLD Congress, Brasilia, Q90 (R43), 25–29.
   Google Scholar
• Ribeiro, M. L., Pfister, M., Schleiss, A. J., & Boillat, J.-L. (2012). Hydraulic design of A-type piano key weirs. Journal of Hydraulic Research, 50(4), 400–408. doi:10.1080/00221686.2012.695041
   Web of Science ®Google Scholar
• Sangsefidi, Y., Tavakol-Davani, H., Ghodsian, M., Mehraein, M., & Zarei, R. (2021). Hydrodynamics and free-flow characteristics of piano key weirs with different plan shapes. Water, 13(15), https://doi.org/10.3390/w13152108
   Web of Science ®Google Scholar
• Sarkardeh, H. (2017). Numerical calculation of air entrainment rates due to intake vortices. Meccanica, 52(15), 3629–3643. doi:10.1007/s11012-017-0687-0
   Web of Science ®Google Scholar
• Sarkardeh, H., Zarrati, A. R., & Roshan, R. (2010). Effect of intake head wall and trash rack on vortices. Journal of Hydraulic Research, 48(1), 108–112. doi:10.1080/00221680903565952
   Web of Science ®Google Scholar
• Schliess, A. J. (2011). From labyrinth to piano key weirs – A historical review. In S. Erpicum, F. Laugier, M. Pfister, M. Pirotton, G.-M. Cicero, & A. J. Schleiss (Eds.), Labyrinth and Piano Key Weirs – PKW2011 (pp. 3–15). Liege: CRC Press.
   Google Scholar
• Schliess, A. J., Erpicum, S., & Matos, J. (2023). Advances in spillway hydraulics: from theory to practice. Water, 15(12), https://doi.org/10.3390/w15122161
   Web of Science ®Google Scholar
• Shemshi, R., & Kabiri-Samani, A. R. (2017). Swirling flow at vertical shaft spillways with circular piano-key inlets. Journal of Hydraulic Research, 55(2), 248–258. doi:10.1080/00221686.2016.1238015
   Web of Science ®Google Scholar
• Sun, H., & Liu, Y. (2015). Theoretical and experimental study on the vortex at hydraulic intakes. Journal of Hydraulic Research, 53(6), 787–796. doi:10.1080/00221686.2015.1076533
   Web of Science ®Google Scholar
• Taştan, K., & Yildirim, N. (2018). Effects of intake geometry on the occurrence of a free-surface vortex. Journal of Hydraulic Engineering, 144(4), https://doi.org/10.1061/(ASCE)HY.1943-7900.0001439
   Web of Science ®Google Scholar
• Taştan, K., & Yıldırım, N. (2023). Improved equations for the profile of a vertical air-core vortex. KSCE Journal of Civil Engineering, 27(5), 2030–2042. doi:10.1007/s12205-023-0811-8
   Web of Science ®Google Scholar
• USBR. (1987). Design of small dams. U.S. Department of the Interior, Bureau of Reclamation.
   Google Scholar
• Yang, J., Liu, T., Bottacin-Busolin, A., & Lin, C. (2014). Effects of intake-entrance profiles on free-surface vortices. Journal of Hydraulic Research, 52(4), 523–531. doi:10.1080/00221686.2014.905504
   Web of Science ®Google Scholar
• Yildirim, N., & Kocabas, F. (2002). Prediction of critical submergence for an intake pipe. Journal of Hydraulic Research, 40(4), 507–518. doi:10.1080/00221680209499892
   Web of Science ®Google Scholar
• Yildirim, N., Tastan, K., & Arslan, M. M. (2009). Critical submergence for dual pipe intakes. Journal of Hydraulic Research, 47(2), 242–249. doi:10.3826/jhr.2009.3352
   Web of Science ®Google Scholar