Abstract
Piano Key (PK) and trapezoidal labyrinth (TL) weirs are nonlinear control structures suitable for narrow channels with high discharge by expanding the crest length of the overflow. In open channels, high discharge flows can increase flow velocity and erode the downstream riverbed. This study investigates the discharge performance, flow characteristics, and energy dissipation over PK and TL weirs under free-flow conditions using the FLOW-3D software. The FLOW-3D model was validated by comparing the experimental data of two heights of type-A PK weirs with the numerical simulation. A good agreement was found between experimental and numerical results, with Mean-Absolute-Percentage-Error (MAPE) values for two PK weirs of 2.24% and 5.78%, which indicate an acceptable precision to simulate the flow over weirs. After this step, two scenarios were presented. In the first scenario, the geometric properties of the two PK weir heights were modified to achieve the optimum hydraulic and best economic designs based on previous recommended geometric parameters, then compared to the same-height TL and linear weirs. In the second scenario, the best economic PK weir was compared to TL weirs with three sidewall angles of 12, 20, and 30°. Overall, sixty-six and twelve simulations were run for the first and second scenarios, respectively. Results demonstrated that linear weirs had the lowest discharge and energy performance compared to PK and TL weirs. In terms of discharge performance, PK weirs are preferred over TL weirs at lower headwater ratios (H/P ≤ 0.20), while TL weirs with smaller angles (α ≤ 12°) are recommended at higher ratios (H: upstream head above weir crest, P: weir height). Energy dissipation rates of TL weirs increase as the sidewall angle increases; thus, TL weirs with larger angles (α > 12°) are recommended over PK weirs. Increasing the weir height by 1.66 times enhances the energy dissipation rate by 24% for all weir types. Finally, PK and TL weirs gain a new performance as energy dissipators since they dissipate energy close to the maximum limit.
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References
Al-Shukur AHK, Al-Khafaji GH (2018) Experimental study of the hydraulic performance of piano key weir. Int J Energy Environ 9(1):63–70
Anderson RM (2011) Piano key weir head discharge relationships. All Graduate Theses and Dissertations. Paper 880. Utah State University School of Graduate Studies, USA
Arjenaki MO, Sanayei HRZ (2020) Numerical investigation of energy dissipation rate in stepped spillways with lateral slopes using experimental model development approach. Model Earth Syst Environ 6:605–616. https://doi.org/10.1007/s40808-020-00714-z
ASCE (2009) Verification and validation of 3D free-surface flow models. Task Committee on 3D free-surface flow model verification and validation. Environmental and Water Resources Institute (EWRI), Reston, VA
Bekheet AA, AboulAtta NM, Saad NY, El-Molla DA (2022) Effect of the shape and type of piano key weirs on the flow efficiency. Ain Shams Engineering Journal 13(3):101620. https://doi.org/10.1016/j.asej.2021.10.015
Ben Said M, Hafnaoui MA, Madi M (2023) Numerical analysis of the influence of approach flow conditions on the efficiency of labyrinth weir. Model Earth Syst Environ 9(1):41–51. https://doi.org/10.1007/s40808-022-01443-1
Chahartaghi MK, Nazari S, Shooshtari MM (2019) Experimental and numerical simulation of arced trapezoidal piano key weirs. Flow Meas Instr 68:101576. https://doi.org/10.1016/j.flowmeasinst.2019.101576
Chamani MR, Rajaratnam N, Beirami MK (2008a) Turbulent jet energy dissipation at vertical drops. J Hydraul Eng 134(10):1532–1535
Chamani MR, Beyrami M, Rajaratnam N, Dehghani AA (2008b) Characteristics of subcritical flow over vertical drops with sloping aprons. Iran J Sci Technol Trans B Eng 32(B5):531–542
Chow VT (1959) Open channel hydraulics. McGraw-Hill, New York
Crookston BM, Tullis BP (2012) Labyrinth weirs: nappe interference and local submergence. J Irrig Drain Eng 138(8):757–765. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000466
Crookston BM, Tullis BP (2013) Hydraulic design and analysis of labyrinth weirs I: discharge Relationships. J Irrig Drain Eng 139(5):363–370. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000558
Crookston BM, Anderson RM, Tullis BP (2018) Free-flow discharge estimation method for Piano Key weir geometries. Journal of Hydro-Environment Research 19:160–167. https://doi.org/10.1016/j.jher.2017.10.003
Crookston BM, Erpicum S, Tullis BP, Laugier F (2019) Hydraulics of labyrinth and piano key weirs: 100 years of prototype structures, advancements, and future research needs. J Hydraul Eng 145(12):02519004. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001646
Crookston BM (2010) Labyrinth weirs. Ph.D. dissertation, Utah State University, Logan, UT
Dabling MR, Tullis BP (2012) Piano key weir submergence in channel applications. J Hydraul Eng 138(7):661–666. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000563
Elsayed K, Lacor C (2011) Numerical modeling of the flow field and performance in cyclones of different cone-tip diameters. Comput Fluids 51(1):48–59. https://doi.org/10.1016/j.compfluid.2011.07.010
Eslinger RK, Crookston BM (2020) Energy dissipation of type a piano key weirs. Water 12(5):1253. https://doi.org/10.3390/w12051253
Farhadi H, Moghadam MK, Sabzevari T, Noroozpour S (2023) Study of relative energy dissipation of trapezoidal and arced piano key weirs equipped with baffles. Water Supply 23(1):80–93. https://doi.org/10.2166/ws.2022.427
Flow Science (2016) Incorporated: FLOW-3D user's manual version 11.2. Santa Fe, New Mexico
Ghaderi A, Abbasi S (2021) Experimental and numerical study of the effects of geometric appendance elements on energy dissipation over stepped spillway. Water 13(7):957. https://doi.org/10.3390/w13070957
Ghaderi A, Daneshfaraz D, Abbasi S, Abraham J (2020a) Numerical analysis of the hydraulic characteristics of modified labyrinth weirs. Int J Water Res 4:425–436. https://doi.org/10.1007/s42108-020-00082-5
Ghaderi A, Daneshfaraz R, Dasineh M, Di Francesco S (2020b) Energy dissipation and hydraulics of flow over trapezoidal–triangular labyrinth Weirs. Water 12(7):1992. https://doi.org/10.3390/w12071992
Ghaderi A, Dasineh M, Aristodemo F, Ghahramanzadeh A (2020c) Characteristics of free and submerged hydraulic jumps over different microroughness. J Hydroinf 22(6):1554–1572. https://doi.org/10.2166/hydro.2020.298
Ghaderi A, Dasineh M, Abbasi S, Abraham J (2020d) Investigation of trapezoidal sharp-crested side weir discharge coefficients under subcritical flow regimes using CFD. Appl Water Sci 10(1):1–12. https://doi.org/10.1007/s13201-019-1112-8
Ghanbari R, Heidarnejad M (2020) Experimental and numerical analysis of flow hydraulics in triangular and rectangular piano key weirs. Water Sci 34(1):32–38. https://doi.org/10.1080/11104929.2020.1724649
Habili MJ, Heidarpour M, Samiee S (2018) Study of energy dissipation and downstream flow regime of labyrinth weirs. Iran J Sci Technol Trans Civ Eng 42(2):111–119. https://doi.org/10.1007/s40996-017-0088-6
Hirt CW, Sicilian JM (1985) A porosity technique for the definition of obstacles in rectangular cell meshes. In International Conference on Numerical Ship Hydrodynamics, 4th
Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39:201–225. https://doi.org/10.1016/0021-9991(81)90145-5
Idrees AK, Al-Ameri R (2023) Investigation of flow characteristics and energy dissipation over new shape of the trapezoidal labyrinth weirs. Flow Meas Instr 89:102276. https://doi.org/10.1016/j.flowmeasinst.2022.102276
Khanahmadi E, Dehghani AA, Alenabi SN, Dehghani N, Barry E (2023) Hydraulic of curved type-B piano key weirs characteristics under free flow conditions. Model Earth Syst Environ. https://doi.org/10.1007/s40808-023-01790-7
Kumar M, Sihag P, Tiwari NK, Ranjan S (2020) Experimental study and modelling discharge coefficient of trapezoidal and rectangular piano key weirs. Appl Water Sci 10(1):43. https://doi.org/10.1007/s13201-019-1104-8
Lempérière F, Vigny JP, Ouamane A (2011) General comments on labyrinth and piano key weirs: The past and present. Proceedings of the International Conference Labyrinth and Piano Key Weirs, Liège B, 17–24. CRC Press, Boca Raton FL
Lempérière F, Ouamane A (2003) The Piano Keys weir: a new cost-effective solution for spillways. Int J Hydropower Dams 10(5):144–149
Li S, Li G, Jiang D (2020) Physical and numerical modeling of the hydraulic characteristics of type-A piano key weirs. J Hydraul Eng 146(5):06020004. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001716
Lopes R, Matos J, Melo JF (2006) Discharge capacity and residual energy of labyrinth weirs. In: Proceedings of the international junior researcher and engineer workshop on hydraulic structures (IJREWHS' 06), Hydraulic Model Report No. CH61/06, Div. of Civil Engineering, the University of Queensland, Brisbane, Australia, 47–55
Machiels O, Pirotton M, Pierre A, Dewals B, Erpicum S (2014) Experimental parametric study and design of piano key weirs. J Hydraul Res 52(3):326–335. https://doi.org/10.1080/00221686.2013.875070
Machiels O (2012) Experimental study of the hydraulic behavior of piano key weirs. Ph.D. thesis. HECE Research Unit, University of Liège, Belgium. http://hdl.handle.net/2268/128006
Magalhães AP, Lorena M (1994) Perdas de energiado do escoamento sobre soleiras em labirinto, Proc. 68 SILUSB/18 SILUSBA, 203–211, Lisboa, Portugal (in Portuguese)
Mahabadi NA, Sanayei HRZ (2020) Performance evaluation of bilateral side slopes in piano key weirs by numerical simulation. Model Earth Syst Environ 6:1477–1486. https://doi.org/10.1007/s40808-020-00764-3
Mattos-Villarroel ED, Ojeda-Bustamante W, Díaz-Delgado C, Salinas-Tapia H, Flores-Velázquez J, Bautista Capetillo C (2023) Methodological proposal for the hydraulic design of Labyrinth Weirs. Water 15(4):722. https://doi.org/10.3390/w15040722
Ouamane A, Lemperiere F (2006) Design of a new economic shape of weir. In: International symposium on dams in the societies of the 21st century, Barcelona, Espana, 1: 463–470
Reclamation UBO (1955) Research studies on stilling basins, energy dissipators and associated appurtenances. Hydraul Lab Rep 2:393–438
Ribeiro L, Pfister M, Schleiss AJ, Boillat AL (2012a) Hydraulic design of A-type piano key weirs. J Hydraul Res 50(4):400–408. https://doi.org/10.1080/00221686.2012.695041
Ribeiro L, Bieri M, Boillat JL, Schleiss AJ, Singhal G, Sharma N (2012b) Discharge capacity of piano key weirs. J Hydraul Eng 138(2):199–203. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000490
Safarzadeh A, Noroozi B (2017) 3D hydrodynamics of trapezoidal piano key spillways. Int J Civ Eng 15(1):89–101. https://doi.org/10.1007/s40999-016-0100-8
Samadi A, Salmasi F, Arvanaghi H, Mousaviraad M (2022) Effects of geometrical parameters on labyrinth weir hydraulics. J Irrig Drain Eng 148(10):06022006. https://doi.org/10.1061/(ASCE)IR.1943-4774.0001695
Savage BM, Crookston BM, Paxson GS (2016) Physical and numerical modeling of large headwater ratios for a 15 labyrinth spillway. J Hydraul Eng 142(11):04016046. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001186
Singh D, Kumar M (2022) Energy dissipation of flow over the type-b piano key weir. Flow Meas Instr 83:102109. https://doi.org/10.1016/j.flowmeasinst.2021.102109
Solidworks (2020) https://www.solidworks.com/ (accessed on 6 October 2022)
Tullis JP, Nosratollah A, Waldron D (1995) Design of labyrinth spillways. J Hydraul Eng 121(3):247–255. https://doi.org/10.1061/(ASCE)0733-9429(1995)121:3(247)
Yakhot V, Orszag SA, Thangam S, Gatski TB, Speziale C (1992) Development of turbulence models for shear flows by a double expansion technique. Phys Fluids A 4(7):1510–1520. https://doi.org/10.1063/1.858424
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All authors contributed to the study conception and design. Materials preparation, data collection, validation, and writing the first draft of the manuscript were performed by AKH. Review, editing, and commented on previous versions of the manuscript by MGE and TS. Read and approved the final manuscript by ME.
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Selim, T., Hamed, A.K., Elkiki, M. et al. Numerical investigation of flow characteristics and energy dissipation over piano key and trapezoidal labyrinth weirs under free-flow conditions. Model. Earth Syst. Environ. 10, 1253–1272 (2024). https://doi.org/10.1007/s40808-023-01844-w
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DOI: https://doi.org/10.1007/s40808-023-01844-w