Abstract
A piano key weir (PK weir) is a non-linear, labyrinth-type weir that benefits of a high discharge capacity, and is well suited for low head dams. Determination of the discharge coefficient (Cd) is considered as one of the most important issues, which plays a substantial role in reducing structural and financial damages caused by floods. The main aim of the present study is to experimentally investigate the variations of PK weirs discharge coefficient (Cd) through altering the geometric parameters. The obtained results revealed that in modified PK weirs (by an 11.5% increase in weir height, changing the crest shape, and fillet installation), the Cd values were about 5–15% more than those of the standard PK weirs. The Cd values of the non-contracted weirs were increased by increasing the inlet/outlet width ratio by 1.4, while this relation was adverse for contracted weirs. In the modified PK weirs, the submergence would occur faster than the standard weirs, while the complete submergence would occur later. Moreover, robust kernel-based approaches (kernel extreme learning machine and support vector machine) were successfully employed to the extensive experimental dataset by taking into consideration the Cd as a function of dimensionless geometric variables of PK weirs. The obtained results showed that the ratio of the upstream hydraulic head (H0) to total weir height (P) plays a significant role in the modeling process.
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Data Availability
The data and materials that support the findings of this study are available on request from the corresponding author.
Abbreviations
- PK weir:
-
Piano Key weir
- Cd :
-
Discharge coefficient
- H0 :
-
Upstream hydraulic head (m)
- Hd :
-
Downstream hydraulic head (m)
- H* :
-
Total submerged-flow upstream head (m)
- P:
-
Total weir height (m)
- Bi/Bo :
-
Length of inlet/outlet cantilever overhang
- Wi/Wo :
-
Inlet to outlet width ratio
- Lc :
-
Length of crest centerline (m)
- Si :
-
Inlet slope
- So :
-
Outlet slope
- W:
-
Total width of weir (m)
- B:
-
Weir length (m)
- Ts :
-
Wall thickness
- N:
-
Cycles number
- Pi :
-
Height of the inlet at entrance measured from the PK weir crest (m)
- Po :
-
Height of the outlet at entrance measured from the PK weir crest (m)
- Pb :
-
Height of the apron level at inlet key (m)
- Pb :
-
Outlet key intersection (m)
- Pb :
-
Height of parapet wall in modified PK weir (m)
- Q:
-
Flow discharge passing over the PK weir (m3/sec)
- ρ:
-
Density
- ν:
-
Kinematic viscosity
- σ:
-
Surface tension
- g:
-
Acceleration of gravity (m/s2)
- V:
-
Velocity (m/s)
References
Abhash A, Pandey KK (2021)Experimental and Numerical Study of Discharge Capacity and Sediment Profile Upstream of Piano Key Weirs with Different Plan Geometries Water Resour Manag 1–18 https://doi.org/10.1007/s11269-021-02800-y
Akbari M, Salmasi F, Arvanaghi H, Karbasi M, Farsadizadeh D (2019) Application of Gaussian Process Regression Model to Predict Discharge Coefficient of Gated Piano Key Weir. Water Resour Manag 33:3929–3947. https://doi.org/10.1007/s11269-019-02343-3
Anderson RM (2011) Piano key weir head discharge relationships, Dissertation, Utah State University
Anderson RM, Tullis BP (2013) Piano key weir hydraulics and labyrinth weir comparison. J Irrig Drain Eng 139:246–253. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000530
Azamathulla HM, Haghiabi AH, Parsaie A (2016) Prediction of side weir discharge coefficient by support vector machine technique. Water Sci Tech-W Sup 16:1002–1016. https://doi.org/10.2166/ws.2016.014
Barcouda M, Cazaillet O, Cochet P, Jones BA, Lacroix S, Laugier F, Odeyer C, Vigny JP (2006) Cost effective increase in storage and safety of most dams using fusegates or PK Weirs. In Transactions of the International Congress on Large Dams
Blanc P, Lempérière F (2001) Labyrinth spillways have a promising future. Int J Hydropower Dams 8:129–131
Dabling MR (2014) Nonlinear weir hydraulics. Dissertation, Utah State University.
Dabling MR, Tullis BP (2012) Piano key weir submergence in channel applications. J Hydraul Eng 138:661–666. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000563
Denys F (2019) Investigation into flow-induced vibrations of Piano Key Weirs. dissertation, Stellenbosch University.
Emiroglu ME, Kisi O (2013) Prediction of discharge coefficient for trapezoidal labyrinth side weir using a neuro-fuzzy approach. Water Resour Manag 27:1473–1488. https://doi.org/10.1007/s11269-012-0249-0
Erpicum S, Nagel V, Laugier F (2011) Piano Key Weir design study at Raviege dam, Labyrinth and Piano Key Weirs – PKW 2011, CRC Press Taylor & Francis group 43–50
Francis JB (1884) Experiments on the flow of water over submerged weirs. Trans Am Soc Civil Eng 13: 303–312
Fteley A, Stearns FP (1883) Description of Some Experiments on the Flow of Water, Made During the Construction of Works for Conveying the Water of Sudbury River to Boston. Trans Am Soc Civil Eng 12:1–118
Han D, Chan L, Zhu N (2007) Flood forecasting using support vector machines. J Hydroinformatics 9:267–276. https://doi.org/10.2166/hydro.2007.027
Henderson FM (1966) Open Channel Flow. Macmillan, New York, USA
Hoosen S (2017) The benefits of combining geometric attributes from Labyrinth and Piano key weirs. Dissertation, University of the Witwatersrand.
Huang GB, Zhou H, Ding X, Zhang R (2011) Extreme learning machine for regression and multiclass classification. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 42: 513–5299. https://doi.org/10.1109/TSMCB.2011.2168604
Kabiri-Samani A, Ansari A, Borghei SM (2010) Hydraulic behaviour of flow over an oblique weir. J Hydraul Res 48:669–673. https://doi.org/10.1080/00221686.2010.507358
Khatibi R, Salmasi F, Ghorbani MA, Asadi H (2014) Modelling energy dissipation over stepped-gabion weirs by artificial intelligence. Water Resour Manag 28:1807–1821. https://doi.org/10.1007/s11269-014-0545-y
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 10:1–9. https://doi.org/10.1007/s13201-019-1104-8
Laugier F (2007) Design and construction of the first Piano Key Weir spillway at Goulours dam. Int J Hydropower Dams 14:94
Laugier F, Lochu A, Gille C, Leite Ribeiro M, Boillat JL (2009) Design and construction of a labyrinth PKW spillway at Saint-Marc dam, France. Int J Hydropower Dams 16: 100-107.
Lempérière F, Jun G (2005) Low cost increase of dams storage and flood mitigation: The piano keys weir. In: Proc. of 19th Congress of ICID.
Lempérière F, Ouamane A (2003) The Piano Keys weir: a new cost-effective solution for spillways. Int J Hydropower Dams 10:144–149
Li K, Xu W, Han Y, Ge F (2020a) A hybrid modeling method for interval time prediction of the intermittent pumping well based on IBSO-KELM. Measurement 151:107214. https://doi.org/10.1016/j.measurement.2019.107214
Li S, Li G, Jiang D, Ning J (2020b) Influence of auxiliary geometric parameters on discharge capacity of piano key weirs. Flow Meas Instrum 72:101719. https://doi.org/10.1016/j.flowmeasinst.2020.101719
Lombaard j (2020) Evaluation of the Influence of Aeration on the Discharge Capacity and Flow Induced Vibrations of Piano Key Weir Spillways. Dissertation, Stellenbosch University.
Machiels O, Erpicum S, Dewals BJ, Archambeau P, Pirotton M (2011) Experimental observation of flow characteristics over a Piano Key Weir. J Hydraul Res 49:359–366. https://doi.org/10.1080/00221686.2011.567761
Mehboudi A, Attari J, Hosseini SA (2016) Experimental study of discharge coefficient for trapezoidal piano key weirs. Flow Meas Instrum 50:65–72. https://doi.org/10.1016/j.flowmeasinst.2016.06.005
Mousavimehr SM, Yamini OA, Kavianpour MR (2021) Performance Assessment of Shockwaves of Chute Spillways in Large Dams. Shock and Vibration 2021:1-17
Novák P, Čábelka J (1981) Models in hydraulic engineering: Physical principles and design applications. Pitman Publishing, London
Olyaie E, Banejad H, Heydari M (2019) Estimating discharge coefficient of PK-weir under subcritical conditions based on high-accuracy machine learning approaches. IJST-T Civ Eng 43:89–101. https://doi.org/10.1007/s40996-018-0150-z
Ouamane A, Lempérière F (2006) Design of a new economic shape of weir. In: Proceedings of21 the International Symposium on Dams in the Societies of the 21st Century.
Pal M, Goel A (2007) Estimation of discharge and end depth in trapezoidal channel by support vector machines. Water Resour Manag 21:1763–1780. https://doi.org/10.1007/s11269-006-9126-z
Parsaie A, Haghiabi A (2015) The effect of predicting discharge coefficient by neural network on increasing the numerical modeling accuracy of flow over side weir. Water Resour Manag 29:973–985. https://doi.org/10.1007/s11269-014-0827-4
Pralong J, Vermeulen J, Blancher B, Laugier F, Erpicum S, Machiels O, Pirotton M, Boillat JL, Leite Ribeiro M, Schleiss AJ (2011) A naming convention for the Piano Key Weirs geometrical parameters. Labyrinth and piano key weirs 271–278
Rostami H, Heidarnejad M, Hosein Purmohammadi M, Kamanbedast A, Bordbar A (2018) Laboratory Study of Discharge Coefficients of One and Two-Cycle Piano Key Weir and Comparison of them with Rectangular Labyrinth Weir. Irrigation and Drainage Structures Engineering Research 19 (2018) 51–66. In Persian. https://doi.org/10.22092/IDSER.2018.110112.1203
Roushangar K, Alami MT, Shiri J, Majedi Asl M (2018) Determining discharge coefficient of labyrinth and arced labyrinth weirs using support vector machine. Hydrol Res 49:924–938. https://doi.org/10.2166/nh.2017.214
Roushangar K, Shahnazi S (2019) Bed load prediction in gravel-bed rivers using wavelet kernel extreme learning machine and meta-heuristic methods. Int J Environ Sci Technol 16:8197–8208. https://doi.org/10.1007/s13762-019-02287-6
Seyedjavad M, Naeeni STO, Saneie M (2019) Laboratory investigation on discharge coefficient of trapezoidal piano key side weirs. Civ Eng J 5: 1327–1340. https://doi.org/10.28991/cej-2019-03091335
Tullis BP, Young JC, Chandler MA (2007) Head-discharge relationships for submerged labyrinth weirs. J Hydraul Eng 133:248–254. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:3(248)
Vapnik V (1998) Statistical Learning Theory. Wiley, New York
Vayghan VH, Saber A, Mortazavian S (2019) Modification of classical horseshoe spillways: Experimental study and design optimization. Civ Eng J 5: 2093–2109. https://doi.org/10.28991/cej-2019-03091396
Zerihun YT, Fenton JD (2007) A Boussinesq-type model for flow over trapezoidal profile weirs. J Hydraul Res 45:519–528. https://doi.org/10.1080/00221686.2007.9521787
Zounemat-Kermani M, Mahdavi-Meymand A (2019) Hybrid meta-heuristics artificial intelligence models in simulating discharge passing the piano key weirs. J Hydrol 569:12–21. https://doi.org/10.1016/j.jhydrol.2018.11.052
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K.R. conceived the study and were in charge of overall direction and planning. M.M.A performed the experiments and contributed to the interpretation of the results. S.S. took the lead in writing the manuscript and carried out the kernel-based modeling. All authors provided critical feedback and helped shape the research, analysis and manuscript.
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Roushangar, K., Majedi Asl, M. & Shahnazi, S. Hydraulic Performance of PK Weirs Based on Experimental Study and Kernel-based Modeling. Water Resour Manage 35, 3571–3592 (2021). https://doi.org/10.1007/s11269-021-02905-4
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DOI: https://doi.org/10.1007/s11269-021-02905-4