A modified piano key weir with a rounded nose and a parapet wall (MPKW) can improve the discharge capacity significantly compared to a standard piano key weir. However, the optimum of the inlet/outlet width ratio (Wi/Wo) on the discharge efficiency of MPKW is still not investigated numerically.The present work utilizedthe numerical modeling to investigate and analyze the effects of the inlet/outlet key width ratios on the hydraulic characteristics and discharge capacity of the MPKW. To validate the numerical model with the experimental data, theresults indicate that the average relative error is 2.96%, which confirms that the numerical model is fairly well to predictthe specifications of flow over on the MPKW. Numerical simulation results indicated that the discharge capacity of the MPKW can be improved up to 8.5% by optimizing the Wi/Wo ratio ranging from 1.53 to 1.67 even if the other parameters of the MPKW keep unchanged. A big Wi/Wo ratio generally leads to an increase in discharge capacity at low heads and a little effect on the discharge efficiency at high heads. The discharge efficiency of the inlet and outlet crests increases up to 9.6% for high heads, while discharge efficiency of the lateral crest decreases up to 23.5% compared with the reference model. The findings of the study revealed that the intrinsic influencing mechanism of the Wi/Wo ratio on the discharge performance of MPKWs.
References
[1]
Blanc, P. and Lempérière, F. (2001) Labyrinth Spillways Have a Promising Future. International Journal on Hydropower & Dams, 8, 129-131.
[2]
Lempérière, F. and Ouamane, A. (2003) The Piano Keys Weir: A New Cost-Effective Solution for Spillways. International Journal on Hydropower & Dams, 10, 144-149.
[3]
Anderson, R.M. and Tullis, B.P. (2013) Piano Key Weir Hydraulics and Labyrinth Weir Comparison. Journal of Irrigation and Drainage Engineering, 139, 246-253.
https://doi.org/10.1061/(ASCE)IR.1943-4774.0000530
[4]
Ribeiro, M.L., Bieri, M., Boillat, J.-L., Schleiss, A., Singhal, G. and Sharma, N. (2012) Discharge Capacity of Piano Key Weirs. Journal of Hydraulic Engineering, 138, 199-203. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000490
[5]
Pralong, J., Vermeulen, J., Blancher, B., Laugier, F., Erpicum, S., Machiels, O., Pirotton, M., Boillat, J.-L., Leite Ribeiro, M. and Schleiss, A. (2011) A Naming Convention for the Piano Key Weirs Geometrical Parameters. Proceedings of the International Conference Labyrinth and Piano Key Weirs, Liège, 9-11 February 2011, 271-278.
[6]
Crookston, B.M., Erpicum, S., Tullis, B.P. and Laugier, F. (2019) Hydraulics of Labyrinth and Piano Key Weirs: 100 Years of Prototype Structures, Advancements, and Future Research Needs. Journal of Hydraulic Engineering, 145, Article ID: 02519004.
https://doi.org/10.1061/(ASCE)HY.1943-7900.0001646
[7]
Chero, E., Torabi, M., Zahabi, H., Ghafoorisadatieh, A. and Bina, K. (2019) Numerical Analysis of the Circular Settling Tank. Drinking Water Engineering and Science, 12, 39-44. https://doi.org/10.5194/dwes-12-39-2019
[8]
Crookston, B.M., Anderson, R.M. and Tullis, B.P. (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
[9]
Koken, M., Aydin, I. and Ademoglu, S. (2022) An Iterative Hydraulic Design Methodology Based on Numerical Modeling for Piano Key Weirs. Journal of Hydro- Environment Research, 40, 131-141. https://doi.org/10.1016/j.jher.2022.01.002
[10]
Li, G., Li, S. and Hu, Y. (2020) The Effect of the Inlet/Outlet width Ratio on the Discharge of Piano Key Weirs. Journal of Hydraulic Research, 58, 594-604.
https://doi.org/10.1080/00221686.2019.1647884
[11]
Li, S., Li, G., Jiang, D. and Ning, J. (2020) Influence of Auxiliary Geometric Parameters on Discharge Capacity of Piano Key Weirs. Flow Measurement and Instrumentation, 72, Article ID: 101719.
https://doi.org/10.1016/j.flowmeasinst.2020.101719
[12]
Machiels, O., Pirotton, M., Pierre, A., Dewals, B. and Erpicum, S. (2014) Experimental Parametric Study and Design of Piano Key Weirs. Journal of Hydraulic Research, 52, 326-335. https://doi.org/10.1080/00221686.2013.875070
[13]
Erpicum, S., Archambeau, P., Pirotton, M. and Dewals, B. (2014) Geometric Parameters Influence on Piano Key Weir Hydraulic Performances. 5th IAHR International Symposium on Hydraulic Structures, Brisbane, 25-27 June 2014.
https://doi.org/10.14264/uql.2014.31
[14]
Anderson, R.M. (2011) Piano Key Weir Head Discharge Relationships. Utah State University, Logan.
[15]
Ouamane, A. and Lempérière, F. (2006) Design of a New Economic Shape of Weir. In: Berga, L., et al., Eds., Dams and Reservoirs, Societies and Environment in the 21st Century, Taylor & Francis, London, 463-470.
[16]
Ribeiro, M.L., Pfister, M., Schleiss, A.J. and Boillat, J.-L. (2012) Hydraulic Design of A-Type Piano Key Weirs. Journal of Hydraulic Research, 50, 400-408.
https://doi.org/10.1080/00221686.2012.695041
[17]
Kabiri-Samani, A. and Javaheri, A. (2012) Discharge Coefficients for Free and Submerged Flow over Piano Key Weirs. Journal of Hydraulic Research, 50, 114-120.
https://doi.org/10.1080/00221686.2011.647888
[18]
Lempérière, F. (2011) New Labyrinth Weirs Triple the Spillways Discharge. Water and Eenrgy International, 68, 77-78.
[19]
Lempérière, F., Vigny, J.-P. and Ouamane, A. (2011) General Comments on Labyrinth and Piano Key Weirs: The Past and Present. In: Erpicum, S., et al., Eds., Labyrinth and Piano Key Weirs—PKW 2011, Taylor & Francis, London, 17-24.
[20]
Machiels, O., Erpicum, S., Dewals, B.J., Archambeau, P. and Pirotton, M. (2011) Experimental Observation of Flow Characteristics over a Piano Key Weir. Journal of Hydraulic Research, 49, 359-366. https://doi.org/10.1080/00221686.2011.567761
[21]
Li, S., Li, G., Miao, Z. and Chen, G. (2016) [Numerical Simulation Study on the Discharge Characteristics of a Piano Key Weir with Various Heights]. Water Resources and Hydropower Engineering, 47, 60-64. (In Chinese)
[22]
Lefebvre, V., Vermeulen, J. and Blancher, B. (2013) Influence of Geometrical Parameters on PK-Weirs Discharge with 3D Numerical Analysis. In: Erpicum, S., et al., Eds., Labyrinth and Piano Key Weirs II—PKW 2013, Taylor & Francis, London, 49-56.
[23]
Bremer, F.L. and Oertel, M. (2017) Numerical Investigation of Wall Thickness Influence on Piano Key Weir Discharge Coefficients: A Preliminary Study. In: Erpicum, S., Laugier, F., Khanh, M.H.T. and Pfister, M., Eds., Labyrinth and Piano Key Weirs III, CRC Press, London, 101-108. https://doi.org/10.1201/9781315169064-14
[24]
Laiadi, A., Athmani, B., Belaabed, F. and Ouamane, A. (2017) The Effect of the Geometric Shape of the Alveoli on the Performance of Piano Key Weirs. In: Erpicum, S., Laugier, F., Khanh, M.H.T. and Pfister, M., Eds., Labyrinth and Piano Key Weirs III, CRC Press, London, 93-100. https://doi.org/10.1201/9781315169064-13
[25]
Li, S. (2020) [Study on Hydraulic Characteristics and Geometric Parameters of Piano Key Weir]. Xi’an University of Technology, Xian.
[26]
Anderson, R.M. and Tullis, B.P. (2012) Comparison of Piano Key and Rectangular Labyrinth Weir Hydraulics. Journal of Hydraulic Engineering, 138, 358-361.
https://doi.org/10.1061/(ASCE)HY.1943-7900.0000509
[27]
Sangsefidi, Y., Mehraein, M. and Ghodsian, M. (2015) Numerical Simulation of Flow over Labyrinth Spillways. Scientia Iranica, 22, 1779-1787.
[28]
Safarzadeh, A. and Noroozi, B. (2017) 3D Hydrodynamics of Trapezoidal Piano Key Spillways. International Journal of Civil Engineering, 15, 89-101.
https://doi.org/10.1007/s40999-016-0100-8
[29]
Chahartaghi, M.K., Nazari, S. and Shooshtari, M.M. (2019) Experimental and Numerical Simulation of Arced Trapezoidal Piano Key Weirs. Flow Measurement and Instrumentation, 68, Article ID: 101576.
https://doi.org/10.1016/j.flowmeasinst.2019.101576
[30]
Ghanbari, R. and Heidarnejad, M. (2020) Experimental and Numerical Analysis of Flow Hydraulics in Triangular and Rectangular Piano Key Weirs. Water Science, 34, 32-38. https://doi.org/10.1080/11104929.2020.1724649
[31]
Li, S., Li, G. and Jiang, D. (2020) Physical and Numerical Modeling of the Hydraulic Characteristics of Type-A Piano Key Weirs. Journal of Hydraulic Engineering, 146, 06020004. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001716
[32]
FLOW-3D (2016) FLOW-3D? Version 11.2 Users Manual. FLOW-3D [Computer Software]. Flow Science, Inc., Santa Fe. https://www.flow3d.com
[33]
Hirt, C.W. and Nichols, B.D. (1981) Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries. Journal of Computational Physics, 39, 201-225.
https://doi.org/10.1016/0021-9991(81)90145-5
[34]
Abbasi, S., Fatemi, S., Ghaderi, A. and Di Francesco, S. (2020) The Effect of Geometric Parameters of the Antivortex on a Triangular Labyrinth Side Weir. Water, 13, Article No. 14. https://doi.org/10.3390/w13010014
[35]
Ghaderi, A., Daneshfaraz, R., Abbasi, S. and Abraham, J. (2020) Numerical Analysis of the Hydraulic Characteristics of Modified Labyrinth Weirs. International Journal of Energy and Water Resources, 4, 425-436.
https://doi.org/10.1007/s42108-020-00082-5
[36]
Roache, P.J. (1994) Perspective: A Method for Uniform Reporting of Grid Refinement Studies. Journal of Fluids Engineering, 116, 405-413.
https://doi.org/10.1115/1.2910291
[37]
Sicilian, J.M., Hirt, C.W. and Harper, R.P. (1987) FLOW-3D. Computational Modeling Power for Scientists and Engineers. Report FSI-87-00-1. Flow Science, Los Alamos.
[38]
Gharahjeh, S., Aydin, I. and Altan-Sakarya, A.B. (2015) Weir Velocity Formulation for Sharp-Crested Rectangular Weirs. Flow Measurement and Instrumentation, 41, 50-56. https://doi.org/10.1016/j.flowmeasinst.2014.10.018
[39]
Hager, W.H. and Schleiss, A.J. (2009) Constructions Hydrauliques: Ecoulements Stationnaires. Presses Polytechniques et Universitaires Romandes, Lausanne.
[40]
Zech, Y. (2010) Constructions Hydrauliques: Ecoulements Stationnaires [Hydraulic Structures—Steady Flows]. Journal of Hydraulic Research, 48, 555-556.
https://doi.org/10.1080/00221686.2010.492096
[41]
Machiels, O. (2012) Experimental Study of the Hydraulic Behaviour of Piano Key Weirs. Université de Liège, Liège, Belgium.
[42]
Machiels, O., Erpicum, S., Archambeau, P., Dewals, B. and Pirotton, M. (2013) Parapet Wall Effect on Piano Key Weir Efficiency. Journal of Irrigation and Drainage Engineering, 139, 506-511. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000566
[43]
Ribeiro, M.L., Bieri, M., Boillat, J.-L., Schleiss, A.J., Delorme, F. and Laugier, F. (2009) Hydraulic Capacity Improvement of Existing Spillways: Design of Piano Key Weirs. Vingt Troisieme Congres Des Grands Barrages Brasilia, Brasília, Brazil, May 2009.
