Evaluation of the Discharge Coefficient of Piano Key Weir under the Unsteady - Gradual Varied Flow with Increasing Discharge

Document Type : Research Article

Authors

1 M.Sc. Student, Water Eng. and Hydraulic Structures, Department of Civil Engineering, Islamic Azad University, Isfahan (Khorasgan), Iran.

2 Department of Civil Engineering, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran

Abstract

Introduction: Weirs or spillways are one of the most important types of hydraulic structures that are divided into linear and nonlinear weir categories based on the shape of the plan. The most important types of nonlinear wires are labyrinth wires and piano key weirs that increase the discharge of flow by increasing the length of the spillway crown. These types of weirs are usually made outside the dam body. The most important advantages of these weirs is high flow coefficient, speed in construction and economic efficiency. These weirs are one of the most suitable options for dam weir implementation in free-flow mode. Floods, snow melting, performance changes of hydraulic structures and many other unsteady flow factors are observed abundantly in nature. Therefore, in this study, the discharge coefficient of piano key weirs under the unsteady-gradual varied flow with increasing discharge has been evaluated. Also, in this research, the calibration of discharge coefficient due to changes in the weir height and the effect of weir height changes on the discharge coefficient and other effective hydraulic parameters in the upstream of the spillway under the unsteady-gradual varied flow with increasing discharge has been investigated.

Methodology: The experiments were carried out in a rectangular channel of Islamic Azad University, Isfahan University (Khorasgan) with a length of 10 meters and a width of 0.6 meters. The height of the channel was the same and unchanged along the way, as well as its floor was made of galvanized sheets and its walls were made of tempered glass and completely sealed. Considering the relationships and previous studies and dimensional analysis, the effect of effective parameters on flow discharge coefficient was investigated. In the current research, three types of A-type rectangular piano key weir with variable heights of 10, 15 and 20 cm were used. Other geometrical parameters were constant and experiments done under the unsteady-gradual varied flow with increasing discharge in the flow range of 30 to 50 Lit/s. The experiments has been studied under the range of discharge changes of 5,3 and 1 liter per second and range of time changes of 5,10 and 15 seconds. Therefore, according to the said contents, 27 different modes have been analyzed in this thesis. Flow depth was reported by laser altimeter sensors at the top of the channel. PLC device was used to measure discharge and water head at different times. A magnetic flow meter is attached to the PLC device, which measures the discharge in liters per second and the height of water from the channel floor by sensors installed in millimeters.

Results and Discussion: Discharge coefficient under the unsteady-gradual varied flow with increasing discharge was obtained by deriving from the relationship provided by Machiels et al. Considering that the dc/dt value is not known, the relationships of past researchers for the flow discharge coefficient of type A rectangular piano key weir presented. And comparing the percentage of error in each relationship was done. Finally, it was concluded that the relationship presented by Javaheri and Kabiri-Samani had a lower error percentage. And it was derived from this relationship relative to time, until determine the dc/dt value. Then, according to the experimental data and weir specifications of the discharge coefficient under the unsteady-gradual varied flow with increasing discharge, it was obtained. The results showed that with increasing the weir height, the slope of the discharge charts and the height of the water decreased and the slope of the head-discharge diagrams increased. With increasing the height of the weir, the discharge coefficient increased and in contrast to the froud number and the ratio of water height to the height of the weir decreased. As a result, the height of the weir is directly related to the discharge coefficient and is in contrast to the froud number and the height of the water at the inlet and upstream of the weir. According to the results obtained in the unsteady-gradual varied flow with increasing discharge that led to the calibration of the flow, it was found that the calibrated discharge coefficient (average) in three weirs with heights of 10, 15 and 20 cm is a number between 1.693 and 3.776.

Conclusion: By comparing three type A piano key weirs, it was found that the weir with a height of 20 cm is more efficient than the weir with heights of 10 and 15 cm according to the higher discharge coefficient. It can also be stated that the higher height weir is much more applicable in floods and high flow discharges and better diverts the flow. In fact, all the results indicate that the height of the weir plays an important role in the amount of the flow coefficient of the piano key weir. And by increasing it, the efficiency of the flow discharge can be increased.

Keywords

References

Abhash, A. and Pandey, K.K. (2021). Nonlinear Regression Analysis Between Discharge and Head for Piano Key Weirs with Increasing Developed Length (L/W) Ratio and Constant Channel Width. Water Resources Management and Reservoir Operation, Chapter 20, 241-250. Springer Cham.
Anderson, R.M. and Tullis, B. (2011). Influence of Piano Key Weir geometry on discharge. In proceedings of the International Conference Labyrinth and Piano Key Weirs, 75-80.
Barcouda, M., Cazaillet, O., Cochet, P., Jones, B. A., Lacroix, S., Laugier, F., Odeyer, C. and Vigny, J.P. (2006). Cost effective increase in storage and safety of most dams using fusegates or PK Weirs. Proc. 22nd CIGB/ICOLD congress, Barcelona, Spain.
Blanc, P. and Lempérière, F. (2001). Labyrinth spillways have a promising future. International Journal on Hydropower & Dams, 8(4), 129-131.
Bortoni, E.C., Rocha, M.S., Rodrigues, M.A. and Laurindo, B.C. (2017). Calibration of weirs using unsteady flow. Flow Measurement and Instrumentation, 57, 73-77.
Cicero, G.M. and Delisle, J.R. (2013). Discharge characteristics of Piano Key weirs under submerged flow. Labyrinth and Piano Key Weirs II–PKW 2013, 101-109.
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.
Henderson, F.M. (1966). Open channel flow Mac Millan Publishing Co. Inc., New York, pp. 288-324.
Chi Hien, T., Thanh Son, H., Ho Ta Khanh, M. (2006). Results of some ‘piano keys’ weir hydraulic model tests in Vietnam. Proc. 22nd Intl Congress of Large Dams, Q87, R39, Vol. IV, ICOLD, Barcelona, Spain, 581–595.
Kabiri-Samani, A. and Javaheri, A. (2012). Discharge coefficients for free and submerged flow over Piano Key weirs. Journal of Hydraulic Research, 50(1), 114-120.
Karamvand, A., Hajikandi, H. and Sharafati, A. (2020). Comparison of Discharge Coefficient Between Arced Piano Key Weir and Non-Arc Piano Key Weirs. Water Resources Engineering, 13(47), 15-26. (In Persian)
Kumar, B., Kadia, S. and Ahmad, Z. (2019). Evaluation of discharge equations of the Piano Key Weirs. Flow Measurement and Instrumentation, 68, 101577, https://doi.org/10.1016/j.flowmeasinst. 2019.101577
Laugier, F. (2007). Design and construction of the first Piano Key Weir spillway at Goulours dam. International Journal on Hydropower and Dams, 14(5), 94-101.
Laugier, F., Lochu, A., Gille, C., Leite Ribeiro, M. Boillat, J-L. (2009). Design and construction of a labyrinth PKW spillway at Saint-Marc dam, France. Hydropower & Dams, 15(5), 100-107.
Lempérière, F. and Ouamane, A. (2003). The Piano Keys weir: a new cost-effective solution for spillways. International Journal on Hydropower & Dams, 10(5), 144-149.
Lempérière, F., Vigny, J.P., Ouamane, A. (2011). General comments on Piano Kew Weirs: The past and present. Proc. Intl Workshop on Labyrinths and Piano Key Weirs PKW 2011, CRC Press, 17-25.
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(3), 359-366.
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(6), 506-511.
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(3), 326-335.
 
Novák, P. and Čabelka, J. (1981). Models in Hydraulic Engineering: Physical principles and design applications. Monographs & surveys in water resources engineering.
Ouamane, A. and Lempérière, F. (2006). Design of a new economic shape of weir. Proc. Intl Symposium on Dams in the Societies of the 21st Century, Barcelona, Spain, 463-470.
Ribeiro, M., Boillat, J.L. and Schleiss, A. (2011). Experimental parametric study for hydraulic design of PKWs. Proc. of International Conference on Labyrinth and Piano Key Weirs (PKW 2011), 183-190. CRC Press, Taylor & Francis Group.
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(4), 400-408.
Pfister, M. and Schleiss, A.J. (2013) Comparison of hydraulic design equations for A-Type Piano Key Weirs. Proceedings of the International Conference on Water Storage and Hydropower Development for Africa (AFRICA 2013), April, 1–8.
Pralong, J., Vermeulen, J., Blancher, B., Laugier, F., Erpicum, S., Machiels, O., Pirotton, M., Boillat, J.L., Leite Ribeiro, M. and Schleiss, A.J. (2011). A naming convention for the Piano Key Weirs geometrical parameters. Proc. Intl Workshop on Labyrinths and Piano Key Weirs PKW 2011, CRC Press, 271-278. 
Seyedjavad, M., Naeeni, S. and Sanei, M. (2020). Experimental Study of Discharge Coefficient and Flow Streamlines in a Trapezoidal Piano Key Side Weir. Iranian Journal of Soil and Water Research, 50(9), 2261-2273. (In Persian)

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History

  • Receive Date: 05 September 2022
  • Revise Date: 01 December 2022
  • Accept Date: 24 December 2022

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