Comparing the Behavior of Ogee and Piano Key Weirs under Unsteady Flows

Document Type : Original Article

Authors

1 شهرک کارشناسان میدان فرهنگ کوچه یاسمن 2 پلاک 112

2 Associate Professor, Department of Civil Engineering, University of Zanjan, Zanjan, Iran.

Abstract

Analysis of the unsteady flow on the weir end sill is fundamental to determining the passing flow's exact flow discharge and height. Due to the difference between the steady and unsteady flows and the effect of different terms of the Saint-Venant equation, the weirs' stage-discharge curves under the two types of flows are different. In the present study, 3D free-surface flow on the Ogee and the Piano-key weirs under steady and unsteady flows was modeled using the FLOW-3D numerical model, and the effect of different input hydrographs for multiple time bases was investigated. Based on the obtained results, the steady flow condition's unit stage-discharge curve turned into a circular curve in the case of the unsteady flow condition. In both types of the weirs, by increasing the hydrograph time base, the stage-discharge curve changed from a circular curve into a unit curve and finally conformed to the steady-state's stage-discharge curve. In both types of studied weirs, for a constant flow discharge, the water head difference was more considerable for the hydrograph with smaller base-time, i.e. the hydrograph with steeper ascending and descending branches. The amount of head difference in the ogee weir due to your hydrographs with time steps of 4, 10, and 40 seconds is 0.023, 0.013, and 0.008, respectively, and for the piano key weir is 0.024, 0.019, and 0.009. In other words, for steeper input hydrographs on the end-sill of the weirs located on the channels or the weirs used as a diversion, an unsteady flow analysis should be performed. For a fixed weir height and a fixed input hydrograph, water head changes of the Piano key weir were greater than the Ogee weir.

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امینی، ر.، ح. قدوسی و ک. شاهوردی. 1397. شبیه­سازی جریان غیرماندگار ناگهانی در کانالهای آبیاری با استفاده از روش عددی MacCormack-TVD. نشریه مهندسی آبیاری و آب ایران، سال دهم، شماره 39، ص 21-13.
قاسم زاده، ف.، ص. کوچک زاده. 1396. جریان غیرماندگار در سرریز لبه­تیز مثلثی واقع در انتهای یک مخزن. نشریه تحقیقات آب و خاک ایران، دوره 48، شماره 3، ص514-503.
Anderson, R.M. 2011. Piano key weir head discharge relationships. M.S. thesis. Utah State Univ, Logan, U.
Aricò, C., C. Nasello and T. Tucciarelli. 2009. Using unsteady-state water level data to estimate channel roughness and discharge hydrograph. Advances in Water Resources, 32.8.1223.
Bazaz, A. 2008. Discharge coefficient of weirs in unsteady flow. MSc thesis. Tehran University (In Persian).
Bos, MG. 1989. Discharge measurement structures. Publication no. 161. Delft Hydraulic Laboratory, Delft: The Netherlands (Also Publication no. 20. ILRI. Wageningen. The Netherlands).
Carter, R.W., R.G. Godfre. 1960. Storage and flood routing. USGS report iv p 81-104: ill. ;23 cm.
Chanson, H., H. Wang. 2013. Unsteady discharge calibration of a large V-notch weir. Flow Measurement and Instrumentation. 29.19– 24.
Chaudhry, M.H. 2008. Open-Channel Flow. Second Edition. Springer Science+Business Media, LLC. New York.
Chow, V.T. Open channel Hydraulics. Mc Graw- Hill Company.
Clemmens, A.J., T.L. Wahl, M.G. Bos and J.A. Replogle. 2001. Water Measurement with Flumes and Weir Publication no, 58. ILRI. Wageningen. The Netherlands.
Cunge, J.A. 1969. On the subject of a flood p opaga ion compu a ional me hod J H d aul esou.
Dabling, M.R., B.P. Tullis. 2017. Modifying the downstream hydrograph withstaged labyrinth weirs. Journal of Applied Water Engineering and Research.
De Laine, R.J. 1964. Calibration of weirs using the rate of pondage drawdown. Journal of hydrology, 2.130-140.
Fiorentini, M., S. Orlandini. 2013. Robust numerical solution of the reservoir routing equation. Advances in Water Resources, 59. P.123–132.
Fread, D.L. 1985. Channel routing. Hydrological Forecasting. John Wiley and sons Ltd New York. John Wiley and Sons, p.437–503.
Hager, W., R. Sinniger. 1985. Flood Storage in Reservoirs. J. Irrig. Drain Eng, 111(1). 76–85.
Henderson, F.M. 1966. Open channel flow. New York. MacMillan, 522 p.
Hormodka, T.V., G.L. Guymon. 1983. Mass lumping model of the linear diffusion equation. Adv in Water Resource, 6.79-83.
Jolliffe, I.B. 1989. Computation of dynamic waves in channel networks. J hydraulic Eng ASCE, 110(10).1357-1370.
Johnson, F. A., C.S. Green. 1977. The calibration of sharp crested weirs by the pondage drawdown method. Journal of Hydrology, 33-363-373.
Kuhnle, R.A., A.J. Bowie. 1992. Loop Rating Curves from Goodwin Creek. Proceedings of the Hydraulic Engineering sessions at Water Forum 92. Baltimore. Maryland. August. 2–6.1992 (Published by American Society of Civil Engineers).
Lighthill, M.J., G. B. Whitham. 1955. on Kinematic Waves: 1. Flood Movement in Long Rivers Proceedings Royal Society of London Series, A.229.pp. 281-361.
Ponce, V.M. 1990. Generalized diffusive wave equation with inertial effects. Water Resource, Res 26(5).1099-1101.
Raghunath, H.M. 2006. Hydrology: Principles Analysis Design New Age International (P) Ltd Publishers.
Ramamurthy, AS., US. Tim and MVJ. Rao. 1987. Flow over sharp-crested plate weirs. J Irrig Drainage Eng ASCE, 113(2): 163–172.
Singh, V.P., G.T. Wong and D.D. Adrian. 1996. Flood routing based on diffusion wave equation using mining cell method. Hydrological processes, 11.1881-1894.
Woolhiser, D.A., J.A. Liggett. 1967. Unsteady one-dimensional flow over a plane: the rising hydrograph. Water Resources Research, 3(3).753-841.