|Water Science and Engineering 2018, 11(1) 75-80 DOI: https://doi.org/10.1016/j.wse.2018.03.004 ISSN: 1674-2370 CN: 32-1785/TV|
|Current Issue | Archive | Search [Print] [Close]|
Experimental and numerical analysis of flow over a rectangular full-width sharp-crested weir
Ghorban Mahtabia, *, Hadi Arvanaghib
a Department of Water Engineering, Faculty of Agriculture, University of Zanjan, Zanjan 4537138791, Iran b Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz 5166616471, Iran
Weirs are a type of hydraulic structure, used for water level adjustment, flow measurement, and diversion of water in irrigation systems. In this study, experiments were conducted on sharp-crested weirs under free-flow conditions and an optimization method was used to determine the best form of the discharge coefficient equation based on the coefficient of determination (R2) and root mean square error (RMSE). The ability of the numerical method to simulate the flow over the weir was also investigated using Fluent software. Results showed that, with an increase of the ratio of the head over the weir crest to the weir height (h/P), the discharge coefficient decreased nonlinearly and reached a constant value of 0.7 for h/P > 0.6. The best form of the discharge coefficient equation predicted the discharge coefficient well and percent errors were within a ±5% error limit. Numerical results of the discharge coefficient showed strong agreement with the experimental data. Variation of the discharge coefficient with Reynolds numbers showed that the discharge coefficient reached a constant value of 0.7 when h/P > 0.6 and Re > 20000.
|Keywords： Discharge coefficient Measurement Numerical model Sharp-crested weir Weir height|
|Received 2016-05-16 Revised 2017-05-08 Online: 2018-01-31|
|Corresponding Authors: firstname.lastname@example.org (Ghorban Mahtabi)|
|About author: email@example.com (Ghorban Mahtabi)|
Aliparast, M., 2009. Two-dimensional finite volume method for dam-break flow simulation. International Journal of Sediment Research 24(1), 99-107. https://doi.org/10.1016/S1001-6279(09)60019-6.
Ata, R., Pavan, S., Khelladi, S., Toro, E.F., 2013. A weighted average flux (WAF) scheme applied to shallow water equations for real-life applications. Advances in Water Resources 62, 155-172. https://doi.org/10.1016/j.advwatres.2013.09.019.
Causon, D.M., Ingram, D.M., Mingham, C.G., Yang, G., Pearson, R.V., 2000. Calculation of shallow water flows using a Cartesian cut cell approach. Advances in Water Resources 23(5), 545-562. https://doi.org/10.1016/S0309-1708(99)00036-6.
Erduran, K.S., Kutija, V., Hewett, J.M., 2002. Performance of finite volume solutions to the shallow water equations with shock-capturing schemes. International Journal for Numerical Methods in Fluids 40(10), 1237-1273. https://doi.org/10.1002/fld.402.
Fraccarollo, L., Capart, H., Zech, Y., 2003. A Godunov method for the computation of erosional shallow water transients. International Journal for Numerical Methods in Fluids 41(9), 951-976. https://doi.org/10.1002/fld.475.
Harten, A., Lax, P.D., van Leer, B., 1983. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Review 25(1), 35-61. https://doi.org/ 10.1137/1025002.
García-Navarro, P., Vázquez-Cendón, M.E., 2000. On numerical treatment of the source terms in the shallow water equations. Computer and Fluids 29(8), 951-979. https://doi.org/10.1016/S0045-7930(99)00038-9.
Kim, D.H., Cho, Y.S., Kim, H.J., 2008. Well-balanced scheme between flux and source terms for computational of shallow-water equations over irregular bathymetry. Journal of Engineering Mechanics 134(4), 277-290. https://doi.org/10.1061/(ASCE)0733-9399(2008)134:4(277).
Kim, H.J., Cho, Y.S., 2011. Numerical model for flood routing with a Cartesian cut-cell domain. Journal of Hydraulic Research 49(2), 205-212. https://doi.org/10.1080/00221686.2010.547037.
Liang, Q., Borthwick, A.G.L., Stelling, G., 2004. Simulation of dam- and dyke-break hydrodynamics on dynamically adaptive quadtree grids. International Journal for Numerical Methods in Fluids 46(2), 127-162. https://doi.org/10.1002/fld.748.
Liang, Q.H., 2011. A structured but non-uniform Cartesian grid-based model for the shallow water equations. International Journal for Numerical Methods in Fluids 66(5), 537-554. https://doi.org/10.1002/fld.2266.
Pu, J.H., Cheng, N.S., Tan, S.K., Shao, S.D., 2012. Source term treatment of SWEs using surface gradient upwind method. Journal of Hydraulic Research 50(2), 144-153. https://doi.org/10.1080/00221686.2011.649838.
Sanders, B.F., Bradford, S.F., 2006. Impact of limiters on accuracy of high-resolution flow and transport models. Journal of Engineering Mechanics 132(1), 87-98. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:1(87).
Sweby, P.K., 1984. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM Journal on Numerical Analysis 21(5), 995-1011. https://doi.org/10.1137/0721062.
Toro, E.F., 1999. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, second ed. Springer, Berlin.
Toro, E.F., 2001. Shock-capturing Methods for Free-surface Shallow Flows. John Wiley & Sons, Chichester.
van Albada, G.D., van Leer, B., Roberts, W.W., 1982. A comparative study of computational methods in cosmic gas dynamics. Astronomy and Astrophysics 108(1), 76-84.
van Leer, B., 1974. Towards the ultimate conservative difference scheme, II. Monotonicity and conservation combined in a second-order scheme. Journal of Computational Physics 14(4), 361-370. https://doi.org/10.1016/0021-9991(74)90019-9.
van Leer, B., 1979. Towards the ultimate conservative difference scheme, V. A second-order sequel to Godunov’s method. Journal of Computational Physics 32(1), 101-136. https://doi.org/10.1016/0021-9991(79)90145-1.
Wu, W.M., Marsooli, R., 2014. A depth-averaged 2D shallow water model for breaking and non-breaking long waves affected by rigid vegetation. Journal of Hydraulic Research 50(6), 557-575. https://doi.org/10.1080/00221686.2012.734534.
|1．Ji-Sung KIM;Chan-Joo LEE; Won KIM;Yong-Jeon KIM.Roughness coefficient and its uncertainty in a gravel-bed river[J]. Water Science and Engineering, 2010,3(2): 217-232|
|2． Michael HARTNETT, Stephen NASH.An integrated measurement and modeling methodology for estuarine water quality management[J]. Water Science and Engineering, 2015,8(1): 9-19|
|3．Lei TANG, Wei ZHANG, Ming-xiao XIE, Zhen YU.Application of equivalent resistance to simplification of Sutong Bridge piers in tidal river section modeling[J]. Water Science and Engineering, 2012,5(3): 316-328|
|4．Zheng GONG; Chang-kuan ZHANG; Cheng-biao ZUO; Wei-deng WU.Sediment transport following water transfer from Yangtze River to Taihu Basin[J]. Water Science and Engineering, 2011,4(4): 431-444|
|5．Yan ZHU; Yuan-yuan ZHA; Ju-xiu TONG; Jin-zhong YANG.Method of coupling 1-D unsaturated flow with 3-D saturated flow on large scale[J]. Water Science and Engineering, 2011,4(4): 357-373|
|6． Fernando Alvarez, Shun-qi Pan .Predicting coastal morphological changes with empirical orthogonal functionmethod[J]. Water Science and Engineering, 2016,9(1): 14-20|
|7．Xu-hua REN, Hai-jun WANG*, Ji-xun ZHANG.Numerical study of AE and DRA methods in sandstone and granite in orthogonal loading directions[J]. Water Science and Engineering, 2012,5(1): 93-104|
|8．Azadeh Gholami, Hossein Bonakdari, Ali Akbar Akhtari.Assessment of water depth change patterns in 120° sharp bend using numerical model[J]. Water Science and Engineering, 2016,9(4): 336-344|
|9．Ze-yu MAO, Jing YUAN, Jun BAO, Xiao-fan PENG, Guo-qiang TANG.Comprehensive two-dimensional river ice model based on boundary-fitted coordinate transformation method[J]. Water Science and Engineering, 2014,7(1): 90-105|
|10． Xiao-kang XIN, Ke-feng LI, Brian FINLAYSON, Wei YIN.Evaluation, prediction, and protection of water quality in Danjiangkou Reservoir, China[J]. Water Science and Engineering, 2015,8(1): 30-39|
|Copyright by Water Science and Engineering|