Estimation of waterfall height in the downstream of ogee spillways to hydraulic jump control

Document Type : Research/Original/Regular Article

Authors

1 Ph.D. Candidate/ Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran

2 Ph.D. Candidate/Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran

3 Associate Professor/Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran

4 Professor/Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran

Abstract

Introduction
The purpose of this study is to generate the relationships to directly calculate waterfall height at the downstream of the spillway to form a jump at the toe of the spillway and to prevent erosion and destruction of the downstream river bed or body of the spillway in a submerged and free hydraulic jump.
Materials and Methods
The purpose of this study is to provide a relationship to directly calculate the waterfall height (h) without the need for a trial and error procedure. For this purpose, the application of the momentum relationship between two sections (1and 2) yields the waterfall height (h) according to Eq. (1). 
      h=y1 .....                                                                                                                                                            (1)
Since in Eq. (1), Fr1 and y1 are themselves a function of the waterfall height (h), so this equation must be solved by trial and error or by using design charts provided by other researchers. To calculate the waterfall height in oscillating jump conditions (2.5<Fr1<4.5) and also for steady and strong jump conditions (4.5<Fr1<15.5), by assuming different values ​​for p, y0, yt and C (where C is the discharge coefficient), 300 and 1146 series of numbers have been generated by trial and error, respectively. Then, the parameters in Eq. 1 (y1, Fr1) were also calculated. The final waterfall height (h) was obtained for each series of numbers. Using the existing variables, dimensionless parameters ( ) and Fr1 were extracted. Then, multiple linear and nonlinear multiple regression relationships were tested for direct calculation of . Finally, the best relationships with the least error were selected. The results of multiple regression (MR) relationships are also compared with the results of ANN and SVM methods.
Results and Discussion
The proposed non-linear multiple regression relationship (MR-3) shows higher accuracy in estimating the waterfall height, compared to MR-1 and MR-2 regression models based on three statistical indices (RE%, RMSE, R2) for 2.5<Fr1<4.5 and 4.5<Fr1<15.5. Therefore with having the Froude number related to the initial hydraulic jump depth (Fr1), tail water depth (yt), weir height (P) and initial jump depth (y1), the calculation of waterfall height (h) will be possible using MR-3 model without any trial and error procedures. Moreover, the results show that among the intelligent models, the ANN model has very close results to the proposed nonlinear regression relation (MR-3) based on the statistical indices.
Conclusion
A new method for calculating the height of a waterfall at the toe of the ogee spillway was presented to control hydraulic jump. To calculate the height of the waterfall directly, multiple nonlinear regression (MR) relationships were presented for two ranges of different Froude numbers. The MR, ANN, and SVM models showed good performance in predicting the height of the waterfall downstream of spillways, but the ability of the two MR and ANN models were better than the SVM.

Keywords

References

Abbaspour, A., Hosseinzadeh Dalir, A., Farsadizadeh, D., & Sadraddi, N. (2009). Effect of sinusoidal corrugated bed on hydraulic jump characteristics. Hydro-environmental Research, 3, 109-117.
Abrishami, J., & Saneie, M. (1994). Hydraulic jump in adverse basin slope. International Journal of Water Resources Engineering, 2(1), 51-63.
Achour, B., & Debabeche, M. (2003). Control of hydraulic jump by sill in triangular channel. Journal of Hydraulic Resources, 41(3), 319-325.
Arra, N. (2015). Marun Reservoir Dam and power plant. Peyab Sazeh Gostar Co. Archived from https://archive.is/20150119204215/http://www.peyab.org/maruneng.htm#, Retrieved 19 January 2015.
Asafi, M., & Zeyaee, A.N. (2011). Two-dimensional numerical simulation of hydraulic jump on inverted sloping surfaces with stairs at bottom with FLUENT software. 6th National Congress of Civil Engineering, Semnan, Iran (in Persian).
Beirami, M.K. (2016). Water conveyance structure. 13th Edition. Isfahan Technical University Press, 462 Pages (in Persian).
Boser, B.E., Guyon, I.M., & Vapnik, V.N. (1992). A training algorithm for optimal margin classifiers. Proceedings of the 5th Annual Workshop on Computational Learning Theory (COLT’92), Pittsburgh, 144-152.
Carvalho, R.F., Lemos, C.M., & Ramos, C.M. (2010). Numerical computation of the flow in hydraulic jump stilling basins. Journal of Hydraulic Research, 46, 739-752.
Daneshfaraz, R., Chabokpour, J., & Nezafat, H. (2019a). Experimental investigation of the scouring due to hydraulic jump in screens. Iranian Journal of Soil and Water Research, 50(5), 1039-1051 (in Persian).
Daneshfaraz, R., Sadeghfam, D., & Hasanniya, V. (2019b). Experimental investigation of energy dissipation the vertical drops equipped with a horizontal screen with the supercritical flow. Iranian Journal of Soil and Water Research, 50(6), 1421-1436 (in Persian).
Defina, A., Susin, F.M., & Viero. D.P. (2008). Bed friction effects on the stability of a stationary hydraulic jump in a rectangular upward sloping channel. Physics of Fluids, 20(3), 036601.
Esmaely, K., & Abrishami, J. (2002). Determination of relationship between depth before and after jump and step elevation to control hydraulic jump on reverse and steep slopes (positive and negative). Proceedings of the International Conference on Hydraulic Structures, Kerman, Iran Pp. 601-612 (in Persian).
Gazanfari Hashemy, A., & Shahidi, S. (2012). Prediction of scour depth around bridge pier by support vector machines. Modares Civil Engineering Journal, 12(2), 23-36 (in Persian).
Ghassemi, A., Omid, M., Nasr Abadi, M., & Raeesi Estabragh, A. (2017). Evaluate and develop new relationships to estimate submerged hydraulic jump characteristics. Iranian Journal of Soil and Water Research, 47(4), 755-764 (in Persian).
Gunn, S.R. (1998). Support vector machines for classification and regression. University of Southampton publication, England, 66 pages.
Habibzadeh, A., Loewen, M., & Rajaratnam, N. (2011). Exploratory study of submerged hydraulic jumps with blocks. Journal of Hydraulic Engineering, 137(6), 706–710.
Hsu, E., Kolupaila, S., Jaeger, C., Laushey, L.M., Viparelli, M., Weaver, R.M., Woodward, S.M., & Yates, F.M. (1950). Discussion of control of the hydraulic jump by sills. Ed. by J. W. Forster and R. A. Skrinde. Transactions of the American Society of Civil Engineers, 115(1), 988-991.
Kiani, S., Fathi-Moghadam, M., Behroozi-Rad, R., & Davoodi, L. (2017). Control of hydraulic jump in the stilling basins with perforated sill. Irrigation and Water Engineering, 7(4), 26-36 (in Persian).
Norouzi, R., Daneshfaraz, R., & Ghaderi, A. (2019). Investigation of discharge coefficient of trapezoidal labyrinth weirs using artificial neural networks and support vector machines. Applied Water Science, 9(7), 148.
McCorquodale, J.A., & Mohamad, M.S. (1994). Hydraulic jump on adverse slopes. Journal of Hydraulic Research, 32(1), 119-130.
Minaei, A., Ghodsian, M., & Mehraein, M. (2016). Experimental investigation of hydraulic jump in stilling basin with stepped sill. Modares Civil Engineering Journal, 16(1) 146-156 (in Persian).
Parsamehr, P., Farsadizadeh, D., Hosseinzadeh Dalir, A., Abbaspour, A., & Nasr Esfahani, M.J. (2017). Characteristics of hydraulic jump on rough bed with adverse slope. ISH Journal of Hydraulic Engineering, 23(3), 301-307.
Pourabdollah, N., Heidarpour, M., Abedi Koupai, J., & Mohamadzadeh, J. (2018). Study of characteristics of submerged hydraulic jump on bed roughness and adverse slopes. Iranian Journal of Soil and Water Research, 49(3) 683-693 (in Persian).
Pourabdollah, N., Honar, T., &. Fatahi, R.A. (2014). The influence of roughness in adverse bed slopes on conjugate depth and energy losses of hydraulic jump.  Journal of Water and Soil Science, 18(67), 165-174.
Rajaratnam, N. (1976). Hydraulic jumps: Advances in Hydroscience. ACADEMIC Press, 4, 84 pages.
Salmasi, F. (2018). Effect of downstream apron elevation and downstream submergence in discharge coefficient of Ogee weir. ISH Journal of Hydraulic Engineering, 10.1080/09715010.2018.1556125.
Salmasi, F., Nouri, M., Sihag, P., & Abraham, J. (2021). Application of SVM, ANN, GRNN, RF, GP and RT models for predicting discharge coefficients of oblique sluice gates using experimental data. Water Supply, 21(1), 232–248.
Yousefi, F., Mozaffari, J., & Mohseni Movahed, S. (2019). Laboratory comparison of hydraulic jump models in different flow regimes. Irrigation and Water Engineering, 9(2), 1-11 (in Persian).
Water and Soil Management and Modelling
Volume 1, Issue 1
March 2021
Pages 1-12

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History

  • Receive Date: 07 March 2021
  • Revise Date: 15 April 2021
  • Accept Date: 15 April 2021

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