Numerical Solution of the Discharge Coefficient of Trapezoidal Arced Labyrinth Weirs with Different Middle Cycles Using Flow 3D Software

Document Type : Research Article

Authors

1 Department of Water Science Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

2 Department of Water Science and Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz,Iran

3 Department of Water Science Engineering, Ahvaz branch, Islamic Azad University, Ahvaz, Iran

Abstract

In the present study, a three-dimensional hydraulic flow simulation was carried out on these weirs using Flow3D software and the modeling results were compared with the experimental results to study the discharge coefficient of trapezoidal arced labyrinth weirs. Moreover, these models were tested under laboratory conditions in a rectangular flume with a length of 12m, a width of 0.6m, and a height of 0.6m in clear water conditions. The results indicated that the numerical model data showed adequate conformity with the experimental model data. In general, the discharge coefficients in the results of the numerical model were 1.2 to 18.9% lower than the experimental model. The difference between the discharge coefficients in the numerical model and the experimental model increased with an increase in the arc radius. As a result, with the R/w1=5 and R/w1=15 radius ratios, the discharge coefficients of the numerical model were approximately 1.2% and 18.9% lower than the experimental model, respectively.
One of the pitfalls of the existing conventional linear weirs is their low discharge capacity due to the limited width of these weirs. The use of labyrinth weirs is considered an efficient and cost-effective solution for increasing the flow rate. These weirs provide a higher discharge capacity for the same hydraulic head than direct weirs due to the increase in the crest length in a given width. The flow running over the weirs within the peak flood hours has to flow within a short period of time. Therefore, it seems necessary to build a weir structure with a high discharge coefficient. Labyrinth weirs are used for this purpose because the amount of flow running through them is larger than linear weirs (Falvey 2003).
Labyrinth weirs are used as cost-effective technical solutions for controlling flow in different conditions such as in dam weirs. Labyrinth weirs may also be used to control discharge capacity, reduce channel water level slope, distribute water between irrigation channels, etc. (Neveen Sad and Fattouh Ehab 2017). The plans of labyrinth weirs are classified into three categories, namely the triangular, trapezoidal and rectangular plans. Most weirs are built with rectangular, trapezoidal, or isosceles plans to increase their performance and facilitate their construction (Crookston 2010). The discharge coefficient in these weirs is determined by various factors such as the weir water level, the walls angle, and the crest thickness and shape (Ghare et al. 2008).

Dimensional analysis is among the basic methods for experimental research, which serves to determine the dimensionless ratios. In the first step of this method, the variables affecting the discharge of labyrinth weirs are identified and then the dimensionless parameters are determined based on Buckingham’s theory, . After determining the dimensionless parameters, their effect on the discharge of the weirs can be studied to obtain satisfactorily rational results.
The comparison of the experimental results with the results of the numerical model for the discharge coefficient of trapezoidal arced labyrinth weirs with different middle cycles and different arc ratios in Flow-3D software is presented in the following diagrams.
As seen in figures (5), (6) and (7), the discharge coefficient decreased with an increase in the hydraulic head. In other words, the results of the experimental model show higher discharge coefficient values than the numerical modeling results in Flow3D. In figures (5), (6) and (7), the trapezoidal labyrinth weir has a hydraulic head ratio of 0.1 to 0.7 in the adhesion and complete aeration phase and from 0.7 to 1 in the partial aeration and suffocation stage. Moreover, the arc radius ratio of 15 has the highest discharge coefficient values as compared to the 10 and 5 ratios. In other words, with an increase in the arc radius ratio, the hydraulic efficiency of the weir increases along with its hydraulic efficiency. As seen in figures 6 and 7, with an increase in the hydraulic head, the difference between the discharge coefficients in the numerical and experimental models decreased. Moreover, according to these diagrams, with an increase in the arc radius, the difference between the discharge coefficients in the numerical and experimental models increased, which could be attributed to an error in the numerical model in detecting the small variations in the arc radius. In other words, in the numerical model, the discharge coefficient did not differ significantly from the arc radius variations, whereas in the experimental model, the effect of the arc radius on the discharge coefficient was more significant.

A comparison of labyrinth weir discharge coefficients resulting from the numerical and experimental models revealed that the discharge coefficients of the experimental values are higher than the numerical modeling results. Besides, the labyrinth weir properly completes the four hydraulic stages in the experimental and numerical conditions, reflecting the proper hydraulic performance of the weir. When the weir is in the full aeration state, the weir is in the maximum hydraulic efficiency state. It is worth stating that when the weir is in the partial aeration condition, its hydraulic efficiency starts to decline. Finally, if it reaches the suffocation stage, the weir loses its hydraulic efficiency, the energy is maximized, the entire length of the weir crest is fully submerged, and thus the weir functions as an obstacle in the flow path. The energy loss is maximized when the hydraulic head is maximized. As a result, the nappes collide in the weir outflow keys, resulting in a drastic energy loss. From the quantitative viewpoint, in the weir with a radius ratio of R/w1=5, the numerical and experimental results satisfactorily overlap, and for hd/p>0.2 in the two diagrams, they are fully in line. In the weir with the R/w1=10 radius ratio, the numerical model outflow discharge coefficient is 10.2 percent smaller than the experimental results on average. Besides, with the R/w1=15 radius ratio in the results of the numerical model, the discharge coefficients are approximately 18.9 percent lower than the experimental model. In general, with an increase in the weir arc radius, the difference between the flow coefficients in the numerical model and the experimental results increases.

Keywords

Main Subjects


Ghaderi, A., Daneshfaraz, R., Dasineh, M. & Di Francesco, S. (2020). Energy Dissipation and Hydraulics of Flow over Trapezoidal–Triangular Labyrinth Weirs. Water, 12(7), 1992, https://doi.org/10.3390/w12071992.
Ghaderi, A., Daneshfaraz, R., Abbasi, S. & Abraham, J. (2020). Numerical analysis of the hydraulic characteristics of modified labyrinth weirs. International Journal of Energy and Water Resources, 4, 425–436.
Azimi, A. & Seyed Hakim, S. (2018). Hydraulics of flow over rectangular labyrinth weirs. Irrig Sci, 37(12), 183-193.
Bijankhan, M. & Ferro, V. (2017). Dimensional analysis and stage-discharge relationship for weirs: A review.  J. Agri Eng., 48(1), 1–11.
Bijankhan, M. & Kouchakzadeh, S. (2017). Unified discharge coefficient formula for free and submerged triangular labyrinth weirs. Flow Meas Instrum, 57, 46-56.
Christensen, N.A. (2012). Flow Characteristics of Arced Labyrinth Weirs. MSc thesis, Utah State University, Logan, Utah.
Crookston, B.M. & Tullis, B.P. (2013). Labyrinth Weirs: Nappe Interference and Local Submergence. J Irrig Drain Eng., 138(8), 757–765.
Crookston, B.M. & Tullis, B.P. (2012a). Arced labyrinth weirs. J Hydraul Eng, 138(6), 555-562.
Crookston, B.M. & Tullis, B.P. (2012b). Discharge efficiency of reservoir-application-specific labyrinth weirs. J Irrig Drain Eng, 138(6), 773–776.
Crookston, B.M. (2010) Labyrinth weirs. PhD thesis, Utah State University, Logan, Utah.
Emami, S., Arvanaghi, H. & Parsa, J. (2018). Numerical Investigation of Geometric Parameters Effect of the Labyrinth Weir on the Discharge Coefficient. J Rehabil Civ Eng, 6(1), 01-09.
Falvey, H.T. (2003). Hydraulic Design of Labyrinth Weirs. USA, ASCE press.
Ghare, A.D., Mhaisalkar, V.A. & Porey, P.D. (2008). An Approach to Optimal Design of Trapezoidal Labyrinth Weirs. World. Appl Sci J, 3(6), 934-938.
Gharibvand, R., Heidarnejad, M., Kashkoli, H.A., Hasounizadeh, H. & Kamanbedast, A.A. (2018). Numerical analysis of flow hydraulic in trapezoidal labyrinths and piano key weirs. Flow Meas Instrum, 64, 64-70.
Ghodsian, D., Amanian, N. & Marashi, S.A. (2001). Discharge Coefficient of Semicircular Labyrinth Weirs. Amirkabir J Civil Eng Tehran, 13, 76-83. (In Persian)
Lux, F. & Hinchliff, D.L. (1985). Design and construction of labyrinth spillways. In: Proceedings of 15th ICOLD Congress, Q59(R15), 249-274; Lausanne, Switzerland.
Monjezi, R., Heidarnejad, M., Masjedi, A.R., Purmohammadi, M.H. & Kamanbedas, A.A. (2018). Laboratory Investigation of the Discharge Coefficient of Flow in Arced Labyrinth Weirs with Triangular Plans. Flow. Meas. Instrum, 64, 64-70.
Neveen, Y.S. & Fattouh Ehab, M. (2017). Hydraulic characteristics of flow over weirs with circular openings. Ain Shams Eng J., 8, 515–522.
Norouzi, R., Daneshfaraz, R. & Ghaderi, A. (2019). Investigation of discharge coefficient of trapezoidal labyrinth weirs using artificial neural networks and support vector machines. Journal of Applied Water Science, 148(9), 1–10.
Sangsefidi, Y. & Ghodsian, M. (2019). Investigation of Effects of Entrance Channel Walls on the Hydraulic Performance of Arced Labyrinth Weirs. Modares Civil Eng J., 19(1), 181-193. (In Persian)
Tullis, B.P. (2018). Size-Scale Effects of Labyrinth Weir Hydraulics. In: Proceedings of 7th IAHR International Symposium on Hydraulic Structures, 15–18.