Flow velocity pattern around trapezoidal piano key side weirs

Highlights

• Numerous tests have been performed to determine type-A trapezoidal piano key weirs that it is in the lateral position in the channel.

• In both modes, the weir is located on the main channel on the side.

• The outflow from the weir is investigated.

• Mode 2 had better performance than Mode 1 due to the lack of a base at the inlet of the weir, which impedes the impact of velocity vectors.

Abstract

In general, the side weirs are the structures installed along a channel or river. When the flow depth rises above the weir crest, the overflow passes through these weirs and enters the lateral canal. Nowadays, piano key weirs are considered as an important alternative to labyrinth weirs to modify the weirs encountering with difficulty to pass the maximum flow discharges. The present study investigates the hydrodynamic performance and the effect of the uniformity of velocity field on the resultant kinetic energy in the trapezoidal piano key side weirs with 90° installed laterally in the main channel wall. These weirs are classified as A-Type piano key weirs and two approaches (main: Mode 1 and adverse: Mode 2) were used to investigate the effect of the weirs' placement on their performance. The results showed that for velocity vectors in both modes, on average, the maximum flow discharge through the side weir occurred in the x and y directions (V_x and V_y) at Z*<0.2 and 0.2<Y*<0.7. The results also showed that at the control surface of X* = 1, the maximum values of α occur due to existing the inverse flow and increasing the deflection angle of the velocity vectors. The performance of the weir in Mode 2 was more appropriate Mode 1 due to the lack of weir base at the flow inlet, which is an obstacle for the deflection angle of the velocity vectors.

Introduction

The main channels in an irrigation and drainage network are usually regulated using flow control structures and direct the flow to the downstream channels [1]. The weirs are used as separating structures in these channels. The flow hydraulics in this type of weirs are completely different from direct weirs and the flow regime in these weirs is spatially varied flow. In this regard, Lucas et al. [2] investigated three models of side channels and their weirs. In recent years, a new type of weirs has been designed based on labyrinth weirs [3]. Piano key weirs have been introduced as the new geometry of non-linear free weirs with the idea of reducing the positioning length as compared with the Ogee weirs as well as increasing the useful flow-through length in comparison with the labyrinth weirs. The results of the studies conducted on the hydraulic characteristics of weirs have shown that the weirs play an important role in the flow pattern [4]. Numerical and experimental studies have been done on labyrinth and piano key weirs. Carrillo et al. [5] numerically investigated the labyrinth side weirs and found that, regardless of the turbulence model under subcritical flow regime, the flow depth downstream of labyrinth side weirs obtained from numerical model is well-matched with experimental data. Rostami et al. [6] studied a rectangular labyrinth side weir and found that by increasing the ratio of H_d/P (tail water depth/weir height), the discharge coefficient of these weirs decreases. Furthermore, the number of cycles in this weir is an effective parameter in this type of weirs, so that one-cycle labyrinth side weir has an appropriate performance for ratio of H_d/P < 0.3. Salehiet al. [7] examined the effect of sedimentation rate on the performance of semi-circular weirs. They found that high kinetic energy in this type of the weirs is sufficient for passing the floating objects in the water and to prevent the sedimentation upstream of this weir. Gharibvand et al. [8] studied trapezoidal labyrinth weirs and direct rectangular piano key weirs, and reached the conclusion that the discharge coefficient of piano key weirs is 30% more than that of the labyrinth weir and this difference decreases with increasing the hydraulic head. The hydraulic characteristics of flow around the vertical circular overflow with the input of a piano key weir was investigated. The results showed that the presence of piano key weir has a significant effect on reducing the power of the vortex flow and increases the weir discharge coefficient [9]. In addition, numerous CFD numerical methods have been studied on direct rectangular piano key weirs, in which, the flow turbulence has been addressed. Finally, in these studies, some corrections have been made for A-Type rectangular direct piano key weirs [10]. Olyaie et al. [11] investigated four numerical models of Least-Square Support Vector Machine (LS-SVM), Extreme Learning Machine (ELM), Bayesian ELM (BELM), and Logistic Regression (LR) for experimental data of a direct rectangular piano key weir. The results showed that BELM model is a simple and efficient algorithm and, therefore, can be used to estimate discharge coefficient. In a comprehensive numerical study to better understand flow patterns around a piano key weir (PKW), Han Hu et al. [12] found that by increasing the upstream water surface, the longitudinal flow velocity along the input keys, the submerged flow in the output keys, interference between nappe flow and falling the flow along the input keys reduces the discharge efficiency. Haghiabi et al. [13] concluded that the MARS is an appropriate mathematical model in estimating the discharge coefficient (C_d) of the weirs. Experimental studies on several geometric parameters affecting the weir discharge coefficient of direct trapezoidal piano key weirs have shown that the performance of this type of weir is about 22% higher than the rectangular piano key weirs. The weir discharge coefficient of the trapezoidal piano key weir (TPKW) is affected by the ratio of L^'/W (effective length/width of weir), however, Wi/Wo (inlet width/outlet width) has the least effect [14,15]. Karimi Chahartaghi et al. [16] examined the effect of arc angle on hydraulic performance of arced direct trapezoidal piano key weirs (ATPKW) and concluded that ATPKW models have suitable performance in comparison with the liner rectangular piano key weir (LPPKW) models. Karimi et al. [17] studied the angled rectangular piano key side weirs and found that for Froude numbers more than 0.35, the discharge coefficient increased and it was observed in the key angle of 30-degree. Kumar et al. [18] validated four equations provided by other researchers for the discharge coefficient of direct piano key weir in previous studies. Saghari et al. [19] studied experimentally the different types of trapezoidal piano key side weirs in an arced channel. They concluded that with increasing the weir head, the efficiency of piano key side weirs decreases in comparison with rectangular classic side weirs. For (y₁/P) > 1.45 (the ratio of upstream depth to the weir height), the efficiency of piano key side weirs decreases and becomes asymmetric to a constant value. Ghaderi et al. [20] evaluated the parameters affecting the discharge coefficient of trapezoidal sharp-crested side weirs. They concluded that in this type of the weirs, the intensity of flow deflection and kinetic energy increase for those parts of side weirs with high crest length. Al-Fawzy et al. [21] investigated the hydraulic jump and its relation with the physical characteristics of the gabion spillways. Ghanbari and Heidarnejad [22] investigated the effect of a triangular slit on the discharge coefficient of rectangular piano key weirs and concluded that the outputs of numerical model were consistent appropriately with the laboratory model data. It was observed that discharge coefficient of triangular piano key weirs was 25% higher than the rectangular piano key weirs. It was also observed that the change in slit shape on the input keys of the weirs increased the weir discharge coefficient by 36% and 13% for the weir heights of 5 cm and 7.5 cm, respectively. Kumar et al. [23] experimentally studied the discharge coefficient of direct rectangular and trapezoidal piano key weirs and found that the ratio of L^'/W and the weir height (P) have a significant effect on the weir discharge coefficient. Denys and Basson [24] examined the hydrodynamic behaviors of direct rectangular piano key weirs. They observed that the input keys were of the utmost importance in terms of the vortex. According to the studies conducted on piano key weirs and the importance of this structure in flow transfer and control through the channels, the present study examines the hydraulic performance of trapezoidal piano key side weirs with angle of 90° on the main channel wall. As shown in the previous research, there are few studies on this type of weir and its performance. In the present study, the importance of the effect of upstream water depth on the outflow velocity from the weir, the deflection of velocity vectors, the effect of kinetic energy correction coefficient and the amount of energy generated by the weirs have been discussed. In addition, the flow pattern over the weir has been evaluated in two modes.