Comparison of Downstream Scour of the Rectangular and Trapezoidal Piano Key Weirs

Weirs are hydraulic structure commonly used for controlling flow characteristics and water level (Vischer, 1998). Also, in dams, weirs are responsible for the controlled release of flood flows from the dam reservoir to the downstream channels. One of the types of weir is piano key weir (PKW). Piano key weirs are also very cost-effective and cheap to maintain, increase reservoir storage capacity, and offer better flood control (Ortel, 2018). The main problem at the downstream of hydraulic structures, such as weir, is the scour and movement of bed materials. Scouring in the downstream of weirs is an important issue for weir stability and has been extensively researched. In this study, the geometry of scour holes in the downstream of piano key weirs was investigated by the use of experimental models.
According to previous researches, trapezoidal piano key weirs (TPKW) are more efficient than rectangular piano key weir (RPKW) (Mehboudi, 2016). While there are limited studies on scour downstream of RPKWs, the scouring downstream of the trapezoidal piano key have not yet been researched according to the authors' knowledge(Jüstrich, 2016). So it is important to study their scour, and it is necessary to compare the performance of these two types of PKWs in terms of scouring issues.
Due to the fact that the geometric shape of the weir affects the downstream scour condition, in this study the downstream scour of the piano key weir with trapezoidal geometric shape has been considered and the characteristics of the scour and its rate of was compared to a rectangular geometric shape.
Accordingly, the impact of discharge and the tail water depth on the characteristics of the scour hole at the downstream of the rectangular and trapezoidal piano key weirs and the comparison of these changes in the two models have been considered. Measurements were made to predict the scour specifications of the rectangular and trapezoidal piano key weirs, including the maximum depth of the scour hole, the distance between maximum scour depth and weir foundation, and the length of the scour hole (Figure 2).
Methodology: In this study, two experimental models of PKWs with rectangular and trapezoidal geometry were made and tested in a flume with a length of 6.0 m, a width of 1.0 m and a height of 0.6 m. 2.0 m length with an average thickness of 25 cm was formed from sandy material with median grain size d_50=7.8 m (Figure 3). Three hydraulic conditions in upstream and three different tail water depth considered in downstream and totally 18 experimental runs were conducted. A summary of the initial conditions, numbers, and codes of the experiments is given in Table 2.
The range of changes in discharge in this research is between 19 to 33 liters per second. The reason for choosing this range for discharge is to examine the conditions of the scour profile in a wide range of flow rate changes. In addition, the dimensions of the channel and the pump used do not allow the discharge to exceed 33 liters per second.
Results and discussion: Effect of discharge on the scour hole profile downstream of the rectangular and trapezoidal PKW models are shown in Figure (8). It can be seen that in all models, as discharge and upstream head increase, so do the hole depth and hole length and the distance of maximum scour depth from the weir toe. Previous studies have reported similar findings for linear and nonlinear weirs (Jüstrich, 2016). As shown in Figure (4),In this study, the arrangement of inlet and outlet keys of weirs was considered different from previous researches, so it was observed that the maximum depth of downstream scour occurs below the output keys, the reason for this is the external spill jets from the output keys, which cause the scour hole to fall into the downstream through vertex. Also, comparison the scour hole characteristics of downstream rectangular and trapezoidal piano key weirs in Figure (9) shows that the maximum scour hole depth downstream of the rectangular model is higher than the trapezoidal model. The higher score hole depth in the downstream of the rectangular model than the trapezoidal model in similar hydraulic conditions can be attributed to the fact that, for any given flow rate, upstream-downstream total head difference is greater in the rectangular weir comparison to the trapezoidal weir . As shown in Figure (11), For both rectangular and trapezoidal models, at a constant flow rate, the depth and length of the scour hole have decreased with the increase of tail water depth. It is due to a decrease in the height of the drop jet and increase in jet speed during impact to downstream flow. To determine the effect of the geometric shape of PKW and the tailwater depth, the scour characteristics in rectangular and trapezoidal models in the range of conducted experiments were examined and compared based on the configuration of Equation ∅_s/H=a〖F_rd〗^b (H/h)^c. Then, the nonlinear regression method was used to determine the coefficients a, b, and c and formulate a number of equations for predicting the maximum scour depth, its location, and the scour hole length for rectangular and trapezoidal PKWs. These equations are presented in Table (3) .
Conclusion: The measurement results of the cascade characteristics showed that with increasing the flow rate and decreasing the tail water depth, the geometric characteristics of the score hole increase in both models. Also, the depth of scour in the rectangular model is more than the trapezoidal model. in all discharges, on averagely, get decreases %7 the ratio of dimentionless maximum scour depth of trapezoidal piano key to the rectangular model. but this difference decreases with increasing flow and total head on the weir, so that when in F_rd>3.9 this difference becomes insignificant and there is not a significant difference in the shape of the hole for both models. Using the regression method, several equations with appropriate accuracy were formulated for predicting the maximum scour hole depth, its location, and the scour hole length downstream of the models.