Introduction
Piano key weirs (PKWs) are a new form of non-linear weir that has a higher flow capacity than other similar weirs. These weirs have rectangular, triangular, and trapezoidal shapes in plan. They are available in four types: A, B, C, and D. Many researchers have investigated the effects of flow, additional structures, bed material diameter, and other factors on the maximum scour depth. Researchers such as Fathi et al. (2024, 2025), Abdi Chooplou et al. (2024a & b), and Kazerooni et al. (2024) have investigated the effect of flow, material diameter, tailwater depth, and additional structures on the maximum scour depth. Considering the existing studies on localized scour downstream of PKWs, there is still a need for cheaper and more efficient solutions to reduce scour in these weirs, especially type B PKWs. In the present study, a type B trapezoidal PKW with riprap downstream was used under submerged flow conditions. Also, three different flow rates, three different tailwater depths, gravel bed materials, and riprap materials with lengths of 0.10, 0.20, and 0.30 m were used downstream of the weir. Furthermore, an equation derived through dimensional analysis demonstrated a high correlation (93.73%) with the observed data for predicting the maximum scour depth.
Methodology
The experiments were conducted in a flume 10 m long, 0.8 m wide, and 1 m high. The flow was fed into the channel from an underground reservoir by a Programmable Logic Controller (PLC), a pump, and an 8-inch diameter pipe. The width of the weir inlet keys (Wi) is 0.215 m, the width of the weir outlet keys (Wo) is 0.075 m, the length of the weir side wall (B*) is 0.4 m, the length of the upstream overhang of the weir (Bi) is 0.15 m, the thickness of the weir crest (Ts) is 0.01 m, and the length of the weir crest (L*) is 3.27 m. The weir has three outlet keys, two inlet keys, and two inlet half keys (Fig. 2). The average diameter of the riprap material (dr) is 0.033 m. Three different lengths of riprap, 0.1, 0.2, and 0.3 m, were used downstream of the weir. The thickness of the ripraps was constant in all experiments and was three times the diameter of the riprap material (i.e., 0.1 m) (Lidya et al., 2022). Table 1 presents the hydraulic and sedimentary parameters that affect downstream scouring for a type B PKW with riprap under submerged flow conditions. A total of 27 experiments were conducted under these conditions to calculate the maximum scour depth.
Results and Discussion
The flow from the weir inlet keys was transferred downstream as a free jet into the outlet keys and downstream as an inclined jet from the outlet keys. The flow converged at the beginning of the outlet keys and entered them. Unlike in free-flow conditions, a localized immersion zone does not form at the beginning of the outlet keys under submerged flow. Consequently, a higher flow height is also not observed in that area. The formation of surface vortices in the outlet keys results from the interaction of two flows: the undercurrent in the outlet keys and the overriding current from the inlet keys. As mentioned, these vortices entered the bed superficially and with less force. Ripraps are heavier, and surface eddies cannot easily carry them downstream. Clearly, the data show that the maximum scour depth increases with increasing flow rate. Furthermore, the maximum scour depth decreases significantly with increasing riprap length. As the tailwater depth increases, the flow downstream of the weir has a lower velocity, and the tailwater depth reaches a point where it mixes with the flow exiting the weir. The flow slows down, and its velocity decreases. As the depth of the outfall increases, the propagation length of the jets that hit the bed materials increases. Figures 3, 4, and 5 show the effect of flow rate, tailwater depth, and riprap length on the maximum scour depth under submerged flow conditions. On average, in a 0.10 m riprap, the maximum scour depth increases by 65.1% and 76.5%, which is associated with a 14.3% and 25% increase in flow rate, respectively. Similarly, in a weir with a 0.20 m riprap, the maximum scour depth increases by 71.9% and 81.5% with 14.3% and 25% increase in flow rate, respectively. Furthermore, in a weir with a riprap of 0.30 m, the maximum scour depth increases by approximately 76.6% and 85.4% with a 14.3% and 25% increase in flow rate, respectively. On average, in a weir with a 0.10 m riprap, the maximum scour depth decreases by approximately 1.24% and 1.51% with an 8% and 14.8% increase in the tailwater depth, respectively. Similarly, in a weir with a 0.20 m riprap, the maximum scour depth decreases by approximately 28% and 48.8%, with 8% and 14.8% increase in the tailwater depth, respectively. Furthermore, in the weir with a 0.30 m riprap, the maximum scour depth decreases by about 28.2% and 55.9%, respectively, and is accompanied by 8% and 14.8% increase in the tailwater depth.
Conclusion
This study investigated the reduction of local scour downstream of the PKW Type B using riprap under submerged flow conditions. The presence of riprap significantly reduced the maximum scour depth, with ripraps of 0.30 m length being more effective than ripraps of other lengths.
Key Findings:
• Riprap significantly reduces scour depth in submerged flow mode.
• Due to the absence of an overhang downstream of the Type B PKW, the outflow from the inlet keys flows close to the weir toe, which increases scour along the weir toe.
• Riprap lengthens the scour hole and moves the maximum scour depth away from the weir toe.
• With taller ripraps, the scour depth is reduced.
• The scour index shows the lowest value for the submerged flow condition with the longer riprap.