Experimental and Simulation Studies on Water Discharge Coefficients of Rectangular Piano Key Weirs

The piano key weir (PKW) is a developed type of labyrinth spillway with the ability to transfer large amounts of discharge by keeping executive costs constant. In this study, the parameters affecting the discharge coefficient of nine models were evaluated using physical models and simulations by Flow-3D software. The PKW models included: PK1.0, PK1.1, PK1.2, PK1.3, PK1.4, PK1.5, and PK1.6 representing the width ratios of the inlet (W_i) to outlet (W_o) keys of 1.0, 1.1, 1.2, 1.3, 1.4, 1.5 and 1.6 respectively and the other two models were PKT (PK1.1 with a thicker wall) and PKTP (PK1.1 with a thicker wall and an enhanced crown). According to the results of experimental and simulation evaluations, the model of PK1.4 was selected as the optimal model, which increased the discharge rate by 30% compared to the control weir. Moreover, increasing wall thickness (PKT model) led to an increase in the discharge and installing a parapet wall (PKTP model) resulted in an increase in discharge and a uniform distribution of flow lines on the weir. Considering the superiority of models PK1.4, PKT, and PKTP, the geometric properties of these models can be used to optimize the design of PKWs.

Flow-3D; Overflow; Parapet wall; Physical models; Piano key weir; Water flow

    Recent technological advances have created vast facilities for constructing large dams, reservoirs, and canals. Increasing the water discharge has a decisive role in increasing the reliability of water storage structures such as dams, and in this case, spillways are designed to pass large discharges through a hydraulic structure without causing major damage to the structure and its surroundings (Karimi Chahartaghi et al., 2020).

    Based on dam failure reports, one-third of failures were caused by low overflow discharge capacity (Kabiri-Samani & Javaheri, 2012). By conducting numerous studies, the researchers concluded that overflows should be constructed non-linearly to achieve high-performance economic structures. One of the simple and affordable solutions is to design piano key weirs (PKWs) (Lempérière & Ouamane, 2003; Erpicum et al., 2014). The PKW is a new shape of labyrinth spillway presented by the Hydrocoop research institute in collaboration with the University of Biskra, Algeria, in 2003 (Lempérière & Ouamane, 2003; Pralong et al., 2011). This type of weirs has the advantages of having a high discharge capacity, being slightly affected by ground constraints, and being economically efficient (Li et al., 2020). It can easily be used in irrigation and drainage networks to increase the water head and reduce the water’s extra energy. According to the conducted studies, the flow passing through a PKW is at least four times that of traditional spillways. Furthermore, these types of overflows are applicable for modifying the vortex in circular vertical overflows, which sometimes reduce the flow rate or cause vibration, crash, cavitation, distribution, and separation of flow lines and in many cases, endanger the safety of structures. In fact, the anti-vortex blades created by these overflows can slow down the flow (Shemshi & Kabiri-Samani, 2017). Many studies have been carried out on the PKWs, all of which have concluded that, at low head pressures, increasing the number of overflow openings increases the efficiency of the overflow (Machiels et al., 2012; Ribeiro et al., 2012; Anderson & Tullis, 2013). The studies conducted by Hien et al. (2006) indicated that six openings in low head pressures and five to seven openings in high head pressures increase the discharge coefficient. Noui and Ouamane (2011) and Hien et al. (2006) found that if the inlet opening is chosen larger than the outlet opening, it will have resulted in an increase in the discharge of the overflow.
    Studies by Eslinger and Crookston (2020) showed that increasing the ratio of the inlet to outlet key width (W_i/W_o) increased the hydraulic efficiency of the piano key weirs significantly and had very little effect on energy dissipation. The experiments of Khassaf and Al-Baghdadi (2018) showed that the effect of increasing the ratio of W_i/W_o to 2.5 reduced the discharge coefficient of piano key weirs by 12%.
    Although most studies (Seyedjavad et al., 2019; Feili et al., 2020; Kumar et al., 2020) have now shifted to trapezoidal piano key weirs, the benefits of rectangular piano key weirs, such as simple physical and software modeling, simple execution, and uniform distribution of incoming loads, has led to studies to improve quality and quantity of these types of overflows.
    Today, computer models based on numerical solutions are increasingly used in a wide range of applied research (Šimunek et al., 2008; Syaiful et al., 2017; Agrebi et al., 2019; Yanuar et al., 2020). Flow-3D is one of the most powerful 3D software packages for computational fluid dynamics with a wide range of applications and capabilities (Parsaie et al., 2015) due to its critical features such as user-friendly specifications, high simulation efficiency, and strong graphical interface (Taghavi & Ghodousi, 2015).
    Despite the extensive studies on PKWs, there is still no comprehensive and accurate information on flow characteristics in this kind of overflow, as well as the relationships illustrating the straightforward changes of the inlet (W_i) and outlet (W_o) openings ratios, wall thickness and the height or flanging of outlet keys have not been provided till now. Therefore, the overall aim of this study was to improve the discharge coefficient of piano key weirs, and to achieve this aim; experiments were performed with the following objectives: (i) providing an optimum ratio of the inlet to outlet keys widths (W_i/W_o) of rectangular PKWs in the range of 1-1.6 through experimental models and Flow-3D simulations, (ii) maintaining the effects of changing in wall thickness and height of the outlet keys on weir performance.

    In the present study, the optimal condition of geometrical parameters affecting the discharge coefficient was determined by physical models and the Flow-3D software. The results of Flow-3D simulations were consistent with the experimental results. A geometrical analysis of the models revealed that the discharge coefficient could be improved without changing the keys' length or width. By increasing the wall thickness in the study range, vibrations on the weir were reduced, and the shape of the water blade became more regular, while the flow rate was significantly increased. The crest heightening by adding a parapet wall increased discharge and uniform distribution of flow lines on the weir, in addition also to removing the turbulent flows and snail-shaped vortices. In general, modifying the geometry of the weirs should be taken to increase the useful width of the inlet keys and reduce the local submergence in outlet keys. The outcomes of this research can be used to optimize the parameters and design of rectangular piano key weirs.

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