Experimental study of cavitation index in an ogee spillway by considering convergence angle of sidewalls Open Access

Chutes and ogee spillways are utilized as the most popular structures in the construction of dams (Wei 2006; Barati 2012; Shahheydari et al. 2015; Hosseini et al. 2016; Arami-Fadafan et al. 2018a; Bananmah et al. 2020; Tajnesaie et al. 2020). These types of structures are at the risk of cavitation due to the high level and velocity of water flow (Arami-Fadafan et al. 2018b). The cavitation is defined as the formation of a bubble or void within a liquid. The phenomena associated with cavitation are among the most important factors in which many hydraulic engineers are interested. The cavitation should be considered in both study and design of dam construction and other similar projects. The cavitation bubbles will collapse as they travel to areas with relatively higher local pressure (Rafi et al. 2012; Kermani et al. 2013; Rajasekhar et al. 2014; Usta 2014; Adama Maiga et al. 2016; Koen 2017; Yusuf & Micovic 2020; Karimi Pirmoosaei & Mardookhpour 2020; Kocaer & Yarar 2020). The cavitation can cause damage to a spillway or create a hole at high speeds of flow current, as the collapse of vapor cavities results in high pressure shock waves. Ogee spillways are widely used in the design of hydraulic structures because of their ability to release surplus water from upstream to downstream efficiently and safely when properly designed and implemented. In order to gain a better understanding of the ogee spillways and their characteristics, it is also understood that a deviation from the standard design parameters such as a change in upstream flow conditions, modified crest shape, or change in approach channel owing to local geometric properties can change the flow properties. Therefore, it is essential to test a hydraulic model with different spillways relevant to various dams with certain geometric conditions as the construction of dams and relevant facilities is costly. Moreover, there may be possible property damage, as well as loss of life, if a spillway does not function properly.

Ball (1976) examined the effects of flow on nonplanar surfaces on cavitation. He showed that cavitation occurs in velocities higher than 30 m/s, even indents equal to 3 mm. Chanson (1988) conducted comprehensive studies on aeration and aeration devices in a spillway model. He expressed that cavitation begins in the presence of poor nuclei. Kramer (2004) stated that cavitation mostly occurs in hydraulic machines and structures. This phenomenon lies in low pressure associated with high speeds, which usually occurs along the boundaries of hydraulic structures, such as chutes, spillways, and bottom drain pipes. After the cavitation occurs, such instabilities, including corrosion and erosion, can cause damage to the system. Based on observations of damage caused by cavitation, the general design guide only dependent on the critical cavitation number is presented in Table 1.

Zhang et al. (2013) measured impact pressures of up to 300 MPa due to the collapse and rebound of cavitation bubbles. Frizell et al. (2013) presented a correlation between the critical cavitation index and the common friction factor for flow on stepped spillways. Parsaie et al. (2016) simulated cavitation phenomena along a spillway's flip bucket of the Balaroud dam using Flow 3D software, and their results indicated that occurrence of cavitation based on cavitation index equal to 0.25 is not possible along the spillway. Kermani et al. (2018) applied the fuzzy k-nearest neighbor algorithm to cavitation damage prediction on dam spillways, and they found that the algorithm was efficient and suitable for this purpose. Ghazi et al. (2019) simulated the three-dimensional model of Shahid Madani Dam's spillway using Flow 3D software to study the probability of occurrence of the cavitation phenomenon. Their results indicated that at any flow rate with a return period of 1,000 years, the cavitation index is not lower than the critical cavitation number. Barzegari et al. (2019) used a numerical software to model the flow on the spillway of Aydoghmush Dam, and they found that cavitation did not occur at any of the considered flow rates. Yusuf & Micovic (2020) studied a prototype-scale modeling of cavitation damage to a newly resurfaced spillway. Factors that contributed to the cavitation damage for this spillway, including the duration of continuous spill and the increased cavitation potential of both a smooth concrete surface compared to one that is uniformly rough and sharp-edged steps compared to steps with rounded edges, were reviewed. Samadi-Boroujeni et al. (2020) focused on the modeling of the effect of bed roughness height of chute spillways on the cavitation index. Their results indicated that reducing the roughness height from 2.5 to 1 mm would not change significantly the value of the cavitation index at a 95% confidence interval. The focus of the present study is on the analysis of the effects of convergence angle of sidewalls on the cavitation index of the arc-plan ogee spillways. Three important limitations for the selection of a spillway location are as follows: (1) narrow width of the channel or reservoir outlet; (2) narrow width of the downstream river or narrow diameter of downstream exiting tunnels; and (3) the high amount of kinetic energy of the flow in the spillway downstream, which cause cavitation phenomenon and impose exorbitant costs of the stilling basin structure. The considered that ogee spillway can fade all of three aforementioned limitations. The narrow width of the channel or reservoir outlet can be eliminated by increasing the length of the spillway by an arc plan. The narrow width of the downstream river can be considered by convergence angle of sidewalls. The cavitation phenomenon can be controlled by stepped structure downstream of the proposed spillway. To this end, a physical model of this type of ogee spillway was constructed on a 1:50 scale. Then, it was tested with four different convergence angles, including 0°, 60°, 90°, and 120° relative to the spillway's sidewalls. Each one of the convergent cases was examined at six different flow rates per unit width, including 6.74, 16.88, 27.02, 30.39, 40.52, and 48.42 (l/s)/m.

The experiments were conducted at the Soil Conservation and Watershed Management Research Institute (SCWMRI) in Tehran, Iran. The structure of the spillway model was constructed using a polyethylene waterproof material. Plexiglas was used to construct the walls and bottom of the channel prototype. Table 2 summarizes the design parameters for 3D converging ogee spillway models with a 1:50 scale and the design parameters of the channel prototype.

As it is well known the impact of gravity was typically more important compared to the impact of viscosity and surface tension for free surface flows as considered for spillways in the present study (Falvey 1990; Crowe et al. 2009). Therefore, the model and prototype were generally based on the Froude (Fr) similarity in the scale relationship without considering the viscosity effect. This occurs when the Reynolds number is larger than a certain limit (= 104).

The experiment's first phase was executed at an angle of 120° with L_ch/L = 0.21. It should be stated that L is the crest length and L_ch denotes the downstream channel width. For all experiments, the discharge was monitored and measured using a sharp triangular weir with an apex angle of 90° at the channel output, where the channel was kept at a rough zero slope. The water surface profiles were monitored using a point gage along the centerline of the spillway with the other two specific lines located on either side. Uncertainties associated with experimental measurement for water elevation reading were ±1 mm. To monitor the pressure on the spillway, several taps were placed along the centerline of the spillway as well as the two abovementioned specific lines, which included 12 stations with known coordinates and then they were connected to the piezometers board. This approach to measure pressure was also used by Johnson & Savage (2006) and Naghavi et al. (2011). The velocity values were calculated by using the continuity equation with the known flow rate, width and flow depth in each station. Given the fixed downstream channel width, creating each angle changes the crest length of the spillway model due to operational constraints in the design of the prototype. Figure 1 illustrates the model from four angles, and Figure 2 presents a side view of the model.

In the second phase of the experiments, the constructed physical model was tested with three convergence angles between the sidewalls, including 0°, 60°, and 90° with three different L_ch/L ratios of 0.98, 0.32, and 0.26. In order to consider the constant downstream channel width, a changing spillway's length of the crest for every angel θ was considered. As can be found in Table 3, flow rates were considered with variation of θ based on the unit discharge flow rate (q) at the crest in order to maintain constant conditions for all of the convergence angles of different tests.

Falvey (1990) presented a complete set for another rough answer. For example, he showed that the tunnel spillways with indexes equal to or lower than 0.2 are influenced by cavitation. However, tunnel spillways with indexes higher than 0.2 are not influenced by cavitation.

In the present study, the physical model of the spillway of Garmi Chai dam in East Azerbaijan province, Iran with a scale of 1:50 was used. This spillway has an angle of 120° and its Qpmf (probable maximum flood) and maximum allowable head respectively are 717 m³/s and 5 m. The spillway tested in the first part of the experiments at an angle of 120° with Lch/L = 0.21 at the highest allowable head and it could not pass the maximum flow rate. The reason for this situation was the sharp angle and excessive shrinkage of the ratio of the downstream channel width to spillway crest length. Therefore, the experiments in the second phase led to the use of smaller angles that had a larger Lch/L ratio (i.e. increasing the width of the downstream channel). By considering this issue, 90°, 60° and 0° angles were selected and tested in the experiments. Based on the obtained experimental data, a continuous and supercritical flow that ran over the studied spillway at different angles can be observed. This occurred in all cases except the following conditions: at the angles of 90° and 120° with L_ch/L ratios of 0.26 and 0.21, where the spillway was submerged in flow rates per unit width of 48.42 and 40.52 (l/s)/m, respectively. Moreover, the flow regime changed to subcritical flow. The convergence of the sidewalls at 60°, 90° and 120° led to the occurrence of the rooster tail phenomenon at the toe of the spillway, as shown in Figure 3.

According to the experimental observations, the flows over two sides of the spillway were similar, which agrees with the results reported by Roushangar et al. (2020). Therefore, the average values of the cavitation index in removable sectors were compared at different flow rates and angles. The cavitation index for the angle of 120° and flow rate per unit width of 16.88 (l/s)/m in the five different sectors presented in Figure 4 to provide a better understanding of the similarity of the flows over both sides of the spillway. The lowest cavitation index in all cases was observed at the station with an X/H_d of 2.42. This parameter was found to be 1.54 at the angle of 0° with L_ch/L of 0.98, while being equal to 2.20 at the angle of 60° with L_ch/L of 0.32, at the constant flow rate per unit width of 40.5 (l/s)/m.

The cavitation index was calculated at 2.18 for the angle of 90°, L_ch/L = 0.26, and flow rate per unit width of 30.39 (l/s)/m, while it was found to be 1.95 for the angle of 120°, L_ch/L = 0.21, and flow rate per unit width of 16.88 (l/s)/m. As can be seen, the most critical index is not necessarily observed in the maximum flow rate as previously discussed by USBR (1995). However, the obtained results indicated that with the rise in the flow rate, the cavitation index decreases relatively at both chute and crest of the spillway, but increasing at its toe. Figure 5(a)–5(d) depicts the cavitation index for different flow rates per width at various angles, including 0°, 60°, 90°, and 120°. The vertical axis of the chart was plotted for only the cavitation indexes of up to 15 as the purpose of plotting the charts is to show the changes in the values closer to the critical indexes.

As can be seen in Figure 5, the areas prone to damages caused by cavitation are the bottom chute and toe of the spillway, given the minimal values of the cavitation index at different angles based on the critical cavitation index (Cr = 0.2σ).

The variations of the cavitation index for four convergence angles 0°, 60°, 90°, and 120° are presented in Figure 6. As can be seen in the area between the crest and the middle of the chute of the spillway, changes in the convergence angle have no effect on the cavitation index. However, at the end of the chute and the toe of the spillway, the cavitation index rises with the convergence angle. The Froude number over the spillway for four convergence angles 0°, 60°, 90°, and 120° is depicted in Figure 7. As can be seen, the convergence angle for a fixed flow rate per unit width increases when the Froude number decreases. These results indicate that if the convergence angle increases, the gravity force surpasses the inertial force in the hydraulic flow. Consequently, the growth rate of the depth increases with respect to the velocity.

The present study focused on the experimental study of the convergence angle effects on the convergence angle of an ogee spillway's sidewalls with an arc in the plan. The convergence angle was varied in the range of 0° to 120°. Moreover, six different flow rates per unit width were considered in the range 6.74–48.42 (l/s)/m. According to experimental observations and analysis of them, the similarity of the flow at both sides of the spillway was found for all considered convergence angles. The lowest cavitation index was 1.54 at an angle of 0° with X/H_d = 2.33, L_ch/L = 0.98, and flow rate per unit width of 40.52 (l/s)/m. It was observed that the most critical index was not necessarily observed at the maximum flow rate. As the flow rate increased, the cavitation index declined relatively at both crest and chute of the spillway while growing at its toe. Such changes in the cavitation index were observed for all convergence angles 0°, 60°, 90°, and 120°. In the area between the crest in the middle of the chute and the toe of the spillway, the cavitation index increased with the increase in the convergence angle and the consequent reduction in the ratio of L_ch/L. When considering more sets of experiments, the use of numerical simulation tools can be considered as numerical experiments in future research. The presented results of physical experiments can be used to validate the numerical model. Finally it can be said that the proposed ogee spillway can be used by design engineers with execution details for real field projects.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.