Effects of a conical enlarging shaft on hydraulic performances of siphon-shaft spillways

Spillways can be grouped into controlled (gated) and uncontrolled (free overflow) spillways in general. Thanks to the controlled spillways, the water level can be adjusted precisely or kept constant above the crest level. Thus, a better reservoir operation can be achieved by minimizing the level changes in the reservoir. However, the biggest problem of this type of spillway is the maintenance, repair, and operating costs of the moving hydraulic elements, although they cannot be operated very often. In the other type, free overflow spillway, water is allowed to pass freely over a fixed spillway profile when it exceeds the crest level. However, since it is not possible to control the water level, large level changes occur during floods and thus an effective reservoir operation cannot be achieved. Siphon-shaft spillways can offer the advantages of these two spillway types together. Siphon-shaft spillways do not need any movable control elements, and water level changes in reservoirs do not affect the spillway discharge much. They also have the capability to sluice below the crest level (like bottom outlets). Thus, more effective flood control can be achieved in the reservoir when necessary. Since siphon-shaft spillways are placed inside the reservoir, they can be used safely even in embankment and arch dams where spillways have a placement problem. However, it is still recommended to build a free overflow second spillway due to the operating modes and limited capacities of these spillways. One of the most important problems to be considered in the design of these spillways is cavitation. Siphon vacuum pressures need to be controlled and therefore their operating heads are limited. Another problem is limited sluice capacities.

The use of siphons in dam spillways has attracted the attention of researchers since the beginning of the 20th century. Davis & Stickney (1914), Stickney (1922), and Lawaczeck (1930) developed different siphon designs for dam spillways. Rousselier & Blanchet (1951), Head (1971), Charlton (1971), Ackers & Thomas (1975), Head (1975), Unser (1975), Ali & Pateman (1980), Ervine & Oliver (1980), and Bollrich (1994) conducted various theoretical and experimental studies on the design and performance of siphon spillways. Since the beginning of the 21st century, many researchers have tried to determine the performances by analyzing siphon spillways in different designs and hydraulic conditions with experimental and numerical methods (Babaeyan-Koopaei et al. 2002; Houichi et al. 2006; Yücel 2008; Jourabloo 2010; Ghafourian et al. 2011; Musavi-Jahromi 2011; Tadayon & Ramamurthy 2013; Aydın et al. 2015; Petaccia & Fenocchi 2015).

Although there are many studies on both siphon and shaft spillways, there are limited studies on siphon-shaft type spillways, as a hybrid spillway. The idea of equipping a shaft spillway with a siphon was first put forward by Iyer (V.G.) in 1933–1934 in order to rapidly increase and maximize the flow of a shaft spillway. Later, Binnie (1938) applied a siphon to a bell-mouthed shaft spillway. This type of spillway, which will be called siphon-shaft, was first applied at Marconahali (India) dam and then again at Hirebhasagar dam in India. Binnie (1938) conducted experiments on the siphon-shaft weir that he created by adding a hood to the shaft weir to be used as a spillway in the existing diversion tunnel. Ağıralioğlu (1977) suggested that the section above the cavitation critical height could be enlarged in order to reduce vacuum pressures in high-head siphon-shaft weirs. Khatsuria (2005) pointed out that some precautions must be taken to prevent the formation of cavitation by vacuum pressures in a siphon spillway. Aydin & Ulu (2021) studied the aeration performance of the aeration holes to prevent cavitational pressures based on the idea of Ağıralioğlu & Müftüoğlu (1989). This study focuses on the enlargement effect of the siphon-shaft profiles on the vacuum pressures in the shaft, which is able to trigger cavitation. Aydın & Ulu (2023a), inspired by Ağıralioğlu (1977), developed a pressure-controlled siphon-shaft spillway profile based on Bernoulli's principle. A disadvantage of this profile, which can adjust cavitation pressures very effectively, is that it creates a large footprint. In this study, the aim is to examine the expansion effect at the shaft mouth by using linear profiles instead of non-linear profiles (Wagner's profile and the pressure-controlled profile offered by Aydın & Ulu (2023a)). For this, some conical profiles with different enlarging angles were applied to a siphon-shaft spillway and their effects on cavitation pressure and discharge performance were investigated.

According to the nappe head on the crest, the spillway flow is controlled by three different flow conditions: free flow, submerged, and full orifice. In all three cases, hydraulic sections do not operate at full capacity due to effects such as swirling, vibration, turbulence, and air intake. The hydraulic performance of shaft spillways depends on the hydraulic profile at the entrance of the shaft. While using the Wagner profile that fits the free flow jet suggested by USBR on a solid shaft spillway, crest shapes such as daisy, labyrinth, and piano-key were also tried in addition to morning-glory in order to increase the discharge capacity (Aydin & Ulu 2023b). Siphon-shaft spillways, which are formed by covering the top of the shaft spillways with a hood and operating them with the siphon effect, can be operated with pressure and full hydraulic capacity even at low water heads or reservoir levels below the crest. However, the low siphonic pressures of these spillways must be kept under control. For this purpose, a shaft profile specifically for siphon-shaft spillways was first developed by Aydın & Ulu (2023a). Developed based on the Bernoulli principle, this pressure-controlled siphon-shaft profile offers a very effective performance in terms of high discharge and pressure control, while giving a wide footprint.

Ağıralioğlu (1977) conducted a series of physical model studies in a hydraulic laboratory to develop a head shape for a siphon-shaft spillway and to verify the mathematical model results he obtained. Some data of this experimental model are used as a benchmark (for c = 75, a = 160, d = 110 mm) to validate the numerical model. In the benchmark model, the shaft profile was described based on the USBR (1987) design principles for the submerged flow condition of the shaft spillway. A standard profile (Wagner profile) was applied to the shaft entrance in order to keep the head dimensions small. Since the shaft inlet is always full during a siphonic flow, it was stated that it would be appropriate to determine the shaft inlet profile according to the submerged state of sharp-edged shaft weirs. The shaft profile for the physical model was obtained from Wagner (1956) tables for Q = 60 l/s, R_s = 0.16 m, H_o = 0.12 m, P_c = 0.32 m, operating head H = 0.124 m, and H/R_s = 0.775. The shaft diameter (D) was obtained as D = 0.18 m by trial and error, assuming 75% full at the flow rate at the project operating head, so that the difference between the crest level and the base outlet elevation was 1.0 m. According to the recommendation of USBR (1987), the radius of curvature of the elbow was chosen greater than 1.5 times the diameter of the gallery, and the radius of curvature of the inner wall was taken as 2D = 0.36 m and thus the radius of curvature of the elbow center was taken as 0.45 m.

An uncertainty analysis, Grid Convergence Index (GCI), was also performed to reveal the grid sensitivity on the numerical solutions based on the ASME procedure (Roache et al. 1986; Freitas 1993; Celik et al. 2008). Three grid sizes (fine, medium, and coarse grids) were applied to the numerical domain with a grid refinement factor of 1.4. The maximum numerical uncertainty for the velocity profiles in the fine-grid solution was reported as 0.16%, which corresponds to ±0.0026 m/s for the centerline, and 3.1%, which corresponds to 0.052 m/s. The global average of the local order of accuracy was determined as 18.02 for shaft-centerline and 8.01 for shaft-edge, which indicates good calculations. The maximum relative errors are 0.8 and 2.8%, respectively. It can be noticed that all uncertainties are within reasonable limits with respect to the grid size.

In Figures 8(c) and 8(d), the velocity distributions near the shaft surface are given for the minimum and the maximum operating heads, respectively. As seen in these plots, the conical profiles reduce flow velocities toward the crest from 15 to 2 m/s for H_min = 10 m, and from 20 to 3 m/s for H_max = 20 m. The average decreases in flow velocities are between 25 and 50% with P2–P4 conical profiles for Z ≥ 0. For Z < 0, an average increase of 20–25% was observed at the velocities in the shaft due to the increase in the discharge capacity with the conical profiles. In general, the coning angle has an increasing effect on the pressure distribution and a decreasing effect on the velocity distribution along the conical shaft. These effects are more pronounced for high operating heads (Figure 8).

This study focuses on the effect of a linear expanding shaft profile (conical shaft) on the hydraulic performance of siphon-shaft spillways. For this purpose, conical shaft profiles with three different coning angles were used together with a linear shaft profile. The prepared models were analyzed with a three-dimensional CFD technique, the accuracy of which was tested by a reliable procedure in the literature. In the model calibration tests, the results of the CFD models showed a maximum deviation of 4.4% from the experimental results in terms of spillway discharges. The maximum grid uncertainty for the velocity profiles was calculated as 3.1%, which corresponds to an edge velocity of ±0.052 m/s. Numerical analysis details are shown that increasing the coning angle significantly decreases the vacuum pressures and velocities in the siphon-shaft. Therefore, it is noted that the use of conical shaft mouths in siphon-shaft spillways significantly reduces the risk of cavitation, as well as increasing discharge performance. It also provides an average 11% increase in discharge efficiency. In addition, it can provide economy thanks to a lower footprint, but attention should be paid to the streamlining capability due to sudden turns in the transition sections. In terms of better hydraulic efficiency, the pressure-controlled profile developed for siphon-shaft spillways by Aydın & Ulu (2023a) may be a more suitable option despite a larger footprint. It should also be stated that this study was carried out under certain limitations with three different cone angles (0 ≥ α ≥ 20°), an operating head range of 10 m ≥ H ≥ 20 m, and a shaft diameter of D = 4 m. It is recommended to carry out a detailed hydraulic modeling study where dimensionless parameters will be applied so that the study can be applied to different dimensions and hydraulic conditions.

This study was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) with the project No. 219M006.

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

The authors declare there is no conflict.