## ABSTRACT

A spillway is the essential part of the dam body, which releases surplus flows. At higher floods, the spillway operates at high heads, which results in high flow velocities along the chute and may cause negative pressures and cavitation. Therefore, to minimize such issues, aerators are provided along the spillway's chutes. This study aims to analyze the performance of the high-head overflow spillway of Mohmand Dam, Pakistan, having a steep chute of 32° with multiple aerators. Based on Froude's law of similitude, the physical model study was carried out at Irrigation Research Institute, Nandipur, on a scale of 1:60, while FLOW-3D numerical models were used to compare different hydraulic parameters, i.e., flow depth, velocity and pressure. The numerical models were validated with the results of a physical model, which were found in an acceptable range (i.e., 4.93%), and the hydraulic performance of two aerators was evaluated at different discharges. The models indicated negative pressures inside the aerator cavity, which allowed the suction of air to the lower nappe. The maximum air entrainment at the first aerator was about 8.5%. The results also showed that air entrainment to the lower nappe decreased when discharge was increased, whereas the maximum air detrainment reached 11.3% downstream of the second aerator**.**

## HIGHLIGHTS

This study investigated the use of multiple aerators for air entrainment and detrainment at high-head overflow spillway.

Positive and negative pressure profiles were examined along the spillway chute.

The CFD model was validated on the basis of physical model results of water surface profile and cavity pressures.

This study aimed to analyze the spillway chute performance against the cavitation effects by determination of the cavitation index.

## INTRODUCTION

Large dams include high-head spillways and outlets which release high-magnitude floods. For the design of spillways, with high return periods and large-magnitude floods, hydraulic design engineers face multiple challenges which can damage the spillway, if not properly addressed. One of the challenges in spillway design is cavitation control along the length of the chute. Cavitation is the process in which liquid transforms into vapor state due to the lowering of local pressure to vapor pressure at a certain temperature. This reduction in localized pressure is found to be the result of turbulence and vortex in the flow (Falvey 1990; Jahani 2011). High-head spillways are mostly provided with steep chute slopes over which flow velocities are large enough to cause the development of negative pressures increasing cavitation potential at the concrete surface. Pinto *et al.* (1982) pointed out the implication of the sensitivity of pressure fields at a high flow velocity of 40 m/s. Also, Pinto (1988) stated damage possibility to concrete surfaces for a cavitation index of less than 0.25. A later study by Falvey (1990) suggested initiation of cavitation if the cavitation index falls below 0.2 and flow velocity exceeds 30–32 m/s. These are critical limits for monitoring cavitation on spillways.

According to Damiron (2015), the phenomenon of cavitation is not alarming unless it occurs near a solid boundary, i.e., side walls, chute slab, stilling basin floor and baffle blocks. Due to the collision with solid boundaries, bubbles start removing the material from the surface. Bahena *et al.* (2018) developed a large-scale (1:21) physical model for the Huites Dam spillway with a prototype design discharge of 11,225 m^{3}/s, to study the combined effect on air entrainment of crest pier and aerator at the bottom of the smooth spillway. The study showed the variation in air concentration at/near the chute floor due to the impact of shock waves that are generated at the impingement point of the trajectory from the aerator ramp.

The environmental impact of artificially entrained air through aerators is also important. The air introduced through spillway aerators increases the dissolved oxygen (DO) content in a spillway which is beneficial for downstream ecology (Aras & Berkun 2010). Emiroglu & Baylar (2005) studied the influence of sill slope and angle for labyrinth-type spill weirs on the aeration of a downstream stream. Aras & Berkun (2008) studied the effect of aeration from spillway releases on streams with deficient DO content. According to Aras & Berkun (2010), spillways provide an increase in DO content due to aeration along the spillway chute and steps and turbulence in the stilling basin. They compared the effect of smooth and steeped spillways on stream re-aeration.

When prototype data are not available at a project under design or study, a physical model is used to validate the computational fluid dynamics (CFD) model. According to Roache (2008), validation can be defined as the process of determining the degree to which a model is an accurate representation of the real-world situation to confirm the intended purpose of the model. Researchers, such as Kanyabujinja (2015), Burnham (2012) and Gessler (2005), employed FLOW-3D numerical models for spillways and validated their models with physical or experimental studies. Sarwar (2018) carried out physical testing for the Bunji Dam orifice spillway to observe the effect of ramp angle on jet trajectory. In this study, physical model results were used to validate the CFD model of the spillway.

According to Pfister & Chanson (2014), in free surface flows the similitude is based on Froude's similarity that allows correct representation of the dominant forces, i.e., gravitation and inertial forces. As a result, the flow properties such as those due to capillary and viscous forces might be incorrectly reproduced, affecting the air entrainment and transport capacity of a high-speed model flow. Early researchers such as Pinto *et al.* (1982), Kobus (1984), Koschistzky *et al.* (1984) and May (1987) pointed out scale effects in physical models when dealing with spillway flow aeration. Aydin (2017) performed a physical model study for a spillway aerator using a laboratory flume setup with a high-speed water jet connected to a high-level reservoir. His study concluded the efficiency of bottom inlet aerators for Froude numbers lower than 5.0 for wider chutes, utilizing air ducts arranged along the chute width for uniform aeration. When modeling aerators, in addition to gravitational forces, similarity with respect to surface tension and viscous forces is also essentially required which are addressed by the Reynolds number and Weber number, respectively (Pfister & Chanson 2014). If the similarity of Reynolds and Weber numbers is not achieved, scale effects are produced. Models developed for Froude number will perform well for flow depth, velocity and pressure measurements owing to similarity regarding gravitational forces (Aydin 2017). The decrease in model size increases the scale effects which in turn affect the results of the physical model (Curtis 2016). Aydin *et al.* (2020) comprehensively discussed the model size and scale effects with respect to the work of previous researchers and concluded that the rates of air entrainment from the 1:60 scale model will have significant scale effects, emphasizing the importance of model scale and scale effect elimination.

Yang *et al.* (2020) used CFD models to study two-phase flows on a large dam spillway located in Sweden. The study recommended that CFD models may be employed for the investigation of spillway aeration because due to the scaling effects physical models were found to be limited in reproducing the aeration phenomena. Many researchers have employed aerators for the spillway chute; however, a few of the most relevant studies are highlighted here. Kurt (2016) studied aerator performance using a single aerator set based on previous studies by Demiröz (1985) and Aydin & Ozturk (2009) and suggested multiple aerators for cavitation prevention on large spillway chutes.

For the physical modeling of spillway aeration, the scale of the physical model has to be appropriately large enough so that the phenomena can be well represented. This is one of the major problems faced by modelers and hydraulic engineers. Due to the advancement in computer technology and numerical models, hydraulic engineers nowadays are able to model a full-scale prototype of the spillway, which greatly helps the design and performance evaluation of high-head overflow spillways with multiple aerators. Therefore, in view of the above-mentioned, a 3D hydraulic numerical model using the code FLOW-3D is configured to assess the performance of the Mohmand Dam high-head overflow spillway with a steep chute of 32° having two aerators in its upper spillway. The CFD model is simulated for three different discharges, i.e., 14,000, 18,000 and 22,500 m^{3}/s, and aerators’ performance is evaluated by experimental investigation of water surface profile, flow velocity and pressures. The results of the present numerical model are validated with the physical model.

Previous studies on spillway aeration and aerators point toward the importance of air entrainment to lower nappe for cavitation prevention. Kurt (2016) suggested a systematic study of multiple aerators for long spillway chutes where a single aerator is insufficient. It is worth mentioning here that the introduced air from aerators to the lower nappe should be controlled because excessive air entrainment may result in high flow depths along the chute and overtopping of spillway sidewalls as seen at Nurek Dam spillway, Tajikistan, where seven aerators were initially provided to safeguard against cavitation (Chanson 2012). The required number and spacing of aerators are, therefore, to be worked out with care, considering all possible factors that may contribute to excessive air entrainment. This case study will add to the knowledge set of multiple aerator analyses on a high-head overflow spillway using both physical experiments and numerical (CFD) modeling.

## STUDY AREA

The dam site is situated about 37 km from Peshawar City and 5 km upstream of Munda Headworks. It consists of an ogee-crested overflow spillway with seven radial gates, each 15 m wide and 21 m high. The dam crest and spillway crest elevations are 563.0 and 539.0 a.m.s.l. The spillway design capacity is about 25,360 m^{3}/s (240 m^{3}/s/m) with a design head of 17.63 m. The energy dissipation arrangement of the spillway consists of the upper and lower stilling basins. The spillway has 32° steep chute slopes where flow velocities reach 30 m/s and may result in cavitation of the spillway chute. To prevent cavitation damage, multiple aerators have been provided to inject air into the lower nappe of chute flows to minimize negative pressures.

## MATERIAL AND METHOD

In the first phase, a physical model is developed and operated for different scenarios. Hydraulic parameters for each scenario are observed and recorded against operated discharges. In the second phase, the numerical modeling code FLOW-3D is used. The second phase consists of the preparation of three-dimensional spillway geometry, numerical model configuration, sensitivity analysis, validation, 3D simulation, etc.

### Physical model study

A physical model study was carried out on a 1:60 scale model of Mohmand Dam, constructed by the WAPDA Model Study Cell at Irrigation Research Institute, Nandipur. The aim of the physical model study was to physically observe hydraulic parameters along the spillway chute. Hydraulic parameters, such as water surface profile, flow velocity and pressures, were observed at 14,000, 18,000 and 22,500 m^{3}/s, respectively. The experimental setup consisted of a 502 cm long and 172 cm high scale model of the spillway with transparent plexiglass sidewalls and chute floor, fixed in place on a steel frame. The model transparency through plexiglass sheets helped monitor the water surface and observe profile fluctuations and flow behavior at aerators and in the stilling basin. Using stage gauges in the upper spillway reach, the water surface profile was measured at 12 points while velocity using the current meter was recorded at 6 locations. The pressures inside each aerator cavity were also measured using piezometers, respectively. The physical model was constructed according to Froude's Law of Similitude. The conversion relation between the scale model and prototype dimensions is determined accordingly and given below:

Length (Lr) = 1:60;

Flow velocity (Vr) = Lr

^{1/2}1:7.75;Pressure (Pr) = Lr 1:60;

Discharge (Qr) = Lr

^{5/2}1:27885.5.

As said earlier, the basis for the physical (experimental) model is Froude's similarity. An assessment for scale effects on the physical model is also made. The maximum values of Froude, Reynolds and Weber number determined for both prototype and scale model are given in Table 1, which shows that prototype and model Froude's number achieve the desired similarity, but there is a significant difference between Reynolds and Weber number similitude. The similarity of both Weber and Reynolds numbers cannot be achieved conjunctively with Froude number similarity. Therefore, the experimental setup developed by the 1:60 scale model is subjected to scale effects.

. | Froude number . | Reynolds number . | Weber number . |
---|---|---|---|

Prototype | 5.30 | 15.59 × 10^{9} | 2.11 × 10^{6} |

Experimental model | 5.26 | 33.54 × 10^{6} | 13.15 × 10^{3} |

. | Froude number . | Reynolds number . | Weber number . |
---|---|---|---|

Prototype | 5.30 | 15.59 × 10^{9} | 2.11 × 10^{6} |

Experimental model | 5.26 | 33.54 × 10^{6} | 13.15 × 10^{3} |

### Development of numerical model

At present, FLOW-3D is considered to be an efficient numerical code to investigate the hydraulic, scour and air entrainment phenomena. The model uses Reynolds-averaged Navier–Stokes (RANS) models to discretize Navier–Stokes equations such as the continuity and momentum equation. The solution of the RANS models is carried out on the finite volume method, which is solved in each computational cell. To track the free surface such as air entrainment, the model employs the volume of fluid (VOF) method as used in the present study. According to Hirt & Nichols (1981), the VOF method is capable of performing two-phase flow computations without disturbing the boundary face. The VOF method is an interface tracking scheme addressing the topological changes of the air–water interface in free-surface flows. To describe hydraulic performance, the VOF model is often used to simulate aerated flow at spillways (Aydin & Ozturk 2009). The true-VOF method tracks the sharp interface accurately and does not require the computation of dynamics in the void and air regions. The code further assumes the ‘law of the wall’ to mimic the flow behavior close to the obstacles (Sarwar 2018). The complex geometric regions in FLOW-3D are modeled using the fractional area/volume of obstacle representation technique (Minor 2000; Erfanain & Kamanbedast 2013; Usta *.*2014; Tokyay & Kurt 2019; Ebrahimnezhadian & Manafpour 2019).

In numerical modeling, a modeler at times makes certain assumptions and defines uncertainties for his simulations. These include model geometry (complete or partial), adopted model boundaries, selection of turbulence models (*k*-*Ԑ*, *k*-*w*, Renormalized Group (RNG)), numerical discretization such as grid size and quality, water properties (density, surface tension and viscosity), CFD model validation with prototype or experimental data, scale effects, etc. The reliability of model results depends on these uncertainties and assumptions. For this study, these have been addressed in the proceeding sections and the selection of each has been defined. The scale effects have been discussed in the previous physical modeling section since the CFD model is configured to prototype dimensions.

*u*,*v*,*w*= fluid velocity components;*x*,*y*,*z*= Cartesian coordinate directions;*A*= area fractions for flow;*R*= mass source;*V*= fractional volume open to flow;_{F}*R*_{SOR}= density source term;ξ = coefficient; 0 for Cartesian geometry and 1 for cylindrical geometry;

*G*,_{x}*G*,_{y}*G*= body accelerations;_{z}*f*,_{x}*f*,_{y}*f*= viscous accelerations;_{z}*b*,_{x}*b*,_{y}*b*= flow losses in porous media or across porous baffle plates._{z}

In addition, on the recommendation of (Zaffar *et al.* 2023; Zaffar & Hassan 2023), the RNG *K*-*ε* model is utilized for turbulence modeling while for air entrainment, under physical module, air entrainment, drift and density evaluation models are selected.

Modeling extent . | Meshing . | Modeling reasons/preferences . | Modeled scenarios . | |||
---|---|---|---|---|---|---|

Bay(s)/modeling width (m) . | Scale . | Cell size (m) . | Quality . | Number of cells . | ||

7 bays | Complete | 1 | Coarse | 31,897,058 | Higher cell numbers and computational cost | X |

3 bays | Partial | 1 | Coarse | 13,402,125 | Significantly larger computational time even for coarse mesh | X |

0.5 | Fine | 107,186,000 | ||||

1 bay | Partial | 1 | Coarse | 5,956,500 | ||

0.5 | Fine | 47,638,223 | ||||

5 | Partial | 2 | Coarse | 101,088 | Successful model run, reasonable geometry resolution and less computational time | ✓ |

1 | Coarse | 941,976 | ||||

0.5 | Fine | 7,716,436 | High resolution of geometry, reasonable computation cost, i.e., time and storage | |||

0.25 | Fine | 59,550,660 | ||||

1 | Partial | 1 | Coarse | 413,712 | Simulation results are gradually refined, (coarse to fine) ensuring model stability | X |

0.5 | Fine | 3,307,044 | ||||

0.25 | Fine | 24,261,380 |

Modeling extent . | Meshing . | Modeling reasons/preferences . | Modeled scenarios . | |||
---|---|---|---|---|---|---|

Bay(s)/modeling width (m) . | Scale . | Cell size (m) . | Quality . | Number of cells . | ||

7 bays | Complete | 1 | Coarse | 31,897,058 | Higher cell numbers and computational cost | X |

3 bays | Partial | 1 | Coarse | 13,402,125 | Significantly larger computational time even for coarse mesh | X |

0.5 | Fine | 107,186,000 | ||||

1 bay | Partial | 1 | Coarse | 5,956,500 | ||

0.5 | Fine | 47,638,223 | ||||

5 | Partial | 2 | Coarse | 101,088 | Successful model run, reasonable geometry resolution and less computational time | ✓ |

1 | Coarse | 941,976 | ||||

0.5 | Fine | 7,716,436 | High resolution of geometry, reasonable computation cost, i.e., time and storage | |||

0.25 | Fine | 59,550,660 | ||||

1 | Partial | 1 | Coarse | 413,712 | Simulation results are gradually refined, (coarse to fine) ensuring model stability | X |

0.5 | Fine | 3,307,044 | ||||

0.25 | Fine | 24,261,380 |

#### Model physics, operation, limiters, initial and boundary conditions

The CFD model requires the selection of flow physics which has to be done with respect to the hydraulic phenomena taking place, e.g., hydraulic jump, turbulence, scouring, air entrainment, etc. In this study, the CFD model needs to be configured for air–water mixtures to study air entrainment. Therefore, the selected flow physics included the models for air entrainment, density evaluation, viscosity and turbulence and drift flux. This flow physics will allow the code to simulate considering factors such as viscosity and surface tension that could not be reproduced in the physical model due to scale effects. To represent the actual conditions of the prototype/physical model spillway (Chanel & Doering 2008), the numerical model is operated under boundary conditions, as provided in Table 3.

Cartesian plane . | Mesh block face . | Boundary condition . |
---|---|---|

X_{min} | Back | Specified pressure |

X_{max} | Front | Outflow |

Y_{min} | Right side | Symmetry |

Y_{max} | Left side | |

Z_{min} | Bottom | Wall |

Z_{max} | Top | Specified pressure |

Cartesian plane . | Mesh block face . | Boundary condition . |
---|---|---|

X_{min} | Back | Specified pressure |

X_{max} | Front | Outflow |

Y_{min} | Right side | Symmetry |

Y_{max} | Left side | |

Z_{min} | Bottom | Wall |

Z_{max} | Top | Specified pressure |

To simulate the present 3D numerical model, two different fluid regions are assigned as initial conditions. The first fluid region is fixed as the spillway's reservoir on its upstream, while on the downstream as per pond levels, tailwater levels are given for investigated models. The limiters for different fluid regions in terms of their fluid block face and Cartesian plane are provided in Table 4.

Cartesian plane . | Fluid block face . | Limiters (upstream reservoir) . | Limiters (downstream tail water) . |
---|---|---|---|

X_{min} | Back | Start of reservoir upstream of spillway crest- | The extent to which tailwater will extend at the chute floor |

X_{max} | Front | Fluid horizontal limit from start of U/s floor to spillway crest | Max. length to which tailwater extends; length of stilling basin |

Y_{min} | Right side | None | None |

Y_{max} | Left side | None | None |

Z_{min} | Bottom | U/s floor level | None |

Z_{max} | Top | Reservoir level | Tailwater level |

Cartesian plane . | Fluid block face . | Limiters (upstream reservoir) . | Limiters (downstream tail water) . |
---|---|---|---|

X_{min} | Back | Start of reservoir upstream of spillway crest- | The extent to which tailwater will extend at the chute floor |

X_{max} | Front | Fluid horizontal limit from start of U/s floor to spillway crest | Max. length to which tailwater extends; length of stilling basin |

Y_{min} | Right side | None | None |

Y_{max} | Left side | None | None |

Z_{min} | Bottom | U/s floor level | None |

Z_{max} | Top | Reservoir level | Tailwater level |

### Validation of a numerical model

A numerical model was validated against physical model results at 14,000 m^{3}/s, comparing the free water surface profiles along the spillway chute. The physical measurement of hydraulic parameters has already been discussed in Section 3.1. Using stage gauges, in the upper spillway reach, the water surface profile was measured at 12 points along the model chute, respectively. According to Jothiprakash *et al.* (2015) and Chanel & Doering (2008), the performance of numerical models is good if the difference between the observed and simulated values remains within 6%. After comparing the results of flow depths, the maximum error between the observed and simulated values reached 4.93% which indicated a good agreement. The pressure inside the cavity of aerator no. 2 was also measured which was negative and in good similarity to CFD results. The negative pressure values observed in the physical model and simulation results from the CFD model are given in Table 5.

Hydraulic parameters . | Physical model . | Numerical model . | Difference (m) . | Difference (%) . |
---|---|---|---|---|

Cavity Pressure (m) | −0.60 | −0.62 | −0.02 | −0.03 |

Hydraulic parameters . | Physical model . | Numerical model . | Difference (m) . | Difference (%) . |
---|---|---|---|---|

Cavity Pressure (m) | −0.60 | −0.62 | −0.02 | −0.03 |

Based on the successful comparison of hydraulic parameters at 14,000, 18,000 and 22,500 m^{3}/s discharges, the results of water surface profiles, flow velocity, pressure distribution and air entrainment are drawn in Section 4.

## RESULTS AND DISCUSSION

### Water surface profile along spillway chute

The results of the free surface profiles also indicated that modeled water surface profiles remained within the sidewalls which were stable along the chute slope and did not overtop the sidewalls. However, results indicated large free surface fluctuations in the stilling basin about 200 m downstream of the spillway crest. In addition, due to the presence of a secondary weir at the end of the stilling basin, the flow depths increased significantly, as shown in Figure 7. The results further showed that even in case of an increase in tailwater levels the second aerator remained safe from the backwater effects.

### Flow velocities along spillway chute

Thereby, to prevent cavitation in that region, the second aerator was installed immediately downstream of that location. In addition, after the hydraulic jump in the stilling basin, the flow depth increased and as a result of the flow velocity in the stilling basin area was reduced to less than 10 m/s.

### Cavitation along the spillway chute

The simulation results show that determined cavitation indexes are above the minimum required threshold, indicating its safety against cavitation. As discussed in the previous sub-section and shown in Figure 8, the flow velocities continue to increase along the spillway chute with a decrease in the cavitation index (Figure 8). This is because air entrainment takes place at the aerators which increases the air volume content of spillway flow resulting in bulking. The air entrainment and pressures along the spillway chute are also discussed in subsequent sections.

### Pressure distribution along the spillway chute

### Air entrainment and detrainment at spillway chute

^{3}/s discharges on the spillway chute of Mohmand Dam. Two aerators were provided on the upper spillway chute. The first aerator entrained about 8% of air at investigated discharges which reduced as the flow progressed downstream. Air introduced to at first aerator was detrained along the chute length as air bubbles escaped into the atmosphere. Simulation results show maximum air detrainment of 2% downstream of the first aerator, reducing available air concentration in the flow to about 6%. These are the minimum thresholds defined in the literature for the amount of air in chute flows to prevent cavitation initiation. Therefore, a second aerator is provided to meet the requirement for additional air entrainment.

The CFD results show that the second aerator entrains a maximum of 29% air at investigated discharges. Due to the significant differences in air entrainment between the first and second aerators, the cavity lengths were higher downstream of the second aerator. Considerable air is detrained during flow mixing and hydraulic jump formation in the stilling basin which is located about 200 m from the spillway crest. The same is represented between points 9 and 11 in Figure 11.

^{3}/s discharges. The numerical results indicated that installed aerators formed cavities at the location of negative pressures, which permitted suction of air from the aeration shafts. At the aerator's locations, the air was mixed with the water, and it escaped in the form of bubbles as the flow moved toward the stilling basin (Falvey 1990; Chanson 1994; Kramer 2004). After point 8 as shown in Figures 12–14, the amount of air entrainment was reduced; however, it remained within the threshold limits (6%). After comparing the air entrainment results for the present spillway chute, the minimum requirements of entrained air were within the limits suggested in the literature by Sarwar

*et al.*(2021), Chanson (1989) and Wood (1991). In addition, the results further indicated that as discharge increased air entrainment decreased. However, the minimum entrained air was within threshold limits along the spillway chute.

## CONCLUSIONS

In this study, hydraulic performance was evaluated for the high-head overflow spillway of Mohmand Dam. A physical model study was carried out to physically observe hydraulic parameters such as flow depth, velocity, water surface profile and negative pressures. FLOW-3D hydraulic models were developed to validate the physical model. The validation results showed that the water surface profiles at investigated discharge were found in good agreement for which the maximum error reached 4.93%. Based on the results, the following conclusions are outlined for the present study.

The CFD model was validated using experimental model results for water surface profile and cavity pressure. A good similarity of the CFD model (prototype dimensions) was achieved with Froude's scale model.

Scale effects were observed for the 1:60 scale model since there was a considerable difference between Reynolds and Weber numbers. Model-prototype similarity with both these dimensionless numbers is essential for representative values of hydraulic parameters, which depend on surface tension and viscous forces (such as air entrainment).

The water surface profile along the chute was stable and did not overtop the sidewalls.

Numerical models showed that maximum flow velocity reached 34 m/s and went beyond the cavitation velocity range specified in the literature. Despite the increasing velocity, the flow velocity of the cavitation index determined is above 0.2, which shows safety against cavitation damages.

The pressure distribution along the spillway chute indicated negative pressure in the aerator cavity for which the maximum drop in pressure was reached −0.62 m in the second aerator cavity. On the contrary, the positive pressures along the spillway chute indicated that the aerators successfully entrained air to the lower nappe. The cavitation index, both upstream and downstream of the aerators, remains above the minimum required threshold.

The first aerator fed air was detrained along the steep slope and reached the critical threshold for minimum air concentration. The air deficiency due to detrainment was covered by entrainment from the second aerator. It entrained about 29% air to the lower nappe. Although air detrained downstream of the second aerator, the flow air concentration remained within literature-specified limits of about 6%, until the terminal point of the spillway chute.

The flow analysis indicated that air entrainment decreased with an increase in spillway flows, while air detrainment occurred along the chute.

Based on the results of physical and numerical models, the overall performance of aerators was satisfactory. The second aerator successfully complemented the air entrainment downstream of the first aerator. Furthermore, from CFD model validation and simulation results, it is also believed the FLOW-3D hydraulic models are efficient in capturing the air entrainment phenomena for the high-head spillways. However, as the present study has focused on limited discharges, it suggests investigating the minimum requirement of air entrainment for other higher discharges using multiple aerators. The study shows that along longer chute lengths, more than one aerator is required to ensure cavitation-free operation of the spillway with an incremental supply of air to the lower nappe.

## DATA AVAILABILITY STATEMENT

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

## CONFLICT OF INTEREST

The authors declare there is no conflict.

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