Bottom outlets are significant structures of dams, which are responsible for controlling the flow rate, operation, or removal of reservoir sedimentation. The service gate controls the outlet flow rate, and whenever this gate is out of order, the emergency gate which is located at upstream is utilized. The cavitation phenomenon is one of the common bottom outlets’ problems due to the rapid flow transfer. The present research is a numerical study of the flow pattern in a dam’s bottom outlet for different gate openings by the use of Flow-3D software and RNG

Bottom outlets are utilized as one of the dam’s hydraulic structures to control the reservoir impoundment, the reservoir evacuation in case of emergency, and the removal of the sediments entering the reservoir. Hence, they require careful design and harmful factors identification [

Sadat Helbar et al. (2021) studied on the size and shape of bottom outlet gates, which affect the outflow discharge, and flushing efficiency. The purpose of their study was to investigate the effect of the area, shape, and number of the bottom outlet gates on the velocity and concentration of the sediments [

In these structures, due to the high-velocity flow and the channel’s water level fluctuation, the flow may separate from the channel’s wall, and flow pressure may reduce locally. If the flow pressure is less than the water vapor pressure, the water state shifts from a liquid to a gas, and air bubbles form. The flow may carry air bubbles to a higher pressure area in order to collapse, and a negative pressure wave enters the flow. If air bubbles explode near the wall’s surface, they can damage the channel’s wall [

The service gate’s downstream area and the area between the emergency gate and the service gate, as well as the gate slots that create an uneven surface against the flow hold the highest risk of cavitation [

Ruan et al. (2007) examined the hydraulic performance of aerators used at the base of Goupitan Dam’s bottom discharge channel in a laboratory. The results indicate an increase in the inlet air flow rate into the stream in case of a decrease in the channel’s slope after aeration. This correction has an effective role in protecting the discharge channel against cavitation damage [

Nikseresht et al. (2012) simulated the bottom intake No. 5 of Sefidrud Dam using a three-dimensional limited volume method and showed that the lowest pressure inside the tunnel occurs at 20% opening of the emergency gate, in which case the cavitation index is lower than the critical value. The use of aeration was proposed to eliminate the risk of cavitation. It is attempting to separate the high-velocity flow along the tunnel by using the appropriate system of aeration. Then, flow can be achieved in the tunnel lining when the risk of cavitation is decayed [

Numerical simulation of the flow field in the bottom outlets and hydraulic structures in general, spillways, and energy dissipation systems are crucial for designing such structures. The experience of researchers in such simulations has shown that Flow-3D software has a better capability in modeling this type of hydraulic structures among the existing software packages. Flow-3D provides a complete and versatile CFD simulation platform for engineers investigating the dynamic behavior of liquids and gas in a wide range of industrial applications and physical processes. One of the significant features of the Flow-3D for hydraulic analysis is its ability to model free-surface flows, which are modeled using the VOF (volume of fluid) technique reported by Hirt and Nichols (1981) [

The two-equation model renormalization group (RNG)

The turbulent kinetic energy equation

The turbulent kinetic energy consumption rate equation

In the above equations, _{k} and _{ε} are the inverse effective Prandtl numbers for

Sardab Dam has been built on Sardab River in Iran. The dam site’s height is 2712 meters above sea level’ the dam’s reservoir area is 270 hectares with a total reservoir capacity of 48 million cubic meters (Table

General specifications of Sardab Dam.

Dam | Type | Crest elevation (m. a. s. l. | Dam Height (m) | Crest length (m) |

Earth dam | 2528 | 53 | 752 | |

Reservoir | Maximum water level (PMF) (m) | Normal water level (m) | Minimum water level (m) | Minimum volume (m^{3}) |

2527 | 2524.6 | 2488.6 | 1,000,000 |

Two sliding gates (service and emergency) with dimension (height ∗ width) 1.4 × 1.1 m are located in a row inside the dam’s bottom channel. Geometric details of Sardab Dam’s bottom outlet is shown in Figure

Geometric details of Sardab Dam’s bottom outlet (all dimensions are in mm).

In order to calculate the channel flow rate, assuming the gates are fully open, with the help of Bernoulli’s equation and considering the channel loss, we have^{3}/s) is the volume flow rate; ^{2}) is the cross-sectional reference area; ^{2}) is the gravitational acceleration;

In different parts of the channel, to calculate the total head loss and the total flow rate, a section should be selected as the reference, and the location under the gate is considered a reference section.

Head loss is the potential energy that is converted to kinetic energy. Head losses are due to the frictional resistance of the bottom outlet system (valves, gates, fittings, pipe, entrance, exit losses, etc.). To calculate the total head loss, we have

The contraction coefficient due to the constriction for the 45-degree angle will be about 0.95.

In the above equation, ^{2}) is the output cross-sectional area, ^{2}) is the cross-sectional reference area, and

According to the theoretical issues stated and equations (^{3}/s (velocity in reference area is 18.9 m/s). Table

The flow rate passing through the channel in the openings of service gates and different heads.

_{o} | _{max} = 51.35 m | ||||||
---|---|---|---|---|---|---|---|

0.1 | 3.17 | 3.1 | 2.97 | 2.8 | 2.62 | 2.43 | 1.98 |

0.2 | 6.29 | 6.15 | 5.89 | 5.56 | 5.2 | 4.81 | 3.93 |

0.3 | 9.29 | 9.07 | 8.7 | 8.2 | 7.67 | 7.1 | 5.8 |

0.4 | 12.18 | 11.9 | 11.41 | 10.75 | 10.06 | 9.31 | 7.6 |

0.5 | 15.03 | 14.67 | 14.07 | 13.26 | 12.41 | 11.49 | 9.38 |

0.6 | 17.67 | 17.25 | 16.54 | 15.59 | 14.59 | 13.5 | 11.03 |

0.7 | 20.06 | 19.59 | 18.78 | 17.71 | 16.56 | 15.33 | 12.52 |

0.8 | 22.29 | 21.77 | 20.87 | 19.68 | 18.41 | 17.04 | 13.91 |

0.9 | 24.35 | 23.77 | 22.8 | 21.49 | 20.1 | 18.61 | 15.2 |

1 | 26.64 | 26 | 24.93 | 23.51 | 21.99 | 20.36 | 16.62 |

The volume flow rate at different openings and heads.

The first feature of Flow-3D is that it employs a highly variable rectangular gridding system for gridding. This characteristic makes the grid or geometry separable from each other. In simpler terms, it does not utilize a fixed grinding system connected to geometry or finite elements. It is also possible to use multiple gridding systems to increase efficiency and flexibility in gridding. The entire outlets flow rigid body is designed with all its details in three dimensions by SolidWorks software to model the bottom outlets’ hydraulic conditions flow in Flow-3D software (Figures

Complete bottom outlet geometry with Howell Bunger valve, aerator, and butterfly valve made in SolidWorks software.

Details of construction of 3D geometry of Sardab Dam’s bottom outlet (all dimensions are in m).

In order to cover the entire rigid body of the outlet with the branch valve, the mesh should be selected so that there is as little space as possible in the channel area as empty space. The following figures show the grid’s details (12825258 cells), the computational cells, and the bottom outlet boundary conditions. It should be noted that the elements of the Flow-3D numerical model are of the cuboid element type. Size of the cells in mesh block 1, 2, 3, and 4 in each direction (_{Min}, _{Max}, _{Min}, _{Max}, _{Min}, and _{Max}. It is worth noting that all these specifications are defined in one block, and separate boundary conditions must be defined for each in the case of several blocks (Figures

Numerical model’s gridding and meshing blocks for bottom outlets and branch in Flow-3D numerical model.

Boundary conditions applied in flow simulation in the bottom outlets.

In the present research, a mesh sensitivity analysis was conducted with 5 different cell sizes. Table

Mesh sensitivity analysis.

Parameters | Type of mesh | ||||
---|---|---|---|---|---|

Cell size 20% smaller | Cell size 10% smaller | Main | Cell size 10% larger | Cell size 20% larger | |

Velocity (m/s) | 18.21 | 18.13 | 18.05 | 17.42 | 17.1 |

Analytical velocity (m/s) | 18.9 | 18.9 | 18.9 | 18.9 | 18.9 |

Error (%) | 3.65 | 4.07 | 4.49 | 7.83 | 9.52 |

In order to evaluate the numerical model results’ calibration and validation in various bottom outlet’s gate openings, the output flow rate of the manual analysis should be compared with the output flow rate of the numerical model for the same applied head conditions using the analytical solution performed in the previous sections (Figure

Numerical model results for output flow rate at various gate openings during Flow-3D numerical model implementation.

Comparison of analytical solution results and numerical modeling of output flow rate in varying valve openings.

As indicated in Figure

Results of Flow-3D numerical model for the valve’s output flow rate at the service gate’s different openings during model execution.

Comparison of analytical solution results and numerical modeling of output flow rate in different gate openings.

The results manifested in Table

Changes in bottom outlet’s output flow rate for different gate openings.

Gate openings (%) | Flow rate (gate) (m^{3}/s) | Flow rate (valve) (m^{3}/s) |
---|---|---|

0 | 0.00 | 0.00 |

20 | 6.32 | 5.30 |

40 | 12.90 | 5.26 |

60 | 17.51 | 5.14 |

80 | 22.30 | 4.63 |

100 | 24.70 | 3.86 |

The hydraulic parameter modeling results show that the velocity value at 100% opening in the section below the gate is about 18 m/s (Figure

Output velocity of the gate and valve in 100% gate and valve opening.

Output velocity of the gate and valve in 40% gate and 100% valve opening.

Output velocity of the gate and valve in 80% gate and 100% valve opening.

Output velocity of the gate and valve in 60% gate and 100% valve opening.

Output velocity of the gate and valve in 20% gate and 100% valve opening.

The gate slot’s velocity values are about 2-3 m/s, in which case no flow separation and undesirable circular flow are observed in the slot. These conditions function almost the same for all openings. Figure

Velocity change’s size and vectors in the gate slots at 100% gate and valve opening.

Investigation of velocity values in the branch and stiffener area is presented in Figure

Velocity change’s size and vectors in the branch area at 100% gate and valve opening.

In outlet tunnels, the fluid movement may increase the pressure in the flow direction in the face of an obstacle. Such a pressure change is called the inverse pressure gradient. The fluid in this flow boundary layer area is affected by this increasing pressure so that this fluid velocity also slows down. However, because the fluid’s kinetic energy within the boundary layer is low, it will likely stagnate and be reversed, causing the boundary layer to separate and deviate from it. The separation of the main stream from the boundary is called the separation phenomenon, which is caused by the reverse pressure gradient. A reverse pressure gradient is a necessary condition and not a sufficient condition for the separation of the flow. In other words, there can be a reverse pressure gradient without separation, while separation without a reverse pressure gradient cannot occur. The pressure amount in the channel area in different gate openings can be seen in Figures

Three-dimensional view of the pressure in the whole model.

The pressure amount in the channel area leading to the gate and the branch in the state of 100% opening (100% valve opening).

The pressure amount in the channel area leading to the gate and the branch in the state of 60% opening (100% valve opening).

The pressure amount in the channel area leading to the gate and the branch in the state of 20% opening (100% valve opening).

The flow under the gate creates a circular flow downstream, the main feature of which is a sharp pressure loss. This pressure loss is a function of the gate’s opening, the water head behind the gate, and the channel’s geometry. On the other hand, severe pressure fluctuations lessen that area’s local pressure, and the potential for cavitation increases due to the high-velocity [

Pressure distribution under the gate for 100% opening mode (100% valve opening).

Pressure distribution under the gate for 20% opening mode (100% valve opening).

Flow pattern around the stiffener and no flow separation in this area (100% valve opening).

Flow pattern around the siphon and no flow separation in this area (100% valve opening).

According to Figure

Fluid volume fraction contour between two gates in 50% opening state.

As can be seen in Figures

Pressure changes in the bottom outlet’s tunnel of Sardab Dam at the time of 50% opening of service and emergency gates.

The flow’s hydraulic conditions are checked for the completely closed valve state and 100% open branch valve using numerical modeling in this case.

As can be seen in Figures

Pressure changes in the bottom outlet’s tunnel of Sardab Dam for a fully closed gate and 100% open branch valve.

Pressure changes in the bottom outlet’s branch area of the Sardab Dam for a fully closed gate and 100% open branch valve.

As can be seen in Figure ^{3}/s.

Velocity changes in the branch area for fully closed gate mode and 100% open branch valve.

Cavitation along the channel is usually checked based on a dimensionless number called the cavitation index (

The cavitation index is a function of local pressure and fluid velocity, and this index’s critical value is (0.2–0.25) along the channels and 0.2 inside the slots [

In the bottom outlet channels, when the gate opening is 100%, the maximum velocity and, as a result, the maximum discharge capacity is created in the channel. Subsequently, the study and control of cavitation index in 100% opening is considered for this channel. Since the Sardab Dam will be built at an altitude of approximately 2500 meters above sea level and with an ambient temperature of approximately 20 degrees Celsius, to calculate the cavitation index, we will have

Equation (

The parameters’ values of the above equation are defined as follows:

For air-fluid, the value of

It should be noted that the fluid vapor pressure will be equal to

To calculate the relative pressure values of

Considering the flow head equal to 51.35 m for the two sections of the gate slot and the output section, there will be a flow (in the output section, the relative pressure is equal to zero, and the velocity is equal to 18.9 m/s).

At the output section,

Also, the cavitation values in the service gate slot, as one of the most critical points for cavitation occurrence, are calculated as follows:

The gate slot should be checked using the slot characteristics in order to examine the possibility of cavitation. Considering that the slot’s retraction angle is 1 : 12 and

Dam bottom outlets which contain valves and pumps play a vital role in dam operation and safety, as they allow controlling the water surface elevation below the spillway level. Probability of the formation of cavitation due to the concentrated vortices is too high. The vorticity distribution near the branch entrance exhibited high values due to the cylindrical shape of the bottom outlet which contributed to high amount of flow separation [^{1/2}. For new facilities, the possibilities of the Flow-3D for identifying the flow patterns and for computing the pressure and velocity fields should be helpful for designing the aeration system.

In the present study, Sardab Dam’s bottom outlet and Howell Bunger valve’s hydraulic performance in different opening conditions, including 20, 40, 60, 80, and 100%, with different flow rates, was investigated. These examinations comprise the service gate’s single operation, the service gate and the Howell Bunger valve’s simultaneous operation, and the Howell Bunger valve’s single operation. The results presented for different opening conditions for velocity values with 100% opening in the section below the gate is about 18 m/s, and the maximum velocity under the gate for 40% opening is equal to 23.1 m/s. The velocity values in the gate slot are about 2-3 m/s, in which case no flow separation and undesirable circular flow are observed in the slot. This condition is true for all gate openings. The velocity values at the branch entrance are variable 2-5 m/s, no flow separation and other adverse conditions occur in this area, and the velocity values increase after passing through the branch entrance. There is no undesirable change in the distribution of pressure along the tunnel and in the gate areas, and there is no drastic reduction of pressure in this area. It should be noted that there are no undesirable hydraulic phenomena in these sections, including flow separation and local vortices. For 50% opening of the gates in the gate’s upper areas, the desired pressure values are reduced, and in the areas between the two gates, the pressure values are reduced. Moreover, with the installation of aerators, the possibility of cavitation in this area is reduced. For fully closed gate mode and 100% open branch valve, no circular flow and undesirable pressure changes are created in the tunnel. Also, the velocity behind the valves in the fully closed state is zero, and at the branch entrance point, it is 5-6 m/s. At the valve output, the velocity has increased by about 36% compared to when the gates are fully open. Based on these conditions, the branch valve’s output flow rate is estimated to be about 5.3 m/s. The presented results show that due to the bottom outlet operation in the reservoir’s maximum head condition, the probability of cavitation in the area between the two gates is very high. This analysis suggests that numerical modeling with the Flow-3D can be helpful for the design of this kind of hydraulic works.

All data used to support the findings of the study are included within the article.

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

The authors declare that there are no conflicts of interest regarding the publication of this paper.