# Influence of Sill on the Hydraulic Regime in Sluice Gates: An Experimental and Numerical Analysis

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## Abstract

**:**

_{d}) has an inverse relationship with gate opening. Regarding sill state, the discharge coefficient is higher than no-sill state. In the case of non-suppressed sills, the C

_{d}decreases compared to the smaller openings as the opening of the gate changes. The results showed that the C

_{d}with a sill in the tangent position upstream of the gate is higher than the downstream tangent and below situations. Increasing the sill length leads to an increase in flow shear stress and consequently a decrease in C

_{d}. The C

_{d}of gates with different sill thicknesses is always higher than the no-sill state, but due to the constant ratio of the fluid depth above the sill to the gate opening, the C

_{d}increases to a certain extent and then decreases with increasing sill thickness.

## 1. Introduction

_{2}O method and intelligent models such as DL, RF, GBM, and GL. Based on their results, the H

_{2}O machine learning method yields good performance for estimating the discharge coefficient. Daneshfaraz et al. [16] examined the position of the gates, including vertical or inclined/oblique gates. They reported better performance for upward inclined positions than other gate positions in discharge coefficient increases. Kubrak et al. [17] analyze the possibilities of using an irrigation sluice gate in submerged conditions to measure water flow rate. Based on their results, relationships for discharge coefficients of the analyzed sluice gate were developed. Salmasi et al. [18] used experimental data and intelligence models to investigate the gate discharge coefficient. Lauria et al. [19] investigated broad crested weirs’ sluice gate discharge coefficient. Based on their results, it is possible to identify the minimal opening of the gate such that viscous effects can be neglected. Salmasi and Abraham [20] conducted laboratory experiments to determine the discharge coefficient for inclined slide gates. Their results showed that the inclination of the slide gates has a progressive effect on discharge coefficient and increases capacity through the gate. Silva and Rijo [21] used different discharge estimation methods. Their results show that the discharge assessment under the sluice gates for free and submerged flow conditions using energy models had better accuracy.

## 2. Materials and Methods

#### 2.1. Experimental Equipment

#### 2.2. Relation Related to Flow Passing through the Sluice Gate

^{3}T

^{−1}), C

_{d}is the discharge coefficient (-), W is the channel width (L), G is the gate opening (L), g is the gravitational acceleration (LT

^{−2}), H

_{0}is the upstream water depth (L), and Z is the sill height (L). For the no-sill case, Z is equal to zero; therefore, the sluice gate discharge equation with the no-sill case is written (Rajaratnam and Subramanya [3], Swamee [5]):

^{2}). According to Equation (2), the flow rate through the gate with suppressed sill is calculated based on the fluid depth over the sill (H

_{0}− Z). Equation (3) calculates the flow rate through the gate with the non-suppressed sill.

_{1}= b

_{1}G

_{1}, A

_{3}= b

_{3}G

_{1}, and A

_{2}= BG

_{2}are the flow area in, beside, and over the sill (L

^{2}), respectively. Figure 3 shows a sluice gate without and with a sill state relative to the gate.

_{0}is the water depth above the sill (L), and A

_{total}is the total flow area under the gate (L

^{2}), which is equal to A

_{total}= A

_{1}+ A

_{2}+ A

_{3}.

#### 2.3. Flow Governing Equations

_{i}is the velocity component in the direction i. For 3D flow analysis, the software solves Navier–Stokes equations using the finite volume method. Navier–Stokes equations are momentum equations governing the flow of viscous Newtonian fluids. This Equation is generally expressed as Equation (5) (Daneshfaraz et al. [16]).

_{i}is the volumetric force in direction i, µ is the fluid’s dynamic viscosity, x

_{i}, x

_{j}, and x

_{k}are the flow coordinates in the spatial direction i, j, and k, respectively. δ

_{ij}represents the Kronecker delta; if i = j, its value is 1; otherwise, it has a value equal to zero.

#### 2.4. Defining the Solution Network, Boundary Conditions, and Selecting the Turbulence Model

## 3. Results and Discussion

#### 3.1. Validation Results

^{2}and the maximum percentage relative error are 0.996 and ±4.68%, respectively.

#### 3.2. Discharge Coefficient of the Gate with No-Sill Case

_{d}) and the ratio of the upstream depth to gate opening (H

_{0}/G). According to Figure 7a, the values of the C

_{d}are inversely related to the gate opening. Figure 7b shows the stage–discharge diagram for the various openings of the sluice gate in the no-sill case. The gate opening is inversely related to the upstream water depth at a certain flow rate. As it increases, the fluid depth decreases. For an opening of 1 cm, the average C

_{d}value is higher than the openings of 2, 4, and 5 cm by 7.75%, 16.51%, and 18.35%. Similarly, the maximum values of C

_{d}are 16.62%, 28.9%, and 23.51%, respectively.

#### 3.3. Discharge Coefficient of the Gate with Suppressed and Non-Suppressed Sill Case

_{d}for a sluice gate in different positions. According to Figure 8, for a sill below and tangential to the gate, C

_{d}increases with increasing sill width. A sill with the smallest width has a minimum value of the coefficient. By increasing the upstream fluid depth ratio to the sill width, C

_{d}has an increasing trend. By comparing the C

_{d}in different positions, the discharge coefficient in the upward tangent position of the sill is higher than the position below the sluice gate. The reason for this is the placement of the sill. In the tangent position, the entire thickness of the sill is located behind the gate, so that a larger volume of water passes through the gate. In the below position, half of the sill is located after the gate so that it acts as a barrier and increases the friction coefficient of the flow. This consequently increases the fluid depth upstream of the gate more than in the tangent position. For the downward tangent gate position compared to the sill below position, C

_{d}is higher and lower than the upward tangent gate position. As in the upward tangent gate position, the upstream fluid depth is less than for the below and downward tangent gate positions. The greatest depth is related to the sill below the gate. Therefore, the non-suppressed sill of the tangential model can be used due to its optimal performance in terms of increasing the efficiency of the flow rate and preventing the accumulation of sediments behind the gate.

_{d}with different discharges and positions is presented for some of the sills. In addition, the effect of the gate opening with sill is investigated in Figure 9. Comparison of the C

_{d}for different openings with a sill in different positions indicates a decrease in C

_{d}compared to the gate with a lesser opening. In all sill placement models, the maximum value is related to the upward tangent gate position.

_{d}. Streamlines behind the gate for the tangential position continue a smooth tangential trajectory and experience a relatively smaller energy loss.

_{0}. Therefore, reducing the pressure and suction of the flow leads to an increase in the discharge coefficient.

#### 3.4. Hydraulic Parameters of the Gate with Various Geometry of the Sill

_{d}and C are related to the gate discharge coefficient with and without a sill, respectively. Increasing the ratio of Z/G initially increases the discharge coefficient, so that, at Z/W = 3, the sill has a maximum effect on the discharge coefficient. In addition, for ratios greater than Z/G > 3, the increase in discharge coefficient is less.

^{3}/s. As can be seen, with the construction of the sill, the pressure on the gate and the opening section is reduced. In addition, the pressure distribution is hydrostatic, but near the gate’s opening, the pressure distribution becomes hydrodynamic.

## 4. Conclusions

- Out of the three studied sill positions, the under-gate sill case has a lower discharge coefficient than other sill positions.
- A comparison of discharge coefficients obtained from the application of sills showed that the highest value of discharge coefficients is related to the tangential model upstream of the gate. In the suppressed sill case, on average, the value of discharge coefficient for the upward tangential sill, downward tangential sill, and under gate sill positions are 0.779, 0.731, and 0.686, respectively.
- The flow depth upstream of the gate in the tangential upward position has the lowest value compared to other sill positions, leading to an increased discharge coefficient.
- The discharge coefficient is higher when the suppressed sill is broader and thicker until specified thicknesses and then begins to decrease. This conclusion is based on using various sill dimensions as well as the constant ratio of upstream fluid depth to the gate opening.
- By increasing the length of the suppressed and non-suppressed sill, the shear stress increases, and the value of the discharge coefficient decreases.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Schematic view of the gate (

**a**) no-sill case; (

**b**) with the non-suppressed and suppressed sill in various positions; 1, 3: upward and downward tangent gate positions; 2: under gate position.

**Figure 6.**Comparison of numerical solution results with experimental results: (

**a**) data scatters; (

**b**) longitudinal flow profile.

**Figure 7.**(

**a**) Changes in discharge coefficient; (

**b**) stage–discharge for different gate openings in the no-sill state.

**Figure 8.**Changes of discharge coefficient in different positions of the sill: (

**a**,

**d**) under gate position; (

**b**,

**e**) downward tangent gate position; (

**c**,

**f**) upward tangent gate position, in various gate opening.

**Figure 10.**Comparison of discharge coefficient between the no-sill and suppressed sill states: (

**a**) 1 cm opening; (

**b**) 2 cm opening.

**Figure 12.**Distribution of average flow velocity along the channel length in the cross-section behind the gate at the sill with thicknesses of (

**a**) 0.05 m; (

**b**) 0.15 m; (

**c**) 0.25 m.

**Figure 13.**Schematic view (section x–y) of shear stress at the sill with different thicknesses of (

**a**) 0.25 m (

**b**) 0.15 m. (

**c**) Diagram of shear stress along the sill thickness.

**Figure 14.**Discharge coefficient of the gate in different thicknesses of sill (

**a**) non-suppressed (

**b**) suppressed.

**Figure 15.**(

**a**) Effect of sill height on discharge coefficient; (

**b**) effect ratio of sill height to gate opening on discharge coefficient.

Hydraulic Characteristics | ||||

Q (L/min) | Upstream Water Depth (m) | Froude Number (-) | Reynolds Number (-) | |

150–850 | 0.05–0.44 | 0.024–0.515 | 11,111–47,222 | |

Geometric Characteristics | ||||

Gate opening | Sill height (m) | Sill length (m) | Sill width (m) | Sill position |

0.01–0.02 0.04–0.05 | 0.03–0.06–0.09 | 0.05–0.15–0.25 | 0.025–0.05–0.075–0.10 0.15–0.20–0.25–0.30 | Under gate, upward, and downward tangent gate positions |

Test No. | Size of Cells (m) | Assumed Turbulence Model | Mean RE% | RMSE | KGE | |||
---|---|---|---|---|---|---|---|---|

H_{0} | C_{d} | H_{0} (m) | C_{d} (-) | H_{0} (m) | C_{d} (-) | |||

1 | Mesh block 1: 0.014 Mesh block 2: 0.007 | RNG | 14.12 | 9.28 | 0.0735 | 0.0914 | good | good |

2 | Mesh block 1: 0.013 Mesh block 2: 0.0065 | 6.35 | 5.72 | 0.0285 | 0.0348 | Very good | Very good | |

3 | Mesh block 1: 0.012 Mesh block 2: 0.007 | 3.9 | 2.95 | 0.0185 | 0.0245 | Very good | Very good | |

4 | Mesh block 1: 0.012 Mesh block 2: 0.006 | 2.94 | 1.60 | 0.0079 | 0.0117 | Very good | Very good | |

5 | Mesh block 1: 0.010 Mesh block 2: 0.005 | 2.86 | 1.50 | 0.0076 | 0.0114 | Very good | Very good |

Optimal Mesh Size | Turbulence Models | RMSE | |
---|---|---|---|

H_{0} (m) | C_{d} (-) | ||

Test No. 4 | RNG | 0.0079 | 0.0117 |

k-ε | 0.0085 | 0.0123 | |

k-ω | 0.0094 | 0.0128 | |

LES | 0.0083 | 0.0120 |

Q (m^{3}/s) | C_{d} (-)Exp | C_{d} (-)Num | RE (%) | H_{0} (m)Exp | H_{0} (m)Num | RE (%) |
---|---|---|---|---|---|---|

0.00583 | 0.6515 | 0.6575 | 0.93 | 0.124 | 0.122 | 1.67 |

0.00625 | 0.6538 | 0.6661 | 1.89 | 0.140 | 0.135 | 3.39 |

0.00750 | 0.6625 | 0.6743 | 1.77 | 0.192 | 0.185 | 3.27 |

0.00833 | 0.6786 | 0.6927 | 2.09 | 0.224 | 0.215 | 3.86 |

0.00917 | 0.6823 | 0.6995 | 2.53 | 0.266 | 0.253 | 4.68 |

0.01000 | 0.6865 | 0.7016 | 2.16 | 0.311 | 0.298 | 4.10 |

0.01042 | 0.6877 | 0.6845 | 0.46 | 0.335 | 0.338 | 0.90 |

0.01083 | 0.6862 | 0.6921 | 0.86 | 0.363 | 0.357 | 1.65 |

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**MDPI and ACS Style**

Daneshfaraz, R.; Norouzi, R.; Abbaszadeh, H.; Kuriqi, A.; Di Francesco, S.
Influence of Sill on the Hydraulic Regime in Sluice Gates: An Experimental and Numerical Analysis. *Fluids* **2022**, *7*, 244.
https://doi.org/10.3390/fluids7070244

**AMA Style**

Daneshfaraz R, Norouzi R, Abbaszadeh H, Kuriqi A, Di Francesco S.
Influence of Sill on the Hydraulic Regime in Sluice Gates: An Experimental and Numerical Analysis. *Fluids*. 2022; 7(7):244.
https://doi.org/10.3390/fluids7070244

**Chicago/Turabian Style**

Daneshfaraz, Rasoul, Reza Norouzi, Hamidreza Abbaszadeh, Alban Kuriqi, and Silvia Di Francesco.
2022. "Influence of Sill on the Hydraulic Regime in Sluice Gates: An Experimental and Numerical Analysis" *Fluids* 7, no. 7: 244.
https://doi.org/10.3390/fluids7070244