# Numerical Investigation of Hydraulics in a Vertical Slot Fishway with Upgraded Configurations

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

^{®}model. Namely, five variants of angles between baffles, four different pool widths, and another upgraded version of VSF by introducing cylindrical elements positioned after the opening behind the baffles were tested. Results show that smaller angles between baffles increase the Vmax and decrease the maximum turbulent kinetic energy (TKE

_{max}); the opposite result was obtained when increasing angles between baffles. Namely, the Vmax was increased up to 17.9% for α = 0° and decreased up to 20.37% for α = 37°; in contrast, TKE

_{max}decreased up to −20% for α = 0° and increased up to 26.5% for α = 37°. Narrowing the pool width increased the Vmax linearly; nevertheless, it did not significantly affect the TKE

_{max}as the maximum difference was only +3.5%. Using cylinders with a large diameter decreased the Vmax and increased TKE

_{max}; in contrast, using cylinders with smaller diameters further reduced the Vmax velocity inside the pool while increasing the TKE

_{max}. However, in the case of cylinders, the dimension of the recirculation depended on the configuration and arrangement of the cylinder within the pool. Overall, the maximum velocity was reached at near 77% of the water depth in all cases. Finally, solution-oriented findings resulted from this study would help water engineers to design cost-effective VSF fishways to support the sustainable development of hydraulic structures while preserving aquatic biodiversity.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Geometrical Configuration

_{0}= 0.59 m and a slope of 1.67%. Field measurements were performed in steady-flow conditions, with a 1.0 m

^{3}/s discharge and an average water depth of 1.3 m (see Bombač, et al. [20] for more details). Several new VSF fishways were analyzed numerically to upgrade the reference design (Figure 2A1) to evaluate the enhancement of the hydraulic properties. Thus, We began by reducing in the pool width and setting to four values: W = 2 (10%), 1.85 (15%), 1.75 (20%) and 1.65m (25%) (Figure 2A2), considering five variants of angles between baffles, i.e., α = 0° (1dx width move to upstream), 12° (0.5dx width move to upstream), 20° (reference position), 30° (0.5dx width move to downstream), and 37° (1dx move to downstream) (Figure 2A3). The dx and dy are the width and length of a small baffle. In addition, another upgraded version of VSF by introducing cylindrical elements positioned after the opening behind the baffles was tested. Cylindrical elements consist of three different diameters, namely 0.3 (b

_{0}/2), 0.15 (b

_{0}/4), and 0.1 (b

_{0}/6), with heights of 0.4 m invariants of the arrangement (Figure 2A4 and Figure 3).

#### 2.2. Hydrodynamic Simulations

#### 2.2.1. FLOW-3D^{®} Model

#### 2.2.2. Flow Equations

_{F}the volume fraction of fluid in each cell, A

_{x}, A

_{y}, and A

_{z}the fractional areas open to flow in the subscript’s direction, ρ is the fluid density, P the hydrostatic pressure, G

_{i}the gravitational acceleration in subscript direction and fi the Reynolds stress. The VOF transport equation is expressed:

#### 2.2.3. Turbulence Model

^{®}has the capability of performing turbulence simulation using different models such as standard turbulence models, the k-ε turbulence model, and the RNG turbulence model. In this study, the RNG k-ε turbulence model estimates the shear stress near the wall. It has been proven to be sufficiently accurate; see Pourshahbaz, et al. [34] and Ghaderi, et al. [33], based on Yakhot and Orszag [35]. The RNG k-ε model can better deal with the high strain rate and the greater curvature of streamline flow. This model showed satisfactory outcomes in previous studies in complex geometry and flow fields on hydraulic structures such as spillways, culverts, and other hydraulic structures [31,33,36,37,38,39]. The RNG k-ε model is based on two equations; the first one (Equation (4)) expresses the energy in turbulence, called turbulent kinetic energy (TKE) (k), and the second one (Equation (5)) is the turbulent dissipation rate (ε), which determines the kinetic energy dissipation rate.

_{k}is the generation of turbulent kinetic energy caused by the average velocity gradient. G

_{B}is the generation of turbulent kinetic energy caused by buoyancy. S

_{k}and S

_{ε}are source terms. α

_{k}and α

_{ε}are inverse adequate Prandtl numbers for k and ε, respectively. μ

_{eff}is the effective viscosity μ

_{eff}= μ + μ

_{t}. The μ

_{t}is the eddy viscosity.

_{µ}= 0.0845, C

_{1ε}= 1.42, C

_{2ε}= 1.68, C

_{3ε}=1.0, σ

_{k}= 0.7194, σ

_{ε}= 0.7194, η

_{0}= 4.38, and β = 0.012.

#### 2.2.4. Numerical Domain

_{coarse}/Gf

_{ine}), a value of 1.3, as Celik et al. [40] recommended. For this purpose, a refinement ratio of 1.34 was considered for reducing the grid sizes. Table 1 shows some characteristics of the computational grids.

_{1}, f

_{2}, f

_{3}are the parameters obtained from CFD simulations (f

_{1}corresponds to the fine mesh) and r is the refinement rate. Using the Richardson error estimator to compare the three grids, the fine-grid convergence index is defined as:

_{2}− f

_{1})/f

_{1}is the approximate relative error between the medium and fine grids, respectively. Dimensionless indices GCI

_{12}and GCI

_{23}can be calculated as:

_{12}) are small if compared to the coarser one (GCI

_{23}), it can be concluded that the aim of a grid-independent solution is reached, and no further mesh modification is necessary. Computed values of GCI

_{23}/rpGCI

_{12}close to 1 indicate that the numerical solutions are within the asymptotic range of convergence. As a result, the selected mesh consists of a containing block with 3.5 cm cells and a nested block with 2.6 cm cells. (Figure 5).

## 3. Results and Discussion

#### 3.1. Model Validation

^{2}+ v

^{2})

^{0.5}from the numerical results is compared with the experimental data as shown in Figure 7. According to Figure 7, the results show that the trend and value obtained from numerical modeling satisfactorily agree with the experimental data. Table 3 summarizes the velocity magnitude values in some vertical distance for calculated and measured data.

#### 3.2. The Flow Pattern of Vertical Slot Fishway

_{1}, u

_{2}, u

_{3}, …, u

_{n}), the value of the root mean square velocity, u

_{rms}, is obtained as:

#### 3.3. Influence of Angle between Baffles on V_{max} and TKE in the Slot

#### 3.4. Influence of the Pool Width on V_{max} and TKE

#### 3.5. Influence of the Cylinder’s Adjunction on V_{max} and TKE

_{0}/2, placed after the opening behind the baffles (C1). Other cylinders with different diameters and arrangements were placed in the periphery of the larger diameter inside the pool (Figure 19C2–C6). Figure 19 illustrates the velocity streamlines for fishway models with cylinders inside the pool and in different arrangements. The results show that the jet from the slot widened in the pool before converging towards the following slot. For an obstacle located in the jet in the middle of the pool, the principal flow, of width higher than the geometry diameter, turned around the obstacle on each side. The diameter and arrangement of the cylinder modified the flow pattern. For example, the cylinders of type C6 reduces the vortices in the recirculation zone.

## 4. Conclusions

_{max}and decrease the maximum turbulent kinetic energy (TKE

_{max}); the opposite result was obtained when increasing angles between baffles. Namely, the V

_{max}was increased up to 17.9% for α = 0° and decreased up to 20.37% for α = 37°; in contrast, TKE

_{max}decreased up to −20% for α = 0° and increased up to 26.5% for α = 37°.

_{max}linearly; nevertheless, narrowing the pool width did not significantly affect the TKE

_{max}as the maximum difference was only +3.5%. Using cylinders with a large diameter decreased the V

_{max}and increased TKE

_{max}; in contrast, using cylinders with smaller diameters further reduces the V

_{max}velocity inside the pool while increasing the TKE

_{max}. In the case of cylinders, in addition to the diameter, the configuration and arrangement of the cylinder within the pool have a significant influence on the V

_{max}and TKE

_{max}variation. In that regard, the C6 model demonstrated the best performance, especially regarding the flow regime and principal flow velocity inside the pool. Overall, the maximum velocity was reached at near 77% of the water depth in all cases.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**VSF Blanca’s prototype geometry and slot and pool details after Bombač, et al. [20].

**Figure 2.**Plan views of fishway pools: (

**A1**) Reference; (

**A2**) reducing pool width; (

**A3**) with variants of angles between baffles and (

**A4**) with cylinders.

**Figure 9.**Turbulent kinetic energy and dissipation rate at a mid-depth horizontal plane for the reference VSF: (

**a**) k (j/kg); (

**b**) ε (j/kg/s).

**Figure 11.**Streamlines of velocity for reference VSF (α = 20°) and VSF with various angles between baffles.

**Figure 13.**Contours of turbulent kinetic energy (J/kg) for reference VSF (α = 20°) and VSF with various angles between baffles.

**Figure 14.**Maximum turbulent kinetic energy for the reference VSF and the VSF with various angles between baffles at three cross-sections.

**Figure 17.**Contours of turbulent kinetic energy (J/kg) for the reference VSF and the VSF with various pool widths.

**Figure 18.**Maximum turbulent kinetic energy for the reference VSF and the VSF various pool widths at three cross-sections.

**Figure 20.**Velocity magnitude and maximum flow velocity for the reference VSF and the VSF with various cylinders arrangement.

**Figure 21.**Contours of turbulent kinetic energy (J/kg) for reference VSF and VSF with various cylinders arrangement.

**Figure 22.**Maximum turbulent kinetic energy for the reference VSF and the VSF with various cylinders arrangement.

Mesh | Nested Block Cell Size | Containing Block Cell Size | Number of Cell | Mesh |
---|---|---|---|---|

1 | 3 cm | 4 cm | 1,078,157 | Coarse |

2 | 2.85 cm | 3.8 cm | 1,689,598 | Medium |

3 | 2.6 cm | 3.5 cm | 2,268,478 | Fine |

Quantity | f_{3} | f_{2} | f_{1} | p | GCI_{12} | GCI_{23} | Asymptotic Range |
---|---|---|---|---|---|---|---|

V_{1} (m/s) | 1.09 | 1.21 | 1.36 | 3.11 | 0.55 | 0.62 | 0.9 |

V_{2} (m/s) | 0.86 | 0.95 | 1.07 | 4 | 0.39 | 0.47 | 0.9 |

Location | x = 0.5 m | x = 1.0 m | x= 1.5 m | x = 2.0 m | x = 2.5 m | |||||
---|---|---|---|---|---|---|---|---|---|---|

Num | Exp | Num | Exp | Num | Exp | Num | Exp | Num | Exp | |

y = 0.9 m | 0.085 | 0.156 | 0.121 | 0.142 | 0.155 | 0.138 | 0.149 | 0.120 | 0.149 | 0.310 |

y = 1.2 m | 0.196 | 0.148 | 0.521 | 0.360 | 0.541 | 0.350 | 0.537 | 0.328 | 0.248 | 0.301 |

y = 1.5 m | 1.401 | 1.263 | 1.421 | 1.212 | 1.214 | 1.043 | 1.114 | 0.954 | 1.164 | 0.946 |

y = 1.8 m | 1.472 | 1.365 | 0.987 | 0.971 | 1.131 | 1.051 | 1.113 | 1.091 | 1.124 | 1.150 |

y = 2.1 m | 0.179 | 0.205 | 0.070 | 0.059 | 0.213 | 0.32 | 0.389 | 0.661 | 0.638 | 0.891 |

Mean Error (%) | 6.20 | 10.4 | 9.74 | 4.61 | 5.67 |

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**MDPI and ACS Style**

Ahmadi, M.; Ghaderi, A.; MohammadNezhad, H.; Kuriqi, A.; Di Francesco, S.
Numerical Investigation of Hydraulics in a Vertical Slot Fishway with Upgraded Configurations. *Water* **2021**, *13*, 2711.
https://doi.org/10.3390/w13192711

**AMA Style**

Ahmadi M, Ghaderi A, MohammadNezhad H, Kuriqi A, Di Francesco S.
Numerical Investigation of Hydraulics in a Vertical Slot Fishway with Upgraded Configurations. *Water*. 2021; 13(19):2711.
https://doi.org/10.3390/w13192711

**Chicago/Turabian Style**

Ahmadi, Mohammad, Amir Ghaderi, Hossein MohammadNezhad, Alban Kuriqi, and Silvia Di Francesco.
2021. "Numerical Investigation of Hydraulics in a Vertical Slot Fishway with Upgraded Configurations" *Water* 13, no. 19: 2711.
https://doi.org/10.3390/w13192711