# Numerical Modelling of Turbulence Kinetic Energy in Open Channel Flows with Mixed-Layer Vegetation

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## Abstract

**:**

## 1. Introduction

## 2. Vegetation Formation

^{3}. A flowmeter installed in the inlet pipe monitors the flow of inlet discharge. During the experimental tests, an adjustable tailgate is located downstream of the channel to set the flow depth (H). In addition, the flume inlet has an acceleration ramp and honeycomb diffusers to curb large-scale turbulent structures.

## 3. Numerical Modelling

#### 3.1. Geometric Modelling and Dimension of Computational Field

^{−6}, which determines the threshold for considering a cell as either water or air. Additionally, the Courant number, a dimensionless parameter governing time step size and mesh size, is set to 0.25, ensuring stability in the simulation. By incorporating these adjustments, the simulation effectively captures multi-phase behaviour in an open channel flow scenario, providing reliable and accurate results.

#### 3.2. Numerical Validation

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Dowel arrangement for cases 1–4. (

**a**) Dowel arrangement designed by Ansys SpaceClaim. (

**b**) Measurement locations for four different cases.

**Figure 2.**Schematic diagram of the model (i.e., case 1) and the boundary conditions applied in numerical modelling.

**Figure 3.**Comparison of experimental and numerical velocity profiles for location 1, behind the tall dowel.

Case | h_{s} (Height of Short Dowel in cm) | h_{t} (Height of Tall Dowel in cm) | Q (L/s) | Drag Coefficient (C_{D}) | H (cm) |
---|---|---|---|---|---|

1 | 10 | 20 | 43.33 | 1.1 | 18.7 |

2 | 10 | 20 | 42.86 | 1.1 | 18.6 |

3 | 10 | 20 | 44.12 | 1.1 | 18.9 |

4 | 10 | 20 | 42.67 | 1.1 | 18.5 |

Equation | $\mathit{\varphi}$ | ${\mathsf{\Gamma}}_{\mathit{k}}$ | ${\mathit{S}}_{{\mathit{\varphi}}_{\mathit{k}}}$ |
---|---|---|---|

Continuity | 1 | 0 | 0 |

Momentum X | u | ${\mu}_{eff}$ | $-\frac{\partial P}{\partial x}+\rho {g}_{x}$ |

Momentum Y | v | ${\mu}_{eff}$ | $-\frac{\partial P}{\partial y}+\rho {g}_{y}$ |

Momentum Z | w | ${\mu}_{eff}$ | $-\frac{\partial P}{\partial z}+\rho {g}_{z}$ |

Turbulence Kinetic Energy | k | $\frac{{\mu}_{eff}}{{\sigma}_{k}}$ | ${G}_{k}-\rho \epsilon $ |

Turbulent dissipation rate | ε | $\frac{{\mu}_{eff}}{{\sigma}_{\epsilon}}$ | $\rho {C}_{1}S\epsilon -\rho {C}_{2}\frac{{\epsilon}^{2}}{k+\sqrt{\nu \epsilon}}$ |

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**MDPI and ACS Style**

Rahimi, H.; Fael, C.M.S.; Taborda, C.S.B.; Yuan, S.; Tang, X.; Singh, P.K.; Fardoost, E.; Santos, C.A.V.
Numerical Modelling of Turbulence Kinetic Energy in Open Channel Flows with Mixed-Layer Vegetation. *Water* **2023**, *15*, 2544.
https://doi.org/10.3390/w15142544

**AMA Style**

Rahimi H, Fael CMS, Taborda CSB, Yuan S, Tang X, Singh PK, Fardoost E, Santos CAV.
Numerical Modelling of Turbulence Kinetic Energy in Open Channel Flows with Mixed-Layer Vegetation. *Water*. 2023; 15(14):2544.
https://doi.org/10.3390/w15142544

**Chicago/Turabian Style**

Rahimi, Hamidreza, Cristina Maria Sena Fael, Cátia Sofia Batista Taborda, Saiyu Yuan, Xiaonan Tang, Prateek Kumar Singh, Emad Fardoost, and César Augusto Vaz Santos.
2023. "Numerical Modelling of Turbulence Kinetic Energy in Open Channel Flows with Mixed-Layer Vegetation" *Water* 15, no. 14: 2544.
https://doi.org/10.3390/w15142544