# A Comparative Study on 2D CFD Simulation of Flow Structure in an Open Channel with an Emerged Vegetation Patch Based on Different RANS Turbulence Models

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Numerical Models

#### 2.1.1. Standard k-ε Model

#### 2.1.2. RNG k-ε Model

#### 2.1.3. Realizable k-ε Model

#### 2.1.4. Standard k-ω Model

#### 2.1.5. SST k-ω Model

#### 2.1.6. RSM

#### 2.2. Simulation Setup

#### 2.3. Model Validation

#### 2.3.1. Grid Independence Validation

#### 2.3.2. Time Step Independence Validation

## 3. Results and Discussion

_{1}. The length of the wake recovery segment is represented by L

_{2},${L}_{2}=L-{L}_{1}$ [3].

#### 3.1. Comparative Analysis of Mean Velocity Profile and Wake Segment Simulation

_{1}and L

_{2}, respectively, mark the distribution of the mean flow velocity $\overline{u}$ in the steady wake segment and the wake recovery segment from the experimental data of Zong and Nepf [3]. The flow velocities in the wake stable segment L

_{1}simulated by the three turbulence models of the k-ε series were remarkably larger than those of the experimental data. In addition to the SST k-ω model, the other five turbulence models predicted that the wake recovery segment was highly downstream. Only the realizable k-ε model and RSM model poorly predicted the distribution and magnitude of the mean flow velocity $\overline{u}$ after the wake. Among the six turbulence models, the worst prediction results were provided by the RSM model. The simulation results of the RSM model were unsatisfactory in the wake segment, and the flow velocity prediction after the wake section highly differed from that in the experimental data. The relative velocity of the experimental data at x = 23D is about 0.9, while about 0.8 for RSM. Meanwhile, the numerical simulation results of the standard k-ε model were better than those of the RNG k-ε model and realizable k-ε model. This finding is unexpected because the realizable k-ε model shows better performance than the standard k-ε model in most previous numerical simulation examples.

_{1}, the six turbulence models predicted longer values than that obtained from the experiments (about 20.7% to 93.1% excess of the experimental data). For the wake recovery segment length L

_{2}, the simulation results of the standard k-ε model were the most consistent with the experimental data (the difference is less than 3% of the experimental data). The predicted L

_{2}values by the RNG k-ε model and realizable k-ε model were larger than the experimental values, and the predictions of the standard k-ω model, SST k-ω model, and RSM model were smaller.

#### 3.2. Simulation Results of Flow Field after Vegetation Patch

#### 3.3. Comparative Analysis of Longitudinal Outflow Intensity

#### 3.4. Computational expenses

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Top view of the numerical simulation arrangement. An emerged vegetation patch is arranged at the central line of a rectangular channel.

**Figure 2.**Computational grid for the cases of D = 22 cm and $\varphi $ = 0.1: (

**a**) a close view of the wake area grid, (

**b**) a detailed view of the grid near the circular hole, and (

**c**) a feature view of the grid near the wake behind the vegetation patch.

**Figure 3.**The simulation results of case V, case VII, and case VIII are compared with those of Zong and Nepf [3]. The diameter of the vegetation patch is 22 cm, and the data in the figure are the centerline (y = 0) longitudinal mean velocity ($\overline{u}$) distribution. The gray part indicates the internal area of vegetation patches.

**Figure 4.**The simulation results of case V, case VIII, and case X are compared with those of Zong and Nepf [3]. The data in the figure is the centerline (y = 0) longitudinal mean velocity ($\overline{u}$) distribution. The gray part indicates the internal area of vegetation patches.

**Figure 5.**(

**a**) Contour of longitudinal velocity u distribution of water flow obstructed by a vegetation patch, and (

**b**) streamlines colored by velocity u near the stable wake segment; both are the numerical simulation results of SST k-$\omega $ turbulence model.

**Figure 6.**The longitudinal flow profiles simulated by six turbulence models are illustrated in comparison with the experimental results of Zong and Nepf ($\Phi $ = 0.1, D = 22 cm) [3], where the longitudinal mean velocity $\left(\overline{u}\right)$ is measured at the centerline, y = 0. The gray part indicates the internal area of vegetation patches.

**Figure 7.**Transverse velocity $\overline{v}$ is measured at line y = D/2; the black dot plot in the figure is the experimental data of Zong and Nepf ($\Phi $ = 0.1, D = 22 cm) [3].

**Figure 8.**The lengths of the wake segments obtained from the cases and experiments of Zong and Nepf are illustrated [3]; blue indicates the stable wake segment, and green indicates the wake recovery segment; the blue and green dashed line indicates the L

_{1}and L

_{2}of experiments. The gray part indicates the internal area of vegetation patches.

**Figure 9.**Contours of instantaneous velocity distribution for $\Phi $ = 0.1 and D = 22 cm colored by velocity u. (

**a**) case I, (

**b**) case II, (

**c**) case III, (

**d**) case IV, (

**e**) case V, and (

**f**) case VI. Arrows indicate the direction of the vortex rotation.

**Figure 11.**The black curve indicates the transient longitudinal flow velocity u distribution, and the green area indicates the cumulative plot of the mean longitudinal flow velocity $\overline{u}$ to the line $\overline{u}/{U}_{\infty}$ = 0. (

**a**) case I, (

**b**) case II, (

**c**) case III, (

**d**) case IV, (

**e**) case V, and (

**f**) case VI.

**Table 1.**Information of numerical simulation cases. Geometric and hydrodynamic parameters are given.

Case | $\Phi $ | $\mathit{a}\left({\mathrm{cm}}^{-1}\right)$ | D (cm) | D (cm) | U_{∞} (cm/s) | $\mathit{R}{\mathit{e}}_{\mathit{d}}$ | Turbulence Model | Time Step (s) | Grid Cells (k) |
---|---|---|---|---|---|---|---|---|---|

I | 0.1 | 0.2 | 22 | 0.6 | 9.8 | 588 | Standard k-ε | 0.01 | 349 |

II | 0.1 | 0.2 | 22 | 0.6 | 9.8 | 588 | RNG k-ε | 0.01 | 349 |

III | 0.1 | 0.2 | 22 | 0.6 | 9.8 | 588 | Realizable k-ε | 0.01 | 349 |

IV | 0.1 | 0.2 | 22 | 0.6 | 9.8 | 588 | Standard k-ω | 0.01 | 349 |

V | 0.1 | 0.2 | 22 | 0.6 | 9.8 | 588 | SST k-ω | 0.01 | 349 |

VI | 0.1 | 0.2 | 22 | 0.6 | 9.8 | 588 | RSM | 0.01 | 349 |

VII | 0.1 | 0.2 | 22 | 0.6 | 9.8 | 588 | SST k-ω | 0.01 | 258 |

VIII | 0.1 | 0.2 | 22 | 0.6 | 9.8 | 588 | SST k-ω | 0.01 | 489 |

IX | 0.1 | 0.2 | 22 | 0.6 | 9.8 | 588 | SST k-ω | 0.05 | 349 |

X | 0.1 | 0.2 | 22 | 0.6 | 9.8 | 588 | SST k-ω | 0.005 | 349 |

Model Validation | Turbulence Model | Time Size (s) | Grid Cells(k) | |
---|---|---|---|---|

Grid independence validation | Case VII | SST k-ω | 0.01 | 258 |

Case V | SST k-ω | 0.01 | 349 | |

Case VIII | SST k-ω | 0.01 | 489 | |

Time step independence validation | Case IX | SST k-ω | 0.05 | 349 |

Case V | SST k-ω | 0.01 | 349 | |

Case X | SST k-ω | 0.005 | 349 |

**Table 3.**Some results of cases V, VII, and VIII for grid independence validation, where ${L}_{1}$ is defined in Section 3.

Case | Global Maximum Mean Velocity (cm/s) | Maximum Longitudinal Mean Velocity (cm/s) | ${\mathit{L}}_{1}\left(\mathit{D}\right)$ |
---|---|---|---|

VII | 13.08022 | 13.07509 | 4.6 |

V | 13.07974 | 13.07616 | 4.5 |

VIII | 13.07767 | 13.07593 | 4.5 |

**Table 4.**Some results of cases V, IX, and X for time step independence validation, where ${L}_{1}$ is defined in Section 3.

Case | Global Maximum Mean Velocity (cm/s) | Maximum Longitudinal Mean Velocity (cm/s) | ${\mathit{L}}_{1}\left(\mathit{D}\right)$ |
---|---|---|---|

IX | 13.05878 | 13.05489 | 4.9 |

V | 13.07974 | 13.07616 | 4.5 |

X | 13.08012 | 13.08474 | 4.5 |

Case | Turbulence Model | Grid Cells (k) | Time Step (s) | Relative Iteration Time |
---|---|---|---|---|

I | Standard k-ε | 349 | 0.1 | 1.00 |

II | RNG k-ε | 349 | 0.1 | 1.07 |

III | Realizable k-ε | 349 | 0.1 | 1.06 |

IV | Standard k-ω | 349 | 0.1 | 1.46 |

V | SST k-ω | 349 | 0.1 | 0.87 |

VI | RSM | 349 | 0.1 | 1.21 |

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**MDPI and ACS Style**

Yu, S.; Dai, H.; Zhai, Y.; Liu, M.; Huai, W. A Comparative Study on 2D CFD Simulation of Flow Structure in an Open Channel with an Emerged Vegetation Patch Based on Different RANS Turbulence Models. *Water* **2022**, *14*, 2873.
https://doi.org/10.3390/w14182873

**AMA Style**

Yu S, Dai H, Zhai Y, Liu M, Huai W. A Comparative Study on 2D CFD Simulation of Flow Structure in an Open Channel with an Emerged Vegetation Patch Based on Different RANS Turbulence Models. *Water*. 2022; 14(18):2873.
https://doi.org/10.3390/w14182873

**Chicago/Turabian Style**

Yu, Songli, Huichao Dai, Yanwei Zhai, Mengyang Liu, and Wenxin Huai. 2022. "A Comparative Study on 2D CFD Simulation of Flow Structure in an Open Channel with an Emerged Vegetation Patch Based on Different RANS Turbulence Models" *Water* 14, no. 18: 2873.
https://doi.org/10.3390/w14182873