# Three-Dimensional Numerical Simulation of Flow Structure in Annular Flume Based on CFD Study of Water

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## Abstract

**:**

## 1. Introduction

## 2. Model Development

#### 2.1. Annular Sink Description and Instrumentation

#### 2.2. Model Selection and Governing Equations

_{i}, x

_{j}denote the coordinate positions when i or j is 1, 2, and 3, respectively, denoting the three x, y, and z directions; u

_{i}denotes the velocity in the x

_{i}direction; $\rho $ is the density; t is the time; p is the pressure on the fluid micro-element; $\mu $ denotes the viscosity coefficient; ${S}_{{u}_{i}}$ is denoted as the generalized source term of the momentum conservation equation; G

_{k}denotes the turbulent kinetic energy due to the laminar velocity gradient; G

_{b}denotes the turbulent kinetic energy due to buoyancy; and Y

_{m}denotes the fluctuations generated by the diffusion of the transition in compressible turbulence. The model constants ${C}_{1\epsilon}$, ${C}_{2\epsilon}$, ${C}_{\mu}$, ${\alpha}_{K}$, ${\alpha}_{\epsilon}$, ${C}_{\epsilon 1}$, ${C}_{\epsilon 2}$, ${\eta}_{0}$ and $\beta $ for the above equations take the values 1.44, 1.92, 0.0845, 1.39, 1.39, 1.42, 1.68, 4.377 and 0.012, respectively.

#### 2.3. Calculation Methods and Boundary Conditions

^{−4}. (All of the above were set up in the ANSYS Fluent software; details can be found in Ansys Resource Center | Webinars, White Papers and Articles.)

#### 2.4. Mesh Profiling

#### 2.5. Grid Convergence Analysis

#### 2.6. Model Validation

## 3. Simulation Results and Analysis

#### 3.1. Cross-Sectional Axial Flow Velocity Contour Distribution

#### 3.2. Cross-Sectional Velocity Vector Distribution

#### 3.3. Shear Force Distribution at the Bottom of the Flume

#### 3.4. The Variation Pattern of Secondary Flow Intensity with the Size of Speed Ratio

^{2}) is concentrated near the bottom of the flume and the water surface (0 < y < 0.05 m vs. 0.025 < y < 0.3 m), as shown in Figure 9. The intensity of secondary flow at the bottom of the sink and the surface water both decrease with the increase in the speed ratio, and the intensity of secondary flow at the bottom of the sink is greater than that of the surface water, with the increase in the speed ratio R and the weakening trend of secondary flow at the bottom of the sink being more obvious than that near the water surface, so 0 < y < 0.05 m of the bottom of the sink was chosen as the key study area of secondary flow intensity.

## 4. Conclusions

- (1)
- As the speed ratio increases, the negative flow velocity gradually expands from the side wall to the center of the flume, the axial flow velocity of the annular flume gradually shows a “U”-type distribution and the axial flow velocity distribution becomes more uniform. The relative value of axial flow velocity is more in line with the natural law than the absolute value of axial flow velocity for the calculation of the Reynolds number. In addition, in terms of water flow structure stability, the water flow structure is more complex as the speed ratio increases.
- (2)
- When the speed ratio R ≤ 0.24, the speed ratio and the bottom shear size show a positive correlation, and the bottom shear distribution tends to be flat. The speed ratio R = 0.24 is the critical point when the bottom shear distribution is most uniform; when R > 0.24, the bottom shear peak position is shifted to the inner wall side, the bottom shear distribution is extremely uneven, and the sediment is more likely to accumulate on the outer wall side at this time.
- (3)
- When the speed ratio R < 0.28, the secondary flow intensity shows a negative correlation with the size of the speed ratio. When the speed ratio R = 0.28, the secondary flow intensity of the annular sink reaches the lowest value, which is only 39.28% of the secondary flow intensity of the annular sink driven by the shear ring. When the velocity ratio R = 0.24, the annular flume water flow structure is the most stable and controllable.
- (4)
- Compared with the previous research results, this study investigates the axial flow velocity and the development of vortex flow in the flume with increasing speed ratios in more detail. This study can provide technical support for research in sedimentation, pollutant release, transport and dispersion and other related scientific fields.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Contour distribution of axial flow velocity in annular flume at different speed ratios, where (

**a**) is the control group driven by the shear ring only; (

**b**–

**l**) are the different working conditions obtained by different turn–continuity ratios.

**Figure 7.**Distribution of shear force at the bottom of the flume at different speed ratios, where x is the distance from the center of the circle.

Scheme | Grid Size/cm | Local Encryption | $\overline{\mathbf{u}}/\mathbf{cm}\xb7{\mathbf{s}}^{-1}$ | $\overline{{\mathit{u}}_{\mathit{R}}}/\mathbf{cm}\xb7{\mathbf{s}}^{-1}$ | Error |
---|---|---|---|---|---|

A | 3 | No | 130.21 | 94.04 | 38.47% |

B | 1 | No | 103.92 | 94.04 | 10.51% |

C | 1 | Yes | 97.37 | 94.04 | 3.54% |

D | 0.5 | No | 97.31 | 94.04 | 3.48% |

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**MDPI and ACS Style**

Yan, J.; Zhang, L.; Xu, L.; Chen, S.; Peng, G.; Wang, M.
Three-Dimensional Numerical Simulation of Flow Structure in Annular Flume Based on CFD Study of Water. *Water* **2023**, *15*, 651.
https://doi.org/10.3390/w15040651

**AMA Style**

Yan J, Zhang L, Xu L, Chen S, Peng G, Wang M.
Three-Dimensional Numerical Simulation of Flow Structure in Annular Flume Based on CFD Study of Water. *Water*. 2023; 15(4):651.
https://doi.org/10.3390/w15040651

**Chicago/Turabian Style**

Yan, Jun, Litao Zhang, Linjuan Xu, Sainan Chen, Guanghong Peng, and Meng Wang.
2023. "Three-Dimensional Numerical Simulation of Flow Structure in Annular Flume Based on CFD Study of Water" *Water* 15, no. 4: 651.
https://doi.org/10.3390/w15040651