# The Effect of Variations of Flow from Tributary Channel on the Flow Behavior in a T-Shape Confluence

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Laboratory Model

_{t}= 0.17 m

^{3}/s with h = 0.296 m, resulting in a Froude number of Fr

_{t}= 0.37, was used in the calibration test.

#### 2.2. Numerical Model

#### 2.3. Governing Equations

#### 2.4. Turbulence Modeling

_{t}represents eddy viscosity, G

_{b}and G

_{k}are generations of the turbulent kinetic energy due to buoyancy and mean velocity gradients, respectively; Y

_{M}is the contribution of the fluctuating dilatation incompressible turbulence to the overall dissipation rate; C

_{1ε}, C

_{2ε}, C

_{3ε}, and C

_{μ}are constants (1.44, 1.92, 0.09, and 0.09 respectively); ${\mathsf{\sigma}}_{\mathrm{k}}$ and ${\sigma}_{\epsilon}$ are turbulent Prandtl numbers for k and ε (1.0 and 1.3, respectively). The RNG model used equations analogous to the equations for the k-ε model. However, constants that were found empirically in the standard k-ε model were derived explicitly in the RNG model. Generally, the RNG model has wider applicability than the standard k-ε model. In particular, the RNG model is known to present more accurately for low-intensity turbulence flows and flows with strong shear regions [2].

#### 2.5. Boundary Conditions and Gridding

## 3. Model Verification

^{2}= 0.93, MAE = 0.13, and RMSE = 0.26) with less consumed time of simulation compared to RNG (with R

^{2}= 0.91, MAE 0.15, and RMSE = 0.29) and k-ω (with R

^{2}= 0.93, MAE = 0.15, and RMSE = 0.25) was opted as the optimum turbulence model. A comparison of the stream-wise component of velocity (U) calculated with the computational fluid dynamics (CFD) code with that of experimental data showed acceptable accuracy of the numerical results (see Figure 2 and Figure 3).

#### Simulation Scenarios

_{sc}) to Froude number of flow in the main channel (Fr

_{mc}), as well as the Froude number of the overall flow after the confluence (FR*), as varying parameters in simulation scenarios would provide better understanding and could result in better and more generalized conclusions.

## 4. Results and Discussion

#### 4.1. Velocity Distribution

_{t}= 0.31 for case 7) in comparison with other cases. It could be interpreted through the increased width of the recirculation zone in the channel in case (7) compared to other cases. Generally, it could be inferred that increasing the Froude number of the side-channel or the ratio between the Froude numbers of side-channel to the Froude number of the main channel might result in higher velocity gradients near the bed, which might result in increased sediment scour, as well as increased sedimentation due to the increased area of recirculation zone.

_{sc}) and that of main channel (Q

_{mc}) could result in relatively similar stream-wise velocity distribution (Figure 6a,c), yet, the main difference, which caused variations in flow patterns, was caused by significant fluctuations in V.

#### 4.2. Flow Patterns and Vortical Structure

#### 4.2.1. Flow Surface Profile

#### 4.2.2. Streamlines and Flow Patterns

#### 4.3. Turbulent Kinetic Energy

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**A comparison of the accuracy of velocity calculations from different turbulence models in estimating U-component of velocity at x = 8.82 (x* = 2 Wc) and (

**a**) y = 0.25 Wc, and (

**b**) y = 0.5 Wc.

**Figure 4.**The distribution of the stream-wise component of velocity (U) for (

**a**–

**d**) case 1, and (

**e**–

**h**) case 4, and (

**i**–

**l**) case 7.

**Figure 5.**The distribution of the normal component of velocity (V) for (

**a**–

**d**) case 1, and (

**e**–

**h**) case 4, and (

**i**–

**l**) case 7.

**Figure 6.**The comparison of velocity components at transverse planes (

**a**) U at x = 7.91, (

**b**) V at x = 7.91, (

**c**) U at x = 8.35m, and (

**d**) V at x = 8.35m.

**Figure 7.**Longitudinal flow surface profiles at (

**a**) Y = 0.905m and (

**b**) Y = 0.455m (channel centerline).

**Figure 8.**Three-dimensional streamlines at the confluence (

**a**) downstream view of recirculation, (

**b**) upstream view, and (

**c**) tributary flow.

**Figure 9.**The effect of Fr* on the flow pattern at different elevations for (

**a**–

**d**) case 1 and (

**e**–

**h**) case 4, and (

**i**–

**l**) case 7.

**Figure 10.**Transverse profile of recirculation zone at x = 8.35 (x = 0.5 Wc downstream of confluence).

**Figure 11.**Transverse profile of recirculation zone at x = 8.35 (x = 0.5 Wc downstream of confluence).

**Figure 12.**Transverse distribution of turbulent kinetic energy (TKE) at (

**a**) x = Wc and (

**b**) x = 1.5 Wc.

Case No. | Q_{sc} (Lit/s) | Q_{mc} (Lit/s) | Q_{t} (Lit/s) | Q* = Q_{sc}/Qt | Fr_{sc} | Fr_{mc} | Fr_{t} | Fr* = Fr_{sc}/Fr_{mc} |
---|---|---|---|---|---|---|---|---|

1 | 35 | 127 | 162 | 0.22 | 0.07 | 0.26 | 0.33 | 0.28 |

2 | 42 | 127 | 169 | 0.25 | 0.09 | 0.26 | 0.34 | 0.33 |

3 | 49 | 127 | 176 | 0.28 | 0.10 | 0.26 | 0.36 | 0.39 |

4 | 56 | 127 | 183 | 0.31 | 0.11 | 0.26 | 0.37 | 0.44 |

5 | 56 | 115 | 171 | 0.33 | 0.11 | 0.23 | 0.35 | 0.49 |

6 | 56 | 106 | 162 | 0.35 | 0.11 | 0.22 | 0.33 | 0.53 |

7 | 56 | 95 | 151 | 0.37 | 0.11 | 0.19 | 0.31 | 0.59 |

_{sc}is the discharge from the side-channel. Q

_{mc}is the discharge from the upstream main channel. Q

_{t}is the total discharge after confluence. Q* is ratio between discharge of tributary flow and the main channel flow. FR* is the ratio between Froude number of tributary flow and the main channel flow.

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**MDPI and ACS Style**

Azma, A.; Zhang, Y.
The Effect of Variations of Flow from Tributary Channel on the Flow Behavior in a T-Shape Confluence. *Processes* **2020**, *8*, 614.
https://doi.org/10.3390/pr8050614

**AMA Style**

Azma A, Zhang Y.
The Effect of Variations of Flow from Tributary Channel on the Flow Behavior in a T-Shape Confluence. *Processes*. 2020; 8(5):614.
https://doi.org/10.3390/pr8050614

**Chicago/Turabian Style**

Azma, Aliasghar, and Yongxiang Zhang.
2020. "The Effect of Variations of Flow from Tributary Channel on the Flow Behavior in a T-Shape Confluence" *Processes* 8, no. 5: 614.
https://doi.org/10.3390/pr8050614