# Experimental and Numerical Investigation of Mixing Phenomena in Double-Tee Junctions

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Setup

#### 2.2. Measurement Procedure and Apparatus

#### 2.3. Numerical Modeling

#### 2.3.1. Passive Scalar Model

**v**is the advection velocity vector. Physically, Equation (3) can be interpreted as an additional transport of a scalar quantity c by the fluid flow. Since this approach models steady flow, it is less computationally expensive than the multiphase model (Section 2.3.2). In this study, the additional Equation (3) is implemented into the steady-state OpenFOAM solver SimpleFoam. Boundary conditions for velocity $\mathbf{v}$ are Dirichlet boundary conditions (DBC) and the values at the inlet and outlet of pipes is defined to be the same as the experimental values. The no-slip boundary condition is used at the pipe walls. The Neumann boundary condition (NBC) is assigned for pressure p at the inlet of both pipes and at the pipe wall while at the outlets it is defined as zero to obtain a positive gradient. The dimensionless scalar c is defined as 1 at the inlet of pipe 1 (Figure 1) and 0 at the inlet of pipe 2, while the NBC is set at the outlets and pipe wall. Turbulence model variables k and $\u03f5$ are estimated [19] and assigned at the inlets and NBC set at the outlet. Turbulence wall functions are defined at the pipe walls. Boundary condition types for all variables being solved are summarized in Table 2.

#### 2.3.2. Multiphase Model

## 3. Results and Discussion

#### 3.1. Experimental Results

#### 3.1.1. Complete Mixing

#### 3.2. CFD Results

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Two different experimental configurations with variable distance between two Tee junctions where inlet pipes are labeled as 1 and 2 and outlet pipes as 3 and 4. D represents distilled water, T represents tap water and M represents mixture: (

**a**) Distilled water inlet and mixture outlet branch on opposite sides (configuration S). (

**b**) Distilled water inlet and mixture outlet branch on the same side (configuration U).

**Figure 3.**Experimental results for the S configuration—relationship between branch outlet to main inlet pipe conductivity ratio ${R}_{c}$ and inlet flow ratio ${R}_{f}$ compared with previous studies [8,9] of cross junction mixing results. Dashed lines represent the value of mixing parameter s used in EPANET-BAM [12].

**Figure 4.**S and U configuration experimental results—normalized branch inlet conductivity ratio ${R}_{{c}_{*}}$ to normalized main pipe inlet flow ${R}_{{f}_{*}}$ compared with the previous study [16] and shown in relation to the complete mixing line: (

**a**) Configuration S, (

**b**) Configuration U.

**Figure 5.**Influence of Tee junctions distance on complete mixing—the relationship between inlet flow ratio ${R}_{f}$ and outlet conductivity ratio ${R}_{{c}_{complete}}$: (

**a**) Configuration S (

**b**) Configuration U.

**Figure 6.**Relation between the outlet conductivity ratio ${R}_{{c}_{complete}}$ and Tee-junction distance.

**Figure 7.**S pipe configuration—comparison of experimental results with passive scalar and multiphase model results for different Tee-junction distances: (

**a**) 5.6D, (

**b**) 10D, (

**c**) 15D, (

**d**) 25D.

**Figure 8.**U pipe configuration - comparison of experimental results with passive scalar and multiphase model results for different Tee-junction distances: (

**a**) 5.6D, (

**b**) 10D, (

**c**) 15D, (

**d**) 25D.

**Figure 9.**CFD tracer streamlines visualization for identical inlet flow ratio: (

**a**) Configuration S, 5.6D, (

**b**) Configuration S, 10D, (

**c**) Configuration U, 5.6D, (

**d**) Configuration U, 10D.

Parameter | Value | Unit |
---|---|---|

Internal pipe diameter (D) | 18 | (mm) |

Inlet pipes length | 20D | (-) |

Outlet pipes length | 40D | (-) |

Tee distances | 5.6D, 10D, 15D, 20D, 25D, 30D, 70D, 120D, 130D, 150D | (-) |

Inlet flow range | 0.08–0.43 | (l/s) |

Reynolds number range | 6000–30,000 | (-) |

Inlet flow ratios (5.6D, 10D, 15D) | 3:1, 2:1, 1:1, 1:2, 3:1 | (-) |

Inlet flow ratios (20D, 25D, 30D, 70D, 120D, 130D, 150D) | 1:1 | (-) |

**Table 2.**Boundary conditions summary for the passive scalar model (

**n**represents the normal vector) and ${\tau}_{wall}$ refers to the wall shear stress.

Variable | Inlets | Outlets | Pipe Walls |
---|---|---|---|

$\mathbf{v}$ | $\mathbf{v}$ | $\mathbf{v}$ | $\mathbf{v}$ |

p | $\partial p/\partial \mathbf{n}=0$ | p | $\partial p/\partial \mathbf{n}=0$ |

c | c | $\partial c/\partial \mathbf{n}=0$ | $\partial c/\partial \mathbf{n}=0$ |

k | k | $\partial k/\partial \mathbf{n}=0$ | $f\left({\tau}_{wall}\right)$ |

$\u03f5$ | $\u03f5$ | $\partial \u03f5/\partial \mathbf{n}=0$ | $f\left({\tau}_{wall}\right)$ |

Variable | Inlets | Outlets | Pipe Wall |
---|---|---|---|

$\mathbf{v}$ | $\mathbf{v}$ | $\mathbf{v}$ | $\mathbf{v}$ |

p | $\partial p/\partial \mathbf{n}=0$ | p | $\partial p/\partial \mathbf{n}=0$ |

$\alpha $ | $\alpha $ | $\partial \alpha /\partial \mathbf{n}=0$ | $\partial \alpha /\partial \mathbf{n}=0$ |

k | k | $\partial k/\partial \mathbf{n}=0$ | $f\left({\tau}_{wall}\right)$ |

$\u03f5$ | $\u03f5$ | $\partial \u03f5/\partial \mathbf{n}=0$ | $f\left({\tau}_{wall}\right)$ |

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**MDPI and ACS Style**

Grbčić, L.; Kranjčević, L.; Lučin, I.; Čarija, Z. Experimental and Numerical Investigation of Mixing Phenomena in Double-Tee Junctions. *Water* **2019**, *11*, 1198.
https://doi.org/10.3390/w11061198

**AMA Style**

Grbčić L, Kranjčević L, Lučin I, Čarija Z. Experimental and Numerical Investigation of Mixing Phenomena in Double-Tee Junctions. *Water*. 2019; 11(6):1198.
https://doi.org/10.3390/w11061198

**Chicago/Turabian Style**

Grbčić, Luka, Lado Kranjčević, Ivana Lučin, and Zoran Čarija. 2019. "Experimental and Numerical Investigation of Mixing Phenomena in Double-Tee Junctions" *Water* 11, no. 6: 1198.
https://doi.org/10.3390/w11061198