# CFD Simulation of a Submersible Passive Rotor at a Pipe Outlet under Time-Varying Water Jet Flux

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## Abstract

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## 1. Introduction

- Use of a passive rotor at the water tank pipe outlet to increase the effluent drainage rate from the effluent tanks in water treatment facilities [5];
- Use of a passive rotor at the outlet of pipe outfall to improve mixing;
- Using a passive rotor upstream of a water level control gate to adjust the upstream water afflux by controlling the rotation of the passive rotor without the need to change the gate opening [3].
- Using passive rotors downstream of a sluice gate for energy dissipation

## 2. Method Statement

#### 2.1. Study Objectives

#### 2.2. Physical Experiment

#### 2.3. Measurements via Video Tracking

#### 2.4. Accuracy of Measuring the Angular Speed Using Video Auto-tracking Tracking

#### 2.5. Numerical Techniques for Rotating Elements in FLUENT

_{max}, the variation of ω with time, and the equation of ω as a function of υ. The 6DOF results were compared with those obtained from the physical model [5]. The verification includes both ω

_{max}and the variation of ω with time. After that, the ω equation as a function of υ was investigated. Then, the sliding mesh technique was used after adding that equation to the User-Defined-Functions (UDF). The accuracy of both CFD methods and the time consumed are discussed. Finally, the results and a discussion of the sliding mesh model are tackled.

#### 2.6. Assumptions and Simplifications

- There is no eccentricity for the shaft of the rotor to the center of the pipe outlet;
- The shaft of the rotor revolves smoothly around its pivot without resistance;
- The shaft and its rotor have the same angular speed (i.e., no slipping took place);
- No deformation is allowed regarding the blades of the rotor during the simulation;
- The rotor blade is assumed rigid enough, and its deformation is neglected;
- The direction of the water flux from the pipe outlet (before impinging on the rotor) is mainly horizontal, with no inclination;
- For practical reasons, the main focus of the simulation is directed on capturing the decelerated period for the rotor (refer to the calibration section) since this period is the dominating stage, and the accelerating zone lasts less than 1.5% of the whole simulation time.

## 3. Numerical Model Development

#### 3.1. Workflow Development

- Start the simulation using the dynamic mesh method using the 6DOF solver for about 21% of the required total simulation time (for the study on hand, for the first 40 s);
- The k-e turbulence model will be initially selected, and the accuracy of the generated mesh will be checked near the boundaries by assessing the y+ plot;
- The simulation will be repeated many times, and each time, a different turbulence model will be tried, and the rotor’s angular speed results will be compared with the measurements;
- Identify the most relevant turbulence model that gives the best match with the measurements;
- Based on the obtained results of the optimal turbulence model, identify the relation between the rotor’s angular speed (ω) and the pipe outlet velocity (υ) and create a user-defined function (UDF) for it;
- Switch the model to the sliding mesh (SM) technique while adopting the optimal turbulence model, and start the simulation until the end of the simulation time.

#### 3.2. The Geometry of the CFD Model

^{−3}and 1.086 × 10

^{−2}mm

^{2}, with an average of 6.716 × 10

^{−2}mm

^{2}.

#### 3.2.1. The Boundary Conditions

#### The Inlet Boundary

#### The Outlet Boundary

#### The Top of the Model and the Other Boundaries

#### 3.2.2. Solver Parameters

## 4. Calibration and Accuracy Assessment of the Numerical Model

#### 4.1. Measurements of the Rotor’s Angular Speed

_{max}). Three distinct stages appear in Figure 8a. The first zone is the acceleration stage (from A to B), where the rotor speed accelerates to achieve its maximum angular speed. Interestingly, the rotor is accelerating at this stage, even though the pipe flow is decelerating. In the second stage (from B to C), the angular speed starts linearly and progressively decreases with time until it reaches point C, where the tank becomes wholly drained. In the last stage (from C to D), the transmission pipe rapidly drains until it reaches point D. This rapid decrease in angular speed may be explained by the substantial difference between the tank and pipe cross-section areas.

_{r}= ω.d

_{r}/2, and Vo is the water pipe outlet mean velocity. Figure 8b shows the variations in the rotor’s tip speed rotation (TSR) over the course of time. The figure shows that TSR varies from about 1.6 to 1.9, which means that the tip rotor speed is almost 60 to 90% faster than the outlet water velocity.

#### 4.2. Model Discretization and GCI Analysis

#### 4.3. Checking Model Discretization near the Boundary

#### 4.4. The Sensitivity of the Turbulence Model

#### 4.4.1. The Maximum Angular Speed

#### 4.4.2. Comparison of the Temporal Variation in the Rotor’s Angular Speed

#### 4.5. Computational Resources

#### 4.6. The Relation between the Angular Speed and the Pipe Outlet Water Velocity

## 5. Results and Discussion

#### 5.1. Perturbation of Angular Speed

#### 5.2. Effect of the Outlet–Rotor Gap Distance

#### 5.3. Effect of the Passive Rotor on the near Downstream Flow Field

_{av}= 30 cm/s and ω = 293.5 rpm). The path lines are also color-coded based on the corresponding values of flow velocity, where a relatively high flow velocity exists near the rotor (within a distance of 2–3 d, where d is the pipe outlet diameter), and the flow velocity significantly decreases downstream. The figure illustrates how a spiral flow is developed by the passive rotor when a rotating wake occupies a flow domain whose average lateral size exceeds the rotor’s diameter (≈2.3 D, where D is the rotor’s diameter). The rotating wake influence is also observed to extend downward to the front wall of the tank (x ≈ 15 d, where d is the pipe outlet diameter).

#### 5.4. Effect of the Passive Rotor on the Turbulence Intensity

_{av}=30 cm/s and ω = 293.5 rpm). The figure shows that the turbulence intensity at the pipe outlet varies between 1.19 and 1.95%, with an average value of 1.3%. Slightly further downstream, the passive rotor causes the turbulence intensity to sharply increase to reach significantly higher values than the values downstream of the pipe outlet. It is also noticed that the turbulence intensity substantially decreases as the flow goes far from the passive rotor.

## 6. Conclusions and Challenges

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Samples of proposed applications where passive rotors could be utilized. (

**A**) at the outlet of a drainage tank, (

**B**) at the outlet of pipe outfall, (

**C**) at the upstream of a sluice gate, (

**D**) at the downstream of a sluice gate.

**Figure 2.**Experimental setup: (

**A**) a snapshot of the experimental setup, (

**B**) Elements of the experimental setup, (

**C**) side view of the rotor, (

**D**) front view of the rotor.

**Figure 3.**Auto-tracking of the rotor’s angular speed via the Tracker (camera capturing rate = 240 fps).

**Figure 4.**Setup of the assessment of accuracy experiments (using two different methods) for the angular speed measurements: oblique-plan view, side view.

**Figure 6.**Schematic Figure of the CFD model: (

**a**) Side view of the CFD model dimension, (

**b**) Front view of the CFD model dimension, (

**c**) Side view of the CFD model boundary, (

**d**) Front view of the CFD model boundary.

**Figure 7.**Passive rotor grid model: (

**a**) The mesh on the rotor surface, (

**b**) The detail of the mesh on one of the blades (dotted line zone in Figure 5a), (

**c**) The detail of the mesh of the rotor, the inlet, and the walls.

**Figure 8.**Video analysis measurements of the temporal variations of (

**a**) the normalized rotor’s angular speed and (

**b**) the tip speed ratio (TSR).

**Figure 9.**The relationship between the position on the blades and the y+ value at the maximum angular velocity. (

**a**) Spatial variations of the wall y+ value along transect A-A, (

**b**) Color contours of y+ over the whole rotor.

**Figure 10.**Predicted rotor’s angular speed based on different turbulence models. (

**a**) maximum angular speed, (

**b**) percentage error in the maximum angular speed.

**Figure 11.**The variation in the rotor’s angular speed: (

**a**) The time span from rest to 40 s, (

**b**) Zoom in for the accelerating zone. (for explanation of points A–C, refer to Figure 8a).

**Figure 12.**The relationship between the angular velocity (rpm) and the time (s) for the experimental and sliding mesh-CFD models.

**Figure 13.**Effect of the pipe outlet-rotor gap distance on the gained rotor’s angular speed: (

**a**) Temporal variation with time, (

**b**) Maximum rotor’s angular speed.

**Figure 15.**Effect of the passive rotor on the turbulence intensity at υ

_{av}=30 cm/s and ω = 293.5 rpm. (

**a**) Color contour map (vertical plan) of the turbulence intensity downstream of the rotor. (

**b**) Spatial variations in turbulent intensity along the x-x transect. (

**c**) Spatial variation of TI along the y-y transect.

Parameters | Settings |
---|---|

Solver | Pressure-based, transient |

Velocity formulation | Absolute |

Turbulence model | Standard k-ε |

Water density | 998.2 kg/m^{3} |

Water viscosity | 0.001003 kg/m·s |

Pressure discretization | Body Force Weighted |

Gravity | 9.81 m/s^{2} |

The inlet | Unsteady mass flow inlet |

The outlet | Pressure outlet |

The top of the tank | Symmetry |

All other boundaries | Wall |

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## Share and Cite

**MDPI and ACS Style**

Farouk, M.; Kriaa, K.; Elgamal, M.
CFD Simulation of a Submersible Passive Rotor at a Pipe Outlet under Time-Varying Water Jet Flux. *Water* **2022**, *14*, 2822.
https://doi.org/10.3390/w14182822

**AMA Style**

Farouk M, Kriaa K, Elgamal M.
CFD Simulation of a Submersible Passive Rotor at a Pipe Outlet under Time-Varying Water Jet Flux. *Water*. 2022; 14(18):2822.
https://doi.org/10.3390/w14182822

**Chicago/Turabian Style**

Farouk, Mohamed, Karim Kriaa, and Mohamed Elgamal.
2022. "CFD Simulation of a Submersible Passive Rotor at a Pipe Outlet under Time-Varying Water Jet Flux" *Water* 14, no. 18: 2822.
https://doi.org/10.3390/w14182822