# Experimental Study on the Air Concentration Distribution of Aerated Jet Flows in a Plunge Pool

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Methods

_{0}(2 cm, 3 cm, 4 cm, 5 cm), the initial air concentration C

_{0}(10%, 15%, 30%, 40%, 50%, 60%), the clear water flow rate Q

_{w}(14.0 L/s–35.2 L/s), and the air flow rate Q

_{a}(2.1 L/s–42.0 L/s), as listed in Table 1.

_{0}= 2 cm, C

_{0}= 30%, Q

_{w}= 16.8 L/s), an experimental photograph and a contour map of the air concentration distribution on one side of the jet axis are shown in Figure 3. The majority of the air bubbles flow with the jet flow in the free jet region, before being blocked by the flume floor and deflected by 90 degrees into the wall jet region on both sides. Afterwards, the air bubbles flow gradually towards the water surface, with some eventually escaping into the surrounding air, whereas the rest are carried into the swirling region.

## 3. Results and Discussion

#### 3.1. Air Concentration Distribution in the Free Jet Region

_{w}, the initial air concentration C

_{0}, and the clear water flow rate Q

_{w}were adopted, and a series of experiments were performed to test each effect on the air concentration attenuation, as shown in Figure 4. Under a different initial water velocity (3 m/s < V

_{w}< 8 m/s) and a clear water flow rate (21.1 L/s < Q

_{w}< 35.2 L/s), the attenuation of C

_{m}/C

_{0}varies in a similar pattern along the jet axis. The reason for the results is that the velocity attenuation along the jet axis changes little with different flow conditions, including the initial jet velocity and the clear water flow rate [33].

_{m}and the distance from the nozzle x’ = H − y, normalized by the initial air concentration C

_{0}and the jet flow thickness d

_{0}in the plunge pool, respectively, is written as:

_{0}is a coefficient, suggested as approximate 1.2 in this study.

_{0}in a short distance ($\frac{H-y}{{d}_{0}}\approx 5$) from the nozzle exit. Due to the influence of the pressure gradient near the plunge floor, further from the nozzle exit, the air concentration distribution was more dispersed in the free jet region. It can be derived from the experimental results that the air concentration distribution along lateral cross-sections in the free jet region conformed to the Gaussian distribution law, as shown in Figure 5b. In the free jet region, no significant influence of different initial flow conditions was observed on the cross-sectional air concentration distribution, which tended to be self-similar. Downstream of the free jet region, the cross-sectional air concentration distribution was affected by the swirling jet in the plunge pool.

_{m}is the corresponding air concentration along the jet axis, and y’ is the transverse distance from the jet axis.

#### 3.2. Air Concentration Distribution in the Swirling Region of the Plunge Pool

_{1};

_{2};

_{3}.

_{1}, C

_{2}, and C

_{3}. When calculating the axial air concentration attenuation and the lateral diffusion in the three stages mentioned using Equation (13), separately, the jet flow distance x’ and the transverse distance from the axis y’ can be expressed as:

_{0}.

_{m1}and the initial velocity u

_{0}is:

_{ms}can be expressed as:

_{1}from the jet axis can be written as:

_{2}from near the plunge pool floor can be written as:

_{3}from the free surface can be written as:

_{1}and C

_{2}, and zero degrees in calculating C

_{3}.

#### 3.3. Comparison of Calculated and Experimental Results

_{0}< 40%, the calculated results agreed well with the experimental measurements. When the initial air concentration was large, such as C

_{0}> 40%, the calculated results could essentially reflect the variation of the air concentration distribution in the region close to the jet axis, such as x/d

_{0}< 15–20. In the downstream region, on the other hand, such as x/d

_{0}> 15–20, the calculated results were somewhat different from the experimental measurements.

_{0}= 2 cm, C

_{0}= 60%, Q

_{w}= 14.5 L/s, the absolute value of the air concentration was essentially less than 0.05 in the downstream region, such as x/d

_{0}> 10. Consequently, the present analysis model can essentially predict the air concentration distribution of aerated jet flows in the swirling region of the plunge pool.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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No. | d_{0} (cm) | C_{0} (%) | Q_{w} (L/s) | No. | d_{0} (cm) | C_{0} (%) | Q_{w} (L/s) |
---|---|---|---|---|---|---|---|

1 | 2 | 10 | 18.6 | 16 | 3 | 30 | 21.1 |

2 | 2 | 15 | 16.1 | 17 | 3 | 40 | 21.1 |

3 | 2 | 30 | 14.0 | 18 | 3 | 40 | 23.9 |

4 | 2 | 30 | 16.8 | 19 | 3 | 50 | 23.9 |

5 | 2 | 30 | 19.6 | 20 | 4 | 15 | 27.8 |

6 | 2 | 30 | 22.4 | 21 | 4 | 30 | 21.1 |

7 | 2 | 40 | 16.7 | 22 | 4 | 30 | 28.2 |

8 | 2 | 50 | 14.7 | 23 | 4 | 40 | 28.2 |

9 | 2 | 60 | 14.5 | 24 | 4 | 50 | 21.1 |

10 | 2.3 | 10 | 21.1 | 25 | 4 | 50 | 23.9 |

11 | 2.3 | 15 | 23.9 | 26 | 4 | 50 | 27.8 |

12 | 2.5 | 15 | 21.1 | 27 | 5 | 30 | 35.2 |

13 | 2.5 | 30 | 21.1 | 28 | 5 | 30 | 21.1 |

14 | 3 | 10 | 21.3 | 29 | 5 | 40 | 35.2 |

15 | 3 | 15 | 21.1 | 30 | 5 | 50 | 23.9 |

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Xu, W.; Chen, C.; Wei, W.
Experimental Study on the Air Concentration Distribution of Aerated Jet Flows in a Plunge Pool. *Water* **2018**, *10*, 1779.
https://doi.org/10.3390/w10121779

**AMA Style**

Xu W, Chen C, Wei W.
Experimental Study on the Air Concentration Distribution of Aerated Jet Flows in a Plunge Pool. *Water*. 2018; 10(12):1779.
https://doi.org/10.3390/w10121779

**Chicago/Turabian Style**

Xu, Weilin, Chunqi Chen, and Wangru Wei.
2018. "Experimental Study on the Air Concentration Distribution of Aerated Jet Flows in a Plunge Pool" *Water* 10, no. 12: 1779.
https://doi.org/10.3390/w10121779