# Research on the Similarity Scale of Flood Discharge Atomization Based on Water-Air Two-Phase Flow

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model of FDA and Its Solution

#### 2.1. Mathematical Model of FDA

#### 2.2. Model Solution Strategy

#### 2.3. Calculation Example Verification

^{−5}. Figure 1 shows that the iterative convergence process of pressure is relatively slow, while the iterative solution process of velocity is faster.

## 3. Influence of the Geometric Scale on FDA

#### 3.1. Calculation Model

^{3}/s. The pressure boundary conditions are as follows: the model outlet is a known pressure boundary, the pressure below the water surface is calculated by water depth, and the pressure above the water surface is calculated by elevation coordinates; the top of the model is a known pressure boundary; and the pressure of the remaining parts is obtained by calculation. The concentration boundary conditions are as follows: the concentration boundary below the spillway inlet water surface is known, and the concentration in the rest of the area is obtained by calculation. For models with other geometric scales, the speed at the boundary is reduced according to the geometric dimensions, which meets the criterion of equal Froude number, while the pressure boundary conditions and concentration boundary conditions are consistent with the 1:1 model.

#### 3.2. Evolution Process of Atomization Wind Speed and Rainfall

#### 3.3. Influence of Geometric Scale on the FDA Wind Field and Rain Field

^{3}/s. The atomization wind speed at 7 measuring points and the atomization rain intensity at 21 effective measuring points were monitored (Figure 10) [22]. Generally, we pay more attention to the maximum value and the influence range of atomized rainfall. Therefore, measuring point #22 with the largest rainfall intensity among all monitoring points (left bank 230 m platform) is selected, and the stable atomization wind speed and rainfall intensity obtained under different geometric scale conditions are plotted in Figure 11 and Figure 12.

#### 3.4. Influence of Atmospheric Pressure on the Model Test

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Distribution of liquid phase volume fraction at different moments: (

**a**,

**a’**) Initial; (

**b**,

**b’**) Transient state; (

**c**,

**c’**) Stable.

**Figure 3.**Comparison between theoretical value and calculated value of water velocity at different distances from pipeline inlet.

**Figure 10.**FDA scene and atomization rain intensity monitoring points of Shuibuya Hydropower Station.

**Figure 12.**Intensity of atomized rain at the stable moment under different geometric scale conditions.

**Figure 13.**Comparison of simulated rainfall intensity (

**a**) and wind speed (

**b**) with prototype observations under different geometric scale conditions.

**Figure 14.**Model atomization rainfall and atomization wind speed under different geometric scale conditions.

**Figure 15.**Comparison of simulated wind speed (

**a**) and rainfall intensity (

**b**) with prototype observations under the condition of similar atmospheric pressure.

Geometric scale ${\mathrm{L}}_{r}$ | 1:2 | 1:5 | 1:10 | 1:20 | 1:50 | 1:100 |

Rain intensity conversion coefficient ${n}_{{S}_{r}}$ | 1.734 | 1.879 | 1.582 | 1.252 | 1.019 | 1.127 |

Rain intensity scale ${S}_{r}={\mathrm{L}}_{r}{}^{{n}_{{S}_{r}}}$ | 3.33 | 7.88 | 38.19 | 42.55 | 53.86 | 179.47 |

Wind speed conversion coefficient ${n}_{{\mathrm{V}}_{r}}$ | 1.07 | 1.43 | 1.21 | 0.942 | 0.672 | 0.572 |

Wind speed scale ${\mathrm{V}}_{r}={\mathrm{L}}_{r}{}^{{n}_{{\mathrm{V}}_{r}}}$ | 2.10 | 4.81 | 16.22 | 16.81 | 13.86 | 13.93 |

**Table 2.**Atomization wind speed and rainfall conversion coefficient n under different geometric scale conditions.

Geometric scale ${\mathrm{L}}_{r}$ | 1:2 | 1:5 | 1:10 | 1:20 | 1:50 | 1:100 |

Rain intensity conversion coefficient ${n}_{{S}_{r}}$ | 1.014 | 0.800 | 0.795 | 0.726 | 0.634 | 0.581 |

Rain intensity scale ${S}_{r}={\mathrm{L}}_{r}{}^{{n}_{{S}_{r}}}$ | 2.02 | 2.41 | 6.24 | 8.80 | 11.94 | 14.52 |

Wind speed conversion coefficient ${n}_{{\mathrm{V}}_{r}}$ | 0.824 | 0.683 | 0.672 | 0.634 | 0.579 | 0.553 |

Wind speed scale ${\mathrm{V}}_{r}={\mathrm{L}}_{r}{}^{{n}_{{\mathrm{V}}_{r}}}$ | 1.77 | 2.12 | 4.70 | 6.68 | 9.63 | 12.76 |

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**MDPI and ACS Style**

Liu, G.; Tong, F.; Tian, B.; Lan, J.
Research on the Similarity Scale of Flood Discharge Atomization Based on Water-Air Two-Phase Flow. *Water* **2023**, *15*, 442.
https://doi.org/10.3390/w15030442

**AMA Style**

Liu G, Tong F, Tian B, Lan J.
Research on the Similarity Scale of Flood Discharge Atomization Based on Water-Air Two-Phase Flow. *Water*. 2023; 15(3):442.
https://doi.org/10.3390/w15030442

**Chicago/Turabian Style**

Liu, Gang, Fuguo Tong, Bin Tian, and Jiaxin Lan.
2023. "Research on the Similarity Scale of Flood Discharge Atomization Based on Water-Air Two-Phase Flow" *Water* 15, no. 3: 442.
https://doi.org/10.3390/w15030442