# Numerical Simulation Calculation of Thermal Discharge Water Diffusion in Coastal Nuclear Power Plants

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Overview of the Study Area

^{3}/s and a designed temperature rise of 8.2 °C.

#### 2.2. Model Introduction

#### 2.2.1. Control Equation

- (1)
- MIKE fluid dynamics equation (Equations (1)–(3)) [42]:

- (2)
- MIKE temperature transport equation (Equations (4) and (5)):

- (3)
- Boundary control conditions

#### 2.2.2. The Difference between the Temperature–Salinity Module and the ECO Module

## 3. Model Setup and Verification

#### 3.1. Grid and Water Depth Settings

#### 3.2. Model-Driven Conditions

#### 3.3. Model Parameter Configuration

^{2}°C according to Equations (13)–(16) using actual hydrological and meteorological data observed near the power plant.

^{−8}(W·m

^{−2}·°C

^{−4}); $\alpha $ is the surface evaporation coefficient (W·m

^{−2}·hPa

^{−1}); and ${V}_{w}$ is the wind speed at 1.5 above the water surface (m/s).

#### 3.4. Model Validation

## 4. Results and Analysis

#### 4.1. Hydrodynamic Characteristics

#### 4.2. Cross-Sectional Temperature Rise Distribution

#### 4.3. Planar Temperature Rise Distribution

^{2}, which is significantly larger than the bottom 4 °C temperature rise area of 0.05 km

^{2}, and the surface-to-bottom 1 °C, 2 °C, 3 °C, and 4 °C temperature rise areas are significantly reduced. Model 2 only considers the heat transfer process during the calculation process. The thermal plume is uniformly mixed in the vertical direction, and the heat is uniformly distributed in the vertical direction so that the high-temperature water mass is diluted; the surface 4 °C temperature rise area is 0.71 km

^{2}, and the bottom 4 °C temperature rise area is 0.68 km

^{2}. The similarity of temperature rise areas between each layer can reach 99%, and the surface 4 °C temperature rise area is reduced by 45.8% compared to that of Model 1. The summer half-month tide temperature rise envelope area is shown in Table 4.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Geographic location map of the study area. (

**a**) The figure illustrates the extent of the study area and the location of the open boundaries. (

**b**) The figure displays the locations of hydrological observation stations and power plant discharge outlets.

**Figure 2.**Model grid setup: (

**a**) the grid distribution in the area near the power plant; and (

**b**) the grid refinement at the drainage outlet.

**Figure 3.**Distribution of water depth in the study area: (

**a**) the distribution of water depth in the water near the power plant.

**Figure 7.**Characteristics of flow field distribution during rapid rise and fall of semi-monthly tide in summer: (

**a**) the distribution of rapid tidal currents rising in the water near the project site; and (

**b**) the distribution of rapid tidal currents ebbing in the water near the project site.

Model | Model 1 | Model 2 |
---|---|---|

Temperature and Salt Module | ECO Module | |

Diffusion coefficient | k−ε turbulence models | |

Coriolis force coefficient | $f=2\omega \mathrm{sin}\Phi \omega $ | |

Summer surface heat exchange amount | Latent heat flux: 20 W/m^{2} °C | Comprehensive heat dissipation of water surface: 45 W/m^{2} °C |

Sensible heat flux: 12 W/m^{2} °C | ||

Long-wave radiation flux: −17 W/m^{2} °C | ||

Short-wave radiation flux: 30 W/m^{2} °C | ||

Water surface temperature | 30 °C | |

Air temperature | 32 °C | |

Wind speed | 3.32 m/s | |

power plant discharge volume | 150 m^{3}/s | |

Drainage temperature rise | 8.2 °C |

Evaluation Items | Site Name | Skill Value | Model Evaluation | Pearson Correlation Coefficient |
---|---|---|---|---|

Water level | T1 | 0.5 | Very good | 1.0 |

T2 | 0.5 | Very good | 0.9 | |

T3 | 0.6 | Very good | 1.0 | |

T4 | 0.6 | Very good | 1.0 | |

Flow velocity | S1 | 0.9 | Excellent | 0.8 |

S2 | 0.8 | Excellent | 0.8 | |

S3 | 0.9 | Excellent | 0.8 | |

Flow direction | S1 | 1.0 | Excellent | 1.0 |

S2 | 1.0 | Excellent | 1.0 | |

S3 | 0.9 | Excellent | 0.9 | |

Temperature | Model 1 | 0.8 | Excellent | 0.7 |

Model 2 | 0.6 | Excellent | 0.5 |

Model | 1 °C | 2 °C | 3 °C | 4 °C |
---|---|---|---|---|

Model 1 | 0.031864 | 0.017612 | 0.012696 | 0.009568 |

Model 2 | 0.033712 | 0.028649 | 0.022336 | 0.016069 |

$\mathrm{M}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}2-\mathrm{M}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}1$ | 0.001848 | 0.011037 | 0.009641 | 0.006501 |

**Table 4.**Statistics of temperature rise envelope area during summer half-moon tide for Model 1 and Model 2 (km

^{2}).

Model | Tide Type | Vertical Position | 1 °C | 2 °C | 3 °C | 4 °C |
---|---|---|---|---|---|---|

Model 1 | Summer half-moon tide | Surface layer | 17.75 | 5.89 | 2.62 | 1.31 |

Mid-layer | 12.16 | 0.55 | 0.23 | 0.13 | ||

Bottom layer | 8.53 | 0.17 | 0.09 | 0.05 | ||

Model 2 | Summer half-moon tide | Surface layer | 18.91 | 2.89 | 1.20 | 0.71 |

Mid-layer | 18.89 | 2.82 | 1.17 | 0.70 | ||

Bottom layer | 18.76 | 2.70 | 1.13 | 0.68 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, X.; Shi, H.; Zhan, C.; Zhu, J.; Wang, Q.; Li, G.
Numerical Simulation Calculation of Thermal Discharge Water Diffusion in Coastal Nuclear Power Plants. *Atmosphere* **2023**, *14*, 1371.
https://doi.org/10.3390/atmos14091371

**AMA Style**

Zhang X, Shi H, Zhan C, Zhu J, Wang Q, Li G.
Numerical Simulation Calculation of Thermal Discharge Water Diffusion in Coastal Nuclear Power Plants. *Atmosphere*. 2023; 14(9):1371.
https://doi.org/10.3390/atmos14091371

**Chicago/Turabian Style**

Zhang, Xuri, Hongyuan Shi, Chao Zhan, Jun Zhu, Qing Wang, and Guoqing Li.
2023. "Numerical Simulation Calculation of Thermal Discharge Water Diffusion in Coastal Nuclear Power Plants" *Atmosphere* 14, no. 9: 1371.
https://doi.org/10.3390/atmos14091371