# Research on Sea Spray Distribution of Marine Vessels Based on SPH-FEM Coupling Numerical Simulation Method

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Methods

#### 2.1. Governing Equations

^{3}. $B$ is used to limit the maximum change in density, taking $B=\frac{{c}_{0}^{2}{\rho}_{0}}{\gamma}$ in the fluid, ${c}_{0}$ is the sound speed.

#### 2.2. Coupling Wall Boundary Treatment

## 3. Method Validation Analysis

#### 3.1. Methods Analysis

#### 3.2. Method Validation

## 4. Case and Analysis of Calculation Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**This figure shows the model built imitating the Dehghani model: (

**a**) schematic of the MFV used as the ship model for the model of 3-D spray cloud by Dehghani (2018) [40], and (

**b**) schematic of the MFV used as the ship model for the model of 3-D spray cloud by using SPH method.

**Figure 4.**This is the sea spray generation process: (

**a**) the ship is placed in the current particles, (

**b**) waves begin to form sea spray, (

**c**) sea spray particles start to disperse, (

**d**) sea spray particles start to rise, and (

**e**) sea spray particles continue to rise to the highest point.

**Figure 7.**The deck droplet distribution for both models: (

**a**) Dehghani et al. (2018) droplet distribution in the impact deck [40] and (

**b**) SPH model arithmetic example of droplet distribution on impact deck.

**Figure 8.**Four models with different levels of wave height: (

**a**) four-level sea state simulation scheme, (

**b**) five-level sea state simulation scheme, (

**c**) six-level sea state simulation scheme, and (

**d**) seven-level sea state simulation program.

**Figure 9.**These are the two working conditions of Scenario 1: (

**a**) conditions in the fourth-level sea state when waves hit the hull and (

**b**) conditions when the fourth-level sea state’s sea spray particles settle.

**Figure 10.**These are the two working conditions of Scenario 2: (

**a**) conditions in the fifth-level sea state when waves hit the hull, and (

**b**) conditions when the fifth-level sea state’s sea spray particles settle.

**Figure 11.**These are the two working conditions of Scenario 3: (

**a**) conditions in the sixth-level sea state when waves hit the hull, and (

**b**) conditions when the sixth-level sea state’s sea spray particles settle.

**Figure 12.**These are the two working conditions of Scheme 4: (

**a**) conditions in the seventh-level sea state when waves hit the hull, and (

**b**) conditions when the seventh-level sea state’s sea spray particles settle.

**Figure 13.**(

**a**) The number of particles on the hull and their share in the number of wave particles and (

**b**) number of returning particles and their share in the number of particles in the hull.

**Table 1.**The calculation parameters of wave impacting hull forming ocean droplet model calculations.

FEM (Hull) Parameters | Value | SPH Parameters | Value |
---|---|---|---|

Material density/(kg/m^{3}) | 7850 | Fluid particle density(kg/m^{3}) | 998 |

Grid spacing/m | 0 | Initial spacing of fluid particles/m | 0.01 |

Number of grids | 1067 | Number of fluid particles | 26,570 |

Modulus of elasticity/MPa | 2.06 × 10^{5} | Smooth kernel functions | Wendland |

Poisson’s ratio | 0.25 | Smooth length/m | 0.015 |

Global damping factor | 0.00 | Pressure correction algorithm | CSPM algorithm |

FEM Time step/s | 1.0 × 10^{−4} | Viscosity coefficient | 0.3 |

Sound velocity coefficient | 10 | ||

Fluid dynamic viscosity/(Pa·s) | 1.0 × 10^{−3} | ||

SPH Time step/s | 1.0 × 10^{−4} |

**Table 2.**A comparison between the results of 2-D and 3-D models, field observations, and previous data.

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**MDPI and ACS Style**

Chen, J.; Bai, X.; Wang, J.; Chen, G.; Zhang, T. Research on Sea Spray Distribution of Marine Vessels Based on SPH-FEM Coupling Numerical Simulation Method. *Water* **2022**, *14*, 3834.
https://doi.org/10.3390/w14233834

**AMA Style**

Chen J, Bai X, Wang J, Chen G, Zhang T. Research on Sea Spray Distribution of Marine Vessels Based on SPH-FEM Coupling Numerical Simulation Method. *Water*. 2022; 14(23):3834.
https://doi.org/10.3390/w14233834

**Chicago/Turabian Style**

Chen, Jiajing, Xu Bai, Jialu Wang, Guanyu Chen, and Tao Zhang. 2022. "Research on Sea Spray Distribution of Marine Vessels Based on SPH-FEM Coupling Numerical Simulation Method" *Water* 14, no. 23: 3834.
https://doi.org/10.3390/w14233834