# Numerical Simulation on the Local Scour Processing and Influencing Factors of Submarine Pipeline

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Methods

#### 2.1. Continuity Equations

_{x}, A

_{y}, A

_{z}are the fractional areas open to flow in the x, y and z directions, respectively.

#### 2.2. The Turbulence Model

_{F}is the volume fraction, G

_{T}is the turbulent energy term generated by buoyancy, P

_{T}is the kinetic energy generated by the velocity gradient, k

_{T}is the turbulent kinetic energy, ε

_{T}is the turbulent energy dissipation rate, CDIS1, CDIS2 and CDIS3 are all dimensionless adjustable parameters, which have defaults of 1.44, 1.92 and 0.2; Diff

_{ε}is the diffusion of dissipation.

#### 2.3. Sediment Transport Model

_{50}is the median sediment particle diameter, ρ

_{f}is the fluid density, ρ

_{s}is the density of the sediment, μ is the dynamic viscosity of fluid, and g is the magnitude of the acceleration of gravity.

_{s}is the outer normal vector perpendicular to the sedimentary mass and α is the starting parameter. The setting velocity equation proposed by Soulsby [24] is used:

_{f}is the kinematic viscosity of fluid.

_{b}is the volumetric bed-load transport rate.

_{s}, E and u

_{s}are the suspended sediment mass concentration, diffusivity and suspended sediment velocity, respectively.

#### 2.4. Boundary Conditions

## 3. Validation Models

## 4. Numerical Results and Discussion

_{50}was 0.4 mm and its density ρ

_{s}was 2650 kg/m

^{3}. The velocity was v = 0.4 m/s and the initial gap between the pipeline and the seabed ratio was e/D = 0, which means the pipeline was bottom-seated on the seabed. After specifying the sediment’s scour parameters and other physical properties, the numerical model could be studied in detail.

#### 4.1. Process of Scour

_{c}, the sediment particles will be moved away, and the uplift force of the sediment is greater than the force impeding the uplift. On the contrary, when the shear stress near the bed’s surface is less than the critical shear stress, the flow will not be able to cause the sediment to move. The critical shear stress of the sediment particles in Flow-3D can be calculated by the critical Shields number θ

_{c}, and the instantaneous shear stress can be calculated by the turbulent dynamic energy method, which can be expressed as:

^{2}, v′

^{2}, w′

^{2}represent the fluctuating velocity of horizontal x, transverse y and vertical z near the bed surface, respectively, c is a constant, generally to 0.19, and ρ is water density (Hirt and Nichols, 1988). Flow-3D introduces sheer stress excess in post-processing, which can be expressed as:

_{e}is shear stress excess, τ is instantaneous shear stress, and τ

_{c}is critical shear stress. When the shear stress excess is greater than zero, the seabed will be scoured. With the scour terrain expanding, the bed surface’s shear stress will decrease, and when the shear force excess is less than zero, the seabed sediment will no longer move.

#### 4.2. Scour Depth and Terrain under the Influence of Multiple Factors

_{50}= 0.2, 0.3, 0.4 and 0.5 mm, respectively. Other parameters are the same as the Table 2 settings. Figure 9a shows the variation in the maximum scour depth under the pipeline with time under the condition of different sediment diameters. The variation of scour depth is similar, and there is little difference in scour depth under different sediment sizes, which means that sediment size has little effect on scour depth. However, as the sediment size becomes smaller, the scour depth becomes deeper. As shown in Figure 9b, at the same velocity, the smaller the sediment mean diameter, the smaller the critical shear force required to initiate, and the higher the sediment transport rate. Therefore, in the case of d

_{50}= 0.2 mm, the sedimentary mound and the influence area of sediment accumulation behind the pipeline is larger than the other cases. The scour depth under the pipeline gradually decreases with the increase in d

_{50}, because the smaller the median particle size of the sediment, the easier it is to scour.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Comparison of scour depth and terrain under the pipeline at various velocities. (

**a**) The scour depth and (

**b**) The scour terrain.

**Figure 9.**Comparisons of scour depth and terrain under the pipeline for different sediment mean diameters. (

**a**) The scour depth and (

**b**) The scour terrain.

**Figure 10.**Comparisons of scour depth and terrain under the pipeline for different pipeline diameters. (

**a**) The scour depth and (

**b**) The scour terrain.

**Figure 11.**Comparisons of scour depth and terrain under the pipeline for a different initial gap. (

**a**) The scour depth and (

**b**) The scour terrain.

Total number of grids | 41,000 | 52,000 | 67,600 |

Scour depth | 0.0642 m | 0.0621 m | 0.0618 m |

Time | 75,200 s | 88,490 s | 124,270 s |

Parameters | v | D | d_{50} | e/D | ρ | ρ_{s} |
---|---|---|---|---|---|---|

Value | 0.4 m/s | 0.15 m | 0.4 mm | 0 | 1000 kg/m^{3} | 2650 kg/m^{3} |

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**MDPI and ACS Style**

Hu, K.; Bai, X.; Vaz, M.A.
Numerical Simulation on the Local Scour Processing and Influencing Factors of Submarine Pipeline. *J. Mar. Sci. Eng.* **2023**, *11*, 234.
https://doi.org/10.3390/jmse11010234

**AMA Style**

Hu K, Bai X, Vaz MA.
Numerical Simulation on the Local Scour Processing and Influencing Factors of Submarine Pipeline. *Journal of Marine Science and Engineering*. 2023; 11(1):234.
https://doi.org/10.3390/jmse11010234

**Chicago/Turabian Style**

Hu, Ke, Xinglan Bai, and Murilo A. Vaz.
2023. "Numerical Simulation on the Local Scour Processing and Influencing Factors of Submarine Pipeline" *Journal of Marine Science and Engineering* 11, no. 1: 234.
https://doi.org/10.3390/jmse11010234