# Numerical Investigations on Scour and Flow around Two Crossing Pipelines on a Sandy Seabed

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## Abstract

**:**

## 1. Introduction

## 2. Model Setup and Validation

#### 2.1. Governing Equations

_{bedload}is related to the volumetric transport rate ${q}_{b}$

#### 2.2. Model Validation

#### 2.2.1. 2D Scour Simulation and Mesh Sensitivity Analysis

^{−3}s. Considering both efficiency and accuracy, the mesh density level of Mesh B is adopted in the following studies.

#### 2.2.2. Simulation of 3D Scour Process

_{h}) is calculated through the curves and is presented in Table 3. The present numerical result of V

_{h}agrees well with those published by Xu [23] and Cheng et al. [16], as shown in Table 3.

## 3. Scour below Two Crossing Pipelines

## 4. Flow Structures around the Pipelines

## 5. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Sumer, B.M.; Fredsøe, J. The Mechanics of Scour in the Marine Environment; World Scientific: Singapore, 2002. [Google Scholar]
- Mao, Y. The Interaction between a Pipeline and an Erodible Bed. Ph.D. Thesis, Technical University of Denmark, Lyngby, Denmark, 1986. [Google Scholar]
- Fredsøe, J.; Sumer, B.M.; Arnskov, M. Time scale for wave/current scour below pipelines. Int. J. Offshore Polar Eng.
**1992**, 2, 13–17. [Google Scholar] - Sumer, B.M.; Truelsen, C.; Sichmann, T.; Fredsøe, J. Onset of scour below pipelines and self-burial. Coast. Eng.
**2001**, 42, 313–335. [Google Scholar] [CrossRef] - Gao, F.; Yang, B.; Wu, Y.; Yan, S. Steady currents induced seabed scour around a vibrating pipeline. Appl. Ocean Res.
**2006**, 28, 291–298. [Google Scholar] [CrossRef] [Green Version] - Yang, L.; Shi, B.; Guo, Y.; Wen, X. Calculation and experiment on scour depth for submarine pipeline with a spoiler. Ocean Eng.
**2012**, 55, 191–198. [Google Scholar] [CrossRef] - Mohr, H.; Draper, S.; Cheng, L.; White, D.J. Predicting the rate of scour beneath subsea pipelines in marine sediments under steady flow conditions. Coast. Eng.
**2016**, 110, 111–126. [Google Scholar] [CrossRef] - Zang, Z.; Tang, G.Q.; Chen, Y.; Cheng, L.; Zhang, J. Predictions of the equilibrium depth and time scale of local scour below a partially buried pipeline under oblique currents and waves. Coast. Eng.
**2019**, 150, 94–107. [Google Scholar] [CrossRef] - Brørs, B. Numerical Modeling of Flow and Scour at Pipelines. J. Hydraul. Eng.
**1999**, 125, 511–523. [Google Scholar] [CrossRef] - Liang, D.; Cheng, L.; Li, F. Numerical modeling of flow and scour below a pipeline in currents: Part II. Scour simulation. Coast. Eng.
**2005**, 52, 43–62. [Google Scholar] [CrossRef] - Zhao, M.; Cheng, L. Numerical investigation of local scour below a vibrating pipeline under steady currents. Coast. Eng.
**2010**, 57, 397–406. [Google Scholar] [CrossRef] - Zhao, M.; Cheng, L. Numerical modelling of local scour below a piggyback pipeline in currents. J. Hydraul. Eng.
**2008**, 134, 1452–1463. [Google Scholar] [CrossRef] - Zang, Z.; Cheng, L.; Zhao, M.; Liang, D.; Teng, B. A numerical model for onset of scour below offshore pipelines. Coast. Eng.
**2009**, 56, 458–466. [Google Scholar] [CrossRef] - Fuhrman, D.R.; Baykal, C.; Sumer, B.M.; Jacobsen, N.G.; Fredsøe, J. Numerical simulation of wave-induced scour and backfilling processes beneath submarine pipelines. Coast. Eng.
**2014**, 94, 10–22. [Google Scholar] [CrossRef] - Liu, M.; Lu, L.; Teng, B.; Zhao, M.; Tang, G. Numerical modeling of local scour and forces for submarine pipeline under surface waves. Coast. Eng.
**2016**, 116, 275–288. [Google Scholar] [CrossRef] - Cheng, L.; Yeow, K.; Zhang, Z.; Teng, B. Three-dimensional scour below offshore pipelines in steady currents. Coast. Eng.
**2009**, 56, 577–590. [Google Scholar] [CrossRef] - Cheng, L.; Yeow, K.; Zang, Z.; Li, F. 3D scour below pipelines under waves and combined waves and currents. Coast. Eng.
**2014**, 83, 137–149. [Google Scholar] [CrossRef] [Green Version] - Wu, Y.; Chiew, Y.M. Three-Dimensional Scour at Submarine Pipelines. J. Hydraul. Eng. ASCE
**2012**, 138, 788–795. [Google Scholar] [CrossRef] - Wu, Y.; Chiew, Y.M. Mechanics of Pipeline Scour Propagation in the Spanwise Direction. J. Waterw. Port Coast. Ocean Eng.
**2015**, 141, 04014045. [Google Scholar] [CrossRef] - Sui, T.; Staunstrup, L.H.; Carstensen, S.; Fuhrman, D.R. Span shoulder migration in three-dimensional current-induced scour beneath submerged pipelines. Coast. Eng.
**2020**, 164, 103776. [Google Scholar] [CrossRef] - Alam, M.S.; Cheng, L. A parallel three-dimensional scour model to predict flow and scour below a submarine pipeline. Cent. Europ. J. Phys.
**2010**, 8, 604–619. [Google Scholar] [CrossRef] - Cheng, L.; Zhao, M. Numerical Model for Three-Dimension Scour Below a Pipeline in Steady Currents. In Proceedings of the 5th International Conference on Scour and Erosion, San Francisco, CA, USA, 7–10 November 2010; pp. 482–490. [Google Scholar]
- Xu, F. Numerical Modeling of Local Scour Beneath Offshore Pipeline (pile) in Steady Currents. Master’s thesis, Shanghai Jiao Tong University, Shanghai, China, 2017. [Google Scholar]
- Shi, S.; Liang, D.; Huang, J.; Zhang, J. Three-dimensional modeling of scour around underwater pipes. Chin. J. Hydrodyn
**2019**, 34, 166–173. [Google Scholar] - Flow-3D User Manual v9.4; Flow Science, Inc.: Santa Fe, NM, USA, 2009.
- Van Rijn, L.C. Sediment transport, art I: Bedload transport. J. Hydraul. Div. Proc. ASCE
**1984**, 110, 1431–1456. [Google Scholar] [CrossRef] - Soulsby, R.L.; Whitehouse, R.J.S.W. Threshold of sediment motion in coastal environments. In Pacific Coasts and Ports′97. Proceedings; University of Canterbury: Christchurch, New Zealand, 1997; Volume 1, pp. 149–154. [Google Scholar]

**Figure 3.**Comparison of scour hole profiles below the pipeline: (

**a**) t = 10 min; (

**b**) t = 30 min; (

**c**) t = 200 min.

**Figure 4.**Numerical results of 3D scour below a pipeline, (

**a**) vertical profiles along the pipeline axis, (

**b**) development of span length with time.

**Figure 6.**The 3D profiles of scour hole for α = 0°: (

**a**) t = 0 s; (

**b**) t = 50 s; (

**c**) t = 100 s; (

**d**) t = 125 s.

**Figure 7.**The 3D profiles of scour hole for α = 30°: (

**a**) t = 0 s; (

**b**) t = 100 s; (

**c**) t = 200 s; (

**d**) t = 350 s.

**Figure 11.**Streamlines around the pipelines for α = 0°: (

**a**) t = 5 s; (

**b**) t = 25 s; (

**c**) t = 50 s; (

**d**) t = 150 s.

**Figure 12.**Streamlines around the pipelines for α = 30°: (

**a**) t = 10 s; (

**b**) t = 50 s; (

**c**) t = 200 s; (

**d**) t = 900 s.

Inlet Velocity v _{o} (m/s) | Pipeline Diameter D (m) | Sediment Density ρ (kg/m ^{3}) | Medium Diameter d _{50} (mm) | Embedment Ratio e/D |
---|---|---|---|---|

0.35 | 0.1 | 2650 | 0.36 | 0 |

Case | Total Number of Cells | Y Direction | Z Direction | ||||
---|---|---|---|---|---|---|---|

Minimum Size (m) | Maximum Size (m) | Grid Number | Minimum Size (m) | Maximum Size (m) | Grid Number | ||

Mesh A | 96,000 | 0.005 | 0.005 | 600 | 0.001 | 0.005 | 160 |

Mesh B | 28,800 | 0.010 | 0.010 | 300 | 0.002 | 0.010 | 96 |

Mesh C | 18,480 | 0.013 | 0.012 | 240 | 0.003 | 0.013 | 77 |

Mesh D | 12,800 | 0.015 | 0.015 | 200 | 0.003 | 0.015 | 64 |

v_{o}(m/s) | D (m) | p (kg/m ^{3}) | d_{50}(mm) | θ | e/D | V_{h} (mm/s) | ||
---|---|---|---|---|---|---|---|---|

Present | Xu [23] | Cheng et al. [16] | ||||||

0.35 | 0.1 | 2650 | 0.36 | 0.040 | 0 | 0.811 | 0.793 | 0.802 |

Cases | S (mm) | S/D | T (s) | T* |
---|---|---|---|---|

Isolated | 60.2 | 0.60 | 155.5 | 0.43 |

α = 90° | 69.5 | 0.70 | 157.8 | 0.43 |

α = 45° | 78.9 | 0.79 | 180.7 | 0.50 |

α = 30° | 86.5 | 0.87 | 192.3 | 0.53 |

α = 15° | 96.3 | 0.96 | 202.2 | 0.56 |

α = 0° | 111.3 | 1.11 | 207.4 | 0.57 |

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**MDPI and ACS Style**

Zhang, F.; Zang, Z.; Zhao, M.; Zhang, J.; Xie, B.; Zou, X.
Numerical Investigations on Scour and Flow around Two Crossing Pipelines on a Sandy Seabed. *J. Mar. Sci. Eng.* **2022**, *10*, 2019.
https://doi.org/10.3390/jmse10122019

**AMA Style**

Zhang F, Zang Z, Zhao M, Zhang J, Xie B, Zou X.
Numerical Investigations on Scour and Flow around Two Crossing Pipelines on a Sandy Seabed. *Journal of Marine Science and Engineering*. 2022; 10(12):2019.
https://doi.org/10.3390/jmse10122019

**Chicago/Turabian Style**

Zhang, Fan, Zhipeng Zang, Ming Zhao, Jinfeng Zhang, Botao Xie, and Xing Zou.
2022. "Numerical Investigations on Scour and Flow around Two Crossing Pipelines on a Sandy Seabed" *Journal of Marine Science and Engineering* 10, no. 12: 2019.
https://doi.org/10.3390/jmse10122019