# 3D CFD Study of Scour in Combined Wave–Current Flows around Rectangular Piles with Varying Aspect Ratios

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Model

#### 2.1. Hydrodynamic Model

#### 2.2. Free Surface Model

#### 2.3. Modelling of Sediment Transport

#### Suspended Sediment Load Transportation

## 3. Model Validation

## 4. Results And Analysis

## 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 1.**Results of the model validation for scour around a pile group caused by a combined wave–current effect Qi et al. [33].

**Figure 2.**Comparison between the numerical simulations and experimental data obtained by Qi and Gao [34] for the phenomenon of scouring around a pile under the influence of waves and currents.

**Figure 3.**Grid convergence study for the phenomenon of scour around a group of piles in an environment affected by both waves and currents. Red line represents the numerical results, while the discrete points represent the experimental results acquired by Qi et al. [33].

**Figure 4.**The layout of the rectangular piles for CFD simulations with different aspect ratios ($B:A$) of 1:1 (

**left**), 1:2 (

**middle**), 2:1 (

**right**). B is the length of rectangular piles and A is the breadth of the piles.

**Figure 5.**3D view of the rectangular piles for CFD simulations with different aspect ratios (B:A) of 1:1 (

**left**), 1:2 (

**middle**), and 2:1 (

**right**). B is the length of rectangular piles and A is the width of the piles.

**Figure 6.**Contours of bed topography for combined wave−current parameter ${U}_{cw}$ of 0.4 and $KC$ = 3.9 for varying aspect ratios of the rectangular pile. The side (B) of the rectangular pile is 0.18 m and the period (T) of the wave is 4.5 s. Duration of the simulation run is 3600 s.

**Figure 7.**Temporal variations of normalized scour depth versus normalized time for $KC$ = 3.9 and combined wave–current parameter ${U}_{cw}$ = 0.40. The wave period (T) is 4.5 s.

**Figure 8.**Contours at the end of the simulation period for combined wave−current (${U}_{cw}$= 0.4) case for $KC$ = 5.75 for varying aspect ratios of the rectangular pile. The side (B) of the rectangular pile is 0.14 m and the period (T) of the wave is 4.5 s. Duration of the simulation run is 3600 s.

**Figure 9.**Temporal variations of normalized scour depth versus normalized time for $KC$ = 5.75 for combined wave current parameter (${U}_{cw}$) of 0.4. The wave period (T) is 4.5 s.

**Figure 10.**Contours of bed topography for combined wave−current (${U}_{cw}$= 0.4) case for $KC$ = 10 for varying aspect ratios of the rectangular pile. The side (B) of the rectangular pile is 0.08 m, and the period (T) of the wave is 4.5 s. Duration of the simulation run 3600 s.

**Figure 11.**Temporal variations of normalized scour depth versus normalized time for $KC$ = 10 in a wave and combined wave–current flows. The wave period (T) is 4.5 s.

**Figure 12.**Vorticity contours for $KC$ number = 3.9 and wave−current parameter (${U}_{cw}$ = 0.4) for varying aspect ratios of the rectangular pile.

**Figure 13.**Vorticity contours for $KC$ number = 5.75 for and wave−current parameter (${U}_{cw}$ = 0.4) for varying aspect ratios of the rectangular pile.

**Figure 14.**Vorticity contours for $KC$ number = 10 and wave−current parameter (${U}_{cw}$ = 0.4) for varying aspect ratios of the rectangular pile.

**Figure 15.**Isosurfaces visualizing turbulent structures for Q = 1 ${s}^{-2}$, $KC$ number = 3.9, and wave current parameter (${U}_{cw}$) = 0.4 for different aspect ratios of the rectangular pile.

**Figure 16.**Isosurfaces visualizing turbulent structures for Q = 1 ${s}^{-2}$, $KC$ number = 5.75, and wave current parameter (${U}_{cw}$) = 0.4 with different aspect ratios of the rectangular pile.

**Figure 17.**Isosurfaces visualizing turbulent structures for Q = 1 s${}^{-2}$, $KC$ number = 10, and wave current parameter (${U}_{cw}$) = 0.4 with different aspect ratios of the rectangular pile.

**Figure 18.**Normalized scour depth plotted against the $KC$ number for different aspect ratios of the rectangular pile.

**Figure 19.**Normalized equilibrium scour depth plotted against the velocity-based Froude number ($F{r}_{a}$).

**Table 1.**Summary of sediment parameters used for model validation. $\theta $ denotes shields paramter, ${d}_{50}$ denotes median grain size, $\eta $ denotes porosity, ${D}_{r}$ denotes relative density, and ${\gamma}^{\prime}$ denotes submerged unit weight.

Cases | $\mathit{\theta}$ (-) | ${\mathit{d}}_{50}$ (mm) | $\mathit{\eta}$ (-) | ${\mathit{D}}_{\mathit{r}}$ (-) | ${\mathit{\gamma}}^{\prime}$ (KN/m${}^{3}$) |
---|---|---|---|---|---|

Validation 1 (Figure 1) | 0.409 | 0.15 | 0.35 | 0.62 | 10.65 |

Validation 2 (Figure 2) | 0.045 | 0.38 | 0.435 | 0.352 | 9.03 |

Validation 3 (Figure 3) | 0.409 | 0.15 | 0.35 | 0.62 | 10.65 |

Cases | Run | Time Period (s) | ${\mathit{U}}_{\mathit{m}}$ (m/s) | ${\mathit{U}}_{\mathit{c}}$ (m/s) | ${\mathit{U}}_{\mathbf{cw}}$ | $\mathit{KC}$ | S/D |
---|---|---|---|---|---|---|---|

Validation | W-C scour (Figure 1) | 1.8 | 0.25 | 0.23 | 0.48 | 5.63 | 1.5 |

W-C scour (Figure 2) | 1.4 | 0.303 | 0.23 | 0.43 | 1.28 | 0.41 | |

W-C scour (Figure 3) | 1.8 | 0.25 | 0.23 | 0.48 | 5.63 | 1.08 | |

Analysis | W-C scour (Figure 6a) | 4.5 | 0.156 | 0.104 | 0.4 | 3.9 | 0.138 |

W-C scour (Figure 6b) | 4.5 | 0.156 | 0.104 | 0.4 | 3.9 | 0.132 | |

W-C scour (Figure 6c) | 4.5 | 0.156 | 0.104 | 0.4 | 3.9 | 0.151 | |

W-C scour (Figure 8) | 4.5 | 0.179 | 0.119 | 0.4 | 5.75 | 0.214 | |

W-C scour (Figure 8b) | 4.5 | 0.179 | 0.119 | 0.4 | 5.75 | 0.172 | |

W-C scour (Figure 8c) | 4.5 | 0.179 | 0.104 | 0.4 | 5.75 | 0.218 | |

W-C scour (Figure 10a) | 4.5 | 0.178 | 0.118 | 0.4 | 10 | 0.301 | |

W-C scour (Figure 10b) | 4.5 | 0.178 | 0.118 | 0.4 | 10 | 0.279 | |

W-C scour (Figure 10c) | 4.5 | 0.178 | 0.118 | 0.4 | 10 | 0.323 |

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**MDPI and ACS Style**

Dutta, D.; Afzal, M.S.; Alhaddad, S.
3D CFD Study of Scour in Combined Wave–Current Flows around Rectangular Piles with Varying Aspect Ratios. *Water* **2023**, *15*, 1541.
https://doi.org/10.3390/w15081541

**AMA Style**

Dutta D, Afzal MS, Alhaddad S.
3D CFD Study of Scour in Combined Wave–Current Flows around Rectangular Piles with Varying Aspect Ratios. *Water*. 2023; 15(8):1541.
https://doi.org/10.3390/w15081541

**Chicago/Turabian Style**

Dutta, Debasish, Mohammad Saud Afzal, and Said Alhaddad.
2023. "3D CFD Study of Scour in Combined Wave–Current Flows around Rectangular Piles with Varying Aspect Ratios" *Water* 15, no. 8: 1541.
https://doi.org/10.3390/w15081541