# Numerical Simulation of Local Scour around Three Cylindrical Piles in a Tandem Arrangement

^{*}

## Abstract

**:**

## 1. Introduction

_{c}between the approach flow velocity, U, and the flow velocity, U

_{c}, at the beginning of the sediment movement with Total Sobol Index (TSI) of 0.514, and the opposite trend of scour with a ratio m/n (TSI = 0.023), between the number, m, of piles inline with the flow and that, n, of piles perpendicular to the flow.

_{50}) of 0.15 mm has a bulk density of 1990 kg/m

^{3}. The depth and velocity of the water were set to 0.25 m and 0.225 m/s, respectively. Uniform mesh of 0.008 m was generated in this study with a total of more than forty-two million cells. Due to its compromised model accuracy and the requirement for simulation power, k-ε turbulence model was chosen which can achieve reasonably high resolution with low CPU time requirement. The boundary conditions applied are the same as for the single pile study in Table 2. After running for 180 min, the maximum local scour depths around the front and rear piles were 0.058 m and 0.043 m.

_{50}) of 0.85 mm was placed as bed sediment with a thickness of 0.15 m. The minimum and maximum cell sizes used in this numerical study were 0.003 m and 0.025 m. The boundary conditions applied are similar to the previous study by Zhang et al. [12], the only difference being the wall boundary conditions on the front and back sides. However, this study does not clearly explain the maximum sediment scour depth generated for the front and rear piles. After running for 5 min for the flow of V/Vc = 0.91, Hassan et al. [44] reported that the scouring depth recorded at the rear pier was the smallest in all simulations.

## 2. Numerical Method

#### 2.1. Governing Equations

#### 2.2. Turbulence Model

#### 2.3. Sediment Transport Model

#### 2.3.1. Critical Shields Number

_{cr,i}correlates with the minimum or critical bed shear stress τ

_{cr}required to remove sediment particles from the packed bed interface [48]. Sediment erosion can occur depending on the size of the sediment, its density, and body forces acting on it [28].

_{i}is sediment grain size, and ρ

_{i}and ρ

_{f}are mass density of sediment grain and fluid density.

_{cr,i}can be defined as the prescribed value and calculated value using the Soulsby-Whitehouse equation. The prescribed value means that the critical shields number is calculated by Flow-3D itself, then the other is determined using the equation of Soulsby-Whitehouse below [50].

_{i}/ρ

_{f}and ${v}_{f}$ is the fluid kinematic viscosity. The critical shields number θ

_{cr,i}can be specified with a default value of 0.05 [36].

#### 2.3.2. Bed-Load Transport

#### 2.3.3. Maximum Packing Fraction

#### 2.3.4. Bed Shear Stress

_{rough}is the user-definable coefficient obtained by the ratio of Nikuradse roughness k

_{s}to the median grain diameter in packed sediment d

_{50}which has a recommended value of 2.5 [36].

#### 2.3.5. Sediment Characteristics

#### 2.4. Meshing

#### 2.5. Boundary Conditions

## 3. Verification of the Present Model

#### 3.1. Experimental Setup

_{50}of 0.00085 m at a depth of 0.2 m. The experiment was carried out at a bulk inflow velocity of 0.25 m/s, which corresponds to a uniform flow depth of 0.186 m, a Reynolds number Re = 46,000 and a Froude number Fr = 0.18 for approximately 50 min until the equilibrium depth was reached. The maximum scour depth measured was about 0.076 m occurring at an angle of 45° from the upstream horizontal plane.

#### 3.2. Numerical Setup

#### 3.2.1. Sediment Scour and Turbulence

_{50}ratio are 0.64 and 2.5 for fine sand sediment with an average particle size diameter d

_{50}of 0.00085 m which has a density of 1602 kg/m

^{3}, while the critical shields number, entrainment coefficient, bed load coefficient, and angle of repose are 0.05, 0.005, 0.053, and 32°, respectively.

#### 3.2.2. Geometry and Meshing

_{h}in turbulent flow for an open channel with a rectangular cross sections is calculated using the equation of Cengel & Cimbala [57], yielding an entrance length of 6 m.

_{h}is hydraulic diameter, and $a$ and $b$ are water depth and channel width.

_{h}of 6 m. For the meshing setup, several grid tests were performed to check the sensitivity of the mesh modeled in this numerical study. In addition, two mesh planes in the x and y directions with finer resolution were applied to increase the accuracy of the model around the pile. The total number of 400,000 cells formed by 400 × 50 × 20 cells in x, y, and z directions have met the requirements as described in Table 3, assessed using the FAVOR option which produces a good solid geometry shape and surface model, showing that the number of cells is sufficient.

#### 3.3. Validation Result

## 4. Numerical Simulation of Three Cylinders

#### 4.1. Sediment Scour and Turbulence

_{50}, sand density, and angle of repose are described in Table 4 below.

#### 4.2. Geometry and Meshing

#### 4.3. Boundary Conditions

#### 4.4. Numerical Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Time evolution of scour depth between the present model and the experimental result [55] around a single pile. Copyright 2011 Elsevier Ltd. All rights reserved.

**Figure 4.**The bed elevation contours at the equilibrium state between the present model and the experimental result [55] in units of cm. Copyright 2011 Elsevier Ltd. All rights reserved.

Numerical Research | Wang et al. [32] | Ghasemi [23] | Zhang et al. [12] | Omara & Tawfik [33] | Jalal & Hasan [31] | Nazari et al. [34] | |
---|---|---|---|---|---|---|---|

Properties | |||||||

Type of arrangements | Single pile | Single pile | 3 piles, tandem | Single pile | Single pile | Single pile | |

Channel dimension, L × W × H (m) | 2.7 × 0.8 × 1.0 | 1.0 × 0.4 × 0.3 | 19 × 8 × * | 4.628 × 0.89 × * | 1.12 × 0.46 × 0.28 | 5.1 × 0.405 × 1.2 | |

Packed sediment thickness (m) | * | 0.12 | 0.12 | 0.2 | 0.127 | 0.2 | |

Pile diameter, D (m) | 0.03 | 0.03 | 1.5 | 0.089 | 0.0508 | 0.04 | |

Pile spacing, S (m) | * | * | 2 | * | * | * | |

Water depth (m) | 0.25 | 0.3 | * | * | 0.15 | 0.2 | |

Flow velocity, υ (m/s) | 0.225 | * | 2 | 0.2927 | 0.25 | 0.56 | |

Flow rate, Q (L/s) | * | 19 | * | * | * | 45 | |

Turbulence model | k-ε | RNG k-ε | RNG k-ε | RNG k-ε | RNG k-ε | RNG k-ε | |

Critical shields number definition | Soulsby-Whitehouse eq. | * | Soulsby-Whitehouse eq. | Soulsby-Whitehouse eq. | Soulsby-Whitehouse eq. | Soulsby-Whitehouse eq. | |

Bed-load transport rate equation | * | * | Meyer, Peter and Müller eq. | Van Rijn eq. | Meyer, Peter and Müller eq. | Meyer, Peter and Müller eq. | |

Bed roughness/d_{50} ratio, C_{rough} | 2.5 | * | * | 2.5 | 1.0 | * | |

Sediment size, d_{50} (mm) | 0.15 | 0.72 | 5, 10, and 20 | 1.8 | 0.385 | 0.72 | |

Angle of repose, φ (degrees) | * | * | 32 | * | 32 | 45 | |

Critical shields number, θ_{cr} | 0.048 | 0.031 | 0.048 | 0.05 | 0.05 | * | |

Entrainment coefficient | 0.018 | * | 0.018 | 0.005 | 0.018 | 0.018 | |

Bed-load coefficient | * | * | 8 | 0.053 | 12 | 8 | |

Min. and max. cell size (m) | 0.008 | * | * | 0.003 and 0.025 | 0.005 and 0.01 | 0.006 and 0.01 | |

Total amount of cells | >42,000,000 | 20,000 | * | * | 252,000 | 1,100,000 | |

Max scour depth for present model (m) | 0.055 | 0.034 | 0.74 | 0.0397 | 0.036 | 0.042 | |

Max scour depth for experimental (m) | 0.043 | * | 0.79 | 0.04 | 0.04 | 0.041 | |

Experimental studies | Wang et al. [32] | Heidarpour et al. [35] | Gengsheng Wei et al. [36] | Ahmed & Rajaratnam [37] | B W Melville [38] | Balouchi & Chamani [39] |

Numerical Research | Wang et al. [32] | Ghasemi [23] | Zhang et al. [12] | Omara & Tawfik [33] | Jalal & Hasan [31] | Nazari et al. [34] | |
---|---|---|---|---|---|---|---|

Boundary conditions | |||||||

X Min | Left boundary | Specified velocity | Volume flow rate | Specified velocity | Specified velocity | Specified velocity | Volume flow rate |

X Max | Right boundary | Outflow | Outflow | Outflow | Outflow | Outflow | Outflow |

Y Min | Front boundary | Symmetry | Wall | Symmetry | Symmetry | Symmetry | Wall |

Y Max | Back boundary | Symmetry | Wall | Symmetry | Symmetry | Symmetry | Wall |

Z Min | Bottom boundary | Wall | Wall | Wall | Wall | Wall | Wall |

Z Max | Top boundary | Symmetry | Symmetry | Specified pressure | Specified pressure | Symmetry | Symmetry |

Mesh Directions | Number of Cells | Minimum Cell Size | Maximum Cell Size | Maximum Adjacent Ratio | Maximum Aspect Ratios |
---|---|---|---|---|---|

x | 400 | 0.00769 | 0.08443 | 1.08046 | 2.92517 |

y | 50 | 0.01667 | 0.05091 | 1.20545 | 1.00000 |

z | 20 | 0.0225 | 0.0225 | 1 | 1.65846 |

Sediment Type | Mean Particle Diameter, d_{50} (m) | Density (kg/m ^{3}) | Angle of Repose (Degrees) |
---|---|---|---|

Fine gravel | 0.005 | 1922 | 35 |

Medium gravel | 0.01 | 1682 | 36 |

Mesh Plane | Pile Config. | Mesh Direction | Number of Cells | Cell Size | Max. Adjacent Ratio | Max. Aspect Ratio | |
---|---|---|---|---|---|---|---|

Min | Max | ||||||

x | 380 | 0.12 | 0.60 | 1.09 | 1.00 | ||

Single | y | 70 | 0.12 | 0.60 | 1.21 | 1.00 | |

pile | z | 58 | 0.12 | 0.12 | 1.00 | 1.00 | |

Total | 1,542,800 | ||||||

x | 414 | 0.12 | 0.60 | 1.14 | 1.00 | ||

Tandem | y | 70 | 0.12 | 0.60 | 1.21 | 1.00 | |

G/D = 2 | z | 58 | 0.12 | 0.12 | 1.00 | 1.00 | |

Total | 1,680,840 | ||||||

x | 430 | 0.12 | 0.60 | 1.22 | 1.00 | ||

Tandem | y | 70 | 0.12 | 0.60 | 1.21 | 1.00 | |

G/D = 3 | z | 58 | 0.12 | 0.12 | 1.00 | 1.00 | |

Total | 1,745,800 |

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**MDPI and ACS Style**

Tang, J.-H.; Puspasari, A.D.
Numerical Simulation of Local Scour around Three Cylindrical Piles in a Tandem Arrangement. *Water* **2021**, *13*, 3623.
https://doi.org/10.3390/w13243623

**AMA Style**

Tang J-H, Puspasari AD.
Numerical Simulation of Local Scour around Three Cylindrical Piles in a Tandem Arrangement. *Water*. 2021; 13(24):3623.
https://doi.org/10.3390/w13243623

**Chicago/Turabian Style**

Tang, Jyh-Haw, and Aisyah Dwi Puspasari.
2021. "Numerical Simulation of Local Scour around Three Cylindrical Piles in a Tandem Arrangement" *Water* 13, no. 24: 3623.
https://doi.org/10.3390/w13243623