# Investigating the Effect of Heterogeneous Hull Roughness on Ship Resistance Using CFD

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Approach

#### 2.2. Numerical Modelling

#### 2.2.1. Mathematical Formulations

#### 2.2.2. Modified Wall-Function Approach

#### 2.2.3. Geometry and Boundary Conditions

#### 2.2.4. Mesh Generation

## 3. Results

#### 3.1. Verification Study

#### 3.2. Effect of Heterogeneous Roughness on Ship Resistance

#### 3.3. Rationale behind the Effect of Heterogeneous Roughness

## 4. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Percentage differences between the current CFD simulations and the EFD result [27].

Smooth | 1/4-bow-rough | 1/4-aft-rough | |||||||

Fr | CFD | EFD | %D | CFD | EFD | %D | CFD | EFD | %D |

0.2 | 4.29 × 10^{−3} | 3.95 × 10^{−3} | −8.0% | 4.71 × 10^{−3} | 4.66 × 10^{−3} | −1.1% | 4.61 × 10^{−3} | 4.31 × 10^{−3} | −6.5% |

0.25 | 4.63 × 10^{−3} | 4.38 × 10^{−3} | −5.3% | 5.09 × 10^{−3} | 5.19 × 10^{−3} | 1.8% | 4.96 × 10^{−3} | 4.68 × 10^{−3} | −5.7% |

0.3 | 5.25 × 10^{−3} | 5.03 × 10^{−3} | −4.3% | 5.83 × 10^{−3} | 5.91 × 10^{−3} | 1.3% | 5.60 × 10^{−3} | 5.35 × 10^{−3} | −4.5% |

0.35 | 5.17 × 10^{−3} | 4.95 × 10^{−3} | −4.2% | 5.80 × 10^{−3} | 5.92 × 10^{−3} | 2.0% | 5.58 × 10^{−3} | 5.33 × 10^{−3} | −4.4% |

0.4 | 6.16 × 10^{−3} | 6.08 × 10^{−3} | −1.4% | 6.77 × 10^{−3} | 6.96 × 10^{−3} | 2.7% | 6.61 × 10^{−3} | 6.50 × 10^{−3} | −1.7% |

1/2-bow-rough | 1/2-aft-rough | Full-rough | |||||||

Fr | CFD | EFD | %D | CFD | EFD | %D | CFD | EFD | %D |

0.2 | 5.11 × 10^{−3} | 5.11 × 10^{−3} | −0.1% | 4.98 × 10^{−3} | 4.69 × 10^{−3} | −5.8% | 5.76 × 10^{−3} | 5.81 × 10^{−3} | 0.9% |

0.25 | 5.50 × 10^{−3} | 5.70 × 10^{−3} | 3.6% | 5.34 × 10^{−3} | 5.19 × 10^{−3} | −2.8% | 6.18 × 10^{−3} | 6.40 × 10^{−3} | 3.6% |

0.3 | 6.25 × 10^{−3} | 6.40 × 10^{−3} | 2.4% | 5.99 × 10^{−3} | 5.84 × 10^{−3} | −2.6% | 6.89 × 10^{−3} | 7.20 × 10^{−3} | 4.5% |

0.35 | 6.34 × 10^{−3} | 6.48 × 10^{−3} | 2.2% | 6.08 × 10^{−3} | 5.96 × 10^{−3} | −2.1% | 7.13 × 10^{−3} | 7.38 × 10^{−3} | 3.4% |

0.4 | 7.34 × 10^{−3} | 7.66 × 10^{−3} | 4.4% | 7.15 × 10^{−3} | 7.18 × 10^{−3} | 0.3% | 8.25 × 10^{−3} | 8.58 × 10^{−3} | 4.0% |

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**Figure 7.**${C}_{T}$ of the Wigley hull with smooth and full-rough conditions obtained from the current Computational Fluid Dynamics (CFD) simulations and the Experimental Fluid Dynamics (EFD) result [27].

**Figure 8.**${C}_{T}$ of the Wigley hull with ¼-bow-rough and ¼-aft-rough conditions obtained from the current CFD simulations and the EFD result [27].

**Figure 9.**${C}_{T}$ of the Wigley hull with ½-bow-rough and ½-aft-rough conditions obtained from the current CFD simulations and the EFD result [27].

**Figure 10.**${C}_{F}$ of the Wigley hull with different hull conditions predicted from the current CFD simulations.

**Figure 11.**${C}_{R}$ of the Wigley hull with different hull conditions predicted from the current CFD simulations.

**Figure 13.**Increase in the ${C}_{f}$ on the Wigley hull ($\mathsf{\Delta}{C}_{f}={C}_{f,\text{}\mathrm{rough}}-{C}_{f,\text{}\mathrm{smooth}}$), $Fr=0.3$.

**Figure 15.**Boundary layer represented by slices limited to axial velocity (${V}_{x}/{V}_{ship}=0.9$), $Fr=0.3$.

Length | $L$ (m) | 3.00 |

Beam at waterline | $B$ (m) | 0.30 |

Draft | $T$ (m) | 0.1875 |

Beam/draft ratio | $B/T$ | 1.6 |

Total wetted surface area | $S$ (m^{2}) | 1.3383 |

Wetted surface area of first quarter | ${S}_{Q1}$ (m^{2}) | 0.3066 |

Wetted surface area of first half | ${S}_{H1}$ (m^{2}) | 0.6691 |

Displacement | $\nabla $ (m^{3}) | 0.0750 |

Block coefficient | ${C}_{B}$ | 0.4444 |

Towing speed | $\mathrm{V}$ (m/s) | 1.08–2.17 |

Froude number | $Fr$ | 0.2–0.4 |

Reynolds number | $R{e}_{L}$ | 2.6–5.3 × 106 |

Water temperature | ${T}_{w}$ (°C) | 12 |

**Table 2.**Spatial and temporal convergence study of the Wigley hull simulation, Fr = 0.3, smooth hull.

Spatial Convergence | No.Cells | $\Delta t$
(s) | ${\mathit{C}}_{\mathit{T}}$ | |

Coarse | 414,173 | 0.01 | 5.292 × 10^{−3} | |

Medium | 776,227 | 0.01 | 5.273 × 10^{−3} | |

Fine | 1,587,310 | 0.01 | 5.267 × 10^{−3} | |

${\mathit{U}}_{Grid}$
(Fine) | 0.053% | |||

Temporal Convergence | No.Cells | $\Delta t$
(s) | ${\mathit{C}}_{\mathit{T}}$ | |

Coarse | 1,587,310 | 0.04 | 5.169 × 10^{−3} | |

Medium | 1,587,310 | 0.02 | 5.258 × 10^{−3} | |

Fine | 1,587,310 | 0.01 | 5.267 × 10^{−3} | |

${\mathit{U}}_{\Delta t}$
(Fine) | 0.022% | |||

${\mathit{U}}_{Total}$ | 0.057% |

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**MDPI and ACS Style**

Song, S.; Demirel, Y.K.; De Marco Muscat-Fenech, C.; Sant, T.; Villa, D.; Tezdogan, T.; Incecik, A.
Investigating the Effect of Heterogeneous Hull Roughness on Ship Resistance Using CFD. *J. Mar. Sci. Eng.* **2021**, *9*, 202.
https://doi.org/10.3390/jmse9020202

**AMA Style**

Song S, Demirel YK, De Marco Muscat-Fenech C, Sant T, Villa D, Tezdogan T, Incecik A.
Investigating the Effect of Heterogeneous Hull Roughness on Ship Resistance Using CFD. *Journal of Marine Science and Engineering*. 2021; 9(2):202.
https://doi.org/10.3390/jmse9020202

**Chicago/Turabian Style**

Song, Soonseok, Yigit Kemal Demirel, Claire De Marco Muscat-Fenech, Tonio Sant, Diego Villa, Tahsin Tezdogan, and Atilla Incecik.
2021. "Investigating the Effect of Heterogeneous Hull Roughness on Ship Resistance Using CFD" *Journal of Marine Science and Engineering* 9, no. 2: 202.
https://doi.org/10.3390/jmse9020202