# Numerical Analysis of Full-Scale Ship Self-Propulsion Performance with Direct Comparison to Statistical Sea Trail Results

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## Abstract

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## 1. Introduction

## 2. Mathematical Model

#### 2.1. Governing Equations

#### 2.2. Computational Setup

#### 2.3. Grid Convergence and Sensitivity

_{v}) and pressure (F

_{p}). The force coefficients are defined as:

_{s}) and S refers to the wetted surface area of the hull. For global refinements, the surface mesh size on the ship hull was selected as the base size for grid convergence study, as listed in Table 1, where Δ is the mesh size on the hull surface. The time step was set to a fixed value equals to 0.0047 Lpp/Vs, which is slightly lower than the recommendation of ITTC. From Table 1, the total coefficient of ship resistance achieved a monotonic convergence with convergence ratio R

_{i}= 0.048 and the viscous coefficient and pressure coefficient received slight divergence with convergence ratio −1.33 and 1.44. Compared to the Richardson extrapolation result of C

_{t}, the maximum discrepancy is about 1.27% for C

_{v}and 0.83% for C

_{p}, which is acceptable for numerical analysis. For the total coefficient C

_{t}, the discrepancy between solution from fine mesh and RE result is 0.6%, so the fine mesh was selected and benchmark for local refinement study.

## 3. Sea Trails and Data Analysis

#### 3.1. Ship Heading and Speed Measurement

#### 3.2. Shaft Torque, Power and Revolution Measurements

_{e}is shaft torque in $N\xb7m$, M

_{FS}is the full scale torque in $N\xb7m$, ${V}_{FS}$ is the full scale output (10 V) of system, $E$ is the elasticity modulus of shaft in $N\xb7m{m}^{2}$, ${d}_{i}$ and ${d}_{o}$ is the inner and outer diameter of shaft in mm, ${V}_{EXC}$ is the bridge excitation voltage in V, ${k}_{GF}$ is the gage factor which is specified on strain gage package, $N$ is the number of active gages which is 4, $\mu $ is the Poisson’s ratio of shaft material, ${G}_{XMT}$ is telemetry transmitter gain.

#### 3.3. Trail Environment Measurement and Data Analysis

## 4. Results and Analysis

#### 4.1. Scale Effect of Hull-Propeller and Free Surface Interaction

_{s}= 0.861 for both model- and full-scale simulation.

_{pp}) for full-scale ship, the decrease of wake fraction (deficit of axial velocity) can also be verified by numerical results. Details of axial and transversal velocity distribution at the propeller plane are shown in Figure 7. At full-scale, the velocity deficit region appears primarily in inner radius and shows a relatively obscure hook-like flow field structure. From the comparison of circumferential averaged axial velocity shown in Figure 8, propeller at full-scale runs in a relatively higher velocity field which has lower thrust and torque coefficients but higher efficiency, as listed in Table 3.

#### 4.2. Self-Propulsion Performance Prediction Compared to Sea Trail Results

#### 4.2.1. Self-Propulsion Balance Condition

- Ship resistance
- Propeller performance
- Ship added resistance induced by propeller

#### 4.2.2. Powering Performance Prediction

## 5. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**(

**a**) Illustration of the bow region and free surface refinement; (

**b**) diagram for the direction of positive propeller phase angle.

**Figure 7.**Non-dimensional axial velocity contour and transversal velocity vector at propeller plane: (

**a**) model-scale; (

**b**) full-scale.

**Figure 9.**Single blade unsteady force coefficients in one rotation period: (

**a**) thrust coefficients; (

**b**) torque coefficients.

**Figure 11.**Nondimensional time-averaged axial velocity behind propeller: (

**a**) model-scale with double-model; (

**b**) full-scale with double-model; (

**c**) model-scale with VOF model; (

**d**) full-scale with VOF model.

**Figure 12.**Time-averaged axial velocity at central longitudinal plane (Y = 0). (

**a**) model-scale with double-model; (

**b**) full-scale with double-model; (

**c**) model-scale with VOF model; (

**d**) full-scale with VOF model.

**Figure 13.**Instantaneous iso-surface of nondimensional Q-criterion, colored by axial velocity ratio: model-scale with double-model (

**a**), full-scale with double-model (

**b**), model-scale with VOF model (

**c**), full-scale with VOF model (

**d**).

**Figure 15.**Effect of free surface treatment on full-scale propeller performance (

**a**) and propeller induced resistance (

**b**).

**Figure 19.**Speed-power correlation predicted by full-scale simulations with comparison to statistical sea trial result.

Cell Number | Δ/Lpp | C_{v} (×10^{3}) | C_{p} (×10^{3}) | C_{t} (×10^{3}) | |
---|---|---|---|---|---|

Coarse | 4.27 M | 0.0130 | 1.461 | 0.281 | 1.742 |

Fine | 8.77 M | 0.0091 | 1.452 | 0.269 | 1.721 |

Finer | 21.5 M | 0.0065 | 1.466 | 0.255 | 1.720 |

R_{i} | - | - | −1.33 | 1.14 | 0.048 |

RE | - | - | - | - | 1.720 |

Case | Scale | Propeller | w | R_{v} | R_{p} |
---|---|---|---|---|---|

1 | full | without | 0.2494 | 85.37% | 14.63% |

2 | full | with | - | 67.66% | 32.34% |

3 | model | without | 0.3402 | 84.73% | 15.27% |

4 | model | with | - | 70.43% | 29.57% |

Scale | Double-Model | VOF | |
---|---|---|---|

full | K_{T} | 0.1414 | 0.1547 |

10 K_{Q} | 0.2087 | 0.2232 | |

η_{B} | 0.6129 | 0.5907 | |

model | K_{T} | 0.1855 | 0.1916 |

10 K_{Q} | 0.2777 | 0.2830 | |

η_{B} | 0.5964 | 0.5900 |

Case NO. | Free Surface Treatment | Roughness | ${\mathsf{\Delta}}_{{\mathit{R}}_{\mathit{T}}}^{\mathit{V}\mathit{O}\mathit{F}}$ | ${\mathsf{\Delta}}_{\mathit{T}}^{\mathit{V}\mathit{O}\mathit{F}}$ | ${\mathsf{\Delta}}_{\mathsf{\Delta}\mathit{R}}^{\mathit{V}\mathit{O}\mathit{F}}$ |
---|---|---|---|---|---|

1 | VOF | No | - | - | - |

2 | VOF | Yes | - | - | - |

3 | Double-Model | No | Yes | No | No |

4 | Double-Model | Yes | Yes | No | No |

5 | Double-Model | Yes | Yes | Yes | No |

6 | Double-Model | Yes | Yes | No | Yes |

7 | Double-Model | Yes | Yes | Yes | Yes |

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**MDPI and ACS Style**

Sun, W.; Hu, Q.; Hu, S.; Su, J.; Xu, J.; Wei, J.; Huang, G.
Numerical Analysis of Full-Scale Ship Self-Propulsion Performance with Direct Comparison to Statistical Sea Trail Results. *J. Mar. Sci. Eng.* **2020**, *8*, 24.
https://doi.org/10.3390/jmse8010024

**AMA Style**

Sun W, Hu Q, Hu S, Su J, Xu J, Wei J, Huang G.
Numerical Analysis of Full-Scale Ship Self-Propulsion Performance with Direct Comparison to Statistical Sea Trail Results. *Journal of Marine Science and Engineering*. 2020; 8(1):24.
https://doi.org/10.3390/jmse8010024

**Chicago/Turabian Style**

Sun, Wenyu, Qiong Hu, Shiliang Hu, Jia Su, Jie Xu, Jinfang Wei, and Guofu Huang.
2020. "Numerical Analysis of Full-Scale Ship Self-Propulsion Performance with Direct Comparison to Statistical Sea Trail Results" *Journal of Marine Science and Engineering* 8, no. 1: 24.
https://doi.org/10.3390/jmse8010024