# Ship Bow Wings with Application to Trim and Resistance Control in Calm Water and in Waves

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Methodology

#### Solver Desription

**u**), and an indicator function ($a$). The governing equations integrated over control volume $\Omega $ with a boundary of $\partial \Omega $ are obtained by the following expression:

## 3. Numerical Setup

- (i)
- the extrapolated value$${\phi}_{ext}^{21}=\frac{{r}_{21}^{p}{\phi}_{1}-{\phi}_{2}}{{r}_{21}^{p}-1},$$
- (ii)
- the approximate relative error$${e}_{a}^{21}=\left|\frac{{\phi}_{2}-{\phi}_{1}}{{\phi}_{1}}\right|,$$
- (iii)
- the extrapolated relative error$${e}_{ext}^{21}=\left|\frac{{\phi}_{ext}^{21}-{\phi}_{1}}{{\phi}_{ext}^{21}}\right|,$$
- (iv)
- the fine GCI$$GC{I}_{fine}^{21}=\frac{1.25{e}_{ext}^{21}-{\phi}_{1}}{{r}_{21}^{p}-1}.$$

## 4. Results and Discussion

#### 4.1. Dynamic Trim and Sinkage of the Bare Hull

#### 4.2. Effect of a Wing Arranged in Front of the Bow in Calm Water Conditions

#### 4.3. Effect of the Foil Inclination in Calm Water Conditions

#### 4.4. Effect of the Wing in the Presence of Regular Waves

_{5}) and heave (ξ

_{3}). The heave was nondimensionalized based on the wave amplitude (A), while pitch used wave number (k) times wave amplitude (A). The figure includes both experimental and computational results. First, it was noted that the agreement between the computational results and the measurements was fair. Larger deviation was seen in the heave amplitude for the shortest wavelength in the case of the bare hull. Aside from that, the CFD calculations were in accordance with the experimental results for the bare hull. Regarding the comparison for when the foil was present, it was noted that, although the CFD results followed the experimental trends, there was almost-constant deviation from the measurements. Since in the simulations only the foil was considered, this deviation was attributed to the different configurations considered in the experiment and the simulations.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$\mathrm{Fn}$ | Ship Froude Number |

V | Ship Advance Speed |

${V}_{nom}$ | Ship Nominal Advance Speed (1.42 m/s) |

T | Ship Draft |

Ls | Ship Length |

s, c | Wing Span and chord length |

Lw | Wave Length |

f | Wave Frequency |

k | Wave Number |

A | Wave Amplitude |

${R}_{p}$ | Mean Resistance |

ξ_{3}_{,} ξ_{5} | Heave, Pitch |

${A}_{\phi}$ | Amplitude of Parameter φ |

$\overline{\phi}$ | Mean Value of Parameter φ |

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**Figure 1.**Overview of the computational domain. (

**a**) Side view and (

**b**) top view of the grid. The forcing zones (Z1, Z2, Z3) are noted on the right figure.

**Figure 4.**(

**a**) Free surface elevation and (

**b**) y

^{+}values on the ship hull in calm water conditions for draft T = 0.135 m and Fn = 0.25.

**Figure 6.**Comparison of the CFD data and experimental predictions for the two drafts for (

**a**) trim angle and (

**b**) sinkage.

**Figure 7.**Experimental configuration of the dynamic wing arranged at the bow of the ferry ship model tested in the tank of LMSH at NTUA.

**Figure 11.**Comparison of the predicted resistance for the various angles of attack. The results concern the nominal speed (V = 1.42 m/s) for the heavier condition (T = 0.135 m). The experimental data were corrected by subtracting the resistance of the skegs and vane.

**Figure 12.**Comparison of the predicted trim angle for the various angles of attack. The results concern the nominal speed (V

_{nom}= 1.42 m/s) for the heavier condition (T = 0.135 m).

**Figure 13.**Comparison of the predicted sinkage for the various angles of attack. The results concern the nominal speed (V

_{nom}= 1.42 m/s) for the heavier condition (T = 0.125 m).

**Figure 14.**Numerical results of (

**a**) model resistance and (

**b**) pitch and heave motions with and without the foil over one encounter period. In the left figure, the dotted line corresponds to the mean value of the model’s resistance. Wave frequency: f = 0.55 Hz. Wavelength to ship length: L

_{w}/L

_{s}= 1.62.

**Figure 15.**Numerical results of (

**a**) model resistance and (

**b**) pitch and heave motions with and without the foil over one encounter period. In the left figure, the dotted line corresponds to the mean value of the model’s resistance. Wave frequency: f = 0.67 Hz. Wavelength to ship length: L

_{w}/L

_{s}= 1.09.

**Figure 16.**Numerical results of (

**a**) model resistance and (

**b**) pitch and heave motions with and without the foil over one encounter period. In the left figure, the dotted line corresponds to the mean value of the model’s resistance. Wave frequency: f = 0.75 Hz. Wavelength to ship length: L

_{w}/L

_{s}= 0.87.

**Figure 17.**Comparison between numerical and experimental results for regular waves with and without foil. The figures present the response amplitude operators for (

**a**) nondimensional heave and (

**b**) normalized pitch, where A is the wave amplitude, and k is the wave number.

**Figure 18.**Iso-surface of the density field for ρ

_{m}= 500 kg/m

^{3}colored by the vertical coordinate. The two figures correspond to the heavier draft (T = 0.135 m) for an incident wave frequency of 0.67 Hz; (

**a**) presents the bare hull case and (

**b**) depicts the hull equipped with the static foil.

**Figure 19.**Pressure field at the symmetry plane (y = 0 m) for the two configurations: (

**a**) presents the base hull case, while figure (

**b**) depicts the hull equipped with the static foil. The two figures correspond to the heavier draft (T = 0.135 m) for an incident wave frequency of 0.67 Hz.

Grid-Time-Step | Resistance (kp) | Trim (deg) | Sinkage (cm) |
---|---|---|---|

G3-T_{ref}/2500 | 0.704 | 0.0977 | −0.386 |

G2-T_{ref}/2500 | 0.687 | 0.0954 | −0.388 |

G1-T_{ref}/2500 | 0.682 | 0.0922 | −0.392 |

G2-T_{ref}/500 | 0.686 | 0.0959 | −0.387 |

G2-T_{ref}/250 | 0.686 | 0.0958 | −0.387 |

h_{1} | h_{2} | h_{3} | r_{21} | r_{32} | p | ${\mathit{\phi}}_{\mathit{e}\mathit{x}\mathit{t}}^{21}$ | ${\mathit{e}}_{\mathit{a}}^{21}$ | ${\mathit{e}}_{\mathit{e}\mathit{x}\mathit{t}}^{21}$ | $\mathit{G}\mathit{C}{\mathit{I}}_{\mathit{f}\mathit{i}\mathit{n}\mathit{e}}^{21}$ |
---|---|---|---|---|---|---|---|---|---|

0.0455 | 0.0616 | 0.0860 | 1.35 | 1.40 | 1.53 | 0.674 | 0.73% | 1.26% | 1.56% |

**Table 3.**Contribution of the individual components of the full configuration on the model’s resistance. Three different Froude numbers were examined for the T = 0.135 m draft.

Froude No. | Total [kp] | Hull [kp] | Skegs [kp] | Wing [kp] |
---|---|---|---|---|

0.25 | 0.829 | 0.66 | 0.077 | 0.092 |

0.22 | 0.653 | 0.52 | 0.061 | 0.072 |

0.176 | 0.431 | 0.34 | 0.043 | 0.048 |

**Table 4.**Contribution of the individual components of the full configuration on the mode’s resistance. Three different Froude numbers were examined for the T = 0.125 m draft.

Froude No. | Total [kp] | Hull [kp] | Skegs [kp] | Wing [kp] |
---|---|---|---|---|

0.25 | 0.788 | 0.62 | 0.073 | 0.095 |

0.22 | 0.614 | 0.48 | 0.059 | 0.075 |

0.176 | 0.413 | 0.32 | 0.042 | 0.051 |

**Table 5.**Experimental results for the static wing in various AoAs. All results regard the nominal speed of the vessel (Fn = 0.25 or V

_{nom}= 1.42 m/s) in the case of the heavier condition (T = 0.135 m).

Angle of Attack [deg] | Resistance [kp] | Trim [deg] | Sinkage [cm] |
---|---|---|---|

−3.1 | 1.031 | −0.159 | −0.198 |

−1.6 | 1.007 | −0.039 | −0.291 |

1.6 | 1.028 | 0.264 | −0.494 |

0 | 1.042 | 0.132 | −0.401 |

**Table 6.**Time-step independency study for the case study with regular waves. The table presents the mean value $\overline{\left(\xb7\right)}$ and amplitudes (A) of the heave (${\xi}_{3}$), pitch (${\xi}_{5}$), and resistance (${A}_{p}$).

dt [s] | $\overline{{\mathit{\xi}}_{3}}$ | $\overline{{\mathit{\xi}}_{5}}$ | $\overline{{\mathit{R}}_{\mathit{p}}}$ | ${\mathit{A}}_{{\mathit{\xi}}_{3}}$ | ${\mathit{A}}_{{\mathit{\xi}}_{5}}$ | ${\mathit{A}}_{{\mathit{R}}_{\mathit{p}}}$ |
---|---|---|---|---|---|---|

0.003 | 1.93 | 2.27 | 1.18 | 1.93 | 2.27 | 1.18 |

0.002 | 1.79 | 2.19 | 1.10 | 1.79 | 2.19 | 1.10 |

0.001 | 1.75 | 2.14 | 1.08 | 1.75 | 2.14 | 1.08 |

**Table 7.**Mean resistance per encounter cycle for the bare hull and foil configurations at considered wave excitations.

Wavelength to Ship Length L_{w}/L_{s} | Resistance [kp] Bare Hull | Resistance [kp] with Foil | Gain (%) |
---|---|---|---|

0.87 | 1.153 | 0.883 | +23.5 |

1.09 | 1.165 | 0.801 | +31.2 |

1.16 | 1.177 | 0.774 | +34.2 |

1.62 | 0.854 | 0.747 | +12.5 |

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**MDPI and ACS Style**

Ntouras, D.; Papadakis, G.; Belibassakis, K.
Ship Bow Wings with Application to Trim and Resistance Control in Calm Water and in Waves. *J. Mar. Sci. Eng.* **2022**, *10*, 492.
https://doi.org/10.3390/jmse10040492

**AMA Style**

Ntouras D, Papadakis G, Belibassakis K.
Ship Bow Wings with Application to Trim and Resistance Control in Calm Water and in Waves. *Journal of Marine Science and Engineering*. 2022; 10(4):492.
https://doi.org/10.3390/jmse10040492

**Chicago/Turabian Style**

Ntouras, Dimitris, George Papadakis, and Kostas Belibassakis.
2022. "Ship Bow Wings with Application to Trim and Resistance Control in Calm Water and in Waves" *Journal of Marine Science and Engineering* 10, no. 4: 492.
https://doi.org/10.3390/jmse10040492