# Numerical and Experimental Investigation of the Performance of Dynamic Wing for Augmenting Ship Propulsion in Head and Quartering Seas

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Augmenting Ship Propulsion System in Waves by Controllable Dynamic Wing

#### 2.1. Ship Dynamics Coupled with Unsteady Flapping-Foil Thruster

_{w}) at the ship bow, and its vertical motion h is defined from the ship heave ${\xi}_{3}$, pitch ${\xi}_{5}$ and roll ${\xi}_{4}$ responses, as follows:

#### 2.2. Experimental Investigation of the Model

_{BP}= 3.3 m, with main dimension ratio: L

_{BP}/B = 7.67, B/T = 3.3 and hull coefficients C

_{b}= 0.45, C

_{wl}= 0.73, C

_{m}= 0.82, has been designed, constructed and tested at the NTUA towing tank without and with the operation of a dynamically controllable flapping thruster arranged at the bow; see Figure 1 and Figure 2. The dimensions of the NTUA towing tank are: length 100 m, breadth 4.6 m and maximum depth 3 m. Moreover, the maximum carriage speed is 5 m/s. The model was made out of wood and prepared for testing at two selected drafts, B/T = 3.18 and B/T = 3.44. The foil is constructed by poly (vinyl chloride) (PVC), polished and painted. The foil planform shape is orthogonal; its span is s = 0.50 m with a span to chord ratio of s/c = 4 and thus, its aspect ratio is AR = 4 and the wing planform area is S

_{w}/BT = 1.17. The foil sections are symmetrical NACA0012. The model is painted white and marked with the two waterlines used in the tests in order to provide a reference in the photographs; see Figure 2.

_{L}/L = 1.9. The vertical coordinate of the center of buoyancy is KB/L = 0.024 (from BL) and its longitudinal position LCB = −0.024 L. We consider that the ship trim and heel angle are zero and thus, the longitudinal center of gravity is the same as the center of buoyancy, i.e., X

_{G}/L = −0.024 (aft midship) and Y

_{G}= 0. The vertical center of gravity is KG/T = 0.2(from BL). Furthermore, the longitudinal metacentric height is $G{M}_{L}\approx B{M}_{L}$. Finally, the radii of gyration about the x-axis and y-axis, respectively, are taken R

_{xx}/B = 0.25, R

_{yy}/L = 0.2. The foil is located at a distance x

_{wing}/L = 0.5, with respect to the midship section, and vertically at a submergence depth d/T = 1.6.

- (a)
- The dynamic angle of attack is measured using a potentiometer providing input α(t) to the CS.
- (b)
- The foil angle is measured by using a potentiometer providing input θ(t) to the CS.
- (c)
- The CS instructs the motor to rotate in order to force the linear actuator and rotate the crankshaft, oscillating the vertical rods and transmitting the angular motion θ(t) to the foil which is set equal to:$$\theta \left(t\right)=Ga\left(t-D\right)+O.$$

- (a)
- Wave elevation from the wavemaker and near the tank carriage (near the vessel): η
_{1}(t), η_{2}(t); - (b)
- Ship model motions (heave and pitch of the hull from tank accelerometers): ξ
_{3}(t), ξ_{5}(t); - (c)
- The model resistance in the presence of waves with the dynamic foil in operation: R(t);
- (d)
- The angle of attack α(t) and the foil angle θ(t).

- -
- 0–6 Hz, Gain = 1/ripple 2.75 dB and
- -
- 18–104 Hz, Gain = 0/Actual attenuation −43 dB.

- -
- Analog input for the AoA sensor. Oversampled at 2048 Hz and low pass filtered at 6 Hz.
- -
- Digital serial output to Animatics/Moog brushless servo motor (actuator).
- -
- 5 × 12 bits spare analog outputs for monitoring.
- -
- 3 × 12 bits spare analog inputs for interfacing auxiliary sensors
- -
- 3D gyroscope and 3D accelerometer.
- -
- 3D magnetometer and pressure sensor.
- -
- GNSS and WiFi/Bluetooth.
- -
- GPRS/2 G/3 G.
- -
- CAN Bus interface and uSD card for data acquisition.

- -
- Quaternion estimation and Euler angles.
- -
- Linear acceleration and speed.
- -
- Assisted global positioning and real-time spectral analysis.

#### 2.3. Modeling the Flapping Thruster Performance in Irregular Waves

_{wing}of the wing, we obtain the corresponding spectrum describing the foil vertical motion as

_{s}/L = 0.03 and peak period ${T}_{p}U/L$ = 0.7, where it is also compared with the corresponding spectrum of foil vertical motion in the ship frame of reference traveling at Fr = 0.25 (solid line), in case of head incident waves (β = 180°), as obtained from Equation (12) for head seas.

## 3. Numerical Modeling of the 3D Flapping-Foil Thruster in Quartering Seas

#### 3.1. Time Domain 3D BEM Model with Viscous Corrections

#### 3.2. RANSE Model for Validation and Calibration

^{−6}, chords ensuring a y+ below 1. In the chordwise direction, 600 nodes are placed around the foil. In total, the boundary layer mesh is composed of 65 layers having a growth factor of 1.1. In the spanwise direction, 130 nodes are placed. The computational mesh near the wing region can be seen in Figure 13b. The resulting grid consisted of approximately 9 million cells.

## 4. Numerical Modeling of the 3D Flapping-Foil Thruster in Head and Quartering Seas

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${F}_{foil}$ | Foil Froude number |

$Fr$ | Ship Froude number |

ω | Ship absolute frequency |

${\omega}_{en}$ | Ship encounter frequency |

${a}_{k\ell}$ | Ship added mass coefficient |

${b}_{k\ell}$ | Ship added damping coefficient |

${X}_{k0}$ | Foil forces acting on the ship |

$\eta $ | Free-surface elevation |

$\theta $ | Foil self-rotational motion |

$a$ | Angle of attack |

$\epsilon $ | Angle of attack due to foil vertical oscillation |

$c$ | Foil chord |

$s$ | Foil span |

$G$ | Foil control system gain |

${C}_{T}$ | Ship total resistance coefficient |

${C}_{F}$ | Foil force coefficient |

${C}_{M}$ | Foil moment coefficient |

$d$ | Foil mean submergence |

$\eta $ | Froude efficiency |

$\mathsf{\Phi}$ | Potential field |

${H}_{s}$ | Significant wave height |

${T}_{p}$ | Peak period |

$S$ | Spectrum according to earth fixed reference frame |

${S}^{U}$ | Wave spectrum according to moving observer |

$\beta $ | Wave angle of incidence |

$L$ | Ship length |

${x}_{wing}$ | Horizontal location of the foil |

$\mu $ | Surface dipole intensity or potential jump |

## Abbreviations

BEM | Boundary Element Methods |

EFD | Experimental Fluid Dynamics |

CFD | Computational Fluid Dynamics |

RANSE | Reynolds Averaged Navier Stokes Equation |

RTK | Real Time Kinematics |

VOF | Volume of Fluid |

GPU | Graphics Processing Unit |

HPC | High -Performance Computing |

CAD | Computer Aided Design |

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**Figure 1.**(

**a**) Self-propelled ship with a dynamic wing arranged at the bow operating as a flapping thruster due to its vertical motion h(t) induced by the ship vertical (ξ

_{3}, ξ

_{5}) and transverse (ξ

_{2}, ξ

_{4}) responses in waves, in conjunction with (

**b**) the controlled self-pitching foil motion θ(t).

**Figure 3.**General arrangement of the NTUA tank-scale model with the dynamic wing arranged at the bow.

**Figure 4.**Computer-aided design (CAD) model of the tank-scale model of the dynamic wing used for testing.

**Figure 5.**Tank tests of the hull model in calm water: (

**a**) without the dynamic wing and (

**b**) with the flapping thruster, and determination of resistance.

**Figure 6.**Tank tests of the hull model in waves: (

**a**) without the dynamic wing and (

**b**) with the flapping thruster, and determination of motions and total resistance.

**Figure 8.**Calm water resistance coefficient without and with the flapping thruster for various model speeds and corresponding Froude numbers, and for the two drafts. The Froude number corresponding to design ship speed (Fr = 0.25) is indicated by using a dashed line.

**Figure 9.**Calculated (lines) and measured (symbols) heave and pitch responses in head waves, with and without the operation of the dynamic foil, for Froude number Fr = 0.25 and the smaller draft. (

**a**,

**b**) Heave response without and with the foil, respectively. (

**c**,

**d**) Pitch response without and with the foil, respectively.

**Figure 10.**Sea spectrum (H

_{s}/L = 0.03 and ${T}_{p}U/L$ = 0.7) for head seas (β = 180°), normalized with respect to the peak value of the incident wave spectrum ${S}_{\mathrm{max}}$ and foil’s vertical motion spectrum of the ${S}_{foil}^{U}$.

**Figure 11.**Realization of the vertical motion of the foil (solid line) at the bow of the ship at Fr = 0.25 in comparison with the ship heave motion (dashed line) for the head waves propagating at β = 180° and represented by the spectrum of Figure 10.

**Figure 12.**Realization of the vertical motion of the foil (solid line) at the bow of the ship at Fr = 0.25 in comparison with the ship heave motion (dashed line) for the quartering waves propagating at β = 150° and represented by the spectrum of Figure 10.

**Figure 13.**RANSE solver grid: (

**a**) Overall view of the spherical domain used for the computational domain spanning 100 chords. The grid is fully unstructured as can be seen by a slice of the grid, as shown above; (

**b**) detail of the grid in the near wall vicinity. A slice of the computational mesh is depicted, and a structured-like grid is generated to resolve the boundary layer.

**Figure 14.**Comparison of the predictions using three different grids: (

**a**) Nondimensional forces in the chordwise and (

**b**) the normal direction. Force time history is in very good agreement in all of the grids. The coarser grid (red) gives slightly higher ${C}_{x}$ values at the two peaks, while the other two are almost identical. Consequently, Mesh 2 is used throughout the rest of the study.

**Figure 15.**BEM simulation of the ferry and the dynamic wing in head waves ($\beta =180\xb0$): (

**a**) total free-surface elevation and potential (denoted with colors), interaction with the foil wake located on the ship bow; (

**b**) time evolution of forces and moments acting on the foil; (

**c**) total free-surface elevation and potential (denoted with colors) all over the computational domain.

**Figure 16.**Evolution of motion and loads acting on the dynamic wing in head waves ($\beta =180\xb0$) for the case of Figure 15. Comparison between 2D and 3D calculations: (

**a**) foil vertical motion; (

**b**) pitching angle and angle of attack; (

**c**) thrust coefficient ${C}_{Fx}={F}_{x}/0.5\rho {U}^{2}cs$; (

**d**) lift coefficient ${C}_{Fz}={F}_{z}/0.5\rho {U}^{2}cs$; (

**e**) foil moment about its pivot axis ${C}_{My}={M}_{y}/0.5\rho {U}^{2}{c}^{2}s$.

**Figure 17.**BEM simulation of the ferry and the foil in quartering seas ($\beta =150\xb0$): (

**a**) total free-surface elevation and potential (denoted with colors), interaction with the foil wake located on the ship bow; (

**b**) time evolution of forces and moments acting on the foil; (

**c**) total free-surface elevation and potential (denoted with colors) all over the computational domain.

**Figure 18.**Time history of nondimensional forces and moments acting on the dynamic wing operating in quartering seas ($\beta =150\xb0$) for the case of Figure 17: (

**a**) thrust ${C}_{Fx}={F}_{x}/0.5\rho {U}^{2}cs$; (

**b**) force in spanwise direction ${C}_{Fy}={F}_{y}/0.5\rho {U}^{2}cs$; (

**c**) vertical force ${C}_{Fz}={F}_{z}/0.5\rho {U}^{2}cs$; (

**d**) twisting moment ${C}_{Mx}={M}_{x}/0.5\rho {U}^{2}{c}^{2}s$; (

**e**) pitching moment ${C}_{My}={M}_{y}/0.5\rho {U}^{2}{c}^{2}s$; (

**f**) wing yawing moment ${C}_{Mz}={M}_{z}/0.5\rho {U}^{2}{c}^{2}s$.

λ/L | G = 0 (Foil Fixed) | G = 0.5 | G = −0.25 | G = −0.25 (without the Vane) |
---|---|---|---|---|

1.56 | −12 | −14 | −9 | 2 |

1.12 | 10 | 4 | 14 | 25 |

1.05 | 16 | 6 | 18 | 29 |

0.84 | 1 | −1 | 4 | 15 |

Load Case Number (LC) | Angle of Incidence $\mathit{\beta}$ (deg) | Wave Conditions | Foil Froude Number ${\mathit{F}}_{\mathit{f}\mathit{o}\mathit{i}\mathit{l}}=\mathit{U}/\sqrt{\mathit{g}\mathit{c}}$ | Mean Foil Submergence $\mathit{d}/\mathit{c}$ | Foil Horizontal Location ${\mathit{x}}_{\mathit{w}\mathit{i}\mathit{n}\mathit{g}}/\mathit{L}$ | Figures |
---|---|---|---|---|---|---|

1 | 180 | ${H}_{s}/L=0.03$ ${T}_{p}U/L=0.7$ | 1.35 | 1.71 | 0.6 | Figure 15 and Figure 16 |

2 | 150 | ${H}_{s}/L=0.03$ ${T}_{p}U/L=0.7$ | 1.35 | 1.71 | 0.6 | Figure 17 and Figure 18 |

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**MDPI and ACS Style**

Belibassakis, K.; Filippas, E.; Papadakis, G. Numerical and Experimental Investigation of the Performance of Dynamic Wing for Augmenting Ship Propulsion in Head and Quartering Seas. *J. Mar. Sci. Eng.* **2022**, *10*, 24.
https://doi.org/10.3390/jmse10010024

**AMA Style**

Belibassakis K, Filippas E, Papadakis G. Numerical and Experimental Investigation of the Performance of Dynamic Wing for Augmenting Ship Propulsion in Head and Quartering Seas. *Journal of Marine Science and Engineering*. 2022; 10(1):24.
https://doi.org/10.3390/jmse10010024

**Chicago/Turabian Style**

Belibassakis, Kostas, Evangelos Filippas, and George Papadakis. 2022. "Numerical and Experimental Investigation of the Performance of Dynamic Wing for Augmenting Ship Propulsion in Head and Quartering Seas" *Journal of Marine Science and Engineering* 10, no. 1: 24.
https://doi.org/10.3390/jmse10010024