A submerged hydrofoil interacting with incoming waves produces combined heaving and pitching motion, facilitating the conversion of wave energy into thrust. When the foil is attached to the ship hull, the generated “green” power from wave energy could assist the ship's propulsion system and significantly reduce fuel costs. This study experimentally assesses thrust generation from a fixed mid-hull foil by comparing towing force at different wave and traveling speeds. The optimal mid-hull foil demonstrates a fuel cost reduction ranging from 10.3% to 20.4% at diverse traveling speeds and wave parameters. Thrust generation increases at higher traveling speeds. Additionally, this study mathematically describes the hydrofoil motion with an outer pivot, which better suits the ship–foil model. This study then introduces a Strouhal number ( ) specifically for the ship–foil model, considering ship travel, ship response, and the hydrofoil's rotation around its outer pivot.
REFERENCES
1.
X.
Wu
,
X. T.
Zhang
,
X. L.
Tian
,
X.
Li
, and
W. Y.
Lu
, “
A review on fluid dynamics of flapping foils
,” Ocean Eng.
195
, 106712
(2020
).2.
J.
Xing
and
L.
Yang
, “
Wave devouring propulsion: An overview of flapping foil propulsion technology
,” Renewable Sustainable Energy Rev.
184
, 113589
(2023
).3.
K.
Rozhdestvensky
and
B.
Zhao
, “
Recent advances in hydrodynamics of wing propulsive lifting systems for ships and underwater vehicles
,” Phys. Fluids
35
, 103148
(2023
).4.
J. A.
Bowker
and
N. C.
Townsend
, “
Evaluation of bow foils on ship delivered power in waves using model tests
,” Appl. Ocean Res.
123
, 103148
(2022
).5.
Y.
Li
,
W.
Zhang
,
Y.
Liao
,
Q.
Jia
, and
Q.
Jiang
, “
Multi-energy-system design and experimental research of natural-energy-driven unmanned surface vehicle
,” Ocean Eng.
240
, 109942
(2021
).6.
Z.
Qi
,
M.
Jiang
,
L.
Jia
,
B.
Zou
, and
J.
Zhai
, “
The effect of mass ratio and damping coefficient on the propulsion performance of the semi-active flapping foil of the wave glider
,” J. Mar. Sc. Eng.
8
, 303
(2020
).7.
W.-Q.
Wang
,
W.
Li
,
Y.
Yan
, and
J.
Zhang
, “
Parametric study on the propulsion and energy harvesting performance of a pitching foil hanging under a wave glider
,” Renewable Energy
184
, 830
–844
(2022
).8.
A.
Arredondo-Galeana
,
W.
Shi
,
G.
Olbert
,
M.
Scharf
,
A.
Ermakov
,
J. V.
Ringwood
, and
F.
Brennan
, “
A methodology for the structural design of LiftWEC: A wave-bladed cyclorotor
,” in The 14th European Wave and Tidal Energy Conference
, 2021
.9.
J. A.
Bowker
, “
Coupled dynamics of a flapping foil wave powered vessel
,” Ph.D. thesis (
University of Southampton
, 2018
).10.
Y.
Zhang
,
X.
Han
,
Y.
Hu
,
X.
Chen
,
Z.
Li
,
F.
Gao
, and
W.
Chen
, “
Dual-function flapping hydrofoil: Energy capture and propulsion in ocean waves
,” Renewable Energy
222
, 119956
(2024
).11.
E.
Bøckmann
and
S.
Steen
, “
Model test and simulation of a ship with wavefoils
,” Appl. Ocean Res.
57
, 8
–18
(2016
).12.
R.
McGregor
and
G.
Thomson
, “
Sea trials of wave propulsion of a yacht using a flexible fin propeller
,” Renewable Energy
10
, 335
–338
(1997
).13.
K. A.
Belibassakis
and
G. K.
Politis
, “
Hydrodynamic performance of flapping wings for augmenting ship propulsion in waves
,” Ocean Eng.
72
, 227
–240
(2013
).14.
K.
Belibassakis
and
E.
Filippas
, “
Ship propulsion in waves by actively controlled flapping foils
,” Appl. Ocean Res.
52
, 1
–11
(2015
).15.
E.
Bøckmann
and
S.
Steen
, “
The effect of a fixed foil on ship propulsion and motions
,” in Proceedings of the Third International Symposium on Marine Propulsors SMP
(Australian Maritime College, University of Tasmania, 2013
), Vol.
13
, pp. 553
–561
.16.
F. F.
Siala
,
K.
Kamrani Fard
, and
J. A.
Liburdy
, “
Experimental study of inertia-based passive flexibility of a heaving and pitching airfoil operating in the energy harvesting regime
,” Phys. Fluids
32
(1
), 017101
(2020
).17.
J. R.
Xing
,
D.
Stagonas
,
P.
Hart
,
C. C.
Zhang
,
J. H.
Yang
, and
L.
Yang
, “
Wave induced thrust on a submerged hydrofoil: Pitch stiffness effects
,” arXiv:2209.05551 (2022
).18.
J.
Wang
,
S.
Santhosh
,
O.
Colomés
,
M.
Capaldo
, and
L.
Yang
, “
Experimental study of dynamic response of passive flapping hydrofoil in regular wave
,” Phys. Fluids
35
(7
), 077127
(2023
).19.
E.
Bøckmann
and
S.
Steen
, “
Experiments with actively pitch-controlled and spring-loaded oscillating foils
,” Appl. Ocean Res.
48
, 227
–235
(2014
).20.
E.
Filippas
and
K.
Belibassakis
, “
A nonlinear time-domain BEM for the performance of 3D flapping-wing thrusters in directional waves
,” Ocean Eng.
245
, 110157
(2022
).21.
S.-W.
Huang
,
T.-L.
Wu
,
Y.-T.
Hsu
,
J.-H.
Guo
,
J.-F.
Tsai
, and
F.-C.
Chiu
, “
Effective energy-saving device of eco-ship by using wave propulsion
,” in 2016 Techno-Ocean (Techno-Ocean)
(
IEEE
, 2016
), pp. 566
–570
.22.
E.
Bøckmann
,
A.
Yrke
, and
S.
Steen
, “
Fuel savings for a general cargo ship employing retractable bow foils
,” Appl. Ocean Res.
76
, 1
–10
(2018
).23.
Y.
Zhang
,
L.
Xu
,
Z.
Ding
, and
M.
Hu
, “
Wave propulsion and sea-keeping enhancement for ships in rough sea condition by flapping foils
,” Ocean Eng.
266
, 112802
(2022
).24.
K.
Niklas
and
H.
Pruszko
, “
The retrofitting of ships by applying retractable bow hydrofoils: A case study
,” J. Ocean Eng. Mar. Energy
9
, 767
–788
(2023
).25.
Y.
Zhang
,
L.
Xu
, and
Y.
Zhou
, “
A wave foil with passive angle of attack adjustment for wave energy extraction for ships
,” Ocean Eng.
246
, 110627
(2022
).26.
W.
Tian
,
A.
Bodling
,
H.
Liu
,
J. C.
Wu
,
G.
He
, and
H.
Hu
, “
An experimental study of the effects of pitch-pivot-point location on the propulsion performance of a pitching airfoil
,” J. Fluids Struct.
60
, 130
–142
(2016
).27.
A.
Mackowski
and
C.
Williamson
, “
Effect of pivot location and passive heave on propulsion from a pitching airfoil
,” Phys. Rev. Fluids
2
, 013101
(2017
).28.
Y.
Zhang
,
Y.
Feng
,
W.
Chen
, and
F.
Gao
, “
Effect of pivot location on the semi-active flapping hydrofoil propulsion for wave glider from wave energy extraction
,” Energy
255
, 124491
(2022
).29.
Z.
Wang
,
L.
Du
,
J.
Zhao
, and
X.
Sun
, “
Structural response and energy extraction of a fully passive flapping foil
,” J. Fluids Struct.
72
, 96
–113
(2017
).30.
Y.
Wang
,
X.
Sun
,
D.
Huang
, and
Z.
Zheng
, “
Numerical investigation on energy extraction of flapping hydrofoils with different series foil shapes
,” Energy
112
, 1153
–1168
(2016
).31.
J. M.
Kelly
,
M. S. U.
Khalid
,
P.
Han
, and
H.
Dong
, “
Geometric characteristics of flapping foils for enhanced propulsive efficiency
,” J. Fluids Eng.
145
, 061104
(2023
).32.
M.
Soltani
and
A.
Bakhshalipour
, “
Effect of amplitude and mean angle-of-attack on the boundary layer of an oscillating aerofoil
,” Aeronaut. J.
112
, 705
–713
(2008
).33.
L.
Schouveiler
,
F.
Hover
, and
M.
Triantafyllou
, “
Performance of flapping foil propulsion
,” J. Fluids Struct.
20
, 949
–959
(2005
).34.
P.
Liu
,
Y.
Liu
,
S.
Huang
,
J.
Zhao
, and
Y.
Su
, “
Effects of regular waves on propulsion performance of flexible flapping foil
,” Appl. Sci.
8
, 934
(2018
).35.
D. GL-OS-E301
, “
Offshore standard - position mooring (DNVGL-OS-e301)
,” Edition July 2017 (2017
).36.
R.
Cao
,
E.
Padilla
, and
A.
Callaghan
, “
The influence of bandwidth on the energetics of intermediate to deep water laboratory breaking waves
,” J. Fluid Mech.
971
, A11
(2023
).37.
M.
Triantafyllou
,
G.
Triantafyllou
, and
R.
Gopalkrishnan
, “
Wake mechanics for thrust generation in oscillating foils
,” Phys. Fluids A: Fluid Dyn.
3
, 2835
–2837
(1991
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
