Date April: 2007
Author Pinkster, J;A. and A.). Hermans ress Delft University of liechnology
Ship Hydromechanics Laboratory
Mekelweg 2, 26282 CD Deift
TU Do Ift
Delft University of Technology
A rotating wing for the generation of
Energy from waves
by
l.A. Pin kster and Ail. Hérmans
Report No 1519-P 2007
Proceedings of the 22 International WorkShop on Water Waves and Floating Bodies, Plltvice, Croatia, 15-18 AprIl 2007
Proceedings
22rd
IntErnational Wcrkshcp
on
Water Waves
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Urc1ertheauspues pf the Crbati'a Academy of Screnoes aic!
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for Marffimâ
--1;5 - 18ApriF2QO7, PIiPiice,, CROATIA
Editors:
ime Malenica and Ivo Senjanoviô
221
International Workshop
on
Water Waves
and Floating Bodies
Proceedings
ISBN: 978-953-95746-0-2
Published by: \TIDICI d.o.o., Velika Rakovica, Samobor, Croatia
Foreword
The International Workshop on Water Waves and Floating Bodies is an annual meeting of engineers and scientists with special interests in water waves and the effects of waves on
floating or submerged bodies. The workshop was initiated over twenty years. ago by Professor
Nick Newman from MIT and Professor David Evans from Bristol University. Since its
inception, the workshop has grown from strength to strength and annually brings together marine hydrodynamicists, naval architects, offshore and arctic engineers and other scientists
and mathematicians, from both industry and academia, to discuss current research and
practical problems in a focused week of activity. Attendance is restricted to the authors of submitted extended abstracts that are reviewed for acceptance by a small committee. These proceedings include the extended abstract for every presentation made at the 22 workshop.
The proceedings of previous workshops are available online at www.rina.org.uk thanks to the cooperation of the Royal Institution of Naval Architects. The list of the previous Workshops
is showninthe table below.
The22nd International Workshop on Water Waves and FlOating Bodies was jointly organized by Bureau Veritas - Research Department and Faculty of Mechanical Engineering and Naval Architecture of Zagreb University. The workshop took place in Hotel Jezero at Plitvice Lakes.
in Croatia.
time Malenica & Ivo Senjanovié
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13/04L1988 [MI T(MA)[10/05/1989 lOystese 28/03/lggoIManchester---14th 07/05/1989 15th 16t!1 17th 25/03/1990
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L24/05/22
27/05/1992 VaI de ReuilFrance
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I 23/05/1993 26/05/1993 jst John's Newfoundland
Lcanda
17/04/1994120/04/1gg'IKU3u
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05/04/1995 [Oxford11th 17/03/1996
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NethertancF1 29/03/1998 01/04/1998 LAiphen aan den Rijn
11/04/1999 14/04/1999 Port Huron (MI) 'USA
LL27/2ioo
O1f03/2000CaesareaIsrael
The 22ndIWWWFB is dedicated to Professor Makoto Ohkusu who left us suddenly last year.
Professor Ohkusu was a regular contributor to the Workshop, indeed he hosted the 9th
IWWWFB in Kyushu. He travelled extensively, often with his family, lecturing and
collaborating with colleagues around the world.
After studying with Takao Jnuj at the University of. Tokyo, Makoto began his prolific career at Kyushu University, working initially in association with the late Professor Fukuzo Tasai.
Ohkusu performed seminal research on the hydrodynamic interactions among multiple
floating bodies, which greatly contributed to the development of multi-hull ships and offshore platforms. Later he developed the unsteady wave-pattern analysis method, which provided a new technique for studying ships running with forward speed in waves. He also published many other noteworthy papers, concerning such topics as the nonlinear behaviour of a long flexible cable; a new evaluation method for the oscillating and translating Green function; and
its application to the boundary-value problem for the flow around ships. He performed
extensive studies of the hydroelastic problems associated with very large floating structures
such as floating airports.
In 1981 Ohkusu was promoted as a Full Professor at Kyushu University. He served from 1997
to 1999 as the Director of the University's Research Institute of Applied Mechanics. Many students benefited from his tutelage and support. When he retired in 2001, an International Conference on 'Hydrodynamics in Ship and Ocean Engineering' was held in his honor. From 2004 to 2006 he served as the Director of the Marine Technology Center at the Japan Agency
for Marine-Earth Science and Technology.
We all remember Makoto Ohkusu, both for his kindness and the high quality of his work. His
research and generous spirit have inspired us, and his absence is mourned by our community.
Makoto Ohkusu
22
International. Workshop on Water Waves and 'Floating Bodies
CONTENTS
Bennetts L.G., Biggs N.R.T. and Porter ft. 1
Wave scattering by a circular ice floe of variable thickness
Bhattacharjee J, Karmakar D, and Sahoo T.
On transformation of flexural gravity waves
Bingham H.B., Engsig.Karup A. P. and Liñdberg 0. 9
A high-order finite difference method for nonlinear wave-structure interaction
Bleflkinsopp C.E. and Chaplin J.R. 13
Validity of small-scale physical models involving breaking waves
Bredmose H., Peregrine D.H and Hunt A. 17
Wave height? A study of the impact of wave groups on a coastal structure
Breslin J.P. 21
Prediction of planing forces on prismatic hulls far exceeding expectations by
inconsistent theory
CasettaL. and Pesce C.P. 25
Hamilton's principle for dissipative systems and Wagner's problem
Chaplin J.R, Farley F.J.M. and Rainey R.C.T. 29
Power conversion in the Anaconda WEC
Chatjigeorgiou I.K. and Mavrakos S.A. 33
A semi-analytical formulation for the wave-current interaction problem with a
vertical bottom-seated cylinder including square velocity terms
Chen X.B. and Duan W.Y. 37
Formulations of low-frequency QTF by 0(M)) approximation
Chun.g J.Y., Nahm J.O.,. Kang HJ). and Kwon S.H... 41
-A novel experimental technique in Slamming
Colicchio G., Greco M. and Faltinsen O,M. 45
Influence of gaseous cavities m ship-hydrodynamic problems a simplified study
Delhommeau G., 'Noblesse F. and Guilb and M. 49 Simple analytical' approximation to a ship bow wave
1
-De S., and Mandal B.N. 53
Water wave scattering by two partially immersed barriers- an alternative method of solution
Diebold L. 57
Study of the Neumann-Kelvin problem for one hemisphere
Doctors L. J. 61
A test of linearity in the generation of ship waves
Duan W.V. and Dai Y.S. 65
Integration of the Time-Domain green function
Ducrozet G., Bonnefoy F., Le Touzé D. and Ferrant P. 69
Investigation of freak waves in large scale 3D Higher-Order spectral simulations
Eatock Taylor R. and Meylan M.H. 73
Theory of scattering frequencies applied to near-trapping by cylinders
Elkin J.D. and Yeung 11W. 77
Sway and roll hydrodyiamics of twin rectangular cylinders
Evans D.V. and Porter R. 81
Examples of motion trapped modes in two and three dimensions
Fitzgerald C.J. and McIver P. 85
Approximating near-resonant wave motion using a mechanical oscillator model
Forestier J.M. 89
Evolution equation of a potential flow with a free surface and moving solid boundaries
Gazzola T. 93
A shape optimisation technique for the Wagner problem
Gifioteaux J.C., Ducrozet G., Babarit A. and Clement A.H. 97
Non-linear model to simulate large amplitude motions : application to wave energy conversion
GreavesD. 101
Numerical simulation of breaking waves and wave loading on a submerged cylinder
GrueJ.
105Nonlinear wave-body interaction by a formulation in spectral space
Harter R., Abrahams I.D. and Simon M.J. 109
22 IWVVWFB, PIiMco, Croatia 2007
lafrati A. and Korobkin A.A. 113
Numerical analysis of initial stage of plate impact on water surface
KashiwagiM. 117
Reciprocity relations of waves generated by an antisymmetric floating body
Khabakhpasheva T.I. and Wu G.X. 121
Coupled compressible and incompressible approach for jet impact onto elastic plate
Klopman G., Dingemans M. W. and van Groesen B. 125
Propagation of wave groups over bathymetry using a variational Boussinesq model
Korobkin A. and Malenica . . 129
Steep wave impact onto elastic wall
Malenica .,Senjanovit I., Tomaevié S. and Stumpf E. ' . 133
Some aspects of lydroelastic issues in the design of ultra large container ships
Malleron N., Scolan Y.-M. and Korobkifl A.A. 137
Some aspects of a generalized Wagner model
Miloh T. . 141
Structural acoustics of a floating circular elastic plate.
Molihi B., Kimmoun 0. and Remy F. 145
Non-linear standing wave effects on the weather side of a wall with a narrow gap
Nabergoj R. and Prpié-Orië J. 149
A comparison of different methods for added resistance. predictiOn
Nam B-W. and Kim Y. ' 153
Effects of sloshing on the motion response of LNG-FPSO in waves
Newman J.N. - 157
Trapping structures with linear mooring forces
Noblesse F., Yang C. and Espinosa R. ' 161
Nearfield and farfield boundary-integral representations of free-surface flows
Finkser J.A. and Hermans AJ.
165A rotating wing for the generation of energy from waves'
Pistani K and Thiagarajan K. 169
Experimental campaign on a moored FPSO in complex bidirectional sea' states
Qiu W. and' Peng H. . 173
x
181
Scolan Y.M., Kimmoun 0., Branger H. and Remy F. 177
Nonlinear free surface motions close to a vertical wall Influence of a local varying bathymetry
Sturova I.V
Time-dependent hydroelastic response ofan elastic plate floating on shallow
water of variable depth
Sun H. and Faltinsen 0.M. 185
Hydrodynamic forces ona planing hull in forced heave or pitch motions in calmwater
--Taylor P.H., ZangJ., Walker A.G and Eatoèk --Taylor
R.'
189Second order neár-traping for multi-column structures and near-flat QTFS
Thompson I., Lintón C M. and Porter R. 193
A new approximation method for scattering by large arrays
Tuitman J. and van Aanhold H. 197
Using generalized modes fortime domain seakeeping calculations
Vanden-Broeck J.-M., Parau E. and Cooker M. 201
Three-dimensional capillary-gravity waves generated by moving disturbances
Zang J., Ning D., Liang Q., Taylor P.R., Borthwick A.G.L and EatockTaylor R. 203
A rotating wing
J.A. Pinkster,
Dept.A.J. Hermans, Deift
Introduction
This contribution deals with a concept for a wave energy conversion device which converts wave energy directly into rotational energy. This 'rotating wing' device was conceived based on the kinematics of a regular, long-crested wave. See Figure 1. In this figure the velocity vector in a point in the vertical plane is shown. In all such points, in deep water, the vector is constant in amplitude and rotates with the angular frequency of the wave. Consider a fixed horizontal shaft perpendicular to the plane of the figure with a lifting foil attached as shown in Figure 2. Given proper dimensions etc, the foil will experience a lift force perpendicular to the fluid velocity vector giving rise to a lift force which is perpendicular to the connection between the shaft and the foil. This lift force results in a moment around the shaft inducing rotation in the same direction as the rotating velocity vector. If the foil lags behind the rotating velocity vector, the angle of attack will increase thus increasing the lift force on the foil and the torque on the shaft. This constitutes a stable rotating system which locks on to the rotation frequency of the velocity vector and hence to the regular wave. In effect we have a
synchronous wave energy device. The energy is transmitted by a generator fixed directly to the shaft.
Wave direction
Figure 1: Kinematics in a regular wave
22 (WvVWFB, Plitvice. Croatia 2007
for the generation of
energy from waves
of Ship Hydromechanics, 3ME, TUDe1It <jo.pinkstergmail.com
Inst. of Applied Mathematics, EWI, TUDeIIt < ajh@ajhermans.eu
direction
of
rotation L
Figure 2 Principle of the Rotating foil
Initial model tests carried out at MARIN with a simple model of the foil showed that in
regular waves a weight could be lifted by a thin wire wound around the shaft and running over and overhead pulley. Based on these initial tests, a comprehensive analysis and detailed model tests were carried out by two MSc students , yan Sabben and C. Marburg (see ref 1 and ref 3). This contribution briefly summarises their work which to date has not been published. Finally a novel application of the rotating foil is introduced along with relevant model test results.
Theoretical analysis
The flow in a regular, long-crested wave arounda foil moving along a circular path around a
point in the vertical plane can be approximated from knowledge of the flow around a foil rotating with constant angular motion around the shaft in still water combined with the kinematics of the undisturbed regular wave . See also ref. 2.
Use is made of linearized potential flow described bya potential (phi) satisfying the Laplace
equation and the linearized free-surface boundary condition. The foil is modelled as a line vortex and the waves are perpendicular to an infmitely long foil. The problem is thereby reduced to two dimensions. Due to the assumed linearity, the total potential is the
superposition of the potential of the regular wave and the rotating foil. The complex potential
22- i/VL v-t' -'firuicE c o&ti: 2007
f(z, t) = Ø(x, y, t) + iyi(x,y,.t) of a vortex with position .c(t) moving under a free surface in
two dimensions is given by Wehausen & Laitone (ref. 4)
f(z,t) =
logZ+
' f5j
e_iz_(T)) sin [.J(t
-
r)1,dkdt
The first part is the potential of a vortex and of an additional vortex required to satisfy the kinematic free surface condition. The second part describes the radiated waves related to the pressure condition at the free-surface. The integral is evaluated for the following situations-:
Foil of small dimensions rotating in deep water on a circular path of small radius R with respebt to the wave length (kR small)
The disturbance of the foil is considered to be small so that the shed vorticity is conveyed with the undisturbed flow of the incident waves.
Using the above assumptions the following results are obtained,:
The foil does not create waves up-wave. Waves from the foil are only created in the down-wave direction
The energy absorbed by the device leads to. .a decrease. in the incident wave amplitude caii and higher harmonics of the fundamental wave frequency with amplitude can are generated. As shown in ref (1) , the difference in energy flux is:
F =
P[_2caiiccmcoswhere 7 is the phase difference between the incident and radiated first harmonic
component. The amplitudes can are:
22
nç2çfl0)(0)flR
e
g
n!The moment (torque) exerted on the shaft is equal to the lift force times the moment arm. The force depends on the circulation around 'the foil:
L=.pVXF
Experiments
Model tests were carried out in the High Speed Basin of MARIN (200 m x4 mx 3.6m) with a foil with a span of 1.5 m and a chord length of 0.10 m with a camber of0.022 rn. The thickness distribution was according to NACA 0015 See Figure 3.
The first tests that were carried out were tests in still water. The purpose of these tests was to
verify thetheoretical-prediction-that-wavesare-only:generatedirrone-dfrectioñ i.e. the
166
2
*0.02 0.0 -0.02 (mj .0.02 0.0 R=8Omm,y=.2oommraccto.135o 10 6-°° 14t harnioriic 2h. 3id h. O8...
4.
TheeFigure 4: Wave elevation records to either side of the foil rotating at 3.45 r/s
O-0 ICthefll4oflja
2nd herniae,,,
43---q 3tdvamonje
22nd IWWWFB, Plitvice, Croatia 2007
7.- 4O...
t
r0l0e
Figure 3 : Foil with end disks attached to a rotating shaft
direction corresponding with the direction of motion of the foil when in the highest point. See
above. The following figure shows thewave elevation records in location 3 and 4 shown in
Figure 3 for the foil rotating with constant frequency in still water. Higher harmonics can be seen in wave 4. Results for different frequencies are shown in Figure 5.
YShCft43l94mrn, XTErn 135°
Wave 3
Wave4
167
Frequency ( radls Frequency [rad/sJ
Figure 5 : Computed and measured harmonics of the foil rotating in still water
During tests in regular waves the torque exerted on the shaft was measured as well as the
168
rotation angle and the wave elevations up- and, down-wave. Some results are shown in Fig.6.
Run 1698, Yshafi = -235 mm, aTE = 1100, ..\ = 5 m, ( = 80mm
1J
Time (1/40s]
Figure 6: Wave elevations , foil position and shaft torque in a regular wave
In Figure 6 the dotted line is the incoming wave, the large solid line the down-wave elevation, the small amplitude harmonic is the foil position signal and the constant,just below zero the shaft torque. Noticeable is that the torque is almost constant with little or no higher
harmonics.
A final experiment concerns the application of the concept to a wave direction measuring device. Since the foil is always "down stream" , if the shaft of a short span version is attached
to a vertical,freely turning axis and a "rudder" used to connect foil and shaft, a system is
created that automatically seeks to position the rudder in the vertical plane of the flow. This property can be used to determine wave direction in a regular wave. The concept is shown in Fig. 7 on the left and right the measuring device based on the concept. Results of
measurements of wave direction in MARIN'S Wave & Current Basin are compared with prediction in Fig. 8. As can be seen, the measurements with the device follow the theoretical wave direction (snake wave maker with fixed phase difference between the flaps) very well.
20
-30
Figure 7: Device for measuring wave direction Figure 8 : Measured and adjusted wave direction
References
Sabben, van E. :"Velocity field of a rotating foil in still water and waves ". MSc. Thesis, Deift U of Techn. Deift ,1987
Hermans, A.J., Sabben, E. van ,Pinkster ,J.A. : "A device to extract energy from waves ", Applied Ocean Research. 1990, Vol. 12, No. 4
Marburg, C.: "Investigation on a Rotating Foil for Wave Energy Conversion ", MSc.
Thesis, Deift U. of Techn. Deift, 1994
Wehausen, J.V. and Laitone, E.V.: "Surface Waves",Handb. of Physics, Vol.9,1960
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