8th GRACM International Congress on Computational Mechanics Volos, 12 July – 15 July 2015

MARINE PROPULSION IN WAVES BY FLAPPING-FOIL SYSTEMS

Kostas A. Belibassakis

School of Naval Architecture and Marine Engineering National Technical University of Athens

Heroon Polytechniou 9, Zografos 15773, Athens, Greece e-mail: kbel@fluid.mech.ntua.gr, http://arion.naval.ntua.gr/~kbel/

Keywords: Biomimetic propulsion in waves, Ship Hydrodynamics

Abstract. Flapping foils located beneath the hull of the ship are investigated as unsteady thrusters, augmenting ship propulsion in rough seas and offering dynamic stabilization. The foil undergoes a combined oscillatory motion in the presence of waves. For the system in the horizontal arrangement, the vertical heaving motion of the hydrofoil is induced by the motion of the ship in waves, essentially ship’s heave and pitch, while the rotational pitching motion of the foil about its pivot axis is set by an active control mechanism. For the detailed investigation of the effects of the free surface and waves potential-based panel methods have been developed, and the results are found to be in good agreement with numerical predictions from other methods and experimental data. Also, it has been demonstrated that significant energy can be extracted from the waves for propulsion. 1 INTRODUCTION

Biomimetic propulsion systems is subject of intensive investigation, since they are ideally suited for converting

environmental (atmospheric or sea wave) energy to useful thrust, succeeding efficiencies over 100%. Recent research and development results concerning performance of flapping foils and wings, supported also by extensive experimental evidence and theoretical analysis, have shown that such systems, operating under conditions of optimal wake formation, could achieve such high levels of propulsive efficiency; see, e.g., Triantafyllou et al (2000, 2004), Taylor et al (2010). On the other hand, the complexity of kinematics of flapping wings necessitates the development of sophisticated power transmission mechanisms and control devices, as compared to the standard marine propeller systems, preventing at present its application as the main or sole propulsion system of ships. Oscillating wings located beneath the ship’s hull are investigated as unsteady thrusters, augmenting the overall propulsion of the ship in the presence of waves. Initial attempts in this direction focused on the use of passively flapping wings to transform energy stored in ship motions to useful propulsive thrust, with simultaneous reduction of the motions of the ship; see Rozhdestvensky & Ryzhov (2003) for an extensive review and Naito & Isshiki (2005) for a review in flapping-bow wings on ship propulsion.

A main difference between a biomimetic propulsor and a conventional propeller is that the former absorbs its energy by two independent motions, the heaving and the pitching motion, while for marine propellers there is only rotational power feeding. In real sea conditions, the ship undergoes a moderate or higher-amplitude oscillatory motion due to waves, and the vertical ship motion could be exploited for providing one of the modes of combined/complex oscillatory motion of a biomimetic propulsion system. At the same time, due to waves, wind and other reasons, ship propulsion energy demand in rough sea is usually increased well above the corresponding value in calm water for the same speed, especially in the case of bow/quartering seas. In this work, we present results from the investigation in the framework of the project BIOPROPSHIP (http://arion.naval.ntua.gr/~biopropship/index_en.html) of the performance of actively controlled oscillating wings, located beneath the hull of the ship, examined as unsteady thrust-production mechanism, augmenting the overall propulsion system of the ship. The main arrangement is shown in Fig.1 and consists of a horizontal wing undergoing combined vertical and angular oscillatory motion. The vertical motion is induced by ship heave and pitch, while the wing self pitching motion about its pivot axis is actively set in terms of the vertical motion. A second arrangement has also been considered consisted of a vertical oscillating wing beneath the hull of the ship. In this case, the transverse oscillatory motion is induced by ship rolling and swaying, and the pitching motion of the wing about its pivot axis is properly selected in order to produce thrust with significant generation of anti-rolling moment for ship stabilization. First results, selectively presented below, indicate that high levels of efficiency are obtained in sea conditions of moderate and higher severity, under optimal control settings.

K.A. Belibassakis

Figure 1. (a) Ship hull equipped with a flapping wing located below the keel, at a forward station. Geometrical details of the flapping wings are included in the upper subplot. The main flow direction relative to the flapping wings is indicated by using an arrow. Black arrows indicate ship-hull oscillatory motion and red ones the actively controlled (pitching) motion of the wing about its pivot axis, for which only a quite small amount of energy is provided. (b) Same hull with a flapping wing used in experimental investigation of the system in the towing tank of NTUA.

In recent works by Belibassakis & Politis (2013) and Filippas & Belibassakis (2014), specialized BEMs have been developed and applied to numerically simulate and study novel biomimetic systems based on oscillating hydrofoils operating in the presence of waves and currents, examined for extraction and exploitation of this kind of renewable marine energy resources for ships. It has been demonstrated by previous and ongoing research that flapping foil thrusters operating in waves, while travelling at constant forward speed, operate very efficiently, and could be exploited for augmenting the overall ship propulsion in waves by directly converting kinetic energy from ship motions to thrust; see, also Bockmann & Steen (2014). Predictions are found to be in agreement with CFD methods and experimental data; see e.g. De Silva & Yamaguchi (2012). In this work we examine further the possibility of energy extraction under random wave conditions using active pitch control. More specifically, we consider operation of the foil in head waves characterized by a given frequency spectrum, corresponding to specific sea states. The effects of the wavy free surface are taken into account through the satisfaction of the corresponding boundary conditions. Numerical results concerning thrust coefficient are shown, indicating that significant efficiency can be obtained under optimal operating conditions. The present analysis has been verified by recent experimental work; see, also Bockmann (2015). Thus, the present method can serve as a useful tool for the design, assessment and optimum control of such systems extracting energy from sea waves and augmenting marine propulsion. 2 ACTIVE PITCH CONTROL OF FLAPPING PROPULSOR IN WAVES

The main parameter controlling the unsteady thrust production of flapping systems, advancing at forward speed U in

unbounded liquid, is the Strouhal number 0

2 /St f h U= , where / 2f ω π= is the frequency and0h the amplitude of

vertical (heaving) motion, while the Reynolds number is used to calculate viscous drag corrections. Also, the phase difference ψ between the two oscillatory motions is very important as far as the efficiency of the thrust development by the flapping system is concerned. In the simple harmonic thrust producing case it usually takes the value ψ =90o (see, e.g., Anderson et al 1998, Schouveiler et al 2005), in which case the required torque for wing pitching is found to be minimum when the pivot axis for the angular motion of the wing is located around 1/ 3 1/ 4÷ chord length from the

leading edge. As a result of the simultaneous heaving and pitching motions of the biomimetic wing, in the case of horizontal arrangement (Fig.1), the instantaneous angle of attack is

( ) ( ) ( ) ( ) ( )1 1tan /H

t t t U dh dt tα θ θ θ− −= − = − . (1)

For relatively low amplitudes of harmonic motion and optimum phase difference ψ =90o, the angle of attack becomes

( ) ( ) ( )1

0 0cost U h tα ω θ ω−= − , which can be equivalently achieved by setting the pitch angle ( )tθ proportional to

( )Htθ as follows

( ) ( )1 1tan /t w U dh dtθ − −= , and thus, 0 0

/w h Uθ ω= . (2)

(b) experimental set up U

θ

h

K.A. Belibassakis

In contrast to passively controlled flapping-wing thrusters (see, e.g., Murray & Howle 2003, Bøckmann &Steen 2013)

in the present work an active system is studied based on the above parameter w, introduced in Politis & Politis (2014). The latter pitch control parameter usually takes values in 0<w<1. Decreasing the value of 1-w the maximum angle of attack is reduced and the wing operates at lighter load. On the contrary, by increasing the above parameter the wing loading becomes strong and could lead to leading edge separation and dynamic stall effects. In the present work we exploit the above result as an active pitch control rule of the flapping-wing thruster, not only for purely harmonic

oscillations, but also in the general multichromatic case, applied to the time history of vertical oscillatory motion ( )h t of

the wing. Thus, the instantaneous angle of attack, Eq.(1), takes the form (Belibassakis & Politis 2013)

( ) ( ) ( )1 11 tan /t w U dh dtα − −= − . (3)

In the case of the biomimetic system under the calm or wavy free surface, additional parameters enter into play, as

Froude number(s) ( )1/2/F U gL= , with L denoting the characteristic length(s) and g is gravitational acceleration, as

well as frequency parameter(s) associated with the incoming wave, as 2 /L gµ ω= and /U gτ ω= , the latter being

used to distinguish subcritical ( )1/ 4τ < from supercritical ( )1/ 4τ > conditions; see Nakos & Sclavounos (1990).

3 SHIP DYNAMICS COUPLED WITH UNSTEADY FLAPPING THRUSTER

We consider a ship in waves advancing at constant forward speed U . In the present approach we use the equations of motion derived in the body-fixed frame of reference linearized by assuming small oscillatory amplitudes. Seakeeping analysis in the frequency domain is used to obtain the motions and responses of the examined system (ship and flapping wing) in the vertical plane; see also Belibassakis and Politis (2013). The coupled equation of heave and pitch motion of

the ship (with corresponding complex amplitudes 30ξ and

50ξ ) is as follows (taking the origin at the centre of gravity):

33 30 35 50 30 30D D F Xξ ξ+ = + , (4)

53 30 55 50 50 50,D D F Xξ ξ+ = + (5)

where

33D ( )( )2

33 33 33en enm a i b cω ω= − + + + , ( )( )2

35 35 35 35 35en enD a I i b c pω ω= − + + + + , (6)

( )( )2

53 53 53 53 53en enD a I i b cω ω= − + + + , ( )( )2

55 55 55 55 55en enD a I i b cω ω= − + + + , (7)

jka and , , 3,5

jkb j k = , are added mass and damping coefficients, m is the total mass of the ship and wing and

enp i Umω= − is a Coriolis term. The involved hydrostatic coefficients are

33 WLc gAρ= , ( )35 53 f WL

c c g x Aρ= = − and

55 Lc m gGM= , where

WLA is te aterline area and

fx denotes its longitudinal center. The inertia coefficients involved

in the above system are 2

55 yyI mR= and

35 53 GI I m X= = − , where

GX is the long-center of gravity and

yyR the radius

of gyration with respect to the transverse axis. For simplicity, only head waves (β=180o) are considered here as excitation of the hull oscillatory motion. The frequency of encounter (relative frequency) is

enkUω ω= + , (8)

where k is the wavenumber of the incident waves ω is the absolute frequency, g is the acceleration of gravity and U the

ship speed. The terms0, 3,5

jF j = appearing in the right-hand side of Eqs.(4,5) are the Froude-Krylov and diffraction

vertical force and pitching moment (about the ship y-axis) amplitudes, respectively. Furthermore, the terms 0, 3,5

jX j =

denote additional force and moment amplitudes due to the operation of the horizontal flapping wing as an unsteady

thruster. The latter are dependent on heave ( )3ξ and pitch ( )5ξ responses of the ship, as well as to the incoming wave

field. In general, due to the oscillatory thrust developed by the foil, ship responses are also coupled with surge motion. However, considering the large mass of ship, in conjunction with installation of energy storage and power feed smoothing systems, at first level of approximation that effect is neglected..

K.A. Belibassakis

Hydrodynamics of lifting surfaces attached to the hull, coupled with ship dynamics, have been studied extensively for

design and optimisation purposes. For example, lifting appendages are applied to improve the calm water performance and reduce the unwanted responses in waves, see, e.g. Sclavounos & Huang (1997). Other practical applications are trim tabs attached to the stern of high-speed vessel so as to reduce the resistance in calm water (Cusanelli & Karafiath 1997) and passive and active foils used as anti-rolling stabilizers (e.g., Naito & Isshiki 2005). In the context of 3D BEM applications, Sclavounos & Borgen (2004) developed a panel method in order to study the seakeeping performance of a high-speed monohull with attached foils. Furthermore, Chatzakis & Sclavounos (2006) studied the problem of motion control of marine vehicles in rough seas coupled with the problem of dynamic positioning, using active foil systems. Developments and applications of control theory for marine vessels are extensively discussed in Fossen (2002). The complexity of the selected model depends upon the underlying physics, the properties of the controller and the desired performance of the controlled system, see, e.g., Sclavounos (2006), Thomas & Sclavounos (2007).

In the present work we exploit the approach developed in Belibassakis and Politis (2014) and we use a simplified

lifting-line model to derive expressions of the flapping wing forces ( )ξX in Eqs.(4) and (5). These forces are separated

into two parts:

( ) ( ) ( )ξ ξA B INC

ϕ= +X X X , where 30 50

T

X X = X and ξ

30 50

T

ξ ξ = . (9)

The first part is dependent on the oscillatory ship amplitudes and the second one on the incoming wave potential INCϕ .

The first part produces modifications of the hydrodynamic coefficients and the last part adds on the Froude-Krylov and diffraction forces in the right-hand side; see also Sclavounos & Borgen (2004).

In the examined case the dynamic angle of attack of the flapping wing is approximated by:

( ) ( ) ( ) ( )5

1 INCt t t tU z

ϕα ξ ε θ

∂≈ − + + −

∂, (10)

where ( )tθ denotes the flapping wing self-pitch angle (the controlled variable) with respect to its pivot axis. The second

term in the right-hand side is due to the vertical foil motion

( ) ( )1 dh tt

U dtε ≈ , (11)

where ( ) ( ) ( )3 5wingh t t x tξ ξ=− + denotes the oscillatory motion of the ship at the longitudinal position

wingx of the foil.

As it has been suggested by Belibassakis & Politis (2013) the controlled pitch angle is set proportional to the angle ε ,

i.e. ( ) ( )t w tθ ε= , with the pitch control parameter w ranging from 0 to 1, and thus, the angle of attack finally becomes

( ) ( ) ( ) ( )5

11 INCt t w t

U z

ϕα ξ ε

∂= − + − +

∂. (12)

In the case of wings of relatively large aspect ratio unsteady lifting line theory can be used to obtain its dynamic responses, and the references cited there. In the present work, under the additional assumption of flapping wings operating at relatively low reduced frequencies, the calculation of forces is based on quasi-steady approximation, in conjunction with spanwise integration of sectional lift forces, resulting in the following expressions

2 3

30

1

2

D

w LX U S Cρ= ( )2 2 20

0 30,2

1

2 2 4

D R

w L B INC

Gc hARU S C G X

AR Uρ α ω ϕ≈ = + +

+, (13)

2 3 2 3

50

1 1

2 2

D D

R w M w L wingX U c S C U S C xρ ρ= −

30wingx X≈− , (14)

where Rc denotes the root chord of the foil, ( )30,B INC

X ϕ is the contribution of the incoming wave and

2

2w

ARG U S

ARχπρ=

+. In the latter expression, χ denotes an empirical correction factor that could be calculated by

comparing the quasi-steady lifting line estimations with a-posteriori predictions by more accurate 3D panel methods of the responses of the oscillatory wing, following the same combined forward and oscillatory motion; see, e.g., Belibassakis & Politis (2013, Fig.11). Using the above in Eqs. (4) and (5), we obtain the following modifications of the system (hull and flapping wing) added mass, damping and restoring-force coefficients due to the operation of the horizontal flapping wing thruster:

K.A. Belibassakis

( )233/ 4

Ra Gc Uδ = − , ( )235 53

/ 4wing R

a a x Gc Uδ δ= = , ( )2 2

55/ 4

wing Ra x Gc Uδ =− , (15)

( )331 /b G w Uδ = − , ( )35 53

1 /wing

b b G w x Uδ δ= =− − , ( ) 2

551 /

wingb G w x Uδ = − , (16)

35c Gδ = ,

55 wingc G xδ = − . (17)

Finally, the following expressions are derived concerning the part ( )B INCϕX of the hydrodynamic vertical force and

moment due to the flapping wing which is not dependent on the ship-motion amplitudes:

( ) ( )30/ expX G i U kd ikxω= − + , (18)

( ) ( )50/ exp

wingX G x i U kd ikxω= − − + , (19)

where z d=− denotes the mean position below the free surface of the flapping wing. Finally, the thrust coefficient is obtained from the spanwise integration of sectional lift forces projected on the longitudinal x-axis, as follows

( ) ( )*2

1sin

20.5

X

T L

ww

F ARC c y C dy

AR SU Sθ

ρ= =

+ ∫ , (20)

where ( );L LC C y α= is the lift coefficient depended on the quasi-steady angle of attack and

*θ θ α= + , if the

sectional lift is assumed normal to the instantaneous inflow, or *θ θ= , if it is assumed approximately normal to the

chord line. In the present work which is based on the quasi-steady model described above induced drag effects have been approximately neglected. Enhanced predictions are obtained by means of unsteady lifting line model or 3D nonlinear unsteady panel methods (Politis 2011, Belibassakis & Politis 2013).

4 SHIP RESPONSES IN WAVES AND PERFORMANCE OF THE FLAPPING WING PROPULSOR

The preceding analysis permits us to calculate the ship responses including the effect of the flapping wing operating as an unsteady thruster and compare with the corresponding seakeeping responses concerning the bare hull without the wing. For demonstration purposes, we consider a series 60-Cb0.60 ship hull form, with main dimensions length L=50m, breadth B=6.70m, draft T=2.80m. The exact value of the block coefficient at the above draft is Cb=0.533. From hydrostatic analysis, the immersed volume in the mean position is 500m3, and the corresponding displacement in salt water, which equals the mass of the ship, is estimated to be ∆=512tn. Moreover, in the above draft, the wetted area of the hull is calculated Swet=380m2, the waterplane area AWL=225m2, the center of flotation xf = -1.15m (LCF aft midship), the longitudinal moment of inertia of the waterplane is IL=28800m4, and the corresponding metacentric radius BML=57.6m. The vertical center of buoyancy is KB=1.55m (from BL), and the longitudinal position is LCB=-0.266m. For simplicity, we consider the longitudinal center of gravity to coincide with the center of buoyancy, i.e. XG=-0.266m (aft midship), YG=0, and KG=1.80m (from BL), and thus, the metacentric height in the above condition are estimated to be GM=0.9m.

Also, the longitudinal metacentric height in the above condition is estimated to be L L

GM BM≈ . Finally, the radii of

gyration about the x-axis and y-axis, respectively, are taken Rxx=0.32B, Ryy=0.23L (for definition of the above quantities see, e.g., Lewis 1989). The flapping wing propulsor is located at a distance xwing=15m fore the midship section (station 8 of the ship), at a depth d=7m below WL. The half-wing planform shape is trapezoidal and its span is s=6m. Moreover, the root and tip chords of the wing have lengths cR=1m, cT=0.5m, respectively, and the leading edge sweep angle is Λ=9.4deg (Fig.1). On the basis of the above, the wing planform area is Sw=4.5m2, and its aspect ratio AR=8. The wing sections are symmetrical NACA0012. A low-order Rankine source based BEM, in the frequency domain, is used to obtain the seakeeping analysis of the hull in waves, and to treat the steady problem of the ship advancing with mean forward speed. In both cases, the four-point, upwind finite difference scheme by Dawson (1997) has been used to approximating the horizontal derivatives involved in the (linearized) free surface boundary condition. Details concerning the application of the above method and examples, in the case of the steady problem and in the presence of additional effects from lifting appendages, can be found in Belibassakis (2011) and Belibassakis & Politis (2013).

In Fig.2 results are presented concerning the response of the ship in head seas. To be more specific, in Fig.2(a) the normalized heave response with respect to the incident wave amplitude of the ship is plotted, without the operation of the wing, for various values of the non-dimensional wavelength and Froude numbers.

K.A. Belibassakis 5

Fn Fn

Figure 2. (a) Heave ( )30/Aξ and (b) pitch response ( )50

/ kAξ of the examined ship hull against non-

dimensional wavelength λ/L and Froude numbers. Comparison of (c) heave and (d) pitch responses for ship speed U=5.5m/s, with (bold line) and without (dashed line) the operation of the flapping wing thruster.

The corresponding, ship-pitch response is shown in Fig. 2(b). To illustrate the effect of foil operation, in Figs. 2(c) and 2(d), the same responses are presented in the case of Froude number Fn=0.25 using dashed line. The modified responses taking into account the coupled ship-flapping wing dynamics are overplotted in the same figures using a thick solid line. We observe a significant reduction of the ship heaving motion, especially in the vicinity of the resonance condition. This result is indicative of the extraction of energy from ship motion by the flapping wing. In the case of ship pitch motion, the operation of the flapping wing propulsor leads to reduction of the response, especially for wavelengths longer than the ship length. Thus, the operation of the examined unsteady thruster extracts energy from the waves offering also dynamic stabilization. An extra effect, strongly connected with the reduction of ship responses, is the expected drop of the added wave resistance of the ship. Indicative results concerning the latter additional benefit have been provided in Belibassakis & Politis (2013).

As an example, the thrust augmentation achieved by the operation of the horizontal flapping wing propulsor, in head waves, is illustrated in Figs3, as calculated by the present method. In particular, we consider the ship and flapping wing of Fig.1(a) to travel at constant speed U=10.6kn, in head seas (β=180deg) corresponding to significant wave height Hs=5m, and peak period Tp=11s, corresponding to sea state 5.

(a) (b)

(c) (d)

K.A. Belibassakis

Figure 3. Simulation of the system operating in sea state 5. Results plotted at various instants in one modal period. In the right subplots the distribution of the unsteady pressure coefficient on the flapping foil, located at station xwing =0.4L (with respect to the midship section), at the same instants is plotted, as calculated by the present method.

K.A. Belibassakis

Figure 4. Responses of ship with horizontal flapping wing operating in head seas at ship speed U=10.6kn (F=0.25). (a) Vertical ship motion at station 8 without (solid line) and with (dashed line) the effect of the flapping wing. (b) Vertical wave velocity at the flapping wing. (c) Calculated ship pitch (dashed line) and angle of attack (solid line) at the flapping wing, using w=0.5. (d) Thrust production by the flapping wing (time history). The time average is calculated to be 2900kp and is indicated by using dashed line.

Numerical simulation of the system is presented in Figs. 3 and 4. Results have been obtained using pitch control parameter w=0.5 and setting the pivot-axis concerning the self-pitching motion of the flapping foil at distance c/3 from the leading edge. In particular, in Fig.5 the profile of the ship travelling in random waves and positioned according to the response of the coupled ship-flapping wing system is shown at five instants within a time interval corresponding to one modal period. The hydrofoil is located at forward station xwing =0.3L with respect to the midship section of the ship. In the same figure the trailing vortex curve modelling the foil's wake is plotted, including the calculated dipole intensity (potential jump) on the vortex sheet, which is illustrated by using arrows normal to the wake curve with length proportional to the local dipole strength. The latter result is associated with the memory effect of the generated lifting flow around the flapping foil operating in random incident waves. Moreover, in the right subplots of Fig.3 the instantaneous distribution of the pressure coefficient on the hydrofoil, at the same time instants as the plots to the right, as calculated by the present method. From the calculated sectional pressure distributions, lift and thrust components, associated with the flapping thruster performance, are obtained at each time step by integration.

The results shown in the first subplot of Fig.4(a) concerns the vertical motion at St.8 of the ship, where the horizontal flapping wing is arranged (xwing =0.3L). The second subplot (Fig.4b) shows the incident wave velocity at the same location, and in the next subplot (Fig.4c) the calculated time series of ship pitching angle together the angle of attack at wing sections are plotted. In the final subplot the thrust (kp) produced by the horizontal flapping foil is shown, as calculated by setting the control pitch parameter w=0.5. We observe in the last subplot of Fig.10(d) that the thrust oscillations produced by the horizontal flapping wing in the above sea condition are in the interval 0-20000kp, having an average value of 2900kp which is indicated by using dashed line. Similar analysis for the ship with horizontal flapping thruster travelling in the same sea state with increased speed U=12.9kn leads to lower value of mean thrust 2000kp, a drop which is attributed to the reduction of mean and maximum angle of attack in this case.

(d)

(c)

(b)

(a)

K.A. Belibassakis

Further details concerning the performance examined system in waves can be found in Belibassakis & Politis (2013), Filippas & Belibassakis (2014) and Belibassakis & Filippas (2015). Also, the examination of active and passive pitch-controlle flapping wing propulsors and their effects is presented in Tsarsitalidis et al (2015) and Tsarsitalidis & Politis (2015). Finally, systematic data concerning flapping wing propulsor design are available in Politis & Tsarsitalidis (2014).

6 CONCLUSIONS

The performance of horizontal flapping wings located beneath the hull of the ship is investigated for augmenting ship propulsion in waves and offering dynamic stabliztion in rough seas. The wing undergoes a combined heaving and pitching oscillatory motion, while travelling at constant speed in the presence of waves. In the horizontal arrangement, the vertical wing motion is induced by ship heave and pitch. The self-pitching motion of the wing about its pivot axis is actively controlled in order to produce thrust, with significant reduction of responses and added wave resistance. Ship flow hydrodynamics are modeled in the framework of potential theory using Rankine source-sink formulation, and ship responses are calculated taking into account the additional forces and moments due to the above unsteady propulsion systems. Numerical results are presented indicating significant thrust produced by the examined biomimetic system and reduction of ship responses over a range of motion parameters. Thus, the present method, after experimental verification, which is currently carried out in the towing tank of Ship and Marine Hydrodynamics Laboratory of National Technical University of Athens, can serve as a useful tool for the assessment, preliminary design and control of the examined thrust-augmenting devices, enhancing the overall performance of a ship in waves. In the same direction, application of more elaborate control methods, including feedback control, would be beneficial for optimization of its performance. Finally, the described model permits extension to various directions, as e.g., the inclusion of various non-linear effects (waves and ship hydrodynamics, dynamic stall) and consideration of hydroelasticity effects due to wing(s) flexibility.

ACKNOWLEDGEMENTS

This research has been co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) 2007-2013: Research Funding Program ARISTEIA - project BIO-PROPSHIP: «Augmenting ship propulsion in rough sea by biomimetic-wing system».

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