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Design, implementation, and power estimation of a lab-scale flapping-type turbine

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Abstract

A lab-scale flapping-type turbine with a semi-passive activation mode has been designed and implemented. A non-linear dynamic model, developed in our previous work, is validated by a series of experiments along with computational fluid dynamics (CFD) simulations. Previously, the dynamic model was used only to estimate the dynamic response of a flapping-type turbine. In this work, the applicability of the dynamic model is extended to estimate the hydrodynamic forces, extracted power, and efficiency. It was demonstrated from a comparison of the CFD results and measured values that the dynamic model based on a quasi-steady approach estimates the aforementioned performance parameters of measurements well in cases particularly with a low effective angle of attack, thus demonstrating the usefulness of the dynamic model for a flapping-type turbine at an early stage.

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Abbreviations

\(\bar{c}\) :

Chord length of the hydrofoil, m

B :

Span of the hydrofoil, m

x p :

Pitching axis location from the leading edge, c

ψ :

Flapping angle, °

θ :

Pitching angle, °

l :

Flapping arm length, m

m :

Mass of the flapping arm and or hydrofoil, kg

V :

Volume of the flapping arm and or hydrofoil, m3

FB :

Buoyancy force of the flapping arm and or hydrofoil, N

W:

Weight of the flapping arm and or hydrofoil, N

x l :

Center of Mass location of the flapping arm from the flapping axis, m

x c :

Center of Mass location of the hydrofoil from the leading edge, m

\(O(x,y,t)\) :

Real coordinate system

\(O'(x',y',t')\) :

Image coordinate system

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{C}\) :

Transformation matrix

c x :

Transformation coefficient of the x-axis

c y :

Transformation coefficient of the y-axis

c t :

Transformation coefficient of the time

x {A,B,P,Q,R} :

Position of marker A,B,P,Q,R at the x-axis

y {A,B,P,Q,R} :

Position of marker A,B,P,Q,R at the y-axis

s N :

Fitting function with N number of linear combination of sine and cosine functions

a n :

N-th coefficient of the sine function

b n :

N-th coefficient of the cosine function

V :

Far field inflow velocity, m s−1

V f :

Induced or deflected flow velocity, m s−1

W :

Relative flow velocity, m s−1

I:

Mass moment of inertia of the flapping arm and the hydrofoil about the flapping axis, kg.m2

Ig :

Equivalent mass moment of inertia of the gearbox about the driving gear axis, kg.m2

\(\dot{\psi }\) :

Angular speed of the flapping arm, rad s−1

\(\ddot{\psi }\) :

Angular acceleration of the flapping arm, rad s−2

γ :

Deflection angle of the flow, °

ρ :

Density of the water, kg.m−3

C L :

Lift coefficient of the hydrofoil

C D :

Drag coefficient of the hydrofoil

C M :

Moment coefficient of the hydrofoil

S :

Projected surface area of the hydrofoil, m2

C :

Damping coefficient of the transmission system, N m s

F x :

Horizontal force, N

F y :

Vertical force, N

L :

Lift force, N

D :

Drag force, N

Τ :

Measured holding torque, N.m

M c/4 :

Pitching moment, N.m

M A :

Mathematical holding torque in the dynamic model, N m

M LD :

Moment about the flapping axis due to lift and drag, N m

M H :

Total moment about the flapping axis, N m

Re:

Reynolds number

Υ:

Kinematic viscosity, m2 s−1

d:

Maximum swept distance of the hydrofoil, m

P(t) :

Measured instantaneous power, W

Ω(t) :

Measured instantaneous angular velocity of the output shaft, rad s−1

P F :

Available power from the flow stream, W

P E (t):

Measured instantaneous extracted power at the output shaft, W

P H (t):

Instantaneous generated power due to pure hydrodynamic forces, W

P c/4 (t):

Instantaneous power due to pitching moment, W

\(\bar{P}\) :

Averaged extracted power, W

\(\bar{P}_{H}\) :

Averaged hydrodynamic power, W

Η :

Power extraction efficiency, %

η H :

Hydrodynamic power efficiency, %

f* :

Reduced frequency

ψ m :

Measured flapping angle, °

ψ e :

Estimated flapping angle, °

ψ reference :

Reference flapping angle (CFD or measured), °

α :

Effective angle of attack, °

V x :

Horizontal velocity at the pitch axis, m s−1

V y :

Vertical velocity at the pitch axis, m s−1

P x :

Power due to horizontal force component, W

P y :

Power due to vertical force component, W

TBi :

I-th timing belt

Gi :

I-th gear

CW:

Clock wise rotational direction of the output shaft

CCW:

Counter clock wise rotational direction of the output shaft

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Acknowledgments

This work was a part of a project entitled the “Development of Active-Controlled Tidal Stream Generation Technology” funded by the Ministry of Oceans and Fisheries, Korea (20110171) and a part of a project entitled the “Core Technology Development for Harnessing Ocean Energy” funded by Korea Institute of Ocean Science and Technology (PE99323).

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Correspondence to Jin Hwan Ko.

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Sitorus, P.E., Le, T.Q., Ko, J.H. et al. Design, implementation, and power estimation of a lab-scale flapping-type turbine. J Mar Sci Technol 21, 115–128 (2016). https://doi.org/10.1007/s00773-015-0336-z

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