The Dynamics of a Novel Ocean Wave Energy Converter

Christopher A. Diamond, Bayram Orazov, Oliver M. O’Reilly, and Omer Savas

Department of Mechanical Engineering, University of California at Berkeley, USA

Carolyn Q. Judge

Department of Naval Architecture and Ocean Engineering, United States Naval Academy, USA

Nishanth Lingala and N. Sri Namachchivaya

Department of Aerospace Engineering, University of Illinois at Urbana Champaign, USA

Aims of Research

Our research features the development and analysis of a novel ocean waveenergy converter (WEC). One class of ocean wave energy converter is a buoywhich is resonantly excited by the ocean waves. A novel excitation methodis used with this class of system in order to amplify its energy harvestingcapabilities.

Seabed

Power take off (PTO)

Water surface

Inner float

Outer floatOuter float

The Novel Excitation System

t

y(t)

m(t)

a

b

c

d

µM

1

2

34

5

6

7

7

8

8

9

1: float

2: hollow cylinder

3: mid cylinder

4: upper flaps

5: lower flaps

6: sliding plates

7: added mass µM

8: water flow

9: water surface

The novel excitation scheme has several similarities with the well-known mechanical amplifi-cation produced by parametric excitation and the mechanics of pumping a swing. Variationsof the scheme are possible where mass is only added once per cycle rather than twice.

A Simple, Two Mass Model

F2 sin(

ωf t)

x2(t)

M2

c2 k2 ≈ 0 B

c3 k3

F1 sin(

ωf t)

M1

x1(t)

c1 k1

M1 (1 + µ)

M1 (1 + µ)

M1

M1

dx1/dt

x1

Current work on the wave energy converter features a two degree-of-freedom hybrid systemmodel with state-dependent switching:

[

m1x1m2x2

]

+ C

[

x1x2

]

+ K

[

x1x2

]

=

[

f1 sin (ωτ )f2 sin (ωτ )

]

, (1)

where

K =

[

κ1 + κ2 −κ2−κ2 κ3 + κ2

]

, C =

[

δ1 + δ2 −δ2−δ2 δ3 + δ2

]

. (2)

As a function of damping ζ = B+c2√kM2

, mass modulation µ, and dimensionless forcing frequency

ω = ωf/ω0, the dimensionless system power exhibits a complex topology, which can beseen in the figures below. Generally, mass modulation increases power across the topology,particularly near one of the resonance peaks.

0

1

2

3

0

1

2

30

2

4

6

8

10

ω

µ : 0.00

ζ

P

0

1

2

3

0

1

2

30

2

4

6

8

10

ω

µ : 0.44

ζ

P

0

1

2

3

0

1

2

30

2

4

6

8

10

ω

µ : 0.90

ζ

P

Non-deterministic parameters were computed using a computational fluid dynamics model.We are also working on analysis of the stochastic dynamics of oscillator models for energyharvesters.

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

ω

12 +

g2

1

λ = 0

0

0.8

1.2

1.2

1.4

1.6

2.0

F2sin(

ωft)

Prototype Design and Testing

Preliminary experiments have also been performed on a prototype of the WEC. These ex-periments are intended to examine the feasibility of the novel excitation method.

d

f ∆vRMSnoflaps ∆vRMS

flaps viRMSno flaps vi

RMSflaps

(Hz) (m/s) (m/s) (m/s) (m/s)

0.60 0.041 0.038 0.122 0.1180.64 0.059 0.065 0.132 0.1350.68 0.075 0.086 0.137 0.1380.72 0.117 0.118 0.151 0.1690.76 0.117 0.086 0.141 0.171

Future Work

The following issues associated with the excitation scheme are being re-searched:

•More realistic fluid-structure interaction models.

•Examination of stochastic excitation of models for the WEC.

•Optimization of the design of the water intake system and prototype testing.

Acknowledgments and References

This work was partially supported by the National Science Foundation under Grant No. 1000906. Dr. EduardoA. Misawa is the Program Director.

[1] Orazov, B., O’Reilly, O. M., and Savas, O., 2010. On the dynamics of a novel ocean wave energy converter.Journal of Sound and Vibration, 329(24), pp. 5058–5069.

[2] Orazov, B., O’Reilly, O. M., and Zhou, X., 2012. Forced oscillations of a simple hybrid system: Non-resonantinstability, limit cycles, and bounded oscillations. Nonlinear Dynamics, 67(2), pp. 1135–1146.

[3] Orazov, B., O’Reilly, O. M., and Savas, O., 2012. Experimental testing of a mass modulated ocean waveenergy converter prototype. ASME Journal of Offshore Mechanics and Arctic Engineering. Submittedfor publication.

[4] Namachchivaya, N. S., and Wihstutz, V., 2010. Almost sure asymptotic stability of scalar stochastic delayequations: Finite state Markov process. Stochastics and Dynamics, 12(2), 1150010.

[5] Lingala, N., Namachchivaya, N. S., O’Reilly, O. M., and Wihstutz, V., 2012. “Almost sure asymptoticstability of an oscillator with delay feedback when excited by finite-state Markov noise. Submitted forpublication.

[6] Wihstutz, V., and Namachchivaya, N. S., 2012. Asymptotic analysis of the Lyapunov exponent, the rotationnumber and the invariant measure for scalar delay differential equations perturbed by Markovian noise. Inpreparation.