WAVE ENERGY UTILIZATION Antnio F. O. Falco Instituto Superior - - PowerPoint PPT Presentation

Università degli Studi di Firenze, 18-19 April 2012

WAVE ENERGY UTILIZATION

António F. O. Falcão

Instituto Superior Técnico, Universidade Técnica de Lisboa

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Part 3 Wave Energy Conversion Modelling

• Introduction.
• Oscillating-body

dynamics.

• Oscillating-Water-Column

(OWC) dynamics.

• Model testing in wave

tank.

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Steps in the development of a wave energy converter:

• 1. Basic conception of device
• inventor(s)
• new patent or from previous concept
• 2. Theoretical modelling (hydrodynamics,

PTO, control,…)

• evaluation (is device promising or not?)
• optimization, control studies, …
• requires high degree of specialization

(universities, etc.)

Introduction

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

• 3. Model testing in wave tank
• to complement and validate the

theoretical/numerical modelling

• scales 1:100 (in small tanks) to 1:10 (in very

large tanks)

• essential before full-sized testing in real sea
• 4. Technical demonstration: design, construction

and testing of a large model (~1/4th scale) or full- sized prototype in real sea:

• the real proof of technical viability of the system
• cost: up to tens of M$

1/4 scale

• 5. Commercial demonstration: several-MW plant

in the open sea (normally a wave farm) with permanent connection to the electrical grid.

Introduction

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Theoretical/numerical hydrodynamic modelling

• Frequency-domain
• Time-domain
• Stochastic

In all cases, linear water wave theory is assumed:

• small amplitude waves and small body-motions
• real viscous fluid effects neglected

Non-linear water wave theory may be used at a later stage to

investigate some water flow details.

Introduction

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Frequency domain model Basic assumptions:

• Monochromatic (sinusoidal) waves
• The system (input  output) is linear

Advantages:

• Easy to model and to run
• First step in optimization process
• Provides insight into device’s behaviour

Disadvantages:

• Poor representation of real waves (may be overcome by superposition)
• Only a few WECs are approximately linear systems (OWC

with Wells turbine)

• Historically the first model
• The starting point for the other models

Introduction

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Time-domain model

Basic assumptions:

• In a given sea state, the waves are represented by a spectral distribution

Advantages:

• Fairly good representation of real waves
• Applicable to all systems (linear and non-linear)
• Yields time-series of variables
• Adequate for control studies

Disadvantages:

• Computationally demanding and slow to run

Essential at an advanced stage of theoretical modelling

Introduction

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Stochastic model

Basic assumptions:

• In a given sea state, the waves are represented by a spectral distribution
• The waves are a Gaussian process
• The system is linear

Advantages:

• Fairly good representation of real waves
• Very fast to run in computer
• Yields directly probability density distributions

Disadvantages:

• Restricted to approximately linear systems (e.g. OWCs with Wells turbines)
• Does not yield time-series of variables

Introduction

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Most wave energy converters are complex (possibly multi-body) mechanical systems with several degrees of freedom. We consider the simplest case:

• A single floating body.
• One degree of freedom: oscillation in heave

(vertical oscilation).

Damper Spring Buoy PTO

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Damper Spring PTO

m x Basic equation (Newton):

) ( ) ( t f t f x m

m h

   

PTO

• n wetted

surface excitation force (incident wave) radiation force (body motion) = hydrostatic restoring force (position) m r d

f gSx f f x m       

          x gS f f f f

hs r d h



S

Cross-section

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Frequency-domain analysis Oscillating-body dynamics

• Sinusoidal monochromatic waves, frequency
• Linear system



INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

A and B to be computed (commercial codes WAMIT, AQUADYN, ...) for given ω and body geometry.

x C Kx f m     Linear spring Linear damper

Damper Spring PTO

m x

Damper Spring PTO

m x

m r d

f gSx f f x m       

x B x A f r      

mass added  A damping radiation  B

d

f x K gS x C B x A m       ) ( ) ( ) (     mass added mass radiation damping PTO damping buoyancy PTO spring Excitation force

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

K gS C B i A m F X

d

          ) ( ) (

2

• Regular waves
• Linear system

t i d d t i

e F f e X t x

 

  , ) (

   

t i d d t i

e F f e X t x

 

Re , Re ) (  

• r simply

d

f x K gS x C B x A m       ) ( ) ( ) (     Method of solution:

) sin cos ( t i t e

t i

 



  amplitudes complex general in are , : Note

d

F X

geometry body and given for computed be to ) ( amplitude wave     

d

F

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Power = force  velocity Time-averaged power absorbed from the waves :

2 2

2 2 8 1 B F X i B F B P

d d

   

K gS C B i A m F X

d

          ) ( ) (

2

Note: for given body and given wave amplitude and frequency ω, B and are fixed.

d

F

Oscillating-body dynamics

m K

m K  

B F X i

d

2

0 

 A m K gS      C B 

Resonance condition Radiation damping = PTO damping

P

Then, the absorbed power will be maximum when :

= 0

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

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Capture width L : measures the power absorbing capability

• f device (like power coefficient of wind turbines)

E P L 

= absorbed power

P

E = energy flux of incident wave per unit crest length For an axisymmetric body oscillating in heave (vertical

• scillations), it can be shown (1976) that

  2

max

E P 

• r

  2

max

 L

593 . 

P

C

For wind turbines, Betz’s limit is

Note: may be larger than width of body

max

L

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Oscillating-body dynamics

  2  

• Max. capture

width

Axisymmetric heaving body Axisymmetric surging body

Incident waves Incident waves

wave wave INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

5 7.5 10 12.5 15 17.5 20 T 0.2 0.4 0.6 0.8 1

P P

x a m

2 1

*        a g T T

Example: hemi-spherical heaving buoy of radius a

5 . *  C

2 *  C 5 *  C

If T = 9 s

m 22

• pt

 a

max

P P *

2 1 2 5

  g a C C 

Dimensionless PTO damping Dimensionless wave period

No spring, K = 0

for

max

P P 

6 *

2 1

        a g T T

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Oscillating-body dynamics

How to increase the resonance frequency of a given “small” floater?

Wavebob, Ireland Attach a deeply submerged body.

A m K gS     

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Time-domain analysis

• Regular or irregular waves
• Linear or non-linear PTO
• A.F. de O. Falcão, “Modelling and control of oscillating-body wave energy converters with

hydraulic power take-off and gas accumulator”, Ocean Engineering, vol. 34, pp. 2021-2032, 2007.

• A.F. de O. Falcão, “Phase control through load control of oscillating-body wave energy

converters with hydraulic PTO system”, Ocean Engineering, vol. 35, pp. 358-366, 2008.

• May be require significant time-computing
• Yields time-series
• Essential for control studies

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Time domain

added mass

) , , ( ) ( ) ( ) ( ) ( ) ( ) ( t x x f d x t L t x gS t f t x A m

m t d

          



  

   

PTO radiation hydrostatic excitation forces from () and spectral distribution (Pierson-Moskowitz, …)





n n d d

t f t f ) ( ) (

,

Equation (1) to be numerically integrated

(1)

     d t B t L sin ) ( 2 1 ) (







memory function

Damper Spring PTO

m x

Damper Spring PTO

m x

Oscillating-body dynamics

From Fourier transform techniques:

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

HP gas accumulator LP gas accumulator Cylinder Valve

B A

Buoy Motor

Example: Heaving buoy with hydraulic PTO (oil)

• Hydraulic cylinder (ram)
• HP and LP gas accumulator
• Hydraulic motor

PTO force:

Coulomb type (imposed by pressure in accumulator, piston area and rectifying valve system)

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Example:

• Hemispherical buoy, radius = a

1 2 3 4 5 ka 0.05 0.1 0.15 0.2 0.25 0.3 0.35

B

Analytical Hulme 1982

* B

ka

2 4 6 8 10 12 14 t 0.01 0.01 0.02 0.03 0.04

L

a g t t  * * L

Dimensionless radiation damping coefficient Dimensionless radius Dimensionless time Dimensionless memory function

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

External PTO force: Coulomb type (imposed by pressure in accumulator, piston area and rectifying valve system)

HP gas accumulator LP gas accumulator Cylinder Valve

B A

Buoy Motor

Irregular waves with Hs, Te and Pierson-Moskowitz spectral distribution

) 1054 exp( 263 ) (

4 4 5 4 2    

    

 e e s

T T H S

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

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s 11 m, 3 state Sea   

e s

T H

kW 4 . 178 kN 647 force External damped Optimally  P kW 1 . 83 kN 200 force External damped Under  P kW . 97 kN 1000 force External damped Over  P

m 5 radius Sphere    a

(kW) P

(m) x (m) x

(kW) P

(kW) P (kW) P

(m) x

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

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For point absorbers (relatively small bodies) the resonance frequency of the body is in general much larger than the typical wave frequency of sea waves:

• No resonance can be achieved.
• Poor energy absorption.

How to increase energy absorption?

Phase control ! Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Whenever the body velocity comes down to zero, keep the body fixed for an appropriate perid of time. This is an artificial way of reducing the frequency of the body free-

• scillations, and achieving resonance.

Phase-control by latching

Kjell Budall (1933-89) Johannes Falnes

• J. Falnes, K. Budal, Wave-power conversion by

power absorbers. Norwegian Maritime Research, 6, 2-11, 1978. Phase-control by latching was introduced by Falnes and Budal

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

How to achieve phase-control by latching in a floating body with a hydraulic power-take-off mechanism? Introduce a delay in the release

• f the latched body.

How?

Increase the resisting force the hydrodynamic forces have to

• vercome to restart the body motion.

Oscillating-body dynamics

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600 602 604 606 608 610 612 614 t s 4 2 2 4

x d t d m s , 1 fd N M

600 602 604 606 608 610 612 614 t s 4 2 2 4

x m

600 602 604 606 608 610 612 614 t s 4 2 2 4

x d t d m s , 1 fd N M

600 602 604 606 608 610 612 614 t s 4 2 2 4

x m

No phase-control: Phase-control:

velocity Excit. force displacement

kW . 55  P kW 1 . 206  P

Oscillating-body dynamics

) s ( t ) s ( t

608 608

Regular waves: T = 9 s, amplitude 0.67 m

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700 720 740 760 780 800 t s 3 2 1 1 2 3

x d t d Hs s 1 , 1 fd Hs N M m

700 720 740 760 780 800 t s 2 1 1 2

x Hs

700 720 740 760 780 800 t s 3 2 1 1 2 3

x d t d Hs s 1 , 1 fd Hs N M m

700 720 740 760 780 800 t s 2 1 1 2

x Hs

• excit. force

velocity displacement

Irregular waves: Te = 9 s, Hs = 2 m

2 2

kW/m 2 . 41 

s

H P

2 2

kW/m 114 

s

H P

No phase control With phase control

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Phase control is being investigated by several teams as a way of enhancing device performance. Phase by latching may significantly increase the amount of absobed energy by point absorbers. Problems with latching phase control:

• Latching forces may be very large.
• Latching control is less effective in two-body WECs.

Apart from latching, there are forms of phase control (reactive, unlatching, …).

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Several degrees of freedom

• Each body has 6 degrees of freedom
• A WEC may consist of n bodies (n >1)

P T O b o d y 1 b o d y 2 P T O b o d y 1 b o d y 2 P T O b o d y 1 b o d y 2

All these modes of oscillation interact with each

• ther through the wave fields they generate.

Number of dynamic equations = 6n The interference between modes affects:

• added masses
• radiation damping coefficients

Hydrodynamic coefficients are defined accordingly. They can be computed with commercial software (WAMIT, …).

ij ij

B A ,

Oscillating-body dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Oscillating-body dynamics

Several degrees of freedom

Example: heaving bodies 1 and 2 reacting against each other.

1 2 12 2 12 2 1 2 1 1 1 1 1 1 1 1

) ( ) ( ) (

d

f x B x A x x K x x C x gS x B x A m                   

2 1 12 1 12 2 1 2 1 2 2 2 2 2 2 2

) ( ) ( ) (

d

f x B x A x x K x x C x gS x B x A m                   

21 12 21 12

, B B A A  

Note:

PTO body 1 body 2 PTO body 1 body 2 INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

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uniform air pressure

Two different approaches to modelling:

weightless piston

Oscillating body (piston) model (rigid free surface) Uniform pressure model (deformable free surface)

OWC Dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

OWC Dynamics

) (t q ) (t m 

a



 ) (t q

volume-flow rate displace by free-surface  ) (t m  mass-flow rate of air through turbine



a



air density

 ) (t p

air pressure

 V

air volume pressure

 ) (t p

dt t dp c V t q t m

a a a

) ( ) ( ) (

2

    

Effect of air compressibility Conservation of air mass (linearized)

    radiation excitation rate flow

exc r

q q q INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

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Air turbine

head pressure

• utput

power diameter rotor speed rotational p P D N

t

   

3

ND m

a

   

2 2 D

N p

a

  

5 3 D

N P

a t

  

In dimensionless form: flow pressure head power

) ( ), (      

P w

f f

Performance curves of turbine (dimensionless form): power flow pressure head

OWC Dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Frequency domain

) (t q ) (t m 

a

 ) (t q ) (t m 

a



 

 

t i r r

e Q Q Q M P t q t q t q m t p

 exc exc

, , , , ) ( ), ( ), ( , ), (   

Linear air turbine

   K

 

        e susceptanc radiation e conductanc radiation ) ( ) ( ) ( ) ( C B iC B P Q r    

w

A Q ) ( ) (

exc

   

excitation coeff. wave ampl.

           

2 exc a a a

c V C i B N KD Q P   

OWC Dynamics

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           

2 exc a a a

c V C i B N KD Q P    K gS C B i A m F X

d

          ) ( ) (

2

) (t q ) (t m 

a

 ) (t q ) (t m 

a



) (     

P

f

 

 

t i

e P t p



Re ) (            

2 2 5 3

) ( ) ( ) ( :

• utput

power D N t p f D N t P t

a P a t

 

Ψ

OWC Dynamics

air pressure

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Time domain:

• Linear or non-linear turbine

        

2 2 3

curve pressure vs flow turbine D N p f ND m

a w a

       d t B t g r cos ) ( 2 ) ( function memory





 

) ( ) ( ) ( ) ( ) (

2

t q d p t g t m dt t dp c V

i t r a a a

   



 

     

) (t q ) (t m 

a

 ) (t q ) (t m 

a



To be integrated numerically for p(t)

          

2 2 5 3

) ( ) ( ) ( :

• utput

power D N t p f D N t P t

a P a t

 

OWC Dynamics

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Memory function

Pico OWC

Numerical application

AQUADYN Brito-Melo et al. 2001

(rad/s) 

OWC Dynamics

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Results from time-domain modelling of impulse turbine over  t = 120 s

• Turbine D = 1.5 m, N = 115 rad/s (1100 rpm)
• Sea state Hs = 3 m, Te = 11 s
• Average power output from turbine 97.2 kW

  p(t) Pt (t) Air pressure in chamber Power

Numerical application

OWC Dynamics

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Stochastic modelling

• Irregular waves
• Linear air-turbine
• A.F. de O. Falcão, R.J.A. Rodrigues, “Stochastic modelling of OWC wave power performance”,

Applied Ocean Research, Vol. 24, pp. 59-71, 2002.

• A.F. de O. Falcão, “Control of an oscillating water column wave power plant for maximum

energy production”, Applied Ocean Research, Vol. 24, pp. 73-82, 2002.

• A.F. de O. Falcão, "Stochastic modelling in wave power-equipment optimization: maximum

energy production versus maximum profit". Ocean Engineering, Vol. 31, pp. 1407-1421, 2004.

• Much less time-consuming than time-domain analysis
• Appropriate for optimization studies

OWC Dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Time-averaged

Wave climate represented by a set of sea states

• For each sea state: Hs, Te, freq. of occurrence .
• Incident wave is random, Gaussian, with

known frequency spectrum.

WAVES

OWC

AIR PRESSURE

TURBINE

TURBINE SHAFT POWER

Random, Gaussian Linear system. Known hydrodynamic coefficients Known performance curves

GENERATOR

ELECTRICAL POWER OUTPUT

Time-averaged Random, Gaussian rms: p Electrical efficiency

Stochastic modelling

OWC Dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Stochastic model:

• Linear turbine (Wells turbine)
• Random Gaussian waves

Pierson-Moskowitz spectrum

 

   

                  

2 2 2 2 5 3

2 exp 2 2 ) ( ) ( dp D N p f p D N dp p P p f P

a P p p a t t

    

). 1054 exp( 263 ) (

4 4 5 4 2    

    

 e e s

T T H S

                                        

 



2 2 1 2 2 2

2 exp 2 1 ) ( pdf and where ) ( ) ( ) ( 2 ance with vari Gaussian, random is ) ( system, linear For

p p a a a p

p p f C c V i B N KD Λ d S t p           



OWC Dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Plant rated power (for Hs = 5m, Te=14s) Wells turbine size range 1.6m < D < 3.8m

200 300 400 500 600 700 800 1.5 2 2.5 3 3.5 4

D (m ) R a t e d po w e r ( k W )

50 100 150 200 250 300 1.5 2 2.5 3 3.5 4

D (m ) A n n u a l a v e ra g e d n e t p o w e r (k W )

w a ve c lim a te 3 w a ve c lim a te 2 w a ve c lim a te 1

Annual averaged net power (electrical)

Application of stochastic model

OWC Dynamics

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Theoretical/numerical modelling, based on linear water wave theory, is unable to account for:

• large amplitude waves
• large amplitude motions of bodies and OWCs
• real-fluid effects (viscosity, turbulence, eddies)
• Survival in very energetic seas

Model testing in wave tank is essential to:

• validate theoretical results
• investigate non-linear effects effects
• investigate survival issues

It is an essential step before testing under real sea conditions.

Model Testing

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Model Testing

How to scale up model test results, assuming geometric similarity ?

3

gL F 

2 7

gL P 

2 1

) ( gL V L

Linear dimension Time (wave period) Force Velocity Power

2 1 2 1

L g T



Dimensionless coefficients

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Required testing conditions:

• For power performance: Hs up to 4 - 5 m.
• For survival Hs up to 10 - 15 m (individual wave height 18 – 28 m ?) for
• ffshore devices.
• Tank depth may be important for simulation of mooring systems.

Testing for survival is usually done at smaller scale than for power performance, due to limitations in wave generation by wave makers. Typical scales for power performance testing:

• 1/80 to 1/25 in small to medium tanks.
• Up to 1/10 in very large tanks.

Model Testing

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Model testing of BBDB (floating OWC) HMRC – National Ocean Energy Test Facility, Cork, Ireland

Mid-sized tank Scales 1/50 – 1/30

Model Testing

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

University of Porto, Portugal

Mid-sized tank Scales 1/50 – 1/30

Model Testing

Floating OWC

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Large tank: Ecole Centrale de Nantes, France

Pelamis model testing

Model Testing

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

2 7

gL P  What is the power level in the simulation of a 500 kW full-sized prototype ? Scale Power in model 1/50 0.6 W 1/25 6.4 W 1/15 38 W 1/10 0.16 kW 1/4 3.9 kW

A realistic simulation of the PTO (hydraulic, linear generator, etc.) with control capability in general requires scale larger than 1/10. Some technology developers use tests at scales 1/4 to 1/5 in sheltered sea conditions.

Model Testing

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

Model Testing

OWC testing

• The spring-like effect of air compressibility in the air chamber is important.
• In testing, the air chamber volume should be scaled as not as .
• This may raise practical problems, especially when model testing floating

OWCs.

• The presence of the air turbine is usually simulated by a pressure drop.
• There are several techniques for doing that (orifice, porous plate, …).

2 1

L

3 1

L INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012

END OF PART 3 WAVE ENERGY CONVERSION MODELLING

INTERNATIONAL PhD COURSE XXVII° Cycle UNIVERSITY OF FLORENCE - TU-BRAUNSCHWEIG

Processes, Materials and Constructions in Civil and Environmental Engineering Florence 18-19 April 2012