The Physics of Energy sources
Renewable sources of energy
Wave Power
B. Maffei
[email protected]
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Wave description
!   Surface wave = sine wave of irregular wavelength λ, phase and direction
!   Motion of any particle in water is circular – no net progression
!   Amplitude of particle motion (circular) decreases exponentially with depth
!
 Depth of λ/2π amplitude decreased by 1/e
!
 Depth of λ/2 amplitude motion is negligible
!   For shallow water motion becomes elliptical due to friction
Particle in a circular motion
r
a: wave amplitude, H wave height
Water particles motion
ac=ω2r
θ=ωt
v=ωr T=2π/ω
ω angular speed
T period, ac acceleration
Depth
Deep water
Shallow water
F: resulting force on water surface particles
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Wave propagation
a: wave amplitude, H wave height
The surface wave follows a sinusoidal propagation
⎛ ω 2 x
⎞
h = a sin⎜⎜
− ωt ⎟⎟
⎝ g
⎠
To be compared with a general travelling EM plane wave


2π
E ( x, t ) = E0 sin (kx − ωt ) where k =
is the wave number
λ
In our case, the surface motion is that of a travelling wave with:
λ=
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2πg
ω2
3
Power contained
in waves
It can be shown that the power per
unit of width of the wavefront is
2
ρg a
P=
8π
2
1/ 2
⎛ 2πλ ⎞
⎜⎜
⎟⎟
⎝ g ⎠
(Full derivation in Ref4 pp 404-411)
where ρ is the sea water density, and g the gravity acceleration
!   Power increases as
!   Square of the wave amplitude
!   Square root of the wavelength
!   In order to get large power we need long period, large amplitude waves
Ex: For a wavelength of 100m and an amplitude of 1.5m we get:
(
2
)
2
1/ 2
1025kg.m -3 9.8m.s-2 (1.5m ) ⎛ 2π 100m ⎞
P=
⎜
- 2 ⎟
8π
9.8m.s
⎝
⎠
= 71kW.m -1
Potentially a large amount of energy…
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How to harvest this power ?
!   Many devices have been suggested for extracting this energy
!   The Engineering Committee on Oceanic Resources describes over 40
devices that have reached a stage of advanced development
!   Only a third are operational but as research projects
!   A few have shown potential energy production at a larger scale
!   But as of today ~ 0% of the world energy is produced through
wave power
!   Only 10-15 devices were operational in sea conditions by 2005
!   Not mature enough
!   Needs more developments
!   Let s have a look at a few concepts
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Wave capture system
Probably the simplest in concept
!   Waves are funnelled in through a tapered
channel
!   Concrete walls about 2-3m above sea level
!   With funnelling waves go above the walls
filling the reservoir
!   Water from the reservoir go through hydroturbine
Requirements
Deep water close to shore so that oncoming wave are not dissipated
Small tidal range
Achievements
Tapchan system demonstrated successfully in Norway in 1985 – 350kW
5 years operation
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Oscillating water column
!   Water passes on to a partially
submerged cavity open under water
!   Column of water oscillates  air
movement
!   Air go through a turbine which works
both ways
Achievements
Developed by Queens University Belfast and installed on Scottish Island of Islay
First prototype worked for several years with lower production than expected
Larger version of 500kW (Limpet) installed in 2000 with some commercial operation
Offshore version
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Water profile device
!   Devices float on the surface and move with waves motion
!   Cylindrical sections linked by hinged joints
!   Motion induced in joints  action hydraulic rams  hydraulic motors drive
electrical generators
Achievements
Pelamis wave power device
Prototype of 120m long and 3.5m in diameter was installed in 2004 in Scotland
750kW of power
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Conclusion on wave power
!   Already a few working prototypes but needs further developments
!   Development in labs and simulations  100-1000kW capacity
achievable
!   Possibility of “farms” using many devices
!
!
!
!
 
 
 
 
Very clean and renewable energy
Not enough data on environmental impact
Looks like the price of energy produced might be competitive
Many difficulties for the development
!
!
!
!
 
 
 
 
Wave patterns are irregular in amplitude and direction
Possibility of extreme gales or hurricanes  potential damages
Peak power is generally available in deep water  offshore
Wave period generally 5-10s (0.1Hz)  difficult to couple these slow
frequencies to electrical generators
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References
!   Most of the material of this lecture is coming from
!   Ref4: “Renewable energy resources”, J. Twidell and T. Weir,
second edition, 2006
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