WAVE ENERGY SITES
The Pacific Coast of North America.
California Coast
The Arabian Sea of India and Pakistan.
India – Coastal areas in Tamilnadu,
Wave Power
The concept of capturing and
converting the energy available in the
motion of ocean waves to energy.
a w λ Area a λ Trough x x y y Wave at time θ Wave at time 0 0 Crest m n 2 θ + λ m nθ + λ m nθ dx 2 λ a
A two-dimensional progressive wave that has a free surface
and is acted upon by gravity (figure 1.) is characterized
by the following parameters:
λ
= wave length = cτ, m
a
= amplitude, m
2
a
= height (from crest to trough), m
τ
= Period, s
f
= frequency= 1/ τ, s-1
c
= wave propogation velocity λ/ τ, m/s
n
= phase rate = 2
Π
/ τ, sec-1
The period τ and wave velocity
c
depend upon the
wavelength and the depth of water .
The relationship between wavelength and period
can therefore be well approximated by
λ = 1.56 τ
2
(λ in m, τ in s) (1)
The figure 1. shows an isometric of a two-dimensional
progressive wave, represented by the sinusoidal
simple harmonic wave shown at time 0.
Cross sections of the wave are also shown at
time 0 and at time
θ
. That wave is expressed by
)
2
(
)
2
x
2
(
sin
a
y
θ
τ
π
−
λ
π
=
or
y
=
a
sin (
mx-nθ
) (3)
where
y
= height above its mean level, m
Note that the wave profile at time
θ
has the same shape as that at time 0,
except that it is displaced from it by
a distance
x
=
θ
/ τ =
θ
(
n/m
).
When
θ =
τ,
x=
λ and
the wave profile assumes its original position.
In reality a given particle of water rotates in place
in an elliptical path in the plane of wave propagation,
with specified horizontal and vertical semiaxes,
as can be witnessed when placing a cork on water,
The paths of water particles of different depths
Elliptical paths of water
The horizontal and vertical semiaxes of the
ellipses are given, respectively, by
)
5
(
mh
sinh
m
sinh
a
)
4
(
mh
sinh
m
cosh
a
η
=
β
η
=
α
where α = horizontal semiaxis
β
= vertical semiaxis
h = depth of water
η
= distance from the bottom
The above equations show that in general α > β,
that β varies from 0 at the bottom where η = 0 to a,
at the surface where η = h, and that for large depths α ≈ β ≈ a
and the motion is essentially circular at the surface.
Energy and Power from
Waves
Potential Energy:
The potential energy arises from the
elevation of the water above the mean
sea level (y = 0). Considering a
differential volume y dx, it will have a
mean height y/2.
Potential Energy
(
)
(
)
m
,
x
n
propogatio
wave
of
.
dirn
the
to
.
perp
,
wave
ensional
dim
two
the
of
width
arbitrary
L
m
/
kg
,
density
water
s
.
N
/
m
.
kg
0
.
1
factor
conversion
g
s
/
m
,
on
accelerati
nal
gravitatio
g
kg
,
dx
y
in
liquid
of
mass
m
where
)
6
(
g
g
dx
y
2
L
g
2
yg
L
dx
y
g
2
yg
m
dPE
is
P.E.
the
Thus
3 2 c 2 c 2 c c−
=
=
ρ
=
=
=
ρ
=
ρ
=
=
Potential Energy
(
)
)
7
(
g
L
a
1
2
m
g
g
m
2
La
mx
2
sin
4
1
mx
2
1
g
g
m
2
La
dx
n
mx
sin
g
g
2
La
PE
2 c 2 0 c 2 0 2 c 2λ
ρ
=
λ
ρ
=
−
ρ
=
θ
−
ρ
=
λ λ∫
Potential Energy
The Pot. Energy Density per unit area is ,
where , is then given by
)
8
(
g
g
a
4
1
A
PE
c 2ρ
=
Kinetic Energy
The kinetic energy of the wave is that of
the liquid between two vertical planes
perpendicular to the direction of wave
propagation x and placed one wavelength
apart. From hydrodynamic theory it is
Kinetic Energy
)
9
(
d
g
g
L
i
4
1
KE
cϖ
ω
ρ
=
∫
Where ω is a complex potential given by
)
10
(
)
n
mz
cos(
)
mh
sinh(
ac
θ
−
=
ω
and z is distance measured from an arbitrary reference point. The
integral in the above equation is performed over the cross-sectional
area bounded between two vertical planes.
Kinetic Energy
The result is
and the kinetic energy density is
)
11
(
g
g
)
L
(
a
4
1
KE
c 2λ
ρ
=
)
12
(
g
a
1
KE
2ρ
=
Total Energy and Power
It can be seen that the potential and kinetic
energies of a progressive sine wave are
identical, so that the total energy E is half
potential and half kinetic. The total energy
density is thus given by
)
13
(
g
g
a
2
1
A
E
c
2
ρ
=
Total Energy and Power
Thus the power density, W/m
2
, is given
by
)
14
(
g
g
f
a
2
1
A
P
f
x
A
E
A
P
c 2ρ
=
=
Problem on Wave Energy
Prob.
A 2-m wave has a 6-s period and occurs at the surface of
water 100 m deep. Find the wavelength, the wave velocity,
the horizontal and vertical semi axes for water motion at
the surface, and the energy and power densities of the
wave. Water density = 1025 kg/m
3Sol :
Wavelength λ = 1.56 Χ 6
2=56.16 m
Wave velocity c = λ/τ = 9.36 m/s
Wave height 2a = 2 m
Amplitude a = 1 m
m = 2Π/λ = 2Π/56.16 = 0.1119 m
-1At the surface η = h = 100 m
Problem on Wave Energy
Horizontal semiaxis
Vertical semiaxis
Wave frequency f=1/τ = 1/6 s
Energy density
m
1
19
.
11
sinh
19
.
11
cosh
1
×
=
=
α
m
1
19
.
11
sinh
19
.
11
sinh
1
×
=
=
β
2 2m
/
J
6
.
5027
1
81
.
9
1
1025
2
1
A
E
=
×
×
×
=
Problem on Wave Energy
Power density
2m
/
W
9
.
837
6
1
6
.
5027
f
A
E
A
P
=
×
=
=
Because of large depth, the semiaxes are equal,
so the motion is circular.
Semiaxes are small compared with the
wavelength, so the water motion is primarily
vertical.
Wave energy generation devices fall into two categories –
fixed generating devices, and floating devices
Fixed generating devices are mounted to the ocean floor or shoreline,
and have significant advantages over floating systems where
maintenance costs are high.
The most promising fixed generating device technology is the
Oscillating Water Column (OWC), which uses a two-step procedure
to generate electricity.
Requirements of OWC wave energy converter:
Summary of principles of the energy conversion chain
Linear system Slip-ring induction generator
Mechanical to electrical
Non-linear, load (generator) dependent
Wells turbine Pneumatic to mechanical
Frequency and load
(turbine + generator) dependent Oscillating water column
Wave to pneumatic
Efficiency Structure / device
WAVE ENERGY PLANT IN INDIA
Vizhinjam near Thiruvananthapuram in Kerala in October
1991.
The civil, mechanical and electrical systems of the plant were
designed and fabricated indigenously. The rated capacity of the plant
is 150 kW, with an energy output of 4.45 lakh unitsyear. It operates on
the principle of Oscillating Water Column.
Thus, generation of electricity from ocean waves become a distinct
reality in October 1991 .
The plant continues to generate, electricity which is fed into the grid of
Kerala State Electricity Board.
Chamber Turbine Air flow Air out Wave direction Wave rising Chamber Turbine Air flow Air in Wave direction Wave falling
Oscillating Water Column (OWC) Wave Energy Conversion System
●
● ●
●
WAVE ENERGY CONVERTERS
OFFSHORE AND SHORELINE OWC
WAVE ENRGY CONVERSION BY FLOATS
HYDRAULIC ACCUMULATOR WAVE MACHINE
DOLPHIN TYPE WAVE POWER MACHINE
Government's Initiative
UK Govt: 10 % of Electricity from
Renewables by 2010
India: Power to all by 2012
5E Formula in human life
Importance of 5E in human life :
Ecology
Ethic
Economy
Energy
Esthetic
CONCLUSIONS
Tidal Energy
Intermittent nature of tidal power
Tidal Power Plants: Reliable, Life span : 75-100 Yrs.,
High Capital cost, Low continuous power output;
Ocean Wave Energy Conversion Technology
