Download - Wave Energy Presentation
Dec. 18, 2004ISTE STTP at Electrical Engg.
Deptt, GCOE, Amravati 1
Wave Energy
Dec. 18, 2004ISTE STTP at Electrical Engg.
Deptt, GCOE, Amravati 2
WAVE ENERGY SITES
� The Pacific Coast of North America. California Coast
� The Arabian Sea of India and Pakistan.
� India – Coastal areas in Tamilnadu, Kerala and Gujarat.
Dec. 18, 2004ISTE STTP at Electrical Engg.
Deptt, GCOE, Amravati 3
Wave Power
� The concept of capturing and converting the energy available in the motion of ocean waves to energy.
Dec. 18, 2004ISTE STTP at Electrical Engg.
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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
n θ
dx 2
λ
a
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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 2a = height (from crest to trough), m τ = Period, sf = frequency= 1/ τ, s-1c = wave propogation velocity λ/ τ, m/sn = phase rate = 2Π/ τ, sec-1
The period τ and wave velocity c depend upon the wavelength and the depth of water .
Dec. 18, 2004ISTE STTP at Electrical Engg.
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The relationship between wavelength and period can therefore be well approximated by
λ = 1.56 τ2 (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
x2
(sinay θτ
π−
λ
π=
or y = a sin (mx-nθ) (3) where y = height above its mean level, m
θ = time, sm = 2Π/ λ, m-1
(mx-nθ) = 2 Π (x/ λ - θ/τ) = phase angle, dimensionless
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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 but with the same mean position are shown in figure 2.
Dec. 18, 2004ISTE STTP at Electrical Engg.
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Elliptical paths of water particles at different heights
Dec. 18, 2004ISTE STTP at Electrical Engg.
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The horizontal and vertical semiaxes of the ellipses are given, respectively, by
)5(mhsinh
msinha
)4(mhsinh
mcosha
η=β
η=α
where α = horizontal semiaxisβ = vertical semiaxis
h = depth of waterη = 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.
A wave therefore possesses both pot. and kinetic energies.
Dec. 18, 2004ISTE STTP at Electrical Engg.
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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.
Dec. 18, 2004ISTE STTP at Electrical Engg.
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Potential Energy
( )
( )
m,xnpropogatiowaveof.dirntheto.perp,waveensionaldimtwotheofwidtharbitraryL
m/kg,densitywater
s.N/m.kg0.1factorconversiong
s/m,onacceleratinalgravitatiog
kg,dxyinliquidofmassm
where
)6(g
gdxy
2
L
g2
ygLdxy
g2
ygmdPE
is P.E. theThus
3
2
c
2
c
2
cc
−=
=ρ
=
=
=
ρ=
ρ==
Dec. 18, 2004ISTE STTP at Electrical Engg.
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Potential Energy
( )
)7(g
gLa
4
1
2
m
g
g
m2
La
mx2sin4
1mx
2
1
g
g
m2
La
dxnmxsing
g
2
LaPE
c
2
c
2
0c
2
0
2
c
2
λρ=
λρ=
−
ρ=
θ−ρ
=
λ
λ
∫
Combining Eqs. (6) and (3) and integrating gives
Dec. 18, 2004ISTE STTP at Electrical Engg.
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Potential Energy
The Pot. Energy Density per unit area is , where , is then given by
)8(g
ga
4
1
A
PE
c
2ρ=
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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 given by
Dec. 18, 2004ISTE STTP at Electrical Engg.
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Kinetic Energy
)9(dg
gLi
4
1KE
c
ϖωρ= ∫
Where ω is a complex potential given by
)10()nmzcos()mhsinh(
acθ−=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.
Dec. 18, 2004ISTE STTP at Electrical Engg.
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Kinetic Energy
The result is
and the kinetic energy density is
)11(g
g)L(a
4
1KE
c
2 λρ=
)12(g
ga
4
1
A
KE
c
2ρ=
Dec. 18, 2004ISTE STTP at Electrical Engg.
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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
ga
2
1
A
E
c
2ρ=
Dec. 18, 2004ISTE STTP at Electrical Engg.
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Total Energy and Power
Thus the power density, W/m2, is given by
)14(g
gfa
2
1
A
P
fxA
E
A
P
c
2ρ=
=
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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/m3
Sol :
Wavelength λ = 1.56 Χ 62 =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-1
At the surface η = h = 100 m
Dec. 18, 2004ISTE STTP at Electrical Engg.
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Problem on Wave Energy
Horizontal semiaxis
Vertical semiaxis
Wave frequency f=1/τ = 1/6 s
Energy density
m119.11sinh
19.11cosh1 =×=α
m119.11sinh
19.11sinh1 =×=β
22 m/J6.50271
81.911025
2
1
A
E=×××=
Dec. 18, 2004ISTE STTP at Electrical Engg.
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Problem on Wave Energy
Power density2m/W9.837
6
16.5027f
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.
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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:
Latitudes between 40-60 degrees,
WAVE ENERGY CONVERTERS :
Dec. 18, 2004ISTE STTP at Electrical Engg.
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Summary of principles of the energy conversion chain
Linear systemSlip-ring induction generatorMechanical to electrical
Non-linear, load (generator) dependent
Wells turbinePneumatic to mechanical
Frequency and load(turbine + generator) dependent
Oscillating water columnWave to pneumatic
EfficiencyStructure / deviceType of energy conversion
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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.
Dec. 18, 2004ISTE STTP at Electrical Engg.
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Chamber
Turbine
Air flow
Air out
Wave direction
Waverising Chamber
Turbine
Air flow
Air in
Wave directionWavefalling
Oscillating Water Column (OWC) Wave Energy Conversion System
●● ●
●
● ● ●●
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WAVE ENERGY CONVERTERS
� OFFSHORE AND SHORELINE OWC
� WAVE ENRGY CONVERSION BY FLOATS
� HYDRAULIC ACCUMULATOR WAVE MACHINE
� DOLPHIN TYPE WAVE POWER MACHINE
� DAM – ATOLL WAVE MACHINE
Dec. 18, 2004ISTE STTP at Electrical Engg.
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Government's Initiative
� UK Govt: 10 % of Electricity from Renewables by 2010
� India: Power to all by 2012
Renewable Energy Plan
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5E Formula in human life
Importance of 5E in human life :
� Ecology
� Ethic
� Economy
� Energy
� Esthetic
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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� Uncertain future because of several difficulties in
constructing reliable, safe, economical and durable Ocean Wave Energy Plants.
Dec. 18, 2004ISTE STTP at Electrical Engg.
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R & D Issues
� Wave Energy: cost reduction, efficiency and reliability improvements, identification of suitable sites, interconnection with the utility grid, better understanding of the impacts of the technology on marine life and the shoreline. Also essential is a demonstration of the ability of the equipment to survive the salinity and pressure environments of the ocean as well as weather effects over the life of the facility.
Dec. 18, 2004ISTE STTP at Electrical Engg.
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WHY RENEWABLES ?
� ENERGY COST
� ENERGY INDEPENDENCE
� ENVIRONMENTAL PROTECTION
� NEED OF THE HOUR : Encouraging Renewables to generate
“GREEN POWER”
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Thank you !