wave energy presentation

Dec. 18, 2004ISTE STTP at Electrical Engg.

Deptt, GCOE, Amravati 1

Wave Energy



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.



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

n θ

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 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 .



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



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.



Elliptical paths of water particles at different heights



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.



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,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==



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



Potential Energy

The Pot. Energy Density per unit area is , where , is then given by

)8(g

ga

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 given by



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.



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=



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=



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=

=



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




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=×××=




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.



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 :



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



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

Waverising Chamber

Turbine

Air flow

Air in

Wave directionWavefalling

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

� DAM – ATOLL WAVE MACHINE



Government's Initiative

� UK Govt: 10 % of Electricity from Renewables by 2010

� India: Power to all by 2012

Renewable Energy Plan



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� Uncertain future because of several difficulties in

constructing reliable, safe, economical and durable Ocean Wave Energy Plants.



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.



WHY RENEWABLES ?

� ENERGY COST

� ENERGY INDEPENDENCE

� ENVIRONMENTAL PROTECTION

� NEED OF THE HOUR : Encouraging Renewables to generate

“GREEN POWER”



Thank you !

wave energy presentation

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