Wave Energy Presentation

Wave Energy

Dec. 18, 2004

ISTE STTP at Electrical Engg. Deptt, GCOE, Amravati

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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.

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Wave Power

The concept of capturing and converting the energy available in the motion of ocean waves to energy.

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w

Area λ a Crest

y dx 0

a a

λ 2

x

λ Trough Wave at time 0

y nθ m

λ nθ + 2 m

λ+

nθ m x

Wave at time θ

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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

a 2a τ f

c n

= = = = = = =

wave length = cτ, m amplitude, m height (from crest to trough), m Period, s frequency= 1/ τ, s-1 wave propogation velocity λ/ τ, m/s phase rate = 2Π/ τ, sec-1

The period τ and wave velocity c depend upon the wavelength and the depth of water .

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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 2π 2π y = a sin ( x − θ) ( 2) λ τ or where

y = a sin (mx-nθ) (3) y = height above its mean level, m θ = time, s m = 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.

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Elliptical paths of water particles at different heights

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The horizontal and vertical semiaxes of the ellipses are given, respectively, by

cosh mη (4) sinh mh sinh mη β=a (5) sinh mh α=a

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.

A wave therefore possesses both pot. and kinetic energies. Dec. 18, 2004


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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.

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Potential Energy Thus the P.E. is

dPE = m =

yg yg = (ρ y dx L ) 2g c 2g c

ρL 2 g y dx gc 2

(6)

where m = mass of liquid in y dx, kg g = gravitational acceleration, m / s 2

(

g c = conversion factor 1.0 kg.m / N.s 2

)

ρ = water density, kg / m 3 L = arbitrary width of the two − dim ensional wave, perp. to the dirn. of wave propogation x , m

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Potential Energy Combining Eqs. (6) and (3) and integrating gives ρLa 2 g PE = 2 gc

λ

2 sin ∫ (mx − nθ) dx 0 λ

ρLa 2 g  1 1  =  mx − sin 2mx  2m g c  2 4 0 ρLa 2 g  mλ  = 2m g c  2  1 g = ρ a2 λ L 4 gc

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(7)

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Potential Energy The Pot. Energy Density per unit area is , where , is then given by PE 1 g = ρ a2 A 4 gc

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(8)

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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

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Kinetic Energy 1 g KE = i ρ L ∫ ω dϖ 4 gc

(9)

Where ω is a complex potential given by

ac ω= cos(mz − nθ) sinh(mh)

(10)

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.

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Kinetic Energy The result is KE =

1 2 g ρa (λL) 4 gc

(11)

and the kinetic energy density is KE 1 2 g = ρa A 4 gc Dec. 18, 2004

(12) ISTE STTP at Electrical Engg. Deptt, GCOE, Amravati

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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

E 1 2 g = ρa A 2 gc Dec. 18, 2004

(13)


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Total Energy and Power Thus the power density, W/m2, is given by P E xf = A A P 1 2 g = ρa f A 2 gc

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(14)

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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, 2004


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Problem on Wave Energy Horizontal semiaxis α = 1 ×

cosh 11.19 = 1m sinh 11.19

sinh 11.19 =1 m Vertical semiaxis β = 1 × sinh 11.19 Wave frequency f=1/τ = 1/6 s Energy density

Dec. 18, 2004

E 1 9.81 = × 1025 × 12 × = 5027.6 A 2 1


J / m2

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Problem on Wave Energy Power density

P E 1 = f = 5027.6 × = 837.9 W / m 2 A A 6

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 CONVERTERS :

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,

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Summary of principles of the energy conversion chain

Type of energy conversion

Structure / device

Efficiency

Wave to pneumatic

Oscillating water column

Frequency and load (turbine + generator) dependent

Pneumatic to mechanical

Wells turbine

Non-linear, load (generator) dependent

Mechanical to electrical

Slip-ring induction generator

Linear system

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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.

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Oscillating Water Column (OWC) Wave Energy Conversion System Air out Turbine

●

Air in

●

●

●

Turbine

Air flow

Air flow

●

● ●

Chamber

Wave rising

Dec. 18, 2004

●

Wave direction

Chamber


Wave falling

Wave direction

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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

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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.

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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.

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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 !

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Wave Energy Presentation

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