Wave Power


Table of Contents

  • 8.4.21 - Principle of operation of an Oscilating Water Column (OWC)
  • 8.4.22 - Determining the power per unit length of a wavefront
  • 8.4.23 - Solving wave power problems

8.4.21

Oscilating Water Column

The fundamental functions of wave power devices are to capture waves and then absorb energy from the captured waves, which then are converted into electricity. Most of these devices are called oscillating water columns. These oscillating water columns consists of a "partially submerged, hollow structure" (as seen in diagram one), which is open to the sea below the water line for waves to pass through. The principle of operation of an oscillating water column is that as waves enter the shell chamber or capture chamber (as noted in diagram 2), the level of water rises, compressing and depressurizing the air in the top of the chamber or air column, which is then forced through a blow-hole into the turbine to generate electricity.

When the waves draw back, air returns under pressure into the chamber, keeping the turbine moving at all times. The air that blows in both directions produces enough movement for the turbine to drive a generator. This generator than converts the energy into electricity.

Most often the turbines used in an oscillating water column is the Wells Turbine. A Wells Turbine is a low-pressure air turbine developed for use in oscillating-water-column wave power plants.

Diagrams
external image moz-screenshot.jpgexternal image OWC.jpg external image moz-screenshot-1.jpg














Diagram 1: Operating principle of an oscillating water column (Site: Google images - www.montaraventures.com)



Wave power
Wave power

















Diagram 2: Different angle of the operating principle of an oscillating water column. (Site: Google images - www.virginmedia.com)





8.4.22

The equation for wave power is:
1.png or 10.png

In finding the equation for the power produced by the wave, the equation for the energy produced by the wave must first be derived. Because each particle of the wave moves in a simple harmonic motion, we start our derivations with the equation:
2.png
The variable k can written in terms of period:
3.png
The next step is to plug in the expression above for k in our initial energy equation.

4.png
And knowing that T=1 / f , we can add that into the equation.
5.png
The variable m can then be changed into the following: m = ρV and because V = Sl, m = ρSl
6.png
The variable length can be modified into l = vt
7.png
The final equation to determine the energy of a tidal wave is 8.png
To turn the energy equation into a the power equation for a tidal wave, it is plugged into the equation P = E / t
9.png
To derive the second equation, we replace variable of velocity since:11.png
12.png

List of variables used -
P = power
E = energy
A = amplitude
T = period
m = mass
f = frequency
ρ = density
V = volume
S = surface area
l = length
v = velocity
t = time
g = gravity
d = distance
wave_power.JPG
external image moz-screenshot.jpgexternal image moz-screenshot-1.jpgexternal image moz-screenshot-2.jpg
8.4.23

Example problem of wave power
Two water waves traveling along a surface have the same frequency but one transports three times the power of the other. What is the ratio of the amplitudes of the two waves?
Picture_7.png
Example calculation of tidal power generation
Assumptions:
- p Density of saltwater = 1025kgms^-3
- g is the acceleration due to gravity = 9.81ms^-2
- f Frequency = 1
- d Depth of water = 50m
- A Amplitude = 2m
- S Surface area = 100m2
Calculation:

Picture_13.png

Assuming that efficiency of generator is 30%
Picture_18.png
Bibliography
Giancoli, Douglas C. Physics: Principles with Applications. 5th ed. New Jersey: Prentice Hall.

Harmsworth, Andrew P. "Wave Power." GCSE. 2002. 2 Apr. 2009 <www.gcse.com>.

T. Thorpe "Current statu s and developments in wave energy." Proc. of Conference on Marine Renewable Energies. Institute of Marine Engineers. 2001. 2 Apr. 2009 www.wave-energy.net