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

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

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: or

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:

The variable k can written in terms of period:

The next step is to plug in the expression above for k in our initial energy equation.

And knowing that T=1 / f , we can add that into the equation.

The variable m can then be changed into the following: m = ρV and because V = Sl, m = ρSl

The variable length can be modified into l = vt

The final equation to determine the energy of a tidal wave is To turn the energy equation into a the power equation for a tidal wave, it is plugged into the equation P = E / t

To derive the second equation, we replace variable of velocity since:

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

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?

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: Assuming that efficiency of generator is 30%

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 status and developments in wave energy." Proc. of Conference on Marine Renewable Energies. Institute of Marine Engineers. 2001. 2 Apr. 2009 www.wave-energy.net

## Wave Power

Table of Contents## 8.4.21

Oscilating Water ColumnThe 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.

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

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:orIn 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:

The variable

kcan written in terms of period:The next step is to plug in the expression above for

kin our initial energy equation.And knowing that T=1 /

f, we can add that into the equation.The variable m can then be changed into the following: m =

ρVand becauseV = Sl, m = ρSlThe variable length can be modified into

l = vtThe final equation to determine the energy of a tidal wave is

To turn the energy equation into a the power equation for a tidal wave, it is plugged into the equation

P = E / tTo derive the second equation, we replace variable of velocity since:

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

8.4.23Example problem of wave powerTwo 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?

Example calculation of tidal power generationAssumptions:- 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:Assuming that efficiency of generator is 30%BibliographyGiancoli, 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