Wind and Wave Power By: Jon Riddle, Phillip Timmons, Joe Hanson, Chris Lee-Foss and Xavier Schauls
Equation for power of a wave The equation for the power of a wave is equal to the density of the liquid multiplied by the acceleration due to gravity squared multiplied by the amplitude squared multiplied by the period, over 8 pi. =
Power per unit length of a wavefront The power per unit length of a wavefront is equal to (Density of water)(acceleration due to gravity squared) (Amplitude squared)/(4 times the wave frequency)
Sample Problem Let's find the power of a 100 meter wave with amplitude 2 meters and a frequency of 2 Hz. (1 Kg/m³)*(9.8 m/s²)²*(2 m)² / (4*2Hz)= 48.02 Watt per Meter (48.02 W/m)*(100 m)= 4802 W Therefore this 100 meter wave front contains 4802 W of power. Any energy converting device will lose a portion of this through inefficiency.
Types of wave energy collectors: Oscillating Water Column Hinged Contour Device Buoyant Moored Device
The Oscillating Water Column The Oscillating water column is a device which captures the waves, and forces them into a chamber. This compresses the air in the chamber in order to power a turbine. Note that the chamber is not contained, only on the top part is it whole, which allows the motion of the wave to move in and out. While it is impossible to fully capture the energy of a wave, the efficiency of the column can vary immensely, with a theoretical maximum of 70%. The power available in the OWC chamber is equivalent to (Pressure at turbine duct+air density*air speed squared/2) *Air speed*duct area
Buoyant Moored Device This device floats on water, and is held to the seabed by mooring lines. This enables it to resist the waves, and thereby draw power.
Hinged Contour Device The hinged contour device is composed of several sections on top of the waves. It is moored to the seabed, but slackly. The motion of the waves causes different parts of the device to move, a motion which is resisted by hydraulic pumps.
Wind turbines Wind turbines are the typical method of harvesting wind power. The power output of a generator is proportional to the area which is covered by the rotor, referred to as swept area, and the cube of the wind speed. In addition, one must consider kinetic energy, 0.5 of mass times velocity squared. In order to find the mass of the air, one requires air density multiplied by swept area multiplied by velocity. Thus, the power is equal to 0.5*air density*swept area*velocity cubed. Of course, due to various limiting factors, the result is always much less.
Sample Problem P=½ρAV³ Let's find the power for wind travelling at 7m/s into a wind turbine with a 1.5m² swept area. (1.22521 kg/m3)*(1.5m²)*(7 m/s)³ / 2 = 630.37 W Therefore this wind contains 630 Watts of power. With inefficiencies only 40-50% of this could be converted to usable electrical power.
The Betz Limit The Betz Limit is a law which states that it is impossible for a wind turbine to convert more than 16/27 of the KE of the wind into mechanical energy. This is a result of the design of the wind turbine, which by it's very nature allows much of the wind to escape. In order to have a conversion ratio of 1, a turbine would need to be a round disk stopping all of the wind. However, if this were the case, it would be unable to move. The Betz Limit is the absolute limit to the mechanical design of the turbine. However, this being reality, the limit of what engineers can actually achieve is much lower, as a result of various difficulties in maintaining a large and complex wind turbine to harness wind power in various directions.
Sankey Diagrams Sankey diagrams are flow diagrams used to show proportionally the amount of flow between certain processes. They are mainly used to visualize energy and efficiency for chemical engineering and environmental engineering. They were created by Matthew Henry Phineas Riall Sankey to show the efficiency of a steamship.
Wind Energy Sankey Diagram Energy is lost because of Betz Law, Generator losses, Sub-system losses, and availability factor losses. This leaves only 40-50% output in electrical energy.