Wave power

Large storm waves pose a challenge to wave power development
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Wave power is the transport of energy by ocean surface waves, and the capture of that energy to do useful work — for example for electricity generation, water desalination, or the pumping of water (into reservoirs).

Wave power is distinct from the diurnal flux of tidal power and the steady gyre of ocean currents. Wave power generation is not currently a widely employed commercial technology although there have been attempts at using it since at least 1890.[1] The world's first commercial wave farm was based in Portugal,[2] at the Aguçadoura Wave Park, which consists of three 750 kilowatt Pelamis devices.[3]

Contents

Physical concepts

When an object bobs up and down on a ripple in a pond, it experiences an elliptical trajectory.
Motion of a particle in an ocean wave.
A = At deep water. The orbital motion of fluid particles decreases rapidly with increasing depth below the surface.
B = At shallow water (ocean floor is now at B). The elliptical movement of a fluid particle flattens with increasing depth.
1 = Propagation direction.
2 = Wave crest.
3 = Wave trough.
See Energy, Power and Work for more information on these important physical concepts. See Wind wave for more information on ocean waves.

Waves are generated by wind passing over the surface of the sea. As long as the waves propagate slower than the wind speed just above the waves, there is an energy transfer from the wind to the waves. Both air pressure differences between the upwind and the lee side of a wave crest, as well as friction on the water surface by the wind, making the water to go into the shear stress causes the growth of the waves.[4]

Wave height is determined by wind speed, the duration of time the wind has been blowing, fetch (the distance over which the wind excites the waves) and by the depth and topography of the seafloor (which can focus or disperse the energy of the waves). A given wind speed has a matching practical limit over which time or distance will not produce larger waves. When this limit has been reached the sea is said to be "fully developed."

In general, larger waves are more powerful but wave power is also determined by wave speed, wavelength, and water density.

Oscillatory motion is highest at the surface and diminishes exponentially with depth. However, for standing waves (clapotis) near a reflecting coast, wave energy is also present as pressure oscillations at great depth, producing microseisms.[4] These pressure fluctuations at greater depth are too small to be interesting from the point of view of wave power.

The waves propagate on the ocean surface, and the wave energy is also transported horizontally with the group velocity. The mean transport rate of the wave energy through a vertical plane of unit width, parallel to a wave crest, is called the wave energy flux (or wave power, which must not be confused with the actual power generated by a wave power device).

Wave power formula

In deep water where the water depth is larger than half the wavelength, the wave energy flux is


  P = \frac{\rho g^2}{64\pi} H_{m0}^2 T_{e}
    \approx \left(0.5 \frac{\text{kW}}{\text{m}^3 \cdot \text{s}} \right) H_{m0}^2\; T_{e},

The above formula states that wave power is proportional to the wave period and to the square of the wave height. When the significant wave height is given in meters, and the wave period in seconds, the result is the wave power in kilowatts (kW) per meter of wavefront length.[5][6][7]

Example: Consider moderate ocean swells, in deep water, a few kilometers off a coastline, with a wave height of 3 meters and a wave period of 8 seconds. Using the formula to solve for power, we get


  P \approx 0.5 \frac{\text{kW}}{\text{m}^3 \cdot \text{s}} (3 \cdot \text{m})^2 (8 \cdot \text{s}) \approx 36 \frac{\text{kW}}{\text{m}},

meaning there are 36 kilowatts of power potential per meter of coastline.

In major storms, the largest waves offshore are about 15 meters high and have a period of about 15 seconds. According to the above formula, such waves carry about 1.7 MW/m of power across each meter of wavefront.

An effective wave power device captures as much as possible of the wave energy flux. As a result the waves will be of lower height in the region behind the wave power device.

Wave energy and wave energy flux

In a sea state, the average energy density per unit area of gravity waves on the water surface is proportional to the wave height squared, according to linear wave theory:[4][8]

E=\frac{1}{16}\rho g H_{m0}^2, [A 1][9]

where E is the mean wave energy density per unit horizontal area (J/m2), the sum of kinetic and potential energy density per unit horizontal area. The potential energy density is equal to the kinetic energy,[4] both contributing half to the wave energy density E, as can be expected from the equipartition theorem. In ocean waves, surface tension effects are negligible for wavelengths above a few decimetres.

As the waves propagate, their energy is transported. The energy transport velocity is the group velocity. As a result, the wave energy flux, through a vertical plane of unit width perpendicular to the wave propagation direction, is equal to:[10][4]

P = E\, c_g, \, \

with cg the group velocity (m/s). Due to the dispersion relation for water waves under the action of gravity, the group velocity depends on the wavelength λ, or equivalently, on the wave period T. Further, the dispersion relation is a function of the water depth h. As a result, the group velocity behaves differently in the limits of deep and shallow water, and at intermediate depths:[4][8]


Deep water characteristics and opportunities

Deep water corresponds with a water depth larger than half the wavelength, which is the common situation in the sea and ocean. In deep water, longer period waves propagate faster and transport their energy faster. The deep-water group velocity is half the phase velocity. In shallow water, for wavelengths larger than twenty times the water depth, as found quite often near the coast, the group velocity is equal to the phase velocity.[11]

The regularity of deep-water ocean swells, where "easy-to-predict long-wavelength oscillations" are typically seen, offers the opportunity for the development of energy harvesting technologies that are potentially less subject to physical damage by near-shore cresting waves.[12]

History

The first known patent to utilise energy from ocean waves dates back to 1799 and was filed in Paris by Girard and his son.[13] An early application of wave power was a device constructed around 1910 by Bochaux-Praceique to light and power his house at Royan, near Bordeaux in France.[14] It appears that this was the first Oscillating Water Column type of wave energy device.[15] From 1855 to 1973 there were already 340 patents filed in the UK alone.[13]

Modern scientific pursuit of wave energy was however pioneered by Yoshio Masuda's experiments in the 1940s.[16] He has tested various concepts of wave energy devices at sea, with several hundred units used to power navigation lights. Among these was the concept of extracting power from the angular motion at the joints of an articulated raft, which was proposed in the 1950s by Masuda.[17]

A renewed interest in wave energy was motivated by the oil crisis in 1973. A number of university researchers reexamined the potential of generating energy from ocean waves, among whom notably were Stephen Salter from the University of Edinburgh, Kjell Budal and Johannes Falnes from Norwegian Institute of Technology (now merged into Norwegian University of Science and Technology), Michael E. McCormick from U. S. Naval Academy, David Evans from Bristol University, Michael French from University of Lancaster, John Newman and Chiang C. Mei from MIT.

In the 1980s, as the oil price went down, wave-energy funding was drastically reduced. Nevertheless, a few first-generation prototypes were tested at sea. More recently, following the issue of climate change, there is again a growing interest worldwide for renewable energy, including wave energy.[18]

Modern technology

Wave power devices are generally categorized by the method used to capture the energy of the waves. They can also be categorized by location and power take-off system. Method types are point absorber or buoy; surfacing following or attenuator oriented parallel to the direction of wave propagation; terminator, oriented perpendicular to the direction of wave propagation; oscillating water column; and overtopping. Locations are shoreline, nearshore and offshore. Types of power take-off include: hydraulic ram, elastomeric hose pump, pump-to-shore, hydroelectric turbine, air turbine,[19] and linear electrical generator. Some of these designs incorporate parabolic reflectors as a means of increasing the wave energy at the point of capture. These capture systems use the rise and fall motion of waves to capture energy.[20] Once the wave energy is captured at a wave source, power must be carried to the point of use or to a connection to the electrical grid by transmission power cables.[21]

These are descriptions of some wave power systems:

The front of the Pelamis machine bursting through a wave at the Agucadoura Wave Park

Challenges

These are some of the challenges to deploying wave power devices:

Wave farms

The world's first commercial wave farm opened in 2008 at the Aguçadora Wave Park near Póvoa de Varzim in Portugal. It uses three Pelamis P-750 machines with a total installed capacity of 2.25MW.[3][39] However, in November the units were removed from the water, and in March 2009 the project was suspended indefinitely.[40] A second phase of the project planned to increase the installed capacity to 21MW using a further 25 Pelamis machines[41] is in doubt following Babcock's withdrawal from the project.

Funding for a 3MW wave farm in Scotland was announced on 20 February 2007 by the Scottish Executive, at a cost of over 4 million pounds, as part of a £13 million funding package for marine power in Scotland. The first of 66 machines was launched in May 2010.[42]

Funding has also been announced for the development of a Wave hub off the north coast of Cornwall, England. The Wave hub will act as giant extension cable, allowing arrays of wave energy generating devices to be connected to the electricity grid. The Wave hub will initially allow 20MW of capacity to be connected, with potential expansion to 40MW. Four device manufacturers have so far expressed interest in connecting to the Wave hub.[43][44]

The scientists have calculated that wave energy gathered at Wave Hub will be enough to power up to 7,500 households. Savings that the Cornwall wave power generator will bring are significant: about 300,000 tons of carbon dioxide in the next 25 years.[45]

A CETO wave farm off the coast of Western Australia has been operating to prove commercial viability and, after preliminary environmental approval, is poised for further development. see http://www.ceto.com.au/home.php

Discussion of Salter's Duck

In response to the Oil Crisis, a number of researchers reexamined the potential of generating energy from ocean waves, among whom is Professor Stephen Salter of the University of Edinburgh, Scotland. His 1974 invention became known as Salter's Duck or Nodding Duck, although it was officially referred to as the Edinburgh Duck. In small scale controlled tests, the Duck's curved cam-like body can stop 90% of wave motion and can convert 90% of that to electricity giving 81% efficiency.[46] The machine has never gone to sea.

According to sworn testimony before the House of Parliament, the UK Wave Energy program was shut down on 1982-03-19, in a closed meeting,[47] the details of which remain secret.

An analysis of Salter's Duck resulted in a miscalculation of the estimated cost of energy production by a factor of 10,[48] an error which was identified in 2008. Some wave power advocates believe that this error, combined with a general lack of enthusiasm for renewable energy in the 1980s (after oil prices fell), hindered the advancement of wave power technology.[49]

Potential

Deep water wave power resources are truly enormous, between 1 TW and 10 TW, but it is not practical to capture all of this.[50] The useful worldwide resource has been estimated to be greater than 2 TW.[51][52] Locations with the most potential for wave power include the western seaboard of Europe, the northern coast of the UK, and the Pacific coastlines of North and South America, Southern Africa, Australia, and New Zealand. The north and south temperate zones have the best sites for capturing wave power. The prevailing westerlies in these zones blow strongest in winter. Waves are very predictable. The waves that are caused by winds can be predicted five days in advance. Tidal currents, caused by lunar positions, are known 100 years in advance. Water has a power density that is 832 times greater than air's power density. That means that large amounts of energy can be obtained from relatively small devices. For example, it would require a wind turbine three times its size to generate the same amount of power as a regular-sized underwater turbine.[53]

Tidal currents in the seas affect the wave heights. This translates to greater energy captured by a wave motor. Studies by the Journal of Coastal Research show that the maximum wave height occurs 50-60 min after the tidal current flooding. These tidal currents have a speed of 0.7 m/s.[54]

The UK has an estimated recoverable resource of between 50–90TWh of electricity a year, this is roughly 15–25% of the current UK electricity demand.[55]

Patents

See also

  • CETO Wave Power
  • European Marine Energy Centre

Notes

  1. For a small-amplitude sinusoidal wave \scriptstyle \eta=a\,\cos\, 2\pi\left(\frac{x}{\lambda}-\frac{t}{T}\right) with wave amplitude \scriptstyle a,\, the wave energy density per unit horizontal area is \scriptstyle E=\frac{1}{2}\rho g a^2, or \scriptstyle E=\frac{1}{8}\rho g H^2 using the wave height \scriptstyle H\,=\,2\,a\, for sinusoidal waves. In terms of the variance of the surface elevation \scriptstyle m_0=\sigma_\eta^2=\overline{(\eta-\bar\eta)^2}=\frac{1}{2}a^2, the energy density is \scriptstyle E=\rho g m_0\,. Turning to random waves, the last formulation of the wave energy equation in terms of \scriptstyle m_0\, is also valid (Holthuijsen, 2007, p. 40), due to Parseval's theorem. Further, the significant wave height is defined as \scriptstyle H_{m0}=4\sqrt{m_0}, leading to the factor 116 in the wave energy density per unit horizontal area.

References

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Further reading

External links

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