EE535: Renewable Energy: Systems, Technology & Economics Session 7: Wave Energy (1)

European Theoretical Wavepower IEA (International Energy Association) estimates that there is a potential to generate 1500TWh per year (10% of global demand) from wave power No commercial wave farms yet exist but there are several beta installments European Wave Energy Atlas, Average Theoretical Wave Power (kW))

Irish Context Estimated power of Atlantic coastline is 40kW per meter of exposed coastline Highest energy points are Northwest Mayo, West Galway, West Cork, Kerry Trade-off between the available energy (which increases with distance from land), and practicalities of harnessing and connecting to grid http://www.inference.phy.cam.ac.uk/withouthotair/c12/page_73.shtml

Waves Storm Waves Swell Waves Wave size depends on: Waves located close to the location where they were generated Form complex irregular sea Swell Waves Waves can travel a great distance with minimum loss of energy to produce a swell Wave size depends on: Wind speed Duration Fetch

Wave Formation Ocean waves are generated by wind passing over stretches of water 3 main processes give rise to wave formation and growth: Air flowing over the seas exerts a tangential stress on the water surface Turbulent air close to the water surface creates rapidly varying shear stresses and pressure fluctuations. Where these processes are in-phase with existing waves, further wave development occurs When waves have reached a certain size, the wind can exert a stronger force on the up-wind face of the wave, causing additional growth

Waves It is important to realise that there is no net motion of water in deep water waves Waves contain energy in two forms: Potential energy – energy required to move the water from the trough to the crest Kinetic Energy – energy associated with water moving around (circular motion)

Difficulties facing wave power developments Wave patterns are irregular in amplitude, phase and direction. Difficult to design devices to extract power efficiently over such a wide range of variables Probability of extreme gales or hurricanes – devices need to be able to withstand conditions which are ~ 100 times the power density for which they are normally matched Peak power normally available in deep water from open swells. Very difficult conditions to construct, fix, and maintain devices

Difficulties facing wave power developments Wave periods are typically low frequency (circa 0.1Hz). Difficult to efficiently couple this slow irregular motion via an electrical generator. Many different device types in the public domain – which to choose? Economy of scale? Peak power is generally only available far from land and remote from dense populations Capital costs of structures very high due to necessity to withstand harsh environments

Advantages of Wave Power Large energy fluxes available Predictability of wave conditions over a period of days Low environmental impact – little visual impact Since only a small fraction of wave power is extracted, impact on coastline is minimal Chemical pollution is minimal No obvious problems for marine life Load factor of energy supply from ocean waves matches demand for electricity – wave power largest in winter when demand is increased Economies can be achieved by installing wave generators in groups and connecting to shore via a single submarine cable

Properties of Deep Water Waves Surface waves are sets of unbroken sine-waves of irregular wavelength, phase and direction Motion of any particle of water is circular. Surface form of the wave shows progression, but water particles have no net progression Water on the surface remains on the surface The amplitudes of water particle motion decreases exponentially with depth The amplitude of the wave is independent of λ, c or T A wave will break into white water when the slope of the surface exceeds about 1 in 7 – dissipating energy potential

Wave Motion Wave direction Wave Surface Tangent mrw2 Resultant F F mg Water surface perpendicular to resultant of gravitation and centrifugal Forces acting on an element of water of mass m λ a H w Wave Motion Wave Characteristics

Wave Particle Motion a

Water Particle Acceleration Wave direction x s g Resultant acceleration aw2 g s Ф aw2 aw2 sinώ Note: force due to gravity = mg, centrifugal force = maw2

(particle velocity)

+z crest -z trough

Summary for Deep Water Waves

Power From earlier, we know that the energy per unit wavelength in the direction of the wave is given by E = ½ ρa2gλ Phase velocity c = λ/T, so E = ½ ρa2g cT To calculate the power we need to consider the group behaviour of the waves. Specifically the velocity u at which the energy in the group of waves is carried forward is related to the phase velocity by u = c/2 This property comes about due to the dispersive nature of waves So, Power P = E/(time) = ½ ρa2g (c/2) = ¼ ρa2g c = ¼ ρa2g λ/T

Question What is the power in a deep water wave of wavelength 100m and amplitude 1.5m? We know from earlier that c = 13m/s (group velocity) u = c/2 = 6.4m/s P = ½ (1025kg/m2)(9.81ms-2)(1.5m)2(6.5m/s) P = 73 kW/m