EE535: Renewable Energy: Systems, Technology & Economics

1. EE535: Renewable Energy: Systems, Technology & Economics Tidal (1)

2. Nature of the Resource • Tidal energy is the result of the gravitational pull of the moon, and to a lesser extent the sun • Tidal energy schemes rely on the twice daily tides which produce the ebb and flow of large volumes of water in estuaries and at sea • Other factors such as ocean depths, landmass shapes etc, can accentuate tidal flow • Energy can be extracted from the tidal flow in 2 principal ways: • Tidal Barges • Tidal Streams

3. Centrifugal Effect Gravitational Effect As the earth rotates on its axis, 2 high tides are drawn around the globe as it rotates - 2 high tides every day (24.8 hour period) Lunar Induced Tide moon moon

4. Influence of Solar Effects • The solar tide moves in and out of phase with the lunar tide • Lunar and solar tides are in phase when sun, earth and moon are aligned • Produces tides of maximum range • These are spring tides • Occur twice per month at full and new moons • When sun/earth and moon/earth directions are perpendicular • Produces tides of minimum range • These are neap tides s m e s e m m s e s e or m

5. Tidal Currents • Tidal current over a 21-day period at a location where the maximum current at spring tide is • 2.9 knots (1.5 m/s) and the maximum current at neap tide is 1.8 knots (0.9 m/s). • (b) The power per unit sea-floor area over a nine-day period extending from spring tides to neap tides. • The power peaks four times per day, and has a maximum of about 27 W/m2. • The average power of the tide farm is 6.4 W/m2. http://www.inference.phy.cam.ac.uk/withouthotair/cG/page_315.shtml

6. Power density of tidal pools / barges / Tidal Range Power • Tide pool filled rapidly at high tide and emptied rapidly at low tide • So, change in potential energy every 6 hours is mgh (where h is half the range) • The mass per unit area covered by the tide pool = ρ 2h • So, power per unit area generated by a tide pool • P = 2 ρghgh / 6 hours • Let h = 2meters, density of water = 1000kg/m3, g = 9.81m/s/s • Power per unit area ≈ 3.6 W/ m2 • Assume 90% efficiency: 3W/m2 High water Tidepool h Range (R) Low water sea turbine Power = E/T = ρ A R2g/2T

7. Tidal Streams / Tidal Flow Power • Near coastlines and between islands, tides may produce strong water currents • Tidal flow power conversion is similar to wind power conversion, • Advantage of predictable velocity and greater fluid density (x1000) • Disadvantage of low fluid velocity and an aquatic environment • Power density for in water = ½ ρ v3 • Only a fraction of the power available can realistically be converted (typically about 40%) • Tidal current velocities vary with time approximately as : • V = Vo sin (2πt / τ), where τ is the period of the natural tide (12h 25min for semidiurnal tide), and Vo is the maximum velocity of the current • If η is the efficiency of the conversion device, the electric power per unit cross section = 0.25 ηρVo3

8. Tidal Current Power Device Electric generator Tidal Flow turbine seabed

9. Drawbacks of Tidal Energy • Mismatch of principal lunar driven periods of 12h 25mins and 24hrs50 mins with the human (solar) period of 24hrs – optimum generation not in phase with demand • Tidal range changes over a 2 week period – producing changing power production • Large volume of water at low head necessitates many specially constructed turbines in parallel • Very high capital costs of installations • Potential ecological harm to estuaries and marine regions

10. Resonance Enhancement • Resonant enhancement on the tides in estuaries and bays occurs in the same manner as the resonance of sound waves in a closed pipe • Resonance with the open sea tide occurs when L = jλ/4, j is an odd integer • Natural frequency of the resonance : • fr = 1/Tr = c/λ • Wave of velocity c = √(gh) • So, Tr = λ/c = 4L /jc = 4L/j√(gh) • L/√h = (j/4) √(g)Tf λ/4 Land Open Sea

11. River Severn Example • The River Severn estuary between Wales and England has a length of about 200km and a depth of 30m. • So L/√h = 200x103m / √(30m) = 36000m1/2 • The semidiurnal tidal period is about 12hrs 25mins. • So, resonance for j = 1 occurs when : • L/√h = (45000s/4) √(9.81ms-2) = 36000m1/2 • Hence there is a close matching of the estuary’s resonance frequency with the normal tide frequency. • Large amplitude tidal motions of 10 – 14m range occur

12. Open Hydro http://www.openhydro.com/technology.html