An Introduction to Wave and Tidal Energy Renewable Energy in (and above) the Oceans Frank R. Leslie, BSEE, MS Space Technology 5/25/2002, Rev. 1. 7 fleslie @fit. edu; (321) 674 -7377 www. fit. edu/~fleslie f. leslie @ieee. org; (321) 768 -6629 “It is pleasant, when the sea is high and the winds are dashing the waves about, to watch from shore the struggles of another. ” Lucretius, 99 -55 B. C.
15. O Overview of Ocean Energy l Ocean energy is replenished by the sun and through tidal influences of the moon and sun gravitational forces l Near-surface winds induce wave action and cause windblown currents at about 3% of the wind speed l Tides cause strong currents into and out of coastal basins and rivers l Ocean surface heating by some 70% of the incoming sunlight adds to the surface water thermal energy, causing expansion and flow l Wind energy is stronger over the ocean due to less drag, although technically, only seabreezes are from ocean energy 1. 0 020402
15. Available Energy l Potential Energy: PE = mh l Kinetic Energy: KE = ½ mv 2 or ½ mu 2 l Wave energy is proportional to wave length times wave height squared (LH 2)per wave length per unit of crest length A four-foot (1. 2 m), ten-second wave striking a coast expends more than 35, 000 HP per mile of coast [Kotch, p. 247] l Maximum Tidal Energy, E = 2 HQ x 353/(778 x 3413) = 266 x 10 -6 HQ k. Wh/yr, where H is the tidal range (ft) and Q is the tidal flow (lbs of seawater) l E = 2 HQ ft-lb/lunar day (2 tides) or E = 416 x 10 -4 HV k. Wh, where V is cubic feet of flow 1. 2 020412
15. Ocean Energy l The tidal forces and thermal storage of the ocean provide a major energy source l Wave action adds to the extractable surface energy l Major ocean currents (like the Gulf Stream) may be exploited to extract energy with underwater rotors (turbines) l The oceans are the World’s largest solar collectors (71% of surface) l Thermal differences between surface and deep waters can drive heat engines l Over or in proximity to the ocean surface, the wind moves at higher speeds over water than over land roughness 2. 0 020329
15. Wave Energy l Energy of interchanging potential and kinetic energy in the wave l Cycloidal motion of wave particles carries energy forward without much current l Typical periodicities are one to thirty seconds, thus there are low-energy periods between high-energy points l In 1799, Girard & son of Paris proposed using wave power for powering pumps and saws l California coast could generate 7 to 17 MW per mile [Smith, p. 91] 2. 0 020402
15. Ocean Energy: Wave Energy l Wave energy potential varies greatly worldwide Figures in k. W/m Source: Wave Energy paper. IMech. E, 1991 and European Directory of Renewable Energy (Suppliers and Services) 1991 2. 0 20329
15. Concepts of Wave Energy Conversion l Change of water level by tide or wave can move or raise a float, producing linear motion from sinusoidal motion l Water current can turn a turbine to yield rotational mechanical energy to drive a pump or generator Slow rotation speed of approximately one revolution per second to one revolution per minute less likely to harm marine life Turbine reduces energy downstream and could protect shoreline l Archimedes Wave Swing is a Dutch device [Smith, p. 91] 2. 1 020402
15. Salter “Ducks” l Scottish physicist Prof. Stephen Salter invented “Nodding Duck” energy converter in 1970 l Salter “ducks” rock up and down as the wave passes beneath it. This oscillating mechanical energy is converted to electrical energy l Destroyed by storm l A floating two-tank version drives hydraulic rams that send pressurized oil to a hydraulic motor that drives a generator, and a cable conducts electricity to shore http: //acre. murdoch. edu. au/ago/ocean/wave. html Ref. : www. fujita. com/archive-frr/ Tidal. Power. html © 1996 Ramage 2. 2. 1 020402
15. Fluid-Driven Wave Turbines l Waves can be funneled and channeled into a rising chute to charge a reservoir over a weir or through a swing-gate Water passes through waterwheel or turbine back to the ocean Algerian V-channel [Kotch, p. 228] l Wave forces require an extremely strong structure and mechanism to preclude damage l The Ocean Power Delivery wave energy converter Pelamis has articulated sections that stream from an anchor towards the shore Waves passing overhead produce hydraulic pressure in rams between sections This pressure drives hydraulic motors that spin generators, and power is conducted to shore by cable 750 k. W produced by a group 150 m long and 3. 5 m diameter 2. 2. 2. 1 020402
15. Fluid-Driven Wave Turbines l Davis Hydraulic Turbines since 1981 Most tests done in Canada 4 k. W turbine tested in Gulf Stream l Blue Energy of Canada developing two 250 k. W turbines for British Columbia l Also proposed Brothers Island tidal fence in San Francisco Bay, California 1000 ft long by 80 ft deep to produce 15 – 25 MW l Australian Port Kembla (south of Sydney) to produce 500 k. W 2. 2. 2. 1 020402
15. Air-Driven Wave Turbines (Con’t) l A floating buoy can compress trapped air similar to a whistle buoy l The oscillating water column (OWC) in a long pipe under the buoy will lag behind the buoy motion due to inertia of the water column l The compressed air spins a turbine/alternator to generate electricity at $0. 09/k. Wh The Japanese “Mighty Whale” has an air channel to capture wave energy. Width is 30 m and length is 50 m. There are two 30 k. W and one 50 k. W turbine/generators http: //www. earthsci. org/esa/energy/wavpwr/wavepwr. html 2. 2 020402
15. Air-Driven Wave Turbines l British invention uses an air-driven Wells turbine with symmetrical blades l Incoming waves pressurize air within a heavy concrete box, and trapped air rushes upward through pipe connecting the turbine l A Wavegen™, wave-driven, air compressor or oscillating water column (OWC) spins a two-way Wells turbine to produce electricity l Wells turbine is spun to starting speed by external electrical power and spins the same direction regardless of air flow direction l Energy estimated at 65 megawatts per mile Photo by Wavegen http: //www. bfi. org/Trimtab/summer 01/ocean. Wave. htm 2. 2 020402
15. Ocean Energy: Tidal Energy l Tides are produced by gravitational forces of the moon and sun and the Earth’s rotation l Existing and possible sites: France: 1966 La Rance river estuary 240 MW station - Tidal ranges of 8. 5 m to 13. 5 m; 10 reversible turbines England: Severn River Canada: Passamaquoddy in the Bay of Fundy (1935 attempt failed) California: high potential along the northern coast l Environmental, economic, and esthetic aspects have delayed implementation l Power is asynchronous with load cycle 3. 1 020402
15. Tidal Energy l Tidal mills were used in the Tenth and Eleventh Centuries in England, France, and elsewhere l Millpond water was trapped at high tide by a gate (Difficult working hours for the miller; Why? ) Rhode Island, USA, 18 th Century, 20 -ton wheel 11 ft in diameter and 26 ft wide Hamburg, Germany, 1880 “mill” pumped sewage Slade’s Mill in Chelsea, MA founded 1734, 100 HP, operated until ~1980 Deben estuary, Woodbridge, Suffolk, England has been operating since 1170 (reminiscent of “the old family axe”; only had three new handles and two new heads!) Tidal mills were common in USA north of Cape Cod, where a 3 m range exists [Redfield, 1980] Brooklyn NY had tidal mill in 1636 [? ] 3. 1 020402
15. Tidal Energy (continued) l Potential energy = S integral from 0 to 2 H (ρgz dz), where S is basin area, H is tidal amplitude, ρ is water density, and g is gravitational constant yielding 2 S ρ g. H 2 l Mean power is 2 S ρ g. H 2/tidal period; semidiurnal better l Tidal Pool Arrangements Single-pool empties on ebb tide Single-pool fills on flood tide Single-pool fills and empties through turbine Two-pool ebb- and flood-tide system; two ebbs per day; alternating pool use Two-pool one-way system (high and low pools) (turbine located between pools) 3. 1 020402
15. Tidal Water Turbines l Current flow converted to rotary motion by tidal current l Turbines placed across Rance River, France l Large Savonius rotors (J. S. Savonius, 1932? ) placed across channel to rotate at slow speed but creating high torque (large current meter) l Horizontal rotors proposed for Gulf Stream placement off Miami, Florida 3. 2 020402
15. Tidal Flow: Rance River, France l l l l 240 MW plant with 24, 10 MW turbines operated since 1966 Average head is 28 ft Area is approximately 8. 5 square miles Flow approx, 6. 64 billion cubic feet Maximum theoretical energy is 7734 million k. Wh/year; 6% extracted Storage pumping contributes 1. 7% to energy level At neap tides, generates 80, 000 k. Wh/day; at equinoctial spring tide, 1, 450, 000 k. Wh/day (18: 1 ratio!); average ~500 million k. Wh/year l Produces electricity cheaper than oil, coal, or nuclear plants in France 3. 3 020329
15. Tidal Flow: Passamaquoddy, Lower Bay of Fundy, New Brunswick, Canada l l l l Proposed to be located between Maine (USA) and New Brunswick Average head is 18. 1 ft Flow is approximately 70 billion cubic feet per tidal cycle Area is approximately 142 square miles About 3. 5 % of theoretical maximum would be extracted Two-pool approach greatly lower maximum theoretical energy International Commission studied it 1956 through 1961 and found project uneconomic then l Deferred until economic conditions change [Ref. : Harder] 3. 3 020329
15. Other Tidal Flow Plants under Study l Annapolis River, Nova Scotia: straight-flow turbines; demonstration plant was to be completed in 1983; 20 MW; tides 29 to 15 feet; Tidal Power Corp. ; ~$74 M l Experimental site at Kislaya Guba on Barents Sea French 400 k. W unit operated since 1968 Plant floated into place and sunk: dikes added to close gaps l Sea of Okhotsk (former Sov. Union) under study in 1980 l White Sea, Russia: 1 MW, 1969 l Murmansk, Russia: 0. 4 MW l Kiansghsia in China 3. 3 020402
15. Other Tidal Flow Plants under Study (continued) l Severn River, Great Britain: range of 47 feet (14. 5 m) calculated output of 2. 4 MWh annually. Proposed at $15 B, but not economic. l Chansey Islands: 20 miles off Saint Malo, France; 34 billion k. Wh per year; not economic; environmental problems; project shelved in 1980 l San Jose, Argentina: potential of 75 billion k. Wh/year; tidal range of 20 feet (6 m) l China built several plants in the 1950 s l Korean potential sites (Garolim Bay) 3. 3 0203402
15. Hydraulic Pressure Absorbers l Large synthetic rubber bags filled with water could be placed offshore where large waves pass overhead Also respond to tides A connecting pipe conducts hydraulic pressure to a positive displacement motor that spins a generator The motor can turn a generator to make electricity that varies sinusoidally with the pressure http: //www. bfi. org/Trimtab/summer 01/ocean. Wave. htm 4. 0 020402
15. Ocean Thermal Energy: OTEC (Ocean Thermal Electric Conversion) l French Physicist Jacque D’Arsonval proposed in 1881 l Georges Claude built Matanzos Bay, Cuba 22 k. W plant in 1930 [Smith, p. 94] l Keahole Point, Hawaii has the US 50 k. W research OTEC barge system l OTEC requires some 36 to 40°F temperature difference between the surface and deep waters to extract energy l Open-cycle plants vaporize warm water and condense it using the cold sea water, yielding potable water and electricity from turbines-driven alternators l Closed-cycle units evaporate ammonia at 78°F to drive a turbine and an alternator l Hybrid cycle uses open-cycle steam to vaporize closed-cycle ammonia l China also has experimented with OTEC Ref. : http: //www. nrel. gov/otec/achievements. html 5. 0 020402
15. Wind Energy Equations (also applies to water turbines) l Assume a “tube” of air the diameter, D, of the rotor A = π D 2/4 l A length, L, of air moves through the turbine in t seconds L = u·t, where u is the wind speed l The tube volume is V = A·L = A·u·t l Air density, ρ, is 1. 225 kg/m 3 (water density ~1000 kg/m 3) l Mass, m = ρ·V = ρ·A·u·t, where V is volume l Kinetic energy = KE = ½ mu 2 6. 1 020402
15. Wind Energy Equations (continued) l Substituting ρ·A·u·t for mass, and A = π D 2/4 , KE = ½·π/4·ρ·D 2·u 3·t l Theoretical power, Pt = ½·π/4·ρ·D 2·u 3·t/t = 0. 3927·ρa·D 2·u 3, ρ (rho) is the density, D is the diameter swept by the rotor blades, and u is the speed parallel to the rotor axis l Betz Law shows 59. 3% of power can be extracted l Pe = Pt· 59. 3%·ήr·ήt·ήg, where Pe is the extracted power, ήr is rotor efficiency, ήt is transmission efficiency, and ήg is generator efficiency l For example, 59. 3%· 90%· 98%· 80% = 42% extraction of theoretical power 6. 1 020402
15. C Conclusion l Renewable energy offers a longterm approach to the World’s energy needs l Economics drives the energy selection process and short-term (first cost) thinking leads to disregard of long-term, overall cost l Wave and tidal energy are more expensive than wind and solar energy, the present leaders l Increasing oil, gas, and coal prices will ensure that the transition to renewable energy occurs l Offshore and shoreline wind energy plants offer a logical approach to part of future energy supplies 8. 0 0201402
References: Books, etc. l l l General: Sørensen, Bent. Renewable Energy, Second Edition. San Diego: Academic Press, 2000, 911 pp. ISBN 0 -12 -656152 -4. Henry, J. Glenn and Gary W. Heinke. Environmental Science and Engineering. Englewood Cliffs: Prentice. Hall, 728 pp. , 1989. 0 -13 -283177 -5, TD 146. H 45, 620. 8 -dc 19 Brower, Michael. Cool Energy. Cambridge MA: The MIT Press, 1992. 0 -262 -02349 -0, TJ 807. 9. U 6 B 76, 333. 79’ 4’ 0973. Di Lavore, Philip. Energy: Insights from Physics. NY: John Wiley & Sons, 414 pp. , 1984. 0 -471 -89683 -7 l, TJ 163. 2. D 54, 621. 042. Bowditch, Nathaniel. American Practical Navigator. Washington: USGPO, H. O. Pub. No. 9. Harder, Edwin L. Fundamentals of Energy Production. NY: John Wiley & Sons, 368 pp. , 1982. 0 -471 -083569, TJ 163. 9. H 37, 333. 79. Tidal Energy, pp. 111 -129. Wind: Patel, Mukund R. Wind and Solar Power Systems. Boca Raton: CRC Press, 1999, 351 pp. ISBN 0 -84931605 -7, TK 1541. P 38 1999, 621. 31’ 2136 Gipe, Paul. Wind Energy for Home & Business. White River Junction, VT: Chelsea Green Pub. Co. , 1993. 0 -930031 -64 -4, TJ 820. G 57, 621. 4’ 5 Johnson, Gary L, Wind Energy Systems. Englewood Cliffs NJ: Prentice-Hall, Inc. TK 1541. J 64 1985. 621. 4’ 5; 0 -13 -957754 -8. Waves: Smith, Douglas J. “Big Plans for Ocean Power Hinges on Funding and Additional R&D”. Power Engineering, Nov. 2001, p. 91. Kotch, William J. , Rear Admiral, USN, Retired. Weather for the Mariner. Annapolis: Naval Institute Press, 1983. 551. 5, QC 994. K 64, Chap. 11, Wind, Waves, and Swell. Solar: Duffie, John and William A. Beckman. Solar Engineering of Thermal Processes. NY: John Wiley & Sons, Inc. , 920 pp. , 1991. 9. 1 020402
References: Internet l General: http: //www. google. com/search? q=%22 renewable+energy+course%22 http: //www. ferc. gov/ Federal Energy Regulatory Commission http: //solstice. crest. org/ http: //dataweb. usbr. gov/html/powerplant_selection. html http: //mailto: energyresources@egroups. com http: //www. dieoff. org. Site devoted to the decline of energy and effects upon population l Tidal: http: //www. unep. or. kr/energy/ocean/oc_intro. htm http: //www. bluenergy. com/technology/prototypes. html http: //www. iclei. org/efacts/tidal. htm http: //zebu. uoregon. edu/1996/ph 162/l 17 b. html l Waves: http: //www. env. qld. gov. au/sustainable_energy/publicat/ocean. htm http: //www. bfi. org/Trimtab/summer 01/ocean. Wave. htm http: //www. oceanpd. com/ http: //www. newenergy. org. cn/english/ocean/overview/status. htm http: //www. energy. org. uk/EFWave. htm http: //www. earthsci. org/esa/energy/wavpwr/wavepwr. html 9. 2 020329
References: Internet l Thermal: http: //www. nrel. gov/otec/what. html http: //www. hawaii. gov/dbedt/ert/otec_hi. html#anchor 349152 on OTEC systems l Wind: http: //awea-windnet@yahoogroups. com. Wind Energy elist http: //awea-wind-home@yahoogroups. com. Wind energy home powersite elist http: //telosnet. com/wind/20 th. html 9. 2 020329
Units and Constants l Units: Power in watts (joules/second) Energy (power x time) in watt-hours l Constants: 1 m = 0. 3048 ft exactly by definition 1 mile = 1. 609 km; 1 m/s = 2. 204 mi/h (mph) 1 mile 2 = 27878400 ft 2 = 2589988. 11 m 2 1 ft 2 = 0. 09290304 m 2; 1 m 2 = 10. 76391042 ft 2 1 ft 3 = 28. 32 L = 7. 34 gallon = 0. 02832 m 3; 1 m 3 = 264. 17 US gallons 1 m 3/s = 15850. 32 US gallons/minute g = 32. 2 ft/s 2 = 9. 81 m/s 2; 1 kg = 2. 2 pounds Air density, ρ (rho), is 1. 225 kg/m 3 or 0. 0158 pounds/ft 3 at 20ºC at sea level Solar Constant: 1368 W/m 2 exoatmospheric or 342 W/m 2 surface (80 to 240 W/m 2) 1 HP = 550 ft-lbs/s = 42. 42 BTU/min = = 746 W (J/s) 1 BTU = 252 cal = 0. 293 Wh = 1. 055 k. J 1 atmosphere = 14. 696 psi = 33. 9 ft water = 101. 325 k. Pa = 76 cm Hg =1013. 25 mbar 1 boe (42 - gallon barrel of oil equivalent) = 1700 k. Wh 9. 3 020402
Energy Equations l Electricity: E=IR; P=I 2 R; P=E 2/R, where R is resistance in ohms, E is volts, I is current in amperes, and P is power in watts Energy = P t, where t is time in hours l Turbines: Pa = ½ ρ A 2 u 3, where ρ (rho) is the fluid density, A = rotor area in m 2, and u is wind speed in m/s P = R ρ T, where P = pressure (Nm-2 = Pascal) Torque, T = P/ω, in Nm/rad, where P = mechanical power in watts, ω is angular velocity in rad/sec l Pumps: Pm = g. Qmh/ήp W, where g=9. 81 N/kg, Qm is mass capacity in kg/s, h is head in m, and ήp is pump mechanical efficiency 9. 4 020402
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