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Harvesting of wave energy and converting it into electrical energy is the subject of worldwide efforts for many years. In light of the cost of electricity production from fossil fuels, (for example electricity generated by large scale coal burning power plants costs about 2.6 cents per kilowatt-hour), the target-cost for wave power production is 5 cents per kilowatt-hour or lower, equal to the wind turbine power production cost. However, we must point out two important factors that are missing from the cost of burning fossil fuels; a) the cost of environmental destruction and b) that the fossil fuels on the planet do not last forever. On the other hand in very industrialized countries like Japan, the energy consumption is less than 1% of solar energy reaching the surface of these countries. Therefore, it is very comprehensible the need to utilize the primary and secondary solar energy offered to us profusely and forever. In particular, the net resource (minus "costs") of wave energy is equal to or better than the resources of wind, solar, small hydro plants, or biomass energy. Thus, the use of the wave ocean energy remains a major challenge for many years.
The innovative concept of the proposed converter by HWET is aimed to low cost electric power production. The converter is a linear type attenuator. Unlike any known machine so far its operation is based in the mediation of water between sea waves and a chain from pairs of buoys. Both the mediated water and the buoys are enclosed in a hermetically sealed "floating tube". As the tube interacts with the waves, the buoys are moving up and down and by means of proper transmission mechanism they activate an electric generator enclosed also in the "floating tube". The development and commercialization of a low cost converter for exploitation of the enormous wave energy potential, is beneficial not only for countries with high wave energy potential, but even for countries with moderate wave energy potential and long coast line, as for example, Greece, Japan, etc. Therefore, an ambitious project leading to the development of a low-cost wave-energy converter is a challenge and any possible joint venture would be very welcomed.
Contact: alexandrosanastassiadis@gmail.com
Animations: http://youtu.be/33nXbjlpam4

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  1. 1. Introduction The proposed converter is a linear attenuator Its operation is based in the mediation of water between sea waves and a chain of power units (PU) Power units and water are inside a floating tube The water is the working substance acting as an interface between the sea waves and the power units
  2. 2. Concept requirements Low manufacturing and maintenance cost in order the device to meet the cost requirements (≈ 0,05 €/Kwh) Long device viability High capability of capturing wave power flux Modular structure Environmentally friendly
  3. 3. Main componentsA Power module with m (=1, 2,...,m) PU’s and thegenerator compartment in the middle.(1) Flexible and durable floating tube reinforced with metal rings. The tube is tightly closed.(2) Power unit,(3) Generator compartment hermetically closed(4) Articulated axis with Cardan joints
  4. 4. The power unit (1) Pair of cylindrical buoys (2) Gear systems (3) Protective cage (4) Shaft (5) Cardan joint (6) Buoy supporting arm
  5. 5. The pinion system (1) Arm supporting buoy I, rotating freely around the shaft (2) Arm supporting buoy II, rotating freely around the shaft (3) Pinion mounted on arm 1 performing rotation with center on the shaft (4) Pinion mounted on arm 2 rotating around the shaft, coupling pinion 3 with pinion 5 (5) Pinion coupled to the shaft through a ratchet (not shown in the figure) (6) The shaft. A ratchet (not shown) couples the shaft with the pinion 5
  6. 6. Function of a power moduleThe floating tube is filled with water by half, another 30% of the tube approximately isoccupied by the power units and the generator compartment and the remaining 20% isfree space. Buoys, in a trough contained water, move upward, while buoys on acrest, move downward by following the receding water. The water in the tube isdenoted by blue color, while the dot line stands for the sea wave. Tube sections in wavetroughs sink deeper relative to tube sections on wave crests. This is the Hug effect. If ζand C the sea surface and tube axis deviations correspondingly, then Hug ≡ ABS(ζmax–Cmax)
  7. 7. Power flow associated with a sea waveLet Fw the wave energy flux through a vertical plane of unitwidth perpendicular to the wave propagation direction, then Fw = E 0 c gWhere, E0 the wave energy density E0=ρw g Hs2/16, cg the groupvelocity of the wave in deep-water approximation, cg=g/2ωp, Hs the significant wave height, Tp the peak wave periodof the Pierson-Moskowitz spectrum and ωp = 2π/ Tp. Makingthe replacements ρw≈1000 Kg/m3 and g≈10 m/s2 we obtain Fw ≈ 0,5Hs2 Tp Kw/m
  8. 8. According to Pierson-Moskowitz spectrum Hs=0,021U2 and Tp ~0,73U U the wind speed at 19,5 m high so, Fw=2,5 Hs5/2 and Tp=5,04Hs1/2Fw Kw/m Tp Fw
  9. 9. Power capability of the converter The figure shows a cross-section of a power unit D: floating tube diameter R: buoys radius r: polar distance of the buoy center q: polar angle of the centers of the buoys h: maximum vertical distance traversed by buoys centers
  10. 10. It is easy to prove that maximum work per stroke is obtained ifR = 0,2D, then r = 0,3D, h= 0,447D & -0,841 ≤ q ≤ +0,841 radIf we take Z=1,5D and W the buoys weight, then Wmax = 1,65D4-0,8944WD/1000 KJ/PU (per power unit) Ppuc=(1,65D3 - 0,8944W/1000)D/T Kw/PU (per power unit)1. Assume a sinusoidal wave with T = Tp2. Neglect the weight term as very small compared to buoyancy3. Divide by the PU length (=2D), then we obtain Pc ≡ 0,825D3/Tp Kw/mthe relation above is the definition of the power capability of a converter.Pc is a reference quantity for determining the efficiency of a converter under real sea conditions
  11. 11. Equations of motion Torques associated with a PU Buoyancy torque per buoy Tb(t)=0,018ρgD4(U-sinUcosU)cosq Weight torque per buoy Tw=-0,3WDcosq Driving torque per couple of buoys: Tbw=2(Tb + Tw) Damping torque per couple of buoys Td =a(dq/dt) Inertia torque per couple of buoys TI =-0,18(WD2/g)(d2q/dt2) Equation of motion: TI+Tbw+Td =0
  12. 12. Equation of upward motion: 0,18(WD2/g)(d2q/dt2)=Tbw-a(dq/dt)In the downward motion we neglect inertia term as negligible and thedamping term (a=0) since the buoys fall freely following the waterlevel, then Tbw=0 and consequently U-sinUcosU - (0,3/0,018)W/ρg D3=0The solution is denoted by Uw. The downward motion starts when thenormalized water level Q≡Y/D takes the value Qw given by Qw=0,3sinqmin– 0,2cosUwThe normalized distance Hw ≡ H/D of the buoy center from the water levelQw is given by Hw≡ (ymin-Ymin)/D = 0,3sinqmin-Qw=0,2cosUwThe buoys follow the descending water Q, while Hw remains constant duringthe downward motion so,Equation of downward motion may be written as follows, q=Asin((0,2cosUw+Q)/ 0,3) (Asin stands for the inverse sin)Equations of motion are solved numerically.
  13. 13. Power considerationsThe dissipated power by a damper is given by Pd = Td(dq/dt) = a(dq/dt)2 w/PUSimilarly the power yield of the converter is given by Pyld = Tbwdq/dt = a(dq/dt)2 w/PUFor very low or very high values of a, Pd → 0, so thereis an optimum value of aopt for which Pd becomesmaximum. we determine aopt, we introduce it into theeq. of motion and solve it numerically. The maximumpower yield per power module meter is given by Pyld = (10-3Tbw/2D)dq/dt Kw/m
  14. 14. Water Fluctuation Factor: WFF is an important quantity, defined as two times the standard deviation of Q(t), i.e., WFF ≡ 2<Q(t)2>1/2WFF is strongly dependent on Hs and D and characterizesthe water behavior inside the floating tube. WFF is a factorrequiring measurement in the concept validationexperiment.Efficiency Coefficient: This coefficient characterizes theperformance of a power module and is defined as follows, e ≡ <Pyld>/PcOur simulation model shows strong dependence of e on WFF
  15. 15. Application Solution of eq. of motion for a regular sinusoidal wave Wave parameters: Hs = 3,02 m, Tp =8,76 sec, Fw=40 Kw/m Power module parameters: D=3 m, Hug= 0,43 m, Pc = 2,54 Kw/m, Solution: WWF=0,71%, <Pyld>=2,44 Kw/m, e = 96%,
  16. 16. Tbw vs q Tbw vs Ωthe inscribed area is equal to the work Negative values of Ω, corresponding to produced by the buoys per cycle downward motion, have been neglected
  17. 17. Further analysis gives the following interesting results
  18. 18. Irregular wave-fully developed sea
  19. 19. Plots of Tbw vs. q and Ω for various D’s - Wave characteristics (Hs,Tp, Fw) are fixed
  20. 20. In Figs Tbw vs. Ω, we have omitted negative values of Ω for reasons of clarity. On the other hand the downward motion is not of particular importance. Looking at theplots of Tbw vs q we observe the pattern to shift to higher values of q withIncreasing D. In other words the buoys tend to move to the upper half of the floating tube and their activity is limited to narrower range of q’s. Similarly, thePlots of Tbw vs. Ω (=dq/dt) show that the buoys activity tends to be confined in thevicinity of a straight line as D increases.
  21. 21. Irregular• In the case of the specific irregular wave Pyld, e > Pyld , e corresponding to the regular wave for all D’s. The reason is that in the sea wave there are more numerous time-intervals < Tp between successive troughs or crests than time-intervals > Tp.• Also, in the irregular wave, e increases slightly for 1 ≤ D ≤ 3 m and then decreases for higher values of D, while e, corresponding to the regular wave, always decreases as D increases. This is due to two competing factors. One is the increasing e-width with D, responsible for the increasing of e and the other is the decreasing of WWF with D, responsible for the decreasing of e. The influence of WFF seems to prevail for D>3 m• The behavior of WFF as D varies is almost the same in both kinds of waves, having only slightly lower values.
  22. 22. DiscussionSo far we have developed an innovative concept aimedto a low cost electric power production. Based in thecost of fossil fuels, the target is about 0,05 euros /Kwh.However, we must point out that two important factorsare missing from this estimate, the cost ofenvironmental destruction and the finite amount offossil fuels on the planet. On the other hand the energyconsumption in heavily industrialized countries is lessthan 1% of solar energy reaching the surface of thesecountries. That alone makes comprehensible the need toutilize, in every possible way, the primary and secondarysolar energy offered to us profusely and for ever.
  23. 23. Among a number of important technical issues we choosesome basic ones to discuss below:a. We have made the assumption that the internal water level follows the inverse sea level motion. This is not totally true. Actually, the internal water tends to follow the troughs, but we do not know the exact way. This is an issue which requires thorough investigation under various waves in the beginning of the experimental work.b. The right and the left buoy must remain in the right and left side of the power unit always since if they interchange position, the power unit stops producing work. This may be achieved by introducing a reset buoy on the top of the power unit to reset the unit in upright position, as shown in the figure below. Shown also the limiters of upward/downward buoys motion, as well the electric power cable.
  24. 24. External flexible/durable tube Reset buoy Limiter of upward Protective cage buoys motion Left Buoy Right Buoycable that runs through the unitresulting in sockets at the ends Limiter of downwardof the power module buoys motion
  25. 25. c. A farm may be developed in a zig-zag formation for efficient capture of the wave energy. The zig-zag arrangement ensures yet the direct connection of internal wires between adjacent devices. Loose anchoring Tight anchoring Wave Front
  26. 26. The zig-zag farm is allowed to orient in the direction of the wavepropagation, thanks to the flexibility of the tubes, if the ends, opposite to theincident wave front, are tightly anchored, while the other ones are looselyanchored.
  27. 27. d. A very important issue is the protection of the farm against storm conditions. Only devices that can withstand the strongest storms will survive. Already, the flexibility of the device and the farm as a whole, the matching of the wave with the device, at any time, by equalizing weight and buoyancy along the tube, as well as the mobility of the internal water remove the risk of accumulation of strong stresses in individual points. On the other hand, the forces developed inside the tube by the weight of the accumulated water and the buoyancy of the buoys in the troughs of the wave (action- reaction) are distributed over a large area of the floating tube walls and thus result in the pursuit of relatively low pressure on the walls, i.e. this is a kind of self-protection. However, under conditions of large scale storms, each device of the farm must be able to sink below the surface of the sea. One idea would be the buoys and the floating tube to be filled with water. Technically, this is achieved if the buoys consist of perforated solid outer wall with an air-bladder inside. To achieve immersion, we pump out the air of the buoys and we pump into the floating tube and the buoys sea water.
  28. 28. e. The Concept Proof is a necessary experimental procedure and consist the starting phase for the validation of the concept, before the submission of a proposal, aiming to a commercial device, for financial support from European programs, or/and from the private sector. The latter would concern the next phases as: the Engineering design model, the Process model, the Prototype model, and Demonstration model. The experimental device for the concept proof should be about 10 meters long and 0,4 meters in diameter. The experiment might be performed in two steps: Step 1: Measurement of the two important factors (WFF and hug) in a simplified variation of the device, free of complex mechanical parts. The values of the above factors are determinative for prooving the theoretically expected power yields. This is a very low cost step and it is decisive one in order to proceed to the next more costly experiment. Step 2: In this step the power yield, the buoyancy of the device and the forces exerted upon it, as well as the mooring tensions developed for various kinds of waves.
  29. 29. Main characteristicsI. Low cost electric power production Very simple design leading to low manufacturing cost. Most parts of the device float in the sea and are much lighter than most of the competitive machines. Therefore, a device can be transferred near the sea in parts and be assembled in the sea with consequent cost reduction. The structural flexibility of the device, the movement of the water inside the tube to positions of minimum potential energy and the consequent hugging of the wave minimizes unwanted loadings, securing long viability. The zig-zag layout allows the installation of the main electrical conductor inside the tubes along the farm line and from there to the mains in the mainland reducing this way the total length of the conductor and consequently the cost of the energy transfer. This is compared with farms with scattered formations of other devices A low cost converter would be very appropriate for low wave potential seas. In such seas, the viability of a converter would be rather high, lowering even more the operational cost of the farm.
  30. 30. Main characteristics (continued)II. Friendliness to the marine environment There are no turbines and high pressure pumps which operate with non-ecological liquids. There is no any external protective paint. It is not noisy. The farms are low profile and there are no horizon blocking gigantic structures. Installed a few kilometers away from the coastline they are not being visible from the coast.
  31. 31. Inventors Alexandros Anastassiadis, Physicist, Ph.D. Columbia University N.Y., alexandrosanastassiadis@gmail.com John Anastassiadis, Engineering Science: B.S. The City University of New York, johna@ath.forthnet.gr Dimitrios Papageorgiou, B.S. in Economics and Business Management at SUNY Stonybrook, M.B.A. in Finance & BPR, Athens Laboratory of Business Administration, dipapageor@cosmote.grPatent: In the process of publication