Dynamic Behaviour of the Patented Kobold Tidal Current Turbine.pdf

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<ul><li><p>NotationSymbol Unit Description</p><p>a Interference factorc m Blade chord lengthCd Airfoil drag coefficientCl Airfoil lift coefficientCmc/4 Airfoil quarter chord pitching moment</p><p>coefficientCD Blade drag coefficientCL Blade lift coefficientCp Turbine performance coefficientCq Turbine torque coefficientD N DragdF N Elementary force acting on the elemen-</p><p>tary actuator diskIp kgm</p><p>2 Blade moment of inertiaIT kgm</p><p>2 Turbine moment of inertiaL N LiftM Nm Instantaneous turbine torqueMC Nm Instantaneous load torqueMc/4 Nm Quarter chord pitching momentMm Nm Average turbine torqueN N Blade radial forceNb Number of bladesP W Instantaneous turbine mechanical powerPm W Average turbine mechanical powerR m Turbine radiusRe Blade Reynolds numberS m2 Turbine frontal areaT Nm Blade tangential forceV m/s Local velocityVR m/s Tip speed</p><p>V</p><p>m/s Asymptotic velocityxc/4 %blade</p><p>chordBlade aerodynamic centre position</p><p>xhinge %bladechord</p><p>Floating hinge position</p><p> rad Blade angle of attacktan rad Angle between the local velocity and the</p><p>local tangent at the bladezv rad Blade pitch angle rad/s2 Blade pitch angle acceleration Tip speed ratio R/V</p><p> kg/m3 Fluid density Solidity Nb c /R rad Blade azimuth angle rad/s2 Turbine acceleration rad/s Turbine angular velocity</p><p>Subscriptd Conditions at the downwind actuator</p><p>disku Conditions at the upwind actuator diskh Hinge</p><p>1 IntroductionMarine current energy is a type of renewable energy</p><p>resource that has been less exploited than wind energy. Onlyrecent years, have some countries devoted funds to researchaimed at developing tidal current power stations. Tidal cur-rent turbines, as in the wind community, can be divided intovertical-axis and horizontal axis types. Although horizontalaxis turbines have been more widely used than vertical axistypes for wind energy exploitation, vertical axis turbinescould present significant advantages for tidal current ex-ploitation, because they are simple to build and reliable inworking conditions. Therefore, at beginning of the studies</p><p> Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 77</p><p>Czech Technical University in Prague Acta Polytechnica Vol. 45 No. 3/2005</p><p>Dynamic Behaviour of the PatentedKobold Tidal Current Turbine:</p><p>Numerical and Experimental AspectsD. P. Coiro, A. De Marco, F. Nicolosi, S. Melone, F. Montella</p><p>This paper provides a summary of the work done at DPA on numerical and experimental investigations of a novel patented vertical axis andvariable pitching blades hydro turbine designed to harness energy from marine tidal currents. Ponte di Archimede S.p.A. Company, locatedin Messina, Italy, owns the patented KOBOLD turbine that is moored in the Messina Strait, between the mainland and Sicily. The turbinehas a rotor with a diameter of 6 meters, three vertical blades of 5 meters span with a 0.4 m chord ad hoc designed curved airfoil, producinghigh lift with no cavitation. The rated power is 160 kW with 3.5 m/s current speed, which means 25% global system efficiency. The VAWTand VAWT_DYN computer codes, based on Double Multiple Steamtube, have been developed to predict the steady and dynamicperformances of a cycloturbine with fixed or self-acting variable pitch straight-blades. A theoretical analysis and a numerical prediction ofthe turbine performances as well as experimental test results on both a model and the real scale turbine will be presented and discussed.</p><p>Keywords: vertical-axis-hydro-turbine, variable pitch, Double-Multiple-Streamtube, tidal currents, tidal energy.</p></li><li><p>vertical axis wind turbines were taken as models for hy-dro-turbines. The blades of Darrieus-type vertical axis windturbines are fixed, and they perform well when the blade so-lidity is low and the working speed is high. For this reason, thefirst hydro-turbines were impossible to start. A variable-pitchblade system can be a solution to this problem. Some proto-types with different variants of this system have thereforebeen developed around the world: the Kobold turbine in theStrait of Messina, Italy; the cycloidal turbine in Guanshan,China; the moment-control turbine at Edinburgh University,UK; and the mass-stabilised system turbine by Kirke andLazauskas in Inman Valley, South Australia. The Kobold tur-bine has been under development since 1997: the rotor has aself-acting variable pitch and the Kobold blades have an ad hocdesigned airfoil, called HLIFT, to be cavitation free andto have high lift performance. The methods for calculat-ing the hydrodynamic performances of vertical axis turbinesalso come from wind turbines: in the 1970s Templin devel-oped the Single-Disk Single-Tube model, and then Stricklandput forward the Single-Disk Multi-Tube model. In the 1980sParaschivoiu introduced the Double-Disk Multi-Tube model.The VAWT and VAWT_DYN computer codes, based on thistheory, have been developed to predict the steady and dy-namic performances of a cycloturbine with fixed or self-actingvariable pitch straight-blades. The numerical results havebeen compared with two sets of experimental data: one set isobtained from wind tunnel tests on a scaled model, and theother set is based on field data from the Kobold prototype.</p><p>2 Double multiple streamtubeIn order to analyze the flow field around a vertical axis</p><p>turbine, a DMS model was used. The DMS model is an evolu-tion of the previous momentum models: the single streamtubemodel, the multiple streamtube model and the doublestreamtube model [1]. The DMS model [2] assumes thatthe flow through the rotor can be modelled by examining theflow through several streamtubes, and the flow disturbance,produced by the rotor is determined by equating the aerody-namic forces on the turbine rotor to the time rate of change inmomentum through the rotor as depicted in Fig. 1. In theDMS model, the flow velocities vary in both the upwind anddownwind regions of the streamtube, as well as varying fromstreamtube to streamtube. So DMS is able to analyse the inter-ference between the downwind blade and the upwind blades</p><p>wake in order to evaluate more accurately the local value ofthe velocity and the instantaneous blade load. As shownin Fig. 1., the rotor is modelled as a series of elementarystreamtubes, and each streamtube is modelled with two actua-tor disks in series. Across the actuator disk the pressure dropsand this drop is equivalent to the streamwise force dF on theactuator disk divided by the actuator disk area dA.</p><p>The elementary force dFu and dFd, respectively on the up-wind and downwind disk, given by the momentum principle,are</p><p>d du u uF V A V V ( )2 (1)</p><p>d dd d dF V A V V ( )2 3 (2)</p><p>where Vd, which is the velocity on the downwind actuatordisk, is influenced by the velocity Vu on the upwind actuatordisk. The elementary forces dF on the actuator disks may becalculated using Blade Element Theory.</p><p>If the upwind and downwind interference factors are de-fined as</p><p>aV V</p><p>Va</p><p>V VVu</p><p>ud</p><p>d</p><p>(3)</p><p>the mathematical problem can be reduced to the calculationof au and ad. Because of the non-linearity of the equations, theproblem must be resolved iteratively. If the rotor blades havea fixed pitch angle or an assigned pitch variation (i.e. sinusoi-dal like in Pinson, cycloidal, etc.), the mathematical model isreduced, for each elementary streamtube, to an equation forthe momentum balance for the upwind actuator disk and anequation for the momentum balance for the downwind actua-tor disk.</p><p>a asen</p><p>VV</p><p>C senu uRu</p><p>lu u( ) ( ) tan11</p><p>82</p><p>2</p><p>C</p><p>a a asen</p><p>VV</p><p>du u</p><p>d d uRd</p><p>cos ( )</p><p>( )( )</p><p>tan2</p><p>1 21</p><p>8</p><p>2</p><p>C sen</p><p>C</p><p>ld d</p><p>dd d</p><p>( )</p><p>cos( )</p><p>tan</p><p>tan</p><p>(4)</p><p>If the rotor blades have a self-acting variable pitch angle[3], [4], [5], another equation is also necessary for each actua-tor disk: the hinge moment equilibrium. In this case, in fact,the blade is partially free to pitch under the action of the aero-dynamic and inertia forces so as to reduce the angle of attack</p><p>78 Czech Technical University Publishing House http://ctn.cvut.cz/ap/</p><p>Acta Polytechnica Vol. 45 No. 3/2005 Czech Technical University in Prague</p><p>Downwind disk</p><p>dd</p><p>i</p><p>j</p><p>u</p><p>Upwind disk</p><p>Elementary streamtube</p><p>Circular path of</p><p>the blade</p><p>V V</p><p>Downwind disk</p><p>dAddAu</p><p>V V</p><p>Upwind disk</p><p>V</p><p>dFu dFd</p><p>V</p><p>V</p><p>V V</p><p>V</p><p>V</p><p>V</p><p>d</p><p>Fig. 1: Double multiple streamtube model</p></li><li><p>and hence the tendency of the blade to stall. The allowed an-gular swinging of the blade is limited by the presence of twoblocks. In this way the mathematical model is represented bytwo systems of equations, each constituted of two equations:momentum balance and hinge moment equilibrium. For oneblade and for the upwind actuator disk</p><p>a asen</p><p>VV</p><p>Cu uu</p><p>Rulu u zvu u( ) ( , ,Retan1</p><p>18</p><p>2</p><p>)</p><p>( ) ( , ,Re )</p><p>cos( )tan tan</p><p>tan</p><p>sen C</p><p>C</p><p>u u du u zvu u</p><p>u u</p><p>mc u zvu u nu u zvu u</p><p>c cer</p><p>4</p><p>4</p><p>( , ,Re ) ( , ,Re )</p><p>( )tan tan </p><p>C</p><p>x x </p><p>cos</p><p>( , ,Re )( )</p><p>tan</p><p>zvu</p><p>tu u zvu u</p><p>c cer zvu</p><p>Cx x sen4 0</p><p>(5)</p><p>For the downwind actuator disk</p><p>( )( )</p><p>( ,tan</p><p>1 21</p><p>8</p><p>2</p><p>a a asen</p><p>VV</p><p>C</p><p>d d ud</p><p>Rd</p><p>ld d z</p><p> vd d</p><p>d d dd d zvd d</p><p>d</p><p>,Re )</p><p>( ) ( , ,Re )</p><p>cos(tan tan </p><p>sen C </p><p> tan</p><p>tan tan</p><p>)( , ,Re ) ( , ,Re )</p><p>(</p><p>d</p><p>mc d zvd d nd d zvd d</p><p>c</p><p>C C</p><p>x4</p><p>4</p><p>x</p><p>Cx x sen</p><p>cer zvd</p><p>td d zvd d</p><p>c cer</p><p>) cos</p><p>( , ,Re )( )</p><p>tan</p><p>4 zvd 0</p><p>(6)</p><p>The instantaneous torque and power produced by theblade are given by the moment equilibrium around the tur-bine axis</p><p>M N x x</p><p>T R x x sen</p><p>P M</p><p>( ) cos</p><p>( )</p><p>c hinge zv</p><p>c hinge zv</p><p>4</p><p>4</p><p>(7)</p><p>To obtain the mean torque and mechanical power pro-duced by Nb blades in a revolution it is necessary to averagethe instantaneous values.</p><p>MN</p><p>x x</p><p>T R x x sen</p><p>mb</p><p>c hinge zv</p><p>c hinge</p><p>2 40</p><p>2</p><p>4</p><p>( ) cos</p><p>( ) zv d ,</p><p>(8)</p><p>PN</p><p>x x</p><p>T R x x sen</p><p>mb</p><p>c hinge zv</p><p>c hinge</p><p>2 40</p><p>2</p><p>4</p><p>( ) cos</p><p>( ) </p><p> zv d .</p><p>(9)</p><p>To simulate dynamic performances, we have to resolveonly the equation of the moment equilibrium around turbineaxis (10) for fixed blade or Nb1 equations for Nb floatingblades around their hinge axis (11).</p><p>I M MT ii</p><p>N </p><p>C</p><p>b</p><p>1</p><p>(10)</p><p>I M</p><p>I M</p><p>I</p><p>P zv1 h1</p><p>P zv h2</p><p>P zv</p><p>( )</p><p>( )</p><p>( )</p><p>2</p><p>3 </p><p>M</p><p>I M</p><p>h3</p><p>P zvn hn</p><p>( ) </p><p>(11)</p><p>3 Airfoils and aerodynamiccharacteristicsThe rotor performances were tested using five airfoils:</p><p>three symmetrical airfoils NACA 0012, 0015, 0018 and twocambered airfoils NACA 4415 and HLIFT18. The last namedwas designed at DPA; it is a high lift [6], [7] and no cavitatingairfoil. It has in fact been designed to work in the water on theKOBOLD turbine. For the NACA airfoils, data was taken fromthe literature [2], [8] while for the HLIFT18 airfoil, TBVOR[9], [10], [11] codes were used to generate the values of theaerodynamic coefficients. The airfoil 2D data is corrected, inVAWT and VAWT_DYN codes [12], to take into account thethree-dimensional effects due to the blade finite aspect ratio.To take into account the three-dimensional effects, Prandtlslifting line theory, extended to treat high lift flow, has beenused, evaluating in this way the 3D lift curve beginning fromthe 2D data. This theory is valid only in the linear zone of thelift curve but with care it can also be extended to non linearconditions. The total blade drag coefficient is the sum of theairfoil drag coefficient (Cd), due to skin friction, and theinduced drag coefficient. To take into account the inter-ference between the blade and the support arms, a furtherdrag coefficient increment, CD, has been introduced. More-over, 2D post-stall modelling, based on the Viterna-Corrigancorrelation method, has been introduced to extend the 2Daerodynamic coefficients to this angle range.</p><p> Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 79</p><p>Czech Technical University in Prague Acta Polytechnica Vol. 45 No. 3/2005</p><p>V</p><p>arm</p><p>R</p><p>V</p><p>V</p><p>n</p><p>n</p><p>t</p><p>c</p><p>L</p><p>D</p><p>Mc/4</p><p>zv</p><p>Fig. 2: Hinge moment equilibrium</p><p>j</p><p>i</p><p>Mh1</p><p>Mh2</p><p>Mh3</p><p>M</p><p>MC</p><p>TI</p><p>zv</p><p>:</p><p>Fig. 3: Torques on a Kobold turbine</p></li><li><p>4 Experimental modelsThe reported experimental data is divided into two parts:</p><p> Experimental data measured in the DPA wind-tunnel atthe University of Naples on a small straight-bladed cyclo-turbine, which was designed, developed and assembled atDPA [13];</p><p> Experimental data measured in water on the Koboldprototype (real scale) [12], [14].</p><p>Both the DPA straight-bladed cycloturbine (Model A)and the Kobold prototype (Model B) will be described, asfollows. Both turbines have variable pitch blades with a self--acting system, made up of two balancing masses for eachblade. In this way, the centre of gravity of the blade can bemoved into its optimal position in order to optimize theglobal performance of the rotor, and, using two stops, thepitch blade range can be limited, as shown in Fig. 5.</p><p>Model A in the DPA wind-tunnel is shown in fig. 6. Usingdifferent stop positions, it was possible to test different pitchangle ranges, and while using different numbers of blades itwas possible to take into account different solidity [Nc/R] val-ues. Model A has the following geometric parameters:</p><p>number of blades tested 2, 3, 4, 6blade chord 0.15 m</p><p>blade airfoil NACA 0018blade span 0.8 mAspect Ratio 5.33radius 1.05 mnumber of radial arm 4, 6, 8, 12arm chord 0.05 msolidity 1 0.286solidity 2 0.428solidity 3 0.571solidity 4 0.857</p><p>80 Czech Technical University Publishing House http://ctn.cvut.cz/ap/</p><p>Acta Polytechnica Vol. 45 No. 3/2005 Czech Technical University in Prague</p><p>0 0.2 0.4 0.6 0.8 1</p><p>x/c-0.2</p><p>-0.1</p><p>0</p><p>0.1</p><p>0.2y/c NACA 0012</p><p>NACA 0015NACA 0018</p><p>0 0.2 0.4 0.6 0.8 1</p><p>x/c-0.2</p><p>-0.1</p><p>0</p><p>0.1</p><p>0.2y/c NACA 4415</p><p>HLIFT18</p><p>-30 -20 -10 0 10 20 30</p><p>A lfa [deg]-1.5</p><p>-1</p><p>-0.5</p><p>0</p><p>0.5</p><p>1</p><p>1.5</p><p>2C L NACA 0012</p><p>NACA 0015NACA 0018NACA 4415HLIFT18</p><p>-30 -20 -10 0 10 20 30</p><p>A lfa [deg ]0</p><p>0.1</p><p>0.2</p><p>0.3</p><p>0.4</p><p>0.5</p><p>0.6C D NA CA 0012</p><p>NA CA 0015NA CA 0018NA CA 4415HL IFT18</p><p>Fig. 4: Airfoils tested and aerodynamic characteristics (Re 10e6)</p><p>i</p><p>Stop</p><p>V</p><p>Hinge</p><p>Stop</p><p>Pitch</p><p>Range</p><p>j</p><p>Fig. 5: Balancing mass and blade stops</p><p>Fig. 6: DPA straight-bladed cycloturbine (Model A)</p></li><li><p>The Kobold prototype (Model B) lies out in the Strait ofMessina, close to the Sicilian shore, facing a village calledGanzirri, close to the lake of the same name, as shown inFig. 7.</p><p>In this site the peak current speed is 2 m/s (4 knots), thesea depth is 20 meters and the plant has been moored150 meters offshore. The current changes direction every6 hrs and 12 minutes, and the amplitude period is equal to14 days. A high lift airfoil, called H-LIFT18, is used for theblade sections and has been specially designed at DPA to becavitation free and to optimise the turbine performance.Two arms sustain each blade and the arms have been stream-lined using another ad hoc designed symmetrical airfoil. Theturbine has a very high starting torque, being able in this wayto start spontaneously, also with electrical load connected,without the need for any starting devices. The ENERMARplant is composed of the turbine rotor hanging under afloating buoy that contains the remaining mechanical and</p><p>electrical parts to deliver energy to the grid, as shown inFig. 7. The rotor has a diameter of 6 meters with 6 radial armsholding three blades with a five-meter span and with a chordof 0.4 m employing the H-LIFT18 airfoil leading to an aspectratio of 12.5 and to solidity 0.4. The acquisition data sys-tem is made up of a torque-meter, a tidal current speed-meterand an RPM counter all connected to a PLC that convertsanalog signals t...</p></li></ul>

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