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NotationSymbol Unit Description

a Interference factorc m Blade chord lengthCd Airfoil drag coefficientCl Airfoil lift coefficientCmc/4 Airfoil quarter chord pitching moment

coefficientCD Blade drag coefficientCL Blade lift coefficientCp Turbine performance coefficientCq Turbine torque coefficientD N DragdF N Elementary force acting on the elemen-

tary actuator diskIp kgm

2 Blade moment of inertiaIT kgm

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

V

m/s Asymptotic velocityxc/4 %blade

chordBlade aerodynamic centre position

xhinge %bladechord

Floating hinge position

rad Blade angle of attacktan rad Angle between the local velocity and the

local tangent at the bladezv rad Blade pitch angle rad/s2 Blade pitch angle acceleration Tip speed ratio R/V

kg/m3 Fluid density Solidity Nb c /R rad Blade azimuth angle rad/s2 Turbine acceleration rad/s Turbine angular velocity

Subscriptd Conditions at the downwind actuator

disku Conditions at the upwind actuator diskh Hinge

1 IntroductionMarine current energy is a type of renewable energy

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

Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 77

Czech Technical University in Prague Acta Polytechnica Vol. 45 No. 3/2005

Dynamic Behaviour of the PatentedKobold Tidal Current Turbine:

Numerical and Experimental AspectsD. P. Coiro, A. De Marco, F. Nicolosi, S. Melone, F. Montella

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.

Keywords: vertical-axis-hydro-turbine, variable pitch, Double-Multiple-Streamtube, tidal currents, tidal energy.

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.

2 Double multiple streamtubeIn order to analyze the flow field around a vertical axis

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

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.

The elementary force dFu and dFd, respectively on the up-wind and downwind disk, given by the momentum principle,are

d du u uF V A V V ( )2 (1)

d dd d dF V A V V ( )2 3 (2)

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.

If the upwind and downwind interference factors are de-fined as

aV V

Va

V VVu

ud

d

(3)

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.

a asen

VV

C senu uRu

lu u( ) ( ) tan11

82

2

C

a a asen

VV

du u

d d uRd

cos ( )

( )( )

tan2

1 21

8

2

C sen

C

ld d

dd d

( )

cos( )

tan

tan

(4)

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

78 Czech Technical University Publishing House http://ctn.cvut.cz/ap/

Acta Polytechnica Vol. 45 No. 3/2005 Czech Technical University in Prague

Downwind disk

dd

i

j

u

Upwind disk

Elementary streamtube

Circular path of

the blade

V V

Downwind disk

dAddAu

V V

Upwind disk

V

dFu dFd

V

V

V V

V

V

V

d

Fig. 1: Double multiple streamtube model

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

a asen

VV

Cu uu

Rulu u zvu u( ) ( , ,Retan1

18

2

)

( ) ( , ,Re )

cos( )tan tan

tan

sen C

C

u u du u zvu u

u u

mc u zvu u nu u zvu u

c cer

4

4

( , ,Re ) ( , ,Re )

( )tan tan

C

x x

cos

( , ,Re )( )

tan

zvu

tu u zvu u

c cer zvu

Cx x sen4 0

(5)

For the downwind actuator disk

( )( )

( ,tan

1 21

8

2

a a asen

VV

C

d d ud

Rd

ld d z

vd d

d d dd d zvd d

d

,Re )

( ) ( , ,Re )

cos(tan tan

sen C

tan

tan tan

)( , ,Re ) ( , ,Re )

(

d

mc d zvd d nd d zvd d

c

C C

x4

4

x

Cx x sen

cer zvd

td d zvd d

c cer

) cos

( , ,Re )( )