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Proceedings in Applied Mathematics and Mechanics, 31 May 2013

Influence of pitching on performance of VAWTs

Radu Bogateanu1,, Alexandru Dumitrache2,, Vladimir Cardos2,,andHoria Dumitrescu2,

1 Politehnica University of Bucharest, Splaiul Independentei no. 313, sect. 6,060042 Bucharest2 Institute of Mathematical Statistics and Applied Mathematics, Calea 13 Septembrie no. 13, 050711 Bucharest

Self- starting is the major obstacle to be overcome for successful design of a vertical axis wind turbine (VAWT). In the past has

been suggested that pitching the turbine blades such that pitch angle is not 90 degrees allows for self-starting. To understand

the physics surrounding pitching, an analysis is carried out for a common airfoil profile, NACA 0012. The vortex model is

used to predict aerodynamic performance of VAWT with pitched blades at various angles. As a result of the analysis carried

out for the airfoil at various pitch angles, it was shown that the "dead band" phenomenon could be overcome, but only slightly.

At the same time, to overcome the "dead band" with a level on confidence, torques in the tip speed ratio (TSR ) range of 0.75

to 2.75 must be increased to values further above zero. The paper aimed at giving an insight into the small wind turbine

starting behavior and its influence parameters.

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1 Introduction

In recent years there has been a resurgence of interest in both large-scale and small-scale vertical-axis wind turbines (VAWT)

[1]. The development of large-scale VAWTs is mainly a response to a plateau in the improvement of the aerodynamic perfor-

mance of HAWTs. The research in small-scale VAWTs, with rotor diameters of only several meters, is motivated by the future

demand for a decentralised and sustainable energy supply in cities and rural communities [1]. Despite the obvious advantages

of VAWT, however, in general a VAWT with fixed pitch blades has the disadvantage that it is unable to start on itself. The

main problem for the small wind turbines is the negative power coefficient at low tip speed ratios so that the self-starting is

the major obstacle to be overcome for successful design of a VAWT [3]. This result can be obtained if an airfoil with high lift

coefficients at low Reynolds numbers is used or a passive or active flow control, at least for the starting phase, is used.

2 Basic aerodynamics. Vortex model

As the VAWT have a rotational axis perpendicular to the oncoming airflow, the aerodynamics involved is more complicated

than of the more conventional HAWT [1]. The main benefit of this layout is the independence of wind direction. The main

disadvantages are the high local angles of attack involved at start and the wake coming from the blades in the upwind part and

front the axis.

The rotational speed can be varied by the turbines controller for a certain wind speed and this is therefore represented by

the tip speed ratio (TSR). This parameter gives the tip speed ratioR as factor of the free stream velocityVinf: TSR =

R/Vinf. The Reynolds number is a measure of the viscous behavior of air: Re = Vinfc/

1 + (TSR)2, where thelength and velocity scales are blade chordc and tip speedR;is the kinematic viscosity of air.

The performance of the turbine is given by the power coefficient CP. This coefficient is normally plotted against the tipspeed ratio TSR at a certain Reynolds number or a certain pitch angle.

The main problem for VAWTs (Darrieus) is the negative power coefficient at low TSR. If the coefficient is negative ("dead

band"), the turbine needs extra power to be able to rotate. The region of negative CP is influenced by the airfoil (camber andthickness), Reynolds number of blades and the pitch angle of blade. Most VAWTs built so far use airfoils from the NACA

4-series and most of them use symmetric airfoils. On the other hand these airfoils for the small wind turbines operate at

Reynolds number around105 having specific aerodynamic characteristics which prevent the rotor to enter full-lift driven state(flapping-wing analogy) at the unity TSR.

Description of vortex model. A vortex model [2], [5] is introduced to predict aerodynamic performance of VAWT using

NACA 4 series airfoil for the105 Reynolds number range. The model is based on the marching - vortex concept where motionbegins from an impulsive start with the subsequent generation of a vortex wake modelled by a sequence of discrete vortices

shed at equal time intervals. For steady - state motion, the force and moment responses are achieved asymptotically. The

vortices which are shed during any given time period can be related to the changes in bound vortex with respect to time and

position along the blade. Thus, all variables associated with a particular point - vortex as point coordinates, and velocities as

Corresponding author: e-mail unquradu@gmail.com, phone +40721 258 624, fax +40 21 318 2433 e-mail alex_dumitrache@yahoo.com e-mail v_cados@yahoo.ca e-mail horiadumitrescu@yahoo.com

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2 PAMM header will be provided by the publisher

well as vortex strengths are identified by a double subscript (i, j). The first subscript denotes the blade element from whichthe point-vortex originated and second subscript denotes the time step at which the vortex originated. The spanwise shed

Fig. 1: Power coefficient at different pitches

(Re1 = 360000).

Fig. 2: Power coefficient at different pitches

(Re2 > Re1).

vortex strengths can be written as S(i, j 1) = B(i, j 1)B(i, j).The discrete vorticesS(i, j)are assumed to move

downstream with the local field fluid velocities given by V(i, j) = V+ v l(i, j), where V is the undisturbed freestreamvelocity andv l(i, j)is velocity induced by all discrete vortices in the flowfield, forming the vortex wake lattice. To convect all

the lattice points in the wake, we use an explicit integration formula r S(i, j) =r S(i, j 1)+[3V(i, j) V(i, j 1)]/2 t.The induced velocity at the wake lattice points is computed by application of Biot-Savart law. The closure of the vortex model

is the relationship for the bound vortex strength (B) which can be related to the local relative air velocity (Vrel) sectionchord (c) and section lift coefficient (CL(,Re))through a Kutta-Joukowski type formula: B = 0.5CLcVrel , where whereCL is given by measured lift coefficients tables [4]. It should be noted that the effects of aerodynamic stall are intrinsicallyintroduced into previous equation through the section lift coefficient. For the small VAWTs the Reynolds number is a critical

parameter since if the Reynolds number is too low, the lift curve slope of airfoil will be significantly reduced. This study aims

to predict aerodynamic performance of three-straight-blade VAWT having a reduced solidity value of0.125.

3 Results and conclusion

The measured data for symmetric NACA0012 airfoil at different Reynolds number through angles of attack up to 180 de-

gree was implemented into the computing program. These data at low Re number show anomalous feature, i.e. the linear

dependency ofCL on angle of attack extends to a few degrees followed by a drop to negative values ofCL.The Darrieus turbine starting behavior consists of two-step process: first acceleration step between TSR = 0 to 1 (drag

mode) and second acceleration between TSR = 1 to 3 (lift mode). In the first acceleration step the rotor is alternately driven by

drag (angle of attack between 45 - 180 degrees) and lift (angle of attack between 0 - 45 degrees). In the second acceleration

step, the rotor is solely driven by lift. If the coefficient is negativeCP(dead band), the turbine is unable to start on itself andneed extra power to enter continuous rotation. The region of negativeCPis influenced strongly by the thickness and Reynoldsnumber of blades. The increasing of blade thickness reduces the severity of the dead band of negative torque between TSR =

1 to 3, but does not eliminate it than for NACA 0021, NACA 0018 and NACA 0015 airfoils at Re 3.6 105. The NACA

0012 airfoil forRe 5.0 105

the dead band of negative torque is between TSR = 1 to 3 which shows that the small, NACA0012 three-bladed turbine is unable to start on itself. Another possibility to eliminate or minimize the dead band is to change

the blade pitch angle. For this purpose numerical experiments were performed by changing the pitch angle between 0 and 10

degree (Figs. 1 and 2). At least for the TSR = 1 to 3 the dead band is eliminated.The Reynolds number, thickness and pitch angle of symmetrical NACA blade are the main parameters which influences

the second acceleration step. In this paper a parameter study on the self-starting behavior revealed the airfoils to promotecontinuous generation of thrust for small VAWTs.

Acknowledgements This work was realised through the Partnership programme in priority domains - PN II, developed with support from

ANCS CNDI - UEFISCDI, project no. PN-II-PT-PCCA-2011-3.2-1670.

References

[1] I. Paraschivoiu, Wind Turbine Design (Polytechnic International Press, Montreal, 2002).[2] J. H. Strickland Mauthe, B. T. Webster and T. Nguen, J. of Fluid Eng.101, 500(1979).[3] R. Dominy, P. Lunt, A. Bickerdyke, and J. Dominy, J.of Power and Energie221, 111 (2007).[4] R. E. Sheldahl, P. C. Klimas, Tech.Rep. SAND80-2114, NM, USA (1981).[5] H. Dumitrescu, V. Cardos, Proc. of Romanian Academy,11, 47(2010).

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