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Research Papers: Gas Turbines: Turbomachinery

Aerodynamics of Darrieus Wind Turbines Airfoils: The Impact of Pitching Moment

[+] Author and Article Information
Alessandro Bianchini

Department of Industrial Engineering,
University of Florence,
Via di Santa Marta 3,
Firenze 50139, Italy
e-mail: bianchini@vega.de.unifi.it

Francesco Balduzzi

Department of Industrial Engineering,
University of Florence,
Via di Santa Marta 3,
Firenze 50139, Italy
e-mail: balduzzi@vega.de.unifi.it

Giovanni Ferrara

Department of Industrial Engineering,
University of Florence,
Via di Santa Marta 3,
Firenze 50139, Italy
e-mail: giovanni.ferrara@unifi.it

Lorenzo Ferrari

CNR-ICCOM,
National Research Council of Italy,
Via Madonna del Piano 10,
Sesto Fiorentino 50019, Italy
e-mail: lorenzo.ferrari@iccom.cnr.it

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 12, 2016; final manuscript received August 25, 2016; published online November 16, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(4), 042602 (Nov 16, 2016) (12 pages) Paper No: GTP-16-1331; doi: 10.1115/1.4034940 History: Received July 12, 2016; Revised August 25, 2016

Recent studies have demonstrated that, when rotating around an axis orthogonal to the flow direction, airfoils are virtually transformed into equivalent airfoils with a camber line defined by their arc of rotation. In these conditions, the symmetric airfoils commonly used for Darrieus blades actually behave like virtually cambered ones or, equivalently, rotors have to be manufactured with countercambered blades to ensure the attended performance. To complete these analyses, the present study first focuses the attention on the airfoils' aerodynamics during the startup of the rotors. It is shown that, contrary to conventional theories based on one-dimensional aerodynamic coefficients, symmetric airfoils exhibit a counterintuitive nonsymmetric starting torque over the revolution. Conversely, airfoils compensated for the virtual camber effect show a more symmetric distribution over the revolution. This behavior is due to the effect of the pitching moment, which is usually neglected in lumped parameters models. At very low revolution speeds, its contribution becomes significant due to the very high incidence angles experienced by the blades; the pitching moment is also nonsymmetric between the upwind and the downwind zone. For upwind azimuthal positions, the pitching moment reduces the overall torque output, while it changes sign in the downwind section, increasing the torque. The importance of accounting for the pitching moment contribution in the entire power curve is also discussed in relationship to the selection of the best blade–spoke connection (BSC) point, in order to maximize the performance and minimize the alternate stresses on the connection due to the pitching moment itself.

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References

Figures

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Fig. 1

The three airfoils analyzed

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Fig. 2

CFD simulation domain [24]

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Fig. 3

Computational grid for start-up analyses: (a) rotating domain and (b) control circle region

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Fig. 4

Computational grid for blade–spoke connection analyses: (a) rotating domain and (b) control circle region

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Fig. 5

Conventions for the aerodynamic analysis

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Fig. 6

Blade torque coefficient predicted by CFD at TSR ≈ 0 for the NACA 0018 and the transformed airfoils at c/R = 0.25

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Fig. 7

Vortex shedding from a NACA 0018 airfoil at c/R = 0.25 around ϑ = 90 deg

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Fig. 8

Starting torque (TSR ≈ 0) of the NACA 0018 at c/R = 0.25: upwind and downwind zones superimposed

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Fig. 9

Pressure contours and specific torque produced by the NACA 0018 with c/R = 0.25 at ϑ = 171 deg (α = −171 deg) and ϑ = 189 deg (α = +171 deg), respectively

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Fig. 10

Tangential and normal forces, overall torque exertedby the NACA 0018 airfoil c/R = 0.25 at (a) ϑ = 90 deg (α = −90 deg) and (b) ϑ = 270 deg (α = +90 deg)

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Fig. 11

Aerodynamic force and moment on a Darrieus turbine airfoil not connected by its aerodynamic center [23]

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Fig. 12

Pitching moment on the NACA 0018 airfoil, c/R = 0.25at ϑ = 90 deg (α = −90 deg) and ϑ = 270 deg (α = +90 deg), respectively

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Fig. 13

Experimental pitching moment coefficients [31]

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Fig. 14

CFD torque coefficients at startup (TSR = 0 → w = U) compared to theoretical BEM expectations without (model I) or with (model II) accounting for the pitching moment effect

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Fig. 15

Aerodynamic center position along the chord as a function of AoA for a NACA 0018 airfoil

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Fig. 16

Power coefficient versus TSR without (model I) or with the pitching moment effects (model II). Study turbine in Table 1 built with the transformed airfoil (behaving like the NACA 0018 in motion).

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Fig. 17

Torque coefficients of a single blade over the revolution at TSR = 0.5, without (model I) or with the pitching moment effects (model II). Study turbine in Table 2 with the NACA 0018 (a) or the transformed airfoil (b).

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Fig. 18

Start-up ramps without (model I) or with the pitching moment effects (model II) of the study turbine in Table 2 with the transformed airfoil. Turbine started from ϑ=+30 deg with U = 4 m/s.

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Fig. 19

Comparison between experimental power coefficients (BSC = 0.5c) and CFD simulations having BSC = 0.5c and BSC = 0.25c, respectively

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Fig. 20

Velocity triangles on the airfoils for a turbine with BSC = AC or BSC ≠ AC at different azimuthal positions, so that ACs are aligned [23]

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Fig. 21

Analyzed configurations

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Fig. 22

Torque contributions of the tangential force and the pitching moment at TSR = 2.40

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Fig. 23

Torque contributions of the tangential force and the pitching moment at TSR = 3.30

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Fig. 24

Normal force and moment applied to the connection point at TSR = 2.40

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Fig. 25

Normal force and moment applied to the connection point at TSR = 3.30

Tables

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