0
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.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

AWEA, 2008, “ Small Wind Turbine Global Market Study,” American Wind Energy Association, Washington, DC.
Balduzzi, F. , Bianchini, A. , Carnevale, E. A. , Ferrari, L. , and Magnani, S. , 2012, “ Feasibility Analysis of a Darrieus Vertical-Axis Wind Turbine Installation in the Rooftop of a Building,” Appl. Energy, 97, pp. 921–929. [CrossRef]
Mertens, S. , 2006, Wind Energy in the Built Environment, Multi-Science, Brentwood, UK.
Balduzzi, F. , Bianchini, A. , and Ferrari, L. , 2012, “ Microeolic Turbines in the Built Environment: Influence of the Installation Site on the Potential Energy Yield,” Renewable Energy, 45, pp. 163–174. [CrossRef]
Bianchini, A. , Ferrara, G. , and Ferrari, L. , 2015, “ Design Guidelines for H-Darrieus Wind Turbines: Optimization of the Annual Energy Yield,” Energy Conv. Manage., 89, pp. 690–707. [CrossRef]
Paraschivoiu, I. , 2002, Wind Turbine Design With Emphasis on Darrieus Concept, Polytechnic International Press, Montreal, Canada.
Balduzzi, F. , Bianchini, A. , Maleci, R. , Ferrara, G. , and Ferrari, L. , 2015, “ Blade Design Criteria to Compensate the Flow Curvature Effects in H-Darrieus Wind Turbines,” ASME J. Turbomach., 137(1), pp. 1–10.
Borg, M. , Shires, A. , and Collu, M. , 2014, “ Offshore Floating Vertical Axis Wind Turbines, Dynamics Modelling State of the Art. Part I: Aerodynamics,” Renewable Sustainable Energy Rev., 39, pp. 1214–1225. [CrossRef]
Simão Ferreira, C. , Aagaard Madsen, H. , Barone, M. , Roscher, B. , Deglaire, P. , and Arduin, I. , 2014, “ Comparison of Aerodynamic Models for Vertical Axis Wind Turbines,” J. Phys.: Conf. Ser., 524, p. 012125. [CrossRef]
Rainbird, J. M. , Bianchini, A. , Balduzzi, F. , Peiro, J. , Graham, J. M. R. , Ferrara, G. , and Ferrari, L. , 2015, “ On the Influence of Virtual Camber Effect on Airfoil Polars for Use in Simulations of Darrieus Wind Turbines,” Energy Conv. Manage., 106, pp. 373–384. [CrossRef]
Marten, D. , Bianchini, A. , Pechlivanoglou, G. , Balduzzi, F. , Nayeri, C. N. , Ferrara, G. , Paschereit, C. O. , and Ferrari, L. , 2016, “ Effects of Airfoil's Polar Data in the Stall Region on the Estimation of Darrieus Wind Turbine Performance,” ASME Paper No. GT2016-56685.
Bianchini, A. , Balduzzi, F. , Ferrara, G. , and Ferrari, L. , 2015, “ Virtual Incidence Effect on Rotating Airfoils in Darrieus Wind Turbines,” Energy Conv. Manage., 111(1), pp. 329–338.
Bianchini, A. , Ferrari, L. , and Magnani, S. , 2011, “ Start-Up Behavior of a Three-Bladed H-Darrieus VAWT: Experimental and Numerical Analysis,” ASME Paper No. GT2011-45882.
Hill, N. , Dominy, R. , Ingram, G. , and Dominy, J. , 2009, “ Darrieus Turbines: The Physics of Self-Starting,” Proc. Inst. Mech. Eng., Part A, 223(1), pp. 21–29. [CrossRef]
Dominy, R. , Lunt, P. , Bickerdyke, A. , and Dominy, J. , 2007, “ Self-Starting Capability of a Darrieus Turbine,” Proc. Inst. Mech. Eng., Part A, 221(1), pp. 111–120. [CrossRef]
Bianchini, A. , Ferrari, L. , and Carnevale, E. A. , 2011, “ A Model to Account for the Virtual Camber Effect in the Performance Prediction of an H-Darrieus VAWT Using the Momentum Models,” Wind Eng., 35(4), pp. 465–482. [CrossRef]
Migliore, P. G. , and Wolfe, W. P. , 1980, “ The Effects of Flow Curvature on the Aerodynamics of Darrieus Wind Turbines,” West Virginia University, Morgantown, WV, Technical Report No. ORO-5135-77/7.
Bianchini, A. , Balduzzi, F. , Rain bird, J. , Peiro, J. , Graham, J. M. R. , Ferrara, G. , and Ferrari, L. , 2015, “ An Experimental and Numerical Assessment of Airfoil Polars for Use in Darrieus Wind Turbines. Part I—Flow Curvature Effects,” ASME J. Eng. Gas Turbines Power, 138(3), p. 032602. [CrossRef]
Bianchini, A. , Balduzzi, F. , Rainbird, J. , Peiro, J. , Graham, J. M. R. , Ferrara, G. , and Ferrari, L. , 2015, “ An Experimental and Numerical Assessment of Airfoil Polars for Use in Darrieus Wind Turbines. Part II—Post-Stall Data Extrapolation Methods,” ASME J. Eng. Gas Turbines Power, 138(3), p. 032603. [CrossRef]
XFLR 5 Open Software Official Webpage, accessed Sept. 24, 2015, www.xflr5.com/xflr5.htm
Raciti Castelli, M. , Pavesi, G. , Battisti, L. , Benini, E. , and Ardizzon, G. , 2010, “ Modeling Strategy and Numerical Validation for a Darrieus Vertical Axis Micro-Wind Turbine,” ASME Paper No. IMECE2010-39548.
Balduzzi, F. , Bianchini, A. , Gigante, F. A. , Ferrara, G. , Campobasso, M. S. , and Ferrari, L. , 2015, “ Parametric and Comparative Assessment of Navier–Stokes CFD Methodologies for Darrieus Wind Turbine Performance Analysis,” ASME Paper No. GT2015-42663.
Bianchini, A. , Balduzzi, F. , Ferrara, G. , and Ferrari, L. , 2016, “ Influence of the Blade–Spoke Connection Point on the Aerodynamic Performance of Darrieus Wind Turbines,” ASME Paper No. GT2016-57667.
Balduzzi, F. , Bianchini, A. , Maleci, R. , Ferrara, G. , and Ferrari, L. , 2016, “ Critical Issues in the CFD Simulation of Darrieus Wind Turbines,” Renewable Energy, 85, pp. 419–435. [CrossRef]
Menter, F. R. , Langtry, R. B. , Likki, S. R. , Suzen, Y. B. , Huang, P. G. , and Völker, S. , 2004, “ A Correlation-Based Transition Model Using Local Variables: Part 1—Model Formulation,” ASME Paper No. GT2004-53452.
Daróczy, L. , Janiga, G. , Petrasch, K. , Webner, M. , and Thévenin, D. , 2015, “ Comparative Analysis of Turbulence Models for the Aerodynamic Simulation of H-Darrieus Rotors,” Energy, 90, pp. 680–690. [CrossRef]
Cox, J. A. , Brentner, K. S. , and Rumsey, C. L. , 1998, “ Computation of Vortex Shedding and Radiated Sound for a Circular Cylinder: Subcritical to Transcritical Reynolds Numbers,” Theor. Comput. Fluid Dyn., 12(4), pp. 233–253. [CrossRef]
Balduzzi, F. , Bianchini, A. , Ferrara, G. , and Ferrari, L. , 2016, “ Dimensionless Numbers for the Assessment of Mesh and Timestep Requirements in CFD Simulations of Darrieus Wind Turbines,” Energy, 97, pp. 246–261. [CrossRef]
Islam, M. , Ting, D. , and Fartaj, A. , 2007, “ Desirable Airfoil Features for Smaller-Capacity Straight-Bladed VAWT,” Wind Eng., 31(3), pp. 165–196. [CrossRef]
Abbott, I. H. , and Von Doenhoff, A. E. , 1959, Theory of Wing Sections, Dover Publications, New York.
Rainbird, J. , 2015, “ Blockage Tolerant Wind Tunnel Testing of Aerofoils at Angles of Incidence From 0 deg to 360 deg, With Respect to the Self-Start of Vertical-Axis Wind Turbines,” Ph.D. thesis, Imperial College, London.
Bianchini, A. , Cangioli, F. , Papini, S. , Rindi, A. , Carnevale, E. A. , and Ferrari, L. , 2015, “ Structural Analysis of a Small H-Darrieus Wind Turbine Using Beam Models: Development and Assessment,” ASME J. Turbomach., 137(1), pp. 1–11.

Figures

Grahic Jump Location
Fig. 1

The three airfoils analyzed

Grahic Jump Location
Fig. 2

CFD simulation domain [24]

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 5

Conventions for the aerodynamic analysis

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

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

Grahic Jump Location
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

Grahic Jump Location
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)

Grahic Jump Location
Fig. 11

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 13

Experimental pitching moment coefficients [31]

Grahic Jump Location
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

Grahic Jump Location
Fig. 15

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

Grahic Jump Location
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).

Grahic Jump Location
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).

Grahic Jump Location
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.

Grahic Jump Location
Fig. 19

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

Grahic Jump Location
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]

Grahic Jump Location
Fig. 21

Analyzed configurations

Grahic Jump Location
Fig. 22

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

Grahic Jump Location
Fig. 23

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

Grahic Jump Location
Fig. 24

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

Grahic Jump Location
Fig. 25

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

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In