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Research Papers: Gas Turbines: Turbomachinery

An Experimental and Numerical Assessment of Airfoil Polars for Use in Darrieus Wind Turbines—Part II: Post-stall Data Extrapolation Methods

[+] 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

John M. Rainbird

Department of Aeronautical Engineering,
Imperial College,
South Kensington Campus,
London SW7 2AZ, UK
e-mail: j.rainbird11@imperial.ac.uk

Joaquim Peiro

Department of Aeronautical Engineering,
Imperial College,
South Kensington Campus,
London SW7 2AZ, UK
e-mail: j.peiro@imperial.ac.uk

J. Michael R. Graham

Department of Aeronautical Engineering,
Imperial College,
South Kensington Campus,
London SW7 2AZ, UK
e-mail: m.graham@imperial.ac.uk

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 14, 2015; final manuscript received July 28, 2015; published online September 22, 2015. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(3), 032603 (Sep 22, 2015) (10 pages) Paper No: GTP-15-1304; doi: 10.1115/1.4031270 History: Received July 14, 2015; Revised July 28, 2015

Accurate post-stall airfoil data extending to a full range of incidences between −180 deg and +180 deg are important to the analysis of Darrieus vertical-axis wind turbines (VAWTs), since the blades experience a wide range of angles of attack, particularly at the low tip-speed ratios (TSRs) encountered during startup. Due to the scarcity of existing data extending much past stall and the difficulties associated with obtaining post-stall data by experimental or numerical means, wide use is made of simple models of post-stall lift and drag coefficients in wind turbine modeling (through, for example, blade element momentum (BEM) codes). Most of these models assume post-stall performance to be virtually independent of profile shape. In this study, wind tunnel tests were carried out on a standard NACA 0018 airfoil and a NACA 0018 conformally transformed to mimic the “virtual camber” effect imparted on a blade in a VAWT with a chord-to-radius ratio c/R of 0.25. Unsteady computational fluid dynamics (CFD) results were taken for the same airfoils both at stationary angles of attack and at angles of attack resulting from a slow VAWT-like motion in an oncoming flow, the latter to better replicate the transient conditions experienced by VAWT blades. Excellent agreement was obtained between the wind tunnel tests and the CFD computations for both the symmetrical and cambered airfoils. Results for both airfoils also compare favorably to earlier studies of similar profiles. Finally, the suitability of different models for post-stall airfoil performance extrapolation, including those of Viterna–Corrigan, Montgomerie, and Kirke, was analyzed and discussed.

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References

Figures

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Fig. 1

Investigated airfoils

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Fig. 2

The NACA 0018 mounted in the wind tunnel

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Fig. 3

The bottom assembly of the apparatus, with tunnel floor removed, showing end plate, adapter, force transducer, bearing mount, and the cooling unit of the stepper motor

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Fig. 11

Lift coefficient comparison with literature data for the transformed airfoil (Re = 150,000)

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Fig. 12

Drag coefficient comparison with literature data for the transformed airfoil (Re = 150,000)

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Fig. 10

Drag coefficient comparison with literature data for the NACA 0018 airfoil (Re = 150,000)

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Fig. 9

Lift coefficient comparison with literature data for the NACA 0018 airfoil (Re = 150,000)

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Fig. 8

Comparison of lift and drag coefficients at Re = 150,000 between the NACA 0018 airfoil and the airfoil conformally transformed to account for virtual camber effects (c/R = 0.25)

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Fig. 7

Experimental drag coefficient of the transformed airfoil between −180 deg and 180 deg

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Fig. 6

Experimental lift coefficient of the transformed airfoil between −180 deg and 180 deg

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Fig. 5

Experimental drag coefficient of the NACA 0018 airfoil between 0 deg and 180 deg

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Fig. 4

Experimental lift coefficient of the NACA 0018 airfoil between 0 deg and 180 deg

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Fig. 13

CFD simulation domain [21]

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Fig. 14

Computational grid: (a) rotating domain and (b) control circle region

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Fig. 15

Vorticity contours for the NACA 0018 airfoil around ϑ = 90 deg

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Fig. 16

Lift coefficient data at Re = 150,000 from unsteady CFD of a slow rotating blade versus averaged values for a still blade

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Fig. 17

Lift coefficient data for the NACA 0018 airfoil at Re = 150,000: comparison between experiments, CFD, and post-stall correlations

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Fig. 18

Drag coefficient data for the NACA 0018 airfoil at Re = 150,000: comparison between experiments, CFD, and post-stall correlations

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Fig. 19

Lift coefficient data for the transformed airfoil at Re = 150,000: comparison between experiments, CFD, and post-stall correlations

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Fig. 20

Drag coefficient data for the transformed airfoil at Re = 150,000: comparison between experiments, CFD, and post-stall correlations

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