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Research Papers: Gas Turbines: Turbomachinery

An Experimental and Numerical Assessment of Airfoil Polars for Use in Darrieus Wind Turbines—Part I: Flow Curvature Effects

[+] 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), 032602 (Sep 22, 2015) (10 pages) Paper No: GTP-15-1303; doi: 10.1115/1.4031269 History: Received July 14, 2015; Revised July 28, 2015

A better comprehension of the aerodynamic behavior of rotating airfoils in Darrieus vertical-axis wind turbines (VAWTs) is crucial both for the further development of these machines and for improvement of conventional design tools based on zero- or one-dimensional models (e.g., blade element momentum (BEM) models). When smaller rotors are designed with high chord-to-radius (c/R) ratios so as not to limit the blade Reynolds number, the performance of turbine blades has been suggested to be heavily impacted by a virtual camber effect imparted on the blades by the curvilinear flow they experience. To assess the impact of this virtual camber effect on blade and turbine performance, a standard NACA 0018 airfoil and a NACA 0018 conformally transformed such that the airfoil's chord line follows the arc of a circle, where the ratio of the airfoil's chord to the circle's radius is 0.25 were considered. For both airfoils, wind tunnel tests were carried out to assess their aerodynamic lift and drag coefficients for Reynolds numbers of interest for Darrieus VAWTs. Unsteady computational fluid dynamics (CFD) calculations have been then carried out to obtain curvilinear flow performance data for the same airfoils mounted on a Darrieus rotor with a c/R of 0.25. The blade incidence and lift and drag forces were extracted from the CFD output using a novel incidence angle deduction technique. According to virtual camber theory, the transformed airfoil in this curvilinear flow should be equivalent to the NACA 0018 in rectilinear flow, while the NACA0018 should be equivalent to the inverted transformed airfoil in rectilinear flow. Comparisons were made between these airfoil pairings using the CFD output and the rectilinear performance data obtained from the wind tunnel tests and xfoil output in the form of pressure distributions and lift and drag polars. Blade torque coefficients and turbine power coefficient are also presented for the CFD VAWT using both blade profiles.

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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

Experimental lift coefficient of the NACA 0018 airfoil between 0 deg and 180 deg [6]

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Fig. 4

Experimental drag coefficient of the NACA 0018 airfoil between 0 deg and 180 deg [6]

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Fig. 5

Experimental lift coefficient of the transformed airfoil between −180 deg and 180 deg [6]

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Fig. 6

Experimental drag coefficient of the transformed airfoil between −180 deg and 180 deg [6]

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Fig. 7

Comparison of lift and drag coefficients at Re = 300,000 between the NACA 0018 airfoil and it homologous transformed to account for virtual camber effects (c/R = 0.25)

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Fig. 8

Lift coefficient comparison with literature data for the NACA 0018 airfoil (Re = 300,000)

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Fig. 9

Drag coefficient comparison with literature data for the NACA 0018 airfoil (Re = 300,000)

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Fig. 10

Simulation domain

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Fig. 11

Computational grid for the rotating domain

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Fig. 12

Computational grid for control circle region: (a) transformed airfoil and (b) NACA 0018 airfoil

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Fig. 13

Computational grid: boundary layer discretization at the leading edge

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Fig. 21

CFD computed lift curve of the transformed airfoil and experimental data and xfoil predictions of the NACA 0018 at Re = 300,000

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Fig. 22

CFD computed drag curve of the transformed airfoil and experimental data and xfoil predictions of the NACA 0018 at Re = 300,000

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Fig. 23

CFD computed lift curve of the NACA 0018 and experimental data and xfoil predictions of the transformed airfoil at Re = 300,000

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Fig. 24

CFD computed drag curve of the NACA 0018 and experimental data and xfoil predictions of the transformed airfoil at Re = 300,000

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Fig. 20

Normalized pressure coefficients (π*) at two azimuthal positions: comparison between CFD for the NACA 0018 and xfoil predictions of the equivalent virtual transformed airfoil

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Fig. 19

Normalized pressure coefficients (π*) at two azimuthal positions: comparison between CFD for the transformed airfoil and xfoil predictions of the equivalent virtual NACA 0018

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Fig. 18

Normalized pressure coefficients (π*) at ϑ = 32.8 deg for the transformed airfoil: CFD versus xfoil predictions

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Fig. 17

Signs and reference systems convention

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Fig. 16

Instantaneous torque coefficient over a revolution for different TSRs: transformed airfoil

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Fig. 15

Instantaneous torque coefficient over a revolution for different TSRs: NACA 0018

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Fig. 14

Power coefficient versus TSR for the hypothetical one-blade rotor using either the NACA 0018 or the transformed airfoil

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Fig. 25

Torque coefficient trends at TSR = 3.14: CFD simulation of the transformed airfoil versus BEM predictions using different polars

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Fig. 26

AoA versus azimuthal angles for the investigated configurations

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