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Research Papers

A Modified Beddoes–Leishman Model for Unsteady Aerodynamic Blade Load Computations on Wind Turbine Blades

[+] Author and Article Information
Moutaz Elgammi

Department of Mechanical Engineering,
University of Malta,
Msida MSD 2080, Malta
e-mail: moutaz.elgammi.13@um.edu.mt

Tonio Sant

Department of Mechanical Engineering,
University of Malta,
Msida MSD 2080, Malta
e-mail: tonio.sant@um.edu.mt

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received September 28, 2015; final manuscript received June 18, 2016; published online August 15, 2016. Assoc. Editor: Yves Gagnon.

J. Sol. Energy Eng 138(5), 051009 (Aug 15, 2016) (18 pages) Paper No: SOL-15-1320; doi: 10.1115/1.4034241 History: Received September 28, 2015; Revised June 18, 2016

A modified version of the Beddoes–Leishman (B-L) dynamic stall model is presented. A novel approach was applied for deriving the effective flow separation points using two-dimensional (2D) static wind tunnel test data in conjunction with Kirchhoff's model. The results were then fitted in a least-squares sense using a new nonlinear model that gives a better fit for the effective flow separation point under a wide range of operating conditions with fewer curve fitting coefficients. Another model, based on random noise generation, was also integrated within the B-L model to simulate the effects of vortex shedding more realistically. The modified B-L model was validated using 2D experimental data for the S809 and NACA 4415 aerofoils under both steady and unsteady (oscillating) conditions. The model was later embedded in a free-wake vortex model to estimate the unsteady aerodynamic loads on the NREL Phase VI rotor blades consisting of S809 aerofoils when operating under yawed rotor conditions. The results in this study confirm the effectiveness of the proposed modifications to the B-L method under both 2D and three-dimensional (3D) (rotating) conditions.

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References

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Figures

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Fig. 1

Variation of the effective flow separation point with angle of attack at Re = 1 × 106: (a) S809 aerofoil and (b) NACA4415 aerofoil

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Fig. 2

Variation of the measured and the estimated normal force coefficients with angle of attack at Re = 1 × 106: (a) S809 aerofoil and (b) NACA4415 aerofoil

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Fig. 3

Variation of the measured and the estimated tangential force coefficients with angle of attack at Re = 1 × 106: (a) S809 aerofoil and (b) NACA4415 aerofoil

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Fig. 5

Variation of the measured and the estimated drag force coefficients with angle of attack at Re = 1 × 106: (a) S809 aerofoil and (b) NACA4415 aerofoil

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Fig. 6

A comparison between measured static and unsteady lift coefficient curves for the S809 aerofoil

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Fig. 7

Variation of the experimental 2D steady and unsteady pressure distributions, and the 2D unsteady lift force coefficient distributions against angle of attack for theS809 aerofoil: (a) Re = 0.75 × 106, k = 0.104, α = 20 + 5.5sin(ωt); (b) Re = 0.75 × 106, k = 0.104, α = 20 + 5.5sin(ωt); (c) Re = 0.75 × 106; and (d) Re = 0.75 × 106, k = 0.104, α = 20 + 5.5sin(ωt)

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Fig. 8

Variation of the experimental 2D steady and unsteady pressure distributions, and the 2D unsteady lift force coefficient distributions against angle of attack for the NACA4415 aerofoil: (a) Re = 0.72 × 106, k = 0.121, α = 20 + 10sin(ωt); (b) Re = 0.72 × 106, k = 0.121, α = 20 + 10sin(ωt); (c) Re = 0.75 × 106; and (d) Re = 0.72 × 106, k = 0.121, α = 20 + 10sin(ωt)

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Fig. 11

Results of the proposed models for predictions of the unsteady lift coefficients for various mean angles of attack and reduced frequencies for the S809 aerofoil: (a) Re = 0.78 × 106, k = 0.064, α = 20 + 5.5sin(ωt); (b) Re = 0.74 × 106, k = 0.069, α = 14 + 5.5sin(ωt); (c) Re = 0.75 × 106, k = 0.066, α = 8 + 5.5sin(ωt); (d) Re = 0.76 × 106, k = 0.066, α = 20 + 10sin(ωt); (e) Re = 0.74 × 106, k = 0.068, α = 14 + 10sin(ωt); (f) Re = 0.75 × 106, k = 0.069, α = 8 + 10sin(ωt); (g) Re = 1.42 × 106, k = 0.055, α = 20 + 10sin(ωt); (h) Re = 1.36 × 106, k = 0.055, α = 14 + 10sin(ωt); and (i) Re = 1.41 × 106, k = 0.051, α = 8 + 10sin(ωt)

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Fig. 12

Results of the proposed models for predictions of the unsteady drag coefficients for various mean angles of attack and reduced frequencies for the S809 aerofoil: (a) Re = 0.78 × 106, k = 0.064, α = 20 + 5.5sin(ωt); (b) Re = 0.74 × 106, k = 0.069, α = 14 + 5.5sin(ωt); (c) Re = 0.75 × 106, k = 0.066, α = 8 + 5.5sin(ωt); (d) Re = 0.76 × 106, k = 0.066, α = 20 + 10sin(ωt); (e) Re = 0.74 × 106, k = 0.068, α = 14 + 10sin(ωt); (f) Re = 0.75 × 106, k = 0.069, α = 8 + 10sin(ωt); (g) Re = 1.42 × 106, k = 0.055, α = 20 + 10sin(ωt); (h) Re = 1.36 × 106, k = 0.055, α = 14 + 10sin(ωt); and (i) Re = 1.41 × 106, k = 0.051, α = 8 + 10sin(ωt)

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Fig. 9

Variation of the unsteady lift coefficient against angle of attack where the effect of the vortex shedding is not observed: (a) (S809 aerofoil) Re = 0.74 × 106, k = 0.069, α = 14 + 5.5sin(ωt) and (b) (NACA4415) Re = 0.76 × 106, k = 0.076, α = 14 + 5.5sin(ωt)

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Fig. 4

Variation of the measured and the estimated lift force coefficients with angle of attack at Re = 1 × 106: (a) S809 aerofoil and (b) NACA4415 aerofoil

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Fig. 15

Variation of CN and CT versus blade azimuth angle at U = 15 m/s and Φ = 45 deg

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Fig. 16

Variation of CN and CT versus blade azimuth angle at U = 5 m/s and Φ = 30 deg

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Fig. 13

Results of the proposed models for predictions of the unsteady lift coefficients for various mean angles of attack and reduced frequencies for the NACA4415 aerofoil: (a) Re = 1.01 × 106, k = 0.057, α = 20 + 5.5sin(ωt); (b) Re = 1.01 × 106, k = 0.057, α = 14 + 5.5sin(ωt); (c) Re = 1.01 × 106, k = 0.055, α = 8 + 5.5sin(ωt); (d) Re = 0.72 × 106, k = 0.121, α = 20 + 10sin(ωt); (e) Re = 0.74 × 106, k = 0.116, α = 14 + 10sin(ωt); (f) Re = 0.75 × 106, k = 0.118, α = 8 + 10sin(ωt); (g) Re = 1.22 × 106, k = 0.047, α = 20 + 10sin(ωt); (h) Re = 1.24 × 106, k = 0.045, α = 14 + 10sin(ωt); and (i) Re = 1.25 × 106, k = 0.046, α = 8 + 10sin(ωt)

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Fig. 14

Results of the proposed models for predictions of the unsteady drag coefficients for various mean angles of attack and reduced frequencies for the NACA4415 aerofoil: (a) Re = 1.01 × 106, k = 0.057, α = 20 + 5.5sin(ωt); (b) Re = 1.01 × 106, k = 0.057, α = 14 + 5.5sin(ωt); (c) Re = 1.01 × 106, k = 0.055, α = 8 + 5.5sin(ωt); (d) Re = 0.72 × 106, k = 0.121, α = 20 + 10sin(ωt); (e) Re = 0.74 × 106, k = 0.116, α = 14 + 10sin(ωt); (f) Re = 0.75 × 106, k = 0.118, α = 8 + 10sin(ωt); (g) Re = 1.22 × 106, k = 0.047, α = 20 + 10sin(ωt); (h) Re = 1.24 × 106, k = 0.045, α = 14 + 10sin(ωt); and (i) Re = 1.25 × 106, k = 0.046, α = 8 + 10sin(ωt)

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