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Research Papers

Stochastic Model for Aerodynamic Force Dynamics on Wind Turbine Blades in Unsteady Wind Inflow

[+] Author and Article Information
M. R. Luhur

ForWind-Center for Wind Energy Research,
Institute of Physics,
University of Oldenburg,
Oldenburg 26129, Germany
e-mail: muhammad.ramzan@uni-oldenburg.de

J. Peinke

ForWind-Center for Wind Energy Research,
Institute of Physics,
University of Oldenburg,
Oldenburg 26129, Germany
e-mail: joachim.peinke@uni-oldenburg.de

M. Kühn

ForWind-Center for Wind Energy Research,
Institute of Physics,
University of Oldenburg,
Oldenburg 26129, Germany
e-mail: martin.kuehn@uni-oldenburg.de

M. Wächter

ForWind-Center for Wind Energy Research,
Institute of Physics,
University of Oldenburg,
Oldenburg 26129, Germany
e-mail: matthias.waechter@uni-oldenburg.de

The azimuth angle describes the blade angular position in one cycle measured in clockwise direction such that it is zero when the blade is pointing vertically downwards.

The appearance of harmonics of the 1 P period seems to be typical for the rotating frame of reference of the rotor [30].

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 16, 2014; final manuscript received October 26, 2014; published online April 2, 2015. Assoc. Editor: Carlo L. Bottasso.

J. Comput. Nonlinear Dynam 10(4), 041010 (Jul 01, 2015) (10 pages) Paper No: CND-14-1048; doi: 10.1115/1.4028963 History: Received February 16, 2014; Revised October 26, 2014; Online April 02, 2015

Abstract

The paper presents a stochastic approach to estimate the aerodynamic forces with local dynamics on wind turbine blades in unsteady wind inflow. This is done by integrating a stochastic model of lift and drag dynamics for an airfoil into the aerodynamic simulation software AeroDyn. The model is added as an alternative to the static table lookup approach in blade element momentum (BEM) wake model used by AeroDyn. The stochastic forces are obtained for a rotor blade element using full field turbulence simulated wind data input and compared with the classical BEM and dynamic stall models for identical conditions. The comparison shows that the stochastic model generates additional extended dynamic response in terms of local force fluctuations. Further, the comparison of statistics between the classical BEM, dynamic stall, and stochastic models' results in terms of their increment probability density functions (PDFs) gives consistent results.

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Figures

Fig. 1

Blade segment nomenclature. Taken from Ref. [15].

Fig. 2

Scheme of force components on blade section. Angles are related to the plane of rotation. (a) Local velocities and flow angles on blade element and (b) local forces on blade element. Taken from Ref. [12].

Fig. 3

Flow chart to iterate for induction factors

Fig. 4

Flow chart for aerodynamic calculations

Fig. 5

Excerpt of local axial wind velocity component and AOA time series for a blade element. (a) Local axial wind component experienced by the blade element and (b) local AOA. Note the rotor oscillation at T = 1.13 s in (a) and (b), which possibly stems from ground boundary layer shear effects. The oscillation in (b) is less visible because of short excerpt; however, it is present at the same period.

Fig. 6

Excerpt of the stochastic (Stoch) model, the dynamic stall (Dstall) model, and the classical BEM model aerodynamic forces time series for a blade element. (a) CL,Stoch(t), CL,Dstall(t) and CL,BEM(t), (b) CD,Stoch(t), CD,Dstall(t) and CD,BEM(t), (c) Cn,Stoch(t), Cn,Dstall(t) and Cn,BEM(t), and (d) Ct,Stoch(t), Ct,Dstall(t), and Ct,BEM(t).

Fig. 7

Increment PDFs of the stochastic model force coefficients for a blade element at time lags τ = (0.03, 0.11, 0.26) s in ascending order from bottom to top. The PDFs are added with a Gaussian fit having identical standard deviation (solid line) and shifted vertically for clarity of the display. The force coefficients are normalized with their standard deviations. (a) Lift coefficient increment δCL(t, τ) PDFs, (b) drag coefficient increment δCD(t, τ) PDFs, (c) normal force coefficient increment δCn(t, τ) PDFs, and (d) tangential force coefficient increment δCt(t, τ) PDFs.

Fig. 8

Increment PDFs of the dynamic stall model force coefficients for a blade element at time lags τ = (0.03, 0.11, 0.26) s in ascending order from bottom to top. The PDFs are added with a Gaussian fit having identical standard deviation (solid line) and shifted vertically for clarity of the display. The force coefficients are normalized with their standard deviations. (a) Lift coefficient increment δCL(t, τ) PDFs, (b) drag coefficient increment δCD(t, τ) PDFs, (c) normal force coefficient increment δCn(t, τ) PDFs, and (d) tangential force coefficient increment δCt(t, τ) PDFs.

Fig. 9

Increment PDFs of the classical BEM model force coefficients for a blade element at time lags τ = (0.03, 0.11, 0.26) s in ascending order from bottom to top. The PDFs are added with a Gaussian fit having identical standard deviation (solid line) and shifted vertically for clarity of the display. The force coefficients are normalized with their standard deviations. (a) Lift coefficient increment δCL(t, τ) PDFs, (b) drag coefficient increment δCD(t, τ) PDFs, (c) normal force coefficient increment δCn(t, τ) PDFs, and (d) tangential force coefficient increment δCt(t, τ) PDFs.

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