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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

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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References

Tchakoua, P., Wamkeue, R., Ouhrouche, M., Hasnaoui, F. S., Tameghe, T. A., and Ekemb, G., 2014. “Wind Turbine Condition Monitoring: State-of-the-Art Review, New Trends, and Future Challenges,” Energies, 7(4), pp. 2595–2630. [CrossRef]
Vermeer, L. J., Sørensen, J. N., and Crespo, A., 2003, “Wind Turbine Wake Aerodynamics,”Prog. Aerosp. Sci., 39(6–7), pp. 467–510. [CrossRef]
Liu, S., and Janajreh, I., 2012, “Development and Application of an Improved Blade Element Momentum Method Model on Horizontal Axis Wind Turbines,” Int. J. Energy Environ. Eng., 3, p. 30. [CrossRef]
Åhlund, K., 2004, “Investigation of the NREL NASA/Ames Wind Turbine Aerodynamics Database,” Swedish Defence Research Agency, Stockholm, Sweden, Scientific Report No. FOI-R–1243–SE.
Hansen, M. O. L., and Madsen, H. A., 2011, “Review Paper on Wind Turbine Aerodynamics,” ASME J. Fluids Eng., 133(11), p. 114001. [CrossRef]
Jonkman, J. M., and Buhl, M. L., Jr., 2005, “FAST User's Guide,” National Renewable Energy Laboratory, Golden, CO, Technical Report No. NREL/EL-500-38230.
Laino, D. J., and Hansen, A. C., 2003, “User's Guide to the Wind Turbine Dynamics Computer Program YawDyn,” Prepared for NREL Under Subcontract, University of Utah, Salt Lake City, Technical Report No. TCX-9-29209-01.
Laino, D. J., and Hansen, A. C., 2001, “User's Guide to the Computer Software Routines AeroDyn Interface for ADAMS,” Prepared for NREL Under Subcontract, University of Utah, Salt Lake City, Technical Report No. TCX-9-29209-01.
Mulski, S., 2012, “Simpack Multi-Body Simulation,” Proceedings of the Wind and Drivetrain Conference, Hamburg, Germany, Sept. 26.
Buhl, M. L., Jr., and Manjock, A., 2006, “A Comparison of Wind Turbine Aeroelastic Codes Used for Certification,” Conference Paper National Renewable Energy Laboratory, Golden, CO, Report No. NREL/CP-500-39113.
Øye, S., 1999, “FLEX5 User Manual,” Danske Techniske Hogskole, Technical Report Ver. 5.
Moriarty, P. J., and Hansen, A. C., 2005, “AeroDyn Theory Manual,” National Renewable Energy Laboratory, Golden, CO, Technical Report No. NREL/EL-500-36881.
Weinzierl, G., 2011, “A BEM Based Simulation-Tool for Wind Turbine Blades With Active Flow Control Elements,” Diploma thesis, Technical University of Berlin, Berlin, Germany.
Luhur, M. R., Peinke, J., Schneemann, J., and Wächter, M., 2014, “Stochastic Modeling of Lift and Drag Dynamics Under Turbulent Wind Inflow Conditions,” Wind Energy (in press) [CrossRef].
Laino, D. J., and Hansen, A. C., 2002, “User's Guide to the Wind Turbine Aerodynamics Computer Software AeroDyn,” Prepared for NREL Under Subcontract, University of Utah, Salt Lake City, Technical Report No. TCX-9-29209-01.
Kelley, N. D., and Jonkman, B. J., 2007, “Overview of the TurbSim Stochastic Inflow Turbulence Simulator,” National Renewable Energy Laboratory, Golden, CO, Technical Report No. NREL/TP-500-41137.
Jonkman, B. J., and Kilcher, L., 2012, “TurbSim User's Guide,” National Renewable Energy Laboratory, Golden, CO, Technical Report Draft Ver. 1.06.00.
Méndez, J., and Greiner, D., 2006, “Wind Blade Chord and Twist Angle Optimization by Using Genetic Algorithms,” Proceedings of the Fifth International Conference on Engineering Computational Technology, B.Topping, G.Montero, and R.Montenegro, eds., Civil-Comp Press, Las Palmas de Gran Canaria, Spain, Sept. 6, pp. 12–15.
Manwell, J. F., McGowan, J. G., and Rogers, A. L., 2009, Wind Energy Explained: Theory, Design and Application, 2nd ed., Wiley, Chichester, UK.
Glauert, H., 1935, “Airplane Propellers,” Aerodynamic Theory, W. F.Durand, ed., Springer, Berlin, Germany [CrossRef].
Buhl, M. L., Jr., 2005, “A New Empirical Relationship Between Thrust Coefficient and Induction Factor for the Turbulent Windmill State,” National Renewable Energy Laboratory, Golden, CO, Technical Report No. NREL/TP-500-36834.
Glauert, H., 1926, “A General Theory of the Autogyro,” Vol. 1111, Reports and Memoranda, British ARC, London, UK.
Glauert, H., 1926, “The Analysis of Experimental Results in the Windmill Brake and Vortex Ring States of an Airscrew,” Vol. 1126, Reports and Memoranda, HMSO, London, UK.
Pitt, D. M., and Peters, D. A., 1981, “Theoretical Prediction of Dynamic-Inflow Derivatives,” Vertica, 5(1), pp. 21–34.
Coleman, R. P., Feingold, A. M., and Stempin, C. W., 1945, “Evaluation of the Induced-Velocity Field of an Idealized Helicopter Rotor,” Wartime, National Advisory Committee for Aeronautics, Washington, Report No. NACA ARR L5E10.
Burton, T., Sharpe, D., Jenkins, N., and Bossanyi, E., 2011, Wind Energy Handbook, 2nd ed., Wiley, Chichester, UK [CrossRef].
Risken, H., 1996, The Fokker–Planck Equation, 2nd ed., Springer, Berlin, Germany [CrossRef].
Cordle, A., 2010, “State-of-the-Art in Design Tools for Floating Offshore Wind Turbines,” Deliverable Report Under (SES6), UpWind project, Bristol, UK, Contract No. 019945.
Stoevesandt, B., and Peinke, J., 2010, “Effects of Sudden Changes in Inflow Conditions on the Angle of Attack on HAWT Blades,” Cornell University Library, November, p. 18, e-print arXiv:1011.5396 [stat.AP].
Jonkman, J., 2014, personal communication.
Morales, A., Wächter, M., and Peinke, J., 2012, “Characterization of Wind Turbulence by Higher Order Statistics,” Wind Energy, 15(3), pp. 391–406. [CrossRef]

Figures

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Fig. 1

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

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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].

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Fig. 3

Flow chart to iterate for induction factors

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Fig. 4

Flow chart for aerodynamic calculations

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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.

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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).

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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.

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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.

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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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