A simple frequency-domain method for stress analysis of stall-regulated wind turbines
ABSTRACT A simple method, based in the frequency domain, was developed for calculating the dynamic response of a stall‐regulated wind turbine. Emphasis is placed on two aspects of the method, which are necessary in order to obtain a reasonable linearization of behavior when the blades are stalled. F...
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| Published in | Wind energy (Chichester, England) Vol. 15; no. 5; pp. 773 - 798 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
01.07.2012
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| Abstract | ABSTRACT
A simple method, based in the frequency domain, was developed for calculating the dynamic response of a stall‐regulated wind turbine. Emphasis is placed on two aspects of the method, which are necessary in order to obtain a reasonable linearization of behavior when the blades are stalled. First, the tangential (in‐plane) component of turbulence is included, in addition to the axial component. Second, the linearized relationship between lift coefficient and angle‐of‐attack is adjusted to account for the effects of dynamic stall: separate linearizations are used for excitation and damping of vibration. A thorough comparison is made between linear and non‐linear dynamic‐stall methods, with the conclusion that the accuracy of the linear method depends upon the frequency and amplitude of oscillation. The linear dynamic‐stall method is accurate at blade vibrational frequencies, but it can be inaccurate at frequencies in the vicinity of 1P or below, when the angle‐of‐attack oscillates with an amplitude of 3° or more. Load spectra of a Nordtank 500 turbine, calculated using the frequency‐domain method, are compared with measurements. The frequency‐domain method provides estimates of load spectra and aerodynamic damping (stability) that are useful for preliminary design and optimization, but the method lacks sufficient accuracy and generality to be used for certification. Copyright © 2011 John Wiley & Sons, Ltd. |
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| AbstractList | ABSTRACT
A simple method, based in the frequency domain, was developed for calculating the dynamic response of a stall‐regulated wind turbine. Emphasis is placed on two aspects of the method, which are necessary in order to obtain a reasonable linearization of behavior when the blades are stalled. First, the tangential (in‐plane) component of turbulence is included, in addition to the axial component. Second, the linearized relationship between lift coefficient and angle‐of‐attack is adjusted to account for the effects of dynamic stall: separate linearizations are used for excitation and damping of vibration. A thorough comparison is made between linear and non‐linear dynamic‐stall methods, with the conclusion that the accuracy of the linear method depends upon the frequency and amplitude of oscillation. The linear dynamic‐stall method is accurate at blade vibrational frequencies, but it can be inaccurate at frequencies in the vicinity of 1P or below, when the angle‐of‐attack oscillates with an amplitude of 3° or more. Load spectra of a Nordtank 500 turbine, calculated using the frequency‐domain method, are compared with measurements. The frequency‐domain method provides estimates of load spectra and aerodynamic damping (stability) that are useful for preliminary design and optimization, but the method lacks sufficient accuracy and generality to be used for certification. Copyright © 2011 John Wiley & Sons, Ltd. |
| Author | Muskulus, Michael Moe, Geir Merz, Karl O. |
| Author_xml | – sequence: 1 givenname: Karl O. surname: Merz fullname: Merz, Karl O. email: karl.merz@ntnu.no, Karl O. Merz, Department of Civil and Transport Engineering, Norwegian University of Science and Technology, Høgskoleringen 7A, 7491 Trondheim, Norway., karl.merz@ntnu.no organization: Department of Civil and Transport Engineering, Norwegian University of Science and Technology, Høgskoleringen 7A, 7491 Trondheim, Norway – sequence: 2 givenname: Michael surname: Muskulus fullname: Muskulus, Michael organization: Department of Civil and Transport Engineering, Norwegian University of Science and Technology, Høgskoleringen 7A, 7491 Trondheim, Norway – sequence: 3 givenname: Geir surname: Moe fullname: Moe, Geir organization: Department of Civil and Transport Engineering, Norwegian University of Science and Technology, Høgskoleringen 7A, 7491 Trondheim, Norway |
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| Cites_doi | 10.1016/j.fluidstructs.2007.02.005 10.2172/6548367 10.1016/j.paerosci.2006.10.002 10.1002/we.116 10.1016/0266-8920(88)90006-9 10.1016/0142-1123(82)90018-4 10.1115/1.2847866 10.1002/we.242 10.1002/0470846062 10.1111/j.2517-6161.1965.tb01488.x 10.1016/0038-092X(82)90072-X 10.1002/we.120 10.1016/0167-6105(82)90067-8 10.1016/0022-460X(67)90160-5 |
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| References_xml | – volume: 10 start-page: 551 year: 2007 end-page: 577 article-title: Aeroelastic instability problems for wind turbines publication-title: Wind Energy – volume: 6 start-page: 86 year: 1967 end-page: 97 article-title: Power spectral analysis of non‐stationary random processes publication-title: Journal of Sound and Vibration – year: 1981 – volume: 29 start-page: 363 year: 1982 end-page: 375 article-title: The spectrum of wind speed fluctuations encountered by a rotating blade of a wind energy conversion system publication-title: Solar Energy – start-page: 274 year: 1990 end-page: 278 – start-page: 243 year: 1986 end-page: 265 – year: 2005 – year: 2001 – volume: 3 start-page: 36 year: 1988 end-page: 42 article-title: A perspective on modelling rotorcraft in turbulence publication-title: Probabilistic Engineering Mechanics – volume: 42 start-page: 285 year: 2006 end-page: 330 article-title: State of the art in wind turbine aerodynamics and aeroelasticity publication-title: Progress in Aerospace Sciences – volume: 7 start-page: 133 year: 2004 end-page: 143 article-title: Aeroelastic stability analysis of wind turbines using an eigenvalue approach publication-title: Wind Energy – volume: 117 start-page: 311 year: 1995 end-page: 317 article-title: A complex frequency domain model of wind turbine structures publication-title: Journal of Solar Energy Engineering – year: 1994 – year: 1998 – year: 1959 – volume: 27 start-page: 204 year: 1965 end-page: 237 article-title: Evolutionary spectra and non‐stationary processes publication-title: Journal of the Royal Statistical Society, Series B (Methodological) – volume: 10 start-page: 249 year: 1992 end-page: 262 article-title: Model for power spectra of the blade of a wind turbine measured from the moving frame of reference publication-title: Journal of Wind Engineering and Industrial Aerodynamics – start-page: 429 year: 1997 end-page: 433 – year: 2002 – volume: 23 start-page: 959 year: 2007 end-page: 982 article-title: Dynamic stall model for wind turbine airfoils publication-title: Journal of Fluids and Structures – year: 2004 – volume: 4 start-page: 31 year: 1982 end-page: 40 article-title: Simple rainflow counting algorithms publication-title: International Journal of Fatigue – volume: 34 start-page: 3 year: 1986 end-page: 17 article-title: A semi‐empirical model for dynamic stall publication-title: Journal of the American Helicopter Society – volume: 7 start-page: 211 year: 2004 end-page: 224 article-title: Aeroelastic stability predictions for a MW‐sized blade publication-title: Wind Energy – year: 1995 – year: 1991 – year: 1999 – ident: e_1_2_9_27_1 doi: 10.1016/j.fluidstructs.2007.02.005 – volume-title: Fatigue Testing and Analysis—Theory and Practice year: 2005 ident: e_1_2_9_34_1 contributor: fullname: Lee Y‐L – ident: e_1_2_9_30_1 doi: 10.2172/6548367 – ident: e_1_2_9_14_1 – ident: e_1_2_9_26_1 doi: 10.1016/j.paerosci.2006.10.002 – ident: e_1_2_9_31_1 – ident: e_1_2_9_3_1 – ident: e_1_2_9_11_1 doi: 10.1002/we.116 – ident: e_1_2_9_21_1 doi: 10.1016/0266-8920(88)90006-9 – ident: e_1_2_9_25_1 – ident: e_1_2_9_33_1 doi: 10.1016/0142-1123(82)90018-4 – ident: e_1_2_9_16_1 doi: 10.1115/1.2847866 – ident: e_1_2_9_17_1 – ident: e_1_2_9_7_1 – ident: e_1_2_9_15_1 doi: 10.1002/we.242 – volume-title: Theory of Wing Sections, Including a Summary of Airfoil Data year: 1959 ident: e_1_2_9_29_1 contributor: fullname: Abbott IH – volume-title: Contributions from the department of meteorology and wind energy to the EWEC’94 conference in Thessaloniki, Greece year: 1994 ident: e_1_2_9_6_1 contributor: fullname: Petersen JT – ident: e_1_2_9_2_1 doi: 10.1002/0470846062 – volume-title: Wind Turbine Design, with Emphasis on Darrieus Concept year: 2002 ident: e_1_2_9_28_1 contributor: fullname: Paraschivoiu I – ident: e_1_2_9_19_1 – ident: e_1_2_9_32_1 – ident: e_1_2_9_24_1 – ident: e_1_2_9_22_1 doi: 10.1111/j.2517-6161.1965.tb01488.x – volume-title: Turbulence—An Introduction for Scientists and Engineers year: 2004 ident: e_1_2_9_20_1 contributor: fullname: Davidson PA – ident: e_1_2_9_5_1 doi: 10.1016/0038-092X(82)90072-X – ident: e_1_2_9_12_1 – ident: e_1_2_9_10_1 doi: 10.1002/we.120 – ident: e_1_2_9_18_1 – volume: 34 start-page: 3 year: 1986 ident: e_1_2_9_13_1 article-title: A semi‐empirical model for dynamic stall publication-title: Journal of the American Helicopter Society contributor: fullname: Leishman JG – ident: e_1_2_9_9_1 – volume-title: Proceedings of the fourth IEA symposium on the aerodynamics of wind turbines year: 1991 ident: e_1_2_9_8_1 contributor: fullname: Øye S – ident: e_1_2_9_4_1 doi: 10.1016/0167-6105(82)90067-8 – ident: e_1_2_9_23_1 doi: 10.1016/0022-460X(67)90160-5 |
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A simple method, based in the frequency domain, was developed for calculating the dynamic response of a stall‐regulated wind turbine. Emphasis is... |
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| SubjectTerms | blade design dynamic stall frequency domain stall regulated |
| Title | A simple frequency-domain method for stress analysis of stall-regulated wind turbines |
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