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Research Papers

Flutter Limit Investigation for a Horizontal Axis Wind Turbine Blade

[+] Author and Article Information
Mennatullah M. Abdel Hafeez

Department of Mechatronics,
German University in Cairo,
Cairo 11835, Egypt
e-mail: mennatullah.ibrahim@guc.edu.eg

Ayman A. El-Badawy

Department of Mechatronics,
German University in Cairo,
Cairo 11835, Egypt;
Department of Mechanical Engineering,
Al-Azhar University,
Cairo 11765, Egypt
e-mail: ayman.elbadawy@guc.edu.eg

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 6, 2017; final manuscript received February 7, 2018; published online March 27, 2018. Assoc. Editor: Stefano Lenci.

J. Vib. Acoust 140(4), 041014 (Mar 27, 2018) (12 pages) Paper No: VIB-17-1193; doi: 10.1115/1.4039402 History: Received May 06, 2017; Revised February 07, 2018

This work presents a new aeroelastic model that governs the extensional, chordwise, flapwise, and torsional vibrations of an isolated horizontal axis wind turbine blade. The model accounts for the sectional offsets between the shear, aerodynamic, and mass centers. The centrifugal stiffening effects are also accounted for by including nonlinear strains based on an ordering scheme that retains terms up to second-order. Aerodynamic loading is derived based on a modified Theodorsen's theory adapted to account for the blade rotational motion. A set of four coupled nonlinear partial differential equations are derived using the Hamiltonian approach that are then linearized about the steady-state extensional position. The finite element method (FEM) is then employed to spatially discretize the resulting equations with the aim of obtaining an approximate solution to the blade's dynamic response, utilizing state space techniques and complex modal analysis. Investigation of the blade's flutter stability limit is carried out. Effects of parameters such as wind speed and blade sectional offsets on the flutter limit and dynamic response are also investigated.

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References

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Figures

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Fig. 2

Aerodynamic loads on an airfoil section

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Fig. 1

Coordinate frames used

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Fig. 4

Normal operating rotor speed curve

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Fig. 5

Damped natural frequencies variation of the first six modes with wind speed at normal operating rotor speed: (a) first, second and third flapwise modes; (b) first and second chordwise modes; and (c) first torsional mode

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Fig. 3

WindPACT blade spanwise parameter distribution: (a) flapwise stiffness, EIx, chordwise stiffness, EIz, torsional stiffness GJ and extensional stiffness, EA; (b) mass per unit length, μ; (c) sectional pretwist angle, β; (d) unit length flapwise mass moment of inertia, Ixm, unit length chordwise mass moment of inertia, Izm and unit length polar mass moment of inertia, Jm; (e) mass-shear center offset, rx; and (f) chord, c

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Fig. 6

Damping variation of the first six modes with wind speed at normal operating rotor speed: (a) first, second and third flapwise modes; (b) first and second chordwise modes; and (c) first torsional mode

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Fig. 7

First six mode shapes at rated wind and rotor speeds: (a) first mode, (b) second mode, (c) third mode, (d) fourth mode, (e) fifth mode, and (f) sixth mode

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Fig. 8

Flutter mode variation with rotor speed at still air: (a) damping in log decrement and (b) damped frequency in Hz

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Fig. 9

Sixth mode description at flutter onset: (a) mode shape and (b) tip displacement in response to exciting the flutter mode (sixth mode)

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Fig. 10

Fifth and sixth modes variation with rotor speed at still air: (a) damped frequency in Hz and (b) magnified veering region

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Fig. 11

Mode shapes at a rotor speed of 26 rpm before veering: (a) fifth mode and (b) sixth mode

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Fig. 12

Mode shapes at a rotor speed of 30 rpm after veering: (a) fifth mode and (b) sixth mode

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Fig. 13

Flutter limit against wind speed

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Fig. 14

Sixth mode description at flutter onset at a rated wind speed of 11.5 ms−1: (a) mode shape and (b) tip displacement in response to exciting the flutter mode (sixth mode)

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Fig. 15

Effect of mass-shear center offset on the flutter condition at rated wind speed: (a) flutter rotor speed and (b) flutter frequency

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