Advanced accurate and computationally efficient numerical methods for wind turbine rotor blade design

Paola Bertolini*

*Corresponding author for this work

Research output: Book/ReportPh.D. thesisResearch

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The geometry of wind turbine blades is characterised by the aerodynamic lift generating surface which results in lengthwise geometrical variations (LGVs), namely tapered and twisted cross sections and precurved longitudinal axis. In particular, a tapered beam presents cross-section dimensions which smoothly vary along its longitudinal span and affects the behaviour of the structure. Hence, the stress distributions in tapered structures can be at significant variance with the ones occurring in prismatic beams. The early stages of wind turbine blade design are based on simplified beam models to reduce the computational cost otherwise entailed by 3D full finite element models. The cross-section stiffness properties required for aeroelastic analysis and the prediction of the strains/stresses for structural design and optimization purposes are provided by cross-section analysis methods. Nowadays, the available cross-section analysis methods are based on prismatic hypothesis and consequently the aforementioned taper effects are ignored, notwithstanding the available scientific literature on this matter.

The first part of the thesis sheds light on the effects of taper on the stresses in thinwalled isotropic beams with circular and rectangular cross sections. Elasticity theory is employed to derive closed-form analytical solutions which are compared to 3D finite element models for validation purposes. The analytical equations of the Cauchy stress components provide an insight into the role of taper in the beam behaviour. Indeed, taper evokes geometrical couplings which considerably affect the stress state of the beam. Particularly, shear-axial and shear-bending contributes to the definition of the in-plane shear component and significantly affect the in-plane shear both qualitatively and quantitatively. For instance, neglecting taper effect in structures such as wind turbine blades could result in underestimating the shear components in the proximity of the web adhesive joints, and, therefore, to detrimental designs. In addition, the provided closed-form solutions could be employed for validation of tapered cross-sectional analysis tools. In addition, the provided expressions could be used for validation of tapered cross-sectional analysis tools.

The second part of the thesis investigates an alternative finite element method which suits for cross-section analysis of tapered beams. It models the beam cross-section as a tapered slice consisting of one-layered of solid finite elements. The nodal forces equivalent to axial, bending and shear are derived from the assumed surface traction
acting on the two faces of the slice. In addition, constraint equations for the six rigid body modes, namely three translations and three rotations, are enforced via the Lagrange multiplier method. Parametric studies of the relation between the stresses and the magnitude of the taper angles and the thickness of the slice are conducted on a planar isotropic wedge, whose closed-form solutions in terms of stresses are known. Results reveal the ability of the slice method to predict approximately the stresses in the tapered cross-sections of the wedge.

The present study underlines the importance of the taper effects on the stress components of a tapered beam. Neglecting taper effects can result in a inaccurate stress prediction and accordingly lifetime calculation of tapered beams. The outcome of this project places the foundations for the development of a new advanced tapered cross-section analysis tool where a more accurate prediction of the stress components and lifetime of tapered structures is achieved without exploiting high computational tools.
Original languageEnglish
Place of PublicationRoskilde, Denmark
PublisherDTU Wind Energy
Number of pages154
Publication statusPublished - 2020
SeriesDTU Wind Energy PhD

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