the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 Oct 2023
Comparison of different cross-sectional approaches for the structural design and optimization of composite wind turbine blades based on beam models
Daniel Hardt
Claudio Balzani
Christian Hühne
Abstract. During the preliminary multidisciplinary design phase of wind turbine blades the evaluation of many design candidates plays an important role. Computationally efficient methods for the structural analysis are needed to cover the required effects, e.g., correct prediction of stiffness matrix entries including the (bend-twist) coupling terms. The present paper provides an extended overview of available approaches and shows their ability to fulfill the requirements for the composite design of rotor blades. Three cross-sectional theories are selected and implemented to compare the cross-sectional coupling stiffness terms and the stress distribution based on different multi-cell test cross-sections. The cross-sectional results are compared with the 2D finite element code BECAS and discussed in the context of accuracy and computational efficiency. The most promising approach achieved a better resolution of the stress distribution compared to BECAS and an order of a magnitude less computation time when the same discretization is used. The deviations of the stress distributions are below 10 percent for the most test cases. The results can serve as a basis for the beam-based design of wind turbine rotor blades.
- Preprint
(1342 KB) - Metadata XML
- BibTeX
- EndNote
Edgar Werthen et al.
Status: open (until 11 Dec 2023)
-
CC1: 'Comment on wes-2023-147', Vengalattore Nagaraj, 18 Nov 2023
reply
Comments on “Comparison of different cross-sectional approaches for the structural design and optimization of composite wind turbine blades based on beam models”
Authors: Edgar Werthen, Daniel Hardt, Claudio Balzani, and Christian Hühne
During the preliminary design phase of composite rotor blades of wind turbines and helicopters it is necessary to evaluate of a large number of design candidates. These blades are idealized as beams for the aeromechanics analysis for the prediction of the loads and aeroelastic stability of the rotors. It is necessary to include the effects of laminate stacking and structural coupling effects between bend-twist and extension-twist deformations. A number of design candidates result from these different structural topologies (e.g., number and/or of spars) and concepts for materials used and how they are combined in laminate lay-ups. Consequently, the basic requirement of the approach used in the analysis is a significant reduction of the computation time for model creation and the calculation of internal stresses compared to a high-fidelity FE model. The computation time for the stress calculation scales with the number of iterations of the optimization process. Available computational models include 3-D FE models, 2-D cross-sectional analysis models, and 2-D analytical models.
The use of 3-D FE model in the preliminary design phase can be ruled out due to the high modelling effort and the long computation times. 2-D FE cross-section models also have similar problems due to the remeshing required for each iteration and also due to expensive solving effort compared with a 2-D analytical approach. The requirements of an acceptable high fidelity 2_D analytical model are that it must be capable of modeling beams with closed, single- or multi-cell cross-section geometries that can vary along the beam axis. The cross-sections of the rotor blades are usually thin-walled,andmay have material lay-ups that exhibit bend-twist and extension-twist couplings. In addition, it is necessary to accurately model the influence of cross-section warping and the shear deformation on the stiffness and stress distribution in the cross-section.
The paper under review provides a comprehensive review of available cross-sectional approaches.. The authors have selected three cross-sectional theories to compare their performance in the prediction of the stiffness properties including the influence of cross-sectional coupling stiffness and the stress distribution in the cross-section.. The cross-sectional results are validated with the 2D-finite element code BECAS. (BECAS itself has been validated against VABS, another 2-D FE that is extensively used in the helicopter field). The comparison is carried out using two different cross-sections with different material distributions. The first cross-section as a thin-walled and the second cross-section is a NACA 2412 airfoil with two shear webs , which is representative for a cross-section of a wind turbine rotor blade.
The advantage of the analytical approaches is that they do not need a discretization in contour-thickness-direction, while the 2-D FE approaches like BECAS requires a discretization for each layer of the laminate in the thickness-direction. The authors show that the analytical approach of Jung et al has the advantages of including the influence of transverse shear stress and torsional warping (Vlasov) and gives results that are close to the FE approach while it is an order of magnitude (sometimes even more) faster than BECAS. Also, the computing time for a single load case is around an order of magnitude faster than BECAS.
As a co-author of the Jung et al. papers, I commend the authors’ summary the analytical details of our approach. In their comparisons they have included the details of the cross-section stiffnesses, stress distributions, and the time required for the date preparation and solution of each case.
In summary, I find the paper under review to be a systematic and timely contribution to the literature and is worth publication.
Vengalattore T Nagaraj
Research Scientist. Department of Aerospace Engineering
University of Maryland, College Park, MD.
Disclaimer: this community comment is written by an individual and does not necessarily reflect the opinion of their employer.Citation: https://doi.org/10.5194/wes-2023-147-CC1 -
AC1: 'Reply on CC1', Edgar Werthen, 22 Nov 2023
reply
Dear Dr. Nagaraj,
thank you very much for your comment. We appreciate your feedback.
Kind Regards
Edgar Werthen, Daniel Hardt, Claudio Balzani and Christian Hühne
Citation: https://doi.org/10.5194/wes-2023-147-AC1
-
AC1: 'Reply on CC1', Edgar Werthen, 22 Nov 2023
reply
-
RC1: 'Comment on wes-2023-147', Anonymous Referee #1, 03 Dec 2023
reply
In this paper, the comparison of the estimated cross-sectional stiffness matrix of a rectangular and a blade cross-section by the three semi-analytical approaches (Jung, Song and Wiedemann) and the 2D FE code BECAS (which is considered as the reference method). The paper is well written with a clear structure. Some of the minor comments are provided below for the authors to consider when preparing their revision.
- When obtaining the shear stiffness terms, a calculation model is considered with the blade tip loaded. Do you mean that a blade is assumed with the same cross-sections from the root to the tip? Moreover, is the tip load realistic to consider? In fact, a distributed line load is often used when designing the blade.
- Secondly, do you assume that the blade will experience relatively small deformations and behave as a linear beam globally? Will the geometrical nonlinearity as a blade beam influence the cross-sectional coupling stiffness terms?
- Only one blade cross-section is considered. It might be interesting to consider at least two cross-sections with different aerodynamic profiles.
Citation: https://doi.org/10.5194/wes-2023-147-RC1
Edgar Werthen et al.
Edgar Werthen et al.
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 132 | 38 | 6 | 176 | 2 | 3 |
- HTML: 132
- PDF: 38
- XML: 6
- Total: 176
- BibTeX: 2
- EndNote: 3
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
A comprehensive overview is provided showing available cross-sectional approaches and their properties in relation to derived requirements for the design of composite rotor blades. The analytical approach of Jung shows the best results in terms of accuracy of stiffness terms (coupling and transverse shear) and stress distributions. An improved performance compared to 2D FE codes could be achieved making the approach applicable for optimization problems with a high number of design variables.
A comprehensive overview is provided showing available cross-sectional approaches and their...