the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Modeling unsteady loads on wind-turbine blade sections from periodic structural oscillations and impinging gusts
Abstract. Many traditional methods for wind turbine design and analysis assume quasi-steady aerodynamics, but atmospheric flows are inherently unsteady and modern turbine blades are susceptible to aeroelastic deformations. This study therefore evaluates the effectiveness of simple analytical models for capturing the effects of such unsteady conditions on wind-turbine blades. We consider a pitching and plunging airfoil in a periodic transverse gust as an idealization of unsteady loading scenarios on a blade section. A potential-flow model derived from a linear combination of canonical problems is proposed to predict the unsteady lift on a two-dimensional airfoil in the small-perturbation limit. We then perform high-fidelity two-dimensional numerical simulations of a NACA-0012 airfoil over a range of periodic pitch, plunge, and gust disturbances, and quantify the amplitude and phase of the unsteady lift response. Good agreement with the model predictions is found for low to moderate forcing amplitudes and frequencies, while deviations are observed when the angle-of-attack amplitudes approach the static flow-separation limit of the airfoil. Potential explanations are given for the cases in which the ideal-flow theory proves insufficient. This theoretical framework and numerical evaluation motivate the inclusion of unsteady flow models in design and simulation tools in order to increase the robustness and operational lifespans of wind turbine blades in real flow conditions.
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RC1: 'Comment on wes-2023-164', David Wood, 07 Feb 2024
The classical, unsteady, linearized airfoil theories used in this study are very important in wind turbine aerodynamics, but unsteadiness is commonly ignored or represented by a quasi-steady steady process in models like blade element theory. On the other hand, the classical theories have their limitations which are carefully identified in this study. Significant airfoil thickness, large amplitude pitching and plunging, and high reduced frequencies will all challenge the limits to linearity. Nevertheless, the authors, like others before them, e.g. Chiereghin (2017, extra references below), have found the linear regime surprisingly wide, and, therefore, useful in practice. It is relevant that Prandtl, when introducing lifting line theory to English audiences after the first world war, stressed the perturbative nature of the theory, e.g. Prandtl (1923). This has long since been forgotten because the theory is robust. The novelty of the manuscript is the combined study of pitching and plunging by exploiting the linearity of the classical theories. The results are compared to available experiments and to their own simulations of an unsteady NACA 0012 airfoil. Generally good agreement was found and the route to extension of the modelling was discussed. There is a huge literature on unsteady behaviour of airfoils, from which the authors have drawn a comprehensive and appropriate reference list.
In summary, the manuscript provides a useful and important contribution to wind turbine aerodynamics and can be accepted once the following issues are addressed. I will list these in order.
The authors carefully state that the effects of plunging and pitching are superimposes and then on L83 describe this as a “linear model that results in a linear combination…”. I think ”results” is misplaced as the model is linear by construction.
Small point: “infinite-span airfoil” is a tautology as an airfoil must have infinite span.
Figure 2 shows the two-dimensional (2D) computational domain but then we are told that the unsteady vorticity field was modeled by large eddy simulation (LES) which is inherently three dimensional. How the LES is embedded in the 2D simulation is not described.
Small point: “to perform this transformation” on L190 is vague. I think you mean “to return to the inertial frame”?
The discussion of the Reynolds number (Re) should be improved. My judgement is that Re > 200,000 is a good compromise as it avoids complexities like leading edge separation bubbles, that occur at lower Re while not requiring very fine grids. A vague reference to “the nonlinear effects of high Reynolds-number …” whatever they are, is not needed.
A brief description of the error bars in Figure 3 and the line thickness of the simulations in Figure 4 would help interpret the results. Presumably the latter represent averages over a number of cycles starting after a specified time. These details should be given. Similar remarks apply to the later figures.
The effects of finite Re are mentioned briefly on L370 where the theory is said to be “inviscid”. Since the classical theories contain a model for the wake and use the Kutta condition, a better adjective would be “infinite Reynolds number”.
Extra References
Chiereghin, N., Cleaver, D., & Gursul, I. (2017). Unsteady Measurements for a periodically plunging airfoil. In 55th AIAA Aerospace Sciences Meeting (p. 0996).
Prandtl, L. (1923). Applications of modern hydrodynamics to aeronautics, NACA-TR-116.
Citation: https://doi.org/10.5194/wes-2023-164-RC1 - AC1: 'Reply on RC1', Omkar Shende, 08 Apr 2024
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RC2: 'Comment on wes-2023-164', Anonymous Referee #2, 24 Mar 2024
The authors have done an academic study of unsteady aerodynamics of a symmetric airfoil in inflow with transverse gust under attached flow conditions in 2D. They are considering the plunge and pitch (blade torsion) of the airfoil, and the Theodorsen effect of shed vorticity on the circulatory lift and Sears function for the unsteadiness of the lift variation from the transverse gust variation.
I have recommended that the manuscript is not published in WES because I fail to see the novelty in the work. The authors claim that their model “could yield far-reaching benefits to the operational longevity of wind turbines by better accounting for unsteady fatigue loads in the design process.” However, the authors seem to be unaware of the status of the art within aeroelastic modelling of wind turbines. The last 25 years we have had research and commercially available aeroelastic codes that include the Theodorsen effect in the unsteady aerodynamic lift models, and we have shown that these codes are able to predict the blade and turbine component fatigue loads within 5% relative error to measurements for each wind speed over the entire operational range. The biggest uncertainty in these predictions is not the lack of transverse gust modelling (which is mainly important when the gust “wave-lengths” are of the order of the blade chord) in these codes, but the uncertainty in the inflow modelling. To capture the flapwise fatigue loads on the blades, it is very important include the deterministic components of the inflow (vertical and horizontal shear profiles, veer profiles, and yaw and upflow angles) as well as the structures of the turbulence (at least the intensity variation with height, but new methods also include turbulence reconstruction).
The authors exclude the edgewise (lead-lag) motion of the airfoil (affecting the downwash of the shed vorticity, an effect included in some aeroelastic codes). Edgewise blade vibrations due to negative aerodynamic are often driving the blade design. They are highly affected by the coupling between the edgewise airfoil motion and its pitch (blade torsion) through the lift force. An unsteady aerodynamic model for wind turbines must therefore include the effect of edgewise airfoil motion on the unsteady lift.
Citation: https://doi.org/10.5194/wes-2023-164-RC2 -
AC2: 'Reply on RC2', Omkar Shende, 08 Apr 2024
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2023-164/wes-2023-164-AC2-supplement.pdf
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AC2: 'Reply on RC2', Omkar Shende, 08 Apr 2024
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