the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Sep 2024
A large-eddy simulation analysis of collective wind-farm axial-induction control in the presence of blockage
Abstract. Over the past few years, numerous studies have shown the detrimental impact of flow blockage on wind-farm power production. In the present work, we investigate the benefits of a simple collective axial-induction control strategy on power maximization and load reduction in the presence of blockage. To this end, we perform a series of large-eddy simulations (LES) over a wind-farm consisting of 100 IEA 15MW turbines, and build the wind-farm power and thrust coefficient curves for three different conventionally neutral boundary layer profiles. We show that the wind-farm power and thrust coefficient curves are much flatter than those of an isolated turbine. As a result, the wind-farm thrust coefficient becomes significantly more sensitive to the selected operating point than the power coefficient. Consequently, we find that the optimal wind-farm operating point considerably differs from the Betz limit in practice, particularly under high-blockage conditions. At the optimal point, the results reveal a minor power increase, accompanied by a load reduction of about 5 %, simultaneously. More interestingly, we show that in some cases the loads can be reduced by up to 19 %, at the expense of a power decrease of only 1 %.
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RC1: 'Comment on wes-2024-110', Anonymous Referee #1, 07 Oct 2024
This paper is of sure interest for the field of wind energy and very well written. The results appear robust and original. However, I have a few concerns that should be addressed by the authors:
-p.5: Numerical set-up: Please define the set of equations used in your LES (I guess NS equations with Coriolis and temperature stratification effect with Boussinesq approximation for the potential temperature as in Allaerts & Meyers 2015?). Also some of the used techniques (i.e., the fringe region, the tilting technique, etc) should be discussed in more detail for making the paper more self-contained.- p5: the Smagorinsky coefficient is rather high for wind turbine simulations. Please justify the choice of this value with respect to the literature.
-p5: concerning the grid, in the spanwise direction there is one grid point every 22 meters, while much finer cells are used for the vertical direction. The fact that cells are so elongated in the spanwise direction might constitute a numerical issue. Please validate and/or justify with respect to previous works.
- p.5: "the authors consider a wind farm about 4km longer.... we use the same main domain length". If in Lanzilao & Meyers (2024) the domain was 4km longer, how can you use the same domain length? Please explain.
-p.5 "we artificially extend the height of the precursor field by imposing the geostrophic flow field from 3km to 25 km..." This technique is questionable, since turbulent fluctuations are interrupted abruptly and may induce non physical effects. In fact, the flow field will be subject to abrupt changes, which can affect the results. The authors should clearly show and discuss what happens in the region where this strong discontinuity is imposed, by plotting rms quantities or Reynolds stresses. If a strong discontinuity on these quantities is indeed present, they should consider performing a computation adding a smoothing of the turbulent fluctuations instead of a discontinuity and show that this has virtually no effect on the results.-Figure 2: is the vertical axis indeed in [km]? It is weird to see that the capping inversion is so low while the the domain extends 25 km in the vertical direction. Moreover, please confirm that the laminar geostrophic flow field is added starting from 3km for all the three cases independently of the location of the capping inversion.
- Figure 2 c: in the region where the flow angle becomes constant, there are oscillations of the flow angle. Please justify its origin and its effect on the flow.
- p.6: please discuss the choice of the C_T values, are those typical for a 15MW IEA wind turbine in which operating conditions?
-p7: "the wind-direction controller designed by Allaerts and Meyers (2015) is employed during the precursor phase" Is the controller active only during the precursor simulation or also in the rotor simulations?-p16: "clearly amplified for inflows with a low capping inversion" Please discuss, with reference to the literature, the behaviour in the absence of a capping inversion.
- p17: "axial-induction control approaches". Choosing arbitrarily three different possible operating points and comparing the overall performances cannot be considered really a "control". I suggest modifying this part of the discussion, as well as the title of the paper and the abstract/conclusion, referring rather to an "operational strategy" (or similar) instead of a control.Citation: https://doi.org/10.5194/wes-2024-110-RC1 - AC1: 'Reply on RC1', Theo Delvaux, 13 Dec 2024
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RC2: 'Comment on wes-2024-110', Anonymous Referee #2, 28 Oct 2024
This paper reports LES of a 10 x 10 staggered wind farm subjected to three different atmospheric conditions with the turbines operating at four different thrust coefficients. The aim is to investigate the effect of the axial induction factor (equivalent to changing each turbine’s local thrust coefficient, CT’) on the thrust and power coefficients of the whole wind farm. Using the LES data, empirical fits are provided for these quantities as a function of CT’. Using these fits, the authors conclude that allowing for a small reduction in the generated power can lead to a large reduction in the thrust experienced by the wind farm. The extent to which the CT and CP of the wind farm change on changing CT’ is quantified for the different atmospheric conditions studied here. The paper is well-written and easy to read. I have three major comments and a few minor ones given below.
Major Comments:
- Section 4.4, Fig. 9, Tables 5, 6, 7: This is the main result of this paper. It is already known in the context of an isolated turbine (or implied by the inviscid momentum theory). It would be helpful to show the same result for an isolated turbine and comment on how things are different for a wind farm. Also, the effect of atmospheric conditions (inversion height, lapse rate and boundary-layer height) on the trade-off between CP,f, and CT,f should be studied for a wider range of atmospheric conditions to further support this main result. The authors already have a similar database (Lanzilao and Meyers, 2024) of wind farms subjected to a much wider range of atmospheric conditions which could be used for this analysis.
- Line 314: A least squares method is used to determine fitting coefficients. However, there are only 4 data points per atmospheric condition. How can 3 parameters be fit with only 4 data points? The same comment applies to Eq. (13) where there are further additional parameters but again only 4 data points. Line 315: The authors should clarify what they mean by ‘thorough analysis’ either in the main paper or in an appendix.
- In my understanding, the term ‘control’ is usually used in a dynamical sense, with different axial induction control strategies implying changing the CT’ in response to flow conditions. In this paper, however, the thrust coefficient of each turbine is the same across the wind farm and is also frozen in a given simulation. Perhaps a title and phrasing throughout the paper such as ‘sensitivity’ to operating thrust coefficient would be more appropriate.
Minor Comments:
- What material in Section 2 is novel? For example, the wind turbine representation (Section 2.2) is standard unless I am missing some detail. Are the values mentioned in Tables 1 and 2 different from those used in previous work, i.e. Lanzilao and Meyers (2024)?
- Figure 3: I do not see the black dashed line corresponding to the standard deviation.
- The contours in Fig. 4 appear pixellated and patchy (small rectangles). Is this because of the LES resolution or a plotting artefact? Given the size of the rectangles relative to the turbine diameter, it is probably the way each contour plot is exported and not the LES resolution.
- Sentence on lines 247-249: “This can be visualized by … straight in the latter case”: This is not very clear. Drawing some lines that visualize the wake extents on these contour plots might help, or this should be shown using some profiles. Also, it is not clear how a faster wake recovery is associated with the horizontal extent of the wake remaining ‘straight’.
- Line 262: Why are chord lengths considered in calculating the reference speed? The turbine model is a thrusting actuator disk where the chord length is not an input. Why not simply use a disk-average?
- Line 266: Please clarify in the text that ‘disk-based coefficient’ means CT’.
- Line 272: Do the authors mean Fig. 5(d) here? I cannot distinguish colours between the first few rows in Fig. 5 (d). I understand the overall point that the colour differences are more drastic for panels (a, e, i). But if the authors are commenting on differences between the rows in Fig. 5(d), it would be better to use a different colour scheme where these differences show up more clearly.
- Eq. (13) is missing a ‘CT = ’. Also, there should be a subscript ‘f’ on these if these are farm-averaged quantities.
- Some comments on how sensitive these findings would be to the wind turbine type (e.g. diameter, hub-height) and surface roughness values would be appreciated by the readers.
Citation: https://doi.org/10.5194/wes-2024-110-RC2 - AC2: 'Reply on RC2', Theo Delvaux, 13 Dec 2024
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