the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 01 Apr 2025
Simulating wind farm flows at hub height with 2D Reynolds-averaged Navier-Stokes simulations
Abstract. Wind turbines in an offshore wind farm typically have the same hub height, and in this case, the power of a wind farm could be predicted if the flow field in the horizontal 2D plane at the hub height is predicted accurately. Nevertheless, Reynolds-averaged Navier-Stokes (RANS) simulations of wind farm flows are predominantly made in full 3D domains, which are naturally more computationally expensive than 2D simulations. In this work, a systematic comparison is made between 2D and 3D RANS simulations of various wind farm configurations to assess the differences in computational cost and accuracy. For our numerical setup and the cases considered, which include layouts with up to 144 turbines, it is found that the 2D simulations are at least two orders of magnitude computationally cheaper than their corresponding 3D simulations, while the predicted farm power is within -30 % to 15 % for all cases. Only minor, but necessary, modifications have been made to the governing 2D RANS equations to avoid unphysical decay of turbulence, allowing for a simple direct comparison between the 2D to 3D simulations. Given the low computational cost and already sensible performance of the only slightly modified 2D RANS simulations demonstrated in this work, it appears attractive to further investigate this methodology and possibly introduce additional 2D modifications to improve the accuracy in future work.
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Status: open (until 29 Apr 2025)
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RC1: 'Comment on wes-2025-50', Anonymous Referee #1, 14 Apr 2025
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Please see attachment.
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RC2: 'Comment on wes-2025-50', Anonymous Referee #2, 21 Apr 2025
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This paper presents results from a 2D RANS approach in application to wind farm flows including a single turbine case to be compared with a set of 3D models. The idea of reducing the flow computation to 2D makes sense and RANS is the turbulence approach to model it.
The presented manuscript has a clear focus to assess how much faster 2D simulations can be over 3D, at the expense of a worsen prediction of the flow field and performance.
It is a valuable work but further investigation needs to be made so that this study has a notable contribution to the field.
First, the 2D RANS model is seen to fail when predicting the wake, mainly overestimating the velocity deficit. No assessment is provided in terms of TKE which needs to be included in order to understand what the underlying physics are driving the wake recovery in the 2D flow (please consider adding an analogous of figure 5 with TKE). For the single turbine case, the model does not work well, and authors need to investigate more as to why, and if further modifications to the turbulence model are needed. As it stands, results indicate that 2D RANS is fast but provides much worse predictions that does not encourage its adoption.
Second, only the CPU hours are used as the comparison in performance. Whilst true, there is an expectation that the number of cores used in 3D and 2D RANS are different. With this, authors need to specify how many cores were used in each simulation and, most importantly, if for the 2D simulations only one node was used. The latter would remove inter-node communication and thus be unfair in the comparison. Consider adding details of the chip architecture, cores per node, etc. in the paragraph starting in line 211 to 216. Tables 4 and 5 needs details of how each setup is mapped to a number of processors. Is the same core count per CPU? In line 280, it is mentioned that some cases could have run on slower nodes. Typically when assessing code performance one needs to run a minimum of three times the cases. How many have the authors considered?
The reviewer recommends major revisions, with further minor comments provided below.
Line 19: Three dimensional modelling is needed in all CFD as the flow is 3D so is turbulent. Hence not only LES is 3D, RANS is too and both can be simplified to 2D if at all necessary.
Line 25: 2D EWM only if velocity shear and veer are not considered. This needs clarification.
Table 1: In Vertical shear and ground, there should also be stratification.
Line 91: typo in “characterized”
Eq 11 and 12: in this derivation for the source terms in Eqs 13 and 14, authors basically make that the left hand side of eqs 11 and 12 are equal to the dissipation terms. This is rather confusing. Why would one expect (as in figure 2) that turbulence is self-sustained all the downstream length? This needs more explanation as surely its linked to the performance of the 2D model and its overestimation of wake length.
Line 154: please add an appendix with budgets of tke and dissipation.
Line 156: typo in “were also by”.
Line 166: how do you sample the local velocity Ud?
Lines 178-180: is the choice of AD thickness exclusive of RANS? This should be elaborated more.
Line 205: perhaps I missed it, but what is the turbulence model you use? What is the grid resolution and time stepping?
Table 3: wind directions “0-90”: are only these two values used?
Line 250: “2D mass flow conservation”. Mass should be conserved through the governing equations. The effective turbine section here is more problematic as you consider only the maximum turbine diameter, which is not the representative depth-averaged diameter which perhaps should have been considered.
Line 255: perhaps provide a contour plot of dw/dx to show the balance in the mass conservation
Citation: https://doi.org/10.5194/wes-2025-50-RC2 -
RC3: 'Comment on wes-2025-50', Anonymous Referee #3, 22 Apr 2025
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The manuscript explores the up- and downsides of simulating wind farms with a 2D RANS method, which only considers the flow at hub height. The authors provide a good range of test cases, and comprehensively discuss the effects of this simplification on flow fields, farm power and its distribution over a farm. Additionally, descriptions of the numerical setups and the potential reductions in computational cost are documented very well throughout the paper.
However, the underlying 2D RANS method has not been rigorously derived, with the resulting modifications compared to 3D RANS being minimal. This makes the manuscript feel more like an exploratory “proof of concept” study rather than a fully worked out first step. While this is not necessarily a problem, and the authors acknowledge it in their conclusions, this limitation should be indicated more clearly in both the title and abstract.
Further comments:
- Section 2:
- Line 77: this sentence is the core of how the 2D RANS method is developed. It would be very beneficial to readers to have a more detailed derivation, with an overview of all the terms in the various equations that are left out or replaced by source terms in the 2D approach.
- Section 2.3: the introduction of the source terms is based on uniform flow, so that it seems that the issue of turbulence decaying too fast should also affect uniform 3D RANS simulations. This confuses the link between the source terms and the vertical derivatives they’re supposed to replace in equations 1-5, and makes it difficult to see how these source terms should scale with e.g. veer and shear effects.
Making the explicit connection between a more rigorous stating of the 2D assumptions and the corrective source terms would greatly increase the value of the paper. - Section 2.4: the thrust per unit depth seems to be distributed uniformly over the span of the turbine, resulting in an “infinite ribbon” instead of a disk. This seems like a major problem for 2D RANS simulations of wind farms, but as far as I can tell, no effort is made to address it. For instance, modifying this uniform spanwise distribution through some sort of height-averaging across the rotor disk might result in a better representation of disks in the 2D plane. At minimum, this “actuator strip” method used in the paper should be high-lighted as a shortcoming and an area for future research.
I think it would be very instructive to move section 2.2 to the end of section 2, as currently it divides the overview of the RANS equations from the introduction of the corrective source terms.
- Section 4:
- A figure showing TKE fields when discussing the reduced wake recovery in 2D RANS would clarify the discussion, especially for the single-turbine case.
- Line 305: the authors say that on a farm scale a different blockage effect occurs than for individual turbines. However, the results in Figure 13 look like they could also be caused by the aggregate of all the local blockage effects, which would also result in enhanced bypass velocities, lower power in the front row center, and a beneficial pressure gradient throughout the farm. It’s not clear from the discussion why this would not be the same underlying mechanisms.
Citation: https://doi.org/10.5194/wes-2025-50-RC3 - Section 2:
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