Responses to Reviewer Comments on “Effect of tip spacing, thrust coefficient and turbine spacing in multi-rotor wind turbines and farms”

The authors employ large-eddy simulations (LES) to quantify the difference in wake effects between a four-rotor wind turbine and an equivalent single-rotor wind turbine, for both an isolated wind turbine and a row of five wind turbines. The present work is a continuation of a conference article, where more parameters are investigated. An engineering wake model is calibrated with the LES data and its performance for a row of five four-rotor wind turbine is investigated. The article is well written and provides interesting results. I have written a list of main and minor comments below:

Response: We thank the reviewer for pointing out this oversight. It has been corrected in the revised manuscript.
4. Lines 275-277: When you change the tip clearance, the amount of poten- tial power changes due to the shear. Have you investigated how this affects your results? My guess is that the shear is the main reason why the power of the first wind turbine changes with different tip clearances (as you shown in Figure 11a).

Response:
The reviewer is correct in saying that the potential power is different for 4-rotor turbines with different tip clearances. Due to the sheared inflow velocity profile, the upper rotors of the 4-rotor turbine are subjected to a higher wind speed as compared to the wind speed seen by the 1-rotor turbine. Similarly, the lower rotors of the 4-rotor turbine see a lower wind speed. Thus, the potential power is expected to be dependent on the tip spacing, since the undisturbed velocity seen by the rotors is dependent on the tip spacing. However, we find that this does not explain the differences between the powers of the first turbine shown in Fig. 11b, as explained in more detail below. The potential power is computed as P pot = (πD 2 /8)C P U 3 0,disk , where U 0,disk is obtained by averaging the logarithmic profile (shown in Fig. 2a) over the rotor disks. P pot and P pot /P 1−Rot pot , or the potential power normalized by that of the 1-rotor isolated turbine, are shown in Table 1. A representative value of C P = 0.5625 is used, but this precise number does not matter when we compare the normalized potential powers.
The normalized potential powers can be seen to be almost equal to 1 for all the tip spacings. In fact, the normalized potential powers reduce slightly as the tip spacing increases. The net effect of shear and the chosen dimensions of the turbines is such that the reduction in power of the lower two rotors dominates the increase in power of the upper two rotors. This effect is not very strong, as seen in the Table 1, being only 2.4% for s/d = 0.5. The same conclusion is reached if we use the hub height velocities instead of the disk-averaged velocities in computing P pot . Thus, the differences between the powers of the isolated 4rotor turbines cannot be attributed to differences in the potential powers. These exact same observations hold for the first turbines in the multi-rotor wind farm cases (powers shown in Fig. 12b).
We hypothesize that the differences for different tip spacings is due to discrepancies between the simulations and the predictions of the inviscid actuator disk (AD) theory. The predictions of the AD theory and the current LES can be either due to inadequate resolution, or due to the effect of turbulent mixing (we refer to Nishino and Wilden (2012) for a discussion on the effect of mixing on thrust and power coefficients of a turbine), which is not accounted for in the AD theory. To rule out the effect of grid resolution on the results, the implied nom- inal thrust coefficient (C T ) is shown in Table 2 for the isolated 1-rotor case and the isolated 4-rotor case with s/d = 0.05. These values are calculated from the LES using the definition C T = C T U 2 disk /U 2 0,disk .It is seen that these values are quite well converged. Changing the grid resolution from GR2 to GR3 changes C T by 0.1% for the 1-rotor case and 0.6% for the 4-rotor case. We conclude that the discrepancies with the inviscid actuator disk theory are due to the effects of turbulent mixing, which are different for different tip clearances. In any case, as also appreciated by the reviewer in a separate comment, the discussion in the appendix further clarifies that these differences between the first turbine powers do not affect the qualitative conclusions drawn. To keep the paper focused, we do not include the above discussion in detail in the main manuscript. We have added an appendix quantifying the change in potential power with changing tip spacings (Appendix B) and added a sentence in Sec. 4.2 (lines 309-311) stating that these discrepancies cannot be explained by the differences in power potential. The response to the reviewer in this present document is available online for readers interested in more details. Figure 6c: The single-rotor wind turbine seems to have a much higher disk averaged ambient turbulence intensity. Why is this the case?

5.
Response: We appreciate the reviewer's eye for detail. The larger ambient turbulence intensity seen in Fig. 6c actually corresponds to the 4-Rotor s/d = 1 case. We apologize for the confusion: the line styles chosen for the 1-Rotor and 4-rotor s/d = 1 cases were very similar to each other. In the updated manuscript, a different line style has been used for the s/d = 1 case.
It should be noted that the integrals are carried out over different regions corresponding to the areas spanned by the rotors in the different cases. Thus, the ambient T I disk values are slightly different for all cases. The differences are apparent on the scale of the figure only for the s/d = 1 case, which is why it appears to be an outlier.
When I looked at the integrated added wake turbulence intensity, I found that the four-rotor wind turbine has a higher integrated added wake turbulence intensity in the near wake compared single-rotor wind turbine, while the opposite is found for the far wake, see Figure 18 where is plotted in Figure 1. The subscript 'disk' denotes disk-average and the subscript '0' denotes upstream region, or the region between x/D = −4 to x/D = −1 in our simulations, where the quantities are almost constant. This measure of added turbulence intensity is compared to Figs. 18(b,d,f) of van der Laan et al. (2019). It is seen that ∆I disk for all the 4-rotor cases is always smaller than for the 1-rotor case. The qualitative differences between the near-wake and far-wake regions are not observed in our LES results. A closer examination of the results in van der Laan et al. (2019) suggests that ∆I disk is larger for the 4-rotor case in the near-wake region only for I ref = 5% and 10%, but not for I ref = 20%. Thus, our results may be considered to be qualitatively similar to the results of van der Laan et al. (2019) for I ref = 20%. It is difficult to gauge the accuracy of one LES with another LES as a benchmark, so we refrain from commenting on which LES result is more accurate. This information is included in Fig. 6(d) of the revised manuscript and in Section 3.2 (lines 218-224).
6. Pages 18-22: Engineering wake model vs LES: (a) Please motivate the use of a spatial varying wake expansion parameter k * .
Response: Using a spatially constant k * always leads to a gradual drop in the relative power prediction. The recovery in relative power, which is typically observed after the second turbine in conventional 1-rotor wind farms and after the third turbine in the 4-rotor wind farms with s/d = 0.1 and 0.25, is not seen in the model predictions using a constant k * . This is the reason for preferring a framework where the value of k * is tied to the local turbulence intensity. While this framework relies on an empirical relation between k * and the local turbulence intensity, it yields better qualitative and quantitative results, and is preferred here. It is possible for individual 4-rotor wind farm cases (particularly those with s/d = 0.5) to be better predicted using a constant k * value in combination with some value for σ 0 /D. However, we could not arrive at a simple consistent rule that yielded good predictions for all cases, and conclude that the spatially varying k * framework works better than a spatially-constant k * . We have added Figure 14 to the revised manuscript and accompanying discussion to Sec. 4.3 (lines 358-371).
(b) Do I understand correctly, that you only fit k * from the single-rotor wind farm simulations and use this directly to predict the deficits in a multi-rotor wind farm ( Figure 13)?
Response: Yes, the k * vs I x correlation is derived from only the 1-rotor LES results. This is done for the present to avoid complications arising from lateral merging of the wakes of the four rotors of one 4-rotor turbine and axial merging of wakes of different 4-rotor turbines.
(c) Figures 21 and 22: Please define the numbers colored in red in the caption, I guess it is the relative error. How did you compute it?
Response: The absolute error between the LES result and the model prediction of the relative power is computed at each of the four downstream turbines (turbines 2 through 5), and then averaged. Thus, the numbers in red in Figures  15 and 16 We do not normalize the absolute errors any further (say with the average relative power given by the LES) because it would lead to misleadingly small numbers for cases where the average relative power is large (for example, the S X = 4D, C T = 1 case). The formula for the error is included in the revised manuscript on line 375 and the captions to Figures 15 and 16. 7. Page 20, Discussion: Some wording needs to be changed here: (a) Line 337: Please remove the word novel, since the four-rotor wind turbine design is not new.
Response: The word has been removed.
(b) Lines 338-340: Please remove for the first time, since there are several authors (including yourself ) have investigated the four-rotor wind turbine design.
Response: The phrase has been removed.
8. Line 354: Please change between different units to between different wind turbines, or do you mean something else?
Response: We did mean wind 'turbines'. The word has been replaced as suggested.
9. Line 286 and Lines 363-364: What do you mean by The effect of the axial spacing on the benefit is ambiguous, since it is non-monotonic.?
Response: As seen in Figure 11(d), the wake-related benefits of multi-rotor wind farms are largest for S X = 4D and smallest for S X = 5D (comparing cases with C T = 4/3 only). Thus, the benefits do not monotonically increase or decrease with S X . This is clarified better in the revised manuscript (lines 416-418).
10. Appendix A: It is nice that you have added this appendix in order to make the comparison of a single-rotor and multi-rotor wind farm more fair, but you forgot to refer to it in the text.
Response: A reference to the appendix has been added in Sec. 4.2 of the revised manuscript (lines 322-323).
Minor comments 1. Figures 5, 14 and 15 have very large labels compare to the rest of the figures. I would look nicer to keep the same label size.
Response: The label sizes on these figures have been reduced in the revised manuscript.
2. You have normalized the velocity deficits by u * , but this makes it hard to see how large the deficit actually is. It would be more interesting to normalize by the freestream velocity (which could be an integral over the disk area). When you normalize the turbulent kinetic energy by u 2 * , you could instead plot the turbulence intensity or added wake turbulence intensity, which is more common for wind turbine wake studies.
Response: We agree with the reviewer that normalizing by the (disk-averaged) freestream velocity would be an interesting alternative way of plotting the results. The current way of normalizing by the friction velocity of the ABL is also valuable because it allows for comparison between the different cases presented in any one figure. The reader can compare with Figure 2 to get a sense for the magnitudes of the deficits with respect to the freestream velocity. The turbulence intensity is shown in Figures 6 and 7 for isolated turbine cases and Figures 9, 10 and A1 for multiple turbine simulations.
3. You both mention thrust coefficient and local thrust coefficient when you talk about C T . I would stick with local thrust coefficient everywhere to avoid confusion.
Response: We feel the need to introduce both thrust coefficients because the local thrust coefficient (C T ) is used in the LES while the nominal thrust coefficient (C T ) is used in the analytical model. It would be awkward to denote C T in the model expressions without having introduced it earlier. Figures 8, 9, 10, 12 and 13: I would write the wind turbine number (1,2,3,4,5) on the x-axis instead of x/D. This also corresponds better to the text, because you often talk about wind turbine numbers.

5.
Response: These numbers are included in Figure 8a (as well as in Figure  4a) deliberately, so as to draw attention to specific contour levels, as explained in the figure caption.
6. You could refer to Niayifar and Porté-Agel (2015) when you talk about the relation between the local turbulence intensity and the wake recovery parameter k * . Niayifar and Porté-Agel (2015) derived a relation between the freestream turbulence intensity and k * based on LES data.

Response:
We have referred to this paper in the revised manuscript (Sec. 4.3, lines 366-371).

Response to Reviewer 2
Overall: The article present numerous LES of both single rotor and multi-rotor consisting of 4 turbines. The different turbine configurations are compared, including the effects of tip spacing in the multi-rotor, thrust coefficient asn turbine spacing for farm scenarios. Additionally, the authors compare to the analytical model by Bastankhah and Porté-Agel. The article follows a number of other recent articles on multi-rotors and provides new results. The article is generally well-written and the results are interesting, so the article is recommended for publication with revisions according to the comments below.
Response: We thank the reviewer, Dr. S. J. Andersen, for his careful assessment of our manuscript and for the detailed and constructive comments.
General comments: 1. Resolution and degree of detail.
-The number of grid points are given in Table 1. However, it would be beneficial to report what these values correspond to the actual spatial resolution. Please correct me if wrong, but as far as I can tell, the main grid of 256x128x160 grid points has a width of pi/2*1000m, i.e. the lateral discretization is 1570.8m/128 = 12.3 m. Same resolution in the vertical. This means that there are only 4 points for a single actuator disc and only 2 for a small rotor in the multirotor. Is this correct? Tip spacing clearings corresponding to approximately 0.6m, 1.2m, 2.5m and 3m are investigated. How are the effect of tip spacing properly resolved when the mesh is so coarse?
Response: Assuming that the boundary layer height H is 1000 m, the grid resolution for the main 256 × 128 × 160 grid (G2) is 12.3 × 12.3 × 6.25 m. The single-rotor turbine has a diameter of D = 0.1H = 100 m. Thus, we have approximately 8 grid points across the disk in the spanwise direction and 16 points across the disk in the vertical direction. For each of the rotors in the multi-rotor turbines, the diameter is d = 0.05H = 50 m, which leads to 4 and 8 grid points in the spanwise and vertical directions respectively. It should be noted that for the combined 4-rotor system, the number of grid points is again similar to that for the larger single-rotor configuration (8 × 16). The dimensional values for the tip spacings are (2.5, 5, 10, 12.5, 25, 50) m corresponding to s/d = (0.05, 0.1, 0.2, 0.25, 0.5, 1), respectively.
Using upwards of 8 grid points across the disk is an established rule-ofthumb following the study by Wu and Porté-Agel (2011). Other studies have used smaller number of grid points across the disk, particularly in the spanwise direction (e.g. (Stevens et al., 2014) used only 4 points across the disk in the spanwise direction in their main grid A3). Thus, the resolution used here with grid G2 is consistent with previous studies. In addition, the grid independence study in Section 3.1 of our manuscript quantifies the change in results between grids G2 and G3. The change in mean velocities is marginal, while the change in added turbulent kinetic energy (TKE) is about 9 % near the top-tip height, and about 2% when averaged over the disk regions. We believe this level of convergence is sufficient to derive confidence in our results.
While the tip spacings for several s/d values are smaller than the grid spacing in the spanwise direction, the effect of tip spacing is captured because the actuator disk model appropriately adjusts the distribution of the thrust force across the discretization points. The details between the tips are obviously missed with this coarse resolution, but the wake effects are appropriately captured. The grid independence study referred to above was carried out for the smallest non-zero spacing, s/d = 0.05, as well as for the largest s/d = 1, and showed similar level of convergence. Details of the grid dependence for the s/d = 1 case are not shown in this manuscript for brevity, but may be found in Ghaisas et al. (2018).
-Please rephrase your sentence in the conclusion stating: "are studied in detail for the first time.". This is stretching it too far in my opinion for several reasons: a) It could be argued that the degree of detail was larger in the article by van der Laan et al. (2019) due to higher resolution and using actuator lines rather than actuator disc as well as changing thrust due to a more realistic controller. Likewise, several of the conclusions found here corroborates the findings of other previous studies, but your present article still has merit. Additionally, the majority of the conclusions investigate integral quantities, e.g. power or disk-averaged velocity deficits.
Response: We agree with the reviewer that some of the findings here corroborate those in van der . The phrase pointed out has been removed.
b) A recent article by van der Laan and Abkar (2019) also investigates multirotors in wind farms and find similar conclusions. Please include as reference and discuss when results are similar or different. This is mainly that the benefit of multi-rotors seems to vanish further into the farm, as seen in Figure  9(c)+(f ). The authors should comment on this more, because it also explains why the analytical model ends up giving reasonable results further into the farm as it approaches the same level as for single rotor wind farms. Therefore, the conclusion by the authors "Wind farms comprised of multi-rotor turbines always show benefits over similar..." is perhaps also stretching the conclusions a bit as it does not show a benefit from the 4th turbine onwards.
Response: We thank the reviewer for pointing out this new article. In the revised manuscript, we refer to this article in the introduction as well as in the results sections (lines 46-53 and 272-275). The statement that multi-rotor wind farms are always beneficial is correct in the sense that the relative power averaged over all downstream rows is larger for multi-rotor farms as compared to for single-rotor farms because the relative power of the first downstream row is always larger in the multi-rotor farm compared to in the single-rotor farm. However, we agree with the reviewer that this needs to be qualified, so a statement to the effect that the benefit is only due to the first downstream turbine in realistic tip spacing cases is included in the revised manuscript (lines 414-415).
2. Effect of CT. The authors discuss how a constant CT is used as opposed to the varying thrust level seen in van der . Please comment on what is more realistic. Part of the discussion from the appendix on how to assess to CT could also be included in the main text.
Response: A constant C T vs varying thrust level occurs in two respects. First, the thrust coefficient is fixed in time in our simulations, while in van der Laan et al. (2019), pitch and torque controllers are adopted in the simulations, which effctively lead to dynamically varying force coefficients. This information is included in Sec. 1 (lines 67-70) in the revised manuscript. Second, field measurements and related simulations in  show that the thrust coefficients are different between the top and bottom pairs of rotors in the multi-rotor configuration, while identical thrust coefficients are used for all rotors in our simulations. This information is included in the revised manuscript in Sec. 2.2 (lines 120-124). Following comments from the other reviewer of this manuscript (Dr. M. Paul van der Laan), we realize that the simulations in van der Laan et al. (2019) also impose identical forcing to all rotors of the multi-rotor turbine for the purposes of comparing the wake recovery features.
We could not find a way to incorporate the material in the appendix into the main manuscript without taking the focus away. Hence, we choose to retain the material in the appendix. A reference to the appendix was missing from the main text of the original manuscript, which has now been included in Sec. 4.2 (lines 309-311).
3. Wake superposition. Wake superposition is not a trivial task and the focus of much research. The authors state in p. 5, line 124 that a new hybrid gives the best results. However, please elaborate on this, because it appears somewhat arbitrary. Best by what metric? It would be beneficial to include a comparison in an Appendix.
Response: We agree with the reviewer that wake superposition is an important topic of research currently. We have added an appendix to the manuscript to elaborate on why we use the hybrid method in this manuscript. The appendix shows that linear superposition of adjacent wakes is better than quadratic superposition, and that quadratic superposition of downstream wakes is better than linear superposition.
4. Reference/Comparison. Finding the appropriate reference for comparing a multirotor with a single rotor is not necessarily straightforward. Increasing the tip spacing a lot, has several implications for the presented results: a) The upper multi-rotor will effectively see a higher wind speed than the single turbine and multi-rotor with smaller tip spacing. This will affect all the reported power increases, e.g. in Fig. 11. b) As the tip spacing is increased, the wake merging is delayed and the authors state in p. 9, line 185-186: "...behave independently up to increasingly larger downstream distances". However, that means that it essentially becomes a comparison of a single wake behind a large rotor versus the wake behind a single small rotor. It can be seen in Figure 6(a) which also looks as if they would almost coincide if scaled properly by the corresponding rotor diameter and inflow velocity. Therefore, it seems that the conclusion by the authors is that is is beneficial to separate the rotors as much as possible, e.g. p. 15, line 285 "The benefit of 4-rotor wind farms increases with increasing tip spacing...". However, doing so would remove the potential beneficial interaction of the tip vortices, which makes the wake break down faster, and hence recover faster. The authors state that "...the 4-rotor turbine allows for greater entrainment". This is correct, but part of the increase might simply be an artifact of the reference no longer being appropriate. The question is if the entrainment from the center is more beneficial than the wake interaction? For details of the wake flow and how the wake interact to facilitate a faster breakdown, please see the published presentation with DOI by Andersen and Ramos-Garcia from WESC, 2019.
Response: We thank the reviewer for pointing out the interesting study on the interaction between tip-vortices of adjacent rotors in the multi-rotor configuration leading to a faster breakdown and recovery of the wake. We agree with all the points mentioned: (a) too large of a tip-spacing can lead to diminished benefits because it would reduce the interaction between the tip-vortices; (b) complications involved in designating a single-rotor configuration as being equivalent to a multi-rotor configuration.
With regards to point (a), we have mentioned this in Section 5 (lines 430-433). With regards to point (b), we have calculated the potential power of the multi-rotor turbine for different tip spacings. As discussed in a new appendix (Appendix B) in the revised manuscript, the potential power of the multi-rotor configuration differs from the potential power of the 1-rotor configuration by fairly small numbers (less than 2.4% for s/d up to 0.5). The difference is 5.5% for s/d = 1, which is admittedly large. For the present study, the chosen 1rotor configuration may be considered to be appropriate as a reference, since its potential power varies by less than 2.4% (a small, but admittedly arbitrary number) for the majority of the multi-rotor configurations. This information is included in Appendix B in the revised manuscript.
5. Analytical Model -The text in p. 19, line 310-313 does not seem to match Fig. 13: "Fig. 13(b) also show a similar sensitivity to the value of sigma"? It appears that sigma=0.28 gives better results for the velocity deficit, but worse for the power. Please explain this, because power should be proportional to Uˆ3.
Response: The point we wanted to make here was that σ 0 /D = 0.28 gives better results for the velocity deficit only in the region approximately 1D − 3D downstream of each turbine, but not close to the turbine. σ 0 /D = 0.32 gives better prediction closer to the turbine. Thus, better modeling of the region at and close to the turbine is important for predicting power. We have reworded the paragraph to hopefully make these points more clear.

Technical Corrections:
Response: -p. 1, line 20. Please define the "planform energy flux" Response: We have replaced 'planform energy flux' with the more appropriate 'power density' and defined it in the first paragraph.
-p. 2, line 28-29: I doubt the cubic scaling laws were first realized in 2012. Please rephrase or find older reference.
Response: We tried to find an older reference (in papers and textbooks) without success. The sentence has been slightly rephrased.
Response: The sentence has been rephrased.
-p. 2, line 46: It is a little unclear which article "this paper" refers to, i.e.  or Chasapogiannis et al. (2014). For the former, it is not entirely correct that the study by van der Laan et al. only considered isolated multi-rotors as it shows how the wind farm area can be significantly reduced due to faster wake recovery which inherently deals with multiple multirotors. Please rephrase accordingly.
Response: We meant to refer to . This sentence has been rephrased.
-p. 3, line 71+74: What are the "standard" here? Or what would the nonstandard be? Perhaps it would be beneficial to elaborate on the simulations framework.

Response:
We have included a reference to our previous work (Ghate and Lele, 2017) where equations and numerical details have been mentioned.