Effects of uniform vertical inflow perturbations on the performance of flapping wings

Flapping wings have attracted significant interest for use in miniature unmanned flying vehicles. Although numerous studies have investigated the performance of flapping wings under quiescent conditions, effects of freestream disturbances on their performance remain under-explored. In this study, we experimentally investigated the effects of uniform vertical inflows on flapping wings using a Reynolds-scaled apparatus operating in water at Reynolds number ≈ 3600. The overall lift and drag produced by a flapping wing were measured by varying the magnitude of inflow perturbation from JVert = −1 (downward inflow) to JVert = 1 (upward inflow), where JVert is the ratio of the inflow velocity to the wing's velocity. The interaction between flapping wing and downward-oriented inflows resulted in a steady linear reduction in mean lift and drag coefficients, C¯L and C¯D, with increasing inflow magnitude. While a steady linear increase in C¯L and C¯D was noted for upward-oriented inflows between 0 < JVert < 0.3 and JVert > 0.7, a significant unsteady wing–wake interaction occurred when 0.3 ≤ JVert < 0.7, which caused large variations in instantaneous forces over the wing and led to a reduction in mean performance. These findings highlight asymmetrical effects of vertically oriented perturbations on the performance of flapping wings and pave the way for development of suitable control strategies.


Recommendation?
Major revision is needed (please make suggestions in comments)

Comments to the Author(s)
Please see the attachment (Appendix B).

Decision letter (RSOS-210471.R0)
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Reviewer comments to Author: Reviewer: 1 Comments to the Author(s) This revised manuscript is currently under consideration for Open Science after being transferred from Interface. The authors answered most of my questions. Here are some concerns to be addressed based on the answers the authors provided to my questions. The numbers corresponds to the original question number in the 1st round of revision. 2. I am unclear about how the authors define gust. On one hand, they are motivated by gusty winds but on the other hand, they reply that "majority of the perturbations encountered in realistic environments are likely to be of timescales much lower than those of the wingbeat..." therefore, they assume "wing flapping frequency and simulated as a uniform constant velocity perturbation in the freestream flow". Therefore, in this research gust is not a factor? Why mention it or discuss it? Why not simply remove the entire discussion on gust as it is irrelevant to the studied topic. 4. PIV: How do you decide what is "significant variation between image pairs for each phase were not noted"? Was this a visualize inspection or a statistical test. 10 image pairs seems to be a very low number to enable capturing any dynamic phenomena associated with fluid mechanics, specifically the formation of LEV .
PIV setup: 4 mm light sheet seems a bit large that can cause significant out of plane motion for the particles while moving within the light sheet, was this issue recognized? 6. Wing-wake interaction: It is still unclear bow the authors based on visualize inspection of the velocity field determines whether interaction occurs or not. Interaction can occur within the velocity gradients; for example between the vorticity and stress fields (see Tsinober A, 2001, Introduction to Turbulence). A statistical analysis that provide some insight into the skewness of the interaction between the velocity gradients may indicate the existence of such interaction is only one option out of many procedures that provide a quantitative observation.
Reviewer: 2 Comments to the Author(s) Please see the attachment.

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Are the interpretations and conclusions justified by the results? Yes
Is the language acceptable? Yes

Recommendation? Accept as is
Comments to the Author(s) My concerns has been answered partially because 10 image pairs are not sufficient to deduce any meaningful insight on the fluid dynamics of the phenomena. Yet, I do understand the complexity of performing new experiments. Perhaps, a clear statement by the authors about the validity of their observation that is sensitive to the lack of statistical convergence.

Review form: Reviewer 2
Is the manuscript scientifically sound in its present form? Yes

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? Yes

Recommendation?
Accept with minor revision (please list in comments)

Comments to the Author(s)
Please see my attachment (Appendix D).

Decision letter (RSOS-210471.R1)
We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Dr Mazharmanesh
On behalf of the Editors, we are pleased to inform you that your Manuscript RSOS-210471.R1 "Effects of Uniform Vertical Inflow Perturbations on the Performance of Flapping Wings" has been accepted for publication in Royal Society Open Science subject to minor revision in accordance with the referees' reports. Please find the referees' comments along with any feedback from the Editors below my signature.
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Kind regards, Royal Society Open Science Editorial Office Royal Society Open Science openscience@royalsociety.org on behalf of Prof Kevin Padian (Subject Editor) openscience@royalsociety.org Associate Editor Comments to Author: The reviewers have a few remaining comments notably ensuring some qualification is made regarding the sample size of the study. While the journal will conduct a 'light touch' copyediting during typesetting, you may benefit from seeking additional professional language editing guidance (as has been noted previously).
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Reviewer comments to Author: Reviewer: 1 Comments to the Author(s) My concerns has been answered partially because 10 image pairs are not sufficient to deduce any meaningful insight on the fluid dynamics of the phenomena. Yet, I do understand the complexity of performing new experiments. Perhaps, a clear statement by the authors about the validity of their observation that is sensitive to the lack of statistical convergence.
Reviewer: 2 Comments to the Author(s) Please see my attachment.

===PREPARING YOUR MANUSCRIPT===
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Decision letter (RSOS-210471.R2)
We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.
Dear Dr Mazharmanesh, I am pleased to inform you that your manuscript entitled "Effects of Uniform Vertical Inflow Perturbations on the Performance of Flapping Wings" is now accepted for publication in Royal Society Open Science.
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On behalf of the Editors of Royal Society Open Science, thank you for your support of the journal and we look forward to your continued contributions to Royal Society Open Science. The paper studies the effects of vertically oriented perturbations on the performance of flapping wings inspired by insects' flight in a windy environment. The authors performed controlled study on an airfoil wing mounted on servo motor mimicking heaving and pitching motion as well as vertical motion of the wing which supposed to mimic upward and downward wind perturbation (i.e.: gusts). Force measurements are taken through force transducer and PIV was employed to describe the wake flow developed by these motions. to show few instantaneous/mean velocity and vorticity maps as function of Jvert without any rigorous statistical attempt to identify LEV, characterize wing-wake interaction (i.e.: velocity gradients, velocity profiles or kinetic energy) and seems very loose mainly in comparison to the force balance measurements.
Some specific comments: 1. The Reported Reynolds number is 3600 suggested by the authors to corresponds to "large insects". The Reynolds number follow Weisfogh (1973) definition. Yet, Weisfogh suggest that this Reynolds number corresponds to "tiny insects" (see page 173, before equation 10 in his paper). Since the authors do not specify the insect in study and keep it generic: bees, wasp…and there is range of sizes amongst these species, this discrepancy should be revised. In order to show that a concentrated region of vorticity that developed over a wing during flapping is an LEV, one need to statistically characterize the vorticity field to show its existence rather than a concentrated region of vorticity. For example, using some vortex identification method and so on (Lambert et al., 2019). Without preforming some sort of identification procedure, I find section 3.2.3 questionable.
14. The last section in the conclusion does not provide any meaningful information References: Ben-Gida, H., Gurka, R. and Weihs, D., 2020. Leading-edge vortex as a high-lift mechanism for large-aspect-ratio wings. AIAA Journal, 58 (7)

General remarks
Positives: -The manuscript is better overall.
-It seems appropriate for Royal Society Open Science. Issues: -There are some unresolved technical points.
-The writing needs to be more precise overall.
-Certain figures need more work (mainly formatting).
In summary: the manuscript has improved but numerous issues remain. I can only recommend publication once these have been addressed fully and satisfactorily.

Appendix B
Please accept advanced apologies for any errors, misinterpretations or omissions on my part.

General points
-Please check all writing again very carefully for precision and clarity.
-Please check all figures for clarity, legibility and consistency.
-Please bear in mind how the manuscript will appear when printed in hardcopy, particularly for those with diminished eyesight. -There are instances of "et al." (at least in the Introduction) that still need to be italicised. -Small point: bracketed manufacturer details often include the company location (city and country). Please double-check this with the Editors.

Introduction
-The new opening sentences position the study better. But I suggest rewording the first sentence such that "their" refers grammatically to "insects" and not "agility and manoeuvrability", even if the intended meaning is clear from the context. o Perhaps it should be Conclusions (plural) because there is more than one.
o Some people will only read the Abstract and Conclusion. Quantities such as and Θ should therefore be presented with care. o I think the final paragraph detracts from the conclusions and should be deleted.

Supplementary Material
-How was the velocity gradient tensor calculated for the Q-criterion? -[ Figure S1] The caption says "instantaneous". Are these not phase-averaged flow data? -[ Figure S2] Please check the caption for typos.

Response to reviewers
Our sincerest thanks to the editor and reviewers for insightful comments on our paper. All specific points have been addressed (listed in detail below) and incorporated into the manuscript revisions. Point-by-point response to the reviewers' comments have been highlighted by blue. Corrections have been coloured in red in the revised version of the manuscript. We believe these revisions have greatly improved the quality of the manuscript.
Reviewer: 1 1. I am unclear about how the authors define gust. On one hand, they are motivated by gusty winds but on the other hand, they reply that "majority of the perturbations encountered in realistic environments are likely to be of timescales much lower than those of the wingbeat..." therefore, they assume "wing flapping frequency and simulated as a uniform constant velocity perturbation in the freestream flow". Therefore, in this research gust is not a factor? Why mention it or discuss it? Why not simply remove the entire discussion on gust as it is irrelevant to the studied topic.
We would like to take this opportunity to distinguish the definition of "gust" from "inflow'. In this context, interaction between flapping wings and freestream disturbances may be characterised as either fast or slow, depending on the temporal profile of the disturbance in relation to the wingbeat. Fast disturbances (or "gusts") are those where the duration over which the wing experiences a significant portion of the disturbance magnitude (as a fraction of the wing velocity) is of the same order or smaller than the timescale of their wingbeat. While slow disturbances (or "inflows") may be considered as those with frequencies of variation much lower than the wing flapping frequency. The focus of this study was on simulating slow perturbations (or "inflows") where the spatial extent of the disturbance would also likely be large in comparison to the size of the wing, thus a reasonable simulation of the disturbance can be obtained by plunging the wing at constant velocity in quiescent fluid. Please note that term "inflow" has been used in the text and title.
2. PIV: How do you decide what is "significant variation between image pairs for each phase were not noted"? Was this a visualize inspection or a statistical test. 10 image pairs seems to be a very low number to enable capturing any dynamic phenomena associated with fluid mechanics, specifically the formation of LEV. o Though it is indeed desirable to have taken several image pairs, in this study we took only 10 image pairs for the different conditions. The authors acknowledge that this is a potential limitation of the study. To further check the sensitivity of 10 image pairs and test statistically stationarity we captured the vorticity fields using phase averaging over 5 random image pairs. Comparison between the vector fields obtaining from 10 and 5 image pairs demonstrated nominally similar flow behaviour (Figure 1 (a) and (b)) with less than 5% difference (Figure 1 (c)).  3. "…in two-wing miniature flying vehicles." This seems somewhat incongruous. I suggest moving it up or just deleting it.
We have taken the suggestion to delete " leading to a substantial rolling moment in two-wing miniature flying vehicles".  o The text labels are a bit small. Font size of the text labels was increased.
9. "…phase-averaged forces…". Apologies if I missed this, but how many strokes were used to phase-average the forces? Presumably 10, as for PIV? If missing, please add this information somewhere.
We thank the reviewer for pointing out this issue. The text was revised as follow: The data was phase averaged over 20 strokes and filtered using a low-pass, 4th order,… [line 226] 10. "Results were analysed…". Perhaps this should move up the paragraph for better ordering. We thank the reviewer for pointing out this issue. The sentence was moved up. [line 262 to 263] 11. "This sample size was deemed sufficient as significant variation between image pairs for each phase were not noted.". This implies that the vector fields were inspected visually, which alone would be insufficient justification for deciding the number of PIV vector fields. But there is perhaps a more fundamental issue: the results figures (notably Figure 9) later show that the time-resolved force profile varies between strokes, particularly for inflows in the 2 regime. This means the flow field varies as well-often in turbulent fashion (line 464). Are just 10 PIV realisations enough to provide robust statistical estimates of the mean flow in turbulent conditions?
Though it is indeed desirable to have taken several image pairs, in this study we took only 10 image pairs for the different conditions. The authors acknowledge that this is a potential limitation of the study and we need to have statistical stationarity. To further check the sensitivity of 10 image pairs we captured the vorticity fields using phase averaging over 5 random image pairs. Comparison between the vector fields obtaining from 10 and 5 image pairs demonstrated the nominally similar flow behaviour (Figure 1 (a) and (b)) with less than 5% difference (Figure 1 (c)).

Results and discussion
12. "…decreased rapidly during pronation…". This seems like the same issue as before (concerning − ). Please check this and other instances carefully again.
The sentence was revised as follow: … the profile of the phase-averaged time traces of and matched those measured in quiescent conditions. [line 309] 14. Please change "however" to "but".
"however" was changed to "but". [line 331] 15. [ Figure 5] This figure is now easier to read, but please address the caption-it mentions both phase-averaged and instantaneous, which strictly are different. "instantaneous" was deleted.
16. "…appears to be translated upwards…". This flow feature is at the crux of the study. Is it not possible to be more definitive? While we appreciate the reviewer's feedback, we believe that the translation of the wakes during different strokes has been clarified in Section 3.2.1. Therefore, no changes were made in the text.
17. [line 346] "…downward flow region…". With my previous comment about reference frames, I was referring to the reference frame of the vector fields in Figure 6, not the panels in the figure. Nonetheless, the addition of roman numerals is helpful. While we appreciate the reviewer's feedback, we believe that referring to the reference panels (roman numerals) clarifies sufficiently the flow fields for different inflow conditions in the text. Therefore, no changes were made in the text.
o "…at / =0.25…". This prompted a thought: if the stroke is regarded as the smallest unit of repeating motion, is the use of wingbeat period actually relevant or correct? Please also revisit Figure 5, whose plots present averaged data from single strokes (cf. p. 10, line 245) across / =[0,0.5]. In these plots, the time clock effectively 'resets' at / =0.5 with the beginning of a new stroke, not a new wingbeat, so may not the best denominator. Perhaps define and use a stroke period instead. While we appreciate the reviewer's feedback, we respectfully disagree. The definitions of the wingbeat and stroke have been already clarified in Section 2.2. We believe that introducing a new parameter for time such as stroke period makes the text more confusing. Thus, no changes were made in the text.
o Please convert the colour bar labels to vector text. Format of the colour bar labels was changed.
o Response- Figure 4 certainly indicates that the upflow is lower in magnitude and of much lesser extent than the downflow. Still, it is important at least to acknowledge the presence of upflow (the Figure 6 caption also says vertical flow, which includes both directions). I suggest either (i) addressing upflow in the text/caption and clarifying that the colour bar is one-sided, or (ii) a new colour bar with one colour for upflow and another for down, blended together via white at zero, e.g., We have taken the suggestion and amended the caption as advised.
19. "While for…". Please check this sentence for readability and errors.
The sentence was rephrased as follow: However, the circulation effects suggested in the previous studies were diminished for downwards inflow because the wake created during stroke reversal was likely translated well below the stroke path. 23. [ Figure 8] o As in Figure 6, please show a coarser field of larger vectors. The arrows were removed from Figure 8. The same tone of blue was used for all figures.

Conclusion
25. This section needs attention. I suggest phrasing the points more succinctly. o Perhaps it should be Conclusions (plural) because there is more than one. "Conclusion" was changed to "Conclusions".
o Some people will only read the Abstract and Conclusion. Quantities such as and Θ should therefore be presented with care.
has been already defined in the Abstract and Conclusions. Moreover, definition of Θ was added to the Conclusions. The effective angle of attack (Θ , determined from the velocity vector arrays obtained from DPIV images) was found to be strongly affected by … , the theoretical angle of attack (Θ ℎ , calculated based on the known velocity of the wing and inflow) resulting in….[line 485 to 489] o I think the final paragraph detracts from the conclusions and should be deleted.
The final paragraph was deleted.

How was the velocity gradient tensor calculated for the Q-criterion?
The velocity gradient tensor was calculated through Equation (1).
These are phase-averaged flow data. The caption was changed as follow: Vortex identification. Phase-averaged Q-criterion at … 28. [ Figure S2] Please check the caption for typos. The caption was revised as follow: Variation in force production per stroke. Evolution of � ̅ ⁄ and � ̅ ⁄ . The mean standard deviation ( �) was obtained by time-averaging the phase-averaged σ under each .
Review of manuscript for R. Soc. Open Sci.

Effects of Uniform Vertical Inflow Perturbations on the Performance of Flapping Wings
by Mazharmanesh et al.
In summary: the manuscript has improved. I must restate, though, my nagging concern about the low number of data samples. This issue should be addressed in the manuscript with, for example, mention of the limitations it places on how the data can be used and the conclusions that can be drawn from them. This seems possible-I offer suggestions below.
Please accept advanced apologies for any errors, misinterpretations or omissions in my review. o Have out-of-plane effects truly been "minimized"? I strongly suggest "lessened" instead (or "reduced", but this would clash with "by reducing"). -[line 257] "…until acceptable signal to noise…". I suggest "…still ensuring an acceptable signal-to-noise ratio.". The SNR could even be given.  Figure 7 is the only one (if I recall correctly) that relies on numerical data; and that uses a column-average, which is presumably better. Still, I would consider rounding PIV-derived flow angles to zero decimal places (line 405 onwards). o There are obvious trends in the data, even at this low simple size (as in the response to Reviewer 1).

Appendix D
To some extent, this sample-size issue also applies to the force data ( = 20). Limitations should be acknowledged in that case, too.

Results and discussion
-[line 281] "…was changed…". Perhaps "…as was varied…"? -[line 328] "phase averaged" is missing its hyphen. In other places, it has it-please check this throughout for consistency.

Supplementary Material
-On the Q-criterion, I was interested in how the velocity gradients were calculated from the vector field. By a differencing approach? Or did the PIV algorithm supply them?
Our sincerest thanks to the editor and reviewers for comments on our paper. All specific points have been addressed (listed in detail below) and incorporated into the manuscript revisions. Point-by-point response to the reviewers' comments have been highlighted by blue. Corrections have been coloured in red in the revised version of the manuscript.

Reviewer: 1
My concerns has been answered partially because 10 image pairs are not sufficient to deduce any meaningful insight on the fluid dynamics of the phenomena. Yet, I do understand the complexity of performing new experiments. Perhaps, a clear statement by the authors about the validity of their observation that is sensitive to the lack of statistical convergence.
We agree that PIV sample size ( =10) is a potential limitation of the study and acknowledge this limitation in the manuscript. However, we believe that there are obvious trends in the data, even at this low simple size.
The following sentences were added to the text and sample size has been explicitly mentioned in the caption of figures 6 and 9: Despite the low PIV sample size (N=10), key flow features commonly noted on flapping wings such as LEVs, were clearly discernible, however further detailed measurements of the flow profile will be beneficial. o Have out-of-plane effects truly been "minimized"? I strongly suggest "lessened" instead (or "reduced", but this would clash with "by reducing"). "minimized" was replaced by "lessened". "…and the effects of out of plane motion were lessened by reducing exposure during frame acquisition still ensuring an acceptable signal-to-noise ratio." [line 257] 5. "…until acceptable signal to noise…". I suggest "…still ensuring an acceptable signal-to-noise ratio.". The SNR could even be given.
We have taken the suggestion to revise the sentence as above. [line 258] 6. The visualisations supplied to Reviewer 1 are instructive, but the very low PIV sample size ( =10) is still concerning. At this stage, it is best simply to acknowledge this limitation in the manuscript. Some points that might be mentioned: o Sample size is less important for firstorder statistics, including the mean (convenient, as the main PIV figure shows mean flow). o The vector and vorticity fields are used in a qualitative way, i.e., for making observations about patterns in the flow, rather than any deep quantitative analysis. Large sample sizes and accurate statistics are therefore less important. Figure 7 is the only one (if I recall correctly) that relies on numerical data; and that uses a column-average, which is presumably better. Still, I would consider rounding PIV-derived flow angles to zero decimal places (line 405 onwards). o There are obvious trends in the data, even at this low simple size (as in the response to Reviewer 1).
The authors would like to thank the reviewer for this advice. We have taken this suggestion to address the low PIV sample size as a limitation in this study. The following sentences were added to the text and sample size has been explicitly mentioned in the caption of figures 6 and 9: Despite the low PIV sample size (N=10), key flow features commonly noted on flapping wings such as LEVs, were clearly discernible, however further detailed measurements of the flow profile will be beneficial.

[line 267 to 269]
To some extent, this sample-size issue also applies to the force data ( =20). Limitations should be acknowledged in that case, too. While we appreciate the reviewer's feedback, we respectfully disagree. The standard deviation in Figure S2 (original version) demonstrates that the levels of uncertainty in the force measurements are sufficiently low, thus the sample size is large enough for force data.
Results and discussion 7. "…was changed…". Perhaps "…as was varied…"? The sentence was changed as follow: "… decreased rapidly during pronation as was varied from 0 to -0.3" [line 284] 8. "phase averaged" is missing its hyphen. In other places, it has it-please check this throughout for consistency. We thank the reviewer for pointing out this issue. "phase averaged" was changed to "phaseaveraged". [line 330] 9. My original point was that the word "appears" might convey uncertainty about this important result.
We have taken the suggestion to revise the sentence as follow: "… the wake, which is normally shed beneath the wing, is translated upwards and into the path of the reciprocal stroke…". [line 343] 10. On my previous point: stroke period (defined early and used exclusively) might be more relevant because only individual strokes are considered in the data-not full wingbeats. As such, the range 0.5< ⁄<1 does not exist. Not worth considering? While we appreciate the reviewer's feedback, we believe that wingbeat frequency has been commonly used in the literature to normalize time. To generalize time scaling and make it less confusing, is used as the denominator. o The omission of the Q-criterion results still seems unusual to me. Why not include some of them in Figure 8? As it stands, the text refers to Figure 8, then Figure S1, then Figure 8 again.
Overall, the Q-criterion results do not seem to be discussed with the necessary conviction.
We have taken the suggestion to move Figure S1 from the Supplementary Material to the main text. We also reordered sentences in the first paragraph of Section 3.2.3. The following sentences were added to the text: o Might "…smaller LEV forming…" be better?
We thank the reviewer for this suggestion. The sentence was revised as follow: "…result in smaller LEV forming over the wing…". [line 440]

Supplementary Material
12. On the Q-criterion, I was interested in how the velocity gradients were calculated from the vector field. By a differencing approach? Or did the PIV algorithm supply them?
The velocity gradients were calculated by a differencing approach.