Numerical Investigation of a Dynamic Stall on a Single Rotating Blade
Round 1
Reviewer 1 Report
In the manuscript, the authors investigate the computational results of a dynamic stall on a 3D rotating blade. The DLR solver TAU is used to solve the flow around the airfoil using both Spalart-Allmaras and k-omega SST RANS models. The authors investigated the vortex dynamics around the rotating wing to explain its contribution to the dynamic stall characteristics.
In the abstract, the authors try to use the word “gap” to explain the difference between the 3D rotating blade and the 2D pitching airfoil. This word seems unclear to what the authors try to explain. Please clarify what is the “gap” is in the authors’ study, and what authors try to figure out from the current 3D simulation. Furthermore, from the reviewer’s point of view, the Lambda-shape vortex structure and the swell structure are not “newly noticed”. Please clarity whether it is “newly noticed” in your study or not.
Authors mentioned in the abstract at line 39 that the SST turbulence model works better for predicting the force of the wing. A lot of previous studies using URANS computation with rotor-relevant flow conditions reported that the SA model is able to capture the dynamic stall characteristics in rotor relevant flow conditions, which is striking to the current authors' statement. Furthermore, the flow condition of the current study is M~0.5 with the advancing ratio μ=0.2, which implies the strong compressibility effect could dominate a formation of the dynamic stall vortex, which could also occur in the authors’ study. The following references described compressible dynamic stall phenomena.
- L.W. Carr, M. Chandrasekhara, (1996), “Compressibility effects on dynamic stall”, Progress in Aerospace Sciences, vol. 32, pp. 523–573.
- T.C. Corke, F.O. Thomas, (2015), “Dynamic stall in pitching airfoils: aerodynamic damping and compressibility effects”, Annual Review of Fluid Mechanics, vol. 47, pp. 479–505.
- T. Kim, S. Kim, J. Lim, S. Jee, (2020), “Numerical investigation of compressibility effect on dynamic stall”, Aerospace Science and Technology, vol. 105(1), p. 105918-1 – 105918-19.
Please explain why the authors mention that the validation part is “destroy” the continuity of the manuscript. The well-validated computational result is one of the most important procedures during the numerical study. Please amplify the validation process which can support your study, and report further information on the validation that authors’ have been investigated. It might contain not only thrust and pressure profile but also the other variables like torque, skin friction, and flow fields to encourage the authors’ numerical approach.
In Fig. 2, the authors used the force residual rather than the continuity residual. What is the definition of the force residual and also Cauchy criteria? Please define it with mathematical formulation for clarity. Moreover, the residual of O(10e-3) seems too large despite the authors have sufficient inner-iteration for the single physical time step. What numerical method did the authors use? Please let readers know the detailed information on the computational setups. And how about the continuity residual in the authors’ simulation?
In Fig. 3, the thrust and the moment from the SA and the SST turbulence model seems quite similar. Why authors think that the discrepancy of the pitching moment is large (at line 150). In the reviewer’s point of view, both the SA and the SST model well capture the dynamic stall feature around the blade. And, please notify why authors choose the sectional force location which is r/R=0.607, 0.785, and 0.928? How about a dynamic stall around the in-board section?
In Fig. 11, the authors extracted the vortex core with respect to the azimuthal position, which is quite a tricky part. How the authors extracted the vortex core? Which numerical or physical approach is used to capture the vortex core?
In chapter 3.4, the authors try to explain the difference between the 2D dynamic stall and the 3D blade stall. Here, it is natural to expect that the 2D dynamic stall and the 3D blade stall show a different force and moment hysteresis due to the physical domain. There’s a lack of information to explain the difference between the dynamic stall of the airfoil and the section of the rotating blade, which is the authors’ main goal of the study to reduce the “gap”. Further investigation is highly recommended to support the authors’ statements.
Line 300: it is questionable that the shape factor could be the “absolute” separation criteria? How about skin friction?
Issues other than the results are listed below.
The overall manuscript needs to go through proofreading. Sentences are hard to read. Please rewrite intricate sentences.
Line 30: current sentence does not support the authors’ numerical method at all.
Line 35: please check the typo before submitting the paper
Line 52: please define the Rossby number.
Line 72: why the capital letter is here?
Line 82: what do the authors want to explain with the current sentence?
Line 190: please don’t use words that only familiar with the authors, such as rotx, roty, and rotz.
Fig. 9: clarify which part is r/R=0.4875 and 0.625. Also, match the significant digit of the results.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper presents a u-RANS study of the dynamic stall on a single rotating blade, and a comparison with an equivalent pitching airfoil. As noted in the conclusion, this is an original study very relevant to helicopter main rotor blades. Yet, there are several questions and doubts that need to be addressed to fully rely on the presented results.
Major comments:
1 – In section 2.1, many angles are either undefined (phi and psi) and not properly defined. A sketch should be added to define without ambiguity.
2 – In section 2.1 and in the appendix, the grid strategy is described in detail, but no real grid study and convergence is achieved. Actually, can we consider the observed differences with experiment in the appendix acceptable? 20% error on a Cp seems quite large. Could you please provide it on either test case? A full grid convergence and turbulence assessment must be provided.
3 – In section 2.1, I do not see any convergence study of the results. How many rotations have you calculated and do the forces and moments vary in the number of rotations? Some kind of polar plots to show the convergence of the unsteady simulations should be provided to assess the quality of the simulations with Tau.
4 – In section 2 two turbulence models are mentioned and, in the introduction, you mention that the SA is inaccurate and the k-w SST is. Why not showing and comparing both in more details? A journal article article should not be a preliminary study or work in progress, but presents definite results, the readers can rely on.
5 – In section 3.2, what are rotx, roty? These are undefined. What are causing the discontinuities in figure8 (red curve)? Any difference between rotx and gamma_x for instance? This whole section needs to be clarified and the variables properly defined with a single symbol.
6 – In section 3.2, figure 7, the vortical structures seem very big and coherent. Did you check the effect of grid refinement and did you try a high-order scheme? The effect of the turbulence model can also be questioned here. You should provide some comparison with the more accurate k-w SST model.
7 – bottom of p.12: What do you mean by “Such assumption needs, however, future work to confirm.”? Further grid refinement, another physical modeling, etc… ? (see also the correct form of the sentence below).
8 – p.13: “If a control volume for the swell coherent structure is taken for analysis…” Could you please specify how you define your control volume on the sketch of the swell structure with the corresponding coordinate system (to define y properly)? In this paragraph, why don’t you track the vortex center properly with an adequate, more exact criterion? Please show the sensitivity to the criterion.
9 - In section 3.3, how valid are the proposed criteria for such a highly three-dimensional flow? Could the authors please check with some friction coefficient contours on the blade? This should be compared and probably replace the contours of H on the blade in figure 13.
10 – I actually do not understand the sentence: “The flow along spanwise direction is not considered when analysing the shape factor since observing from the blade, the main component of the flow is perpendicular to the front edge of the blade.” With the centrifugal force, the boundary layer is three-dimensional with a high radial component close to the wall, which cannot be neglected. Streamlined should be actually provided to verify that what the authors call flow separation are actually flow separation and not highly radial flow.
11 – In section 3.4, the sentence “…for both cases the maximum Cn reaches its climax..” is a tautology (a maximum is a climax). What do you mean exactly?
12 – In section 3.4, figure 16, couldn’t the difference between the pitching airfoil and the pitching rotating blade be simply a time delay of the vortex shedding?
13 – In the sentence, “… the LEV forms itself into an arched form and yet not pinched off ...” it is unclear what you are referring to. Throughout the text, I am not sure that the verb “pinch” or “pinch off” is appropriate (and the latter form does not exist). Do you mean that the vortex stays attached and do not separate from the blade?
14 – At the end of section 3.4, I do not understand “… a drop of Cn from point (b) to (c), contrary to the continuously climbing curve in the case of pitching airfoil.” From point (b) (triangle) to (c) (square), I see exactly the same drop followed by a climb in both cases. The difference is seen on Cm instead where the drop is delayed on the rotating blade.
15 – “Appendix A. Validation of Grid Strategy and Turbulence Model” does not comply with its title as mentioned above. Please revise.
16 – Overall the text should be fully revised by an English-speaking person as there are many improper formulations (I have noted a few below), several articles are missing, and many spaces are either missing or misplaced. Moreover, most references are incomplete.
Other comments:
p.1, line 20: The references should also show the year of the publication (same problem on p.2).
p.1, line 28: “…. shedding as a result…”
p.1, line 30: “With the development... " (many articles missing in the text)
p.1, lines 33,34 : several missing spaces.
p.2, line 35: “citeauthorVisbal” should be corrected.
p.2, line 78: “…with the hovering case of...”
p.3, line 102: "... the URANS DLR-TAU code." (why plural in the text?)
p.3, line 103-104: “…that resolves the boundary layer and that does …”
p.3, line 107: “…and does pure rotation.”
p.5, line 123: “… with an inclined cylindrical ring …”
p.8, line 187: “…with the blade tip vortex to a great extent…”
p.11, line 215: “The interaction of the leading edge vortex with the tip vortex…“
p.11, line 228: “… "pinned" at the leading edge ( Ellington et al)…” (article + space)
p.12, line 257: “… to the rotational axis axis (Smith et al).” (adjectives + spaces)
p.12, line 262: “… stretches in the chord-wise direction as it moves outwards. We have drawn in …”
p.12, line 264: “Such an assumption needs, however, to be confirmed by future work.”
p.13, line 267: “…component to an extent…“
p.16, line 317: “…and the Q contours of both…“
p.16, line 327: “…and on the rotating blade the Q contours show a shed vortex…“ (you never have a single contour)
p.18, line 362: “…the suction side, resulting into a deficit value…”
p.18, line 363: “Whereas 2D simulation shows a strong negative y-vorticity which magnifies the force in the early stage of dynamic stall process.” This is not a sentence, please revise. Note that the following sentence has also an unusual construction.
I am sure that there are many more typos or grammatical errors to be corrected as mentioned in the major comments.
Consequently, given the above comments, this article cannot be published before major revisions.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The revised version does not address several of my previous comments (I recall the numbers below) and as mentioned before I cannot recommend provided these various suggestions are implemented. As already mentioned, a journal article should not be a preliminary study or work in progress but presents definite results, the readers can rely on.
1 – When I asked to properly define the many angles, I was not referring to a nomenclature, but I asked for a sketch that shows how the angles are defined with respect to the reference frames and the blade. Please provide such a figure.
In a nomenclature, you do not define a symbol with several interpretations (theta). You change the notations to have one symbol per variable. Note also, you still have vorticity with Gamma and omega.
2 – In section 2.1, the grid study and convergence are necessary at least for one case. A “rough convergence” cannot be accepted in a scientific article that should provide definite results that future readers can reproduce and rely on. The lack of time is not a justification either: you can always ask for an extension is justified.
3 – The time convergence of thrust is fine and could be added to the manuscript. What about the time convergence of the moment coefficient?
4 – The turbulence model assessment in figure 3 should be provided when the grid convergence is achieved (point 2 above).
6 – Again “In section 3.2, figure 7, the vortical structures seem very big and coherent. Did you check the effect of grid refinement and did you try a high-order scheme? The effect of the turbulence model can also be questioned here.” Even though you provided the comparison with the k-w SST model, the grid question still holds: even though the grid spacing is much smaller than the vortical structure, the onset of the latter and the consequent roll-off and thickness/size of the vortex will depend on the grid size when the flow separation starts.
8 – p.13: “If a control volume for the swell coherent structure is taken for analysis…” Could you please specify how you define your control volume on the sketch of the swell structure with the corresponding coordinate system (to define y properly)? In this paragraph, why don’t you track the vortex center properly with an adequate, more exact criterion? Please show the sensitivity to the criterion. This has not been addressed at all. If you cannot define the control volume, then the argument does not hold.
9 - In section 3.3, how valid are the proposed criteria for such a highly three-dimensional flow? Could the authors please check with some friction coefficient contours on the blade? This should be compared and probably replace the contours of H on the blade in figure 13.
This is still confusing: you can have radial but attached flow on the blade (yielding Cfx=0). You need to look at the complete wall shear stress here. This could in turn change the flow features on the blade. Similarly, the boundary layer thicknesses should not be considered in 2D (at a constant radius) as the boundary layer is most likely very three-dimensional with high radial flow close to the wall (figure 12 is misleading). Consequently, I have serious doubts about your H factor calculation. Actually, seeing your answer to my point 10, you are clearly wrong and should update the plots.
10 – Again provide the streamlines to verify that what the authors call flow separation is actually flow separation and not highly radial flow.
15 – “Appendix A. Validation of Grid Strategy and Turbulence Model” does not comply with its title as mentioned above. Please revise.
You need definite answers, proofs here, no conjectures, no beliefs…. Please ask the editor to have more time if needed. Moreover, please take the time to have a native English speaker revise your manuscript.
Comments for author File: Comments.pdf
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Round 3
Reviewer 2 Report
The effort on providing some grid convergence is apreciated and the additional details provided are fine, noticeably the discussion about flow separation is now adequate and proper.
My only recommendation is to update the unconverged result on the 0.8 ds fine mesh. The paper can be then accepted when it is done.
Author Response
Dear reviewer,
I tried to provide the result of 2 Revs of the 0.8ds fine grid, nevertheless the time limit and queue system of the high-computation center made this unable to accomplish within this week. The 0.8ds fine grid has 84million cells, due to the refinement of the pitching-block, the meshes in Rotating-block also increase drastically, which is in more than twice of the size of the current grid. (the case in paper has a mesh with 38million cells).
We use currently 30 Nodes x 64 cores/Node = 1920 cores for the numerical simulation, with nominal frequency 1.3GHz. Each time step (400 inner iterations) needs approximately 45s/(50 inner iterations) x 8 (50 inner iterations)= 360s. 1 Rev = 720 x 360/3600 h = 72 h. While the maximum time limit for the simulation on the cluster is 48 hours. Therefore with the current cluster, we cannot provide 1 Rev in time.
Previously I missed a command in the sbatch file, and the cluster didn't write out the result after 360 time steps, hence last week the simulation was starting from the very beginning. We have here only the result until 432 time steps, but we think it's meaningless to compare with the other cases, considering the 0 rev deviate a lot from the "converged" revolutions.
Moreover, we have amended the manuscript with the help of native English speakers from the US. And the newer version is mainly revised in the language aspect.
https://drive.google.com/file/d/1gj5BJjUcCxlMzIvgPt-PAdiIucF_9Nbn/view?usp=sharing (Figure for C_T plot for 432 time steps)
I kindly ask for your understanding that the numerical simulation takes a long time. Currently we don't consider using super-computing, since the current case doesn't reach the lower limit of the core-hours/year of the computation center.
Best regards,
Yin
