Analysis of a Linear Model for Non-Synchronous Vibrations Near Stall^†

Round 1

Reviewer 1 Report

Mandatory Request Changes:Mandatory Changes: Requested changes which are essential for the understanding and completeness of the paper. Paper of author(s) who have not complied with these requests may be rejected.:
    The paper is well written already. My comments are only suggestions below.

Introduction

“shaft frequency”, This needs to be clear. (e.g. frequency induced by engine order excitation).

The references are currently shown in the alphabetical order. Can you number them and quote the number in the paragraph to make easier for the readers to find the references?

“in-vacuo frequency”, Can you be more specific? Frequency of what?

“a stable operating condition”, can you be more specific? Do you mean stability of aerodynamic damping? Or, stall stability? Do you mean this happens before it stalls?

Can you site some papers for AIC?

“why flutter and convective NSV are two…..” It is useful to put one bullet point to explain the definition of classical flutter that you’re trying to compared with.

Also, it’s good idea to add just a sentence explaining about the rotating stall for the readers.

Review of NSV model

q moment induced by unsteady lift is not explained in the nomenclature.

Rotor stability analysis

“trictly”, do you mean strictly speaking?

Figure 4, (a) Aero damping and what’s (b)?

Discussion

“While the last one is valid for a tuned blisk.” I am not sure why this has to be blisk rather than the conventional bladed-disc if it is still tuned.

Recommended Requested Changes:Recommended Changes: Changes will improve the quality of the paper. Authors are strongly encouraged to comply with these requests.:
    Be much more clear about the difference between the classical flutter and convective NSV that will be very interesting information for the unsteady aero community. Currently, the paper focuses on citing NGV papers, but not citing any papers about the fundamental mechanisms of classical flutter. However, the paper still tries to focus on explaining the distinction between them. Hence, reader may feel the summary from classical flutter is missing for better understanding.

Author Response

Dear reviewers and session chairs
Thank you very much for the thorough review of our paper. We have responded to the requests by the reviewers and made changes to improve the paper. For some specific questions please find an individual statement below.
Reviewer 1:
The paper is well written already. My comments are only suggestions below.
Introduction:
• “shaft frequency”, This needs to be clear. (e.g. frequency induced by engine order excitation).
This has been clarified in the introduction.
• The references are currently shown in the alphabetical order. Can you number them and quote the number in the paragraph to make easier for the readers to find the references?
We would like to, but this is not permitted in the ETC conference format.
• “in-vacuo frequency”, Can you be more specific? Frequency of what?
The sentence has to be modified to: and the frequency of vibration measured differed from the in-vacuo structural frequency.
• “a stable operating condition”, can you be more specific? Do you mean stability of aerodynamic damping? Or, stall stability? Do you mean this happens before it stalls?
This bullet point has been modified. The NSV operating point is not stable but NSV occurs before stall.
• Can you site some papers for AIC?
An explanation and reference have been added: AICs are coefficients describing the forcing (amplitude and phase) generated by an oscillating blade on other blades in the assembly. They are normally used to determine the aerodynamic damping in all nodal diameters from a single vibrating blade, in experiments as well as simulations. Detailed explanation can be found in, for example, Crawley 1988 or Nipkau 2011.
• “why flutter and convective NSV are two…..” It is useful to put one bullet point to explain the definition of classical flutter that you’re trying to compared with.
We have added a description and definition of flutter in the introduction.
• Also, it’s good idea to add just a sentence explaining about the rotating stall for the readers.
A comment to clarify that NSV occurs before stall and is not caused by rotating stall has been inserted.
Review of NSV model
• q moment induced by unsteady lift is not explained in the nomenclature.
This has been added.
Rotor stability analysis
• “trictly”, do you mean strictly speaking?
Yes, thank you. This sentence has been removed to avoid confusion.
• Figure 4, (a) Aero damping and what’s (b)?
This has been added in the caption and is also explained in the text.
Discussion
• “While the last one is valid for a tuned blisk.” I am not sure why this has to be blisk rather than the conventional bladed-disc if it is still tuned.
This is true. That was an oversight and ‘bladed disk’ has been added.
• Be much more clear about the difference between the classical flutter and convective NSV that will be very interesting information for the unsteady aero community. Currently, the paper focuses on citing NGV papers, but not citing any papers about the fundamental mechanisms of classical flutter. However, the paper still tries to focus on explaining the distinction between them. Hence, reader may feel the summary from classical flutter is missing for better understanding.
We have added a summary of flutter in the introduction. We also added additional equations in “Review of NSV model” and explained the difference between flutter, forced response and NSV.

Reviewer 2 Report

Mandatory Request Changes:Mandatory Changes: Requested changes which are essential for the understanding and completeness of the paper. Paper of author(s) who have not complied with these requests may be rejected.:
    ---

Recommended Requested Changes:Recommended Changes: Changes will improve the quality of the paper. Authors are strongly encouraged to comply with these requests.:
    Minor clarifications and typos, see pdf review file on the review platform

Comments for author File: Comments.pdf

Author Response

Dear reviewers and session chairs
Thank you very much for the thorough review of our paper. We have responded to the requests by the reviewers and made changes to improve the paper. For some specific questions please find an individual statement below.

Reviewer 2:
Minor clarifications and typos, see pdf review file on the review platform
Response:
1. Yes, typo has been fixed. Thank you.
2. We have reviewed the point
3. This is only an integer value if the circumferential wave number of the disturbance aliased on the number of rotor blades is the same as the nodal diameter, i.e. if they phase-lag of the aerodynamic disturbance matches that of the structure. The wording preceding Eq. 18 has been changed to explain its derivation.
4. The calibration process has been explained in the “Validation” section
5. Thank you, this has been corrected.

Reviewer 3 Report

Mandatory Request Changes:Mandatory Changes: Requested changes which are essential for the understanding and completeness of the paper. Paper of author(s) who have not complied with these requests may be rejected.:
    Overall Comment:  The article presents valuable scientific work related to a proposal for an analytical model to handle NSV vibrations behaving, under certain assumptions, like a convective flutter, which differs from a classical flutter. The paper is well structured; however, to support their demonstration, the authors have referred to many details presented in other of their previous publications. This sometimes makes reading the present paper quite difficult. For this reason, authors are encouraged to improve the paper by making it more “self-sufficient”.

Section “NOMENCLATURE”: Please add the definition of the following parameters
- q (Page 3)
- c1 (Page 3)
- L_alpha(Page 3)
- L_gamma(Page 3)
- NV: Nodal diameter

Section “REVIEW OF NSV MODEL”:
- Page 3: Please, be more specific about the “simplifying assumptions” used to get equation 2
- Page 3: “the blade deflections are assumed to be small”. What is the blade deflection range covered by this assumption?

Section “ROTOR STABILITY ANALYSIS”:
- Page 9 (validation of the frequency domain): Few lines depicting the CFD strategy used to perform the computations would be welcomed (definition of the numerical domain, solver used, amplitude of the prescribed blade displacement…)
- Page 9 (Figure 4): please add more details about the way Fa* and Fv were computed from the CFD results.
- Page 9 (application to cases from literature): I suggest reworking this section which is not clear at all:
o What does the following statement means? “The forcing coefficients were as calibrated above but the vibration frequency and propagation speed were adjusted”
o Page 9 (table 1): What should be look at in this table? The comparison between experiment and the results of the model?
o Page 10: “…the effects of which are well known.” It would be preferable to state what these effects are.
o Please, be more specific about that the way Fa* and ra are computed from the CFD.

Recommended Requested Changes:Recommended Changes: Changes will improve the quality of the paper. Authors are strongly encouraged to comply with these requests.:
    Section “FREQUENCY DOMAIN DESCRIPTION”:
Page 7: Regarding the AIC approach, I suggest to add a referenced paper describing this approach

Section “CONCLUSION”:
I suggest to underline in the conclusion the main distinction between a classical flutter and a convective flutter, since the description of this distinction appears in the introduction as one of the objectives of the article. 

Author Response

Dear reviewers and session chairs
Thank you very much for the thorough review of our paper. We have responded to the requests by the reviewers and made changes to improve the paper. For some specific questions please find an individual statement below.

Reviewer 3:
The article presents valuable scientific work related to a proposal for an analytical model to handle NSV vibrations behaving, under certain assumptions, like a convective flutter, which differs from a classical flutter. The paper is well structured; however, to support their demonstration, the authors have referred to many details presented in other of their previous publications. This sometimes makes reading the present paper quite difficult. For this reason, authors are encouraged to improve the paper by making it more “self-sufficient”.
Thank you for the comment. We have added informations about the method throughout the text and removed dependencies on previous publications. Unfortunately it is not possible to completely review the background of the model in sufficient depth but the main points which make the presented publication self-sufficient are the following:
1. We have explained in detail how we divide the forcing into self forcing due to vibration and forcing due to convected disturbance, which was the main outcome of the referenced paper in JSV.
2. We provide a linearized formulation that considers contributions of blade vibrations for low disturbance decay rates which cannot be found in literature
3. We compare the formulation to a classical AIC approach and use the outcomes to differentiate the observed phenomenon from classical flutter
4. We validate the linearized model in the frequency domain with multiple cases from literature and provide a parameter sensitivity analysis which has not been shown before
5. In the presented formulation the model is fully defined and can be implemented rapidly, also representative calibration parameters are provided making it a useful method for both analysis of experiments and in the design process.
Mandatory
Section “NOMENCLATURE”:
• Please add the definition of the following parameters
- q (Page 3) Added
- c1 (Page 3) Added
- L_alpha(Page 3) This is contained in the subscripts and has been explained in the text in the revised version
- L_gamma(Page 3) This is contained in the subscripts and has been explained in the text in the revised version
- NV: Nodal diameter Added
Section “REVIEW OF NSV MODEL”:
• Page 3: Please, be more specific about the “simplifying assumptions” used to get equation 2
The assumptions have been explicitly stated and a reference to the derivation has been added
• Page 3: “the blade deflections are assumed to be small”. What is the blade deflection range covered by this assumption?
A linear relationship holds for less than two degrees. This has been added.
Section “ROTOR STABILITY ANALYSIS”:
• Page 9 (validation of the frequency domain): Few lines depicting the CFD strategy used to perform the computations would be welcomed (definition of the numerical domain, solver used, amplitude of the prescribed blade displacement…)
A description has been added.
• Page 9 (Figure 4): please add more details about the way Fa* and Fv were computed from the CFD results.
The CFD simulations and calibration is now explained.
• Page 9 (application to cases from literature): I suggest reworking this section which is not clear at all:
o What does the following statement means? “The forcing coefficients were as calibrated above but the vibration frequency and propagation speed were adjusted”
This has been rephrased: The forcing coefficients F_v and F_a were not changed from the calibrated values, but the vibration frequency omega_v and propagation speed Omega_a^R were adjusted for each case, based on information from literature.
o Page 9 (table 1): What should be look at in this table? The comparison between experiment and the results of the model?
All vibration nodal diameters in this table were correctly predicted by the model. A column has been added and the text modified to clarify this.
o Page 10: “…the effects of which are well known.” It would be preferable to state what these effects are.
It has been stated that this changes the shape of the aerodamping curve, adding higher harmonics, and a reference to AIC method has been added.
o Please, be more specific about that the way Fa* and ra are computed from the CFD.
This has now been explained in the Section “Validation of frequency domain model”
Recommended Requested Changes
Section “FREQUENCY DOMAIN DESCRIPTION”:
• Page 7: Regarding the AIC approach, I suggest to add a referenced paper describing this approach
An explanation and reference have been added: AICs are coefficients describing the forcing (amplitude and phase) generated by an oscillating blade on other blades in the assembly. They are normally used to determine the aerodynamic damping in all nodal diameters from a single vibrating blade, in experiments as well as simulations. Detailed explanation can be found in, for example, Crawley 1988 or Nipkau 2011.
Section “CONCLUSION”:
• I suggest to underline in the conclusion the main distinction between a classical flutter and a convective flutter, since the description of this distinction appears in the introduction as one of the objectives of the article.
The reviewer is right, we have revised the paper to more clearly differentiate NSV from flutter.

Thank you again for your thorough reviews and helpful comments.
Sina Stapelfeldt
Christoph Brandstetter