Effects of Aeroelastic Walls on the Aeroacoustics in Transonic Cavity Flowâ€
Round 1
Reviewer 1 Report
The paper proposes to study the effect of elasticity of a cavity on the acoustic field generated by a high speed flow over it. A comparison is performed between wind tunnel experiments and a hybrid RANS-LES calculation with and without fluid-structure interaction coupling. The ability to take into account or not the elasticity of the cavity allows to perform physical interpretations on the interaction between Rossiter modes and vibration modes of the cavity. The numerical model is validated by comparing the effect of several DES closures (SA-DDES and SA-IDDES) and the use of a simplified configuration. In the data analysis, a spectral proper orthogonal decomposition (SPOD) is performed to obtain spatially global informations and to visualise pressure modes and cavity displacement modes.
The paper in interesting and complete in the sense that numerical simulations, experimental data and advanced data analysis are compared and discussed together in a complex fluid-structure interaction configuration to extract physical interpretations, with some practical applications. The study is overall rigorously performed, and well written. I do not see methodological novelty, but the novelty of the paper lies in the specific study of the impact of elasticity in this flow configuration. I believe that this paper deserves publication, however before I can recommend it, some issues have to be raised. They are of three kind: i) typos ii) some additional informations and descriptions are required for the study to be fully reproducible, iii) some methodological issues in the SPOD analysis detailed further. The last point may require to regenerate some results, thus I have to recommend major revisions.
1) Introduction
- In the introduction, the objectives are well stated and justified.
- l.19: "Random components": It is not really clear what "random" means, which assumes a probability space, while the data come from a deterministic computation. I could agree, but it requires a developed explanation. "Broad-band contribution" would be more suited.
- l.20 "periodic component" suggests a mathematically pure periodicity. In practice, after a very long time, due to turbulence, the phase can be lost. "Tonal" component? or quasi-periodic?
2) Numerical methods
- l.86, the temporal scheme used is not clear to me (then not reproducible). Please provide a better description and/or a reference.
3) Simulations with rigid cavity models
- The problem is well defined, with the effort to simulate numerically the experimental wind tunnel, and with some level of validation of the numerical model.
- Maybe I missed it, but the turbulence LES model and the wall function are not described. Maybe, the wall function is standard, but still requires a reference.
- l.154 "It is well known that..." Should be justified by some references.
- l.188 "In general..." some reference is needed, or reformulation if there is none.
- Suggestion: l.200, it is told that the simulations of this section are a reference to compare with the FSI results. Even if I understood this during the reading, it could be stated as well at the beginning of the section to avoid any misinterpretation.
4) Finite element model and the modal representation
- l.206: "a prestudy..." Could some informations be added in order to understand how the element thickness is determined? How "reasonable magnitudes of wall displacements" are chosen? Is it based on some experimental observations? Typical scalings? I believe that this point is important since it should affect the rigidity of the structure, then the vibration frequencies.
- l.214. (and before) What kind of elements are chosen? More precisely what order of accuracy? This information determines indeed the number of elements per wavelength through a modified wavenumber analysis (spectral accuracy). I then agree that the rule of 4 element per wavelenght is not a universal rule and is in fact function of the element type and the desired level of accuracy.
- l.218. I am a bit confused. Why the grid is not used in the modal solver? Are the modes determined analytically? Apparently not, by reading l.223. Some precisions are required on the methods used to obtain the modes (reference, type of method, concise explanation,...).
5) Results with elastic cavity
- In the description of figure 10, I do not understand why a main focus is performed on the 4th Rossiter mode, while we can see as main effect some amplitude variations on the 3 first modes. I believe that before focusing on the 4th Rossiter mode (which seems to be involved in some FSI mechanisms), a paragraph describing the impact of elasticity on the 3 first peaks could be welcome.
- Is it possible (before figure 10) to superimpose experimental Kulite SPL with rigid/elastic models? At least to assess if adding elasticity improves predictions compared to experiments?
SPOD
- l.271 It is stated that SPOD is performed on p' and d. Is it performed separately (1 SPOD for p' and 1 SPOD for d)? Or is it performed together with a well chosen inner-product? This should be clarified.
- l.274: "stochastic data". This description is imprecise. The data used are deterministic, but the block by block variability (then the Fourier projection coefficients) is interpreted as a random process. Please rephrase.
- 6 Blocks are not much for SPOD. 2^{14}=16384 time steps is quite large. In other words, the frequencies are very well resolved, but the variability hard to converge. Could you justify this choice? Maybe there are good reasons for that, but I would naively have used a more balanced compromise between spectral accuracy and convergence of the ensemble by multiplying at least by 10 the number of blocks and dividing by 10 their length (eventually sacrificing very low frequency components).
Some guidelines could be found in "Guide to Spectral Proper Orthogonal Decomposition" (Schmidt & Colonius, AIAA Journal 2020).
To stress my point, in Nekkanti et al (2021) and in Towne et al (2018) cited by the authors, a more balanced compromise between number and size of the blocks is considered, and this is to my knowledge a general trend in SPOD computations.
- A related remark concerns the spectra and SPOD. We can see some amplitude variability in the peaks when elasticity is switched on, which seems to be physical. In Schmidt & Colonius 2020, a method to obtain confidence bounds of SPOD eigenvalues is given. Since 8 segments for the spectra and 6 blocks for SPOD are considered (low values), it would be worth to check (even necessary) if the amplitude variations are significant.
- Moreover in the results, SPOD modes 1 to 3 are analysed. I strongly doubt on the convergence of SPOD modes 2 and 3 computed with 6 samples.
6) Conclusion:
- l.366 "strike" is not a very scientific term. The phenomenological description should be rephrase in a more non-ambiguous manner.
Minor remarks.
- l.104 and 105, there is not verb in the two sentences.
- l.164 "... and therefore is no resolved..." -> and therefore there is no resolved ?
- l.253 "the first coincide" -> coincides.
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments for author File: Comments.zip
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have answered all my concerns. The paper has been improved in terms of clarity. I can now recommend it for publication.
Author Response
We thank you for the review of our manuscript.
Reviewer 2 Report
The authors have significantly improved the manuscript and answered most of my comments. However, two comments are still not answered completely.
Comment 9: You added two new figures to demonstrate the mesh utilized in this study. However, you did not answer my questions. It seems you have utilized one structured mesh for the cavity volume, where you have a constant fine grid spacing in the streamwise direction at x=+-10" and in the normal direction at z=0". When taken throughout the computational domain, such fine constant spacings result in a larger number of cells and can also impose numerical issues in the simulation. When solving the cavity model, did you encounter any numerical issues caused by the mesh? Did you consider using a coarser mesh spacing far from the cavity to reduce the number of cells?
Comment 14: You answered that no experimental data are available for the time-averaged pressure coefficient on the cavity floor. Yet, in Figure 10(k), you present the OASPL from the Kulite transducers on the cavity floor (k20-k29) along with the numerical results. Since you have the time-dependent pressure data from the Kulite transducers (based on which you present the OASPL results), you can easily extract the time-average pressure coefficient distribution on the cavity floor (Cp vs. x/L) and compare it with the results from the three models (SA-DDES WT, SA-IDDES WT, and SA-IDDES SM). I suggest the authors add such a figure to improve their final manuscript.
Author Response
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Round 3
Reviewer 2 Report
No further comments.
