The Application of a Linear Microphone Array in the Quantitative Evaluation of the Blade Trailing-Edge Noise Reduction

Round 1

Reviewer 1 Report

Some of the sentences are extremely long. Please shorten the sentences for better comprehensibility. It is better to make two sentences than one big one.

Author Response

Some of the sentences are extremely long. Please shorten the sentences for better comprehensibility. It is better to make two sentences than one big one.

Dear reviewer, thank you very much for taking your valuable time to review our manuscript and let us know your constructive comments to help us improve the quality of the manuscript. Thank you very much for your comments. Motivated by your comments, the long sentences have been shortened for better comprehensibility. We are sorry that we can not give the shortened sentences one by one here. The revised contents have been marked in red in the revised paper.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper addresses the qualitative evaluation of the blade trailing-edge noise reduction with serrated trailing-edges using a linear microphone array based on the Clean-SC algorithm.

The Authors propose a clear structure of the manuscript, starting with an introduction to the topic and its applicability and explaining the steps of the study. The algorithm presented by the authors provide good results that are validated with a benchmark case and the statements are supported by results. An experimental case is also presented.

In my opinion, some more analysis of the data is missing in the manuscript. Instead of just stating that the results provided by the algorithm are good or that they match better with a reference case than those obtained by other authors/models, it might be interesting to explain the reasons of this better agreement (assumptions of the model, limits of validity, etc.).

At the same time, there are some rather shortcomings in the paper that must be addressed prior the paper can be published in the opinion of this reviewer. These shortcomings are listed below:

1. I suggest the authors to include some information about the Clean-SC algorithm in the manuscript explaining what it is, how it works, assumptions and limitations, etc. This will help some readers in a better understanding of the text.
2. In general, the numbers in the legends and the axis of the figures are too small and barely visible. I suggest the authors to increase the font size.
3. Line 101: The authors state that the sampling rate is 51.2 kHz. Is there any specific reason for it (frequency range of the study, etc.)? If so, it is interesting to specify it in the text.
4. Line 114: In Figure 4, significant differences can be observed between the results of the different studies. Could the authors give an overview of the reason of those differences in the extreme cases? E.g., why does “TUD GO” work at low frequencies and not at higher ones?
5. Figure 10: Why are the lobes placed between x=-0.3 and x=-0.1 identified by both algorithms, but not those appearing at higher x?

Author Response

1. I suggest the authors to include some information about the Clean-SC algorithm in the manuscript explaining what it is, how it works, assumptions and limitations, etc. This will help some readers in a better understanding of the text.

Dear reviewer, thank you very much for your valuable time and professional comments. We are so grateful to receive your positive feedback on our work and we highly appreciate the opportunity you give us to revise the manuscript. Motivated by your comments, the following contents have been included about the Clean-SC algorithm.

“The Clean-SC is an improved version of the classical deconvolution method Clean[38] employed in Astronomy. It was proposed to overcome the disadvantages of PSF-based methods and it takes advantages of the fact that the main-lobes are spatially coherent with their side-lobes. The beam pattern of each noise source was determined by solving the measured spatial coherence rather than by using the synthetic PSF’s. Better noise identification results might be achieved by Clean-SC compared with other deconvolution methods such as DAMAS[34], due to the fact that Clean-SC does not assume theoretical beam patterns. In addition, Clean-SC is an efficient deconvolution method which takes only twice of the data-processing time for conventional beamforming[36].” Please see Pages 2-3, lines 91-99 in the revised paper.

2. In general, the numbers in the legends and the axis of the figures are too small and barely visible. I suggest the authors to increase the font size.

Dear reviewer, thanks for your comments. We are sorry for the inconvenience. We use the normal font size in Tecplot to make the figures. It is conjectured that the unclear contents are due to the small size of the figure itself. The figures have been enlarged in the revised paper. We hope the figures are clear now.

3. Line 101: The authors state that the sampling rate is 51.2 kHz. Is there any specific reason for it (frequency range of the study, etc.)? If so, it is interesting to specify it in the text.

Thanks for your professional comments. In this study, the sampling rate is determined by the frequency range of interest, the Nyquist sampling theorem and the desired frequency resolution. As we know, if the sampling rate is Fs, then the upper-limit frequency that can be obtained is Fs/2 according to the Nyquist sampling theorem. The frequency resolution is defined by Fs/N, where N is data points used for Fourier transformation. In this part, the upper-limit frequency of interest is 20000 Hz. The sampling rate is chosen as 51.2 kHz and the data points for FFT is 1024, then the upper-limit frequency is 25.6 kHz and the frequency resolution is 50 Hz. We have explained the reason in the revised paper. Please see Page 3, lines 111-113 in the revised paper.

4. Line 114: In Figure 4, significant differences can be observed between the results of the different studies. Could the authors give an overview of the reason of those differences in the extreme cases? E.g., why does “TUD GO” work at low frequencies and not at higher ones?

Thanks for your valuable comments. We have added some discussions about the different methods as follows.

“The results from other groups provide results generally within an error of 1 dB with two exceptions. The first one is the Orthogonal Beamforming (OB) method from BTU (BTU ORTH). The OB method assumes that the sources have different intensity[39]. Therefore, it is expected that the OB method obtains relatively higher error with several equally sources. The other exception is the Global Optimization (GO) method[40] from TUD with the differential evolution as the optimization method. The underlying reason for the large error at higher frequencies might be due to the larger number of local optima. A different optimization method could be used to improve the results. In addition, the implementation details such as the stopping criterion for the iteration in Clean-SC and DAMAS, the different grid resolutions and the different steering vectors used can also contribute to the differences.” Please see Page 5, lines 130-140 in the revised paper.

5. Figure 10: Why are the lobes placed between x=-0.3 and x=-0.1 identified by both algorithms, but not those appearing at higher x?

Thank you very much for your professional comments. The side-lobes placed between x=-0.3 and x=-0.1 might be caused by the fact that the jet noise at the wind tunnel exit is a distributed noise source, while the leading- and trailing-edge noise sources are more concentrated. Therefore, no obvious side-lobes are observed at higher x.

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors have used a linear microphone array to evaluate blade trailing-edge (TE) noise reduction with serrated TEs in an indoor open-jet wind tunnel. TE noise reduction is sensitive to both the amplitude and wavelength. The flow speed influences the noise reduction of the serrated TEs. The paper could be published subject to the revisions below:

The discussion and conclusions should be more focused on technical solutions that emerge from the experiments. It is quite general as it is now.

 The data could be useful in the development of acoustic (and CFD) models, and the authors should refer to relevant papers below: 

Loiodice et al., Journal of Sound and Vibration, 429, Pages 245-264, 2018; and  Journal of Sound and Vibration, 412, 336–348, 2018. 

Ritos et al.  Journal of Sound and Vibration, 443, 90–108, 2019.

They should also discuss the experimental uncertainty in further detail.

Author Response

1. The discussion and conclusions should be more focused on technical solutions that emerge from the experiments. It is quite general as it is now.

Dear reviewer, thank you very much for taking your valuable time to review our manuscript and let us know your constructive comments to help us improve the quality of the manuscript. It is our deep pleasure to receive your positive feedback on our study. We appreciate it very much you gave us the opportunity to revise the manuscript. Motivated by your comments, we have re-written the discussion and conclusions parts to pay more attention on the technical solutions. The revised contents have been marked in red in the revised manuscript. Please see the discussion and conclusions parts.

2. The data could be useful in the development of acoustic (and CFD) models, and the authors should refer to relevant papers below:

Loiodice et al., Journal of Sound and Vibration, 429, Pages 245-264, 2018; and Journal of Sound and Vibration, 412, 336-348, 2018.

Ritos et al. Journal of Sound and Vibration, 443, 90-108, 2019.

Thanks for your valuable comments. It is absolutely a good suggestion for us to develop acoustic models based on the experimental results. We have included the following relevant references. Please see Refs. [43]~[45] in the revised paper.

[43] Loiodice, S., Drikakis, D., and Kokkalis A., An efficient algorithm for the retarded time equation for noise from rotating sources. Journal of Sound and Vibration, 2018, 412, 336-348.

[44] Loiodice, Drikakis, D., and Kollalis A., Emission surfaces and noise prediction from rotating sources. Journal of Sound and Vibration, 2018, 429, 245-264.

[45] Ritos, K., Drikakis, D., and Kokkinakis, I.W., Wall-pressure spectra models for supersonic and hypersonic turbulent boundary layers. Journal of Sound and Vibration, 2019, 443, 90-108.

3. They should also discuss the experimental uncertainty in further detail.

Thanks for your professional comments. In the experiment, the uncertainty of the inlet mean velocity is within 0.5%. We have further discussed the uncertainty as follows.

“The acoustic time signals are recorded with a sampling frequency of 32768 Hz for 10 s. The narrowband spectra are computed with a Hanning window of 50% overlap and a frequency resolution of 32 Hz. The so-called “BT product” is 320, where B is the bandwidth and T is the sampling time. As a result, the autospectral random uncertainty is approximately, which results in a random SPL uncertainty of dB[42]”. Please see Page 8, lines 184-188 in the revised paper.

[42] Bendat J.S., Piersol, A.G., Random data: analysis and measurement procedures (Fourth Edition). John Wiley & Sons, America, 2010.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

I want to thank the authors for applying all the comments and for the worked devoted to improve the quality of the work. All my concerns and questions have been solved, so I consider that the paper is ready for publication.

Reviewer 3 Report

The authors have revised the paper and it can now be accepted as is.