Evaluation of the Oscillation Velocity in the Neck of the Helmholtz Resonator in Nonlinear Regimes

Round 1

Reviewer 1 Report

The manuscript titled “Evaluation of the Oscillation Velocity in the Neck of the Helmholtz Resonator in Nonlinear Regimes” by A. Komkin, et al., gives a brief review of methods for measuring of the acoustic characteristics of orifices. Three methods are reviewed and compared. The paper is well organized and interesting regarding that it could be a good introduction for readers in sound measurement technique.  Below are a few remarks for the authors’ consideration to improve the paper.

1. There are several misprints/typos, for instance, line 85, ap6proach; lines 113 and 114, l0 and l should be italic; the authors should also pay attention to the subscripts: line 127, P2 should be P₂. In the same line, formula (7) should be formula (4) ?
2. In the section: Methods of evaluating of oscillation velocity in orifice, to give a clear idea how the neck oscillation velocity V₀ is derived, more details should be provided. In doing this, it would be helpful for the readers to follow the discussion without extra efforts by further referring other literatures listed in the references section.
3. Paragraph starting from line 139 is the same as the one starting from line 148. This repetition should be avoided. And supplementary materials are missing.
4. In Figure 6 and 10, the data markers for measurements in the chamber are different from the description in the figure caption.

Author Response

1. The misprints are corrected.
2. On the one hand the description of the methods is widely presented in the literature, on the other their detailed description in this article would lead to a significant increase in its volume of the article.
3. The paragraph was deleted.
4. The data markers for measurements in the chamber in Figure 6 and 10 are now correspond with the description in the figure captions.

Reviewer 2 Report

In this paper the authors reviewed methods for measuring of the acoustic characteristics of orifices. I could suggest it to be accepted given my following concerns being addressed.

• In page 6, the neck of the resonator has a diameter of 5 mm and a length of 2 mm. It has been known that for a short/thin hole (e.g. t/d being about 0.5) with a pure bias flow (U_B being the mean bias flow velocity), if St=2\pi f/U_B is of order O(1), the hole could generate rather than absorb acoustic energy; the hole resistance becomes negative. The reactance could also depend nonlinearly on the frequency. These can be seen, for example, in [1,2] for experimental and numerical evidence and [3] for theory. The present study does not consider mean flow, but I suspect similar phenomena (resistant becomes negative) could also happen without mean flow.
• In the middle of page 7, it was said “The fact that the use of microphone methods leads to overestimations of the oscillation velocity compared to direct measurements is apparently due to the fact that the algorithms for evaluating the oscillation velocity in microphone methods are based on the statements of linear acoustics, and therefore, upon transition to nonlinear acoustics, their use is reasonless.” I agree the orifice impedance model is nonlinear, but the acoustic propagation in the impedance tube is till linear, so I don’t think the double microphone method would fail. The authors need to explain what they meant here.
• The gif figures are nice. Is there any way to obtain the vortex shedding near at the edge, and track their movement withing the hole?

References

1. Jing, X. Sun, Effect of plate thickness on impedance of perforated plates with bias flow, AIAA J. 38 (9) (2000) 1573–1578.
2. Su, J. Rupp, A. Garmory, J.F. Carrotte, Measurements and computational fluid dynamics predictions of the acoustic impedance of orifices, J. Sound Vib. 352 (2015) 174–191.
3. Yang, A. S. Morgans, A semi-analytical model for the acoustic impedance of finite length circular holes with mean flow, J. Sound Vib. 384 (2016), 294–311.

Author Response

Indeed, there is linear propagation of waves in the impedance tube but not in the orifice, there nonlinearity takes its place. That is why the recalculation of the oscillation velocity from the tube section to the orifice section by mean of formula (5) is incorrect. The two-microphone method gives good agreement only within the impedance tube itself, where the non-linearities are not developed. The motion of the medium in the orifice in nonlinear regimes is much more complex than in impedance tube and such a direct recalculation cannot be used.

The effect of sound generation by a resonator is based on the interaction of the resonator with a grazing flow. In this experimental setup, there is no resonator itself, and the sound is generated by a speaker at the opposite end of the impedance tube, there is also no grazing flow, so the generation of additional sound seems not to be possible.

Definitely it would be interesting to track medium motion directly in the orifice and get more detailed information about propagation of vortexes but it requires a significant experimental basis improvement. 

Reviewer 3 Report

The manuscript firstly reviewed the methods for measuring of the acoustic characteristics of orifices, and two indirect and one direct methods were introduced. Then, dependences of the oscillation velocity in the resonator neck on SPL were obtained via experiment utilizing the sound pressure in the resonator chamber and the two-microphone method. Finally, a laser visualization method was used to describe the oscillational processes. Overall, the manuscript is well organized. However, some issues need to be clarified before the paper is published.

1. The main question I have for this paper is that whether it is an original research paper or a review paper. The authors spent most of the pages reviewing research progress in this area but fails to give a detailed description of their own model, results and verifications.  

1、Some details in the paper are not clearly described. In the visualization of the oscillational processes, only the scheme of the corresponding experimental setup is presented. How is the system in a real experiment is constructed? In addition, in Figure 10, only the oscillation velocity corresponding to a SPL of 136 dB is obtained based on the visualization method, how to verify the accuracy of the proposed method at other sound pressure levels needs to be explained.

2、A few typos and grammer errors need to be noted in the paper. For example, in line 85, the “ap6proach” should be “approach”, line 113, “l0” seem to be “”, line 224, What does “Fig.3.7” refer to? Line 227, incorrect usage “of the of the”. Moreover, some of the English expressions need further improvement.

Author Response

1. Indeed, the article provides a detailed overview of the methods that have been used in well-known publications for orifice impedance studies in both linear and non-linear regimes. The main purpose of this article is to show that in nonlinear regime one should use direct methods for measuring the velocity of particles in a orifice.
2. The practical implementation of set-up shown on figure 7 was realized on the basis of the impedance tube shown in Figure 5. The visualization method refers to the direct methods of measuring of the oscillation speed and the result obtained in current study is in a good agreement with the result obtained during measurements using a Pitot tube, which allows us to indicate the reliability of the result obtained. Of course, we agree that additional measurements should be made in the future at other sound pressure levels.
3. The mistypes and errors are corrected.

Reviewer 4 Report

The paper features a comparison of methods to determine the particle velocity inside an orifice.

Besides several typing errors, some additional explanations are necessary and the conciseness of the article must be improved. It is for example unclear which orifice was used for the laser measurements.  The geometric parameters of the orifices/resonators must be stated very clearly and concisely. Crucial parameters, like the open area ratio are missing. It must be stated explicitly which orifice was studied in the particular measurements since it is vital for the analysis of the findings.

The paper does not refer to known optical measurement applications as LDV, (acoustic) PIV, etc to address the same issue of determination of particle velocity inside the orifice, the near vicinity, and the formation and development of vortices at the orifice edges. The direct measurement with a Pitot tube is an intrusive measurement with a strong (altering) impact on the local flow field. No assessment is made with respect to probe head size and positioning (in relation to orifice dimensions), temporal and spatial averaging of the static (pressure) measurement process of a highly unsteady flow phenomenon.  

The main finding of the study according to the authors is that the acoustic methods for measuring the particle velocity in the orifice fail at high sound pressure levels. Judging from the results, I oppose this: I think that the 2-microphone-method and the pitot-tube method are equivalent. The deviations between the methods are due to the 2-microphone method measuring the peak particle velocity whereas the pitot tube method measures the time averaged method.  The time averaged particle velocity, calculated from the 2-microphone-measurement, matches the pitot-tube results. This will be discussed in detail in comment #5. The in-situ method is known to be an “inaccurate” method. The study proves the 2-microphone method and the pitot-tube-method to be equivalent and might also show that the translational vortex velocity is more or less similar to the time averaged particle velocity in the orifice. Furthermore, a discussing the results of this manuscript with respect to findings from previous studies would increase the quality of the manuscript.

By making major adjustments to the measurement setup, data processing and results presentation, I think the manuscript might be worth publishing, especially because the authors might have shown that the translational velocity of a vortex coincides with the time averaged particle velocity in the neck of the resonator/orifice.

The paper will now be discussed in detail:

#1) Line 94: Where is this figure from? Some technical background information would be adequate. I assume it is from the numerical simulation. Could the authors please provide some technical information regarding the making of the figure (i.e. what was computed, how it was computed, what sound pressure had the incoming wave, was it a plane wave...). Is the picture from the FDM-simulations in Comsol?

 

#2) Line 198: The specification of the geometric parameters of the resonator is confusing and incomplete. Are two resonators studied? If not, what does the diameter of 160 mm reflect and what does the diameter of 85 mm reflect? What is the open area ratio of the orifice? From the parameters stated, the open area ratio is assumed to be approximately 0.3%

 

#3)Line 210: Is there a particular reason for using a narrow band chirp signal instead of a pure sinusoid? Interaction effects are to be expected for multi tone stimuli of high sound pressure levels. Nevertheless, the acoustic methods should capture the velocity because the true velocity is captured by the incoming and reflected plane waves. The direct method (pitot-tube) is capable of capturing the correct velocity anyway (with above mentioned limitations). Is the assumption correct that only the fundamental frequencies are considered? This should be stated in the experimental setup. Furthermore, it should be stated whether the study is limited to plane waves or not.

4) Line 218: Classification of the flow regimes: The flow regimes can be distinguished by using the Strouhal number St. St compares the particle displacement inside the orifice to the orifice dimensions.

#5) It seems that using the time averaged velocity (derived from acoustic measurements) , the measurements collapse with the pitot-tube results and give very good agreement. Hence, one might conclude that both methods are equivalent. Could using the acoustic peak particle velocities be the reason for the discrepancies between the methods?

#6) Line 226: Could the authors please explain which axis the angle to differentiate between the regimes is referenced to? Or is the slope of the curves referenced by the term? I don't understand this passage.

#7) Line 224: How come the authors find that using the microphone methods are reasonless? Zhou & Bodén (2014) / 10.1260/1756-8277.6.3.267], e.g. justify the use of the two-microphone method by assuming the nonlinearities are only due to the particle velocity inside the orifice. Far away from the orifice, the pressure signals should be purely harmonic. This was experimentally observed by Ingard [8]: He shows that the pressure in the duct is not distorted at very high SPL while the particle velocity inside the orifice shows nonlinear effects.

#8) Line 264: Again the specification of the setup is inaccurate. Is 10 mm the correct orifice diameter or was the orifice diameter of 5 mm used? How thick is the resonator neck and what is the open area ratio? Two resonators of different open area ratios will have different particle velocities in the orifices for a constant SPL. So comparing the measurements, like done in Fig. 10 would not be valid.

Author Response

1) Technical background information was added. Numerical calculations were carried out in COMSOL, a plane wave with an amplitude of 1 Pa was set in the channel, and a resonator was located at the opposite end of the channel.

2) For now, we hope the specification is described a more clearly.

3) When using a chirp signal, the average value of the amplitude in a narrow frequency band is determined, which provides a more reliable estimate than the amplitude readings on a single line of the spectrum of a harmonic signal.

4) In this study, the amplitude of the vibrational velocity of particles in the orifice usually did not exceed 40 m/s, so the reciprocal of the Strouhal number commonly St^(-1)<25.

5) With the acoustic measurement method, we first estimate the amplitude of the oscillation velocity in the tube, and then recalculate it into the amplitude of the oscillation velocity in the orifice based on the assumption, in accordance with formula (5). While with the Pitot tube we determine only the root-mean-square axial velocity, which was then recalculated into amplitude values. So, the observed differences in the results of measurements by the acoustic method and the Pitot tube, apparently, are due to the fact that the oscillation velocity, at its high values, is unevenly distributed over the cross section of this orifice. Besides difference between amplitude and rms values is around 2^0.5, while the difference obtained is higher

6) Corrections have been made to the text.

7) The use of microphone methods is impractical only in non-linear regimes . The reviewer correctly notes that the speed of particles in the orifice changes non-linearly, while microphone methods assume a linear change in the speed of particles in the orifice. This is the difference between the measurements of the microphone method and the Pitot tube. You can read more about this here https://asa.scitation.org/doi/10.1121/10.0001940

8) Figure 10 compares the oscillation velocities for a 10 mm resonator neck.

Reviewer 5 Report

This manuscript presents well-organized scientific results of sound characteristics for linear and nonlinear regimes. I recommend this manuscript to be accepted with minor revision in the abstract in which the importance of nonlinear regime is not properly stated.

Author Response

The abstract is corrected and we hope the importance of nonlinear regimes in acoustics stated more clearly.

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

I have no more major suggestions for this manuscript before it can be published.