Orifice versus Converging-Nozzle Grid Turbulence: A Wavelet Perspective

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors measured the local velocity downstream of two different perforated  plate, OPP and CNPP, and the turbulent fluctuation in each case is investigated with the Fourier transformation and the  wavelet transformation in order to analyze turbulent structures. 

 

Although the objective of the study is clear and the necessity to use wavelet space apparent to emphasizing the characteristics of the analysis in Fourier space, there are still remained concerns and required discussion and rearrangement of the manuscript to accept for publication as follows.

 

[Major]

1. The spatial resolution of three dimensional hot wire
1. The reviewer has a concern the effect of sensor size of the 3D-HW because generally the resolution usually decreases as the dimension of measurement increases about HW. How much is the resolution? The effect of the time series of data are ignorable?  
2. Does 3/5-law appears in the power spectra shown in Figure 5?
1. To prove the accuracy of measurements, the analytical profile of 3/5-law should be plotted as the reference.
3. The cascade of the turbulent kinetic energy is consistent in wavelet analysis shown in Fig. 7?
1. In figure 7, the energy distribution on each wavelet packet is plotted. In the PP case for both Re number, the energy decreases as the packet becomes finer. However, in the CNPP case, there is the jump like inverse cascade between D10-D9. From the viewpoint of the energy cascade in the turbulent eddies, what happens?

 

[minor]

1. Typo,  P. 6, L228.  “Figure 4” is supposed to be “Figure 3”

Author Response

The authors are grateful to the reviewers for many insightful and constructive comments. We have addressed all comments except those related to the shifting around of figures etc. because of the MDPI system. We believe MDPI will take care of these mess-ups.

 

Reviewer 1

The authors measured the local velocity downstream of two different perforated plate, OPP and CNPP, and the turbulent fluctuation in each case is investigated with the Fourier transformation and the wavelet transformation in order to analyze turbulent structures.

Although the objective of the study is clear and the necessity to use wavelet space apparent to emphasizing the characteristics of the analysis in Fourier space, there are still remained concerns and required discussion and rearrangement of the manuscript to accept for publication as follows.

[Major]

The spatial resolution of three dimensional hot wire:

The reviewer has a concern the effect of sensor size of the 3D-HW because generally the resolution usually decreases as the dimension of measurement increases about HW. How much is the resolution? The effect of the time series of data are ignorable?

Thank you for your concern. A Dantec Dynamics triple sensor hotwire gold-plated probe (type 55P95) with a constant temperature anemometer was employed to characterise the flow. The sensing element consists of 5 μm diameter platinum-plated tungsten wires, that is, 5´10^-6 m sensing element whereas the smallest eddies of interest are approximately 1´10^-3 m at 10 kHz. In other words, the sensing element is more than 100 times the smallest turbulent eddies.

Does 3/5-law appears in the power spectra shown in Figure 5? To prove the accuracy of measurements, the analytical profile of 3/5-law should be plotted as the reference.

Thank you for this suggestion. This has been included as Figure 5(b).

The cascade of the turbulent kinetic energy is consistent in wavelet analysis shown in Fig. 7?In figure 7, the energy distribution on each wavelet packet is plotted. In the PP case for both Re number, the energy decreases as the packet becomes finer. However, in the CNPP case, there is the jump like inverse cascade between D10-D9. From the viewpoint of the energy cascade in the turbulent eddies, what happens?

It has been rightly noted, CNPP-induced turbulence exhibits a peak in energy contribution at detail coefficient D₁₀-D₉, 54 Hz to 109 Hz. Specifically, the energy contribution of D₉ for CNPP reaches 18.5% and 19.7% at lower and higher Re_D, respectively, as illustrated in Fig. 7. The elevated energy levels in the detail coefficients for CNPP strongly reinforce our earlier conclusion about the persistence of undissipated low-frequency structures and vortex-vortex interactions within the flow.

[minor]

Typo,  P. 6, L228.  “Figure 4” is supposed to be “Figure 3”

Thank you for picking this up. It has been rectified.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

 

1. Specify in the abstract, the necessity of this study and where is the perforated plate used.

2.  The description of Figure 1 must be on the same page as the pictures a and b.

3. In Figure 2, is the plate positioned in the direction of flow with a diameter of D=38, or with the chamfered side?

4.    Figures 3 and 4 has too much space left between the pictures.

5. In section 4.4.1. Discrete Wavelet Transform, I recommend positioning Table 2 after the text that refers to it, and similarly, Figure 6 should be placed after the sentence presented in the text, or at least on the same page.

6. The picture of Figure 7 is missing.

7.   At the final of the sentence, after “as”, type “:”

8.  I recommend that Table 2 be on a single page.

9.  Also, if possible, Figure 6 should be on one page.

10. The text of chapter 4.4.2. Continuous Wavelet Transform should be on the next page!

11. The picture of Figure 8 is missing.

12. The text referring to Fig. 8 is in the figure's description and needs to be corrected.

13.   If the numbering of the figures continues as presented, Figure 8 becomes Figure 9, and if the space between the images is reduced, it fits on a single page.

14.  Figure 8 presents some results from a CFD simulation, but the text does not provide details about the software used and the boundary conditions.

15. I recommend that you read the work and fix everything that can be fixed!

 

 

Author Response

The authors are grateful to the reviewers for many insightful and constructive comments. We have addressed all comments except those related to the shifting around of figures etc. because of the MDPI system. We believe MDPI will take care of these mess-ups.

 

Reviewer 2

1. Specify in the abstract, the necessity of this study and where is the perforated plate used.

We appreciate this suggestion. The application of perforated plate has been added.

2. The description of Figure 1 must be on the same page as the pictures a and b.

We are equally surprised to see the shifting around. This and other formatting issues are left to the able hands of MDPI.

3. In Figure 2, is the plate positioned in the direction of flow with a diameter of D=38, or with the chamfered side?

This is a general schematic. Both orientations have been employed, furnishing the Orificed versus Converging Nozzle Grid turbulence.

4. Figures 3 and 4 has too much space left between the pictures.

We concur and assume that MDPI will take care of this and other formatting details.

5. In section 4.4.1. Discrete Wavelet Transform, I recommend positioning Table 2 after the text that refers to it, and similarly, Figure 6 should be placed after the sentence presented in the text, or at least on the same page.

We concur and assume that MDPI will take care of this and other formatting details.

6. The picture of Figure 7 is missing.

Figure 7 has been repositioned. Nonetheless, we lean on MDPI to take care of all formatting details.

7. At the final of the sentence, after “as”, type “:”

We are sorry, we cannot locate this typo.

8. I recommend that Table 2 be on a single page.

We concur and assume that MDPI will take care of this and other formatting details.

9. Also, if possible, Figure 6 should be on one page.

We concur and assume that MDPI will take care of this and other formatting details.

10. The text of chapter 4.4.2. Continuous Wavelet Transform should be on the next page!

We concur and assume that MDPI will take care of this and other formatting details.

11. The picture of Figure 8 is missing.

Figure 8 has been repositioned. Nonetheless, we lean on MDPI to take care of all formatting details.

12. The text referring to Fig. 8 is in the figure's description and needs to be corrected.

Description rectified

13. If the numbering of the figures continues as presented, Figure 8 becomes Figure 9, and if the space between the images is reduced, it fits on a single page.

We concur and assume that MDPI will take care of this and other formatting details.

14. Figure 8 presents some results from a CFD simulation, but the text does not provide details about the software used and the boundary conditions.

Thank you. The software utilised, MATLAB, has been included. Please note that this is not a CFD simulation but simply wavelet analysis of empirical data.

15. I recommend that you read the work and fix everything that can be fixed!

Thank you. This has been done.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

I accept this form!