Computational Fluid Dynamics Approach for Oscillating and Interacting Convective Flows

Round 1

Reviewer 1 Report

The authors present their results on oscillating and convective flows by numerically simulating the dynamics of heated fluid columns in a 2D geometry. The paper is well written and fit for publication in MDPi Fluids, pending minor revision.

1. Please expand your literature review to include recent work on this topic, and explain why is the significance and novelty of your work, and the difference between your work and previous studies.
2. Please explain the motivation for your work, and its applications clearly. 
3. L29: I would recommend uploading the specific movies concerning the Otsu method as supplementary material along with this article, in addition to citing the YouTube channel in line 29. This is because the life of the YouTube channel depends on so many factors, whereas movies submitted as supplementary material will stay forever in the journal’s repository. 
4. L34: “It was concluded that at a constant Helium flow yield the oscillation frequency of the rising gas column decreases in from of a power law as a function 35  of the nozzle diameter.” Please check this sentence.
5. L67: Replace drown with drawn; and is with are.
6. Please remove the dots in (1) except the one between u and del. Please include a dot between del and u in (2)
7. Line 180: you talk about grid independency. Please give more details, and show some results in the form of a figure to justify that statement “used space-discretization (grid) and chosen time-step does not influence the observed trends”
8. Caption of fig. 11, please use lowercase k for kg.

Author Response

We acknowledge with thanks the helpful comments of the Reviewer. Following His/Her suggestions we approved our manuscript as it is detailed below:

1. As the Referee suggested we extended our literature review with some relevant works dealing with the oscillation and instabilities observed in gas jets in air. This is done now in the first introductory paragraph. At the end of this paragraph we do mention now, that the novelty of our work is to consider the collective behavior of this interacting and oscillating jets.
2. We included a more detailed motivation of our work in the second paragraph of the Introductory section.
3. We will upload the movies also as the YouTube channel where we plan to upload also a video-abstract for our work.
4. We reformulated this sentence, and hopefully now is more clear.
5. Thanks, for pointing this out, we did the modification.
6. In equations (1) and (2) we did the suggested modification.
7. Following the recommendation of the Referee, regarding the grid independent nature we included more details. In this sense we first included Figure 2 where we show the topology of the used grid. In the text and in Figure 4 we now illustrate the grid independent nature of the jet’s oscillation on the used grid size. For large grids used in our simulations, considering successfully much smaller sizes does not change considerably the detected oscillation period. For the collective behavior we find similar results that are discussed in the last paragraph of section 2 and illustrated in Figure 15.
8. We have changed through the whole manuscript “Kg” to “kg”.

We thank the Referee for the constructive comments that improved the message of our manuscript.

Reviewer 2 Report

The paper is generally well prepared and can be accepted after minor revision:

The used numerical method is to be stated in the Abstract.

The main findings are to be added to the abstract.

It is better to avoid the discussion of the validation in the introduction.

A figure presenting the used mesh is to be added.

A grid sensitivity test is to be performed.

A frequential study (frequency spectrum + phase diagram) may be performed.

The discussion is to be improved by adding some physical interpretations. It is not sufficient to consider the problem only from mathematical and numerical point of views.

The paper is to be checked against misprints and grammatical mistakes.

Author Response

We thank the Referee for his/her valuable comments and suggestions. Please find below our answers together with the modifications we have considered in our manuscript.

1.-2. The abstract was modified in the lines requested by the Referee. The used numerical methods were detailed and the main findings were added.

3. As the Referee suggested the phrase “validation” was changed, although we kept in the introductory section the presentation of the relevant experimental results that are modeled in our manuscript. We believe that the logic and motivation of our work is more clear by emphasizing the results we aim to reproduce right from the beginning.
4. We added Figure 2 for illustrating the grid topology.
5. For the large grid sizes used in our simulations the grid independent nature of the results is illustrated now in Figures 4 and 15. Figure 4 shows, that the detected oscillation periods are not influenced at the used resolution by considering smaller or larger grid sizes. Figure 15 shows the same for the studied collective behavior.
6. Studying the oscillation’s frequency and its dependence on the relevant system parameters was one of our main goal from the beginning. As response to the Referee’s request we have included now Figure 5, illustrating the used Fourier transform method for determining the frequency of the observed oscillations.
7. In the discussion section we have included a new paragraph (the last by one) in which we discuss the results in a broader physical view in the framework of  the general spontaneous synchronization phenomenon. We discuss here also the possible limitations of the considered 2D approach and argue on the limitations to consider a more realistic 3D simulation with the computational resources available to us.
8. We performed a thorough spell-check on the manuscript.

We conclude by thanking the Referee for helping us to improve our manuscript.

Round 2

Reviewer 1 Report

The paper may be published

Reviewer 2 Report

After revision, the paper can be accepted for publication