Grid-Characteristic Method for Calculation of Discontinuous Non-Steady Flows of a Multicomponent Reacting Gas in Channels

Round 1

Reviewer 1 Report

In the manuscript, a numerical technique for simulating quasi-1D nonstationary flows of reacting gas mixtures is discussed and applied to studying two flows: in the supersonic wind tunnel and in the shock tube. Some comparisons with experimental data are discussed.

I believe that the manuscript cannot be accepted in the present form. It can be resubmitted if the authors address the following issues.

1. It is absolutely necessary to emphasize explicitly what is the novelty of the study. The grid-characteristic method was developed earlier by the same authors, see Refs. 5-7. In particular, the abstract of Ref.5 (published in 2008) coincides with the main part of the Abstract of the present manuscript (lines 8-14). What is the difference in the present algorithm compared to that proposed in Refs. 5-7? Moreover, in lines 265-266 it is written: ‘The grid-characteristic method described above has been tried on a large number of test problems [5-7]‘. What does this mean? If the method is developed in the present manuscript (as is indicated in the Abstract), it could not be applied in the previous papers, one of which was published 15 years ago. If it is developed earlier, then it is not necessary to repeat it in the manuscript, it is sufficient to give a reference and focus on the applications.

2. What is the difference of the results on methane-air combustion from those obtained in Ref. 19? This should be clearly indicated.

3. There are multiple studies of nonstationary flows with interaction of strong and weak discontinuities. The state-of-the-art provided in the Introduction is not satisfactory since it does not discuss other approaches to the problem and their limitations compared to the authors’ approach. See, for instance, [C. Garbacz et al, Physics of Fluids (2022) 34, 026108. https://doi.org/10.1063/5.0078233] and references there.  

4. Text in Fig. 4a is indistinguishable. It is impossible to make quantitative comparison with experiments based on this figure. Therefore, the conclusion about agreement with experimental results (see lines 299-301) is not supported by the data.

5. In the problem of flow of stoichiometric methane-air combustible mixture behind a reflected shock wave it is argued that the results are compared with experiments [17]. However, the results are compared only with old solution of Ref. 14. This is rather misleading.

6. In the Abstract, a ‘set of programs’ (software package?) is mentioned. However, no software description is given in the text.

7. Equations (1)-(11) do not form the ‘system of equations’ (see line 96), these are equations describing different flows (in particular, with equilibrium and nonequilibrium chemical reactions).

8. It is difficult to distinguish between ‘thin solid’ and ‘thick solid’ lines in Fig. 3. Why not using different colours?

9. In Eq.(8) there are two parameters, m and n, whereas in Table 2 there is only m. What’s about n values? Notation for A dimension has to be checked, too.

It is necessary to double check the English. Some terminology is incorrect. What does ‘cinematically’ mean (line 240)? What is the meaning of ‘auto-modeling’ (maybe self-similar?)?  

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Reviewer 2 Report

The manuscript deals with a numerical technique for the study of discontinuous non-steady flows of a multicomponent reacting gas in a channel. The topic is interesting, but the presentation of the model is
unclear, and the cited bibliography is partial. To make the article understandable, it is necessary to
explain which mathematical physical model is employed, which assumptions are introduced, and which
mathematical properties the equations have. Furthermore, the novelty of this work should be better clarified.
Is there any other literature on the subject that has not been cited by the authors? English is understandable.

 

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Round 2

Reviewer 1 Report

Although the authors agree with my previous comments and wrote the answers, they have not improved substantially the text itself. I see only a couple of references added and one paragraph in page 8; Figure 4 is somewhat improved but still very difficult to read; Figure 3 is unsatisfactory since 'thick' and 'thin' lines cannot be distinguished.

I am not convinced about the novelty of results. If this is a review article (which can be considered, too), then the number of references is insufficient, and state-of-the art is not described at all. The references are mainly to Russian papers (only 2 are from other countries). It seems that the authors are not familiar with studies of scientific groups from other countries.

If this is a research article, then I don't see enough original results. As is proposed in my first report (see comment 1)), the novelty has to be clearly described in the text, and not only in the answers. The same is for comments 2), 3), 5) of the previous report. Corresponding discussions have to be included in the text. 

The English was improved in the revised manuscript. However, minor editing would be useful. 

Author Response

All of the reviewer's comments have been processed. Changes made to the text are marked in yellow. Also, according to the remark, Figure 3 has been rearranged.

Round 3

Reviewer 1 Report

I am satisfied with the revised version.