Mechanism of Evolution of Shock Wave of Muzzle Jet under Initial Interference and Its Simplified Model

Round 1

Reviewer 1 Report (Previous Reviewer 2)

A long barrel (30 meters long) and a large caliber (300 millimeters in diameter) launch device was chosen as the object of research for the presented study. A large charge is used to fire a shot from a long barrel large diameter launch device, which can result in a very strong impact force from the muzzle jet on the projectile, and can be affected by the initial jet produced by the moving body. The purpose of this manuscript is to describe the evolution of shock waves and vortices in the muzzle jet under interference with the initial jet through numerical calculations. In addition to the simulation, the work includes an experimental part. The experimental operation of this large-scale launch device is a time-consuming and labor-intensive process that requires significant resources. Each experiment conducted with this device is valuable. Through comparisons of simulation with the experiment and comparisons of simplified simulations with more detailed simulations, conclusions about the engineering applications of each model are drawn. Thanks to the combination of a full-scale experiment and a computational one, the work definitely deserves attention. However, there are some significant comments about the way the results are presented and the grounds for its relevance and novelty. The paper could be improved if the authors devoted more attention to comparing what was measured with what was simulated. The manuscript fits the scope of the Aerospace Journal and the special issue “Shock-Dominated Flow”, but it requires a major revision.

My detailed comments and recommendations are given below.

The title of the article does not correspond to the content.

Regarding the abstract, there are too many common words. It is not clear from the text what relates to the experiment and what relates to the calculations. It is not clear what conclusions relate to one or another of the four discussed models. While the qualitative characteristics are provided, the lack of quantitative values makes it difficult to fully understand the significance of the results. The most significant results of the study are not clearly highlighted.

Lines 93-98. There is no clear plan for describing the characteristics of individual models and their differences in the content. For some reason, the description begins with the second model without mentioning the first one at all. The use of "model" in the singular and plural form is inconsistent. The meaning of "initial interference jet" is not clear, and it is not explained how it differs from "initial jet". The authors should adhere to a consistent terminology throughout the text to make the text more understandable.

Lines 99-102. “<…> neglects the model of the moving body, including the initial interference jet formed by the gas being squeezed out of the bore as well as the gas jet formed by gunpowder gas” Are you sure? It is not entirely clear what remains in the end after all the simplifications, if there is nothing left to model. It looks like something is written wrong here.

Lines 158-159. “Case 3 ignored the moving body altogether, as shown in Fig. 1 (c), and involved only the initial jet and the muzzle jet.” The specific initial conditions of the problem are not clearly defined. How does initial jet form in the absence of any body movement?

Comment to the section 2.3 Grid Model. In addition to information about the total number of cells in a grid, it is also important to provide information on the size of cells in the area of interest, as well as the minimum and maximum cell size on a grid. This information would give a better understanding of the spatial resolution of the composed grid.

Lines 172-173. “A widely accepted technique is to consider only a quarter of the physical model, rather than the entire model, to reduce computational time and cost.” This approach may be acceptable if the solution is axisymmetric, but it is not entirely clear whether this would be the case in relation to the experiment involving placing the muzzle above the Earth's surface. Have there been attempts to assess the impact on the overall picture of the development of the vortex flow and the shape of the shock wave of the 3D axisymmetric calculation and calculation in a full 3D formulation?

The section "2.4 Boundary Conditions and Solution Methods" should be revised to properly describe the boundary conditions for all four cases and all boundaries. The current description is not acceptable.

Lines 192-193. “The boundary condition at the inlet of pressure was set for the muzzle, and it was controlled by using a UDF program.” What does UDF abbreviation mean? What is a UDF program? The details of this should be provided here. Is it true that in all cases, the inlet pressure boundary condition was the same? Why is the pressure inlet in Figure 3 with the moving body located at the tube exit?

Fig.3 has some small differences from Fig.1a. Why do we need two figures instead of one?

Lines 228-231. The procedure for dynamically changing the configuration of the calculation grid (dynamic mesh method) is not clearly explained. The procedure for adding and removing cells remains unclear. Additionally, there are fewer variables in the formulas provided than are listed in the description (for example, constants Cs and C1).

Comment to the section “2.7 Grid Independence Verification”. A more convincing demonstration of the convergence of the solution is required, as well as its independence from the grid used and the accuracy of the overall solution. Since a structured computational grid is employed and the process is dynamic, a criterion must be defined to assess accuracy. For example, the dependence of the maximum pressure in the entire computational domain on time could be used as an integral criterion.

Line 249. “a total distance of 30 m traveled by the moving body” How long was the tube in total?

Line 250. “A schematic diagram of the model is shown in Fig. 8” A word “model” is a little confusing here. Note that the authors use this word very frequently with different meanings. Please be more accurate in your terminology.

Fig.8. Please provide the dimensions of the entire installation and its individual parts, as shown in the figure. This includes the balance object type, cannon tube, and projectile tube. Also, please specify where the projectile (the moving body) was located at the initial moment. Additionally, indicate the height above ground level at which the muzzle was positioned. What do Vb and Vp stand for?

Section 3.1 “Test Equipment and Plan”. Please provide more details about the pressure sensors used. What model were they? What is their measurement limit? How sensitive are they? What pressure measurement error do they have? What high-speed camera model was used for recording? Who manufactured it? What recording frequency was used? What frame resolution was used in the recordings? What type of recording device was employed? What was the sampling rate, bit depth, and accuracy of the device? How much did the powder charge weigh? What was velocity range of launch device?

Fig.9. In the figure, the diagram is shown from a top-down perspective. It is not clear at what height above the ground the sensors were located. Please specify the height in the image or in the text. Also, please describe how the (X, Y, Z) axes are positioned and where the origin is located.

Fig.10. You have to indicate the time instances when each frame was shot.

Lines 299-301. What model is used in the simulation? What does the record “the point (3000, 500, 200)” mean? If it is coordinates in the form (X,Y,Z), then how are the axes arranged and where is the origin? What are the coordinates of the muzzle center? The explanation should be placed there a new thing appears first time. In the conclusion sentence you should denote the specific model instead of giving a general statement “the method of simulation used in this paper could accurately simulate the characteristics of the muzzle jet” since more than one model has been presented.

Line 324. I do not understand what “the initial interference jet” should be meant I am wondering if there is any difference between it and what is called the "initial jet"? This is a question of both understanding and language.

Lines 322-332. Is it right that Case 1 is being discussed here?

Lines 326-327. What parameters does the shock wave have in front of a moving body at the 63 ms time instant? What is the velocity of the shock wave at that time?

Fig.12. Why does the pressure become zero after the moving body? Is it not part of the calculation domain?

I am thinking, based on the text, the Case 1 (the model with interference from the initial jet) and the complete model are the same thing. This means that Figs.12 and 13 represent the same simulation. Is it true? If it is not true, then the text needs to be corrected to clarify the issue. It is not clear why there is no calculation domain in the tube on the Fig.13, and what boundary conditions were used for this case.

Lines 350-360. What is the muzzle jet? What does it differ from the high-temperature and high-pressure gas jet?

Line 372. Figure 13(e)

Line 390. I think there should be “CS” instead of “BS”.

Line 402. What does “the three-muzzle jet structure” mean?

Line 428. The title of Fig.15 have to be corrected: see Fig.14.

Fig.16. It would be good to compose it like the other ones, i.e. to show plots at times 1, 2, 4, 6 and 10 ms.

Line 424. What does “a multi-level shock wave” mean? We see a complex wave structure in a typical underexpanded free jet.

Section 4.2.”Structure of the Vortex”. The vortex structure is very sensitive to the size of the grid cells. Have you investigated how the structure of the vortices will change on different grids? How does the lifespan of a vortex depend on the grid resolution (cell size)?

Line 461. Figure 20.

Lines 488-489. “The parameters of the moving body were different between the models.” What type of parameter was different? Size? Mass? Why?

Line 494. What is “impact force”? I mean how it is calculated.

Line 504. It is more correct here to say “a projectile” than “a muzzle”.

Lines 506-507. “These results provide a reference for numerical simulation based analysis in surface engineering.” The sentence is incomprehensible. What do you mean by that?

Lines 503-505. The difference in the values of all parameters (pressure, velocity, drag and lift) in both cases is very small, and compared to the error (or accuracy) of the method, the difference can be considered negligible. What could be affected by this revealed difference between the two calculations? With regard to ballistics, it might be more accurate if we built an integral dependence on the deviation of magnitude (force, resistance, and lift) over time. How much error would there be in this case?

How can we explain this inconsistency? On the one hand, in Figure 22b, the speeds at 2.0 milliseconds differ by no more than 0.01%, which is less than 0.1 meters per second. On the other hand, in Figures 20 and 21, the body is approximately 1.5 and 2.6 meters away, respectively. This means that the increase in speed should be more than 50%. In Figures 13 and 14, however, the body is located at approximately the same distance, 2.6 meters. It is possible that one of these figures, either 20 or 21, is not showing the correct time.

In Table 3, we see the peak values, i.e., the maximum error or difference. What about the averages?

Please, in Table 4, specify the order in which the coordinates appear in the Location column. Why is there no point at coordinates (3000, 500, 200)? This is a point from section 3.2.

Line 530. Figure 25.

Author Response

Dear reviewer,
Please refer to the attachment for details.

Best regards,

Zijie Li

Author Response File: Author Response.docx

Reviewer 2 Report (New Reviewer)

The authors examined the shock wave propagation and vortex structure of the muzzle jet. The topic is very practical, and the method is described nicely. The results of the simulation and experiment agree well. However, the manuscript needs minor revisions. My comments are as follows:

1.      Line 110: 'Therefor' should be 'Therefore'

2.      Section 2.1: When using RANS to simulate shock problems, we often use the k-ω turbulence model rather than k-ε. Why did the authors choose the current turbulence model? Did you conduct a validation for the turbulence model?

3.      Section 2.2: What is the diameter of the moving body? It would also be better to provide the blockage ratio.

4.      Section 2.3: How many boundary layers did you apply near the tube wall? And what is the y+ value in this study?

5.      Section 2.4: It would be better to provide the time step size and the convergence criteria. 

Minor editing of English language required

Author Response

Dear reviewer,

Please refer to the attachment for details.

Best regards,

Zijie Li

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report (Previous Reviewer 2)

I appreciate the authors try to consider the criticism. My comments were reflected in the revised version of the manuscript in whole or in part. Despite that, I still have to pay attention to several issues.

I absolutely disagree with the use of the term "multi-level" in reference to shock waves. I mean the phrase “a multi-level shock wave composed of Mach disc with overlapping discontinuities”. If the authors want to say that the muzzle jet forms a complex wave system consisting of shock waves, including a coronal shock wave, a bottom shock wave, a reflected shock wave, and a Mach disc, with overlapping contact discontinuities, as they wrote in their reply, then they should write this instead of coming up with new doubtful terms. The shockwave is indeed a discontinuity by itself if only the detailed internal structure of the shock wave on a molecular level is not the object of the study.

By asking a clarifying question, as a reader, I expect that the answer will be provided in the text of the manuscript. However, the authors have limited themselves to answering many such questions in the cover letter. It is my suggestion that the authors consider providing more information in the manuscript to address these questions. In cover letter, the authors argue that due to space limitations, they did not provide a detailed description of the dynamic grid method. Moreover, for a detailed description, they refer to the Fluent documentation. However, it should be noted two things. The first ones, there are no any references to Fluent documentation. The second ones, if you look at the aims of Aerospace journal, you could read that researchers are encouraged to publish the results of their recent theoretical and experimental developments with as much detail as possible, and there is no restriction on the maximum length of the papers. Therefore, there are no restrictions to accompany all important aspects of the work by a proper detailed description. The remark concerns the other sections of the manuscript as well. In order to avoid unnecessary repetition of known facts, the author, if they wish, could instead provide links to relevant sources for readers. In particular, it should be emphasized what was done by the authors themselves in the Fluent program which was used for simulations, I mean what was implemented as user-defined functions, which were referred to by the abbreviation “UDF” without providing an explanation. A text that contains a large number of abbreviations without providing definitions for them is difficult to understand. I suggest providing a detached section for abbreviations. All notes above concern the manuscript in general.

There are a few short notes. The text in the cover letter differs from what was added to the text of the manuscript. For example, an unnecessary word “medicine” appeared in the text in line 261 of the manuscript. In the cover letter, this word is missing correctly. In line number 235 of “Dynamic Mesh Method”, I should point out to inequality. The signs “<” or “>” in formulae should be checked over. In addition, for what constant C1=0.2 is used is still left in question.

I would like to conclude by reiterating that the paper would have been looked advantageous if the authors had given more attention to the direct comparison of a full-scale experiment with the results of full-scale numerical simulation.

Author Response

Dear reviewer,

Please  refer to the attachment.

Best regards,

Zijie Li

Author Response File: Author Response.pdf

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Review on” Investigating the Mechanism of Evolution of Shock Wave of Muzzle Jet under Initial Interference”

In the article "Investigating the Mechanism of Evolution of Shock Wave of Muzzle Jet under Initial Interference," Zijie Li and Hao Wang delve into the complex dynamics of muzzle jets in large-caliber, long-barrel weaponry, focusing on the evolution of shock waves under initial jet interference. The research is articulated through four case studies: Case 1 presents a comprehensive model including both internal and external muzzle dynamics; Case 2 simplifies this by focusing only on external dynamics; Case 3 further abstracts the model by excluding the moving body and analyzing the interplay between the initial and gas muzzle jets; and Case 4 offers the most streamlined perspective, concentrating solely on the external gas muzzle jet. A pivotal finding is the effectiveness of the simplified models (Cases 2 and 3) in accurately depicting the flow field dynamics beyond 5 meters from the muzzle, highlighting their utility in scenarios where full-scale modeling is computationally demanding. This study is particularly notable for its detailed exploration of the actual flow field's complexity in Case 1, capturing intricate interactions and phenomena, thereby providing profound insights valuable for both aerodynamics and military engineering. With minor corrections suggested, the article should be ready for publications.

My comments on the article as follows:

1. Typographical and Formatting Corrections:

• The term 'girds' (Lines 178, 183, 186) appears to be a typographical error and should be corrected to 'grids'.
• In Line 205, 'use to capture' should be revised to 'used to capture' for grammatical accuracy.
• The spacing in Line 279 seems off and should be formatted properly for clarity.
• It's important to ensure consistent descriptions when referring to figures throughout the document, for example, maintaining a uniform format between 'Fig. 13 (b)' (Line 292) and 'Figure 11 (e)' (Line 317) and Figure 18 (Line 467)."
• For clarity, Figure 12 should be formatted similarly to Figure 13.
• In Figures 25 and 26, the plots should be distributed similarly to maintain consistency in data presentation.
• The reference to the year in 'A. Moumen, 202' (Line 42) appears to be a typo. It should likely be a full year, such as '2020' or another appropriate year.
• Concerning Figures 12 and 14, the absence of contour lines in the contour plots decreases visual clarity. Including these lines would significantly enhance interpretability.

2. Technical recommendations

• With respect to Figure 11, I recommend enhancing the experimental validation aspect of the study. The current Figure 11 is missing many data points. The current validation, based on a single point, may not comprehensively represent the complexities captured by the CFD simulations. Including experimental pressure data at multiple points (specifically points A through H) in Figure 25, plotted alongside the results from Cases 1 and 4, would provide a more robust validation and a clearer correlation between the experimental data and simulation results. I would recommend removing figure 11 all together and modify figure 25.
• "Regarding the data in Figure 11, the signal appears excessively filtered to match the simulation results closely. Including a mildly filtered/raw signal, along with details of the frequency cut-off used, would allow for a more authentic comparison. Additionally, detailing the specifications of the pressure transducer used in the experiments would greatly enhance the manuscript.
• The manuscript lacks detailed information regarding the turbulence model and discretization schemes employed in the computational simulations. Providing this information is crucial for a comprehensive understanding of the study's methodology.

The manuscript is well-written but needs proofreading for typographical errors, grammatical refinement, and consistent figure referencing to enhance clarity and readability

Reviewer 2 Report

The flow field formed around a long barrel fired from a large-caliber 300-mm launch device is studied computationally by using 3D simulation. The manuscript fits the scope of the Aerospace journal. Unfortunately, the manuscript is not well prepared and must be rejected in the present form.

My detailed comments are given below.

(1) The introduction section should be seriously improved to make it more systematic. The list of references should be enlarged thus there are many relevant to the topic publications are existed.

(2) The overall structure of the manuscript should be improved. The whole text should be presented with the clear logic. The problem formulation, the model description, the experimental and simulation results are mixed the one with another at now. The aim of the study should be clearly formulated.

(3) The methodological part of the manuscript is incomplete. A clear mathematical statement of the problem should be provided. In addition, a reader must have the possibility to reproduce the results without guessing the authors preferences and choices.

(4) The results are presented in non-systematic way. The main part of text is a simple description of what is depicted on the figures in common without the critical analysis of research. There are no parallels with the results of similar works.

(5) The conclusions are trivial.

Beside that, there are many small remarks like the next ones:

(1) At line 42: check the year for the reference of A. Moumen

(2) At line 55: incorrect using acronym N-S, replace to Navier-Stokes

(3) Fig.6: no “Ma”, therein pressure and “MPa” should be

(4) At lines 184-185: the one-point conclusion is incorrect

(5) Fig.9 yields little information. How many pressure sensors was installed in total? In which locations? In what distance and at which angle the camera was installed? What was the dimensions in meters? What does the pink rectangle means?

(6) At line 205-206: there no any signs of the formation and development of the overpressure field, which would be seen on the images, captured by a high-speed camera.

(7) At line 207 and at line 208: check the English grammar for “ignited” and “drove”

(8) Fig.10a: very dark, arrow to the muzzle is misaligned

(9) Fig.11: only a one point, where is the others?

(10) Fig.12: what is the pressure distribution inside the tube at a time moment 63 ms?

(11) Fig.13: this is a Case 1. Why is the tube filled up with a white color? Where did the pressure field go?

(12) Fig.13 and Fig.14: it is difficult to compare one to the other, give both in the same style: flowfield or contour plot.

(13) Is it exist a link between the Fig.24 and the Fig.9 or the positions of pressure measured points in the experiment and in the simulation?

I recommend to the authors to have a look at an impressive article about imaging of shock waves, explosions and gunshots written by Gary S. Settles [1] and one of the cited work [2]. I think the given results of the publication [2] have a many parallels with the present work.

[1] https://www.americanscientist.org/article/high-speed-imaging-of-shock-waves-explosions-and-gunshots DOI: 10.1511/2006.57.22

[2] Z. Jiang, K. Takayama, B. W. Skews; Numerical study on blast flowfields induced by supersonic projectiles discharged from shock tubes. Physics of Fluids 1 January 1998; 10 (1): 277–288. https://doi.org/10.1063/1.869566

Generally, the manuscript is writing on the English, which was very difficult to understand. The writing style is completely incomprehensible.