Geometric Design of a Low-Power Arcjet Constrictor and Determination of Velocity of Air-Based Plasma by Means of Analytical and Numerical Methods
, Luis Enrique Marron Ramirez, Jean Fulbert Ituna-Yudonago *, Pablo Alejandro Arizpe Carreón and Carlos Manuel RodrÃguez Roman
Round 1
Reviewer 1 Report
Comments about P. J. Argumedo Teuffer et al.
Geometric design of a low power arc-jet constrictor and determination of velocity of air-based plasma by the mean of analytical and numerical methods
General comments:
Interesting paper
I suggest checking this paper by English native people due to errors, here and there
This paper gives the impression of writing by several authors. All along the paper, numerous times, the verbs are in one form then suddenly move to another form.
Abstract: ok
Key words: ok
Introduction
Very clear and interesting introduction, which sounds like a review and gives right reasons of the work.
2. materials and methods
Between 2.1 and 2.2 paragraphs, I would introduce one section describing the assumptions concerning the two methods you use below.
Perhaps, this could be at another point but it seems relevant to present earlier these points.
2.2 Analytical method
Please, add at the beginning of this section, reference of the Stine Watson model. It is not clear for me the different references presented below.
Page 8 Line 254 and following
Please, define the different terms in equations 5, 6, 7
I was surprised that no term concerns pressure influence in this model. Could you clarify this?
I guess terms definitions seem absent for all the equations in this paragraph. Please add.
Figure 6 page 15. I did not understand figure 6 c. what does it show?
Table 3 page 16. Concerning the mesh size what does “M1 M2 and so on M9”? References to meshes size? Where are they located?
Figures 8, 9 and 10. It is not the enthalpy used in y axe but specific enthalpy or mass enthalpy.
Line 453 page 18. Why choosing the position “10% of the constrictor length” for analysis?
Same remarks for 30% of the constrictor length concerning figure 18
3.3 comparison
It is strange to present at this point the differences of assumptions concerning the two methods. I understand you want to clarify the reasons of the differences between results from the two approaches but it would be relevant to point out only these reasons and not presenting all the assumptions here, which seems too later.
Do you have references of experimental measurements for comparison with your two types of results? Which consequences could result from these calculations on the thruster behavior?
I have difficulties to understand figures 23 and 24. Is there another way to represent the errors from the two ways?
Conclusion
I was a little bit disappointed reading your conclusions because it seems only confirming previous results. Furthermore, at this point, you engage discussion with previous results (ref 16 and ref 44) which could be introduced deeper previously.
Good job. best.
Author Response
Dear Reviewer,
We would like to thank you for all the comments, recommendations and suggestions you made on our manuscript, with the aim of improving its content.
We inform you that we have answered all the questions and also have improved the content of the manuscript based on your suggestions.
All modifications made in the manuscript are written in red color.
Please find the responses to each of the comments below.
We wish you a good reception.
Sincerely
Responses to Comments from Reviewer n°1
General comments
Comment #1: I suggest checking this paper by English native people due to errors, here and there
Answer :We appreciate your suggestion. The manuscript has been reviewed by native English speaker.
Comment #2: This paper gives the impression of writing by several authors. All along the paper, numerous times, the verbs are in one form then suddenly move to another form.
Answer : Thank you for your observation. The grammar mistakes were corrected in the manuscript.
- Materials and methods
Comment #3: Between 2.1 and 2.2 paragraphs, I would introduce one section you use below. Perhaps, this could be at another point but it seems relevant to present earlier these points.
Answer : Thank you very much for your recommendation. A new subsection (2.2) describing the assumptions concerning the two methods was introduced in the manuscript.
2.2 Analytical method
Comment #4: Please, add at the beginning of this section, the reference of the Stine Watson model. It is not clear for me the different references presented below.
Answer : We appreciate your suggestion. The reference of Stine-Watson model was added at beginning of section 2.3.
Comment #5: Page 8 Line 254 and following
Please, define the different terms in equations 5, 6, 7
Answer : We apologize for this mistake. All terms in the equations 5, 6, 7 and others have been defined in the manuscript.
Comment #6: I was surprised that no term concerns pressure influence in this model. Could you clarify this?
Answer : We appreciate your comment. In the analytical method, the model of Stine & Watson, on page 6, establishes that the Specific Enthalpy, Electric Conductivity and Thermal Conductivity are in function of the temperature and pressure. This comment has been added in the manuscript, specially on page 7, lines 245 - 246 and the graphs of thermal and electrical conductivities also have been added in the manuscript (see figure 3a).
Comment #7: I guess terms definitions seem absent for all the equations in this paragraph. Please add.
Answer: We apologize for this mistake. All terms in the equations have been defined in the manuscript.
Comment #8: Figure 6 page 15. I did not understand figure 6 c. What does it show?
Answer : The former figure 6 c, now figure 7 c shows the refined mesh at the tip of the cathode which is the zone of major importance for the analysis where the electric arc occurs. These comments were added in the manuscript.
Comment #9: Table 3 page 16. Concerning the mesh size, what does “M1 M2 and so on M9”? References to mesh size? Where are they located?
Answer : We apologize for this mistake. “M1 M2 and so on M9” refer to mesh size. This comment was added in the manuscript.
Comment #10: Figures 8, 9 and 10. It is not the enthalpy used in y axe but specific enthalpy or mass enthalpy.
Answer : We apologize for this mistake. The enthalpy used in y axe is the specific enthalpy. The descriptions of the former figures 8, 9 and 10, now 9a, 9b and 9c have been modified in the manuscript.
Comment #11: Line 453 page 18. Why choosing the position “10% of the constrictor length” for analysis? Same remarks for 30% of the constrictor length concerning figure 18.
Answer : The choice of the location of 10 % of the constrictor length is justified by the fact that it is the location near the tip of the cathode where the flow is not fully developed as shown in the analytical results, especially in Figures 10a, 10b y 10c. Additionally, it was observed in the same Figures that the velocity reaches the maximum value at 30 % of the constrictor length and then remains constant until the exit.
These comments were added in the manuscript.
3.3 Comparison
Comment #12: It is strange to present at this point the differences of assumptions concerning the two methods. I understand you want to clarify the reasons of the differences between results from the two approaches but it would be relevant to point out only these reasons and not presenting all the assumptions here, which seems too later.
Answer : We appreciate your suggestion, The assumptions concerning two methods have been deleted in the subsections 3.3 and added in the subsections 2.2.
Comment #13: Do you have references of experimental measurements for comparison with your two types of results? Which consequences could result from these calculations on the thruster behavior?
Answer : Thank you very much for your comment: No experimental work related to a constrictor with the same characteristics of a low power arc jet using air as a propellant has been recorded. That is why the analytical method based on the Stine & Watson model was included in this manuscript, which is widely used in the literature to compare the results with those of the numerical method.
Comment #14: I have difficulties to understand figures 23 and 24. Is there another way to represent the errors from the two ways?
Answer : The former Figures 23 and 24, now Figures 17a and 17b show the error graph between the results of both methods. The oblique lines shown in the graphs are the upper and lower limits with a 25 percent of error margin between the analytical and numerical studies. In both Figures, it can be seen that, between 0 and 2,500 m/s, the points stick a lot to the side of the -25 % line, this means that in this interval the numerical results have a greater deviation compared to the analytical results. The opposite behavior is observed, above 2,500 m/s in Figure 17a and above 3000 m/s in Figure 17b where the points stick very close to the 25 % line.
In addition, the percentage relative error between the analytical and numerical results of the velocity profiles was calculated. The results showed that the relative percentage error between both results is 13.369 $\%$ when the temperature of the electric arc is 9,000 $K$ and 16.328 $\%$ when the electric arc temperature reaches 10,000 $K$..
All these comments were added in the manuscript.
Conclusion
Comment #15: I was a little bit disappointed reading your conclusions because it seems only confirming previous results. Furthermore, at this point, you engage discussion with previous results (ref 16 and ref 44) which could be introduced deeper previously.
Answer : Thank you very much for your observation. The conclusions were improved. More detail has been produced on the results obtained in our study, especially related to the advantage of the new design of the proposed constrictor.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This article is written in a long and verbose way, but does not see something new and attractive, more like a task.
1. Figure 1 and Figure 2 are too cumbersome, a more concise diagram can be used to describe the structure clearly. Figure 5 and Figure 6 can also be further optimized.
2. The introduction is too wordy, the descriptions that are not relevant to the topic can be deleted.
3. The calculation method in this paper, which needs to be validated for reasonableness; including the conductivity model.
4. The conclusions in this paper are based on a self-proposed structure, and the generalizability and significance of the conclusions after adopting this structure are to be explained.
5. The title of Figure 15 is covered by figure 16.
Author Response
Dear Reviewer,
We would like to thank you for all the comments, recommendations and suggestions you made on our manuscript, with the aim of improving its content.
We inform you that we have answered all the questions and also have improved the content of the manuscript based on your suggestions.
All modifications made in the manuscript are written in red color.
Please find the responses to each of the comments below.
We wish you a good reception.
Sincerely
Responses to Comments from Reviewer n°2
Comment #1: Figure 1 and Figure 2 are too cumbersome, a more concise diagram can be used to describe the structure clearly. Figure 5 and Figure 6 can also be further optimized.
Answer : We appreciate your suggestion. The old Figure 1 is removed and instead, a detailed drawing of the constrictor geometry is presented in the new Figure 1. The quality of former Figures 5 and 6, now Figures 6 and 7 was improved.
Comment #2: The introduction is too wordy, the descriptions that are not relevant to the topic can be deleted.
Answer : Thank you very much for your observation. The introduction of our manuscript was improved and all details less important for this study were removed.
Comment #3: The calculation method in this paper, which needs to be validated for reasonableness; including the conductivity model.
Answer : Thank you very much for your comment: No experimental work related to a constrictor with the same characteristics of a low power arc jet using air as a propellant has been recorded. That is why the analytical method based on the Stine & Watson model was included in this manuscript, which is widely used in the literature to compare the results with those of the numerical method.
Comment #4: The conclusions in this paper are based on a self-proposed structure, and the generalizability and significance of the conclusions after adopting this structure are to be explained.
Answer : We appreciate your observation. The conclusions were improved. More detail has been produced on the results obtained in our study, especially related to the advantage of the new design of the proposed constrictor.
Comment #5: The title of Figure 15 is covered by figure 16.
Answer : We apologize for this mistake. These two graphs were separated and the titles are clearly visible.
Author Response File: Author Response.pdf
Reviewer 3 Report
The MS titled “Geometric design of a low power arc-jet constrictor and determination of velocity of air-based plasma by the mean of analytical and numerical methods”Authors by Pedro José Argumedo Teuffer et al, studied on an arc-jet constrictor with theoretical analysis and numerical simulations. This study is of significance to readers. However, there are still some issues should be clarified before its published.
1. The introduction is too tardy and lengthy. A commonsense discussion of the rocket section does not make much sense for the content of the MS. Perhaps it would be more compact and reasonable to start directly with electric propulsion. In addition, increasing the discussion of various propulsion devices would increase the readability of the MS.
2. Pages2 line 36-37, the authors claimed that "The electromagnetic thruster mainly named Hall effect has the disadvantage of using propellant with the high cost", This view is biased. Hall thruster is currently the most widely used electric propulsion device in space. Xe, Kr, Ar, I2 are all used as propellant. Obviously, high cost are not its leading shortcoming relative to arc-jet.
3. The shortcoming of different types of electric thrusters is related to kinds of space mission. It is obviously unreasonable to talk about shortcomings beyond the limitations of space mission. it should be modified and evaluated reasonably in introducions. not for Hall thruster also for other types of electric propulsions.
4. Page 4, line 163-176, the discussions of methodes of experimental, analytical and numerical. Require multiple indicators to evaluate the different dimensions. Similarly, differently methodes have their applied scope. Advantages and disadvantages are with what they use to do. Additionally, what is disadvantages ofnumerical method?
5. Figure 1. 3D constrictor geometric model: A) Inlet; B) Outlet. and Figure 2. Projected and sectional views of the constrictor geometry are duplicate information. Also Figure 5. It should be combined and merged.
6. Air is a mixture of gas,how does the author consider the impact of different components in the calculation process? Why the author choose to consider the different temperatures of 9000 K, 10,000 K, 11000 K.
7. Comparison of analytical and numerical results are insufficient. The possibility of causing a difference is obvious. But, why the Errors is different at defferent numerical velocity range should be discussed.
Author Response
Dear Reviewer,
We would like to thank you for all the comments, recommendations and suggestions you made on our manuscript, with the aim of improving its content.
We inform you that we have answered all the questions and also have improved the content of the manuscript based on your suggestions.
All modifications made in the manuscript are written in red color.
Please find the responses to each of the comments below.
We wish you a good reception.
Sincerely
Responses to Comments from Reviewer n°3
Comment #1.
The introduction is too tardy and lengthy. A commonsense discussion of the rocket section does not make much sense for the content of the MS. Perhaps it would be more compact and reasonable to start directly with electric propulsion. In addition, increasing the discussion of various propulsion devices would increase the readability of the MS.
Answer : Thank you very much for your suggestion. The introduction of our manuscript was improved and starts directly with electric propulsion. All details less important for this study were removed.
Comment #2.
Pages2 line 36-37, the authors claimed that "The electromagnetic thruster mainly named Hall effect has the disadvantage of using propellant with the high cost", This view is biased. Hall thruster is currently the most widely used electric propulsion device in space. Xe, Kr, Ar, I2 are all used as propellant. Obviously, high cost are not its leading shortcoming relative to arc-jet.
Answer : Thank you very much for your suggestion. It is sure that the Hall thruster has more advantages than arc-jet such as: relatively simple power conditioning, desirable specific impulse range and compact. But, its main disadvantages are the high beam divergence and the use of single propellants (no mixture) compared with arc-jet which can use single and mixture gasses, as reported by George P. Sutton and Oscar Biblarz in their book entitled “Rocket propulsion elements”, chapter 17, page 626.
Comment #3.
The shortcoming of different types of electric thrusters is related to kinds of space mission. It is obviously unreasonable to talk about shortcomings beyond the limitations of space mission. it should be modified and evaluated reasonably in introduction. not for Hall thruster also for other types of electric propulsions.
Answer : We fully agree with you regarding the comparison between the different types of electric thrusters. We have added details in the introduction of our manuscript about the different types of missions performed by each of the electric thrusters. These details are written on page 1, lines 28 to 45.
Comment #4.
Page 4, line 163-176, the discussions of methods of experimental, analytical and numerical. Require multiple indicators to evaluate the different dimensions. Similarly, different methods have their applied scope. Advantages and disadvantages are with what they use to do. Additionally, what are the disadvantages of numerical method?
Answer : Thank you very much for your comments. On page 4, lines 148 to 155, advantages and disadvantages of the numerical method were added in the introduction.
Comment #5. Figure 1. 3D constrictor geometric model: A) Inlet; B) Outlet. and Figure 2. Projected and sectional views of the constrictor geometry are duplicate information. Also Figure 5. It should be combined and merged.
Answer : We appreciate your suggestion. The old Figure 1 is removed and instead, a detailed drawing of the constrictor geometry is presented in the new Figure 1. The quality of former Figure 5, now Figure 6 was improved.
Comment #6. Air is a mixture of gas,how does the author consider the impact of different components in the calculation process? Why did the author choose to consider the different temperatures of 9000 K, 10,000 K, 11000 K.
Answer : Thank you very much for your questions: Air is a mixture of gasses. The magnitudes of thermophysical and electrical properties of the air-based plasma were calculated considering the different components of the air including the mole fraction of each component.
Moreover, the choice of the temperature of the electric arc of 9,000 K, 10,000 K and 11,000 K, is motivated on the one hand by the process of air ionization as detailed by Bauer [REFERENCE] and on the other hand by the behavior of air-based plasma specific heat between 9,000 K, 10,000 K and 11,000 K. First, Bauer [REFERENCE] states in his paper that, most of the particles in the air are ionized when its temperature reaches 9,000 K, and above 12,000 K the air particles are completely ionized. Secondly, the behavior of air-based plasma specific heat between 9,000K and 12,000 K shows a peak or maximum magnitude at 10,000 K as described in Figure 3b in our manuscript. Based on these two reasons, we decided in our study to analyze the behavior of the air-based plasma velocity in the constrictor when the electric arc temperature varies from 9,000 K to 11,000 K.
Comment #7. Comparison of analytical and numerical results are insufficient. The possibility of causing a difference is obvious. But, why the Errors is different at different numerical velocity ranges should be discussed.
Answer : Thank you very much for your comments: Due to the fact that no experimental work related to a constrictor with the same characteristics of a low power arc jet using air as a propellant has been found in the literature, we decided in our study to use analytical and numerical methods. The analytical method based on the Stine & Watson model was chosen because it is widely used in the literature for studying the behavior of the arc-jet. This model considers the axial convection terms in the specific enthalpy gradient based on which the axial and radial velocities of a propellants can be easily determined. Regarding the variations in the error for the two simulations (at 9000 K and 10,000 K), the reason can be attributed on the one hand to the turbulent kinetic energy of the area-based plasma which positively influences the velocity distribution in the constrictor as shown in Figure 14. On the other hand, it should be noted that the analytical method considers that the flow is laminar and this is a fundamental reason why there are errors between the results of these two methods since the numerical method considers that the flow is turbulent.
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
The authors have replied all my comments. I think the MS can be published as it.
