High Enthalpy Non-Equilibrium Expansion Effects in Turbulent Flow of the Conical Nozzle
Round 1
Reviewer 1 Report
Reviewers Report:
This manuscript investigates the effects of a conical nozzle under different expansion angles of the expansion section, curvature radius of the throat, throat radius, and convergence angle of the convergent section. I have several questions and suggestions, which I would like the authors to address:
1) It’s not clear, what substantial results obtained by the authors of an article?
What is really new (method/ model/ theory, etc.) in this paper?
2) Authors considered only one (there are three regions) Non-Equilibrium Region of the enthalpy flow in the nozzles , and do not discussed affects of other two regions on flow parameters.
3) Please specify the number of cells and time steps for your grid and order of accuracy of your numerical scheme.
4) Line 234 - "Smax should be between 1 and 5%".
How you defined this number?
5) Section 3.2, Line 250 - "... their chemical energy is negligible relative to the total gas flow... "
How much is this ratio for 7-species Ions?
Did you estimate this number for 5-species Ions?
6) Type errors and corrections, for example, in Section 5. Conclusions - "contraction Angle", "errors34" (Line 230), etc.
Line 59 - Reference source error!
7) You should have mentioned recent papers related to the topic, e.g.:
Campbell, N.S.; Hanquist, K.; Morin, A.; Meyers, J.; Boyd, I. Evaluation of Computational Models for Electron Transpiration Cooling. Aerospace 2021, 8, 243. https://doi.org/10.3390/aerospace8090243
Rudinskii, A.V.; Yagodnikov, D.A.; Ryzhkov, S.V.; Onufriev, V.V. Features of Intrinsic Electric Field Formation in Low-Temperature Oxygen–Methane Plasma. Tech. Phys. Lett. 2021, 47, 520–523.
Maier, W.T.; Needels, J.T.; Garbacz, C.; Morgado, F.; Alonso, J.J.; Fossati, M. SU2-NEMO: An Open-Source Framework for High-Mach Nonequilibrium Multi-Species Flows. Aerospace 2021, 8, 193. https://doi.org/10.3390/aerospace8070193.
Your manuscript could be accepted for publication should you be prepared to incorporate moderate revisions.
Comments for author File: 
Comments.pdf
Author Response
Dear Reviewer:
We are very grateful to Reviewer for reviewing the paper so carefully. We have tried our best to improve and made some changes in the manuscript.
Point 1 : It’s not clear, what substantial results obtained by the authors of an article?
What is really new (method/ model/ theory, etc.) in this paper?
Response 1: Thanks. High enthalpy wind tunnel is the main ground equipment for simulating high enthalpy flow. However, the high enthalpy flow field exists thermochemical non-equilibrium phenomenon, which makes the flow field of high enthalpy nozzle outlet different from the flight environment. It is necessary to study the flow of high enthalpy nozzle in order to reduce the non-equilibrium effect. The research results of this paper can serve as a useful reference for the design of high enthalpy nozzles.
Firstly, the thermochemical non-equilibrium effects are sensitive to the maximum expansion angle and throat radius but not to the radius of throat curvature and contraction angle. Secondly, as the maximum expansion angle decreases and the throat radius increases, the flow approaches equilibrium state. Finally, the maximum expansion angle and throat radius not only affect the position of the freezing point but also the flow field parameters, such as temperature, Mach number, and species mass fraction.
Point 2 : Authors considered only one (there are three regions) Non-Equilibrium Region of the enthalpy flow in the nozzles , and do not discussed affects of other two regions on flow parameters.
Response 2: We appreciate it very much for this good suggestion. We discuss these issues on lines 365 to 380.
“The contraction section and the throat are upstream of the freezing point of the high enthalpy nozzle. The CA θc and TCR rc are varied to investigate the thermochemical non-equilibrium effect. In the subsonic region upstream of the throat, the flow is the equilibrium state. The variation of nozzle geometry in the equilibrium flow area has almost no impact on the non-equilibrium effect of the flow field. Cases 3, 7, and 8 in Table 2 are selected to study the influence of CA on the non-equilibrium effects. The freezing position and vibrational temperature of the flow field are almost unchanged (see Figure 9). The change in the TCR has a minor impact on the non-equilibrium effect, and the freezing position and vibrational temperature of the flow field are almost unchanged. The calculation results of cases 3, 9, and 10 are shown in Figure 10. As the airflow passes through the throat, the non-equilibrium effects begin to increase, and the flow freezes quickly downstream of the throat.
”
Point 3 : Please specify the number of cells and time steps for your grid and order of accuracy of your numerical scheme.
Response 3: We agree that you need to specify these parameters. The number of cells is in Line 203. Add to Line 173 “The time-step size is 1.0×10-6s, and the Number of time steps is less than 5000.” The order of accuracy of numerical scheme is in Line 173 to Line 175.
Point 4: Line 234 - "Smax should be between 1 and 5%". How you defined this number?
Response 4: We are very sorry for our negligence of the explanation. Smax should be between 1 and 5%, because initial and boundary conditions are usually not known with a higher accuracy[36]. For the detailed explanation here, see reference [36] . “Section3. Precision estimates，P347.”
Point 5: Section 3.2, Line 250 - "... their chemical energy is negligible relative to the total gas flow... " How much is this ratio for 7-species Ions? Did you estimate this number for 5-species Ions?
Response 5: We appreciate it very much for this good suggestion. Under current conditions, the proportion of NO+and e- in the mass of 7-species ions is less than 0.03% of the total mass compared to 5-species ions.
Point 6: Type errors and corrections, for example, in Section 5. Conclusions - "contraction Angle", "errors34" (Line 230), etc. Line 59 - Reference source error!
Response 6: We are very sorry for our incorrect writing and it is rectified at Line 59 and Line 230
Point 7:You should have mentioned recent papers related to the topic, e.g.:
Campbell, N.S.; Hanquist, K.; Morin, A.; Meyers, J.; Boyd, I. Evaluation of Computational Models for Electron Transpiration Cooling. Aerospace 2021, 8, 243. https://doi.org/10.3390/aerospace8090243
Rudinskii, A.V.; Yagodnikov, D.A.; Ryzhkov, S.V.; Onufriev, V.V. Features of Intrinsic Electric Field Formation in Low-Temperature Oxygen–Methane Plasma. Tech. Phys. Lett. 2021, 47, 520–523.
Maier, W.T.; Needels, J.T.; Garbacz, C.; Morgado, F.; Alonso, J.J.; Fossati, M. SU2-NEMO: An Open-Source Framework for High-Mach Nonequilibrium Multi-Species Flows. Aerospace 2021, 8, 193. https://doi.org/10.3390/aerospace8070193.
Response 7: We appreciate it very much for this good suggestion, and we have done it.
The number of references increased from 34 to 37.
Reviewer 2 Report
Title: Review Report for the Research Article "High Enthalpy Non-Equilibrium Expansion Effects in Turbulent Flow of the Conical Nozzle"
Article Summary:
The research article titled "High Enthalpy Non-Equilibrium Expansion Effects in Turbulent Flow of the Conical Nozzle" presents a comprehensive CFD study on the turbulent flow characteristics and high enthalpy non-equilibrium expansion effects in a conical nozzle. The manuscript showcases the authors' efforts and thoroughness in investigating this complex phenomenon. However, before it can be accepted, there are several minor errors that need to be addressed.
Review Observations:
Abstract Improvement:
The abstract provides a concise overview of the research objectives and methodology. However, it would greatly benefit from the inclusion of key quantitative results of the findings. Adding specific numerical values or metrics related to the high enthalpy non-equilibrium expansion effects in the conical nozzle would enhance the abstract's clarity and make it more informative. This improvement will enable readers to quickly grasp the significance and impact of the research.
Elaboration in the Literature Review:
The literature review in the manuscript is informative, but it could benefit from further elaboration on the specific parameters attempted in this study. Providing more detailed information on the parameters, their relevance to the research, and any previous studies conducted on them would enhance the reader's understanding of the study's context and contribute to the overall comprehensiveness of the article.
Line 59 Error:
There is an error in line 59 that needs to be corrected. The specific nature of the error is not mentioned in the review request, so the authors are advised to carefully review the sentence and make the necessary corrections.
Missing Nomenclatures:
Several nomenclatures used in the differential equations are missing from the nomenclature section. It is essential to include all the relevant nomenclatures, along with their definitions, in order to provide clarity and facilitate the understanding of the mathematical formulations presented in the manuscript.
Stagnation Enthalpy in Table 3:
There is an error in the suffix used for the stagnation enthalpy in Table 3. The correct suffix should be applied to accurately represent the stagnation enthalpy values. The authors are advised to review and correct this error accordingly.
Spelling Correction:
In line 270, there is a spelling error in the word "Discussion." Please correct this error to ensure the manuscript's overall accuracy and professionalism.
Proper Usage of Degree Symbol:
Throughout the manuscript, ensure that there is no space provided before the degree symbol. Additionally, make sure the correct degree symbol is utilized consistently across the manuscript, including figures. This attention to detail will enhance the visual presentation and professionalism of the article.
Recommendation:
I recommend addressing the mentioned errors and making the necessary corrections before finalizing the manuscript for acceptance. By addressing these minor issues, the article will become more polished, accurate, and effectively convey the research findings.
Overall Assessment:
The research article "High Enthalpy Non-Equilibrium Expansion Effects in Turbulent Flow of the Conical Nozzle" demonstrates a high level of technical expertise and thoroughness in investigating the turbulent flow behavior and high enthalpy non-equilibrium expansion effects. The manuscript is well-written and presents a detailed CFD study.
With the suggested improvements and corrections, the article will be ready for acceptance. The authors' efforts and dedication to their research are commendable, and their findings contribute to the understanding of this complex phenomenon. The study has the potential to advance the field and be of great interest to researchers and practitioners in the relevant domain.
Author Response
Dear Reviewer:
We are very grateful to Reviewer for reviewing the paper so carefully. We have tried our best to improve and made some changes in the manuscript.
Point 1 : Abstract Improvement:
The abstract provides a concise overview of the research objectives and methodology. However, it would greatly benefit from the inclusion of key quantitative results of the findings. Adding specific numerical values or metrics related to the high enthalpy non-equilibrium expansion effects in the conical nozzle would enhance the abstract's clarity and make it more informative. This improvement will enable readers to quickly grasp the significance and impact of the research.
Response 1: We appreciate it very much for this good suggestion.
“Secondly, as the maximum expansion angle decreases and the throat radius increases, the flow approaches equilibrium state. When the maximum expansion angle decreases from 120 to 40, the freezing temperature decreases from 2623K to 2018K. Throat diameter increased from 10mm to 30mm, freezing temperature decreases from 2442 K to 2140 K..“
Point 2 : Elaboration in the Literature Review:
The literature review in the manuscript is informative, but it could benefit from further elaboration on the specific parameters attempted in this study. Providing more detailed information on the parameters, their relevance to the research, and any previous studies conducted on them would enhance the reader's understanding of the study's context and contribute to the overall comprehensiveness of the article.
Response 2 : Thanks.
MEA is a key parameter in the design of the nozzle expansion section, which determines the length of the nozzle and the expansion process of the airflow. TCR is the curve connecting the contraction section and expansion section of the nozzle, where the airflow changes from subsonic to supersonic in this area. TR is the nozzle throat, which determines parameters such as nozzle outlet pressure and Mach number. CA determines the length of the contraction section.
Point 3 : Line 59 Error:
There is an error in line 59 that needs to be corrected. The specific nature of the error is not mentioned in the review request, so the authors are advised to carefully review the sentence and make the necessary corrections.
Response 3 : We are very sorry for our incorrect writing and it is rectified at Line 59. ”Unreasonable design parameters can lead to a large error[9,15,20].”
Point 4 : Missing Nomenclatures:
Several nomenclatures used in the differential equations are missing from the nomenclature section. It is essential to include all the relevant nomenclatures, along with their definitions, in order to provide clarity and facilitate the understanding of the mathematical formulations presented in the manuscript.
Response 4 : We have revised the text to address your concerns and hope that it is now clearer.
Line 113 to 114. “k is the coefficient of heat conduction. Sv is the vibrational source terms of the species. wi is the chemical source term. H is total enthalpy. ”
Point 5 : Stagnation Enthalpy in Table 3:
There is an error in the suffix used for the stagnation enthalpy in Table 3. The correct suffix should be applied to accurately represent the stagnation enthalpy values. The authors are advised to review and correct this error accordingly.
Response 5: We are very sorry for our incorrect writing and it is rectified. “h0”
Point 6 : Spelling Correction:
In line 270, there is a spelling error in the word "Discussion." Please correct this error to ensure the manuscript's overall accuracy and professionalism.
Response 6: We are very sorry for our incorrect writing and it is rectified.
Point 7 : Proper Usage of Degree Symbol:
Throughout the manuscript, ensure that there is no space provided before the degree symbol. Additionally, make sure the correct degree symbol is utilized consistently across the manuscript, including figures. This attention to detail will enhance the visual presentation and professionalism of the article.
Response 7 : We appreciate it very much for this good suggestion. We have revised the text to address your concerns and hope that it is now the visual presentation and professionalism.
Point 8 : Comments on the Quality of English Language
With the suggested improvements and corrections, the article will be ready for acceptance. The authors' efforts and dedication to their research are commendable, and their findings contribute to the understanding of this complex phenomenon. The study has the potential to advance the field and be of great interest to researchers and practitioners in the relevant domain.
Response 8: We have revised the text to address your concerns and hope that it is now clearer. We would like to thank the referee again for taking the time to review our manuscript.
Author Response File: 
Author Response.doc
