Study on the Influence of Hall Effect on the Performance of Disk Generation Channel

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1)        Generally, a cylindrical coordinate system is used in disk MHD generator, actually, X-axis and Z-axis are the same in the Figure 1. Equations and graphs need to be modified in the cylindrical coordinate

2)        In Figure 2, the location and geometry of the throat need to be given

3)        Some of the vectors in the control equations are labeled with arrows and some are labeled with bold letters, and the same labeling needs to be used

4)        Equation (12) lacks the corresponding plasma reaction equation

5)        In control equation 24, J and B are vectors, while PL is not a vector. In control equation 26, PL is also not a vector

6)        In disk MHD generator, the load is generally given instead of the load factor in boundary conditions, because the internal resistance varies with the flow field and ionization characteristics

7)        This paper is a three-dimensional numerical simulation, but the analysis of plasma properties is mainly based on one-dimensional graphing, and there is a lack of key distribution maps of electron density and electron temperature. The corresponding simulation results need to be supplemented

8)        As to “Methods and Model Validation”, in the model validation, the authors cite the data in Figure 2 of reference 23, which were analyzed in the absence of magnetic field conditions (B=0). At this point, the ionization and flow characteristics of the plasma in the disc MHD channel differ significantly from those in the presence of a magnetic field. In addition, the power generating working media in the reference 23 is pure argon, while the authors analyzed a mixed He/Xe plasma, and the ionization characteristics of the two are quite different, which is not convincing enough for the validation of the model

9)        Lines 251 through 253 of the text, describes the change in conductivity, but there is no corresponding graphical representation, whereas Figure 6 gives the electron temperature

10)    In Figure. 10, there is no difference between the X and Z axes

11)    Figure (13) contains only four data points, which is insufficient to adequately illustrate the trend of the curve, Why does the trend of this curve not exhibit an initial increase followed by a decrease when β is set to 5?

12)    In line 311, with the Hall parameter given, by its definition, then the total collision frequency of electrons with heavy particles is also determined. Further explanation is needed from the authors as to why the total collision frequency of electrons with heavy particles varies in Fig. 12(b).

13)    the authors need to give the curves of the variation of parameters such as gas temperature, pressure, velocity, current density, electric field strength, etc. along the radial direction in the disk channel.

Author Response

Comments 1:Generally, a cylindrical coordinate system is used in disk MHD generator, actually, X-axis and Z-axis are the same in the Figure 1. Equations and graphs need to be modified in the cylindrical coordinate.

Response 1:Thank you for pointing this out.I agree with this comment.Therefore,I have made the corresponding modifications. In the revised draft, the coordinate system of the geometric model in Figure 1 has been changed to the cylindrical coordinate system, and the associated charts, formulas, and related analysis contents have been adjusted accordingly. The specific modification locations are as follows: line 120 (Figure 1), line 124 (Figure 2), line 140 (expression of electric field E), line 148 (expression for current calculation), line 222 (Formula (32)), line 344 (Figure 12), line 369 (Figure 13), and line 371 (Figure 14), etc. 

Comments 2:In Figure 2, the location and geometry of the throat need to be given.

Response 2:Thank you for pointing this out.I agree with this comment.Therefore, the corresponding modifications have been made. The throat region has been marked with a dotted line. It is important to note that the model's entrance is not located at the throat. The specific modification can be found at line 124  (Figure 2).

Comments 3:Some of the vectors in the control equations are labeled with arrows and some are labeled with bold letters, and the same labeling needs to be used.

Response 3:Thank you for pointing this out.I agree with this comment.Therefore, the corresponding modifications have been made. All vectors in the text have been uniformly marked with bold letters. The specific modification locations are as follows: line 154 (Equation (13)), line 164 (Equation (17)), line 177 (Equation (23)), line 178 (Equation (24)), line 179 (Equation (25)), and line 181 (Equation (26)).

Comments 4:Equation (12) lacks the corresponding plasma reaction equation.

Response4:Thank you for pointing this out.Based on your hint, does it mean that equation (13) lacks the corresponding plasma reaction equation? When consulting relevant literature, I found that most of them only provide the ion continuity equation and the ionization and recombination rate coefficients of electrons and ions, without explicitly presenting the plasma reaction equation. Therefore, following the common practice in existing literature, I did not list the plasma reaction equation.

Comments 5:In control equation 24, J and B are vectors, while PL is not a vector. In control equation 26, PL is also not a vector.

Response 5:Thank you for pointing this out.I agree with this comment.Therefore, I have corrected J, B and PL to vector form. The specific modification positions are at line 178 (Equation (24)) and line 181 (Equation (26)).

Comments 6:In disk MHD generator, the load is generally given instead of the load factor in boundary conditions, because the internal resistance varies with the flow field and ionization characteristics.

Response 6:Thank you for pointing this out.I agree with this comment.Based on the practices in relevant literature, I made corresponding modifications. The specific modification locations are lines 223 to 225.

Comments 7:This paper is a three-dimensional numerical simulation, but the analysis of plasma properties is mainly based on one-dimensional graphing, and there is a lack of key distribution maps of electron density and electron temperature. The corresponding simulation results need to be supplemented.

Response 7:Thank you for pointing this out.I agree with this comment.Therefore, I have added the one-dimensional graph of the variation in electron number density, as well as the two-dimensional distribution graphs of static pressure and Mach number.

Comments 8:As to “Methods and Model Validation”, in the model validation, the authors cite the data in Figure 2 of reference 23, which were analyzed in the absence of magnetic field conditions (B=0). At this point, the ionization and flow characteristics of the plasma in the disc MHD channel differ significantly from those in the presence of a magnetic field. In addition, the power generating working media in the reference 23 is pure argon, while the authors analyzed a mixed He/Xe plasma, and the ionization characteristics of the two are quite different, which is not convincing enough for the validation of the model.

Response 8:Thank you for pointing this out.I agree with this comment.At present, only the cases without magnetic field have been verified, which indeed has certain limitations. In the subsequent research, I will further improve the relevant work to ensure that the research results are more comprehensive and reliable. Besides, the working medium used in the verification model is pure argon gas, while my research adopts He/Xe mixed gas, which also leads to certain deficiencies. However, whether it is pure argon gas or He/Xe mixed gas, the form of the ion continuity equation（equation（13）） is the same, and the main difference lies in the specific ionization rate and three-body recombination rate parameters. Therefore, despite the above differences, the verification model still has certain reference value.

Comments 9:Lines 251 through 253 of the text, describes the change in conductivity, but there is no corresponding graphical representation, whereas Figure 6 gives the electron temperature.

Response 9:Thank you for pointing this out.I have already switched to the correct graphic.The specific location is at line 262 (Figure 6).

Comments 10:In Figure. 10, there is no difference between the X and Z axes.

Response 10:Thank you for pointing this out.I agree with this comment.Therefore, I made modifications to the coordinate axes. The specific modification location is at line 344 (Figure 12).

Comments 11:Figure (13) contains only four data points, which is insufficient to adequately illustrate the trend of the curve, Why does the trend of this curve not exhibit an initial increase followed by a decrease when β is set to 5?

Response 11:Thank you for pointing this out.I agree with this comment.Therefore, I have changed the curves in the figure to broken lines and reanalyzed the relevant data. The specific modification locations are lines 418 to 431 and Figure 15.

Comments 12:In line 311, with the Hall parameter given, by its definition, then the total collision frequency of electrons with heavy particles is also determined. Further explanation is needed from the authors as to why the total collision frequency of electrons with heavy particles varies in Fig. 12(b).

Response 12:Thank you for pointing this out.I agree with this comment.Therefore,I have made a detailed explanation in the text. Specifically, the electron collision frequency determined by the four Hall parameter values is a definite average value and has no correlation with the electron-heavy particle collision frequency in Figure 14(b).The specific modifications are located on lines 383 to 388.

Comments 13:the authors need to give the curves of the variation of parameters such as gas temperature, pressure, velocity, current density, electric field strength, etc. along the radial direction in the disk channel.

Response 13:Thank you for pointing this out.I agree with this comment.Therefore,I have added the distribution diagrams of static pressure and Mach number in the r-z plane, as well as the radial distribution diagram of electron number density, and conducted a detailed analysis of the relevant data.The specific modifications are located from line 279 to line 320 in the text.

Reviewer 2 Report

Comments and Suggestions for Authors

The simulation model and simulation results need to be further elaborately explained.

Comments on the Quality of English Language

No

Author Response

Comment1：The simulation model and simulation results need to be further elaborately explained.

Response1:Thank you for pointing this out,I agree with this comment.Therefore,I have provided further detailed explanations.

Reviewer 3 Report

Comments and Suggestions for Authors

In this manuscript, magnetohydrodynamic (MHD) electrical power generation using a disk-shaped Hall-type generator is discussed based on numerical simulations. The simulations are of a high level and merit discussion. However, there are numerous previous studies on disk-shaped Hall-type MHD generators, making it difficult to identify the novel contributions of this study. Below are comments for revising the manuscript.

1.Unclear Novelty of the Study：While the study investigates the effects of the Hall effect on the performance of the power generation channel, this field has already been extensively researched. The study’s unique contributions are not clearly articulated, and differentiation from existing studies is insufficient.

2.Lack of Detailed Discussion on the Impact of the Hall Effect：The influence of the Hall effect on plasma stability and current distribution is mentioned, but the underlying mechanisms are not thoroughly discussed, leaving the theoretical basis weak.

3. Insufficient Measures to Address Anode Corrosion：While the study highlights the risk of anode corrosion due to strong circular Faraday currents and high temperatures, it fails to propose concrete design improvements to mitigate this issue.

4.Lack of Detail in Boundary Condition Settings：The description of the simulation’s boundary conditions is insufficient, making it challenging for other researchers to replicate the study. For example, details on specific temperature and pressure settings at the inlet and outlet are missing.

5.Inadequate Interpretation of Figures and Graphs：While many figures are included, the accompanying explanations are insufficient to help readers fully understand the results. For instance, the descriptions of Figures 10 and 11 are overly concise.

6.Lack of Discussion on Practical Implementation：Despite targeting space applications, the study fails to address the practical challenges or considerations for real-world implementation of the proposed power generation channel.

Author Response

Comments 1:Unclear Novelty of the Study：While the study investigates the effects of the Hall effect on the performance of the power generation channel, this field has already been extensively researched. The study’s unique contributions are not clearly articulated, and differentiation from existing studies is insufficient.

Response 1:Thank you for pointing this out.I agree with this comment.Regarding the novelty of the research, it has been elaborated on from line 92 to 100 in the text. In subsequent studies, I will continue to delve deeper into this field to enhance the novelty and practical application value of the research outcomes.

Comments 2:Lack of Detailed Discussion on the Impact of the Hall Effect：The influence of the Hall effect on plasma stability and current distribution is mentioned, but the underlying mechanisms are not thoroughly discussed, leaving the theoretical basis weak.

Response 2:Thank you for pointing this out.I agree with this comment.Therefore, in Section 4.1 of the text (lines 279 to 320), I have analyzed the mechanism by which the Hall effect influences the stability of the flow field structure, striving to make the theoretical foundation of the thesis more solid.

Comments 3:Insufficient Measures to Address Anode Corrosion：While the study highlights the risk of anode corrosion due to strong circular Faraday currents and high temperatures, it fails to propose concrete design improvements to mitigate this issue.

Response 3:Thank you for pointing this out.I agree with this comment.Therefore，I propose a method of using insulating partitions to block part of the Faraday current at the anode to solve the anode corrosion problem. The specific content is between lines 451 and 453 in the text. 

Comments 4:Lack of Detail in Boundary Condition Settings：The description of the simulation’s boundary conditions is insufficient, making it challenging for other researchers to replicate the study. For example, details on specific temperature and pressure settings at the inlet and outlet are missing.

Response 4:Thank you for pointing this out.I agree with this comment.Therefore，I have added inlet static pressure, outlet gauge pressure and backflow total temperature in the "Import/Export Boundary Conditions" section.The specific modifications are at lines 233 and 241 in the text.

Comments 5:Inadequate Interpretation of Figures and Graphs：While many figures are included, the accompanying explanations are insufficient to help readers fully understand the results. For instance, the descriptions of Figures 10 and 11 are overly concise.

Response 5:Thank you for pointing this out.I agree with this comment.Therefore，I have revised the analysis content of Figure 12 (originally Figure 10 in the original manuscript) and Figure 13 (originally Figure 11 in the original manuscript), providing a more detailed and clear analysis. The specific revisions are located between lines 366 and 344 (for Figure 12) and lines 363 and 369 (for Figure 13) in the text.

Comments 6:Lack of Discussion on Practical Implementation：Despite targeting space applications, the study fails to address the practical challenges or considerations for real-world implementation of the proposed power generation channel.

Response 6:Thank you for pointing this out.I agree with this comment.Therefore，I have made some elaborations, the specific content of which is from line 464 to line 482 in the text.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

1. L66, “Shahar equation” should be “Saha equation”
2. L91, “Institute of Electrical Engineering at the Chinese Academy of Sciences”, should be “ Institute of Electrical Engineering of Chinese Academy of Sciences”
3. L126, the throat position in Figure 2 does not match the text description, in which the throat r1 is 0.04m , but it is clearly not 0.04m in the figure.
4. Line154，the plasma reaction equations genrally include the ionization equation, excitation equation, and other associated equations. According to Formula 13, this study exclusively considers single-ionization and three-body recombination reactions while entirely disregarding the presence of excited-state particles and the significant Penning ionization process. This omission may result in a notable reduction in the accuracy of the results.
5. Line 214，the Y-axis coordinate system in Section 2.4.1 still exists.
6. Line 172 and Line 373, according to Formula (22), it can be observed that the variation trend of Ven is consistent with that of β. Therefore, the changing trends of all curves should be consistent, and the abscissas of the highest points should be the same. However, Figure 14(b) clearly shows certain differences.
7. Line 301, Figure 10 shows that the Mach number is about 1.8 in the throat r1=0.04m, which is usually about 1, please give the explain.
8. Finally, model validation based on a magnetic field of 0 is not convincing. Without a magnetic field, there is no magnetohydrodynamic power generation process, there is no non-equilibrium ionization in a disk MHD generator, and there is no Hall effect and Hall parameters .... Therefore, there is no way to verify the model.

Comments on the Quality of English Language

Please ask native English speaker to modify.

Author Response

Comments 1:L66, “Shahar equation” should be “Saha equation”

Response 1:Thank you for pointing this out.Therefore,I have already changed "Shahar equation" to "Saha equation".

Comments 2:L91, “Institute of Electrical Engineering at the Chinese Academy of Sciences”, should be “ Institute of Electrical Engineering of Chinese Academy of Sciences”

Response 2:Thank you for pointing this out.I have already changed "Institute of Electrical Engineering at the Chinese Academy of Sciences" to "Institute of Electrical Engineering of Chinese Academy of Sciencesn".

Comments 3:L126, the throat position in Figure 2 does not match the text description, in which the throat r1 is 0.04m , but it is clearly not 0.04m in the figure.

Response 3:Thank you for pointing this out.There was an error in the description in the text. The entrance is not located at the throat. The description of the entrance in the text has been modified. The specific modification is on line 133 of the text.

Comments 4:Line154，the plasma reaction equations genrally include the ionization equation, excitation equation, and other associated equations. According to Formula 13, this study exclusively considers single-ionization and three-body recombination reactions while entirely disregarding the presence of excited-state particles and the significant Penning ionization process. This omission may result in a notable reduction in the accuracy of the results.

Response 4:Thank you for pointing this out.During the course of this research, the excited state particles and Penning ionization process were indeed not taken into account. Due to the current limitations of research conditions and data, it is temporarily impossible to supplement and improve this part. However, the comments you raised are of great reference value for our subsequent research. We will fully consider these suggestions in future studies to enhance the comprehensiveness and accuracy of our research.

Comments 5:Line 214，the Y-axis coordinate system in Section 2.4.1 still exists.

 Response 5:Thank you for pointing this out.I have changed "y" to "z" at line 224 in the text.

Comments 6:Line 172 and Line 373, according to Formula (22), it can be observed that the variation trend of Ven is consistent with that of β. Therefore, the changing trends of all curves should be consistent, and the abscissas of the highest points should be the same. However, Figure 14(b) clearly shows certain differences.

 Response 6:Thank you for pointing this out.Theoretically, the abscissa of the peak points should be identical. However, Figure 14(b) clearly exhibits discrepancies, which may be attributed to an imperfect computational model, leading to inaccuracies in the simulation results.

Comments 7:Line 301, Figure 10 shows that the Mach number is about 1.8 in the throat r1=0.04m, which is usually about 1, please give the explain.

 Response 7:Thank you for pointing this out.In this study, the inlet of the geometric model is not the throat. The description in line 133 of the preceding text was inaccurate and has since been corrected.

Comments 8:Finally, model validation based on a magnetic field of 0 is not convincing. Without a magnetic field, there is no magnetohydrodynamic power generation process, there is no non-equilibrium ionization in a disk MHD generator, and there is no Hall effect and Hall parameters .... Therefore, there is no way to verify the model.

 Response 8:Thank you for pointing this out.I fully agree with your point of view. In this study, there are indeed deficiencies in the method and model validation sections.

Reviewer 2 Report

Comments and Suggestions for Authors

This version of manuscript can be accepted.

Author Response

Thank you for your recognition.

Reviewer 3 Report

Comments and Suggestions for Authors

The response to the reviewers only mentions the revised sections but does not provide sufficient explanations addressing the reviewers’ comments. Please revise and create a more comprehensive response that adequately addresses each point raised.

Author Response

Thank you sincerely for taking the time to review our manuscript again and for offering your valuable suggestions on the revised version. I have carefully studied the shortcomings in my previous responses that you pointed out and am deeply aware that the explanations for the revisions were indeed insufficient. Therefore, I have gone through each of your suggestions, made the necessary modifications, and provided detailed explanations.

Comments 1:Unclear Novelty of the Study：While the study investigates the effects of the Hall effect on the performance of the power generation channel, this field has already been extensively researched. The study’s unique contributions are not clearly articulated, and differentiation from existing studies is insufficient.

Response 1:Thank you for pointing this out.I agree with this comment.The innovation of this research lies in setting the Hall parameter as a constant, which enables obtaining stable current distributions under different Hall parameter conditions. This approach not only simplifies the complex relationship between the Hall parameter and plasma characteristics but also facilitates in-depth analysis of the influence of Hall current and Faraday current on plasma magnetohydrodynamics. Moreover, this method is conducive to systematically studying the plasma flow characteristics under stable current distributions and their variation laws when the current distribution changes, thereby providing a theoretical basis for precisely controlling phenomena such as plasma ionization and flow in experimental research, ultimately achieving a more stable plasma structure and flow field. Regarding the innovation of the research, it has been restated in the paper. For specific details, please refer to the highlighted part from line 94 to line 110 of the paper.

Comments 2:Lack of Detailed Discussion on the Impact of the Hall Effect：The influence of the Hall effect on plasma stability and current distribution is mentioned, but the underlying mechanisms are not thoroughly discussed, leaving the theoretical basis weak.

Response 2:Thank you for pointing this out.I agree with this comment.Based on your comments, I have conducted a more in-depth analysis. I believe that the relationship between Hall current and Faraday current and the resulting Lorentz force can be analyzed. The larger the Hall parameter, the stronger the Hall current, and the change in the Hall parameter directly affects the distribution of the synthetic current. The Hall parameter directly affects the Hall current, and subsequently influences the tangential Lorentz force generated by the Hall current, ultimately having a significant impact on the stability of plasma magnetohydrodynamic flow and the motion of charged particles. Based on this analysis, I have provided a more detailed discussion of Figures 11 and 13 in the paper. For specific discussion content, please refer to lines 340 to 359 and lines 393 to 404 of the paper.

Comments 3:Insufficient Measures to Address Anode Corrosion：While the study highlights the risk of anode corrosion due to strong circular Faraday currents and high temperatures, it fails to propose concrete design improvements to mitigate this issue.

Response 3:Thank you for pointing this out.I agree with this comment.Therefore，based on the principle of the formation of the annular Faraday current, I propose to use periodically arranged insulating partitions to block part of the Faraday current at the anode. This method can effectively reduce the intensity of the Faraday current at the anode, thereby minimizing the impact of anode current erosion. The content regarding this method is between lines 493 and 499 of the paper.

Comments 4:Lack of Detail in Boundary Condition Settings：The description of the simulation’s boundary conditions is insufficient, making it challenging for other researchers to replicate the study. For example, details on specific temperature and pressure settings at the inlet and outlet are missing.

Response 4:Thank you for pointing this out.I agree with this comment.Therefore，I have added inlet static pressure（0.1MPa）, inlet static temperature(1227K),outlet gauge pressure(0Pa) and backflow total temperature(300K) in the "Import/Export Boundary Conditions" section.The specific modifications are at lines 241 and 252 in the text.

Comments 5:Inadequate Interpretation of Figures and Graphs：While many figures are included, the accompanying explanations are insufficient to help readers fully understand the results. For instance, the descriptions of Figures 10 and 11 are overly concise.

Response 5:Thank you for pointing this out.I agree with this comment.Therefore，Based on your comments, I have revised the relevant descriptions of Figures 11, 12, 13 and 14, clarifying the planes on which each figure is located and the distribution of their contour lines. Specifically, I have detailed the planes and contour line distributions of Figures 11 and 12, as well as the planes and directions of Figures 13 and 14. The specific revisions can be found in lines 360 to 361, 377 to 379, 415 to 416 and 417 to 419 of the paper.

Comments 6:Lack of Discussion on Practical Implementation：Despite targeting space applications, the study fails to address the practical challenges or considerations for real-world implementation of the proposed power generation channel.

Response 6:Thank you for pointing this out.I agree with this comment.During the actual research process, the disc-shaped power generation channel encountered numerous challenges, making it difficult to be applied in the space environment. Based on the research achievements of predecessors, this paper elaborately discusses several possible challenges that the disc-shaped power generation channel may face in practical applications. The specific discussion and revision content are presented from line 510 to line 529 of the paper.

Round 3

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript has sufficiently addressed the reviewers’ inquiries and has been appropriately revised. Therefore, I believe it is worthy of publication.