Effects of Fast Elongation on Switching Arcs Characteristics in Fast Air Switches

Round 1

Reviewer 1 Report

Dear all authors,
I have gone through your manuscript. I think that it presents an interest research, mainly concerning the approaches of the mathematical simulation of the effects of high-speed elongation of arcs inside FSs. Basically, the presented research is very solid and the manuscript is well organized, the simulation approaches and results sound reasonable. From my point of view, I think that provided solution, mainly the comparison of achieved simulation results and experimental data, is beneficial and I also see as practical work. In general, the manuscript is very well prepared and is in accordance with Energies journal template. However, I have also some remarks that should be taken into consideration. Going to concrete things that must be changed:
- all variables should be in italics - e.g. Cp in Table 1, T in lines 210 and 211variables, etc.
- all units should not be in italics - e.g. units in lines 192, 211, 218, 340, 413
- value and unit must be on the same line – i.e. lines 151, 164, 217, 349, 367, 374, 417, 451
- check the meaning of presented values in whole manuscript text - i.e. Number_Unit = noun vs. NumberUnit = adjective
- why square brackets in lines 277 and 278?
Yours sincerely

Author Response

Dear Editor,

Dear referee,

Many thanks for your time, and valuable comments on our article. The comments helped us to improve our quality and be able to present our work in a better way. We appreciate it and please see our explanations and required responses hereinbelow of referee’s comments in turn. The modified version of traceable changes (track change in MS-Word) in addition to the clean version of the modified article is attached to prepare a better follow-up.

Refer to the complexity of track change in MS-Word®, to make a convenient followup for the referees, the changes based on referee#1 is colored in brown while for the referee#2 and the referee#3 respectively in blue and green. provided in a separate pdf file named “highlights_Rev1.pdf”

REFEREE REPORT(S):
Referee: 1

I have gone through your manuscript. I think that it presents interesting research, mainly concerning the approaches of the mathematical simulation of the effects of high-speed elongation of arcs inside FSs. The presented research is very solid, and the manuscript is well organized, the simulation approaches and results sound reasonable. From my point of view, I think that the provided solution, mainly the comparison of achieved simulation results and experimental data, is beneficial and I also see as practical work. In general, the manuscript is very well prepared and is following the Energies journal template. However, I have also some remarks that should be taken into consideration. Going to concrete things that must be changed:

- all variables should be in italics - e.g. Cp in Table 1, T in lines 210 and 211variables, etc.

It was modified accordingly and was checked in the rest of the paper.

- all units should not be in italics - e.g. units in lines 192, 211, 218, 340, 413

It was modified accordingly and was checked in the rest of the paper.

- value and unit must be on the same line – i.e. lines 151, 164, 217, 349, 367, 374, 417, 451

It was modified accordingly and was checked in the rest of the paper.

- check the meaning of presented values in the whole manuscript i.e. Number_Unit = noun vs. NumberUnit = adjective

It was checked and modified in the whole of the article for instance in:

- why square brackets in lines 277 and 278?

It was modified to parenthesis

Author Response File: Author Response.pdf

Reviewer 2 Report

This article tries to investigate the effects of high-speed elongation of arcs inside the ultra-fast switches through a simulation model. It is interesting. Some comments are given as follows:

1. The introduction part is too simple and must be improved. More literature survey regarding the simulation modelling and related applications must be given and analyzed. The contributions of your article should be highlighted with evidence.

2. What is the computational effort of your utilized 2-D time-dependent model? Can the proposed approach be applied in real applications as it is complicated with lots of mathematical equations? Please give evidence.

3. How to identify the parameters of your utilized model?

4. Data-driven model is also a key and powerful tool to handle the analysis issues like yours. Please give some comments regarding the difference and potential solutions to combine these techniques for smarter influence analysis.

5. When describe powerful data-driven solutions, please consider these highly related works: An evaluation study of different modelling techniques for calendar ageing prediction of lithium-ion batteries; Modified Gaussian process regression models for cyclic capacity prediction of lithium-ion batteries.

6. Can the proposed method achieve uncertainty quantification as the uncertainty management is a key for fast air switch applications? Please clarify it carefully

7. When describe powerful data-driven solutions, please consider these highly related works: A Data-driven Approach with Uncertainty Quantification for Predicting Future Capacities and Remaining Useful Life of Lithium-ion Battery; Gaussian process regression with automatic relevance determination kernel for calendar aging prediction of lithium-ion batteries.

8. How to handle the measurement noise and shift noise as they would highly affect your simulation results?

Author Response

Dear Editor,

Dear referee,

Many thanks for your time, and valuable comments on our article. The comments helped us to improve our quality and be able to present our work in a better way. We appreciate it and please see our explanations and required responses hereinbelow of referee’s comments in turn. The modified version of traceable changes (track change in MS-Word) in addition to the clean version of the modified article is attached to prepare a better follow-up.

Refer to the complexity of track change in MS-Word®, to make a convenient followup for the referees, the changes based on referee#1 is colored in brown while for the referee#2 and the referee#3 respectively in blue and green. provided in a separate pdf file named “highlights_Rev1.pdf”

REFEREE REPORT(S):
Referee: 2

This article tries to investigate the effects of high-speed elongation of arcs inside the ultra-fast switches through a simulation model. It is interesting. Some comments are given as follows:

1. The introduction part is too simple and must be improved. More literature survey regarding the simulation modeling and related applications must be given and analyzed. The contributions of your article should be highlighted with evidence.

Response: Thanks for this comment. It was modified and more related references (16 new references) were analyzed and added considering our contribution to the topics as below:

The first motivation of this study is to understand the physical mechanisms of arcs elongated inside the fast switches before the current zero. A mathematical model is presented for variable-length AC arcs in contactors with elongating speeds of about 1 m/s, where the arc voltage is described by a series arc concept [1]. It is only applicable to cylindrical arcs when the temperature distribution is radial homogenous. Anther already presented a mathematical model for variable-length arcs tries to relate the arc voltage with the arc volume, but it applies only to the welding arcs when the length is changing vertically with rather low speeds [2]. Problems arising in attempts to accurately represent dynamic processes of an electric arc using simple mathematical models are discussed in [3]. All of these purely mathematical models are either modified versions of the Cassie-Mayr model and rely on energy balance inside the arc, or a modified Ayrton model for DC static arcs [4] or even a static model of welding arcs without diagonal cooling [5]. The relation between the arc length and its voltage and current has been, however, essential in other fields like arc welding, where a robust method is proposed to measure the arc length in [6]. Also, a technique to find the arc current and voltage from arc length in welding has been patented [7]. This fact can express the importance of presenting a reliable model for fast elongating arcs to solve the most critical issue related to the current commutation in hybrid FCLs / HVDC circuit breakers.

Although there are plenty of studies on the current interruption in high voltage gas circuit breaker [8-10], vacuum interrupter [11], and medium voltage load breakers [12-14], only a few reviews on the low-speed load break switch and mostly relying on experimental findings, without MHD simulations [15, 16] are available. Only a few studies are dealing with simulations for VCB [17] and air breakers at contact speed about 2.5 m/s [10] that will result in a short gap before the current zero. This is the second reason for this study. A memory effect of the gap concerning the interrupted current is shown in [18], which is more pronounced at longer contact gaps like what we have here in FS.

2. What is the computational effort of your utilized 2-D time-dependent model? Can the proposed approach be applied in real applications as it is complicated with lots of mathematical equations? Please give evidence.

In general, the MHD method is time-consuming but with less effort and cost in gathering information while many rapid mathematical models do not care about the effort and cost in gathering information. So, some rapid models are so full of coefficients whose detail is so hard to gather that, after an ad hoc implementation, its application is inevitably condemned to death [19]. Therefore, it’s very important to base a model as much as possible on the flow of data and information which is the case of the MHD simulation where a mathematical model stands on such a solid basis will have a high probability to be applied, and so tested and improved, in a continuous way. That’s the reason for the vast utilizing of the MHD  simulations as verification tools for design and performance evaluation of Switchgears [20].

3. How to identify the parameters of your utilized model?

The main parameters of the utilized model are the transport and thermodynamic properties of gas mixtures which would be obtained either from the articles or could be calculated through chemical physics [21, 22] for pressures and mixtures other than what is reported in the articles. Software packages are handling these chemical physics calculations [23].

4. The data-driven model is also a powerful tool to handle the analysis issues like yours. Please give some comments regarding the difference and potential solutions to combine these techniques for smarter analysis.

The process of Data-driven decision making is based on actual data rather than intuition or observation alone. The hard truth is that simulation output alone is not enough. So, making organizational decisions for failure Prediction can be utilized through different modeling techniques[24] like Gaussian Process Regression Models [25] in the next study.

5. When describing powerful data-driven solutions, please consider these highly related works: An evaluation study of different modeling techniques for calendar aging prediction of lithium-ion batteries; Modified Gaussian process regression models for cyclic capacity prediction of lithium-ion batteries.

Thanks for the introduced references. It was a good reference for data-driven solutions and an initiator for the uncertainty studies and was considered.

6. Can the proposed method achieve uncertainty quantification as uncertainty management is key for fast air switch applications? Please clarify it carefully

The breakdown in electrical insulation like an insulating gas inside the circuit breakers (here the air-Al mixture) is instinctively a matter of probability and so on can be explained by the theory of error. For instance, we measure the breakdown voltage at the probability of the breakdown of 50% or 80%, etc. At the end of the twentieth century, the Theory of Error proposed by K. F. Gauss at the beginning of the nineteenth century was replaced by the Theory of Uncertainty[26]. The presented model can be formulated in a black box shape we name it a hybrid numerical- mathematical model an is the target of the next study. Theories formulating a mathematical model are audacious in scope, in large part because scholars proposing them are not inhibited by the ordeal of implementing and validating data-driven models [19]. From the mathematical viewpoint, there is no difference between crisp mathematical programming and classical mathematical programming except for an integral. Thus we may solve it by simplex method, branch-and-bound method, cutting plane method, implicit enumeration method, interior point method, gradient method, genetic algorithm, particle swarm optimization, neural networks, tabu search, and so on [27]. So, the answer is, yes it could be formulated to achieve uncertainty quantification but it will be presented in the next study.

7. When describing powerful data-driven solutions, please consider these highly related works: A Data-driven Approach with Uncertainty Quantification for Predicting Future Capacities and Remaining Useful Life of Lithium-ion Battery; Gaussian process regression with automatic relevance determination kernel for calendar aging prediction of lithium-ion batteries.

Same as the comment #5.

8. How to handle the measurement noise and shift noise as they would highly affect your simulation results?

Practical methods for electrical and mechanical measurement of high speed elongated arc parameters including the measurement noise and shift noise and the practical way to consider their effects in simulations Were explained in [28]. We are aware of two different types of error encountered, one because of the measuring tools and the other due to uncertainty in noise level, etc. the integral method mentioned in the response to comment #7 is investigated and used. It was explained in [28].

1. Z. Wu, et al., IEEE Transactions on Plasma Science. 43, 2730 (2015)
2. A. Sawicki, Przegląd Elektrotechniczny. 89, 6 (2013)
3. A. Sawicki and Haltof M., DOI. 65, 17 (2016)
4. W.B. Nottingham, American Institute of Electrical Engineers, Transactions of the. XLII, 302 (1923)
5. A. Sawicki and Haltof M., Przegląd Elektrotechniczny. 92, 4 (2016)
6. P. Li and Zhang Y.M., IEEE Transactions on Instrumentation and Measurement. 50, 697 (2001)
7. R.M. Hutchison, (2016)
8. M. Seeger, et al., Journal of Physics D: Applied Physics. 38, 1795 (2005)
9. T. Nakano, et al., Journal of Physics D: Applied Physics. 51, 215202 (2018)
10. D.F. Peelo, Current interruption using high voltage air-break disconnectors. (Technische Universiteit Eindhoven, 2004)
11. X. Li, et al., in 2016 IEEE International Conference on Power System Technology (POWERCON). (2016), pp. 1
12. E. Jonsson, Aanensen N.S., and Runde M., IEEE Transactions on Power Delivery. 29, 870 (2014)
13. N.S. Aanensen, Jonsson E., and Runde M., IEEE Transactions on Power Delivery. 30, 299 (2015)
14. N. Støa-Aanensen, Runde M., and Teigset A.D., in 2015 IEEE 61st Holm Conference on Electrical Contacts (Holm). (2015), pp. 101
15. A. Balestrero, et al., IEEE Transactions on Power Delivery. 25, 206 (2010)
16. N.S. Støa-Aanensen, et al., IEEE Transactions on Power Delivery. 31, 278 (2016)
17. P. Sarrailh, et al., IEEE Transactions on Plasma Science. 36, 1046 (2008)
18. E.F.J. Huber, Weltmann K.D., and Froehlich K., IEEE Transactions on Plasma Science. 27, 930 (1999)
19. G. Dellino and Meloni C., Uncertainty Management in Simulation-Optimization of Complex Systems, Algorithms and Applications. (Springer Boston, MA, 2015)
20. M. Kriegel and Uzelac N., in Switching Equipment, edited by H. Ito. (Springer International Publishing, Cham, 2019), pp. 379
21. M. capitelli, colonna G., and D'Angola A., Fundamental Aspects of Plasma Chemical Physics, Thermodynamics. 1 edn. (Springer-Verlag New York, 2012)
22. M. capitelli, Bruno D., and Laricchiuta A., Fundamental Aspects of Plasma Chemical Physics, Transport. 1 edn. (Springer-Verlag New York, 2013)
23. P.M.J. Koelman, et al., Journal of Physics: Conference Series. 682, 012034 (2016)
24. K. Liu, et al., Renewable and Sustainable Energy Reviews. 131, 110017 (2020)
25. K. Liu, et al., IEEE Transactions on Transportation Electrification. 5, 1225 (2019)
26. S. Salicone and Prioli M., Measuring Uncertainty within the Theory of Evidence. (Springer, Cham, 2018)
27. B. Liu, Uncertainty Theory. (Springer Berlin, Heidelberg, 2015)
28. A. Kadivar and Niayesh K., Measurement. 55, 14 (2014)

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper reports the results of numerical study of a fast air switch. The manuscript gives the model description and discuss the influence of different physical effects on the model results. Some results are compared with experiment for validation purpose. The paper is of broad interest for switching arc community.

The material presentation has some deficits. In general, the language must be improved. The authors introduce many acronyms and abbreviations, which are not necessary and make the text hardly understandable. Remove following abbreviations: Ca, An, ACH, HT, MC, TE, EE, LF, TF, T, TDNS. Appropriate acronyms used in the manuscript are CFD, MHD, LTE, HVDC, CB, MCB, FSL and FS. Al and Cu are well known notations for chemical elements. It is not necessary to explain them.

Abstract should be modified in order to fit the paper content. Please emphasise the physical effect, which were “tested” within the model, like e.g. turbulence, evaporation model etc. Put also some results, which appear due to inclusion of those effects (temperature distribution, arc root movement, etc.)

Keywords are partially inappropriate. A suggestion for appropriate keywords: arc plasma; Thomson actuator; magneto-hydrodynamic simulations, fast switch

Introduction gives an adequate overview over the status of fast switch research. However, it should be extended by state-of-the-art of the arc modelling. The MHD approach is one of the most widely used for arcs. It is not depending on the type of the switch. Therefore, a short description of corresponding literature is desired.

Some statements are inappropriate interpretation of the literature data. Few examples:

• There is no statement, that LTE plasma is always symmetric in [27].
• MHD equations have nothing to do with the symmetry (line 91ff). They have general validity for all geometries.
• The electrode heating can cause much higher temperatures as a melting point (line 210ff). As a rough approximation the boiling point can be reached. At such temperatures the thermionic current is significant.

Model description should be also improved. There exists more or less established scheme how to present a model, like e.g. in Ref.  [30]. In the present manuscript, however, it is not clear how the model finally looks like. Is it pure MHD or combination with many other submodels, like e.g. sheath model, evaporation model, spot movement model, turbulence etc. ? Do the authors merge various tools for prediction of some quantities, like e.g. vapor distribution, arc root movement etc? Which components were finally included into simulations: air + Al + Cu + Fe? How the corresponding thermodynamic and transport properties have been determined?  The material properties are in general temperature and pressure dependent. How was the pressure dependence taken into account? Why the temperature dependence of solid materials was ignored? Presented discussion gives no clear answers on those questions.

The scheme shown in Fig 1 is not self-explanatory. It is not clear why it is presented here. Fig 2 (b) must be changed. The boundaries can be notified by letters (ABCD) and the figure should be complemented by a table with used boundary and initial conditions. Please give the dimensions of the electrodes and initial gaps (electrode distance).

Why the authors put so much attention on discussion of axial symmetry? Used model seems to be an infinite slab (or a slab with fixed thickness?).

Discussions about the NEC, various metal vapor admixtures, erosion rates are not clearly formulated. What is the main outcome? How this information was used in the model?

Equation (2) looks very strange. How it was derived? The units of separate terms do not coincide.

The general discussion of numerical difficulties is of less interest in the content of current issue. Moreover, these problems are not new, as well as the ways to solve them. The corresponding text can be shortened. Description of the moving mesh treatment is important.

The presentation of sheath model is insufficient. How the voltage falls in cathode and anode sheath were determined?

At the end of model description the reader should have an idea how the model looks like and what physical effects are included. In the present form a part of this discussion is shifted to the chapter Results. Please correct this.

Results.

What is the difference between the arc core and arc column? How the authors determine the boundary between those parts?

The most figures should be reorganized, since they are overloaded with information. What is the most important message there? For example, in Fig.8 one can compare 6 -9 graphs instead of 30. The text in Fig. 3,5,7,10,12,14,15,16 is too small.

Fig. 6 should be changed to color presentation.

Table 1 fist line should be Cp (not mu_r) and second kappa (not k).

What can the reader learn from amount of data presented? There is no discussion about parameter variation, besides the contact velocity and current. Is the arc finally interrupted or not? Are the arc roots moving or not?

Discussion. Since the sheath model is presented rudimental, it is not clear how the values of sheath voltages were obtained. If there is not physical sheath model, how the sheath width was determined?

The explanation of the influence of arc length on arc parameters is partially misleading. It is well known that the longer the arc length the higher the voltage. Also, the cooling increases with the arc length. What is the novelty here???

In conclusion, the manuscript has to be revised before publishing.

Author Response

Dear Editor,

Dear referee,

Many thanks for your time, and valuable comments on our article. The comments helped us to improve our quality and be able to present our work in a better way. We appreciate it and please see our explanations and required responses hereinbelow of referee’s comments in turn. The modified version of traceable changes (track change in MS-Word) in addition to the clean version of the modified article is attached to prepare a better follow-up.

Refer to the complexity of track change in MS-Word®, to make a convenient followup for the referees, the changes based on referee#1 is colored in brown while for the referee#2 and the referee#3 respectively in blue and green. provided in a separate pdf file named “highlights_Rev1.pdf”

REFEREE REPORT(S):
Referee: 3

The paper reports the results of the numerical study of a fast air switch. The manuscript gives the model description and discusses the influence of different physical effects on the model results. Some results are compared with the experiment for validation purposes. The paper is of broad interest to the switching arc community. The material presentation has some deficits.

In general, the language must be improved.

The machine language editor (Grammarly professional) was used to modify the language, then it was studied by an expert to improve more.

The authors introduce many acronyms and abbreviations, which are not necessary and make the text hardly understandable. Remove the following abbreviations: Ca, An, ACH, HT, MC, TE, EE, LF, TF, T, TDNS.

Ca, An, T, and LF as well as TDNS are well-known notations and commonly used in ref. books; also MC, and TF have been used in the figures for space limitations and we suggest keeping them, but the rest (ACH, HT, TE, and EE) were removed.

Appropriate acronyms used in the manuscript are CFD, MHD, LTE, HVDC, CB, MCB, FSL, and FS.

Al and Cu are well-known notations for chemical elements. It is not necessary to explain them.

Al and Cu are just defined one time and we suggest agree to keep them

The abstract should be modified to fit the paper content. Please emphasize the physical effect, which was “tested” within the model, like e.g. turbulence, evaporation model, etc. Put also some results, which appear due to the inclusion of those effects (temperature distribution, arc root movement, etc.)

Keywords are partially inappropriate. A suggestion for appropriate keywords: arc plasma; Thomson actuator; magneto-hydrodynamic simulations, fast switch

Response: It was modified accordingly

The introduction gives an adequate overview of the status of fast switch research. However, it should be extended by state-of-the-art of the arc modeling. The MHD approach is one of the most widely used for arcs. It is not depending on the type of switch. Therefore, a short description of the corresponding literature is desired.

Response: Thanks for this comment. It was modified and more related references (16 new references) were analyzed and added considering our contribution to the topics as below:

The first motivation of this study is to understand the physical mechanisms of arcs elongated inside the fast switches before the current zero. A mathematical model is presented for variable-length AC arcs in contactors with elongating speeds of about 1 m/s, where the arc voltage is described by a series arc concept [1]. It is only applicable to cylindrical arcs when the temperature distribution is radial homogenous. Anther already presented a mathematical model for variable-length arcs tries to relate the arc voltage with the arc volume, but it applies only to the welding arcs when the length is changing vertically with rather low speeds [2]. Problems arising in attempts to accurately represent dynamic processes of an electric arc using simple mathematical models are discussed in [3]. All of these purely mathematical models are either modified versions of the Cassie-Mayr model and rely on energy balance inside the arc, or a modified Ayrton model for DC static arcs [4] or even a static model of welding arcs without diagonal cooling [5]. The relation between the arc length and its voltage and current has been, however, essential in other fields like arc welding, where a robust method is proposed to measure the arc length in [6]. Also, a technique to find the arc current and voltage from arc length in welding has been patented [7]. This fact can express the importance of presenting a reliable model for fast elongating arcs to solve the most critical issue related to the current commutation in hybrid FCLs / HVDC circuit breakers.

Although there are plenty of studies on the current interruption in high voltage gas circuit breaker [8-10], vacuum interrupter [11], and medium voltage load breakers [12-14], only a few reviews on the low-speed load break switch and mostly relying on experimental findings, without MHD simulations [15, 16] are available. Only a few studies are dealing with simulations for VCB [17] and air breakers at contact speed about 2.5 m/s [10] that will result in a short gap before the current zero. This is the second reason for this study. A memory effect of the gap concerning the interrupted current is shown in [18], which is more pronounced at longer contact gaps like what we have here in FS.

Some statements are the inappropriate interpretation of the literature data. Few examples:

There is no statement, that LTE plasma is always symmetric in [27].

That sentence was removed as it did not affect the structure of this paper.

MHD equations have nothing to do with the symmetry (line 91ff). They have general validity for all geometries.

That sentence was misleading. Of course, the MHD equations have nothing to do with the geometric symmetry. By symmetry, we meant the symmetry in the rate of reaction for ionization and attachments and therefore, the equality of the ions and electron temperature and.

We modified the sentence as single-flow MHD equations instead of two separate flows of electron and ions

The electrode-heating can cause much higher temperatures as a melting point (line 210ff). As a rough approximation, the boiling point can be reached. At such temperatures the thermionic current is significant.

Although the first studies on liquid metals presented in [19] show an explosive electron emission From liquid cathodes in special conditions and for a limited time, as far as we know thermionic emission data exist only for polycrystalline solid-state copper emitters[20] and copper is not the ideal thermionic emitter because of its relatively low melting point (1356 K) which limits the working temperature region to 800- 1l00 K or so[21]. As it is clear from Figure 11, the copper cathode temperature does not reach the melting point in the first cycle, and so on thermionic emission from melted copper is ignored in this study.

The model description should be also improved. There exists a more or less established scheme on how to present a model, like e.g. in Ref.  [30]. In the present manuscript, however, it is not clear how the model finally looks like. Is it pure MHD or a combination with many other submodels, like e.g. sheath model, evaporation model, spot movement model, turbulence, etc. ? Do the authors merge various tools for the prediction of some quantities, like e.g. vapor distribution, arc root movement, etc? Which components were finally included in simulations: air + Al + Cu + Fe?

There is no Fe inside it was just an explanation in NEC dependency and was removed. The metals are Al and Cu and as it was mentioned in the previous comment it is clear from Figure 11, the temperature of the copper cathode does not reach the melting point in the first cycle and so on the ablation of Al is considered in this study.

How the corresponding thermodynamic and transport properties have been determined?

The transport and thermodynamic properties of gas mixtures which would be obtained either from the articles or could be calculated through chemical physics [22, 23] for pressures and mixtures other than what is reported in the articles. Software packages are handling these chemical physics calculations [24]. Here we used the PLASIMO package and you will see the results for different mixture ratios and pressures hereinbelow.

The material properties are in general temperature and pressure-dependent. How was the pressure dependence taken into account?

The changes in the pressure are very small in this study but it could be considered as it was explained in the above response.

Why the temperature dependence of solid materials was ignored? The presented discussion gives no clear answers to those questions.

The changes in the pressure are very small in this study but so its effect on vaporizing temperature is ignorable.

The scheme shown in Fig 1 is not self-explanatory. It is not clear why it is presented here.

Response: It was deleted

Fig 2 (b) must be changed. The boundaries can be notified by letters (ABCD) and the figure should be complemented by a table with used boundary and initial conditions. Please give the dimensions of the electrodes and initial gaps (electrode distance).

The initial gap is 2 mm and the dimension of the electrode is clear from the scaled geometry.

Why the authors put so much attention to the discussion of axial symmetry? The used model seems to be an infinite slab (or a slab with fixed thickness?).

It was mentioned before the equation (2) which is a slab with a fixed thickness of 1 cm.

Discussions about the NEC, various metal vapor admixtures, erosion rates are not formulated. What is the main outcome? How this information was used in the model?

The copper will not be ablated or in case of ablation remains near the electrode[25] but the Al spread with the contact movement and different mixture ratio would be produced by the change of the thickness and the length of the arc. The radiation is very sensitive to the mixture ratio. So the mixture ratio was estimated roughly and considered as in Figure 2(d)

Equation (2) looks very strange. How it was derived? The units of separate terms do not coincide.

It was a typo and was modified.

The general discussion of numerical difficulties is of less interest in the content of the current issue. Moreover, these problems are not new, as well as the ways to solve them. The corresponding text can be shortened. The description of moving mesh treatment is important.

Do agree and the Moving mesh was referenced [26]

The presentation of the sheath model is insufficient. How the voltage falls in the cathode and anode sheath were determined?

Do agree and section 2.7. the arc roots and the sheath model was added

 At the end of the model description, the reader should have an idea of how the model looks like and what physical effects are included. In the present form, a part of this discussion is shifted to the chapter Results. Please correct this.

Considering the modifications based on the provided comment so far and adding the section 2.7 solved this issue

Results.

What is the difference between the arc core and arc column? How did the authors determine the boundary between those parts?

As was mentioned in the result section the arc light is due to radiation that is proportional to T⁴. So, the arc column boundary is defined as σ =1 which is equal to 3300 K but the core is the gliding section of arc (σ > 600 which is similar to 6700 K in air temperature) which is passing more than 80% of the arc current.

Most figures should be reorganized since they are overloaded with information. What is the most important message there? For example, in Fig.8 one can compare 6 -9 graphs instead of 30. The text in Fig. 3,5,7,10,12,14,15,16 is too small.

It shows a full view of the elongation and the change in the arc mood. All mentioned images were replaced by a new one considering the font size, the resolution, and the notation.

Fig. 6 should be changed to the color presentation.

Response: It was modified accordingly. The resolution was extended, and some temperature contours were added too.

Table 1 fist line should be Cp (not mu_r) and second kappa (not k).

Response: It was modified accordingly

What can the reader learn from the amount of data presented? There is no discussion about parameter variation, besides the contact velocity and current.

This topic is almost new and therefore it is very complicated to gather everything in just one article. If you mean the relationship between the contact velocity and Thomson coil current or the variation in actuator parameter it was already published in [27]. The relation between the contact velocity and current is the matter of interruption performance and needs the simulation of Transient recovery voltage (TRV) slopes. it is already published in [28] shown in Fig 6 of the mentioned ref.

Is the arc finally interrupted or not?

As mentioned it needs the study of TRV and son on is the topic of another study published as “Dielectric Recovery of Ultrafast-Commutating Switches used for HVDC and Fault Current Limiting Applications” was already published in [28] figs 5. To clear this vague, the voltage of failure was omitted from Figure 16(a)

Are the arc roots moving or not?

section 2.7. the arc roots and the sheath model was added

Discussion. Since the sheath model is presented rudimental, it is not clear how the values of sheath voltages were obtained. If there is not a physical sheath model, how the sheath width was determined?

A simple model is utilized from [29, 30]

The explanation of the influence of arc length on arc parameters is partially misleading. It is well known that the longer the arc length the higher the voltage. Also, the cooling increases with the arc length. What is the novelty here???

the novelty is about the microscopic voltage drop that although the longer the arc length the higher the voltage but the voltage per unit is decreased against the increment in the cooling so this simple theory can't explain it but the other model definition with the plasma volume is a better explanation. it is already known that elongation increases the cooling and the Varc, total, but it decreases the arc cross-section. All these changes shall increase the resistance per unit length but according to Error! Reference source not found.(g) the resistance remains almost fixed and therefore the Vd per unit length inside the arc is decreased.

In conclusion, the manuscript has to be revised before publishing.

Many thanks for the detailed comments and please see the revised version

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

I think it can be acceptable after handling some typos and speaking errors.

Author Response

Dear Editor,

Dear referees,

Many thanks for your time, and valuable comments on our article. The comments helped us to improve our quality and be able to present our work in a better way. We appreciate it and please see our explanations and required responses hereinbelow of referee’s comments. The modified version of traceable changes (track change in MS-Word) in addition to the clean version of the modified article is attached to prepare a better follow-up.

REFEREE REPORT(S):

Referee: 2
I think it can be accepted after handling some typos and speaking errors.

Many thanks and we applied machine check and also review by a professional to modify the language and clearing the typo errors including a few double spacing, etc.

Reviewer 3 Report

The paper was improved. The suggestions were partially implemented.

I have just few additional remarks.

Acronyms Ca and MC denotes normally Calcium (chemical element) and Monte-Carlo (method), correspondingly. Please replace your acronyms for Cathode and Moving Contact by full words.

Lines 58-59. No, with growing pressure the thermal conductivity do not decrease, it is increasing. Also, the meaning of the sentence is not clear.

Line 60 Figure 1 shows something else, please correct.

Equation (2) has a dz as multiplier for all terms. This make no sense, mathematically as well as physically. Correct or remove.

Author Response

Dear referee,

Many thanks for your time, and valuable comments on our article. The comments helped us to improve our quality and be able to present our work in a better way. We appreciate it and please see our explanations and required responses hereinbelow of referee’s comments. The modified version of traceable changes (track change in MS-Word) in addition to the clean version of the modified article is attached to prepare a better follow-up.

REFEREE REPORT(S):

The paper was improved. The suggestions were partially implemented. I have just a few additional remarks.

Acronyms Ca and MC denotes normally Calcium (chemical element) and Monte-Carlo (method), correspondingly. Please replace your acronyms for Cathode and Moving Contact by full words.

Many thanks for the detailed comments and it was replaced as well as the An for the anode.

Lines 58-59. No, with growing pressure the thermal conductivity does not decrease, it is increasing. Also, the meaning of the sentence is not clear.

We mean at the arc quenching range i.e below the 4-5 kK which is vital for the current interruption and at it is clear for the air up to 100 bar calculated in PLASIMO® it is decreasing in this range. It was modified accordingly in the text.

Line 60 Figure 1 shows something else, please correct.

It was modified accordingly

Equation (2) has a dz as a multiplier for all terms. This makes no sense, mathematically as well as physically. Correct or remove.

Many thanks and dz was removed

Author Response File: Author Response.pdf