The Effect of Electrode Geometry on Excited Species Production in Atmospheric Pressure Air–Hydrogen Streamer Discharge

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors investigate influence of electrode configuration on the streamer breakdown and excited species formation in hydrogen/air mixture by means of two-dimensional axisymmetric fluid modelling. Three cases, with plane-plane, pin-plane and pin-pin electrode geometry, were investigated. The simulation conditions, i.e., gap length and the applied voltage, have been tailored to ensure approximately the same electric field in the gap. The authors then compare the temporal evolution of the streamer development between the electrodes and analyse the energy input to the gas and its effect on the hydrogen and oxygen dissociation in three different geometries. Although not entirely new, the results illustrate how different electrodes can affect the energy input in the gases relevant for the combustion, which is of the interest for the community. From technical point of view, the authors gave a good overview of the modelling studies reported in the literature, and the manuscript is structured and written well (with a few typographical errors in the manuscript). However, some concerns regarding the chosen condition and their effect on the results and conclusions need to be clarified and discussion improved before I can recommend the manuscript for publication. These concerns will be discussed in specific remarks.

Specific remarks:

• Although the authors try to keep the ratio of the applied voltage to the shortest distance constant in all cases (by adjusting the gap and voltage), I am unsure this will make the conditions in all three cases equal. The shape of the electrodes will surely affect the electric field, thus the inception and streamer propagation. This can be clearly seen from observed streamer development. Moreover, with this choice, the authors effectively reduced the gap for latter two cases, which might affect the conclusions on the energy input (since it was calculated as a volume integral). I would suggest to authors to try to keep at least one parameter constant (e.g., keep the same distance and change the voltage accordingly, or other way around) and repeat the analysis to see how it affects the results and conclusions. In my opinion, using the same distance (and adjusting the voltage) would at least make easier comparison of the streamer propagation and ensure the same streamer length at the end of the simulation.
• I would suggest to authors to compare the propagation of the streamers by plotting the spatiotemporal evolution of the number density of electrons and electric field along the axis of symmetry (as in the streak-imaging photos). These figures would be a good addition to the already presented spatial profiles.
• The comparison of the time evolution of the discharge energy is affected by the chosen conditions, i.e., different gaps. The evolution of the energy increase in plane-plane geometry seem to originate from the slower streamer development and the larger volume due to a larger gap length. The authors need to extend this analysis and check their conclusions by simulating streamer development for the same gap lengths and voltage adjusted accordingly.
• The methods of determination of the G-factor and energy density are not entirely clear. Was the G-factor determined from eqs. (6) and (7)? How was energy density determined? Was additional electron energy balance equation solved for electron energy density?
• I would suggest authors to change the title, since the excited states have been investigated indirectly. In my opinion, the focus is more on the streamers in hydrogen/air mixture in general.
• The same times as in Figures 1-3 should be used when comparing energy densities in Figure 7?
• Some of the figures (Figure 1-4 and 7) and equations (eqs. 8-11) are shifted to the left compared to the text. It did not cut off a part of the figure (except in case of Figure 7, where the top and bottom labels are cut off slightly) or equations, but it still needs to be corrected.
• Page 3, line 102: I would suggest “elementary charge” instead of “unsigned electron charge”.
• Page 3, line 116: I am unsure if the term “gradient” should be used for the field. I would suggest “steep density gradients and strong field changes” instead.
• Although well written, there are still some typographical errors throughout the manuscript (e.g., page 1, line 37: “are formation”, page 3, line 131: it should be “plane” instead of “pane”, open parenthesis in y-axis label in Figure 4b, and a few more), which need to be corrected.
• Some references are incomplete, i.e., missing the page numbers. Additionally, the style should be the same for all of the references.

Author Response

see attached

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper investigates how electrode geometry (plane-plane, pin-plane, and pin-pin) influences streamer formation and radical production in atmospheric pressure hydrogen–air mixtures using a fluid model. The results show that geometry affects the electric field distribution and energy deposition, while the radical production efficiency (G-factors) remains similar across cases. However, the authors should consider the following suggestions:

1. Only one set of dimensions is considered for each electrode geometry. Since geometry is the focus of the paper, it would be valuable to include a discussion of how variations in gap distance, tip radius, or curvature might influence the generality of the conclusions, even if additional simulations are not performed.
2. The paper concludes that radical yields depend only on deposited energy, with little effect from electrode geometry. However, high-field regions near pin tips and uniform fields in plane-plane gaps could alter the electron energy distribution function (EEDF). The authors should clarify why such differences do not affect the G-factors and specify the conditions under which this conclusion remains valid.
3. Photoionization is approximated by adding a constant low-density background charge, and earlier studies are cited to justify that this simplification has little impact on streamer development and radical generation. However, most of these references concern N₂ or air discharges, where the photoionization mechanism is well established. In the present H₂/air mixture, the O₂ concentration is lower and H₂ does not contribute significantly to photoionization. The authors should explain why this approximation remains valid in their system or discuss its possible limitations.
4. In Fig. 5, discharge energy is shown for different geometries but over different time ranges, which makes direct comparison unclear. The authors should clarify how the time origin is defined and consider using a common physical reference (e.g., by streamer front reaching L/2) to enable more consistent cross-geometry comparison.
5. The fluid model is based on the local field approximation (LFA). Since LFA can overestimate high-energy electrons in regions with steep field gradients and thus affect radical yields, the authors should clarify why LFA was chosen and discuss whether this approximation is reliable for their system.

Author Response

see attached file

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I commend the authors’ attempt to answer my comments and for making changes to the manuscript. The authors have addressed most issues, clarified some uncertainties, fixed typos and corrected the references. Specifically, the authors repeated calculations for one fixed distance for all three cases (making comparison easier), introduced streak image-like spatiotemporal profiles and explained the method for determining the G-factor. It is now easier to follow the presented results and their reasoning. There are still a few minor issues to be corrected, after which I believe the manuscript can be accepted.

Minor remarks

Page 4, lines 158 and 159: I am unsure if it is just the way of writing, but it seems this sentence implies only one geometry is considered. However, the analysis considers three configurations. An optional suggestion is to clarify this statement in the sentence.

Figure 4: I am still unsure why the authors chose to use different scales for this comparison. Using a logarithm scale for densities and the electric field, with the same range, would illustrate the difference between the three cases better. Again, this suggestion is optional. On the other hand, a higher temporal resolution for the displayed data would be beneficial to avoid the appearance of discrete steps in these plots.

Figures 1-10: The font size in the figures is still too small. Enlarging the font would improve readability.

Figure 7 caption: There is an extraneous open parenthesis in the figure caption that needs correction.

Author Response

see attached.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Authors have addressed all my concerns,  i have no other comments.

Author Response

Thank you for reviewing the manuscript.