Two-dimensional numerical studies of particle motion and deposition in the channel of diesel particulate filters

A numerical investigation on the soot laden flow of gas in a partial diesel particulate filter (PDPF) is presented based on solving the momentum equations for a continuous phase in the Euler frame and the motion equations for the dispersed phase in the Lagrangian frame. The interaction between the gas phase and the particles is considered as a one-way coupling for dilute particle concentration, while the interaction between particles and porous wall is implemented through user-definedsubroutines. To accurately track motion of nanoscale particles, the Brownian excitation and drag force as well as partial slip are taken into account in the particulate motion equation. Two methods are used to verify the gas flow model and reasonable agreements for both comparisons are observed. The effects of inlet velocity, wall permeability and particle size on the filtration efficiency and deposition distribution of the particles along with wall surface of inlet channel are quantitatively studied. The results show that (i) wall permeability plays the primary role in determining the filtration efficiency of PDPF, (ii) both upstream velocity and particle size have an effect on the initial deposition position of particles and (iii) filtration efficiency of PDPF is not markedly proportional to gas flow into inlet channels at a low wall permeability.

1) Introduction -The sentences "Accordingly, measures are needed to remove the deposited particles periodically. The process is known as the regeneration of DPF." should be substantiated by also citing the following work: Chemical Engineering Science, Volume 137, 2015, Pages 69-78.
2) Introduction -The authors wrote "Optimum structure of DPF requires low pressure drop and regeneration frequency.". This is surely true. However, in order to give a more complete picture, they should also highlight in the revised Introduction that, as recently reviewed (see, Catalysts, 2020, 10(11), Article number: 1307), the best strategy to lower both pressure drop and regeneration frequency is to operate a continuous filtration/regeneration process of catalystcoated DPFs.
3) Computational methodology and conditions -Are the computational results gridindependent? The authors should comment on this key issue. 4) Results and discussions/Conclusions -In the discussion, the practical impact of the results obtained in this work should be better pointed out. This should also be done in the section "Conclusions". 5) Conclusions -The authors should also give an outlook on future research work.
I'm willing to review the revised manuscript.

Decision letter (RSOS-211162.R0)
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Dear Dr Wang
The Editors assigned to your paper RSOS-211162 "2D numerical studies of particle motion and deposition in the channel of diesel particulate filters" have now received comments from reviewers and would like you to revise the paper in accordance with the reviewer comments and any comments from the Editors. Please note this decision does not guarantee eventual acceptance.
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We look forward to receiving your revision! Comment 2: The contents and some figures of this manuscript show high similarity with the reference 20 published in 2009. The authors need to rewrite and restructure most of their contents from Introduction to Section 3.1. Comment 6: The figures of the filtration efficiency are lack of the unit. The authors need to clarify if the unit is in % or not. The quality of the Figure 5,6,7 needs to be improved. It is hard to recognize the bar charts, it is suggested to use the line charts for different wall permeabilities. Comment 7: The authors need to carefully use the signal "-" in table 2. There are only 3 different particle sizes (20 100 1000) and 3 different upstream velocities (1 2 8). There are no enough variables to support the analysis. Comment 9: The fraction efficiencies of different velocities, different particle sizes are almost the same. The impact of an open outlet channel has significant impact on the local velocity field in this PDPF. The authors are suggested to present the velocity field (velocity contours in ANSYS Fluent) for a better understanding.
Comment 10: ANSYS Fluent is a commercial software, the authors need to cite it as required by the ANSYS company.
Reviewer: 2 Comments to the Author(s) The work concerns the modelling and simulations on the soot laden flow of gas in a partial diesel particulate filter. The research covered an important area and the article may be of interest to many readers. The manuscript has been correctly-structured. Accurate conclusions are presented, which are supported by research results which are original achievement of the Authors. This paper is well written and it is worth to be published in the journal "Royal Society Open Science" with the very minor modifications needed and indicated below: 1. The abstract is well-written, however the main conclusion in the abstract is too long and should be simplified. 2. Necessary references need to be marked, such as the references on Figure 1a and 1b(lines 31-32), and the assumption (2)(lines 31-32). 3. The meaning of each symbol in the formula should be indicated, such as P and μ in the equation (2); kw (permeability？) in the equation (5); Rep in the equation(10); dp in the equation(11); λ in the equation(12); kB and Δt in the equation(13), etc. 4. The description of "The continuity equation" in line 70 should be changed to "The continuity equation and momentum equation" 5. Some formulas are marked with incorrect symbol and need to be confirmed by the author. For example: ρ in formula (9) should be ρg? Re in formula (10) should be Rep? SCF in line 86 should be italic? 6. Some grammar errors need to be checked throughout, such as "A" in line 54 should be "An"; " has" in line 102 should be "have"; "was" in line 209 should be "is", etc. 7. The url should be added in the "()" in line 241. 8. Is the unit of the flow rate(kg/m3) correct?
Reviewer: 3 Comments to the Author(s) This is an interesting paper addressing an important issue. It can be considered for publication in Royal Society Open Science. However, I have the following comments that the authors should carefully implement in the revised manuscript before publication.
1) Introduction -The sentences "Accordingly, measures are needed to remove the deposited particles periodically. The process is known as the regeneration of DPF." should be substantiated by also citing the following work: Chemical Engineering Science, Volume 137, 2015, Pages 69-78.
2) Introduction -The authors wrote "Optimum structure of DPF requires low pressure drop and regeneration frequency.". This is surely true. However, in order to give a more complete picture, they should also highlight in the revised Introduction that, as recently reviewed (see, Catalysts, 2020, 10(11), Article number: 1307), the best strategy to lower both pressure drop and regeneration frequency is to operate a continuous filtration/regeneration process of catalystcoated DPFs.
3) Computational methodology and conditions -Are the computational results gridindependent? The authors should comment on this key issue. 4) Results and discussions/Conclusions -In the discussion, the practical impact of the results obtained in this work should be better pointed out. This should also be done in the section "Conclusions".

5)
Conclusions -The authors should also give an outlook on future research work.
I'm willing to review the revised manuscript.

===PREPARING YOUR MANUSCRIPT===
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Author's Response to Decision Letter for (RSOS-211162.R0) See Appendix A.

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? No

Recommendation?
Accept as is

Comments to the Author(s)
The revised manuscript is great, everything is well structured and clear. I would like to recommend the paper for acceptance on Royal Society Open Science.

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? No

Recommendation?
Accept with minor revision (please list in comments)

Comments to the Author(s)
The authors have addressed my comments in a satisfactory manner. Overall, the manuscript has been improved after revisions.
I have only one suggestion that could be implemented in the revised manuscript before publication. As ref.
We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Dr Wang
On behalf of the Editors, we are pleased to inform you that your Manuscript RSOS-211162.R1 "2D numerical studies of particle motion and deposition in the channel of diesel particulate filters" has been accepted for publication in Royal Society Open Science subject to minor revision in accordance with the referees' reports. Please find the referees' comments along with any feedback from the Editors below my signature.
We invite you to respond to the comments and revise your manuscript. Below the referees' and Editors' comments (where applicable) we provide additional requirements. Final acceptance of your manuscript is dependent on these requirements being met. We provide guidance below to help you prepare your revision.
Please submit your revised manuscript and required files (see below) no later than 7 days from today's (ie 08-Sep-2021) date. Note: the ScholarOne system will 'lock' if submission of the revision is attempted 7 or more days after the deadline. If you do not think you will be able to meet this deadline please contact the editorial office immediately.
Please note article processing charges apply to papers accepted for publication in Royal Society Open Science (https://royalsocietypublishing.org/rsos/charges). Charges will also apply to papers transferred to the journal from other Royal Society Publishing journals, as well as papers submitted as part of our collaboration with the Royal Society of Chemistry (https://royalsocietypublishing.org/rsos/chemistry). Fee waivers are available but must be requested when you submit your revision (https://royalsocietypublishing.org/rsos/waivers).
Thank you for submitting your manuscript to Royal Society Open Science and we look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. Reviewer: 1 Comments to the Author(s) The revised manuscript is great, everything is well structured and clear. I would like to recommend the paper for acceptance on Royal Society Open Science.

===PREPARING YOUR MANUSCRIPT===
Your revised paper should include the changes requested by the referees and Editors of your manuscript. You should provide two versions of this manuscript and both versions must be provided in an editable format: one version identifying all the changes that have been made (for instance, in coloured highlight, in bold text, or tracked changes); a 'clean' version of the new manuscript that incorporates the changes made, but does not highlight them. This version will be used for typesetting.
Please ensure that any equations included in the paper are editable text and not embedded images.
Please ensure that you include an acknowledgements' section before your reference list/bibliography. This should acknowledge anyone who assisted with your work, but does not qualify as an author per the guidelines at https://royalsociety.org/journals/ethicspolicies/openness/.
While not essential, it will speed up the preparation of your manuscript proof if you format your references/bibliography in Vancouver style (please see https://royalsociety.org/journals/authors/author-guidelines/#formatting). You should include DOIs for as many of the references as possible.
If you have been asked to revise the written English in your submission as a condition of publication, you must do so, and you are expected to provide evidence that you have received language editing support. The journal would prefer that you use a professional language editing service and provide a certificate of editing, but a signed letter from a colleague who is a native speaker of English is acceptable. Note the journal has arranged a number of discounts for authors using professional language editing services (https://royalsociety.org/journals/authors/benefits/language-editing/).

===PREPARING YOUR REVISION IN SCHOLARONE===
To revise your manuscript, log into https://mc.manuscriptcentral.com/rsos and enter your Author Centre -this may be accessed by clicking on "Author" in the dark toolbar at the top of the page (just below the journal name). You will find your manuscript listed under "Manuscripts with Decisions". Under "Actions", click on "Create a Revision".
Attach your point-by-point response to referees and Editors at Step 1 'View and respond to decision letter'. This document should be uploaded in an editable file type (.doc or .docx are preferred). This is essential.
Please ensure that you include a summary of your paper at Step 2 'Type, Title, & Abstract'. This should be no more than 100 words to explain to a non-scientific audience the key findings of your research. This will be included in a weekly highlights email circulated by the Royal Society press office to national UK, international, and scientific news outlets to promote your work.

At
Step 3 'File upload' you should include the following files: --Your revised manuscript in editable file format (.doc, .docx, or .tex preferred). You should upload two versions: 1) One version identifying all the changes that have been made (for instance, in coloured highlight, in bold text, or tracked changes); 2) A 'clean' version of the new manuscript that incorporates the changes made, but does not highlight them. --If you are requesting a discretionary waiver for the article processing charge, the waiver form must be included at this step.
--If you are providing image files for potential cover images, please upload these at this step, and inform the editorial office you have done so. You must hold the copyright to any image provided.
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At
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At
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We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.
Dear Dr Wang, I am pleased to inform you that your manuscript entitled "2D numerical studies of particle motion and deposition in the channel of diesel particulate filters" is now accepted for publication in Royal Society Open Science.
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On behalf of the Editors of Royal Society Open Science, thank you for your support of the journal and we look forward to your continued contributions to Royal Society Open Science. ANSWER: We accept this comment. We have re-organized the contents of boundary condition, please see the revised comments of boundary conditions. 6. The figures of the filtration efficiency are lack of the unit. The authors need to clarify if the unit is in % or not. The quality of the Figure 5,6,7 needs to be improved.
It is hard to recognize the bar charts, it is suggested to use the line charts for different wall permeabilities.
ANSWER: We accept this comment, this is a good suggestion. We re-checked the unit of filtration efficiency and found it was correct. It is true that the quality of the original Figure 5 There are no enough variables to support the analysis.
ANSWER: This is a very good suggestion. We are sorry for the mistake, we have corrected the errors, please see the revised Table. 2. 8. The data in Figure 6 ANSWER: We accept this comment. There are three operation conditions that may affect deposition distribution of particles in a single-channel PDPF studied in our paper, among which the wall permeabilitiy has the most primary effect. The dependence of the particle motion trajectory on upstream velocities and particle sizes is significant at a high wall permeability. However, this effect is alleviated in the cases of small permeabilities, leading to the difference in the fraction efficiencies of different velocities, different particle sizes being not remarkable. Indeed, the velocity field in a PDPF is very different from that in a regular DPF, which has been reported in detail in reference 14. Similar phenomena have also been observed in our numerical simulations. For a better understanding, we have presented the velocity field of continuous phase under two different wall permeabilities (the computational domain was scaled along the transverse direction using a scaling factor equal to 8).
Please see Figure 6.
10.ANSYS Fluent is a commercial software, the authors need to cite it as required by the ANSYS company.
ANSWER: We accept this comment. We cite the software, please see reference [19].

Reviewer: 2
Comments to the Author(s) The work concerns the modelling and simulations on the soot laden flow of gas in a partial diesel particulate filter. The research covered an important area and the article may be of interest to many readers. The manuscript has been correctly-structured.
Accurate conclusions are presented, which are supported by research results which are original achievement of the Authors. This paper is well written and it is worth to be published in the journal "Royal Society Open Science" with the very minor modifications needed and indicated below: 1. The abstract is well-written, however the main conclusion in the abstract is too long and should be simplified. ANSWER: We accept this comment. The main conclusion in the abstract has been simplified. Please see the revised part.