Comparison of Drag Force Models in Liquid–Solid Mixed Batch Simulations by Observing Off-Bottom Suspension Flow Patterns
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis article presents a new approach to evaluate the performance of drag force models in numerical simulations of liquid-solid suspensions in mixing tanks. The authors propose to use an existing experimental technique based on observing the flow patterns formed in the settled particles below a full bottom suspension velocity. These patterns serve as indirect indicators of the behavior of the system. To make the visual readouts precise and consistent, computer image analysis is used to process the images of both the experimental and numerical results. The utility of defining a geometric p-norm for the resulting visuals is demonstrated. Finally, the results obtained from preliminary LES CFD simulations using various drag force models are compared with experimental data on a concrete example to demonstrate the applicability of the method in practical engineering applications.
The article presents an innovative and potentially powerful method to evaluate the accuracy of drag force models in liquid-solid mixing simulations. In particular, the use of computer image analysis and geometric p-norm definition to compare experimental and numerical results reduces subjective evaluations and offers a more quantitative comparison opportunity.
However, there are some points where the article needs more clarity and elaboration.
Experimental Setup and Procedure:
The article needs more details about the experimental setup. Parameters such as the dimensions of the mixing tank used, the type and dimensions of the impeller, particle properties (size, density, shape), and fluid properties (density, viscosity) should be clearly stated.
Procedural steps on how the experiments were performed (e.g. particle loading, mixing speed settings, image acquisition frequency and duration) should be explained in more detail. The phrase "Established experimental technique" is not sufficient; even if references are given, the reader should be able to understand the method from the main text.
Image Analysis and p-norm Definition:
Exactly how the computer image analysis is performed, which algorithms are used (e.g. edge detection, segmentation), and how the p-norm definition is mathematically formulated (by equation or graphical diagram) should be explained in more detail. Since this section is the methodological core of the article, it is vital that the reader fully understands this section.
Can more information be provided on the range in which the p-norm values ​​vary and the effects of different p-norm values ​​on the patterns? For example, what type of pattern is associated with a particular p-norm value?
CFD Simulation Details:
More information is needed on the LES (Large Eddy Simulation) modeling. Technical details such as the LES model used (e.g. Smagorinsky, dynamic Smagorinsky), the cellular network structure (mesh) and its density, time step size, boundary conditions, and convergence criteria should be provided.
What are the drag force models compared? The article only mentions "several drag force models". The mathematical formulations of these models, or at least their names and references, should be clearly stated. This is critical for readers to understand how the results are related to different models.
Presentation and Discussion of Results:
The phrase "Preliminary LES CFD simulations" suggests that the results are preliminary. Could a more comprehensive case study or simulation results with a wider range of parameters be presented to demonstrate the applicability of the paper to practical engineering applications?
Is the comparison between experimental and simulation results based solely on p-norm values? Visual comparisons (side-by-side images of experimental and simulation patterns) would greatly facilitate reader understanding.
Clearer results should be presented on which drag force models perform better under which conditions, and physical explanations for these results should be provided. It should be discussed why certain models capture certain patterns better.
What are the limitations of the method? For example, how does the applicability of this method change as particle concentration increases or the particle size distribution becomes wider?
References:
"Chem. Process Eng." in reference 41 The journal year is stated as "2005" but no volume/page number. Full reference information should be provided.
While some references (e.g. 36-40) appear to elaborate on the topic directly referred to in the text, it could be more clearly stated how they contribute to the overall argument of the article.
Overall, the article presents an original and interesting methodology. The elaborations and clarifications mentioned above would significantly increase the scientific value and clarity of the article.
Author Response
Dear reviewer,
We would like to thank you for your objective and thorough insights. We’ve made sure to address all your concerns individually under your review structure. We have also had the article's English checked by another qualified person on our department to make sure the language quality is sound.
Experimental Setup and Procedure:
Comment 1: The article needs more details about the experimental setup. Parameters such as the dimensions of the mixing tank used, the type and dimensions of the impeller, particle properties (size, density, shape), and fluid properties (density, viscosity) should be clearly stated.
Response 1: The inquired information was stated in the original version in section ‘2.1. Setup of Experiment’ and shown in Figure 5a, b). However, we agree that it was presented somewhat unclearly. To address this, we slightly restructured the paragraphs and moved Figure 5a, b) nearer to relevant text in this section.
Comment 2: Procedural steps on how the experiments were performed (e.g. particle loading, mixing speed settings, image acquisition frequency and duration) should be explained in more detail. The phrase "Established experimental technique" is not sufficient; even if references are given, the reader should be able to understand the method from the main text.
Response 2: We agree this should be edited. We added the missing information to ‘2.1. Setup of Experiment’, moved information concerning the procedure from beginning of ‘3. Results’ to ‘2.1. Setup of Experiment’ and made the text more coherent.
Image Analysis and p-norm Definition:
Comment 3: Exactly how the computer image analysis is performed, which algorithms are used (e.g. edge detection, segmentation), and how the p-norm definition is mathematically formulated (by equation or graphical diagram) should be explained in more detail. Since this section is the methodological core of the article, it is vital that the reader fully understands this section.
Response 3: Thank you for this comment. I agree that this section is where the article is at its strongest and contributes the most. I elaborated on how the p-norm is implemented and how the characteristic values are computed in section ‘2.3. Visual comparison method’. Relevant references have been added as well.
Comment 4: Can more information be provided on the range in which the p-norm values ​​vary and the effects of different p-norm values ​​on the patterns? For example, what type of pattern is associated with a particular p-norm value?
Response 4: Elaborations on this were included together with the changes described in response 3.
CFD Simulation Details:
Comment 5: More information is needed on the LES (Large Eddy Simulation) modeling. Technical details such as the LES model used (e.g. Smagorinsky, dynamic Smagorinsky), the cellular network structure (mesh) and its density, time step size, boundary conditions, and convergence criteria should be provided.
Response 5: We have added the required information to sections ‘2.2.1. Continuum model’ and ‘2.2.2. DEM model’. Together with this, we’ve decided to remove the former section ‘2.2.3. Discussion on parameter independence’ and distribute its contents to 2.2.1. and 2.2.2. to ensure more concise reading.
Comment 6: What are the drag force models compared? The article only mentions "several drag force models". The mathematical formulations of these models, or at least their names and references, should be clearly stated. This is critical for readers to understand how the results are related to different models.
Response 6: We’ve made sure to re-state this information more clearly by abandoning the simplified names used in the software and better referencing to their equations presented in Table 1 throughout the article. The models are now clearly and relevantly declared in the opening paragraph of section ‘2. Experimental and numerical setup and methods’ and in section ‘2.2. DEM model’ to avoid any confusion.
Presentation and Discussion of Results:
Comment 7: The phrase "Preliminary LES CFD simulations" suggests that the results are preliminary. Could a more comprehensive case study or simulation results with a wider range of parameters be presented to demonstrate the applicability of the paper to practical engineering applications?
Response 7: We worded the sentence poorly. The experiments require quite high loadings of fine particles for the shapes to reliably emerge. Simulating such high numbers of DEM particles proved to be very difficult on our hardware, despite it being quite high-end. Therefore, we had to adapt a lot of approximations in comparison to other numerical studies carried out in contemporary literature, as discussed in section ‘2.2. DEM model’. We wanted to be very transparent about this, hence used the phrase ‘Preliminary LES CFD simulations’. We revised this (introduction to section 2.2) and worded it better. Otherwise, we believe the amount of experimental and numerical work done fits the scope of the article.
Comment 8: Is the comparison between experimental and simulation results based solely on p-norm values? Visual comparisons (side-by-side images of experimental and simulation patterns) would greatly facilitate reader understanding.
Response 8: Yes. We revised the ‘results’ section to make clearer how the comparison is made. Side-by-side images of experimental and simulation patterns between experiment and simulation are presented on Figures 8 and 9 and on newly added Figure 11.
Comment 9: Clearer results should be presented on which drag force models perform better under which conditions, and physical explanations for these results should be provided. It should be discussed why certain models capture certain patterns better.
Response 9: We wanted to refrain from making bold definitive statements on this, since the simulations cannot be as rigorous as would be deserved due to computational limitations on these cases, as was described in Response 7. We therefore wanted to keep the conclusions more conservative. However, based on encouraging reviews, we extended the discussion by several paragraphs where we discuss the implications that we can be certain about. This is done in sections ‘3. Results’ and ‘4. Conclusions’.
Comment 10: What are the limitations of the method? For example, how does the applicability of this method change as particle concentration increases or the particle size distribution becomes wider?
Response 10: The limitations of this method have been summarized in the last paragraph of the opening to section ‘2.3. Visual comparison method’.
References:
Comment 11: "Chem. Process Eng." in reference 41 The journal year is stated as "2005" but no volume/page number. Full reference information should be provided.
Response 11: We have checked and fixed any formal mistakes in the references.
Comment 12: While some references (e.g. 36-40) appear to elaborate on the topic directly referred to in the text, it could be more clearly stated how they contribute to the overall argument of the article.
Response 12: Articles are properly cited where relevant information from them is presented. While elaborations could be made on how further they relate to our work, we believe it would bloat the introduction section beyond reasonable proportions.
We once again thank you for your review and hope you find our revisions satisfactory.
Best regards,
Filip Randák
Reviewer 2 Report
Comments and Suggestions for AuthorsGeneral Comments
Interesting work in a field of research still open despite the numerous studies present in the literature. This work is carried out with a good methodology, despite this there are numerous inaccuracies that, in my opinion, should be revised.
Specific comments
- I would better explain what is the innovative aspect of the work compared to what is already present in the literature.
- Bibliographic references for some equations are missing. Please check
- I think it is better to summarize the introduction by focusing on the problem studied and rather extend the results (if significant) that the authors often say not to report in full for brevity.
- Line 307 – 308: “Many factors proven to influence off-bottom suspension are simplified.” It would be better to make them explicit and discuss them.
- There is some confusion, for example in the results table 3 is reported of the conditions in which they conducted the experiments, it does not seem to me the correct section. The authors should review the organization of the document
- I think that from Figure 10 it would be possible to comment on the various models and define their limits and scope of applicability, but this is not done.
- The authors should say how they calculated the mean deviation in table 5.
- The code name is repeated too many times. I think one is enough, this work is not an advertisement but a scientific paper
- Authors should add references where the various compared models are used.
Author Response
Dear reviewer,
We appreciate the insights provided. We found them very beneficial and addressed them all individually to improve the value of the article:
Comment 1: I would better explain what is the innovative aspect of the work compared to what is already present in the literature.
Response 1: We agree. We have decided to rewrite the abstract to better reflect what the strongest original contributions are.
Comment 2: Bibliographic references for some equations are missing. Please check
Response 2: We revised the text and proofed the citing. Table 1 has received an extra column re-stating the references to provide better orientation. References have also been added to other equations in section ‘1. Introduction’.
Comment 3: I think it is better to summarize the introduction by focusing on the problem studied and rather extend the results (if significant) that the authors often say not to report in full for brevity.
Response 3: We left out only large figures analogous to Figures 8 and 9 for solid fractions 2,5% and 10% comparing the full visual results, as they showed similar behaviour, brought little new insights to the reader and their inclusion made the text less cohesive in our opinion. We have made sure to better declare this in the paragraph preceding the Figures 8 and 9. The data for 2,5% and 10% are however still included in the final comparison of figure 10 and not left out. Otherwise, we are quite happy with the scale of research conducted in section ‘1. Introduction’ and believe it is relevant.
Comment 4: Line 307 – 308: “Many factors proven to influence off-bottom suspension are simplified.” It would be better to make them explicit and discuss them.
Response 4: We agree. We have added parentheses listing the simplifications and referred to the section ‘2.2. DEM model’ where they are discussed deeper.
Comment 5: There is some confusion, for example in the results table 3 is reported of the conditions in which they conducted the experiments, it does not seem to me the correct section. The authors should review the organization of the document
Response 5: We agree. We have moved the opening of section ‘3. Results’ to ‘2. Experimental and numerical setup and methods’. The article is now better organized.
Comment 6: I think that from Figure 10 it would be possible to comment on the various models and define their limits and scope of applicability, but this is not done.
Response 6: We wanted to avoid drawing bold general conclusions, since our simulations cannot account for all involved phenomena due to computational limitations and we cannot reach the level of certainty present in other studies that can use fewer DEM particles. However, based on encouraging reviews, we extended the section ‘3. Results’ by several paragraphs where we discuss the implications we can be certain about. Section ‘4. Conclusions’ was also similarly edited.
Comment 7: The authors should say how they calculated the mean deviation in table 5.
Response 7: The paragraph preceding Table 5 and Table 5 itself have been edited to more clearly describe how the deviations were calculated.
Comment 8: The code name is repeated too many times. I think one is enough, this work is not an advertisement but a scientific paper
Response 8: That is a good point. We have removed the unnecessary reiterations with good effect on the conciseness of the text.
Comment 9: Authors should add references where the various compared models are used.
Response 9: Very good point. This has been thoroughly addressed. References have been added to both text and figures. We have also decided to abandon the software’s simplified nomenclature (‘Free particle’ or ‘Packed bed’ model) and reference the models consistently by their author’s names and with proper references to their works.
We thank you for reviewing our article and hope you’ll be satisfied with our replies.
Best regards,
Filip Randák
Reviewer 3 Report
Comments and Suggestions for AuthorsDear authors,
your work is interesting and relevant: the comparison of CFD DEM simulations with experimental off-bottom suspension patterns using image analysis and p-norm geometry. Please, find this issues as a constructive path for improvement.
Your abstract is vague. Could you say clearly what is new? You do good work, but could you show what part is your contribution?
The visual method depends on threshold choice. You explain it, but could you show sensitivity to this? Could you test if the result changes with +-10% in threshold?
You define p-norm shapes well. But could you test how sensitive the final result is to p? Could you test error vs. p variation?
You show average errors. But could you show local mismatch? Could you add an example with experimental vs simulated overlay?
DEM simplifications are well explained. But could you show one test with higher resolution (e.g. without grouping) to prove it’s safe?
Image conditions (light, opacity) are chosen visually. Could you show how much they influence the result? Could you test consistency if changed?
Tank you and best regards,
Author Response
Dear reviewer,
we appreciate the thorough review of our article and your pleasant feedback. We found all your notes very helpful and made sure to address them individually:
Comment 1: Your abstract is vague. Could you say clearly what is new? You do good work, but could you show what part is your contribution?
Response 1: This is an important point and has been raised by another reviewer as well. We have decided to rewrite the abstract to better reflect what the strongest original contributions are. The abstract is now sounder.
Comment 2: The visual method depends on threshold choice. You explain it, but could you show sensitivity to this? Could you test if the result changes with +-10% in threshold?
Response 2: The threshold choice is a very complex issue. Using various thresholds simultaneously could provide description of how much the shapes fluctuate in time and deeper insights into the hydrodynamics. Despite this, we believe it is beyond the scope of this article and would complicate it unnecessarily. Setting the threshold halfway is the most natural way to average these time fluctuations.
Response 3: You define p-norm shapes well. But could you test how sensitive the final result is to p? Could you test error vs. p variation?
Comment 3: We agree this should be elaborated on. Discussions on the influence of the found p value on each shape have been added to section ‘2.3.3. Fitting the shapes’ alongside further elaborations suggested by another reviewer.
Comment 4: You show average errors. But could you show local mismatch? Could you add an example with experimental vs simulated overlay?
Response 4: That is a good idea. Figure 11 has been added to ‘3. Results’ that displays overlays for a chosen case to visualize local mismatch in detail. We found this really highlights the core ideas of the article.
Comment 5: DEM simplifications are well explained. But could you show one test with higher resolution (e.g. without grouping) to prove it’s safe?
Response 5: This has been checked before the simulations were taken – our setup came as a compromise between computability and parameter independence, with the results varying acceptably compared to usual errors associated with visual methods.
Comment 6: Image conditions (light, opacity) are chosen visually. Could you show how much they influence the result? Could you test consistency if changed?
Response 6: We agree this is a strong issue – we have added Figure 13 to section ‘3. Results’ to show how simulations results are sensitive to opacity. We discuss the influence of this parameter and possible remedies for future research.
We hope you found our answers satisfactory.
Best regards,
Filip Randák
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors answered all my questions, thanks.
Author Response
We are happy to hear that! Thank you for the thorough review.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors' replies are satisfactory and I think that now the work is improved and suitable for publication.
Author Response
We agree that the work has improved. Thank you for the insightful suggestions.
Reviewer 3 Report
Comments and Suggestions for AuthorsDear authors,
Thank you very much for your answers! I just have one small comment, which I hope I am not bothering you more.
Regarding your reply to Comment 2: I understand that including many threshold values could complicate the article. However, I still believe that a small sensitivity test (for example, ±10%) would add clarity without overcomplicating the work. Even a single figure or short note in the supplementary would be enough to show that the method is robust.
Thank you again for your effort and for considering this final suggestion.
Best regards,
Author Response
Dear reviewer,
we decided to include the sensitivity study you suggest. A new sub-section 3.1 has been created under '3. Results' that contains the threshold sensitivity study together with the lighting sensitivity study suggested in your previous review. We believe this is an optimal solution that presents the useful data without overwhelming the structure too much.
While the method is sensitive to the threshold choice, the error is eliminated if the same approach is used for all the data - its only a matter of how the method is designed, as explained in the accompanying text.
Thank you for the suggestion. You aren't bothering us at all and we are happy to see your suggestion improve our work.
Best regards from the authors.
