Numerical Study on Bubble Rising in Complex Channels Saturated with Liquid Using a Phase-Field Lattice-Boltzmann Method

Round 1

Reviewer 1 Report

The authors present interesting numerical research concerning the bubble rising in complex channels of different geometries saturated with liquid. A phase-field lattice-Boltzmann method is successfully applied within the research. The paper is well organized and easy to read. The proposed title of the paper is self-descriptive and clearly represents the content of the manuscript. The abstract provides a clear view of the content of the paper including a brief introduction to the presented research as well as the most significant information concerning the obtained results. The introduction section too briefly describes the physical and technical background of the analyzed issues and thoroughly presents the literature review - I would recommend to slightly extend the first one. The numerical setup and validation are properly described. The results and discussion section is well written and presents the high level of scientific soundness. The results are adequately discussed. The conclusions are correctly drawn based on the obtained results.

Therefore, I recommend accepting the paper after updating the introduction section with a more detailed description of the physical and technical background of the analyzed issues and emphasizing the novelty of the carried out research.

Author Response

Response to Reviewer 1:

The authors present interesting numerical research concerning the bubble rising in complex channels of different geometries saturated with liquid. A phase-field lattice-Boltzmann method is successfully applied within the research. The paper is well organized and easy to read. The proposed title of the paper is self-descriptive and clearly represents the content of the manuscript. The abstract provides a clear view of the content of the paper including a brief introduction to the presented research as well as the most significant information concerning the obtained results. The introduction section too briefly describes the physical and technical background of the analyzed issues and thoroughly presents the literature review - I would recommend to slightly extend the first one. The numerical setup and validation are properly described. The results and discussion section is well written and presents the high level of scientific soundness. The results are adequately discussed. The conclusions are correctly drawn based on the obtained results.

Therefore, I recommend accepting the paper after updating the introduction section with a more detailed description of the physical and technical background of the analyzed issues and emphasizing the novelty of the carried out research.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript is interesting and focuses on the numerical simulation of packed multiphase beds. The manuscript is of high quality. However, I would like to point out some parts to be improved before publication.

1. What is the difference between the lattice Boltzmann method, and lattice Boltzmann model? The authors use different abbreviations for lattice Boltzmann, LB model, LB method, LBM, LB equations. Please check it and use uniform abbreviations.
2. It should be stated that the density difference mainly comes from the gas/liquid ratio.
3. Please avoid lumped references; all referenced articles should be assessed with at least half a sentence.
4. The geometry and boundary conditions should be explicitly shown.
5. A mesh independence study should be added. I know when using DNS, there is a limit of the minimum and maximum mesh size; however, in most of the cases, there is room for checking the mesh independence.
6. In packed industrial beds the voidage is often around 0.4-0.5. You have the closest value in Figure 13 a). What is the industrial relevance of other cases?
7. "Flow pattern Aw (ReGr = 100, Eo = 10)" for example. What Aw abbreviation means. The same applies to all abbreviations.
8. Figure 14 and 15 are hard to understand. How were those graphs calculated?
9. A notation should be added.

I think after addressing these comments, the article can be accepted.

Author Response

Response to Reviewer 2:

The manuscript is interesting and focuses on the numerical simulation of packed multiphase beds. The manuscript is of high quality. However, I would like to point out some parts to be improved before publication.

1. What is the difference between the lattice Boltzmann method, and lattice Boltzmann model? The authors use different abbreviations for lattice Boltzmann, LB model, LB method, LBM, LB equations. Please check it and use uniform abbreviations.

Response: Thank you for pointing out our shortcomings about the inconsistent use of abbreviations. For your first question, we think that the research scopes involved in lattice Boltzmann method and lattice Boltzmann model are different, and their relationship is subordinate. The lattice Boltzmann method is one of the direct numerical simulation methods, which includes many lattice Boltzmann models. When lattice Boltzmann method is used for simulation, different lattice Boltzmann models can be selected to deal with different problems. Taking the multiphase flow problem as an example, as listed in the second paragraph of the Introduction, four types of lattice Boltzmann models are often applied in multiphase systems.

We are ashamed of the confusion caused by the various abbreviations. There are three abbreviations we used in the original manuscript about the phrase "lattice Boltzmann": LBM (abbreviation for "lattice Boltzmann method"), LB model (abbreviation for "lattice Boltzmann model") and LBE (abbreviation for "lattice Boltzmann equation"). And these three abbreviations often appear in the literatures about lattice Boltzmann method. After careful checking, we are sorry that the abbreviations "LB method" and "LB equations" you mentioned were not found in our original manuscript.

According to your suggestion, we rechecked all the abbreviations in the manuscript and revised some inappropriate ones. The modifications are distributed in the Abstract, Keywords, the third and fourth paragraphs of the Introduction, the first paragraph of the Section 2, the title of the Section 2.1, the first and last paragraphs of the Section 2.1.1, the second paragraph of the Section 3.2 and the first paragraph of the Section 5 with highlighted yellow marks.

 

2. It should be stated that the density difference mainly comes from the gas/liquid ratio.

Response: Thanks for your suggestion. In response to your suggestion, we have stated the source of large density difference in packed beds, which is mainly reflected in the fourth line of the Abstract and the thirteenth line of the first paragraph of the Introduction in our revised manuscript. And the modified contents are marked in prominent yellow for easy discovery.

 

3. Please avoid lumped references; all referenced articles should be assessed with at least half a sentence.

Response: Thanks for your suggestion. According to the suggestion, several places in Introduction section where lumped references appear have been processed by reducing citations, the revised citations are marked in yellow. But we apologize that the situation of lumped references still exists in the third paragraph of the Introduction and other sections, because it may appear a bit redundant if every referenced article is assessed in some contexts and it seems to be common in general research papers. The serial numbers of References in the entire article have also been adjusted concomitantly due to the reduction of lumped citations.

 

4. The geometry and boundary conditions should be explicitly shown.

Response: Thanks for your suggestion. The geometry and boundary conditions had been described in detail in Section 4.1 of the original manuscript. In order to present these information more clearly and intuitively, the computational domain schematics of two channels containing more explicit geometry and boundary conditions are updated, as depicted in Figure 4 of the revised manuscript. The title of Figure 4 is highlighted in yellow.

 

5. A mesh independence study should be added. I know when using DNS, there is a limit of the minimum and maximum mesh size; however, in most of the cases, there is room for checking the mesh independence.

Response: Thank you for pointing out our omission about grid independence. Actually, the work on grid independence had been done before the major simulation studies, but it was not included in the original manuscript limited by the article length.

In response to your suggestion, an updated Section 4.2 entitled "Grid independence" has been inserted into the manuscript, which contains two paragraphs of text and an updated Figure 5. The Section 4.2 describes the process and results of the grid independence test. Correspondingly, the subtitle numbers in Section 4 and the figure numbers in the following text have been postponed and revised. The added Section 4.2 and the revised subtitle numbers and figure numbers are marked in yellow.

 

6. In packed industrial beds the voidage is often around 0.4-0.5. You have the closest value in Figure 13 a). What is the industrial relevance of other cases?

Response: Thanks for your practical thinking about our results. At present, the voidage of the two types of channels we studied varies from 0.5 to 0.8 approximately due to the variations of the channel widths. The industrial packed beds corresponding to this voidage range include the fixed bed and the slightly-expanded bed, etc.

Unlike the fixed bed with lower voidage, the slightly-expanded bed refers to the bed where the packings have a certain range of expansion rates with the changes of gas and liquid flow velocities, which is commonly used in the industrial processes such as residue hydrogenation. Therefore, we think that most of our current simulation cases have industrial relevance to the slightly-expanded beds, based on some slightly-expanded bed experiments being conducted by our research group.

 

7. "Flow pattern Aw (Re_Gr = 100, Eo = 10)" for example. What Aw abbreviation means. The same applies to all abbreviations.

Response: Thanks for your helpful suggestion and example. For a clear explanation, we take "Aw" and "Bs" as contrasting examples, the subscripts "w" and "s" represent the wave vertical channel and S-shaped curved channel, respectively, while the capital letters "A" and "B" are used to distinguish different bubble flow patterns in the same channel. Based on this naming rule, the four bubble flow patterns in the wavy vertical channel are named Aw, Bw, Cw, and Dw, respectively, and the five flow patterns in the S-shaped curved channel are called As, Bs, Cs, Ds and Es, respectively.

A brief explanation of the abbreviations for bubble flow patterns is inserted in the second paragraph of Section 4.8 in the revised manuscript with a highlighted yellow mark.

 

8. Figure 14 and 15 are hard to understand. How were those graphs calculated?

Response: Thanks for your careful thinking about our results. Figures 14 and 15 (Figures 15 and 16 in the revised manuscript) show the division of bubble flow patterns in our original manuscript, which are helpful for the identification and regulation of bubble flow patterns in practical industry. In Figure 14, flow patterns are distinguished by changing Re_Gr and Eo. And in Figure 15, flow patterns are distinguished by changing channel structures.

As for the calculation process of these two flow pattern diagrams, taking Figure 14 as an example, the channel widths are fixed at L/D_b = 0.719 and H/D_b = 0.875 in the wavy vertical channel and L/D_b = 1.344 and H/D_b = 0.875 in the S-shaped curved channel, then the Re_Gr and Eo are regularly changed within the Re_Gr range of 0 ~ 350 and Eo range of 0 ~ 250 in each simulation, and the corresponding bubble flow patterns under different Re_Gr and Eo conditions can be obtained from the simulation results. Thus the scatter plots of Figure 14 can be drawn, in which different point types represent different bubble flow patterns.

  Similarly, by changing the channel widths under the same Re_Gr and Eo conditions, the different bubble flow patterns can be obtained in the channels with different widths, and then the corresponding flow patterns are marked in the scatter plots, as shown in Figure 15.

 

9. A notation should be added.

Response: Thanks for your suggestion. A summary of symbols has been added before the References in the revised manuscript, in which the main symbolic variables that appear in the manuscript and their meanings are listed in detail. It should be explained that since most symbols are dimensionless variables used in LBM, the information of symbol units is not given in the symbol summary. For easy review, the added symbol summary is marked as highlighted yellow.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The paper has been improved since my previous review and therefore it can attract more attention from the readers. My previous doubts have been adequately addressed by the authors. Therefore I recommend to accept it in the current form.

Reviewer 2 Report

The authors answered my questions, so I think the manuscript can be accepted.