An Impact of the Discrete Representation of the Bubble Size Distribution Function on the Flow Structure in a Bubble Column Reactor
Round 1
Reviewer 1 Report
1. Page 3, line 16: The symbol “dib” is expressed by the volume fraction “alpha ib” and bubble number density “nib”. How is this formula derived?
2. Page 3: Eq.(2) is wrong if we look carefully. The denominator in the parenthesis in the exponential function should be “square of “sigma multiplied by root 2 pai”. It is difficult to express the formula by a sentence. So check and correct it.
3. Page 3: The present reviewer is confused by the words such as “monodisperse” and polydisperse” and the relation of such words with the standard deviation. Reviewer’s understanding is that the standard deviation is zero if BCD is monodisperse. This is the common understanding of the term "monodisperse". Probably the terms "monodisperse" and "polydisperse" in this paper differ from the terms the reviewer means. The terms “monodisperse” and “polydisperse” in this paper should be defined.
4. Page 4: Several factors which affect the force acting on the bubble are taken into account. Some formulas shown in this paper are based on the formulas for solid particles in the fluid. This work deals with the flow of gas bubble and liquid. So the following question arises. One of the most important factors is ignored in this paper. That is, velocity slip on the boundary between the gas phase and the liquid phase is ignored. Due to the velocity slip, the fluid drag on a gas bubble in the liquid is smaller than the drag on a solid particle in the liquid. Theoretical study of low Reynolds number flow shows that the drag on the bubble is two third of the drag on the solid particle. The present reviewer does not know whether there is a formula of the drag on the bubble at the intermediate or a large Reynolds number. At least, the authors should do paper survey. If no previous work of that subject is found. The authors should confess in this paper to ignore the effect of velocity slip.
5. Page 7: The symbol Sc is used in eq.(23). The present reviewer thinks that Sc is the Schmidt number. If he is right, describe so in the paper. Also the reviewer requests the authors to describe the reason of the value 0.8.
6. In the simulation, various empirical formulas are used. Some of them are established. However some others are not established but developing. In such a situation, reliability of computation results depends on the comparison with experimental data. In this paper the only experimental data for comparison is the work ref. 22. If possible, more comparison with measurement should be added. Adding measurement and comparison would increase the value of this paper .
Author Response
Dear Reviewer,
Thank you very much for your attention to our paper and useful remarks.
Point 1. Page 3, line 16: The symbol “dib” is expressed by the volume fraction “alpha ib” and bubble number density “nib”. How is this formula derived?
Response 1. The volume of a single bubble is Vib=π*dib3/6. The bubble number density nib is the total number of bubbles per cubic meter, therefore multiplying the bubble volume by the number density we get the ratio of the total volume of bubbles in one cubic meter per cubic meter, which is αib: αib = Vib * nib, or αib = π*dib3/6 * nib, or (expressing dib) dib = ((6 * αib) / (π * nib))1/3
Point 2. Page 3: Eq.(2) is wrong if we look carefully. The denominator in the parenthesis in the exponential function should be “square of “sigma multiplied by root 2 pai”. It is difficult to express the formula by a sentence. So check and correct it.
Response 2. The equation was checked and corrected (Page3, Eq (2)).
Point 3. Page 3: The present reviewer is confused by the words such as “monodisperse” and polydisperse” and the relation of such words with the standard deviation. Reviewer’s understanding is that the standard deviation is zero if BCD is monodisperse. This is the common understanding of the term "monodisperse". Probably the terms "monodisperse" and "polydisperse" in this paper differ from the terms the reviewer means. The terms “monodisperse” and “polydisperse” in this paper should be defined.
Response 3. In the paper the standard deviation is used to describe a continuous distribution of bubbles. In the monodisperse case the distribution is integrated over the whole range of bubble sizes, resulting in a single class of bubbles whose size corresponds to the mathematical expectation of the distribution. In fact, in this case there is no such term as the standard deviation, since there is no deviation at all, but we decided to keep the same definitions in all cases. The monodisperse case can be considered as a polydisperse one with only one class of bubbles.
We have updated the text according to the reviewer's remark with explanations of what “monodisperse” means in our work (Page3, lines 114-117).
Point 4. Page 4: Several factors which affect the force acting on the bubble are taken into account. Some formulas shown in this paper are based on the formulas for solid particles in the fluid. This work deals with the flow of gas bubble and liquid. So the following question arises. One of the most important factors is ignored in this paper. That is, velocity slip on the boundary between the gas phase and the liquid phase is ignored. Due to the velocity slip, the fluid drag on a gas bubble in the liquid is smaller than the drag on a solid particle in the liquid. Theoretical study of low Reynolds number flow shows that the drag on the bubble is two third of the drag on the solid particle. The present reviewer does not know whether there is a formula of the drag on the bubble at the intermediate or a large Reynolds number. At least, the authors should do paper survey. If no previous work of that subject is found. The authors should confess in this paper to ignore the effect of velocity slip.
Response 4. In fact, according to Eqs. (11) and (12), the resulting drag is reduced to 2/3 of the solid particle drag as Rep tends to 0. In Eq. (11) with Rep < 1.6 the modification constant equal to 2/3 is explicitly introduced, Eq. (12) provides an expression for the CD(Rep) which tends to 16/Rep when Rep tends to 0. This goes directly to the 2/3 * 24/Rep, where CD = 24/Rep being the solid particle drag coefficient. (see Refs. [22], [23] in the paper)
The lift force coefficient was also chosen for the bubble taking into account its non-sphericity.
Point 5. Page 7: The symbol Sc is used in eq.(23). The present reviewer thinks that Sc is the Schmidt number. If he is right, describe so in the paper. Also the reviewer requests the authors to describe the reason of the value 0.8.
Response 5. The typing error in the Sc number value has been corrected (0.83 instead of 0.8), the description of the reason for choosing of this value has been added (Page7, lines 216-217)
Point 6. In the simulation, various empirical formulas are used. Some of them are established. However some others are not established but developing. In such a situation, reliability of computation results depends on the comparison with experimental data. In this paper the only experimental data for comparison is the work ref. 22. If possible, more comparison with measurement should be added. Adding measurement and comparison would increase the value of this paper .
Response 6. Thank you very much for this remark. Of course, validation of the algorithm is very important stage of any numerical simulation. We have extensively tested the developed mathematical model, numerical methods and computer code. The results of the comparison of our simulations with the four sets of experimental data have been published in [20, 31, 32] (see paper References), therefore, we decided not to include a detailed description of the validation in this paper.
Reviewer 2 Report
The paper is interesting and more or less well written.
The description of the numerical method used must be improved in order to be more clear.
The computational resources as well as the size of the computational domain must be reported.
Comparison with studies of bubble dynamics using other approaches (e.g. Lattice Boltzmann) will be helpful.
Author Response
Dear Reviewer,
Thank you very much for your attention to our paper and useful remarks.
Point 1. The description of the numerical method used must be improved in order to be more clear.
Response 1. Description of the numerical method has been improved according to the reviewer remark (Page 7, lines 221-245)
Point 2. The computational resources as well as the size of the computational domain must be reported.
Response 2. Parameters of the numerical method and mesh structure are given in the revised version of the paper (Page 8, lines 264-269)
Point 3. Comparison with studies of bubble dynamics using other approaches (e.g. Lattice Boltzmann) will be helpful.
Response 3. Of course, it would be interesting to compare this approach with other descriptions of polydisperse media. Since the main goal of our work was to construct a simplified model of the polydisperse medium within the framework of the Euler-Euler approach, we have compared the developed model with Euler-Euler models which use other descriptions of interphase interaction and turbulence [31, 32]. We plan to compare the developed model with models based on the Euler-Lagrange approach and on the kinetic theory.
Reviewer 3 Report
Gas-liquid systems (e.g. bubble columns) represent an important example of two phases contacting device. They are commonly applied in industry and are also encountered in natural processes. Large number of papers has been devoted to study and model them. This is evidenced by tools such as e.g. Google Scholar where tens thousand information on flow structure and hydrodynamic properties are given. It can be noticed that numerical methods applicable to describe properties of these systems have systematically been developed in order to accomplish more and more accurate simulations of such systems behaviour. The paper is focused on studying an effect of bubble size distribution on flow structures in bubble column reactors. By using the MUSIG model the authors have carried out a numerical study (simulations) on the effects of polydisperse flows by considering bubble size distribution (BSD) on the basic parameters such as velocity profiles of the carrier and the disperse phases, the volume fraction of the dispersed phase, and the specific area of the interfacial surface. It would be good to test the accuracy of the applied similation effects with experimental data. In the earlier paper of the same authors (J. Phys. Conf. Ser. 2020, 1697, 012236) such test has been demonstrated. In the present paper the authors demonestrated good agreement of their simulations with the experimental data of Lain et al. (2002).
Comments for author File: 
Comments.pdf
Author Response
Dear Reviewer,
Thank you very much for your attention to our paper.
Point 1. Minor English language and style changes
Response 1. The whole text of the paper was checked for spelling and necessary corrections were made (in particular to the reviewer comments on: Page2 lines 77 and 79, Page3 lines 97-98, Page14, lines 376-378)
