CFD Simulation of Solid Suspension for a Liquid–Solid Industrial Stirred Reactor

Round 1

Reviewer 1 Report

The paper presents a numerical study of solid suspension for a liquid-solid stirred reactor. Several issues need to be considered:

- The idea is not new, and there are many papers published in this area.

-Some quantitative results should be presented in the abstract.

- Introduction must be improved. The literature overview in the introduction should be more quantitative.

- The results can be compared with other literature.

Author Response

Dear esteemed Reviewer 1,

Please find in the attached file our addressing to your kind recommendations, marked with green colour, and also all the changes in the paper were marked with green colour in order to better identify them.

Author Response File: Author Response.docx

Reviewer 2 Report

The authors have presented a numerical study on CSTR's using a commercial multiphase CFD tool (ANSYS Fluent). Unfortunately, the manuscript in its current form cannot be considered for publication. This is due to the following major concerns I have:

1) The manuscript lacks an in-depth assessment of the effect of the impeller operation on the overall mixing characteristics in the CSTR. Only the effect of the initial solid distribution is assessed which is insufficient for drawing the conclusions that the authors claim, particularly because the original liquid-liquid reactor is being operated at off-design conditions. The authors could have considered operating the impeller at different speeds to elicit the desired solid distribution. This investigation (which can easily done in the CFD simulations) is missing in the manuscript. Moreover, different impeller designs could also be easily tested in the CFD framework.

1. The contour plots of velocity is clearly indicative that the recirculation of the fluid created by the impeller is insufficient, higher speeds or better design could be desirable. This should be investigated and presented. 

2) Some of the numerical and modelling choices are slightly questionable and incomplete - 

1. Despite having solid particles which are close to neutrally buoyant, the authors disregard the effects of both virtual mass and lift forces in the interphase coupling. The motivation given by the authors, as written in lines 101-102 is applicable for systems which are NOT neutrally buoyant (in these articles ρp ≅2500 kg/m3) as is the case here; i.e the solid to fluid density ratio ≅ 1.1 in this study. This means that the assumptions in the studies referenced by the authors do not hold in this context. 
2. Since, solids are being modelled as a fluid, the granular temperature of the solids phase is a critical aspect of the modelling framework. The description of this concept is missing in the manuscript. Moreover, what is the granular temperature used in the simulations? How was it chosen? What is the sensitivity of the reported results to this chosen value?
3. The fluid shear in the CSTR, coupled with a close to neutrally buoyant system would mean that lift could play a major role in the solid re-suspension (using the impeller action). This could mean that, the results reported in this manuscript could be under-predicting the actual solids distribution. It's actually surprising that gravity settling has such a dominating effect. Is this a physical result? Could you support this with other similar studies from literature?
4. Since the authors do not present any grid and temporal discretization independence studies in the manuscript, the reported results are qualitative at best. How was the current mesh chosen, why is the time step used in the simulations 0.01s (which is quite coarse especially when trying to resolve particle-fluid coupling). Moreover, the convergence criteria of 1e-3 used is too course for complex Eulerian multiphase CFD wherein a well converged velocity field is critical for the interphase coupling. How was the final simulation time of 90s deemed reasonable, what's the motivation?
5. The manuscript would benefit with a conceptual validation study using data from literature on a generic CSTR.

Other minor concerns:

1. In line 81, how is the coupling between the phases achieved using the pressure? Isn't the pressure equation shared?
2. Reference for the form of the continuity and momentum conservation equations (see DOI 10.1080/07373930902827379)
3. Line 87, turbulent dispersion is NOT added to the continuity equation.
4. Reference for the Morsi and Alexander model and some citations to show the wide applicability of this in CSTR's
5. References for the RNG-k-epsilon model and the coefficients for C_mu etc.
6. The fig. 5 could be improved visually and descriptively (in the accompanying text).
7. One could use the volume fraction distribution axially and radially (along different probe lines) to better represent the local re-distribution of the solids.
8. Lines 206-207, how do you propose the operation of the CSTR with an already dispersed initial condition (as in Figure 3b) in reality. An impeller is used for re-suspension or better mixing of solids, how can one start at a fully dispersed initial state? One might then argue, why is the impeller needed at all?
9. The descriptions accompanying the velocity contours can be improved (i.e. Figs 6 - 8). You notice a change in direction of velocity near the impellers while the distribution is uniform else where. Is this physical? Why is there an imbalance in the fields on either side of a symmetric impeller (Figs. 7b and 8b)?  

Author Response

Dear esteemed Reviewer 2,

Please find in the attached file our addressing to your kind recommendations, marked with green colour, and also all the changes in the paper were marked with green colour in order to better identify them.

Author Response File: Author Response.docx

Reviewer 3 Report

Review of the manuscript entitled: CFD simulation of solid suspension for a liquid-solid industrial stirred reactor

The reviewed manuscript is very interesting. Multiphase flow simulation as the Eulerian approach is an actual, interesting, and relatively difficult approach for modeling. Especially as transient simulation. On the other hand, the same situation concerns the experimental object of the proposed model, because of concern with a processes reactor as a mixer. Generally, the manuscript is written well, however contains some elements that need to extend. Below the main elements:
1. Multuiphase simulation flow based on the Eulerian approach is an actual and current case. For better recognition of the manuscript, it would be beneficial to have wider literature research of suspension (or dispersed phase) modeling as an Eulerian approach or general VOF approach. Check and follow:
10.3390/polym12122832

10.1016/j.jfoodeng.2019.109846

https://doi.org/10.3390/fluids5040207

https://doi.org/10.3390/pr8111418

On the other hand, the Eulerian approach for this case should be justified. Why you didn't use i.e. DPM approach? For example check: 10.1016/j.compgeo.2020.103818

2. Initial conditions and simplifications of the case (geometry and simulation model) should be detailed and (the most important) justified.
3. Details about the initial conditions should be justified.
4. Details of the mesh quality testing (quality parameters) should be provided.
5. Details on the criteria for the simulation model and its testing of convergence should be provided. Only selected values and choices without justifying them are not enough.
6. What about comparing CFD and experimental results? Some discussion is necessary. A separate subject is the comparison of the results with the experimental data in the range of critical elongation and the swirled flow character. For example, check the VOF approach with PIV experimental comparison (10.1016/j.jfoodeng.2019.109846)

Also:

7. For fig. 5 the authors should present a velocity vector without scaling. Used vector symbols with length scale don't look correctly.

Generally, the manuscript contains some lack elements that need to extend. I recommend a major revision of the manuscript. I hope that the manuscript will be improved and publish because seems valuable and will quite interesting for potential readers.

Author Response

Dear esteemed Reviewer 3,

Please find in the attached file our addressing to your kind recommendations, marked with green colour, and also all the changes in the paper were marked with green colour in order to better identify them.

Author Response File: Author Response.docx

Reviewer 4 Report

The paper is well organized and technically sound. After a comprehensive introduction, the authors present the equations and methodologies. The description of the model and equations leaves room for improvement, with a more careful definition of the quantities employed. The reported figures illustrate the main results and are visually pleasant.

The aim of this work is very applied. However, inertial particles in turbulent flows have received attention in the recent literature, and it would be beneficial for the paper to complement the applied side with a more theoretical viewpoint. This brief discussion would allow identifying the advantages and limitations of the model employed, thus improving the CFD simulations carried out for applied purposes.
A challenge for the employed model is the representation of dispersed particles as a continuum phase. Indeed, caustics and sling effects can make the continuum velocity field non-smooth (Boffetta et al. EPL, 78 (2007)). Also, the small scales of the fluid flow are critical in the interaction between the fluid and solid phases. In particular, particles clustering and caustics enhance the interaction between the fluid flow gradients and the particle phase (Carbone et al. JFM, 881 (2019)). This effect is beneficial for the reactor since it can improve its efficiency. Finally, turbulence can modify the settling velocity of inertial particles (Wang and Maxey JFM (1993)), and the time before full sedimentation is crucial for the performance of the reactor.
Can the authors briefly comment on these aspects? In particular, it would be beneficial to expand on the small-scale features that the Eulerian multiphase model with an RNG k–ε model can/cannot capture and the implications on the accuracy of the numerical simulations of the reactor.

A few minor points:
14 RNG not defined
47 differentprofessional
57 RSM not defined
eq 5 and 6: Re not defined (particle relative Reynolds number?)
eq 8: how much is the typical Stokes number of the particles? Dimensionless quantities can help to characterize the system better.
eq 15 jumps to eq 18
eq 5-8 and 15-16: please expand on and define more carefully the characteristic quantities and model parameters.

Author Response

Dear esteemed Reviewer 4,

Please find in the attachment our response to your kind suggestions.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Accept in present form

Author Response

Dear esteemed Reviewer 1,

Thank you very much for all your suport!

Reviewer 2 Report

The paper has been improved, however the author's have not addressed a majority of the comments that were posed in the first peer-review round. Based on 'my experiences' in multiphase flows, I am not convinced that the reported results are physical enough to warrant a publication. The references cited by the authors are indeed indicative of the fact that an E-E multiphase model is tractable enough for these types of investigations. However, the conditions simulated in these references are vastly different from the ones reported in this paper and hence would require slightly modified modelling considerations. I will still maintain that the lift forces play a crucial role in these simulations, unless the authors can provide me with any example in literature consisting of close to neutrally buoyant suspensions (which is the case here) where-in this effect was ignored. For the benefit of the authors, I will re-clarify my stance. The paper is at best qualitative and does not add anything novel to the existing knowledge in the field. If on the the other hand, the authors can support their CFD analysis with a relevant experimental comparison (which they seem to have done as well), then the paper has some merit.

My major concerns are still:

1. Since, solids are being modelled as a fluid, the granular temperature of the solids phase is a critical aspect of the modelling framework. The description of this concept is missing in the manuscript. Moreover, what is the granular temperature used in the simulations? How was it chosen? What is the sensitivity of the reported results to this chosen value? --> This is not the 'actual temperature' of the solids, but is a representation of the momentum possessed by them in a continuum-level of abstraction. Please see the Fluent guide: https://www.afs.enea.it/project/neptunius/docs/fluent/html/th/node327.htm  and this paper: https://doi.org/10.1016/j.powtec.2007.12.002
2. The fluid shear in the CSTR, coupled with a close to neutrally buoyant system would mean that lift could play a major role in the solid re-suspension (using the impeller action). This could mean that, the results reported in this manuscript could be under-predicting the actual solids distribution. It's actually surprising that gravity settling has such a dominating effect. Is this a physical result? Could you support this with other similar studies from literature? It would be beneficial if you could actually support this with your own experimental data.
3. Since the authors do not present any grid and temporal discretization independence studies in the manuscript, the reported results are qualitative at best. How was the current mesh chosen, why is the time step used in the simulations 0.01s (which is quite coarse especially when trying to resolve particle-fluid coupling) --> These convergence studies are a requirement for accepting the results reported.
4. Moreover, the convergence criteria of 1e-3 used is too course for complex Eulerian multiphase CFD wherein a well converged velocity field is critical for the interphase coupling. This is a well known problem in E-E methods. The authors should comment on this aspect in the manuscript.
5. The following response from the authors - ' Before we start the numerical experiment, we read an extensive number of research papers in order to obtain the proper setting of the numerical simulation. The research papers that we read indicates the appropriate settings for similar problems, and the numerical results presented in those papers were validated against experimental measurements. So, we applied on our research the same settings for our numerical solution that were previously validated by experiment. '--> Is not a justification. Each problem has a unique setup and the authors need to provide more basis for their simulations settings since they have a vastly different particle-fluid system than the ones they have cited.
6. One could use the volume fraction distribution axially and radially (along different probe lines) to better represent the local re-distribution of the solids. --> Another requirement for the paper to be accepted

Author Response

Dear esteemed Reviewer 2,

Please find in the attachment our answers to your observations.

Author Response File: Author Response.docx

Reviewer 3 Report

Re-review of the manuscript entitled: CFD simulation of solid suspension for a liquid-solid industrial stirred reactor

Like I found the manuscript is corrected well. The authors prepared adequate answers, provide corrections, and improve the manuscript. The re-reviewed paper has limited novelty aspects. The simulated flow in a mixer is well known as a modeled case, so in my opinion, will not fully interesting for potential readers. The paper has a limited practical aspect also. The flow relations between phases are commonly known and consider in a lot of manuscripts.
However, in view of responses and prepared corrections, I recommend accepting the manuscript in the present form.

 

Author Response

Dear esteemed Reviewer 3,

Thank you very much for all your suport!