A Novel Particle-Based Approach for Modeling a Wet Vertical Stirred Media Mill

Round 1

Reviewer 1 Report

The Authors present the application of a coupled numerical approach to the model of wet vertical stirred media mill. The topic is of a certain interest, however, there are some critical concerns that the Authors should address in order to make the paper worth to be published in Minerals journal.

NOVELTY

The Authors should clarify which is the main novelty of their work with respect to previous publications. In the title of the article, they claim that the particle-based approach used is 'novel', but, from my point of view, it does seem to be new. In particular, reference [36] Larrson et al. (2020) seems to use exactly the same formulation for a very similar application.

LIMITATIONS

The Authors do not explain which are the limitations of their method. The used coupled CFD-DEM method can be barely defined as a fully two-way coupled approach because linear momentum and continuity equations of the fluid are not adequately modified to take into account the effect of a dense solid particles distribution, like the ones considered in the numerical examples.

LITERATURE REVIEW

The literature review is quite poor with respect to the computational strategies for multiphase and particle-laden flows. In the specific case of PFEM-DEM approach, at least the first works on particulate flow should be mentioned (e.g. Oñate et al., CPM, 2014; Celigueta et al., CPM, 2016).

MOTIVATIONS

Why did the Authors decide to use the PFEM for this application and not an Eulerian method? And why an ALE formulation in the PFEM framework? These choices should be adequately explained

FURTHER EXPLANATION

The Authors do not give enough details about the fluid formulation. Which elements are used? Which stabilization method (if needed)? Which time integration scheme?

Furthermore, how do the Authors update the mesh according to an ALE description? Which equations do They follow for this purpose? In which parts of the domain?

Finally, no details are given for the solid FEM solution and the FSI coupling. Is the solid really solved or it has prescribed motion conditions?

ENGLISH REVIEW

The article is full of English grammar mistakes (lines 1, 26, 32, 37, 39...). A deep revision of English grammar and forms should be done.

Author Response

The authors would like to thank the reviewer for their help in improving the paper.

Our responses to the reviewer's comments are displayed in Italic text. 

The Authors present the application of a coupled numerical approach to the model of wet vertical stirred media mill. The topic is of a certain interest, however, there are some critical concerns that the Authors should address in order to make the paper worth to be published in Minerals journal.

NOVELTY

The Authors should clarify which is the main novelty of their work with respect to previous publications. In the title of the article, they claim that the particle-based approach used is 'novel', but, from my point of view, it does seem to be new. In particular, reference [36] Larsson et al. (2020) seems to use exactly the same formulation for a very similar application.

The authors argue that the modelling approach presented within the present work is novel. In comparison with our previous publication (Larsson et al. (2020)) we use a different approach for transferring forces between grinding fluid and grinding media through a Reynolds number dependent drag coefficient. In the previous publication we used a constant coefficient. This is mentioned in the abstract, and we have added a clarification in the introduction.

LIMITATIONS

The Authors do not explain which are the limitations of their method. The used coupled CFD-DEM method can be barely defined as a fully two-way coupled approach because linear momentum and continuity equations of the fluid are not adequately modified to take into account the effect of a dense solid particles distribution, like the ones considered in the numerical examples.

The numerical simulations presented in this work used a two-way coupled approach because the DEM particles exert a force on the fluid (included in the external forces of the Navier Stokes equations) and the fluid exert a force on DEM particles. We can call it loose or weak two-way coupling because we don´t model the flow around DEM particle. A detailed explanation about the two-way coupling is presented in Section 3.3 of the paper. Below the Navier Stokes a remark was included to explain that the external forces include the effect of DEM particles on the fluid.

LITERATURE REVIEW

The literature review is quite poor with respect to the computational strategies for multiphase and particle-laden flows. In the specific case of PFEM-DEM approach, at least the first works on particulate flow should be mentioned (e.g. Oñate et al., CPM, 2014; Celigueta et al., CPM, 2016).

The references suggested by the reviewer and some additional references were added to the manuscript.

MOTIVATIONS

Why did the Authors decide to use the PFEM for this application and not an Eulerian method? And why an ALE formulation in the PFEM framework? These choices should be adequately explained

With this research we are aiming at a numerical approach allowing also for mills that are not entirely full of grinding fluid, e.g., ball mills. If the mill is not full of fluid, during the rotation of the mill there is a continuous formation of free surfaces and holes in the grinding fluid. For that reason, we consider the PFEM a good candidate to predict the formation of the free surfaces and holes during the mill motion instead of improved pure Eulerian formulation with a volume of fluid strategy. In this work we use an ALE framework instead of a pure Lagrangian formulation because during some time steps it is only necessary to improve mesh quality and not to identify the formation of new surfaces and holes. In case the internal mesh is distorted we use ALE and in case we need to identity the formation of new surfaces PFEM framework is used. Also, the PFEM is used to identify the region of contact of the grinding fluid with the mill, the shaft, the casing, and the agitator. We can use also an Eulerian formulation to model our problem, but we would then need to include a moving reference frame for the rotating axis and also capabilities like the volume of fluid to predict the formation of holes and free surfaces, we choose an ALE formulation because it is available in the software used in the presented research.

FURTHER EXPLANATION

The Authors do not give enough details about the fluid formulation. Which elements are used? Which stabilization method (if needed)? Which time integration scheme?

A new section was included in the paper that explain the finite element discretization used in this work. The explanation includes the finite element and the stabilization used. The time integration used to discretize the Navier Stokes equation is explained in Section 3.2.4

Furthermore, how do the Authors update the mesh according to an ALE description? Which equations do They follow for this purpose? In which parts of the domain?

In section 3.2.4 an explanation about the mesh motion in ALE framework is present. The fluid domain is discretized using ALE framework (grinding fluid).

Finally, no details are given for the solid FEM solution and the FSI coupling. Is the solid really solved or it has prescribed motion conditions?

More details regarding the FSI used in the present research was added the first paragraph of Section 3.3.

ENGLISH REVIEW

The article is full of English grammar mistakes (lines 1, 26, 32, 37, 39...). A deep revision of English grammar and forms should be done.

A revision of the language of the manuscript has been performed.

Reviewer 2 Report

The paper presents a multi-physics computational model for the numerical study of the wet vertical stirred mill. Conceptually the manuscript is very close to the paper doi:10.1016/j.mineng.2019.106180 published by the authors this year and included in the References as [36] (actually the governing equations and numerical scheme are the same). But this manuscript considers the different structure of the mill and two different working fluids (water and mineral slurry). So, my general conclusion is that the presented study contains some interesting new results and deserves to be published in the Journal.

However, I have some questions and comments that need to be clarified before accepting the manuscript for publication.

1. In Abstract (and similar in Conclusions) we read “The interactions between the different constituents is treated by fully two-way couplings between the PFEM, DEM and FEM models”.

But in Subsection 3.3 we find a different description of the coupling: “A partitioned approach is used for fluid structure interaction (FSI), in which the fluid and solid equations are uncoupled. FSI is realized by a loosely coupled scheme, in which only one solution of either field is required each time step. This is advantageous in terms of computational efficiency since it avoids the iterative step required for convergence. Fluid and grinding media interaction is modelled by a two-way coupling between PFEM and DEM models.”. The authors should be consistent in all parts of the paper.

2. At the beginning of Section 3 the authors specified the code as well as the computer (processor and RAM) used for calculations but said nothing about the computation time. I suggest informing the reader about the time deficiency of the code.

3. In Fig. 5 (for water) the calculated power is a little bit less than the experimental value that can be explained by the approach used where no mechanical or electrical losses are accounted for, nor any product breakage. But in Fig. 6 (for mineral slurry) we see that the simulated power consumption is vice versa greater than the experimental value. Please explain this difference.

4. I suggest rewriting the last sentence of Section 4 “However, there are promising results in the literature where for instance [57] suggested a feed particle breakage model based on the inter-particle contact energies.” (lines 309-310).

Author Response

The authors would like to thank the reviewer for their help in improving the paper.

Our responses to the reviewer's comments are displayed in Italic text. 

The paper presents a multi-physics computational model for the numerical study of the wet vertical stirred mill. Conceptually the manuscript is very close to the paper doi:10.1016/j.mineng.2019.106180 published by the authors this year and included in the References as [36] (actually the governing equations and numerical scheme are the same). But this manuscript considers the different structure of the mill and two different working fluids (water and mineral slurry). So, my general conclusion is that the presented study contains some interesting new results and deserves to be published in the Journal.

However, I have some questions and comments that need to be clarified before accepting the manuscript for publication.

1. In Abstract (and similar in Conclusions) we read “The interactions between the different constituents is treated by fully two-way couplings between the PFEM, DEM and FEM models”.

But in Subsection 3.3 we find a different description of the coupling: “A partitioned approach is used for fluid structure interaction (FSI), in which the fluid and solid equations are uncoupled. FSI is realized by a loosely coupled scheme, in which only one solution of either field is required each time step. This is advantageous in terms of computational efficiency since it avoids the iterative step required for convergence. Fluid and grinding media interaction is modelled by a two-way coupling between PFEM and DEM models.”. The authors should be consistent in all parts of the paper.

The couplings are partitioned, and a loose (or weak) coupling scheme is used, as described in Section 3.3. We have modified the terminology where we refer to the coupling throughout the paper and no longer use “fully two-way couplings” to be concise.

2. At the beginning of Section 3 the authors specified the code as well as the computer (processor and RAM) used for calculations but said nothing about the computation time. I suggest informing the reader about the time deficiency of the code.

The computational time required to run the models was added to Section 3.

3. In Fig. 5 (for water) the calculated power is a little bit less than the experimental value that can be explained by the approach used where no mechanical or electrical losses are accounted for, nor any product breakage. But in Fig. 6 (for mineral slurry) we see that the simulated power consumption is vice versa greater than the experimental value. Please explain this difference.

There are many possible explanations to this difference. The rheology of the mineral slurry was determined experimentally at room temperature but during the operation of the mill the temperature increase and this might cause the rheology to be somewhat different. This temperature dependency was not studied in the present research. In the last paragraph of section 3.3 we have added a note that the viscosity was measured at room temperature. Also, a discussion regarding this was added to Section 4.2.

4. I suggest rewriting the last sentence of Section 4 “However, there are promising results in the literature where for instance [57] suggested a feed particle breakage model based on the inter-particle contact energies.” (lines 309-310).

We decided to remove this sentence.

Reviewer 3 Report

This is a very nice application of the multiphysics to simulating one type of stirred mill. The manuscript brings interesting and novel information and will be publishable with some minor edits, as follows:

For the benefit of the readers, perhaps the authors could discuss in a bit more detail the fluid flow patterns observed in Figure 9.  

Line 26: replace “suggest” with “suggests”.

Line 39: replace “require” with “requires”.

Reference 52 is incomplete: please include institution.

Lines 192-196: present more details of the mineral slurry tested, including solids composition, size (median), solids concentration, etc.

Table 2: please include the mill internal diameter.

Line 208: modify to “…corresponds to fill levels of …”

Line 262: “modify to “…considers…”

Line 310: perhaps the authors could add an additional reference which is even more relevant to the type of mill studied: Oliveira et al. (2020), Miner. Eng. 156, 106487.

Author Response

The authors would like to thank the reviewer for their help in improving the paper.

Our responses to the reviewer's comments are displayed in Italic text.

This is a very nice application of the multiphysics to simulating one type of stirred mill. The manuscript brings interesting and novel information and will be publishable with some minor edits, as follows:

For the benefit of the readers, perhaps the authors could discuss in a bit more detail the fluid flow patterns observed in Figure 9.  

A paragraph discussing the fluid flow patterns observed in the LIC visualization was added to Section 4.3.

Line 26: replace “suggest” with “suggests”.

This was corrected.

Line 39: replace “require” with “requires”.

This error was corrected.

Reference 52 is incomplete: please include institution.

This error was corrected.

Lines 192-196: present more details of the mineral slurry tested, including solids composition, size (median), solids concentration, etc.

More details of the mineral slurry can be found in Section 2.

Table 2: please include the mill internal diameter.

It was the wish of the manufacturing company that this information was not included in the manuscript.

Line 208: modify to “…corresponds to fill levels of …”

This error was corrected.

Line 262: “modify to “…considers…”

This error was corrected.

Line 310: perhaps the authors could add an additional reference which is even more relevant to the type of mill studied: Oliveira et al. (2020), Miner. Eng. 156, 106487.

The reference suggested by the reviewer was added in the manuscript.

Round 2

Reviewer 1 Report

I acknowledge the Authors for having addressed my comments. 

Nevertheless, I am sorry but, in my opinion, the only use of a different drag coefficient is a novelty of not enough significance to justify a new publication. 

However, this is a personal consideration and I leave to the Editor the final decision considering the target and public of the Journal.

Besides this main concern of the poor novelty, the paper is well-written and presents a complex three-dimensional numerical simulation.

Reviewer 2 Report

The authors have improved the quality of the text and addressed all my comments and questions.