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Open AccessArticle
Peer-Review Record

Numerical Modeling of Open-Eye Formation and Mixing Time in Argon Stirred Industrial Ladle

Metals 2019, 9(8), 829; https://doi.org/10.3390/met9080829
Reviewer 1: Anonymous
Reviewer 2: Anonymous
Reviewer 3: Anonymous
Reviewer 4: Anonymous
Metals 2019, 9(8), 829; https://doi.org/10.3390/met9080829
Received: 28 May 2019 / Revised: 8 July 2019 / Accepted: 24 July 2019 / Published: 26 July 2019

Round  1

Reviewer 1 Report

The subject of the paper and the conducted research are very current and meet the needs of the industry. However, the manuscript is prepared very carelessly and requires corrections.

The main objection in terms of editing is the chaos concerning the numbering of drawings. References to numbers of drawings in the text are not adequate and must be corrected.

The main substantive comments are as follows:

line 88 - please provide the basis on which the given values were adopted or which method was used to determine them

line 132 - Fig. 4 - please specify in the paper how the mean values of the open-eye area were determined in the experimental method

line 146 - Figure 5b - incorrect drawing

line 200 - Figure 10d - please state in the text how the value of mixing time was calculated using the experimental method

Author Response

Answers to the Reviewer 1 questions

The main objection in terms of editing is the chaos concerning the numbering of drawings. Reference to numbers of drawings in the text are not adequate and must be corrected.

The main substantive comments are as follow:

1) line 88 – please provide the basis on which the given values were adopted or which method was used determining them

The method for finding the constant values and other values in the manuscript are added to the manuscript.

2) line 132 – Fig.4 – Please specify in the paper how the mean values of the open-eye area were determined in the experimental method.

The mean value of open-eye area for the experiments and simulations was calculated by measuring the area for every second for a period of 60 seconds and averaging it over this time. This is added to the manuscript.

3) line 146 – Figure 5b – incorrect drawing

The Figures 5 to 7 are replaced with exact flow rate values.

4) line 200 – Figure 10d – please state in the text how the value of mixing time was calculated using the experimental method.

During the experiments, samples of the concentration were taken from the ladle at certain intervals for time and at a certain location. The time was noted in the clock, when the concentration was completely dissolved and taking the samples was stopped after that.

Reviewer 2 Report

The article concerns the numerical modeling of open-eye formation in argon stirred industrial ladle. The article is quite interesting. The introduction gives short description of the knowledge in this area and shows the review of articles published from this topic and discussed the results. methodology is appropriate. However, the initial and boundary conditions should be in more detail described. The obtained results are presented graphically and discussed. There are some mistakes that should be corrected:

-          There is some chaos in lietarture –

-          Line 42 – [10 – 12]

-          Line 63 [ 27-28] rather [28,29]

-          There is lack of some symbols in the equation (3) and (4)

-          There are mistakes in Figures – line 117 Figure 2 and 3 instead of 5 and 6

-          Line 120 figure 4 instead of 7

-          Line 112-114 in my opinion not necessary

-          Line 134 Figure 2 to 4 should be 5 to 7

-          Line 142 – if this Figures are correct?

-          There is lack of 23, 24 and 29 literature in text

Author Response

Answers to the Reviewer 2 questions
The article concerns the numerical modeling of open-eye formation in argon stirred industrial ladle. The article is quite interesting. The introduction gives short description of the knowledge in this area and shows the review of articles published from this topic and discussed the results. methodology is appropriate. However, the initial and boundary conditions should be in more detail described. The obtained results are presented graphically and discussed. There are some mistakes that should be corrected:

Initial and boundary conditions are explained in the manuscript.

1) There is some chaos in literature

        The referencing in the literature is been updated in the manuscript.

2)  Line 42 – [10 – 12]

           References number is changed to [10-12]

3)  Line 63 [ 27-28] rather [28,29]

          Reference number is changed to [28,29]

4)  There is lack of some symbols in the equation (3) and (4)

      The symbols and other terms are added to the equations for better understanding.

5)  There are mistakes in Figures – line 117 Figure 2 and 3 instead of 5 and 6

           Figures numbering is been changed now.

6)  Line 120 figure 4 instead of 7

           Figure number is changed to 4 now.

7)  Line 112-114 in my opinion not necessary

          The lines 112-114 are removed from the updated version.

8)   Line 134 Figure 2 to 4 should be 5 to 7

           The figure numbering are changed to  5 to 7

9)   Line 142 – if this Figures are correct?

           The figures are changed with corresponding flow rates numbering

10)   There is lack of 23, 24 and 29 literature in text

The text for the references 23, 24 and 24 in the literature in added to the manuscript.

Reviewer 3 Report

It is a good work and certainly deserves publication.
My questions are as follows:
How is mixing time influenced by the size and shape of the ladle ? Mixing time reported in this study is different from otehr studies, so is my question. 

Mixing time and open eye are validated, but not velocities and turbulence. Why ? Usually, in case for 0.5R, turbulence and velocities are well validated, but open eye is heavily underestimated because of decreased turbulence. Can the authors comment on this ? 

There is no mass transfer included in this paper. Is it not a good idea to include that ?

What is the main objective to use VOF model in the paper ? The advantages of using VOF is not yet visible in the paper. 

What is the steel and slag interaction used in the model ? or there is no interaction assumed ?

Author Response

Answers to the Reviewer 3 questions
It is a good work and certainly deserves publication. 
My questions are as follows:

1) How is mixing time influenced by the size and shape of the ladle ? Mixing time reported in this study is different from other studies, so is my question. 

Yes mixing time is influenced by the size and shape of the ladle. There were many studies on investigating the effect of gas flow rate and nozzle plug arrangement on the mixing time in the water model ladles.

In the current study, the effect of gas flow rate on the mixing time in the industrial scale is been studied. As the experimental data comes from the industry, it is not possible to study the effect of size and shape of the ladle on the mixing as they have fixed geometry and shape. This is the reason why the effect of size and shape of the ladle on the mixing time was not studied in the current work.

2) Mixing time and open eye are validated, but not velocities and turbulence. Why ? Usually, in case for 0.5R, turbulence and velocities are well validated, but open eye is heavily underestimated because of decreased turbulence. Can the authors comment on this ? 

Mixing time and open-eye are validated with the industrial measurements.  The industrial measurements of velocities and turbulence were not available to validate them

3) There is no mass transfer included in this paper. Is it not a good idea to include that ?

Mass transfer was included in the fluid flow.

4) What is the main objective to use VOF model in the paper ? The advantages of using VOF is not yet visible in the paper. 

VOF model is able to track the interfaces between the phases by solving single set of momentum equation. In this work, it is used to track the liquid steel/slag/argon-gas interface phase.  This description is added to the manuscript.

5) What is the steel and slag interaction used in the model ? or there is no interaction assumed ? 

The interaction between the steel and slag in the simulations has been neglected. It is assumed that there is no interaction.

Reviewer 4 Report

Although the paper touches upon an interesting and important issue in steelmaking technology, there is no novelty in the paper because the same model has been presented in another recent paper by this author’s group (Steel Research International,2019,Vol.90 ). Therefore it is unclear what new the authors did in the present paper ? Besides, the paper contains a lot of shortcomings, and many important details are lacking. It is the reviewer’s opinion that the paper is unacceptable in its present form and therefore rejection is recommended. The main deficiencies of the paper are listed below.

1. It seems that a three-dimensional model is used for simulation, however there is no explanation on the ladle geometry and nozzle arrangement at the bottom. It is unclear why Figs.1 and 9 present results for a two-dimensional case.

2. The authors claim that the results of simulation and measurements are in good agreement, for example those shown in Fig.10d. However any explanation on how and at which locations in the ladle the mixing time was measured is lacking.

3. What is difference between meff(Eq.2) and me (Eq.4) ?

4. Numbering of figs.2~6 is wrong

Author Response

Answers to the Reviewer 4 questions

Although the paper touches upon an interesting and important issue in steelmaking technology, there is no novelty in the paper because the same model has been presented in another recent paper by this author’s group (Steel Research International,2019,Vol.90 ). Therefore it is unclear what new the authors did in the present paper ? Besides, the paper contains a lot of shortcomings, and many important details are lacking. It is the reviewer’s opinion that the paper is unacceptable in its present form and therefore rejection is recommended. The main deficiencies of the paper are listed below.

In the earlier paper (Steel Research International,2019,Vol.90) , the water modelling stuff related to the open-eye area was published. We haven’t published anything related to the industrial scale ladle. This paper presents in modelling of open-eye formation in the industrial scale ladle and additional mixing time was calculated in the simulations.

1. It seems that a three-dimensional model is used for simulation, however there is no explanation on the ladle geometry and nozzle arrangement at the bottom. It is unclear why Figs.1 and 9 present results for a two-dimensional case.

Yes it is a three-dimensional model used for simulation. The ladle geometry is taken from the industry, and they have restrictions not to disclose the geometry details in the manuscript. That is the reason why there is no explanation about the ladle geometry and nozzle arrangement. In Figure 1, the mesh is 3-dimensional. The results in Figure 9 are also 3-dimensional, (if you observe clearly, the ladle outer part can be seen) and the results are plotted on the vertical plane in the location where argon gas is injected from bottom.

2. The authors claim that the results of simulation and measurements are in good agreement, for example those shown in Fig.10d. However any explanation on how and at which locations in the ladle the mixing time was measured is lacking.

The explanation of how mixing time was measured in added to the manuscript. The location of the points is shown in Figure 8, exact numerical locations of the points cannot be published due to the restrictions from the industry.

3. What is difference between meff(Eq.2) and me (Eq.4) ?

The equations are modified in the manuscript for better understanding.

4. Numbering of figs.2~6 is wrong

The numbering of the figures is changed in the manuscript.

Round  2

Reviewer 4 Report

Some of these answers and additional explanations raise several questions which must be properly answered. Besides, the paper still contains a number of serious errors and unclear statements.

1.     Usually governing equations of mathematical models in the CFD-related literature are given either in a vector or in a tensor form, if the variable is not a scalar. Why the authors use the mixed formulation for velocity? Please clarify if there is any need to do it.

2.     Equation (1) seems to be written in a vector formulation, but there is no any vector symbol (arrow, bar) above the letters. Besides, the operator nabla needs “nabla dot” formulation

3.     The last term on the right side of Eq.(3) arouses a number of questions.

The statement that ?̇?? and ?? in this equation represent the mass transfer from phase ? to ? is incorrect. Equation (3) is a equation of continuity written for q-phase. Therefore, ?̇?? and ?? may represent sink or source of q-phase. If there are any q-phase related sink or source terms, they must be properly explained and described.   

4.     Is the velocity u in Eq.(10) vector ? If so it needs the appropriate vector symbol

5.     Figure 3 shows predicted open-eye areas. What criteria were used to define the areas numerically ?

6.     Figure 9 depicts distributions of tracer over the molten steel bath and nickel was used as the tracer. The question is why nickel is entering the slag phase ? Another question is why the rising bubbles, which are depicted, I believe by the green chain-like spots, also contain nickel ?

Besides, there is a number of grammatical errors in the text 

Line 125: The finite volume technique was sued of rthe discretization of…

Line 211-212 : The time was noted in the clock, when the concentration was completely dissolved and taking the samples was stopped after that.

Line 213 : It can be seen that with an increase the argon gas flow rate

Author Response

Some of these answers and additional explanations raise several questions which must be properly answered. Besides, the paper still contains a number of serious errors and unclear statements.

1.       Usually governing equations of mathematical models in the CFD-related literature are given either in a vector or in a tensor form, if the variable is not a scalar. Why the authors use the mixed formulation for velocity? Please clarify if there is any need to do it.

All the equations are changed to tensor form for better understanding. The author changed the equations in the first review round, there was some mistakes during that. Now all the equations are changed.

2.       Equation (1) seems to be written in a vector formulation, but there is no any vector symbol (arrow, bar) above the letters. Besides, the operator nabla needs “nabla dot” formulation

The Equation (1) is changed to tensor

3.     The last term on the right side of Eq.(3) arouses a number of questions.

The statement that ?? and ?? in this equation represent the mass transfer from phase ? to ? is incorrect. Equation (3) is a equation of continuity written for q-phase. Therefore, ?? and ??may represent sink or source of q-phase. If there are any q-phase related sink or source terms, they must be properly explained and described.   

The volume of fluid model equations are taken from the Ansys Fluent manual. There was some confusion due the brackets symbol places wrongly. Now the brackets are placed at right place.

4.     Is the velocity u in Eq.(10) vector ? If so it needs the appropriate vector symbol

No it is not a vector.

5.     Figure 3 shows predicted open-eye areas. What criteria were used to define the areas numerically ?

For better understanding, the dynamic movement of the open-eye areas is shown now in Figure 3. The open-eye area value was averaged for a period of 60 sec.

6.     Figure 9 depicts distributions of tracer over the molten steel bath and nickel was used as the tracer. The question is why nickel is entering the slag phase ? Another question is why the rising bubbles, which are depicted, I believe by the green chain-like spots, also contain nickel ?

In the industry, measurements took place to investigate the effect of gas flow rate on the mixing time of nickel alloy. Here, nickel was used as alloying material in the industrial measurements. Nickel is dropped from the top of the ladle, where the open-eye is formed. That is the reason, nickel is entering through the slag phase from the top of the ladle. In the Figure 9, the gas bubbles are also shown to show the complete process (gas injection, slag layer deformation and tracer concentration) through the images. The author thought this images will give the clear information about the complete process. The green chain-like spots are the gas bubbles injected through the inlet from the bottom of the ladle, and it does not contain nickel.

Besides, there is a number of grammatical errors in the text  

Line 125: The finite volume technique was sued of rthe discretization of…

The text is changed to ‘The finite volume technique was used for the discretization of ….’

Line 211-212 : The time was noted in the clock, when the concentration was completely dissolved and taking the samples was stopped after that.

The sentence is reformulated for clear explanation of experimental details.

Line 213 : It can be seen that with an increase the argon gas flow rate

The text is changed to ‘with an increase in the argon gas flow rate’.

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