Hybrid Approach for Mixing Time Characterization and Scale-Up in Geometrical Nonsimilar Stirred Vessels Equipped with Eccentric Multi-Impeller Systems—An Industrial Perspective
, Dominik Schlosser 2, Andreas Lange 2, Michaela Brueckner-Pichler 2, Cécile Brocard 1 and Miroslav Šoóš 3,*
Round 1
Reviewer 1 Report
The work by Martinetz et al. describes an approach to evaluate mixing time by combining CFD simulation and in-situ measurements on systems with different size, filling, and mixing setups (impellers and baffles). This work is of interest for process engineers and other readers of processes journal. However, the manuscript requires a minor revision. My comments are as follow:
- The impeller design ,which is the easiest part to change in a reactor, and its influence on the mixing time should be added to the introduction and discussion. the following ref can be used: Chem. Eng. 115 (3), 2006, 173-193, Chem. Eng. 412, 2021, 128592, Chem. Eng. 413, 2021, 127497, and Processes , 8(8), 2020, 955.
- Part 1.1 should move to experimental.
- Figure 1 should be combined with Figure 3 to show standard behavior and observed data in one figure.
- Table 1 and lines 88-111 are not needed for this manuscript since they do not develop a method to obtain the data. the authors can claim that they chose to use their sensing method in one sentence.
- lines 46-48 should be written as follows: It is well known that fast impeller rotational speed enables short mixing times, avoids high local concentrations of reactants, and reduces aggregation of intermediates.
- There are some corrections to the text writing that should be addressed: misuse of allow, in many cases enable is the correct verb. missing punctuation such as comma before which in a middle of a sentence, and too many connecting words are used in one paragraph such as therefore.
Author Response
The work by Martinetz et al. describes an approach to evaluate mixing time by combining CFD simulation and in-situ measurements on systems with different size, filling, and mixing setups (impellers and baffles). This work is of interest for process engineers and other readers of processes journal. However, the manuscript requires a minor revision. My comments are as follow:
Q1: The impeller design ,which is the easiest part to change in a reactor, and its influence on the mixing time should be added to the introduction and discussion. the following ref can be used: Chem. Eng. 115 (3), 2006, 173-193, Chem. Eng. 412, 2021, 128592, Chem. Eng. 413, 2021, 127497, and Processes , 8(8), 2020, 955.
A1: We agree with the reviewer that this part was omitted in the original version of the manuscript, even though this represents the easiest part to impact mixing time. The text discussing this aspect was added in the revised version of the manuscript.
Q2: Part 1.1 should move to experimental.
A2: The section was moved to Experimental part. In addition, to make the text smooth, we combined discussion about available methods with the description of measuring method used in our work coupled with data analysis.
Q3: Figure 1 should be combined with Figure 3 to show standard behavior and observed data in one figure.
A3: Since we are reporting the measured tracer concentrations and information in Figure 1 does not bring new information, we decide to remove Figure 1 from the text.
Q4: Table 1 and lines 88-111 are not needed for this manuscript since they do not develop a method to obtain the data. the authors can claim that they chose to use their sensing method in one sentence.
A4: We agree that this information is not necessary for the paper. The text was reduced to report available methods including appropriate references.
Q5: lines 46-48 should be written as follows: It is well known that fast impeller rotational speed enables short mixing times, avoids high local concentrations of reactants, and reduces aggregation of intermediates.
A5: We agree with the reviewer and the text was corrected accordingly.
Q6: There are some corrections to the text writing that should be addressed: misuse of allow, in many cases enable is the correct verb. missing punctuation such as comma before which in a middle of a sentence, and too many connecting words are used in one paragraph such as therefore.
A6: The text was corrected.
Author Response File: 
Author Response.docx
Reviewer 2 Report
CFD and k-ε modelling of liquid suspension flows is a very exhausted area of study in fluid mechanics literature with literally hundreds of references to previous work being available.
What is the criterion for the volumetric division of a computational domain into a stationary and a rotational impeller region. What volume of the stirrer tank was rotational with respect to the stationary domain(volume ratio?). How does this relate to scale-up the reactor?
“The modeled transport equations for kinetic energy (k) and energy dissipation rate 171 (ε) in realizable k-ε model”, which was given by eq. (1),(2),(3). What is the numerical value of C2, C1e, C3e. It is value from Fluent software. How did these values change with the scale-up of the reactor?
It should be more information abour mesh quality. Did the authors perform grid independence? Where is the grid independence and convergence results? What is maximum aspect ratio in this mesh?
Also, the authors need to point out what is novel about this work and his main contribution to the field in detail. Predicting mixing time based on the process parameters it's very interesting. What medium does this work for? Will it also work for non-newtonial multiphase systems, for fluids of different viscosities? This should be also described in the text of the article.
Comments for author File: 
Comments.pdf
Author Response
Q1: CFD and k-ε modelling of liquid suspension flows is a very exhausted area of study in fluid mechanics literature with literally hundreds of references to previous work being available.
A1: As reviewer is pointing out, there is not possible to indicate all papers being published about the modelling of stirred vessels by CFD. However, to provide sufficient overview about the topic we pick up few relevant reviews and critical papers.
Q2: What is the criterion for the volumetric division of a computational domain into a stationary and a rotational impeller region. What volume of the stirrer tank was rotational with respect to the stationary domain(volume ratio?). How does this relate to scale-up the reactor?
A2: The volume around the impeller was selected such that it is occupying only small fraction of the vessel volume. This was between 0.5% and 0.5%, depending on the vessel volume and impeller type. Furthermore, in the case of two impellers there was also space limitation and volume was selected such to avoid contact between two rotating zones. This information was added into the revised version of the manuscript.
Q3: “The modeled transport equations for kinetic energy (k) and energy dissipation rate 171 (ε) in realizable k-ε model”, which was given by eq. (1),(2),(3). What is the numerical value of C2, C1e, C3e. It is value from Fluent software. How did these values change with the scale-up of the reactor?
A3: The values of these constants were the same in all simulations and we used the values as provided by Ansys Fluent. We are aware the fact that by changing the values of these constants will have impact on the obtained results, however without any experimental data of velocity profiles, turbulent kinetic energy, and energy dissipation rate, validation of such choice will be rather difficult. Instead, we used the values provided by software, and test the predictive capability of such model over broad range of the scales. As can be seen from comparison of the measured mixing time with that calculated by CFD we obtain good agreement, which supports the choice of these constants in the energy dissipation rate transport equation. This information was added in the revised version of the manuscript.
Q4: It should be more information abour mesh quality. Did the authors perform grid independence? Where is the grid independence and convergence results? What is maximum aspect ratio in this mesh?
A4: Mesh independence study was performed but these results are not included in the study due to rather large number of investigated vessel. Convergence criteria for all residuals was set to 10-5. Furthermore, this was possible only for sufficiently fine mesh, since for coarse meshes we were not able to reach residuals below 10-4. Maximum aspect ratio was for all below 25, however on average the aspect ratio was around 1.5. In addition, the quality of the mesh was supported by good agreement between volume average energy dissipation rate (eps) calculated from eps transport equation and the one from torque, where difference was always below 17%. In the case of low quality mesh there was larger difference between eps calculated from torque compare to volume average eps calculated from its transport equation. This information was added in the revised version of the manuscript.
Q5: Also, the authors need to point out what is novel about this work and his main contribution to the field in detail. Predicting mixing time based on the process parameters it's very interesting. What medium does this work for? Will it also work for non-newtonial multiphase systems, for fluids of different viscosities? This should be also described in the text of the article.
A5: Main novelty is the simulation of the mixing time in vessels used in industrial praxis with non-standard geometry, which is different from those used typically in academic cases. In addition, selected volumes of the vessels are rarely used in CFD studies published in the literature. In the current work, water was used as the working media. There is a possibility to model non-Newtonian in Ansys Fluent, however, this option is available only for laminar flows. This is due to nontrivial description of non-Newtonian fluid behavior under turbulent conditions. Information about Newtonian behavior of the water used in all simulations was added in the revised version of the manuscript.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
After the introduced corrections, the article can be accepted
