Fluid Dynamics in a Continuous Pump-Mixer

Round 1

Reviewer 1 Report

Minor revision

This study proposed an investigation of the fluid dynamics and hydrodynamics in a continuous pump. It is worth publishing, but revisions still need to be done.

1. The introduction need to mention some newly investigations about simulations in hydro machines, such as energy analysis of Francis turbine for various mass flow rate conditions based on entropy production theory, and numerical investigation of pulsating energy evolution in ventilated cavitation around the hydrofoil.

2. Generally, the paper is well written, but there are still some grammar errors, the authors should ask some native English speakers for help to improve the English level of the paper.

Author Response

Dear reviewer,

Thank you for your valuable comments, we made our changes as following:

1. The introduction need to mention some newly investigations about simulations in hydro machines, such as energy analysis of Francis turbine for various mass flow rate conditions based on entropy production theory, and numerical investigation of pulsating energy evolution in ventilated cavitation around the hydrofoil.

The focus of our study is the experimental investigation and the modelling of the pump-mixer, no CFD has been done. Hence, we don’t think this fits the topic of the paper.

2. Generally, the paper is well written, but there are still some grammar errors, the authors should ask some native English speakers for help to improve the English level of the paper.

Justin Tran (acknowledgment) is native speaker and has corrected the document.

 

Author Response File: Author Response.docx

Reviewer 2 Report

This work investigated the fluid dynamic and hydrodynamic behavior of a continuous pump-mixer by experiment. The local holdup of the disperse phase and the droplet size distribution (DSD) were obtained. And a new correlation to predict the Sauter mean diameter was developed. In particular, the paper provided a detailed database, which can be a good benchmark for relevant studies. Some suggestions on the present work are as follows:

1. The MP₄ in Table 1 should be MP_H.  

2. Figure 5: It is not clear to me how to get Figure 5(a), cause the data points between the continuous phase and dispersed phase are no the same. In addition, the flow rate V in the horizontal axis of Figure 5(a) is the total flow rate or dispersed flow rate or other flow rate? What is the feed phase ratios in Figure 5(b)?

3. Figure 9(b): The impeller rotational speeds are suggested to be provided in the figure.

4. Figure 10: When the feed phase ratios are different, the relationships between impeller speed and Sauter mean diameter are different. Could you explain further the reason that causes the formation of fine emulsified droplets？

Author Response

Dear reviewer,

Thank you for your valuable comments, we made our changes as following:

1. The MP₄in Table 1 should be MP_H.  

You are totally right with that, thank you. We have changed that.

2. Figure 5: It is not clear to me how to get Figure 5(a), cause the data points between the continuous phase and dispersed phase are no the same. In addition, the flow rate V in the horizontal axis of Figure 5(a) is the total flow rate or dispersed flow rate or other flow rate? What is the feed phase ratios in Figure 5(b)?

Since the feed phase ratio implies that the flow rate of the disperse and the continuous phase are different this is also the case for their respective pumping curves. Valve V2, which was used for controlling the disperse flow rate, adds additional pressure loss to reduce the flow rate, and changes the pumping curve. This is already explained in Line 294-297.

The flow rate in Figure 5a provides the continuous and the disperse phase “flow rate” is not further specified. In Figure 5b only the pumping curve of the continuous phase is shown, since it was found that the disperse phase has only small influence on the continuous flow rate and can be neglected. Therefore, the feed phase ratio in Figure 5b doesn’t matter. This is already described in Line 297-305. Nevertheless, we added the information of the feed phase ratio for Figure 5b in the caption to ensure it can be easily understood. The total flow rate can easily be calculated by rearranging Equation (5).

3. Figure 9(b): The impeller rotational speeds are suggested to be provided in the figure.

Figure 9b can be interpreted as a meta-analysis, which is necessary to evaluate if there is a dependence of the impeller speed. The additional information of which point is which impeller speed would crash the caption. The information that all impeller speeds are shown is given in the caption. The same diagrams for a fixed impeller speed are shown in Figure 9a and the supplementary material, since their information is not necessary to fully understand the topic.

4. Figure 10: When the feed phase ratios are different, the relationships between impeller speed and Sauter mean diameter are different. Could you explain further the reason that causes the formation of fine emulsified droplets？

Emulsion and fine droplets are generally produced at high energy dissipation, because higher energy input increases droplet breakup. We can just assume on that, detailed investigations on local energy dissipation and flow patterns are required to finally answer this, but this is part of future works.

Author Response File: Author Response.docx

Reviewer 3 Report

The publication presents an interesting approach to mixing two-phase systems using the hydrodynamics of the flow of the phases in question. However, I have a few observations/remarks.

Line 155: Why do two PID controllers control one V1 valve? What happens when there are conflicting control signals?

Line 258: The network CNN used deserves appreciation, but the network designed by Schäfer analyzes two-dimensional images. How does it distinguish between particles further away and those with smaller diameters but closer?

Line 292: The word „kinetic” is crossed. I assume that it is to be removed.

Line 308: The “guide for the eye” lines are in fact pump characteristic curves for your setup (they indeed are second order polynomials). Perhaps it would be better to call them just that?

Line: 457: The sentence is not clear “We assume…”.

Line 488: It would be interesting if the constant C9 in equation 1 would also take a value close to 0.6 for your measurements. Has there been such computational testing done?

Line 501: Figure 13b begs quite a lot to plot the confidence interval for the chosen significance level - but I leave this to the authors' discretion. We would then know how well model 11 explains your experimental data.

Author Response

Dear reviewer,

Thank you for your valuable comments, we made our changes as following:

Line 155: Why do two PID controllers control one V1 valve? What happens when there are conflicting control signals?

There is no second PID controller, there is just one which controls the disperse phase as a ratio (-control) of the continuous phase. There are two valves to control each flow rate separately if needed. By checking the text Line 131-142 this is described as that, I don’t know where you got the information of two PID’s, I assume you accidently confused with the valves.

Line 258: The network CNN used deserves appreciation, but the network designed by Schäfer analyzes two-dimensional images. How does it distinguish between particles further away and those with smaller diameters but closer?

The technique and routine are detailed described in our previous paper https://www.mdpi.com/2076-3417/12/8/4069/htm. Since the technique uses a telecentric lens are the particles imaged by parallel light only. Therefore, the magnification remains constant over large depth of field and the droplets have always the same size, independent of the position to the lens (working distance). Hence, distinguishing between particles that are further away and which are closer is not necessary. Additionally, the network has been trained based on 3D data and can separate these.

Line 292: The word „kinetic” is crossed. I assume that it is to be removed.

Thank you, done.

Line 308: The “guide for the eye” lines are in fact pump characteristic curves for your setup (they indeed are second order polynomials). Perhaps it would be better to call them just that?

That is correct, we added “The lines are the pumping curves calculated as quadratic polynomials as a guide for the eye” in the figure caption

Line: 457: The sentence is not clear “We assume…”.

Correct, we changed to:

We assume that this emulsification is a result of an increased energy dissipation. Since the most emulsification was found at N = 400 rpm, compared to the other impeller speeds, we assume the highest energy dissipation at N = 400 rpm.

Line 488: It would be interesting if the constant C9 in equation 1 would also take a value close to 0.6 for your measurements. Has there been such computational testing done?

Yes, we have tried that in our previous publication https://www.mdpi.com/2076-3417/12/8/4069/htm and found that this chemical system has small to no coalescence tendency. Since -0.6 comes from the Hinze-Kolmogorov theory for pure breakup, we decided that keeping this value is the best choice. For high disperse holdups above 30 vol.-% up to 50 vol.-% C9 can increase little (~ -0.68), because coalescence occurs due to a significant increase in droplet collisions which lead to little bit of coalescence. Hence, -0.6 the most reasonable decision.

Line 501: Figure 13b begs quite a lot to plot the confidence interval for the chosen significance level - but I leave this to the authors' discretion. We would then know how well model 11 explains your experimental data.

Since we use the mean values for our model (Equation 11) I see no way how to calculate the confidence intervals for a value which was not directly fitted. Therefore, we made the parity plot which describes “how well” the experimental data are described. I don’t see a reasonable way to do that, but we publish all our data, may other authors find a better approach.

 

Author Response File: Author Response.docx