Simulation of Ultrasonic Induced Cavitation and Acoustic Streaming in Liquid and Solidifying Aluminum

Round 1

Reviewer 1 Report

The authors aim to create a 3D simulation model using the commercial CFD code FLOW-3D for aluminium alloy A356. In this effort they combine the moving body facility in FLOW-3D for the oscillating immersed probe tip with turbulent flow due to the generated acoustic streaming and acoustic simulations for sound propagation in an idealistic DC caster. A simple generation/dissipation function is used for the presence of cavitation bubbles, treated as a homogenised gas volume fraction in the solution domain.

The authors give a good account of related work by other researchers in the field in their introduction. However, the section describing the numerical method and the physics of the problem causes the greatest concern for the following reasons:

1.  The simulated time for sound propagation is given as 0.0001 s, clearly insufficient to resolve a 20 kHz sound wave. What is the time step used in the simulation? What is the numerical method used? Reflection and transmission through the containing wall is known to modify the sound field. Is this taken into account in the model?

2. Equation (2) addresses the simple production/dissipation of cavitation gas, with rates based on production and dissipation coefficients. Where do the values for these coefficients come from?Equations (3) and (4) refer to evaporation and condensation of gas within the bubbles. As we are dealing with aluminium and hydrogen, evaporation and condensation are negligible at the pressures/ temperatures involved. I therefore have grave doubts as to the applicability of these equations (presumably derived from steady state cavitation in water) for this problem.

3. The speed of sound in a cavitating medium is not constant due to the presence of bubbles (e.g. see Wood's formula). How do the authors address this?

4.  The role of turbulence in the simulation is not at all clear. At the velocities predicted, the Reynolds number is high enough to be in the turbulent regime. Yet, the authors claim the use of a turbulence model does not affect the results, even though the kinetic energy of turbulence appears in the cavitation production/dissipation equations.

5. The 'micro-collision model' is apparently used for acoustic streaming. But we know, acoustic streaming is due to pressure gradients set up in a compressible fluid - in this case due to the presence of gas bubbles - is this model equivalent? Nevertheless, the predicted streaming appears to resemble PIV visualisations that appear in the literature. 

6. There are several other detail comments to address as follows:

•  line 137: 'soliditification' to solidification
• line 157 should read 'distinctive discernible'
• line 242 'fluid can elude .... re-write using 'stream past' rather than elude
• line 243 propagates spherical-ly
• fig 17 prupose to purpose
• lines 279 & 200 homogenout to homogeneous
• caption not informative: Figure 4. Cavitation development and bubble collapse activity for a period of 0.01 s of ultrasonic treatment in A356.
• Caption not helpful in Figure 9. Analysis of shielding effect caused by cavitation cloud – pressure wave propagation in z-direction???

 

 

Author Response

Dear Reviewer,

first of all, we would like to thank you for valuable feedback on our manuscript. We hope that the changes and additions we included will meet your expectations. In the following, we will address your comments successively. The implemented changes based on your recommendations are highlighted in green in the attached pdf-file, others are marked in yellow.

 

The simulated time for sound propagation is given as 0.0001 s (1) clearly insufficient to resolve a 20 kHz sound wave. (2) What is the time step used in the simulation. (3) What is the numerical method used? (4) Reflection and transmission through the containing wall is known to modify the sound field. Is this taken into account in the model?

1. The chosen time frame was mainly selected to investigate the calculated max/min pressures as well as the (half) wavelength and speed of sound within the simulation. We changed the description to „which conforms to two full radiator oscillations“ (65-66)
2. All selected time steps are listed in Table 5.
3. As justifiably stated, there was a backlog in the description of the numerical foundations. For this reason, the following additions have been included into the text:
   • We point out, that the description within the numerical modelling followed the workflow within FLOW-3D to allow an easy reproducing of it (63-64)
   • Described the basic equations for the general mass continuity equation and the consideration of the speed of sound. (72-83)
   • Added a more detailed description on the input of the amplitude. (118-129)
4. For both models, we added that at the mesh boundaries full reflection without any losses are calculated (139-140 and 155-156)

Equation (2) addresses the simple production/dissipation of cavitation gas, with rates based on production and dissipation coefficients. (1) Where do the values for these coefficients come from? (2) Equations (3) and (4) refer to evaporation and condensation of gas within the bubbles. As we are dealing with aluminium and hydrogen, evaporation and condensation are negligible at the pressures/ temperatures involved. (3) I therefore have grave doubts as to the applicability of these equations (presumably derived from steady state cavitation in water) for this problem. 

1. We noted, that the values are predefined by FLOW-3D but can be adjusted easily (97-99)
2. Due to coarse mesh compared to the size of cavity bubbles evaporation and condensation were neglected by FLOW-3D anyway. Nevertheless, the model allows to take surface tension and the density of cavitation bubbles into account (110-113). But we added the indication, that its evaporation and condensation are negligible in case of Al/H at the involved pressures and temperatures (113-116)
3. We are aware of your concern with respect to the applicability and demonstrated here, that the manuscript describes a feasibility study. However, we want to emphasize that an adjustment of the model seems reasonable. (337-343 and 367-368)

The speed of sound in a cavitating medium is not constant due to the presence of bubbles (e.g. see Wood's formula). How do the authors address this?

We would like to thank you for this beneficial comment. A description of this special simulation result can be found here has been included. (283-284 and 288-295).

The role of turbulence in the simulation is not at all clear. At the velocities predicted, the Reynolds number is high enough to be in the turbulent regime. Yet, the authors claim the use of a turbulence model does not affect the results, even though the kinetic energy of turbulence appears in the cavitation production/dissipation equations.

This is a very interesting issue, which we cannot answer in detail yet. An assumption is described here (344-354).

The 'micro-collision model' is apparently used for acoustic streaming. But we know, acoustic streaming is due to pressure gradients set up in a compressible fluid - in this case due to the presence of gas bubbles - is this model equivalent? Nevertheless, the predicted streaming appears to resemble PIV visualisations that appear in the literature.

The “micro-collision model” is just one component of the overall GMO model that’s responsible for the formation of acoustic streaming. We replaced the initial explanation by a, from our point of view, more applicable one. (118-129)

There are several other detail comments to address as follows:

Again, thank you for the suggestions regarding the spelling mistakes! We corrected the mistakes within the words and changed / concretized the captions of Figure 4 and 9.

 

We really appreciate the time and work you invested reviewing the manuscript thereby giving us the opportunity to improve the quality of its content.

Please accept my/our best regards and stay healthy during these unusual times,

 

Eric Riedel

Author Response File: Author Response.pdf

Reviewer 2 Report

See the attachment file.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,

first of all, we would like to thank you for valuable feedback on our manuscript. We hope that the changes and additions we included will meet your expectations. In the following, we will address your comments successively. The implemented changes based on your recommendations are highlighted in green in the attached pdf-file, others are marked in yellow.

 

There are many missing citable literatures other than the author’s list of publication about numerical modeling for the acoustic streaming and cavitation effects in water and aluminum melt. A part of the unlisted literatures is shown below.

We would like to thank the reviewer for the additional references. We added them to Table 1 and changed the design of the table to a leaner one.

The computational grid resolution affects the numerical results. The authors did not validate and check the grid independency on the calculation results.

So far, we did not describe our investigation on the grid independency due to the enormous calculation times resulting from a finer mesh. To address this point, we added a paragraph in which we explain the results obtained so far. (344-354)

The authors solved the wave propagation equation for 0.001 s. There are many types of wave propagation equations. So, show the solved wave propagation equation explicitly.

As justifiably stated, there was a backlog in the description of the numerical foundations. For this reason, the following additions have been included into the text:

• We point out, that the description within the numerical modelling followed the workflow within FLOW-3D to allow an easy reproducing of it (63-64)
• Described the basic equations for the general mass continuity equation and the consideration of the speed of sound. (72-83)
• Added a more detailed description on the input of the amplitude. (118-129)

The authors compared the computational results with the experimental results obtained by the PIV experiment. The authors compared the results quantitatively. However, the qualitative comparison is necessary.

 We inserted an additional paragraph describing the qualitative comparison. (300-304)

 

We really appreciate the time and work you invested reviewing the manuscript thereby giving us the opportunity to improve the quality of its content.

Please accept my/our best regards and stay healthy during these unusual times,

 

Eric Riedel

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

In answer to my questions and comments, the authors have inserted caveats regarding the validity of the methodology used for this problem and the limitations of the commercial software used.

Even though the main flaws of the research and approach used remain, I think the article is interesting enough for researchers working in the field to read, as presenting an alternative modelling approach with future potential.

My recommendation is to publish, following careful editing of the English, especially in the newly added sections.