Regarding three phase flows with phase change

[Shyam Sunder Yadav]

Dear All

I am trying to investigate solidification of a liquid around a gas bubble. Please go through the attached movie.

The bubble rises in a liquid, it stops at a cold wall where solidification of liquid occurs.

I am using the Allen Cahn equation based ternary phase field method for this work.

The problem I am facing is that the solid phase keeps on deforming in-spite of the velocities put to zero in the solid phase.

I have tried the Brinkman panelization approach, I also have directly  put the cell centered  velocities to zero but nothing seems to change the situation.

If someone has experience with the Phase field method please help me here.

People working with solidification are requested to comment.

Thank you.

Regards   

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Dr. Shyam Sunder Yadav
Associate Professor
Mechanical Engineering
BITS Pilani
09902346342
http://www.bits-pilani.ac.in/pilani/ssyadav/Profile

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[Yannick Peng]

Dear Shyam Sunder,

Thank you for sharing your problem. I have encountered a similar issue in my work with a two-phase ice-water system using the phase-field method.

I have tried both the penalty function approach and the direct force method. While these methods do not completely enforce zero velocity within the solid phase, they can significantly reduce the velocity magnitude relative to the external flow. However, achieving convergence within the solid phase often requires smaller time steps, which can be computationally demanding.

In my experience, the penalty function method, inspired by Favier et al. (2019) [https://doi.org/10.1017/jfm.2018.773], seems to be more effective. This approach involves adding a penalty term to the Navier-Stokes equations to enforce near-zero velocity within the solid region. The direct force method involves setting the velocity field within the solid phase to zero (e.g., uf = 0) during the event projection step (i++, last) in the Navier-Stokes solver (centered.h). Both methods have shown some effectiveness, but the penalty function approach seems to be more robust and easier to implement.

If you have any other experience or suggestions, I would be very interested to hear them. I am also eager to learn more effective approaches.

Best regards,
Yannick Peng

[Shyam Sunder Yadav]

Dear Yannick

Thank you very much for the response. Let me explore the suggestions and I will get back to you.

Regards

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Dr. Shyam Sunder Yadav
Associate Professor
Mechanical Engineering
BITS Pilani
09902346342
http://www.bits-pilani.ac.in/pilani/ssyadav/Profile

[Shyam Sunder Yadav]

Dear All

I am able to simulate the solidification around a gas bubble and solidification of a drop under air with a combination of three-phase flow approach (based on three-phase.h) and phase change algorithms by Edoardo Cipriano.

I am not able to attach the simulation movies (I think because of size restrictions).

I want to heartily thank Edoardo for his phase change codes without which this work would not have been possible!

Long live Edoardo Cipriano! 

I will present the work in the November 25 BMM if given a chance.

Regards   

[Edoardo Cipriano]

Hi Shyam,

Thanks a lot! 😃

I am glad you made it and I look forward to your presentation.

Best,

Edoardo

[peng zhang]

Hi Shyam,

I read your post on the solidification of a liquid around a gas bubble, and I am interested in this problem.

May I ask how you treated the interfacial tensions in the ice–water–gas system? Did you take into account all three interfacial tensions, namely ice–water, water–gas, and ice–gas?

Also, I noticed you mentioned a BMM presentation, but I did not find it later. Was this work ever presented somewhere?

Thank you.

Yannick

[Shyam Sunder Yadav]

Dear Yannick

I am sorry for the late reply...

Truly speaking, the problems are not fully resolved, I apologize for the earlier declaration...The surface tension based approach (at gas-solid, liquid-solid interfaces as well) works but results do not match with experiments. I think that's not the right approach. I am now trying Schwart Spencer's IBM based approach and Alexandre Limare's moving embedded boundary based approach. It will take some time. Main problem is the gas-liquid-solid contact point/line behavior.  

I am attaching a code which is supposed to simulate solidification of a liquid (supposed to be water) around a non-solidifiable oil drop. The thermal conductivity of ice is increased just for faster solidification, the surface tensions are totally wrong. I am using an older version of Basilisk (from around 2023) to compile...

The solidification/melting part is, as I mentioned earlier, by Edoardo Cipriano. It works fine, it uses a two temperature based approach, one for solid phase and another for (gas+liquid) phase. We have to make sure that gas and solid phases exchange heat at the gas-solid interface. See how I am doing...  The liquid-solid interface is at saturation temperature...

A high viscosity (10000 Pa.s) is used for the solid phase to suppress the velocities in solid, it gives a smoother interface compared to Brinkman penalization approach. Of Course it runs slower... You can uncomment the Brinkman penalization related preprocessor directives at the start of bubble_at_top.c file to use Brinkman penalization...

Further issue is that if you use a smaller (eta_s ~ 10^{-6}) penalization parameter, it will suppress the Stefan flow effect as well! If this parameter is larger (eta_s ~ 10^{-4}), the solid becomes permeable...It flows...

Same holds with the high viscosity approach....

So it's a multiple-issue problem... If you can improve it, please let me know.

I was not able to present this work in BMM.

Thank you. Regards

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Dr. Shyam Sunder Yadav
Associate Professor
Mechanical Engineering
BITS Pilani
09902346342
http://www.bits-pilani.ac.in/pilani/ssyadav/Profile

[Yuanpeng Zhang (Yannick)]

Dear Shyam,

Thank you very much for your detailed and honest reply. I really appreciate it.

Your explanation was very helpful to me, especially your comments on the gas–liquid–solid contact point/line behavior and the limitations of the surface-tension-based treatment. I am facing very similar issues in my own work.

At the moment, one of the biggest difficulties for me in this research direction is the lack of reliable experimental references. So far, I have mainly referred to the images of methane bubbles freezing in ice from M. Engram’s work. However, I am still unsure what the final frozen shape should look like for centimeter-scale bubbles or oil drops. If you happen to know of any experimental studies on this point, I would greatly appreciate any pointers.

I have also encountered the same difficulty regarding the motion of the gas–liquid–solid contact point/line. In my simulations, I have also found that the treatment of interfacial tension strongly affects the motion of the contact point/line. I also noticed that a similar issue is discussed in the following paper: https://doi.org/10.1016/j.jcp.2021.110795

At present, I am still uncertain about how this should best be treated.

Regarding how to keep the ice phase immobile, or how to impose a no-slip condition on the ice surface, I have been trying both a phase-field approach and Brinkman penalization. On my side, when the solid volume fraction is still small, I have not clearly observed excessive suppression of the Stefan-flow effect. However, Brinkman penalization often does not seem strong enough to overcome other body-force terms, so in some cases it cannot enforce the no-slip condition on the ice surface satisfactorily. This has also been a persistent difficulty for me.

Thank you again for sharing your thoughts and code. If I make any progress on these issues, I will be happy to let you know.

Best regards

  Yannick  

[Shyam Sunder Yadav]

Dear Yannick

I found a talk by Prof. Detlef Lohse which may be useful to you and others working on solidification and melting...

The talk is hosted here: https://cassyni.com/events/KyUbz2S8Bv949NmYhrySEy

At 13 minutes in the video, Prof. Lohse talks about solidification of water around an oil droplet of diameter ~120 microns.

Best wishes

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Dr. Shyam Sunder Yadav
Associate Professor
Mechanical Engineering
BITS Pilani
09902346342
http://www.bits-pilani.ac.in/pilani/ssyadav/Profile

[Yuanpeng Zhang (Yannick)]

Dear Shyam,

Thank you very much for sharing this talk. I really appreciate it.

It looks very relevant to my work, and I will watch it carefully.

Best regards,
Yannick