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Spherical Shell with Fluid what are the Frequencies
Posted Sep 19, 2010, 2:36 p.m. EDT 5 Replies
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To the COMSOL community,
Thank you for reading this message. I am a new-bee in COMSOL and I am having a hard time in simulating the breathing modes frequency of a spherical Shell with a Newtonian fluid inside. This problem has been
solved analytically and I am benchmarking COMSOL against the analytical results.
I read a similar discussion of sphere with breathing mode but the problem talked about a uniform solid sphere.
In my case I am not interested in the modes only the frequencies.
In particular I am having trouble implementing the boundary conditions for the stress and pressure balance. Now this is a benchmark case for me as in the future I will have "n" layers but I start at the second level.
If you do not understand what I am talking about I have included here a two page pdf of an Appendix of one of my references. Equation (B17) contains the boundary conditions for the stress that I need to implement
Stress(r,t) = - Pressure(r,t) (Pressure due to fluid inside).
In the reference I have included there is an analytical result for calculating the frequencies equation (B29) .
To be honest I am unable to get started. I would appreciate any pointers to either constructed similar modules or simply tell me how to to implement this model i.e. using FSI module, Structural Mechanics etc. You may assume that I know how to draw in COMSOL and choose the appropriate study.
Thank you in advance for any help!
Best wishes,
Pablo
Thank you for reading this message. I am a new-bee in COMSOL and I am having a hard time in simulating the breathing modes frequency of a spherical Shell with a Newtonian fluid inside. This problem has been
solved analytically and I am benchmarking COMSOL against the analytical results.
I read a similar discussion of sphere with breathing mode but the problem talked about a uniform solid sphere.
In my case I am not interested in the modes only the frequencies.
In particular I am having trouble implementing the boundary conditions for the stress and pressure balance. Now this is a benchmark case for me as in the future I will have "n" layers but I start at the second level.
If you do not understand what I am talking about I have included here a two page pdf of an Appendix of one of my references. Equation (B17) contains the boundary conditions for the stress that I need to implement
Stress(r,t) = - Pressure(r,t) (Pressure due to fluid inside).
In the reference I have included there is an analytical result for calculating the frequencies equation (B29) .
To be honest I am unable to get started. I would appreciate any pointers to either constructed similar modules or simply tell me how to to implement this model i.e. using FSI module, Structural Mechanics etc. You may assume that I know how to draw in COMSOL and choose the appropriate study.
Thank you in advance for any help!
Best wishes,
Pablo
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5 Replies Last Post Sep 21, 2010, 3:03 a.m. EDT
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Posted:
1 decade ago
Hi
I believe you are starting with a tough case there, you will need to set up the spherical symmetry case (COMSOL by default is in cartesian, there are the KB descriptions to use as C&P for the equations), then it's the question of which physics to use as it's FSI (mostly) and the coordinate transform must apply correctly, or you make up your physics totaly by yourself.
Now you speak of frequencies "but no need for the modes", the way FEM is made up then you need to solve for modes and frequencies so you will get both anyhow. the main point is how to free you from theta and phi and keep only "r" the radius
I would expect to spend several hours to set up such a model, specially to validate it, unfortunately it's too far from my everydays work so I do not see how to give further clues. Last year, when I looked into this issue I tried but without full success (search the forum), to simplify it such to use only one physics for the fluid and structure, as basically both are governed by the same equation, only the stress tensor is simpler for a fluid. I answered at that time as I was basically interested to understand how COMSOL could treat such a case, the others had more scientific interest I believe, and I do not know if they succeeded
--
Good luck
Ivar
I believe you are starting with a tough case there, you will need to set up the spherical symmetry case (COMSOL by default is in cartesian, there are the KB descriptions to use as C&P for the equations), then it's the question of which physics to use as it's FSI (mostly) and the coordinate transform must apply correctly, or you make up your physics totaly by yourself.
Now you speak of frequencies "but no need for the modes", the way FEM is made up then you need to solve for modes and frequencies so you will get both anyhow. the main point is how to free you from theta and phi and keep only "r" the radius
I would expect to spend several hours to set up such a model, specially to validate it, unfortunately it's too far from my everydays work so I do not see how to give further clues. Last year, when I looked into this issue I tried but without full success (search the forum), to simplify it such to use only one physics for the fluid and structure, as basically both are governed by the same equation, only the stress tensor is simpler for a fluid. I answered at that time as I was basically interested to understand how COMSOL could treat such a case, the others had more scientific interest I believe, and I do not know if they succeeded
--
Good luck
Ivar
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Posted:
1 decade ago
Hi Ivar,
Thank you very much for your response! I will see what I can do
it is a challenging problem.
Best regards,
Pablo
Thank you very much for your response! I will see what I can do
it is a challenging problem.
Best regards,
Pablo
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Posted:
1 decade ago
interesting problem! here are a couple of thoughts that came to my mind.
The reference you included seems to be for an inviscid compressible fluid. So I am not sure how you would model this as a Newtonian fluid- perhaps you are thinking analyzing in the limit of small viscosity? If yes you may have stability problems then.
Your problem is essentially 1-D (as Ivar points out, only variation in -r direction is taking place). So I would consider writing out the governing equations with r (and time?) as your independent parameter and trying to solve it in 1-D.
good luck
Ozgur
The reference you included seems to be for an inviscid compressible fluid. So I am not sure how you would model this as a Newtonian fluid- perhaps you are thinking analyzing in the limit of small viscosity? If yes you may have stability problems then.
Your problem is essentially 1-D (as Ivar points out, only variation in -r direction is taking place). So I would consider writing out the governing equations with r (and time?) as your independent parameter and trying to solve it in 1-D.
good luck
Ozgur
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Posted:
1 decade ago
Thank you Ozgur! I appreciate your input.
Briefly, all I want to do is to reproduce the results in the reference.
If I can do it for one I can increase the complexity.
But I will follow your advice!
Thank you!
Pablo
Briefly, all I want to do is to reproduce the results in the reference.
If I can do it for one I can increase the complexity.
But I will follow your advice!
Thank you!
Pablo
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Posted:
1 decade ago
Hi Pablo,
Check the model "coupled vibrations" in the Model Library-> Structural Mechanics Module-> Acoustic-Structure Interaction-> coupled vibrations.
The example shows how to couple a "flat" shell (structural mechanics) to pressure acoustics (3D wave equation), it is straight forwards to modify it to fit curved shells.
Greetings
Ed
PS: Note that you do not have to solve the full 3D problem, you can always take advantages of your problem's symmetries
Check the model "coupled vibrations" in the Model Library-> Structural Mechanics Module-> Acoustic-Structure Interaction-> coupled vibrations.
The example shows how to couple a "flat" shell (structural mechanics) to pressure acoustics (3D wave equation), it is straight forwards to modify it to fit curved shells.
Greetings
Ed
PS: Note that you do not have to solve the full 3D problem, you can always take advantages of your problem's symmetries