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## Fluid flow channel in cantilever beam

Posted Mar 14, 2013, 3:15 PM EDT Version 4.3 10 Replies

My model is the following: a cantilever beam has one longitudinal channel containing a fluid flow. My goal is to find the effects of the fluid flow (viscosity, velocity, size of the channel) on the damping of the beam.

Until now, I was using "Solid Mechanics" looking at the frequency response of the beam around its eigenfrequencies (to estimate damping). But when I add a laminar flow, the results do not change. I have changed the parameters of the fluid, but still no changes.

I would like to know:

1) How to make sure the 2 physics are solved.

2) Am I right to use these 2 physics (Solid mechanics + Laminar flow) over Fluid-flow interaction.

Thanks for your help,

Matthias

you need to see if the equation on the fluid physics changes and accepts the "eigenfrequency" mode (omega development of the time derivativs, I'm not sitting by my WS so Im no longer sure), else you must think how the fluid chages your solid physics and see how to load the "solid" physics accordingly, distributed mass OK, but flow and viscosity, not sure how to ? It depends also on the flow velocity, and if its a simpel or two phase flow

It's an intersting question as its rather fundamental and I have several issues unsolved of that kind, oscillating canteliever imerging in a fluid => eigenfrequency changes ...

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Good luck

Ivar

Thanks for your reply.

NB: the fluid is inside the beam in my case.

I found another discussion thread where you suggested to model the fluid as a linear elastic material with -let's say- Young's modulus = 1/3 Modulus of the beam. That could be an interesting approximation. There will be an eigenfrequency sweep as the E is different, but it should help to see the effect of the flow on the damping of the structure.

Nevertheless, I think there should be a better way to model this problem in COMSOL,

Regards,

Matthias

yes you can cheat a bit like that, but it does not model flow, nor viscosity effects, for that you need the CFD.

If you fluid is a liquid, and its fully filled up, in a close volume, you would probably not have any significant flow, in whch case you can take the fluid mass and distribute it on the solid-fluid Boundary, as an BC added mass (not theat if you add agravity load, I do not believe COMSOL adds it to a Boundary load for this added mass, you must take car of that and add artitificially the "weight" of the liquid, distributed evenly over the solid-fluid boundary too. The same for the eigenfrequency (just check if the frequency does not change when you add an "added mass boundary") then you need to tweak the load eqution to get them dependent on omega too (I believ this depends on the version, and will be taken fully count of in a later release, I have heard, TBC).

What is far trickier is the damping, and if you have a 2 phase flow air liquid that can move around. Then you cannot use the eigenfrquency, I believe, you would need to do it in the time domain, and I wounder if it is not cahotic ? (again TBC to be confirmed)

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Good luck

Ivar

I managed to use a BC to add the liquid mass, however how can I add damping from the viscosity of the liquid? In another thread, you said that it could be modeled as a BC too. Do you have any suggestion for the formula?

Thanks,

Matthias

unfortunately I do not have a validated way to propose, and I know I did a mistake in one of my earlier threads about a year ago on vibration of a cantilever i a fluid, so pls check carefully (also what I'm saying , especially since I'm rather verbose ;)

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Good luck

Ivar

Thanks for the reply. Do you know any other way to model the viscous damping of the fluid? In my case, a viscous fluid is enclosed in the structure and I want to compute the frequency response of whole system (structure + fluid).

Thanks,

Matthias

I believe you can make a FSI model in frequency domain (pls check I'm not by my WS so I cannot just now) but you cannot do it for eigenfrequencies

If not you have only the time domain, which is cumbesome and convergence tricky ;)

I would also like to get a good (validated) example model how to apply structural and fluid interaction in the vibratrional domain (eigenfrequency and frequency domain)

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Good luck

Ivar

I switched to a FSI model, default studies are "Stationary" and "Time Dependent" only, no frequency analysis. I believe this could be a good way to model my problem, in the time domain, I would be able to see the damping from the whole structure depending on the fluid properties.

Modeling:

1) I define my geometry (rectangular beam with a longitudinal circular channel).

2) I select the materials and input their properties (a polymer for the beam, a viscous fluid for the liquid).

3) In the FSI, I assign the domains, add damping to the linear elastic material, add a fixed constraint (cantilever) and a boundary load on the tip.

As you said, the convergence is tricky! If I launch a stationary study, the solver cannot find any values ("NaN or Inf found when solving linear system using GMRES"). And if I try a time dependent study, no consistent initial value is found.

Do I miss something in the model?

The file is attached. Thank you for having a look!

Best,

Matthias

Attachments:

one caution, check carefully the damping node and related doc, as not all damping factors wotk for all solver types (i.e. isotropic solid damping is not compatible with time series but Rayleigh mass and stiffness yes ...)

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Good luck

Ivar

I'm using Rayleigh damping, but I don't think that damping is causing trouble. Do you have a file with a validated 3D FSI? (I already looked at the files form the Model Library). I must be missing something in the model... For now, the solver fails (NaN or infinite values found). Thanks.

Matthias

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