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extrapolating interface curvature onto the wall

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Old   July 29, 2016, 09:56
Default extrapolating interface curvature onto the wall
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Saideep
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Dear FOAMers,

I am trying to extrapolate an internal field variable (interFOAM's - interface curvature variable, k) onto the wall boundary as shown in the picture.

I would like to solve for the following equation:
cos (\theta) = 2ra/(r2+a2).

I know the value of 'r' based on dimensions of my model and based on extrapolation I would like to know the value of 'a' run time and then determine theta.



Can anyone direct me on how to extrapolate the interface curvature onto the wall please.

Thanks,
Saideep
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Old   July 29, 2016, 11:02
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Hi Saideep,

What afkhami did was fit a circle to the part of interface close to wall and thats how he gets the extrapolated contact line. From which you can get the r, a.


Why do you need interface curvature ?
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Old   July 29, 2016, 11:35
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Hi Vignesh;

Thanks for that.

I had a different picture. If I understand you correctly, values are obtained after reaching a steady state..?

I was thinking it is a parameter to be updated from curvature every time step.
--
I am trying to include dynamic c.a. model based on empirical relations. (Cox, Bracke etc) because I never reach a mesh independent solution for my case of capillary rise when gravity is turned off and flow is only due to surface tension force.
So, I was thinking Afkhami's procedure does the trick.

Saideep
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Old   July 29, 2016, 11:45
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Quote:
Originally Posted by Saideep View Post
Hi Vignesh;

Thanks for that.

I had a different picture. If I understand you correctly, values are obtained after reaching a steady state..?

I was thinking it is a parameter to be updated from curvature every time step.
--
I am trying to include dynamic c.a. model based on empirical relations. (Cox, Bracke etc) because I never reach a mesh independent solution for my case of capillary rise when gravity is turned off and flow is only due to surface tension force.
So, I was thinking Afkhami's procedure does the trick.

Saideep
Steady state ... yes more or less. Have you tried introducing slip ? (Navier BC) It also results in mesh independent solution. By the way do you get the results matching the theory ?
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Old   July 29, 2016, 12:09
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Hi,
I tried to introduce partial slip b.c(slip length = delta/2) as he mentions in his paper but still far from convergence. Improves slightly over no-slip b.c but still not satisfactory.

I have a question regarding the dynamic c.a.: hope you can help me out here,
any dynamic c.a. relation is seen to increase the c.a. at wall surface over the static c.a. In my case I have flow caused due to force "\sigma*cos(\theta)".
Upon increase in c.a., the force causing flow is reducing and the results are quite far from analytic predictions. My case in figures.
pic1.jpg
pic2.jpg

Comparing to analytic solution the static c.a seems to be better except that I dont get to a mesh independent solution.
Any idea over that??

Saideep
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Old   July 29, 2016, 12:44
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Code:
I tried to introduce partial slip b.c(slip length = delta/2) as he  mentions in his paper but still far from convergence. Improves slightly  over no-slip b.c but still not satisfactory.
Did you try Afkhami's Dynamic Contact Angle model ? Also have a look at this paper

Comparison between numerical models for the simulation of moving contact lines


Code:
any dynamic c.a. relation is seen to increase the c.a. at wall surface over the static c.a
Not necessarily ... For receding case or when ca < 0 it might be less than the static value.

Code:
Comparing to analytic solution the static c.a seems to be better.
Any idea over that??
For capillary flow in a tube problem (or any spontaneous capillary flow), inertial forces dominate only at the very early stages during which the rise is rapid, after that the rise slows down. So its safe to use static ca. Dynamic ca if used must be switched off after this rapid rise because after this velocity drops down hence the capillary number. So it does not make sense to use DC model.

Have a look at this paper
The transition from inertial to viscous flow in capillary rise by N. Fries, M. Dreyer

My understanding of contact angle and capillary flows is very less. If you find anything wrong please correct me.

Hope this helps !!
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Old   August 1, 2016, 07:09
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Hi,

Thanks for the paper seems to be quite interesting.
I have a quick question. I am using the partial Slip b.c on wall for velocity. But I am dealing with dimensions in scale of e-5m. Partial slip requires me to specify "valueFraction" calculated as 1/(slip length + 1). If I consider my slip length as "delta/2" as mentioned in papers, I always end up with values close to 0.999999---. So, ultimately I am close to a no-slip b.c and see not much of difference.

Any idea how can I better this factor?

Thanks;
Saideep
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Old   August 1, 2016, 07:20
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Hi Saideep,

I have no idea !! But do you see mesh convergence ?
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Old   August 1, 2016, 07:27
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No. Using partial slip also does not solve the problem.
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