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Boundary condition for non newtonian flow (need to solve a differential equation) 

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September 14, 2011, 00:17 
Boundary condition for non newtonian flow (need to solve a differential equation)

#1 
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Guifan Li
Join Date: Apr 2011
Location: New York City, U.S.
Posts: 96
Rep Power: 7 
Hi,
I am now to use nonnewtonian boundary inlet condition for my pipe. But as I notice that: As the velocity profile is not pure parabolic shape. I need to solve the following equation p+(1/r)*(d/dr)*[r(A+(AB)/(1+K*(dV/dr))*dV/dr]=0 Can anyone tell me how to put this equation as boundary condition. Really stuck with it. Please give me some hind on details. 

September 14, 2011, 01:46 

#2 
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Claudio Wolfer
Join Date: Aug 2011
Posts: 9
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Hi,
I never used such a BC, but I would solve your equation externaly (with Matlab) on a face equally like your's and the try to map these solution witch mapFields. I guess that it also should be possible to map the solution directly by a list of points. Good luck. wWW 

September 14, 2011, 02:51 

#3  
Member
Guifan Li
Join Date: Apr 2011
Location: New York City, U.S.
Posts: 96
Rep Power: 7 
Quote:
It worth a try by using directMapped. For this static case, if I can successfully export data in same format directMapped accept, that will do. But what I actually want to do it to implement more complex function that velocity change will time and location. I am not sure directMapped can not manipulate that kind of thing. So I still need to solve an equation that U is a variable inside. Do you have any idea to build a new boundary condition that can solve equations? Cheers! 

September 14, 2011, 07:24 

#4 
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Eysteinn Helgason
Join Date: Sep 2009
Location: Gothenburg, Sweden
Posts: 53
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For a boundary condition changing with time and space you should be able to use groovyBC
See: http://openfoamwiki.net/index.php/Contrib_groovyBC /Eysteinn 

September 14, 2011, 10:37 

#5  
Member
Guifan Li
Join Date: Apr 2011
Location: New York City, U.S.
Posts: 96
Rep Power: 7 
Quote:
Thank for replying. groovyBC is a very powerful tool. But it lack a function I need to implement my velocity. My velocity is dependent on time and locatation. It is like something u(r,t)= real(i*exp(i*w)* Bessel(i*t)) where i is complex number and w is constant. Bessel is the Bessel function that can resolve complex number( This is not conclude in the OpenFOAM). I think the only way to do is to import a math libarary that can resolve Bessel(i*t). That why I want to implement a new boundary in fvPatchfield. Cheers! 

September 15, 2011, 07:48 

#6  
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Bernhard Gschaider
Join Date: Mar 2009
Posts: 3,987
Rep Power: 42 
Quote:
Imag(e^(i w) (i t)^n t^n I_n(t)) with I_n being the modified Bessel function. That shouldn't be to hard to get to a pure "real" form (especially if n=0) 

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