[Nek5000-users] non-newtonian fluid

[nek5000-users at lists.mcs.anl.gov]

Hi Tubois

I can give you some background which may help..

The power law model specifies the visosity as power law in an effective
scalar shear rate gamma* so the viscous stress tau is given by
tau= eta(gamma*) x gamma  where gamma is the  tensor  dvi/dxj  + d vj /dxi

and gamma* is sqrt(1/2 gamma::gamma)  where :: means two consecutive dot
products of the gamma tensor
and the function eta for the power law model is eta= m * (gamma*)^n-1 where
m and n are material parameters
you can start with ket sat n=1/3 or 1/2....etc and the newtonian fluid
limit is n=1

for the case of axisymmetric pipe flow vz=f(r)  where z is the flow
direction and r is the radius ( v_theta=vr=0)

it can be shown that the scalar shear rate gamma*= - d vz /d r  and that
the only stress component is tau_rz and is given by

tau_rz=-m*(- d vz /dr ) ^ n-1 * d vz/dr = -m* (-d vz /dr )^n

note that gamma tensor has only one non zero component
gamma  = dvz /d r * [ 0 0 1 ; 0 0 0; 0 0 0]

the analytical solution is
vz= (n/n+1) *  ( (Po-PL)*R / (2*m*L) )^(1/n)  *R* [1- (r/R)]^-(n+1)/n

Ammar








On Thu, Nov 7, 2013 at 9:12 AM, <nek5000-users at lists.mcs.anl.gov> wrote:

> Hi,
>
> I am willing to simulate some non-newtonian fluids by nek5000. I found in
> the archive some discussions about several models, like *Herschel-Bulkley
> Bukingham, power law* But none of the models is available online.
>
> In the example, there is a var_vis case. I looked into the st2.usr and I
> do not understand which models is about. Is it to calculate \nu (\nabla^
> u)^2 for the diffusion term?  Can someone give a detailed discription for
> this case?
>
> I would like to implement a power-law fluid model. There exists an
> analytical solution in the case of circular pipe so it can be compared
> with. see http://en.wikipedia.org/wiki/Power-law_fluid
>
> If some already implemented this kind of fluids, could you share some
> sources? Or give a guideline, which subroutine to see.
>
> Thank you very much!
>
> Tubois
>
>
>
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> Nek5000-users mailing list
> Nek5000-users at lists.mcs.anl.gov
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>


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