[Nek5000-users] non-newtonian fluid

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

just a small correction
gamma  = dvz /d r * [ 0 0 1 ; 0 0 0; 1 0 0]
and the newtonian limit is n=1 and m= mu

Ammar




On Thu, Nov 7, 2013 at 11:06 AM, amr7684 . <aelghany at gmail.com> wrote:

> 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
>>
>>
>>
>> _______________________________________________
>> Nek5000-users mailing list
>> Nek5000-users at lists.mcs.anl.gov
>> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users
>>
>>
>
>
> --
> http://aelghany.googlepages.com/home
>



-- 
http://aelghany.googlepages.com/home
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/nek5000-users/attachments/20131107/330a2494/attachment-0001.html>