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Reynolds Stresses in Fluent

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Old   June 5, 2010, 11:09
Default Reynolds Stresses in Fluent
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Hello,

I am working the Re=3900 2-D cylinder problem for a turbulence class in graduate school. We were to use the k-e and k-w turbulence models and plot uu Reynolds stress profiles to compare to Kravchenko's paper.

How do I back out the Reynolds stress components I need from the turbulent quantities given by these two models? I imagine I just use the Bouss Approx, and write a UDF to plot them, but I've never used the UDF's.

Can someone give me some idiot-proof step by step instructions on how to do this?

Thanks!
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Old   January 10, 2011, 15:31
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i have the same question right now
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Old   February 1, 2012, 10:50
Default Same doubt
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I'm facing the same problem right now.
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Old   February 1, 2012, 13:57
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You have to use Bous. Approx.
Use the Define->Custom Field Functions to calculate

delu=dx-velocity-dx + dy-velocity-dy + dz-velocity-dz

then calculate strain rate tensor S_uu
S_uu=dx-velocity-dx - 1 / 3 * dukxk

Then use
-u'u'=2*viscosity-turb*S_uu/density - 2/3*turb-kinetic-energy
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Old   September 15, 2013, 07:29
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Quote:
Originally Posted by dynamics View Post
You have to use Bous. Approx.
Use the Define->Custom Field Functions to calculate

delu=dx-velocity-dx + dy-velocity-dy + dz-velocity-dz

then calculate strain rate tensor S_uu
S_uu=dx-velocity-dx - 1 / 3 * dukxk

Then use
-u'u'=2*viscosity-turb*S_uu/density - 2/3*turb-kinetic-energy
What is dukxk ?
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Old   April 14, 2014, 16:26
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Quote:
Originally Posted by dynamics View Post
You have to use Bous. Approx.
Use the Define->Custom Field Functions to calculate

delu=dx-velocity-dx + dy-velocity-dy + dz-velocity-dz

then calculate strain rate tensor S_uu
S_uu=dx-velocity-dx - 1 / 3 * dukxk

Then use
-u'u'=2*viscosity-turb*S_uu/density - 2/3*turb-kinetic-energy
Hi Dynamix,
I need to define Reynolds stresses in fluent with k-e model. I also could not understand the term dukxk and you define in the beginning something called delu but you do not use it anywhere. could you explain what is that one also?
Thank you very much, I really appreciate it.
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Old   December 1, 2015, 11:16
Default Boussinesq aproximation solves the problem
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Miloslav Dohnal
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Hello everyone
Yesterday, I found this thread and spent almost whole day by searching for answer with some, let's say, proof or explanation. I found that the problem raises from the transport equation of k in two equation models; and it's one of the problems in turbulence modeling. In general, we have more unknowns to solve than available equations; and Boussinesq aproximation is used to enclose transport equation of k in one- or two- equation models.

And now, back to problem:
let's have the Boussinesq aproximation

-\rho\overline{u^{'}_{i}u^{'}_{j}}=\mu_t\left(\frac{\partial\overline{u_i}}{\partial{x_j}}+\frac{\partial\overline{u_j}}{\partial{x_i}}-\frac{2}{3}\frac{\partial\overline{u_k}}{\partial{x_k}}\delta_{ij}\right)-\frac{2}{3}\rho k\delta_{ij}

where

\delta_{ij}=
\begin{cases}
1 & \text{if  } i=j \\
0 & \text{if  } i\neq j
\end{cases} is Kronecker delta

and also have those two vectors:
position vector

\vec{x}=(x;y;z)

and velocity vector

\vec{u}=(u;v;w)

if the flow is incompressible, then

-\frac{2}{3}\frac{\partial\overline{u_k}}{\partial{x_k}}\delta_{ij}=0

Now, it only depands what kind of Reynolds stress you want. For instance, if you want to know normal stress \overline{u^{'}u^{'}} simply put i=1 and j=1; then, substitute first element in \vec{u} and \vec{x} to the Boussinesq aproximation and do the math. You will obtain:

-\overline{u^{'}u^{'}}=\frac{\mu_t}{\rho}\left(\frac{\partial\overline{u}}{\partial{x}}+\frac{\partial\overline{u}}{\partial{x}}\right)-\frac{2}{3}k=
\nu_t\left(\frac{\partial\overline{u}}{\partial{x}}+\frac{\partial\overline{u}}{\partial{x}}\right)-\frac{2}{3}k

And if you want to know shear stress \overline{u^{'}v^{'}}, just put i=1 and j=2 and you will get:

-\overline{u^{'}v^{'}}=\frac{\mu_t}{\rho}\left(\frac{\partial\overline{u}}{\partial{y}}+\frac{\partial\overline{v}}{\partial{x}}\right)=\nu_t\left(\frac{\partial\overline{u}}{\partial{y}}+\frac{\partial\overline{v}}{\partial{x}}\right)

Apply same principle for any other Reynolds stress you want to know and just simply put this to Fluent using Custom Field Functions

Reference
Wilcox, D. C., 2006, Turbulence Modeling for CFD, 3rd ed., Dcw Industries, Incorporated.
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