Are you relying on wall functions?

sek · April 23, 2009, 17:21

Hello FOAMers!

This is something that has bene lingering in my mind for some time. I'd like hear what OF developers/gurus have to say about what I'm going to say from now.

Let's say you want to use one of those high-Re models in OpenFOAM. And suppose your first cell off the wall is in fully turbulent region (log-layer), say, at y+ = 100.
With the wall velocity fixed to zero (no slip - yes, it's physically correct!) , Green-Gauss theorem will give you incorrect velocity gradient at wall-adjacent cells. In essence, GG will give something close to Up/yp (Up and yp are velocity and distance from the wall at cell center), whereas the real gradient should be du/dy = u_tau/(kappa*y) based on the law-of-the-wall (LOW), which is significantly smaller than Up/yp. OpenFOAM avoids the potential problems by adjusting nut_w (turbulent viscosity at the wall) so that the multiplication of nut_w*Up/yp recovers the correct wall-shear stress (therefore correct viscous flux at the wall). In addition ,OF computes turbulent kinetic energy (TKE) production at wall-adjancent cells without explicitly using velocity gradient. So, everything looks fine so far.

However, the velocity gradients at wall-adjacent cells get used for discretization of convection and diffusion through others internal faces (e.g., west, east, and north faces, if the south face is on the wall). Then, wouldn't it introduce a serious numerical error? FLUENT, for instance, uses a "slip velocity" concept in which the wall-velocity keeps being updated using the LOW.

I'll appreciate if you read it through.

svens · November 8, 2009, 19:27

Hello Sek

Thanks for your post!

At the moment I'm trying to validate some changes at the REqn of OpenFOAMs Launder-Gibson-RSTM. The idea was to write the pressure-shear-corelation in a way that just by changing some coefficiants you can get different RSTMs. One of them represents the Launder-Gibson-RSTM. Running OpneFOAMs formulation and the equivalent with absolutly the same initial and boundary conditions leads to different results for the Reynolds-Stress-Tensor. Having a deeper look at it shows that the field values for R are absolutly the same but the near wall region have some huge variations.

These brought my to the search for OpenFOAMs near wall treatement. And yes like you wrote - they correct the gradient near the walls with the turbulent viscocity. I tried to figure out how this can be done but didn't could find a satisfing soultion.

Your post sounds like you are pretty familiar with this way of gradiant correction. So please - could you give me some further explanation? I'm really stucked at this point and need some help from extern!

Thank you so much!
Sven

April 23, 2009, 17:21	Are you relying on wall functions?	#1
sek Member Sung-Eun Kim Join Date: Mar 2009 Posts: 76 Rep Power: 17	Hello FOAMers! This is something that has bene lingering in my mind for some time. I'd like hear what OF developers/gurus have to say about what I'm going to say from now. Let's say you want to use one of those high-Re models in OpenFOAM. And suppose your first cell off the wall is in fully turbulent region (log-layer), say, at y+ = 100. With the wall velocity fixed to zero (no slip - yes, it's physically correct!) , Green-Gauss theorem will give you incorrect velocity gradient at wall-adjacent cells. In essence, GG will give something close to Up/yp (Up and yp are velocity and distance from the wall at cell center), whereas the real gradient should be du/dy = u_tau/(kappay) based on the law-of-the-wall (LOW), which is significantly smaller than Up/yp. OpenFOAM avoids the potential problems by adjusting nut_w (turbulent viscosity at the wall) so that the multiplication of nut_wUp/yp recovers the correct wall-shear stress (therefore correct viscous flux at the wall). In addition ,OF computes turbulent kinetic energy (TKE) production at wall-adjancent cells without explicitly using velocity gradient. So, everything looks fine so far. However, the velocity gradients at wall-adjacent cells get used for discretization of convection and diffusion through others internal faces (e.g., west, east, and north faces, if the south face is on the wall). Then, wouldn't it introduce a serious numerical error? FLUENT, for instance, uses a "slip velocity" concept in which the wall-velocity keeps being updated using the LOW. I'll appreciate if you read it through.

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November 8, 2009, 19:27		#2
svens Member Sven Schweikert Join Date: Jun 2009 Posts: 38 Rep Power: 17	Hello Sek Thanks for your post! At the moment I'm trying to validate some changes at the REqn of OpenFOAMs Launder-Gibson-RSTM. The idea was to write the pressure-shear-corelation in a way that just by changing some coefficiants you can get different RSTMs. One of them represents the Launder-Gibson-RSTM. Running OpneFOAMs formulation and the equivalent with absolutly the same initial and boundary conditions leads to different results for the Reynolds-Stress-Tensor. Having a deeper look at it shows that the field values for R are absolutly the same but the near wall region have some huge variations. These brought my to the search for OpenFOAMs near wall treatement. And yes like you wrote - they correct the gradient near the walls with the turbulent viscocity. I tried to figure out how this can be done but didn't could find a satisfing soultion. Your post sounds like you are pretty familiar with this way of gradiant correction. So please - could you give me some further explanation? I'm really stucked at this point and need some help from extern! Thank you so much! Sven