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Danny Tandra July 8, 2003 23:44

Wall Function - Correct me if I am wrong
Dear All:

Could you please correct me if I am wrong about the following:

1. When we are dealing with rough wall, low Reynold number two equations model can not be used. The ONLY option that we have is only implementing wall function, even though it is well documented that the wall function is bad when it comes to flow with separation and adverse pressure gradient.

Thank's in advance

Danny Tandra

gorka July 9, 2003 03:21

Re: Wall Function - Correct me if I am wrong

k-epsilon low Reynolds number models can't take the wall roughness into account. However, k-w low Reynolds models can handle it with a proper boundary condition. Wilcox's book is a good reference.

Hope this helps,


Danny Tandra July 9, 2003 12:04

Re: Wall Function - Correct me if I am wrong
Thank's for the information.

I have Wilcox book in my hand right now, but I can not find section that explained the use of surface roughness in low reynolds K-W model.

There is a section explaining the use of numerical roughness strip used to improve low reynold k-w model. But the numerical roughness strip is not really the physical wall roughness. From my quick reading of that section, this numerical roughness strip is just helping us to choose a better value for W at the wall (smooth wall).

If I am not mistaken, by definition, low reynold two equation model imposed no slip boundary condition, which mean that we set the velocity at the wall to be 0 in all direction. Now, If the surface is rough, it is not clear where you want to put your zero velocity. Unless we want to really incorporate the roughness of the wall in to our grids (which is most of the time this is not really possible, especially when we have "Ugly" wall)


Bart Prast July 10, 2003 06:21

Re: Wall Function - Correct me if I am wrong
I can only speak from our experience (CFX5): Wall roughness can only be used with epsilon based turbulence Modelling (k-eps, RSM eps) but NOT any model with omega. I'm not sure whether this is a limitation of CFX only but as far as I can see the limitation seems quite fundamental.

gorka July 10, 2003 07:35

Re: Wall Function - Correct me if I am wrong
Hi Bart,

In Fluent the wall roughness is considered by the k-w model, almost as is explained in Wilcox's book.

Best regards,


gorka July 10, 2003 07:45

Re: Wall Function - Correct me if I am wrong
Hi Danny,

In "Chapter 4.7.2 Sourface Roughness" (Wilcox), regarding the arbitrary value of w at a wall, it is said: "it provides a natural way to incorporate effects of surface roughness through surface boundary conditions".

As it is explained next, the roughness heigh is taken into account by modifying the value of w at the wall.

Hope this helps,


Bart Prast July 10, 2003 08:14

Re: Wall Function - Correct me if I am wrong
FLUENT rules?!

mike July 15, 2003 11:38

Re: Wall Function - Correct me if I am wrong
Fathi Tarada did some work on the prediction of rough wall boundary layers using a low-Re 2-equation model, Int.J.Heat Fluid Flow , 11(4), 1990, p331. I seem to recall it was a low-Re k-e model rather than the low-Re Wilcox-Kolmogorov model, but I may be wrong.

sylvain July 15, 2003 13:01

Re: Wall Function - Correct me if I am wrong
First of all, low Re number k-eps models have almost nothing to deal with physics, so you are allow to do everything with them since you get the correct behavior.

In fact, if we use the notation from Patel, Rodi and Scheuerer :

f1 is used to increase production of dissipation rate;

f2 is used to decrease destruction of dissipation rate;

this two functions (which have nothing to do with the distance from the wall) are needed because of the proximity of the energetic scales with the dissipatives scales :

at low Re number, real production (I mean production of k) occurs in the dissipative scales, which increase the dissipation rate;

at low Re number, dissipation occurs at energetic scales (without energy cascade K41), which increase the dissipation rate "effect".

The latest function f_nu is needed to damped the viscosity in the vicinity of the wall. This is the less physical part of this kind of models. In fact, turbulence does not decrease as much as low-Re k-eps models try to make us believe. At the opposite, real turbulence is far to be negligeable near the wall, BUT, its effect on the mean velocity is negligeable since in this region, turbulence acts on directions parallel to the wall.

So, this damping function is determined to reach the value of one at the correct y+. This correct y+ is more or less 30, at the begining of the log-law region.

If now, we change this last function to make it reach the value of one sooner, let say y+=10, then the log-low region will be reached sooner, and the constant part of the log-law will be changed (decreased). Which is more or less the effect of rough wall.

So you can adjust your low-Re k-eps model to rough wall.

gorka July 16, 2003 10:44

Re: Wall Function - Correct me if I am wrong

Maybe you can find this paper interesting:

Patel V.C., 1995, "Application of Turbulence Models to Separated Flow Over Rough Surfaces", ASME Journal of Fluids Engineering, Vol 117, pp. 234-241.


Danny Tandra July 16, 2003 13:26

Thank you
Thank you all for the information

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