Wall functions
 

As I mentioned in my previous message I am new to CFD modelling. At the moment I am still getting to grips with what I should be doing and at the moment I am looking at wall functions. Wall functions are used to model the near wall region, but which bit exactly? I use 3 layers to define the near wall region: The viscous sublayer where the flow is almost laminar, a buffer layer where viscous forces and turbulence are equally important and a fully turbulent or log-law layer where the velocity is a logarithmic function of the distance from the wall. After the log-law layer the flow is fully turbulent and the wall has no effect (I call this the core). Some books/manuals, such as Fluent, say that wall fuctions are used to model the viscous sublayer and buffer layer (from this I must assume that turbulence equations are used to model the log law and core). Others say that the wall functions model the viscous sublayer, buffer layer and log-law layer. Which is correct?

Thanks for your help, John

Re: Wall functions
 

Hi, You may want to refer the book, "Turbulence Modeling for CFD" by David C. Wilcox. The book has an accompanyung software that you may find useful.

Abup.

Re: Wall functions
 

Wall functions are used because some turbulence variables such as epsilon or omega are singular or unknown at a wall boundary. Consequently it is difficult to prescribe a boundary condition at the wall and integrating through the sublayer is computationally expensive.

Wall functions are really boundary conditons placed at the first grid point out from the wall (so we are not really modelling the sublayer and buffer layer, we are omitting the near-wall). They use the log-law of the wall to estimate what the velocities and turbulent quantities should be at the first grid point. Therefore to obtain sensical solutions the first grid point should be in the log-law region. So wall functions do not replace the log-law region they are merely an off-wall boundary condition. Ideally the first grid point should be placed as close to the lower bound of the log-law region so that we have as many points in the boundary layer as possible. Also the first grid space should be large to place the first grid point in the log-layer, with subsequent spacings much smaller to increase resolution of the boundary layer.

Beware, the log-law of the wall only holds for simple attached flows - as soon as the pressure gradient becomes significantly adverse, or separated they fail to provide accurate solutions. I never use them.

Re: Wall functions
 

To answer to your question, the post from Steve is quiet good. The aim of my post is just to correct a point in yours.

In the viscous sublayer the flow is NOT laminar, the fact is that turbulence in the boundary layer takes its origin from this region. But, roughtly speaking, almost all the "turbulent eddies" are align with the wall. So the effectif turbulence - perpendicular to the wall - is almost zero, then from a RANS point de vue, the flow looks laminar.

Regards,

Sylvain

Re: Wall functions
 

Thanks everyone for responding to my messages, it is really appreciated. I just require one point of clarification (I am now assuming that wall functions only operate in the FIRST cell from the fixed boundary). In your message Steve you mentioned that wall fuctions use the log law relationship to estimate velocity and turbulence quantities. You also say that they should be close to the lower bound of the log law layer. If this is the case:

1) Why use wall functions at the lower end of the log law relationship (which they can model) when trying to model the viscous sublayer and buffer layer (which they cannot)? Is there not a better relationship and can the k-e turbulence model correctly model the log law layer without modification?

2) If wall functions can correctly model the log law layer why not save computational effort and place them towards the end of this layer?

Re: Wall functions
 

k-e model is drawing to correctly resolved the log law with wall function - i.e y+ in [30:150]. If you want to model the viscous sublayer and the buffer layer, you have to damp the turbulent viscosity to get the correct behavior. More over, for y+ greater than 10, eps behaves like 1/y, so to the mesh has to be very fine in this region.

To answer to the second question : if we know - without curvature of the wall nor adverse pressure gradient - where the log law region begins (y+ > 30), it is very difficult to predict where it stops. Moreover, computed values of u,k and eps at y+=150 are not egal to there BC values at same y+.

Regards,

Sylvain

Re: Wall functions
 

One reason for having the first grid point close to the lower bound is that you do need some resolution of the boundary layer, i.e., you don't want the first point at y+=150, 2nd at Y+=300 etc. The log law is only reliable for a small range of flows so it is best to integrate through as much of the log-layer as possible.

Steve

Re: Wall functions
 

I was just wondering what you do use, steve, instead of wall profiles?

Re: Wall functions
 

Omega based models resolved down to the wall, i.e, with wall boundary conditions (hydraulically smooth conditions for Omega) and a grid with y+<1. The flows I deal with always involve pressure gradient induced separation so this approach is neccessary.

Re: Wall functions
 

Hello Steve,

what is an "omega based model"

Uwe

Re: Wall functions
 

By Omega based models I ment models that use omega (or turbulent frequency) as the second tubulence variable. Examples of these are Wilcox k-omega, SST, BSL, Stress-Omega, EASM k-omega.

Re: Wall functions
 

What is the diffrence in building grid for k-epsilon and k-omega ? Is it much finer in wall region for k-omega? Is k-omega superior over k-epsilon in flows with adverse pressure gradient (b.l. separation)?

Re: Wall functions
 

The reason of using wall functions is to decrease degree of freedoms of the simulation as we discussed above.

But more important fact is the physical phenomena of the flow close to the wall.

Significant amount of turbulent production comes from around wall (related to the fact that Sylvain mentioned). Without resolving this region appropriately, we can not get resonable results from the trubulent flow analysis.

Kim.

Re: Wall functions
 

Yes, a finer grid is neccessary when using k-omega (unless it is a Low Reynolds number k-e model, i.e. integrates down to the wall). K-omega is superior for Adverse Pressure gradient flows as k-epsilon typically will delay separation due to an over-estimate of the length scale in the defect layer region. SST is better again for APGs and does not have the freestream dependence of k-omega.