Solver Yplus and Wall Treatment
 

Hi,

I've just read in CFX help files that the solver Yplus is not the same for Scalable Wall-Functions and Automatic Wall Treatment. There would be a factor 1/4 between them. Can anyone help on this ? I'm not sure to fully understand what is the Solver Yplus about and why there is that factor.

Also, I recently modeled a standard backward-facing step and found differences between the K-E model (with Scalable wall functions) and the SST model (with Auto. Wall Treatment) even though the latter was used on a grid with Y+ around 40. I was expecting to get the same results. Could the 1/4 factor be part of the explaination ?

Thanks

Felix

Re: Solver Yplus and Wall Treatment
 

As I understand SST model must be companied with a Y+ around 1...

Andres.

Re: Solver Yplus and Wall Treatment
 

Hi Andres,

I know that SST model must be used with Y+ < 2 to take full advantage of the K-Omega treatment near the wall. However, this is "standard" Y+ . What is the Solver Y+ influence on the solution?

Regards,

Felix

Re: Solver Yplus and Wall Treatment
 

The variable Solver Yplus is used internally by the ANSYS CFX-Solver. It uses different definitions for the wall distance of the first wall point. This variable is available for backwards consistency, but is of little use to the user.

The Yplus you will define while generating the mesh is the standard Yplus and not the solver Yplus... So for SST you need a Yplus <2

Re: Solver Yplus and Wall Treatment
 

Hello all,

Andres and Luke, thank you very much for your answers but my curiosity isn't fully satisfied yet. Let me reformulate my questions:

1) Why is there a difference in the definition of the Solver Y+ between Scalable Wall-Functions and Automatic Wall Treatment ?

2) Is that difference responsible for the discrepancies between calculations run with the K-E and the SST models when the "standard" Y+ values imply that the SST model doesn't switch to K-Omega (no near wall resolution) ?

3) Am I right thinking that the SST model should in theory give the exact same approximate solution as the K-E model if the first mesh point is at Y+=40 ?

Thanks,

Felix

Re: Solver Yplus and Wall Treatment
 

Hi Felix,

To answer your questions:

1) Why is there a difference in the definition of the Solver Y+ between Scalable Wall-Functions and Automatic Wall Treatment ? Solver Yplus is really an internal value and not of much use to the user. Just ignore it.

2) Is that difference responsible for the discrepancies between calculations run with the K-E and the SST models when the "standard" Y+ values imply that the SST model doesn't switch to K-Omega (no near wall resolution)? No, there are other differences between the SST and k-e models which will affect your results, even if you don't resolve the boundary layer. SST doesn't actually switch between k-e and k-omega, it is always a k-omega like formulation (i.e. solving for eddy frequency, omega), but the terms are expanded differently than in the standard formulation. By removing a particular term in the equation, one can recover a form that is similar to k-e, but not exactly the same. This term is multiplied by a blend factor based on wall distance among other things (0 <= F <= 1). There are some other details as well, but you would be best to get a paper on SST or review the doc to understand this.

3) Am I right thinking that the SST model should in theory give the exact same approximate solution as the K-E model if the first mesh point is at Y+=40? No. Although SST will behave similarly to k-e in the free stream, it is not exactly the same. Also, even though you have a large Y+, the SST treatment of the boundary layer is still slightly different.

Personally, I would worry less about them being the same and concern myself more with which gives the right answer. In most cases this is SST, but results vary.

Regards, Robin

Re: Solver Yplus and Wall Treatment
 

Hi Robin,

Thank you for this highly valuable answer. I had misunderstood the papers of Menter (1994 & 2003 I guess) on the SST model and thought that the formulation of this model was equivalent to the K-E in the free stream. Thanks for the precisions.

Now as you said the SST is usually more accurate than the K-E (although this doesn't seem obvious) but the problem of large aspect ratio cells at separation/reattachment points due to fine boundary layer resolution perpendicular of the wall is still an issue that needs to be considered.

Best regards,

Felix

Re: Solver Yplus and Wall Treatment
 

Hi Felix,

The large aspect ratio should not be a problem with k-e, since it rarely captures separation :)

All kidding aside, a common misconception about SST is that it is more unstable. This is not actually true. SST is much more elegant and it's implementation is more stable numerically than k-e, making it more tolerant to bad grid, etc. However, since SST will capture separation, the solution is often more unstable due to the free shear layers that evolve, which is a problem of the physics, not the model.

Regards, Robin

Re: Solver Yplus and Wall Treatment
 

Hi Felix,

k-epsilon model will usually over-predict eddy viscosity (actally it is a combination of over-predicting k and under-predicting epsilon that occurs...but since all the momentum equations see is eddy viscosity...they don't care about why) this tends to stabalize a flow code. This is much the same issue of numerical viscosity introduced by first order-upwind schemes stabalizing a code. This is why standard k-eps seems more stable in most cases.

There is a close relation with the over-prediction of eddy viscosity with smooth solutions for velocity....which again makes the momentum equations easier to solve...smooth is always easier than sharp in CFD! This is also why a k-epsilon model will not predict or underpredict separation!

That being said both k-eps and SST are 2 equation models which means they are just that....engineering models!

hope this helps....... ;-)

Regards,

Bak_Flow

Re: Solver Yplus and Wall Treatment
 

Hi Robin & Bak_Flow,

Those precisions are very interesting and tend to confirm what I had already observed. The K-E and SST used with a coarse grid at the wall tend to lead to solution convergence. The SST model used properly doesn't. I will run a transient simulation soon and I will keep you updated on whether the SST model converges or not in my case.

In a different geometry I studied in the past months the transient simulation wouldn't converge, though. Not even within a timestep. That is whay I was blaming large Aspect Ratio elements. Hope it will work this time !

Regards,

Felix

Re: Solver Yplus and Wall Treatment
 

Hi Felix,

Convergence does not have the same meaning with a transient simulation. While it is important to sufficiently converge within the coefficient loops of a timestep, the outer loop convergence that you seek in a Steady State simulation has no relevance in a transient.

When you run steady state, the goal is just that: to acheive a steady state. At steady state the solution no longer changes from one iteration to the next, thus the transient term goes to zero along with the outer loop residuals. They never actaully go to zero; because of roundoff and numerical errors, but it is possible to determine an acceptable residual level for a given application. Note that saying the solution isn't changing is not the same as saying the convergence isn't changing (in the latter case the solution could be changing significantly and the residuals are not reducing any further).

In a transient simulation you need to converge within the timestep to accurately capture the transient behavior, but this typically requires a looser convergence level than in a steady state simulation. The solution itself could vary significantly from one timestep to the next.

You also have to be careful about using the standard RANS models, such as k-e and SST, in transient simulations. They tend to overpredict the Eddy Viscosity because they are intended to incorporate the effects of transient mixing due to turbulent eddies into their Eddy Viscosity prediction, wheras the transient solution will also capture these eddies and their transport effects, resulting in a double accounting of the turbulence. As a result, the higher Eddy Viscosity will tend to damp out the development of smaller eddies, thus predicting only the large scale fluctuations.

If you are modelling a large scale system level transient (i.e. large timescale changes in operating conditions) this may be OK, since you won't capture the eddies anyhow. But for smaller timescale transients where you capture fluctuations in shear layers, etc. these effects will be important.

A possible solution is to use transient turbulence models such as LES or DES. The unfortunate consequence is that this breaks continuity with your steady state efforts as the turbulence model is completely different. CFX is developing a more practical solution, known as Scale Adaptive Simulation (SAS), which is consistent with the RANS approach, but you'll have to wait for version 11 to give it a go.

Best regards, Robin