[gbettega]

Hello Forum,
at the tutotla page

https://su2code.github.io/tutorials/Inc_Turbulent_Bend/

it can be read that

"The minimum value of y+ where the wall function is switched off because the mesh is fine enough to be considered fully resolved is 1.0. A value of 5.0 is the default value chosen [...], but lower values are also possible. Note that Spalding’s fit gives us the nondimensional velocity and therefore the wall shear stress in the entire boundary layer. An iterative process (Newton’s method) is used to compute the nondimensional velocity u+ from y+. "

Here, I think, the author of the tutorlal refers to a value of y+ chosen by the user, and written in the .cfg file (in the tutorial y+ = 1.0 is used, and 5.0 is the default value in the cfg file).

Now the Spalding fit:

y+ = (U+) + 0.1108 [ exp(0.4 U+) - 1 - 0.4 (U+) - (1/2) (0.4 U+)^2 ...

(1) Should I interpretet that one manually sets y+, and a corresponding u+ at a node is found inverting the Spalding formula through the mentioned iterative process?

(2) In some cases the solver can issue a warning such

"Warning: y+ < 50 in 36 points, for which the wall model is not active."

in which 50 is set by the user. y+ "is less than" a user value means that the solver computes an y+. So the user value is used for switching/activating the wall function approach?

Being an user of automatic wall treatment in which y+ is automatically evaluated, and the appropriate wall function is selected on the fly, I'm wondering where exactly the arbitrarily in y+ intervent in Su2

Regards

[bigfootedrockmidget]

Hi, I am the author. Sorry for being unclear :-)

We follow the paper of Nichols and Nelson (2004) DOI:10.2514/1.3539


The paper explains this well but basically you do this:

Y+ and u+ are both found iteratively using the wall shear stress tau_w, or the nondimensional version, u_tau=sqrt(tau_w/rho_w). We compute u+(u_tau) and then y+(u_tau) and with the Spalding fit, we can iteratively update tau_w->u_tau->u+->y+


Then about the y+ threshold: So in the paper they basically say: "if y+ < 5, then you do not need wall functions, you are resolving the wall sufficiently. So just switch off the wall functions." Now, the Spalding correlation is correct for y+ <5, so it is not strictly necessary to do this. You are basically just using a model where it is not needed. And the warning that I give is basically saying that your mesh is 'too good', and you can coarsen it if you want. From my study [turbulence modelling with wall functions]
https://su2foundation.org/su2conference2022/
I've found that you resolve the wall sufficiently when y+ < 1, so I recommend this value. However, Nichols and Nelson use y+ = 5 as threshold.

[gbettega]

Originally Posted by bigfootedrockmidget

Hi, I am the author. Sorry for being unclear :-)

We follow the paper of Nichols and Nelson (2004) DOI:10.2514/1.3539


The paper explains this well but basically you do this:

Y+ and u+ are both found iteratively using the wall shear stress tau_w, or the nondimensional version, u_tau=sqrt(tau_w/rho_w). We compute u+(u_tau) and then y+(u_tau) and with the Spalding fit, we can iteratively update tau_w->u_tau->u+->y+


Then about the y+ threshold: So in the paper they basically say: "if y+ < 5, then you do not need wall functions, you are resolving the wall sufficiently. So just switch off the wall functions." Now, the Spalding correlation is correct for y+ <5, so it is not strictly necessary to do this. You are basically just using a model where it is not needed. And the warning that I give is basically saying that your mesh is 'too good', and you can coarsen it if you want. From my study [turbulence modelling with wall functions]
https://su2foundation.org/su2conference2022/
I've found that you resolve the wall sufficiently when y+ < 1, so I recommend this value. However, Nichols and Nelson use y+ = 5 as threshold.

Thank you so much, also for the references,
also for the presentation .pdf.

Another question, coming from the fact that, as I told you, I did not read the code yet: when Su2 founds in a (or serveral) point(s) y+ < 5.0 (say) it continues using Spalding or it switches off the model (and reactivates it after, if neeeded)?
OR the model is always ON, and only the "warning" is issued?

Now I've just simulated incompressible air flow through an "S" shaped fluid domain: see the attached mesh00.png. The air enters the domain (~ BBX 1.0 [m] x 1.0 [m] x 0.1 [m]) with 1.0 [m/s] (see attached inlet.png)

Here, from my side, no accuracy/physical meaning expectations, so coarse mesh, CFL = 100.0, a few hundreds of iterations, ... only for comparing two results for TWO user-defined values of y+, 5.0 and 50.0.

So two simulations:

1) The first: y+ = 5.0 set in the .cfg file

Su2 tells me:
"Warning: y+ < 5 in 140 points, for which the wall model is not active."

And for this case see the attached TKE dist on a clipping plane

2) The second y+ = 50.0 set in the cfg.file
See attached TKE dist on a clipping plane

Su2 tells me:
"Warning: y+ < 50 in 1471 points, for which the wall model is not active."

And for this case see the attached TKE dist on a clipping plane.

The warning is obviously correct, since keeping the same grid, and the same BCs, I "only" increased the "y+" level.
What about the difference between results (I choose TKE) if the Spalding model is always on? It seems that y+ plays an active role in determining the results.

Regards
G

[bigfootedrockmidget]

Hi,

You should not change the value of WALLMODEL_MINYPLUS= 5.0, which is I think what you are doing. This is just a value that switches from the wall model back to 'doing nothing' when the mesh is locally fine enough. In any case it cannot be larger than 5.0 because then the wall is not resolved enough.



Once you have a result, you can view the real y+ value, which is a surface value on the wall. That value should be around 10-100. If it is much larger than 100, say 200, you should make the mesh close to the wall finer, especially in the direction normal to the wall, and if it is smaller than say 1.0, then you could make it coarser to save computational time.