this didnt take long to find, thanks to Simscale haha. I read all these articles already but re-reading with what i know now gives new meaning.
The first cell center needs to be placed in the log-law region to ensure the accuracy of the results. Wall functions are used to bridge the inner region between the wall and the turbulence fully developed region.
First grid cell needs to be 30 < y+ < 300 (If this is too low, the model is invalid. If this is too high, the wall is not properly resolved.
If i understand this correctly:
- This means only the first cell centroid needs to be in the 30-300 range not the all 3 cells (or however many you are using)
The wall functions rely on the universal law of the wall , which basically states that the velocity distribution very near to a wall is similar for almost all turbulent flows. One can interpret y+ as a local Reynolds number, which means that its magnitude can be expected to determine the relative importance of viscous and turbulent processes. Figure 2 shows the fractional contributions to the total stress from the viscous and Reynolds stresses in the near wall region of channel flow. One can easily see that if we are in the viscous wall region with y+ < 50, there is a direct effect of the viscosity on the shear stress. Conversely in the outer layer with y+ > 50, the effect of viscosity is neglibile. (Pope)
Depending on the turbulence model used, different wall functions must be applied to respective fields of the turbulence model, which means that k−ϵ has different wall functions than the k−ω model.
Due to this fact, the different turbulence models and the associated wall functions require different values of y+ as well as different spatial resolutions of the near wall area.
- Since we are using the k−ω turbulence model we dont need to worry about wall functions but we must be aware that our Y+ values could be different because we are using this model. I am not sure if these ranges apply, but i assume now they are pretty universal.
This article is a main source for the simscale wiki article so i read through this as well
The size of your grid cell nearest to the wall (value of y+) is very important. The
value you need depends on the modelling approach chosen.
Using a Wall Function
* First grid cell needs to be 30 < y+ < 300 (Too low, and model is invalid. Too high and the wall is not properly resolved.)
* Use a wall function, and a high Re turbulence model (SKE, RKE, RNG)
* Generally speaking, this is the approach if you are more interested in the mixing in the middle of the domain, rather than the forces on the wall.
- This graph shows a log-law starting point of Y+ = 60. the upper limit of this value range, as shown in the graph above, says that it is determined by the Reynolds number. This means that the normal 30-300 Y+ range is more of a guideline for the first cell size and to fully encapsulate the log law region, the upper limit is dependent on the Reynolds number being measured. So this could be 30-300, 30-500 or 30- 800.
EDIT: Re reading this again i see i have made some false assumptions but have reworded my questions
Now the questions become:
- Should the first layer size be randomly within the 30-(measured Reynolds number range)?
Example using range of 30-300:
starting point of first cell - Y = 50 - lower limit of log-law
OR
starting point of first cell - Y= 250 - upper limit of log-law
(both first cell sizes are within 30-300 range)
-
in continuation of question 1, would it be better for the first cell size be in the middle of the 30-300 range so that changes in mesh sizing still keeps the Y+ Value in the range?
-
What is the upper limit (outside of the log-law region) for the remaining Boundary layer cells or is there sole purpose to reduce a sudden change between any larger neighboring cell sizes?