yPlus values for atmospheric boundary layer over complex terrain with rough surface
Hello dear Foamers,
I am trying to simulate wind flow over a building with a complex geometry within a domain with specified roughness parameter assigned to the building and ground.
First of all, as mentioned by all ABL flow authors, I am tending to simulate an empty domain to solve the problem of inhomogeneity of ABL profiles.
But there is an unsolved problem in simulating ABL flows which concerns height of the first cell adjacent to the wall. here consider the wall to be the ground.
The problem arises when the following relation is needed to be included in calculations:
in which yp is height of the center of the first cell adjacent to the wall and,
Ks is equivalent roughness parameter which can be calculated using specified roughness parameter.
For my case you assume that Ks is 0.3 m. So to obey the relation we have a minimum limit of yp=0.3 m for height of the center of the first cell adjacent to the wall and this yields to first cell height of:
h= 2*yp= 0.6 m
But this is a very large number for a nice mesh resolution near wall. I am using rough wall function for the ground, and as you know there is a need of Yplus higher than 30 to correctly resolve the boundary layer. but in this case my Yplus values are very very large. here is the reason:
yPlus= (UStar*y)/nu and
in which Ustar= sqrt(tau_w/rho) or it can be calculated by fitting velocity profile into experimental profiles. in my case UStar= 2.31 m/s, and therefore:
yPlus_wall= (2.31*0.3)/(15e-6)= 46'200
this is a very large yPlus value. As it is mentioned in some papers, this value must be in the range of 30-60 or 30-100.
So here is the problem. How can I overcome it?
There is a very brief explanation by blocken:
"In this section, the CFD simulation is performed according to common practice for near-ground ABL flow in commercial codes, i.e. by employing a high grid resolution near the bottom of the computational domain (small yP) and by adhering to the requirement KS<yP. The 3D simulations are conducted at a scale of 1/40 (further referred to as ‘‘simulation scale’’) with the reference wind speed U0 mentioned above. The reason for the different scale is to obtain suitable values for the non-dimensionless wall unit y+ (between 30 and 100) for the use of wall functions, without the need to change the reference wind speed or the grid resolution for this purpose. Note that calculations at the reduced scale are allowed because to a first approximation, the location of the separation points at the building surface and the general flow features around the buildings can be considered to be independent of the Reynolds number." 
But I can't understand why.
Any help is greatly appreciated.
1. Blocken, B., Carmeliet, J., Stathopoulos, T., 2007a.
CFD evaluation of wind speed conditions in passages between parallel buildings – effect of wall-function roughness modifications for the atmospheric boundary layer flow. Journal of Wind Engineering and Industrial Aerodynamics 95 (9–11), 941–962.
This is a known issue but unfortunately it has not been resolved until now.
now days lots of researches are done by various authors in the field of applications of CFD to pedestrian wind environment to investigate flow patterns around buildings. but unfortunately they haven't clearly talked about y+ values on the ground or the walls of the buildings.
Clearly, this is a subject of interest and a very hot topic in ABL simulations.
1) maybe one solution is to reduce first cell height to solve the problem of the y+ value, but in this case two major problems arise.
First, the relation yp>Ks is not obeyed. the reason that this relation is important is that it is not physically meaningful to have grid cells with center points within the physical roughness height.
the second reason is concerning grid aspect ratio limitations. in this case because of a very low first cell height, aspect ratio will be in the order of 10000 that is absolutely not acceptable in CFD simulations. maybe one solution relies on reducing grid size near the ground in order to have lower aspect ratios, but this need lots of effort and CPU time. because of the application of Wind engineering, large domains are needed to simulate wind flows, and therefore a normal cell size of 5 or 10 m results in a very large number of cell counts, maybe 1'000'000. So reducing cell size is not actually an option.
2) the second solution, as it has been mentioned in , is explicit modeling of roughness elements. this solution seems to have better results. because the above relation (yp>Ks) is obeyed. because of modeling the roughness elements there is no need to define high scale roughness parameters (i.e 0.5 - 3 m) in rough wall functions. and therefor lower scale roughness parameters (i.e 0.01-0.1) are defined for them and this results in a lower yp and therefore better y+ values. in this case additional drawback are the increased number of cells and the subsequent increase in required computing power and CPU time. but in compare with the first solution this seems to be a better idea.
 Blocken, B., Stathopoulos, T., Carmeliet, J., 2007.
CFD simulation of the atmospheric boundary layer: wall function problems.
Atmospheric Environment 41 (2), 238–252.
Ok, I did some research and this is what I got so far:
"Note that the y∗ value, y∗ = (yp.u∗)/nu, with nu the kinematic viscosity and u∗ the friction velocity, is about 15,000–20,000, which significantly exceeds the recommended value of 500–1000. However, standard wall functions are typically also used in CFD simulations of atmospheric boundary layer wind flow when y∗ is well above the upper limit of 500–1000 without reduced performance for the velocity field (see for example  for simulations with y* = 15,609). This is also demonstrated in previous validated CFD studies in which y∗ values with the same order of magnitude were used  and . The most important reason for using these high y∗ values is that the recommended range of y∗ values (30–500) would yield unnecessarily small near-wall cells." 
 T. van Hooff, B. Blocken, M. van Harten
3D CFD simulations of wind flow and wind-driven rain shelter in sports stadia: influence of stadium geometry
Build Environment, 46 (1) (2011), pp. 22–37
Hi, i'm curious if you've managed to find a way around this or did you accept the high y+ values in the end? I'm modelling ABL over complex terrain and have come up against this exact issue.
I'm using StarCCM and with an Aerodynamic roughness yo = 1.2m for residential areas it's giving me two possible conditions:
y>10yo which gives centroid height 12m
or y = yo*E/C = 1.2*8.75/0.25 giving 42m!
The end result is a y+ value of 400 000!
400 000 is too much ! I think maximum values of y+ is something between 15 000 to 40 000, not more than that.
God bless you man.
Would you please explain more about your solution's method?
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