DChemTech wrote: ↑03 Feb 2020, 13:07
A more CFD-technical question that I have;
You state using SST with wall functions. I thought that the power of SST was, however, in the near-wall regions - properly (for RANS, at least) resolving boundary layer/separation effects. Hence, I though a resolved mesh (Y+ of ~1 in the first layer) is required to make proper use of the SST formulation - and that using SST with wall functions essentially reproduces the k-epsilon model (the bulk formulation of SST). Am I mistaken here? Do you have some comments on what the effect of wall functions will be in this case?
Bit of a technical answer, and one which is dependant on the solver used as well, but I hope this helps explain it:
The flow close to a wall has a viscous sublayer which depends on a few different parameters, such as roughness and the velocity components. It is not too difficult to think about boundary layers, and to realise, that as your Reynolds Number increases, your boundary layer thickness will decrease. You can check the equations, and see that theres an inverse relationship of boundary layer thickness to freestream velocity too.
It is important to keep in mind that the standard models typically used in solvers, are based on isotropy... which is an assumption that is not really valid most of the time... The main disadvantage of these standard models is related to the fluid behaviour within the viscous sublayer. The "damping" of the velocity normals on the wall, is much higher than tangential to the wall, which makes the isotropic assumption even worse. If you have high Re flows, the sublayer thickness decreases quite a bit.. and so, you have two options (most of the time), which would allow you to still resolve the velocity change within the sublayer:
- Resolving the sublayer
- Model the sublayer
Experimentally, it has been found that the velocity behavior in the sublayer follows a logarithmic law. Thats why we can use "Wall Functions" which typically are logarithmic functions. However, the log law is only valid within a set range. If you are using wall functions, you model the sublayer with the log law equation, and therefore the first cell height should be somewhere close to the maximum y+ range you expect to see (you can do a rough blasius flat plate calculation, and correct for curvature based on how aggressive you feel your CAD is in the critical area). If your first cell is too small, you will introduce inaccuracies because the second cell would be still in the log law region, but it will not be applied to it. If you have y+ << 1 there is no need to use wall functions because you are already resolving the viscous sublayer.
Within ANSYS, k-omega SST has only one wall function. One of the benefits of the k-omega SST model is that it will automatically use the low-Re formulation in the viscous sublayer and will use its wall function calculation if the cell height is within the log-law layer. This refers to its "automatic" wall-function... the only one it has. It uses a linear law for omega within one regime,
and another log law for omega within the refined regime.
If I lift a line straight from the solver theory guide:
"The wall boundary conditions for the equation in the models are treated in the same way as the equation is treated when enhanced wall treatments are used with the models. This means that all boundary conditions for wall-function meshes will correspond to the wall function approach, while for the fine meshes, the appropriate low-Reynolds number boundary conditions will be applied"
This part is talking about the k-equation. Enhanced Wall Treatment and Enhanced Wall Function mean almost the same thing. Enhanced wall functions are the blended linear & log standard laws. Enhanced wall treatment uses these enhanced wall functions. And again from the solver guide:
This means that all boundary conditions for wall-function meshes will correspond to the wall function approach, while for the fine meshes, the appropriate low-Reynolds number boundary conditions will be applied.
Now for our case...
My PC can only handle a certain number of million elements. It means that I have to be very careful with how I apply my prism layers and growth rates, in order to ensure that I can "capture the bits I want to, and leave the less interesting bits to be analyzed roughly". What this means is that, for example on the front wing elements, I resolve the boundary layer down to a y+ of about ~0.5 whilst on other areas, such as the top of the nose, I resolve it only to around 60-100. Because of how this "automatic wall function" is applied, the SST model will be used to a pretty decent extent in somewhat critical areas, whilst in less "impactful" areas on the car's performance, it will default to a "wall-function based" solver: which you are correct, will imply something akin to k-epsilon. Also, due to mesh quality, I utilise layer compression, rather than stair-stepping within the prism layers, in order to better capture whats going on. In areas such as gap and overlap of flaps, this is another area in which the local y+ will be quite a lot lower than some of the larger areas on the car.
At the end of the day, CFD in RANS, is literally just "modeling" to begin with. When I get my new PC soon, I will be able to better mesh and capture critical areas, but if I was to run a fully resolved viscous sub-layer, I would need a lot more computational time and power... maybe I'll get lucky and 128Gb will be enough to solve (because often when you resolve your boundary layer cells to that level of refinement, you need to solve in double precision just to "locate" the cell nodes in the correct spot - else the solver will truncate coordinates, and spit out a negative cell volume error).
Note: turbulence is not my "expertise" per se, but I do try to understand the problems that I solve at work, to a fundamental level... I hope that this is correct, but by all means, if I have made a mistake, feel free to jump in and correct me - I love learning!!
"When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first." -- Heisenberg