Enhanced wall treatment is method to implement the enhanced wall function for the two layer model like K-epsilon model ??

Shouldn't that Enhanced wall treatment is a method to make switch from the enhanced wall function (valid through all Y+) to the two layer model (one equation low K-epsilon and standard K-epsilon) when Y+ ~1??

Yes you are correct

regarding to the reply by far

2. K-omega based models were designed originally for the near wall region and therefore does not require the damping functions, hence the hybrid wall functions (blending of near wall and log law function) were implemented directly and same is true for SA model. You can find the details of latest work here for the k-omega and SA model with hybrid wall functions here

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1. First K-omega based models were designed by Kolmogorov 1942. And I really double it is intended only for near-wall simulation

2. "Standard" k-omega (Wilcox 1988) does not require extra viscous modification to be able to predict mean velocity profile in boundary layer, which is not the case for standard K-epsilon

3. However, "Standard" k-omega (Wilcox 1988) will not accurately predict turbulence profile. As a results, a viscous modification (some people called it low Re corrections) is introduced by Wilcox (1991? I may be wrong on the time) in order to capture TKE peak etc. near the wall.

4. Don't get confused with wall function approach

I strongly recommend paper "A half century historical review of the k-w model " by Wilcox 1991.

How about the SST k-w formulation?

Check out the two papers (I do not remember anymore) by Menter 1993. But centrally, it formulated to behave like K-epsilon far from wall (although Omega is the variable), near the wall, it has the formula of the K-omega model (you can use the standard or the one with viscous extension)