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Law of the Wall

Viscous Sub-layer ($0<y^{+}<5$)

We know that the Turbulence at the wall is zero. Therefore regardless of what the flow is, away from the wall, there is always going to be a small layer next to the wall where the flow is laminar. The flow is viscous dominant, therefore linear.

Buffer Layer ($5<y^{+}<30$)

Here the flow is cannot be said to be neither perfectly linear nor exponential. Therefore it is beneficial to use a (Wall) function to spit out the values that should be used at the edge of the Buffer Layer.

Log-Law region ($30<y^{+}<300$)

Flow is majorly turbulent. Makes use of the Turbulence model selected in the simulation.

Calculating Cell height

Formula for $y^{+}$

$$y^{+}=\frac{y{u}_{\tau }}{\nu }$$

Rearranging

$$y=\frac{y^{+}\nu }{u_{\tau }}$$

Given a kinematic viscosity $\nu =1\times 10^{-5}{\mathrm{m}}^2/\mathrm{s}$ (typical for air), and $y^{+}=30$ :

$$y=\frac{30\times 1\times 10^{-5}}{0.05}=0.006\mathrm{m}=6\mathrm{mm}$$