## Tuesday, May 15, 2012

### Thickness of the boundary layer

See this wiki page

For laminar boundary layers over a flat plate, the Blasius solution gives: $\delta \approx 4.91 \sqrt{ {\nu x}\over u_0}$ $\delta \approx 4.91x/ \sqrt{R e_x}$
For turbulent boundary layers over a flat plate, the boundary layer thickness is given by: $\delta \approx 0.382x/ {R e_x}^{1/5}$
where $R e_x = \rho u_0 x/\mu$
the overall thickness (or height) of the boundary layer $\nu$ is the kinematic viscosity $x$ is the distance downstream from the start of the boundary layer $Re_x$ is the Reynolds Number $\rho$ is the density $u_0$ is the freestream velocity $\mu$ is the dynamic viscosit
My parameters $u_0$~10m/s, $\nu$~1.5e-6, x~2 m. $R e_x = \rho u_0 x/\mu$
with $\rho$/ $\mu$ = $\nu$
Re_x= $u_0$ * x / $\nu$=1.33e7 $\delta$laminar=0.0027 m = 2.7 mm $\delta$turbulent=0.0287 m =28.7 mm

In my mesh I will make 30 layers on the body with a total thickness of 30 mm. The thinnest layer will be 0.3 mm thick. With an expansionratio of 1.15 I will need 33 layers for 30 mm