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