openFoamForVelomobiling: Thickness of the boundary layer

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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

openFoamForVelomobiling

Tuesday, May 15, 2012

Thickness of the boundary layer

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