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}
 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

\deltalaminar=0.0027 m = 2.7 mm
\deltaturbulent=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

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