CFD Online Discussion Forums - Permeable plate modeling

Dear All,

I faced with a problem of permeable plate modeling within OF. The scheme of problem can be seen in figure below.

So, it is just a flat plate, but with injection along axial direction. The law of injection is depicted in figure $j_w=\left(\rho u\right)_w\sim 1/\sqrt{x}$ .

In case of incompressible laminar boundary layer it can be solved by Blasius equation
$f^{'''}+0.5ff^{''}=0$
with following boundary conditions:
$\eta=0: \quad f(0)=-2\overline{j}_w\sqrt{\mathrm{Re}_x}, \overline{j}_w= C/\sqrt{x};\quad f^{'}(0)=0$
$\eta=\infty: \quad f(\infty)=1,$
where $\overline{j}_w=\left(\rho u\right)_w/\left(\rho u\right)_{\infty}$ and

.

In OF the main thing is a applying the mass flux at the wall (

). Again for incompressible flow it is prossible to prescribe

directry at the wall.

And the solution is quite close to the Blasius solution (see picture below).
Reduced velocity profile is presented in the picture (symbols are OF solution at difference axial positions, solid curve is Blasius solution).

But for compressible flow it is necessary to set not

only, but $\left(\rho u\right)_w$ .

It looks like it is necessary to implement a new boundary conditions for blowing/suction like it was performed in the following report.

Do you have any ideas how it can be implemented within OF?