How Does Blasius Equation Apply to Jet Exhaust Simulations?

[Clausius2]

I have been doing a simulation of Blasius equation:

F'''+FF''/2=0 with F(eta) where eta is a similarity variable
eta=(y-1)/(x^(1/2))

F'(0)=1 u(y=1,x<<1)=1
F(0)=0 v(y=1,x<<1)=0
F'(infinite)=0 u(y=infinite, x<<1)=0

You can observe that the BC's are different of the flow over flat plate. This is obtained for a mixing thickness in the near field of a two-dimensional jet, near the orifice of exhaust (are you agree?).

in this page:
http://www.rit.edu/~pnveme/Matlab_Course/Matlab_App_ODE.html
where shooting method is employed in Matlab, it is said numerical methods (Runge Kutta, or the internal Matlab function ODE45) have normalized value F'(infinity)=1.

I have programmed it in Matlab but now I don't know how consider the value 0 at infinity instead of 1.
Could you help me?.
Thanks.

 

[Max0526]

particular solution

Hi, Clausius2;
It seems to me, I was wrong in my private message to you about the almightiness of SMM. The only solution that classic SMM can give us is:
F(eta)=6/(eta+C),
where C is an arbitrary constant.
See you in your old thread,
Max.

 

[Clausius2]

I have used the superposition principle:

F(0)=0 F(0)=0 F(0)=0
F'(0)=1 F'(0)=1 F'(0)=0
F'(inf)=0 F'(inf)=2 F'(inf)=2
= -


Hey, it seems it works!, and I did't need your help.

But now, guys, you have to tell me if superposition principle is valid for this equation. Is it linear?. Hands up if you are agree!

 

[stichini2000]

hello... I am in a real bind here. i tried runnning numerous scripts but they don't work... the programme should include runge kutta
ps: Need help pronto!
i would truly appreciate it