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-   -   slip boundary's equation. (https://www.cfd-online.com/Forums/openfoam-solving/132306-slip-boundarys-equation.html)

sharonyue March 28, 2014 20:04

slip boundary's equation.
 
Hi guys,

In inviscid flow, wall's boundary is slip. Lets take account of velocity: the equation of velocity in the slip boundary should be:

u*n=0


The reason is that: n_x=0.n_y=-1,u_y=0.

But in user guide it said:

Code:

The normal vector is fixedValue=0, the tangential vector is zeroGradient;
I can understand the first sentence. Because u_y=0.

So how can I derive that the tangential vector is zeroGradient?

Thanks

bieshuxuhe March 28, 2014 22:03

hello
for incompressible fluid:
i think we could deduce "the tangential vector is zeroGradient" from equation of continuity .

Best Regards
xuhe

sharonyue March 29, 2014 20:28

Quote:

Originally Posted by bieshuxuhe (Post 482743)
hello
for incompressible fluid:
i think we could deduce "the tangential vector is zeroGradient" from equation of continuity .

Best Regards
xuhe

Could you elaborate it more? I want to know how can I get
\nabla u_x = 0
Thanks.

bieshuxuhe March 30, 2014 01:46

may this help you !
 
1 Attachment(s)
Quote:

Originally Posted by sharonyue (Post 482807)
Could you elaborate it more? I want to know how can I get
\nabla u_x = 0
Thanks.

look down the picture !
is it clear ?

bieshuxuhe March 30, 2014 03:05

do you deal with twophase fluid ?



xuhe

sharonyue March 30, 2014 06:23

Quote:

Originally Posted by bieshuxuhe (Post 482821)
do you deal with twophase fluid ?



xuhe

cool, wonderful.

Yep, Im using solver on two-fluid model.

Thanks.:)

Bernhard March 31, 2014 03:21

Your equations are not correct. v(y=0)=0 does mean dv/dy=0 per se (i.e. if v(y=1)=1). Therefore, your statement that du/dx=0 is not correct. A slip boundary is impermable (thus v=0) and stress-free (thus du/dy=0, for your sketch).

bieshuxuhe March 31, 2014 03:47

Quote:

Originally Posted by Bernhard (Post 482945)
Your equations are not correct. v(y=0)=0 does mean dv/dy=0 per se (i.e. if v(y=1)=1). Therefore, your statement that du/dx=0 is not correct. A slip boundary is impermable (thus v=0) and stress-free (thus du/dy=0, for your sketch).

thank you very much!

:p

sharonyue March 31, 2014 03:50

Quote:

Originally Posted by Bernhard (Post 482945)
Your equations are not correct. v(y=0)=0 does mean dv/dy=0 per se (i.e. if v(y=1)=1). Therefore, your statement that du/dx=0 is not correct. A slip boundary is impermable (thus v=0) and stress-free (thus du/dy=0, for your sketch).

Oops, We should be more care about it. Yep, it should be du/dy=0 not du/dx=0.

Just because its stress free. so u(y=0) has no impact on u(y=1). So this du/dy=0. It makes sense.

Thanks.


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