boundary condition for streamline func and vorticity

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June 16, 2018, 13:25
boundary condition for streamline func and vorticity
#1
Senior Member

A. Min
Join Date: Mar 2015
Posts: 305
Rep Power: 10
Hi all
I have a solved domain (2D flow around a circular cylinder) with U field. Now I want to calculate stream function with this formulation:
Code:
```omega = dv/dx - du/dy
solve (laplacian (sai) = - omega)```
But at last the results are wrong!
The BC for sai are:
for top and bottom sai is calculated from the volumetric flux (Q = A.U_in) that is:
Quote:
 sai_top - sai_bottom = U*delta(y) = 1*20 = 20, so: top boundary: sai = 10 bottom boundary: sai = -10 cylinder surface boundary: sai = 0 inlet and outlet boundaries: d(sai)/dn = 0
and for omega:

Quote:
 top, bottom, outlet boundaries: zero Gradient inlet and cylinder : omega = 0
But the constant sai lines are not the same as stream lines:

Are the equations and boundary C. correct?

 June 16, 2018, 15:42 #2 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,249 Rep Power: 67 but vorticity is not zero on the wall of the cylinder!

 Tags boundary condition, streamline, vorticity