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boundary condition for streamline func and vorticity

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Old   June 16, 2018, 12:24
Default boundary condition for streamline func and vorticity
  #1
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A. Min
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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:



Could you please help me?

Are the equations and boundary C. correct?
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Old   June 16, 2018, 13:08
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Santiago Lopez Castano
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Quote:
Originally Posted by alimea View Post
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:


and for omega:



But the constant sai lines are not the same as stream lines:



Could you please help me?

Are the equations and boundary C. correct?
If bottom and top are also walls, they should be zero as well. The inlet BC in principle a distribution of psi if the inlet is nonuniform. Otherwise the formulation seems correct to me. Btw, why do you expect to get the same results?
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Old   June 16, 2018, 13:12
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Quote:
Originally Posted by Santiago View Post
If bottom and top are also walls, they should be zero as well. The inlet BC in principle a distribution of psi if the inlet is nonuniform. Otherwise the formulation seems correct to me. Btw, why do you expect to get the same results?
Thanks Santiago to reply.

top and bottom are p=0 boundaries.
I have tested this boundary for inlet, this is the same as linear distributed sai.

About your question:
"why do you expect to get the same results?"


constant stream function is the same as stream line, isn't it?!

If not, could you please tell me why?
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boundary condition, streamline, vorticity

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