code_saturne User's Forum

Hello,

Now, I am doing comparison study between CFD and theory for 2D Hagen–Poiseuille flow.

This picture show 10m 2D pipe with inlet velocity of 0.01m/s and normal outlet condition by GUI. (Of cource, wall condition and symmetry condition are imposed correctly for other boundaries.) Because this pipe is very long, laminar flow is developed enough from around 7m to 10m(outlet).
Then, I compared the velocity of this CFD result with a velocity obtained by theory of 2D Hagen–Poiseuille flow.

I clipped pipe from 8m to 10m, and accorting to the postprocessing, pressure values for them are 0.02515Pa (at 8m) and 0.00122Pa (at 10m). Therefore, pressure difference (Delta P) is 0.0239Pa. Velocity is 0.0149 m/s for them (8m and 10m).

However, according to theory for 2D Hagen–Poiseuille flow, when Delta P is 0.0239Pa in 2D pipe of laminar flow, maximum velocity should be 0.0074778. This is far from the result of CFD (maximum velocity is 0.0149 between from 8m to 10m).

In this computation, I did not use turbulence model in GUI, because this is laminar flow.

Do someone know why this difference happened?

Best regards,
Tsubasa

Hello

If you set an average/constant inlet velocity of 0.01m/s you will never have a maximum speed lower than this value (0.0074778) due to mass conservation, near the wall the velocity is lower than 0.01, so in the center has to be greater than 0,01. The theory for 2D flow between parallel flat plates state that the average velocity is two-thirds of the maximum velocity, so 0.00149*2/3=0.01, so the profile seems to be ok.

Regards,
Luciano

Hello Luciano,

Thank you for your quick answer.

Actually I did not know about Umean = 2/3*Umax.
I should have studied it before I post this question, sorry, but I cannot find it.

Could you give me some documents showing "Umean = 2/3*Umax" ?

Best regards,
Tsubasa

Hello Luciano,

I found the dosuments.
Sorry I just mixed up with 2 dimenntional and 3 dimentional cases.

Thanks,
Tsubasa