Hagen-Poiseuille Flow

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Line Bergmann

Line Bergmann

December 10, 2012 10:05am UTC

Hagen-Poiseuille Flow

I am having problems getting the same result when I try to model the Hagen poiseuille flow as when I calculate it.

For more information on Hagen-Poiseuille en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_equation

I have a 2d model with a rectangel width 0.1m and length 13m.

At the inlet I have a pressure of 2.52Pa using the pressure, no viscous stress option. And at the outlet 0Pa.

When I calculate the velocity profile for the flow I use the viscosity provided by COMSOL

eta=0.000547

and I calculate the velocity from
u(r)=(R^2-r^2)/(4*eta)*dp/dz

in cylindrical coordinates. R is the radius ie the half width of the rectangel. r i the variable radius.
dp/dz=1.9388Pa/m

I have attached a picture with the development of the flow and the calculated velocity profile. What am I doing wrong here?

Attachments:   Hagen-Poiseuille-flow.jpg  

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Nagi Elabbasi

Nagi Elabbasi
Certified Consultant
Veryst Engineering

December 10, 2012 2:54pm UTC in response to Line Bergmann

Re: Hagen-Poiseuille Flow

Hi Line,

Are you sure you are using a 2D axisymmetric model not a 2D planar model? If so you should only model a rectangle with width equal to the radius (not diameter) of the pipe, and COMSOL will automatically add the symmetry boundary condition on the left side of the rectangle.

Nagi Elabbasi
Veryst Engineering

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Ivar Kjelberg

Ivar Kjelberg

December 10, 2012 3:26pm UTC in response to Nagi Elabbasi

Re: Hagen-Poiseuille Flow

Hi

i was wondering if there is not a factor 2 (/8 instead of /4 ?) missing in there.
I did a quick run in 2D axi SPF aand this gives rather coherent values but is still mesh dependent, and the pressure inlet needs a bout a meter to stabilise fully.

I'm not that astonished that the flow flattens in the middle with high resolution mesh. Also the temperature, you are not using 20°C are you ?, the eta/mu value doest really fit for me.

--
Good luck
Ivar

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Line Bergmann

Line Bergmann

December 12, 2012 12:16pm UTC in response to Ivar Kjelberg

Re: Hagen-Poiseuille Flow

Thank you so much. I still can not get it right but you guys sure did help me on the way.

I changed the model and now I have a 2D axissymmetric model with a radius of 0.05m and a length of 13 m.

you are right I use 323.15K as temperature.

I have an inlet pressure of 0.126024724
and outlet still 0

My maximum velocity calculated by the hagen poiseuille flow is 1.107E-2 m/s
whereas COMSOL have it at 9.98E-3 m/s

This is offcourse closer than before but still I would love it to be a little better.

I have added the COMSOL file if anyone is interested

Attachments:   12-12-Laminar-Straight.mph  

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Nagi Elabbasi

Nagi Elabbasi
Certified Consultant
Veryst Engineering

December 12, 2012 6:26pm UTC in response to Line Bergmann

Re: Hagen-Poiseuille Flow

Close to the theoretical solution, but you should be able to get even closer. Make sure you are using the correct value of the pressure gradient dp/dz. There is a relatively significant pressure loss at the entry which leads to an actual pressure gradient (throughout most of the pipe) that is smaller than what is estimated with P_inlet/ total length.

Nagi Elabbasi
Veryst Engineering

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Ivar Kjelberg

Ivar Kjelberg

December 12, 2012 7:40pm UTC in response to Line Bergmann

Re: Hagen-Poiseuille Flow

Hi

and have you checked the laminar inflow condition ?, note that the pressure inlet is counting also the extra length, I believe (check your results, as the plots will not show the fictuous inlet region, while the pressure difference should give you te drop in the laminar inflow addition length (at least is was so for some versions ago, this might have changed ;)

--
Good luck
Ivar

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