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Laminar pipe flow

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Old   May 10, 2012, 18:55
Default Laminar pipe flow
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vahid
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Hi everyone,
I want to model a laminar flow of water in a 3-D pipe. It's a basic and simple problem which has analytical solutions.
As you know for a laminar flow in a pipe in fully developed region we have:
um=-(r^2/(8.mu)).(dP/dz)
where um is the mean velocity in each cross section and mu is the viscosity.
and also:
uc=2.um
where uc is the maximum velocity in each cross section(center-line velocity).

My problem is here that when I want to validate my modeling by these analytical solutions, there is difference between them and numerical results.
I take the pressure drop value from fluent in each favorite cross section by defining iso-surface in fully developed region and put that value in the above formula but the result didn't match the analytical solution(um or uc).
where is my mistake?how can i know the value of mean velocity in each section?defining an iso-surface and using report surface integrals/ mass weighted average is the right way to that purpose?
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Old   May 10, 2012, 22:12
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Lucky Tran
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Did you verify that your numerical solution has attained the fully developed state by comparing the axial velocity at multiple cross sections? Did you have a developing section or did you use periodic boundary conditions?

did you double check to make sure to use the same mu and everything else as Fluent does?

Quote:
Originally Posted by vahidj View Post
defining an iso-surface and using report surface integrals/ mass weighted average is the right way to that purpose?
define a plane (not sure if iso-surface can give same result) but you must use area weighted average velocity. mass weighted average velocity is not physical.
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Old   May 11, 2012, 07:53
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luckytran, thanks to your reply

yes by cheking the center-line velocity, I'm sure that flow is fully developed and I'm trying to validate the results in that region(Re=1500, D=10mm, L=2000mm). flow is fully developed about z=800mm and boundary conditions are in a simple form like velocity inlet for inlet zone and pressure outlet for outlet zone.
about the properties like viscosity: yes I've checked them on the same iso-surfaces and other section and fluent uses same values that i use in analytical solutions.

The value of mean velocity by defining a plane and using area weighted average is different from the mass weighted average but not equal or at least near to the analytical solution.

what should I do to take exact and correct solution?
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Old   May 11, 2012, 13:27
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Quote:
Originally Posted by vahidj View Post
The value of mean velocity by defining a plane and using area weighted average is different from the mass weighted average but not equal or at least near to the analytical solution.

what should I do to take exact and correct solution?
the bulk velocity, by definition is an area-weighted average velocity. the mass weighted average velocity is rather meaningless.

The only way to recover the bulk velocity from a mass-weighted average is to take a mass-weighted average area calculation. It should be clear now why the mass-weighted average velocity is meaningless.
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