Laminar pipe flow
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:
where um is the mean velocity in each cross section and mu is the viscosity.
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?
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?
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?:(
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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