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May 10, 2012, 18:55 
Laminar pipe flow

#1 
New Member
vahid
Join Date: Dec 2011
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Hi everyone,
I want to model a laminar flow of water in a 3D 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(centerline 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 isosurface 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 isosurface and using report surface integrals/ mass weighted average is the right way to that purpose? 

May 10, 2012, 22:12 

#2 
Senior Member
Lucky Tran
Join Date: Apr 2011
Location: Orlando, FL USA
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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? define a plane (not sure if isosurface can give same result) but you must use area weighted average velocity. mass weighted average velocity is not physical. 

May 11, 2012, 07:53 

#3 
New Member
vahid
Join Date: Dec 2011
Posts: 7
Rep Power: 7 
luckytran, thanks to your reply
yes by cheking the centerline 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 isosurfaces 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? 

May 11, 2012, 13:27 

#4  
Senior Member
Lucky Tran
Join Date: Apr 2011
Location: Orlando, FL USA
Posts: 1,854
Rep Power: 26 
Quote:
The only way to recover the bulk velocity from a massweighted average is to take a massweighted average area calculation. It should be clear now why the massweighted average velocity is meaningless. 

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