Quantitative flow modeling of a 3D problem in 2D

[landersohn]

I have a structure with varying diameter pipes, the diameter gets successivly smaller and a bend. I can model this structure quantitativly in 3D and get results for volume flow and pressure that match the results. Problem is, the calculation is rather lengthy, so I created a 2D model since my geometry has a symmetry plane. I am going from the assumption that the bend does not do much and think of the problem as rotationally symmetric.
My problem is, how do I scale the velocity profile and pressure drop calculated in 2D to their 3D equivalent values?
So far, I have used the exact same velocity profile at the inlet for my desired flow and I used a constant Newtonian viscosity. When I run this in 2D I get a a maximum velocity (in the thinnest portion of my pipes) comes about 12 times smaller in the 2D run vs. 3D. The pressure drop in the 2D run is approximately 24 times smaller compare to 3D

Furthermore, when I run the simulation with a power law viscosity - which is what I am trying to model - the 2D pressure drop is only smaller than 3D by a factor of 6:
Pressure 3D/2D = 24 for Newtonian fluid
Pressure 3D/2d = 6 for non-Newtonian fuid.
The maximum velocities behve more similar between Newtonian and non-Newtonian viscosity:
Max velocity 3D/2D = 13.5 Newtonian
max Velocity 3D/2D = 12.4 non-Newtonian

I have tried to scale with various combinations of pi, radius and whatnot but cannot figure it out. Does anybody have any insights? The observation that the ratio between the 2D and 3D pressure drops is different for the Newtonian and non-Newtonian viscosity models might indicate that this scaling is not possible using purely geometry. Am I stuck having to do 3D simulations to get quantitative results?
P.S.: My reynolds numbers are very small so turbulence does not seem to be a factor.

Thanks everybody. I realize this might be more of a general physics question rather than pure Elmer but maybe one of you can help me out

[landersohn]

forgot to add email notification flag .....

[raback]

Hi

If your problem is rotationally symmetric you could use the "axi symmetric" or coordinate system. If not, then you're stuck in 3D. You could use the symmetry plane and only model half of the geometry.

Basically the flow solver is one of the historical solvers that actually have the possibility that the user defines the metric of the space. So it could be spherical etc. also, if you know the corresponding metrics. There is however, nothing like local coordinate system that would be needed in a case of a "bend".

-Peter

[landersohn]

Thanks Peter

[landersohn]

I have another, related queston: in a power law viscosity, I would think the local viscosity is a function of position since hte local shear rate varies.
Is there a way to export the viscosity field?