Finding centerline of a pipe with shaped profile 1

[PrintScaffold]

Greetings everybody!
I hope you can help me in finding solution to the following problem. I'm trying to find a centerline of a pipe (or cavity) with a complex shaped profile, which can be find in the control valves, for instance. If a pipe/cavity has a constant profile throughout, the solution is trivial. But if its boundaries consist of number of arcs and lines, as can be found in the valves, the solution is much more difficult. Well, for me at least. So far I could not find it and did not find and references to the similar problem in the books. I need this centerline to be able to find the correct cross-sections of the valve cavity later on. The picture included.
Any ideas?

 

[MikeHalloran]

Draw or import into 3D CAD.
Slice.
Find centroid of slices.
Connect centroids into centerline.



Mike Halloran
Pembroke Pines, FL, USA

 

[gerhardl]

Question (Please comment):

Could it be that you actually are after not the geometrical centerline, but rather the centerline for a laminar flow, to theoretically calculate total flow under different conditions?

 

[PrintScaffold]

An interesting idea, Mike. But how to slice? Just create vertical slices? But will their centroids correspond to what I am looking for? They should be inclined at various angles, and ultimately, I am looking for that angles,

 

[PrintScaffold]

I think you are correct, Gerhard. Although I am looking for the areas of sections, they should be the sections the flow passes on its way through the valve.

 

[MikeHalloran]

You seem to want to find the centroids of a set of isobars... which are not necessarily planar.

What problem are you actually trying to solve?



Mike Halloran
Pembroke Pines, FL, USA

 

[PrintScaffold]

I am trying to find areas of sections through which the flow passes on its way through the cavity.

 

[PrintScaffold]

Any ideas anybody?..

 

[MikeHalloran]

The equations that are used for flow in a pipe are not really valid over the typical cross section in a valve, so finding the transverse areas or centerline won't really do you a lot of good.

What you have to do is solve the flow equations for a large number of small volumes of fluid, and integrate them over the volume of the cavity. The number of equations that you need to solve at once is very large. Fortunately, that's just the sort of thing that computers can do well.

Look up Computational Fluid Dynamics.




Mike Halloran
Pembroke Pines, FL, USA