Axisymmetric Averaging

So I have a CFD simulation where the domain is axisymmetric. For simplicity sake, let’s call it a tube.

Due to flow characteristics, it needs to be run in full 3D. However, it’d be nice to get statistics that take the average as if it is run as a 2D axisymmetric simulation.

In integral form, it would be (I think at least):

Where part [-]a takes the line average of the circle and part [-]b divides by the circle length. I know the ‘r’ would cancel each other out, I figured I’d just be explicit.

It would be some form of programmable filter, but I can’t figure out how exactly I’d go about doing it through that. Most of the programmable filter’s I’ve done up to now are just taking existing field quantities, manipulating them, then saving them to the exact same “location” point. Any ideas/or help?

For reference, the TCFD from CFD Support (if that’s the company name) has this for Paraview, but it appears proprietary.

For tagging purposes: meridional averaging, circumferential averaging

I’ve been working on a similar problem, trying to compute spherical averages. I made some progress, if you’re still interested in this topic.

While I don’t really need it anymore, I’m still definitely interested in a solution to it as I often need to do other variants of spacial averaging.

I had some first steps here: Old-style Programmable Filter

Let me see if I can dig up my most current filter. I’ll update it there.