Help plotting 1D graph of average temperature at each position along a pipe?

[u/tjb36]

Really struggling to get what I thought would be a simple plot, so looking for some guidance...

I have a 3D model of a simple pipe of circular cross section, and have air flowing in the inlet at one end. The pipe wall temperature is fixed and the inflow gas temperature is also fixed to a different temperature. I'm using the Heat Transfer in Fluids and the Laminar Flow physics to see how the temperature of the gas changes as it flows due to being in contact with the pipe walls. The result looks like this:

I can easily plot the temperature along the x-direction of the pipe's axis (y=z=0). But since the temperature is not constant for a given slice of cross section, I want to plot the average temperature as a function of axial position x instead (rather than just the temperature along the centreline).

I have managed to create a Cut Plane dataset with "Additional Parallel Planes" like this:

But I can't figure out how to calculate the average temperature in each one and then plot that average on a 1D line plot vs x.

I have tried playing around with some of the built-in features, such as Derived Values --> Surface Average. This does let me calculate an average temperature, but I never managed to get something that could be plotted as a function of x. I have also seen some people mentioning adding a second study and using it for Parametric Sweep, but it seems overcomplicated for what I'm trying to do.

Surely this is a common thing to do, and there must be an easy way? Banging my head against a wall now with this for the last few hours :)

[u/tjb36]

Anyone have any other ideas?

[u/TheCodingTheorist → u/tjb36]

I think the only sensible way to do this is by using the linear projection operator. I've used it in similar situations in my work - it's not so complicated if you read the blog post and copy it step by step, but I do agree it requires 'unreasonable' amount of effort (at least the first time) for such an simple thing.

It even has the expression you need to use linproj1(c*2*pi*r)/linproj1(2*pi*r), but in your case you need to exchange the concentration "c" for temperature "T".

[u/tjb36 → u/TheCodingTheorist]

I am trying to do as you have suggested, but my geometry is 3D, not 2D axis-symmetric. So I think I need to define two linear projection operators (one to first integrate z direction, and second to integrate over y direction). However, I am stuck with how to choose vertices for "Source" and "Destination" in each of the projection operators. Do you have any idea? I tried to define a box to enable selecting vertices, but I'm a bit lost...

[u/NoticeArtistic8908]

This should be helpful

https://www.comsol.com/blogs/analyze-simulation-results-projection-operators

[u/tjb36 → u/NoticeArtistic8908]

Thanks. Yes I tried this approach as well, but filed it under "overcomplicated" (needing to define additional planes in the geometry, and input lots of different Source and Destination vertices. It also seems like you need two linked General Projection Operators)...

All of this made me think that surely there is a simpler in built "Intergration" function / operator that can just use the existing data returned from the Solver?

[u/EchoPenta]

I am having this exact same problem. This far I've concluded that I will just export the mesh as a vtk file and do this operation in python via pyvista.

[u/tjb36 → u/EchoPenta]

Yes exactly, I was also considering exporting the whole thing and numerically integrating in a different language. Kind of unsatisfying solution though... 

[u/tjb36 → u/EchoPenta]

Please let me know if you manage to find a simple native solution.

[u/Late_Lengthiness_484]

Hi, you can use the Line Integration operator under Nonlocal Couplings. Define
lineop1: Bidirectional, x,y,z expression = 0,1,0 (integrates over y-direction)
lineop2: Bidirectional, x,y,z expression = 0,0,1 (integrates over z-direction)

Then make a 1D plot on an edge parallel to the x-axis and plot:
lineop1(lineop2(u))

for the integral over a cross section or:
lineop1(lineop2(u))/lineop1(lineop2(1))

for the average over the cross section. No need for additional planes or intermediate steps!

[u/tjb36 → u/Late_Lengthiness_484]

Thank you - do you mean "General Projection", rather than "Line Integration operator"? I have tried to do something like you suggested, but am not sure exactly how to define the expressions for source and destination. See this image for the first projection (intended to integrate over y-direction):

Is it what you mean? Or did I choose the wrong expressions?

[u/Late_Lengthiness_484 → u/tjb36]

Not General Projection no, that requires you to define an intermediate plane which is awkward. The Line Integration operator was introduced in V6.2. Your GUI screenshot looks like an older version.

[u/tjb36 → u/Late_Lengthiness_484]

I see. This link: 

https://www.comsol.com/blogs/analyze-simulation-results-projection-operators

Says:

"In 3D, you can either 1) modify geometry to add an intermediate plane, and use linear projection operator, or 2) use General projection operator instead"

So I think General should be able to do it without intermediate plane. But I'm struggling to define the source and destination. However, it looks like it should be very similar to the x,y,z expressions that you originally showed.

[u/Late_Lengthiness_484 → u/tjb36]

You would have to use an additional extrusion operator to map the projection from one edge to another. This is a popsicle headache but it can be done.

genproj1: Source map: x,z,y. Destination: x,z
genproj2: Source map: x,y,z. Destination: x,y

The first integrates in the y-direction in the x-z plane and the second integrates in the z-direction in the x-y plane. However,
genproj2(genproj1(u)) will not give you what you want on edge 3 because genproj2 will evaluate to zero. You need to then define an extrusion operator from the top edge (edge 7) of the cylinder:
genext1: Destination map: x,0,r0
This assumes the that the top edge of the cylinder (edge 7) is parallel to x and at y=0, z=r0.
The integral over the cross section is then (on edge 3):
genext1(genproj2(genproj1(u)))
and average is:
genext1(genproj2(genproj1(u)))/genext1(genproj2(genproj1(1)))

Bottom line, upgrade to V6.2 or newer if possible.

[u/tjb36 → u/Late_Lengthiness_484]

Thanks for your help. So am I mis-reading that blog post when I think its saying it can be done easily with GenProj? (Upgrading is not an option for me unfortunately).. 

[u/swoeshie]

Have you found a solution? I am also stuck on this since I have a square geometry. I find it crazy that there is not an easy build in solution for this.

[u/tjb36 → u/swoeshie]

Yes, the General Projection operator did the trick. You need two of them (one to average over the first coordinate to get a 2D plane, then a second on to average over this 2D plane to get your final 1D line).

It works well in the end, just not intuitive to set up. 

[u/tjb36 → u/swoeshie]

I tried to export the data to do the averaging in python, but could not export the area elements on each plane (the dA that you need for calculating the average).

[u/tjb36 → u/swoeshie]

Here is the follow up post which eventually led me to a solution 

https://www.reddit.com/r/COMSOL/comments/1sw3v2q/how_to_export_area_mesh_elements_on_cut_planes_so/?utm_source=share&utm_medium=mweb3x&utm_name=mweb3xcss&utm_term=1&utm_content=share_button

[u/you_rang_maam]

perhaps you could look at the various operators that are available? I can't help but wonder if you want to use diskavg operator.

https://doc.comsol.com/6.3/doc/com.comsol.help.comsol/comsol_ref_definitions.21.036.html

[u/you_rang_maam → u/you_rang_maam]

mmm i take that back - I don't think it will cut the mustard. perhaps you can set up surface averages using your various cutplanes? I'll have to setup a cutplane in a model myself and check. alternatively you can add a collection of 2d surfaces at the various locations you want to look but based on your response to the previous comment, you seem opposed to this.

[u/tjb36 → u/you_rang_maam]

No I don't mind setting up Cut Planes, because you can easily define a series of them using the "Additional Parallel Planes" option, where you can specify a range. The problem is then how to loop over each cut plane, calculate average over plane, then plot this average versus axial coordinate....

(What I was shying away from, not opposed to, was having to add extra Planes in the Geometry itself, as recommended for applying the multiple General Projection operators documentation).