Radiation, test case

Numerical methods and mathematical models of Elmer
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MrBenson
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Radiation, test case

Post by MrBenson »

Hi,

I'm trying to find some results of a basic radiation test case. It's a vacuum cavity between two concentric cylinders as shown below.
The attachment radiation.PNG is no longer available
r1 = 0.07m
r2 = 0.08m
r3=0.14m
r4=0.15m.

- The cylinders are perfect conductors i.e. conductivity = 100000000
- At the inner surface of the smaller cylinder (S1) the surface temperature is 20°C
- At the outer surface of the larger cylinder (S4) the surface temperature is 0°C
- The heat transfer between the outer surface of the smaller cylinder (S2) and the inner surface of the larger cylinder (S3) occurs by radiation only. The emissivity is 0.9 for both surfaces.

I take a diffuse gray model of radiation. I compute the view factors first, perform the simulation and compute the total heat flux through S2 and S3.

Unfortunately I do not find the right heat flux which is 44.12 W/m.

Here are the steps :
- Create the msh file form gsmh
- Convert the msh to elmer mesh file (ElmerGrid 14 2 temp.msh)
- Compute the view factors
- ElmerSolver


Thanks for your help.
Attachments
radiation.PNG
radiation.PNG (29.83 KiB) Viewed 3277 times
MrBenson
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Re: Radiation, test case

Post by MrBenson »

I forget to add some attached file, sorry !
temp.geo
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The attachment temp.geo is no longer available
MrBenson
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Re: Radiation, test case

Post by MrBenson »

temp.sif
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raback
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Re: Radiation, test case

Post by raback »

Hi

Your main problem was that you give a too high conductivity to the materials. Then the nonlinear solution is not sensitive anymore to the gradients within the materials. Imagine a correct solution and a solution that is constant at each circle. Their difference tends towards zero as the conductivity tends towards infinity.

So you should either make all the linear/nonlinear tolerances stricter. Or perhaps rather use some conductivity that results to finite gradient. I used 1e3 with success.

Also I added optiomal computation of fluxes using sum of reaction heat loads. See the attachment.

If you study this further it would be interesting to know the values of heat conductivity giving still good results.

Have fun!

-Peter
Attachments
temp.sif
improved flux computation
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MrBenson
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Re: Radiation, test case

Post by MrBenson »

Hello Peter,

Thanks a lot for your answer, in fact the issue was the too large conductivity value.
I do understand the way to compute the flux via the load temperature but i don't understand why i do not get the same value using the diffusive flux and the convective flux as show below

Code: Select all

Operator 1 = "Diffusive flux"
Variable 1 = "Temperature"
Coefficient 1 = "Heat Conductivity"
	
Operator 2 = "convective flux"
Variable 2 = "temperature flux"
Moreover i don't know why the max and min value of these computations always appear in the outfile.

Best regards
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