Using radiation models for plasmas
 

Hello,

I'm currently trying to add a radiation model to my solver.

The goal is to simulate a plasma with temperatures up to 30000K.
Because of these high temperatures radiation is the dominant heat transfer mechanism, so it must be considered in the solver.

In the literature a grey radiator with a grey factor of maybe 0.7 is often assumed.

Now I have added the radiation code to my solver and tried different models:

1. P1 model with Marshak boundary condition and constantEmissionAbsorption model.
2. fvDOM with greyDiffusive boundary condition and constantEmissionAbsorption model.

For both models I tried using different absorptivity and emissivity coefficients.

With P1 I don't really see any change to using no radiation, but in the source it says it's for optically thick media, so it may not be good anyway.
With fvDOM the solver crashes on the first temperature approximation.

I would also like the walls to absorp most of the radiation hitting them, how can I accomplish this?

How does the grey factor relate to the emissivity/absorptivity coeffs in the model? Is it identical?
What is emission contribution E?
And is the emissivity in the BC the same as in the model for the volume?
Can the high temperatures lead to numerical problems? 30000^4=8.1e17...

After looking into
http://www.tfd.chalmers.se/~hani/pdf...aLicThesis.pdf
and
http://arxiv.org/ftp/arxiv/papers/1301/1301.0650.pdf ,

I figured out that a common simplified approach to handle radiation in thermal plasmas is to use a simple source term in the energy equation, 4 * pi * epsilon_r, where epsilon_r is the net emission coefficient (see section 2.5 in the second link).

However, I need to know the radiative energy flux through the boundaries. Does anyone have an idea how to get this with such a term? As far as I can see this term simply represents an energy sink, meaning that the radiated energy is removed from the case because it leaves its boundaries?
Integrating it over the volume would give the total energy lost due to radiation, but how to resolve it spacially at the walls, assuming an isotropic radiation?

I think I may be going in the direction of the DO-model again...

I played around with the emissivity factor of the P1 model, increasing it by two orders of magnitude each step until I saw an influence in my simulation. It is now very high, on the order of 1e5 - 1e6. I'm not quite sure if these values are realistic or not, as I don't completely understand the physical meaning of them. The results look somewhat promising, but my equations don't seem to solve properly anymore (the values look like numeric problems), and I think I might need smaller timesteps or some sort of underrelaxation. Unfortunately I don't quite know yet how underrelaxation works in detail, so I can't implement it properly without knowing what to look out for.

Is there any information avaiable that explains the concept of UR in detail without involving any other complex algorithms like PISO, PIMPLE, etc..?

On another note, is it possible or sensible to scale the temperature, lets say to work with kK instead of K? This would maybe bring me to more sensible numerical ranges in the radiation equations?