Ceramic foam exposed to concentrated radiation
 

Hi everybody!

I'm modeling the heat-up behavoir of a ceramic foam exposed to concentrated radiation. At the same time the foam is penetrated by a gas flow. The foam is modeled as a porous domain (fluid and solid) which is placed between two fluid domains.

Problem discription: Radiation which penetrates into the foam interacts only with the fluid in the porous domain (if participating media is selected, otherwise no interaction) and not with the solid. In reality radiation is absorbed by the solid part which afterwards heats up the fluid. From my point of view this is implemented incorrectly in CFX.

Question: Does anybody know if there is a way to add interaction of radiation with the solid part of the porous domain?

:) Let's have a look at what you are doing before we jump to conclusions....

Does the radiation only interact with the front face of the ceramic? Do you need to model the radiation or can it be modelled as simply a heat source? Is the fluid passing through the ceramic transparent (or close to it)?

Hi Glen, thanks for your reply!

No, it interacts with the volume of the ceramic (porous domain) but only if participating media is selected under thermal radiation in the fluid models tab (and absorption and scattering coefficients are defined >0 for the fluid). In this case I assume that the radiation is absorbed by the fluid. But I would like to have direct interaction of radiation with the solid.

One option would be to model radiation only in the fluid domains adjacent to the porous domain and define for the solid in the porous domain an effective heat conductivity (keff = thermal conductivity + radiative conductivity). The interface fluid-porous could be modeled as opaque for radiation thus, radiation is absorbed at the interface. I think in this case the radiative energy (heat flux) is then applied to the fluid in the porous domain. The problem which I have is how to apply the absorbed radiative heat flux to the energy equation of the solid (in the porous domain) and not to the fluid? By default I think its applied to the fluid. Do you think it's possible to subtract it by a heat sink from the fluid and add it with a heat source to the solid?

Yes, in reality the fluid is transparent (Ar). As mentioned before, if the fluid is modeled transparent (absorption=0, scattering=0) there is no interaction with radiation.

Best,
Philipp

What version of CFX are you using?

I think heat transfer in porous domains was only included in V14.

I'm using V14.5 but it was already included in V13

OK, so you have a version of CFX which supports heat transfer between the solid and fluid phases in a porous domain - so far so good.

I am not sure the radiation is supported per se in the solid phase in a porous domain. You will need to investigate this. You will certainly need the monte carlo model if it is supported, the other radiation models will not handle this.

Another thought - Does the radiation change? Or is it coupled to the fluid or ceramic in some way? You might also be able to apply the radiation heat load as a volumetric heat source on the porous domain and not directly model the radiation at all.

Hi Glen,

Thanks for your answer.

• That's exactly the problem, radiation in the solid of a porous domain is not supported. Thus, radiation heat transfer can only be modeled in the fluid part of the porous domain. But in my case I would like to have the interaction with the solid.
• Unfortunately, radiation is not constant but dependent on the temperature of the surrounding surfaces which emit radiation (which are also not constant).

Due to these problems I'm thinking about not modeling radiation in the porous domain but account for it by increasing the thermal conductivity of the solid of the porous domain.
=> if I do so, I have radiation models in the adjacent fluid domains but non in the porous domain (pls see picture attached). I'm worried about what happens with the radiation part at the interfaces of fluid-porous-fluid. What do you think?

I cannot see how changing the thermal conductivity of the material can be a substitute. You are replacing a radiation heat load with a change in thermal conductivity. They are totally different things.

Also your picture was not attached.

Some questions: How far into the porous material does the radiation penetrate? Just the surface? Or a significant distance inside? If it penetrates, how - is the porous material partially transparent or is it very sparse?

I think there will be a few ways to work around this, I just need to understand what you are doing a little better.

A common approach to simplify modeling heat transfer in a porous media (conduction, convection, radiation) is the following approach: Instead of modeling the radiative HT (for example via Monte-Carlo) an effective conductivity of the porous media (k_effective) is assumed which is composed of the solid conductivity (k_solid) and an equivalent radiation conductivity (k_radiation) which is determined based on theorethical or empirical models. Thus k_effective = k_solid + k_radiation. Do you understand what I mean?

Reference: Laubitz, M., Thermal Conductivity of Powders. Canadian Journal of Physics, 1959. 39(7): p. 11.

Sorry for that, didn't worked to attach it. No it should work.Attachment 24098

• The ceramic foam looks similar to the picture attached.Attachment 24099

• The extiction coefficient is on the order of 250 m-1. Thus, radiation penetrates considerably into the porous material.

• Yes, the porous material is partially transparent.

This would be really great because I'm struggling for quiete a while already with this problem!:)

So how about this: If CFX ignores radiation in the solid part of the porous region, then how about you use an elevated absorption coefficient in the fluid in the region of the porous material. This models the additional radiation captured by the solid materail compared to the fluid. And for the re-radiated stuff (if this is significant enough to need to be modelled) you can use a radiation source term to generate radiation from the porous material, although it will actually be a source term on the fluid in the porous region.

I agree, this could work. From my point of view including a source term to account for emitted radiation is not even needed becasue CFX should also account for that. If participating media for the fluid part in the porous domain is selected then CFX accounts for absorption, scattering and emission. Do you agree?

Why do you say the source term for emitted radiation should not be needed? The solid component of the porous material does not participate in the radiation model, so if you want to include the emitted radiation from the porous material you are going to have to have a source term to include it.

Is the fluid totally transparent? Or does the fluid have some absorbance, scattering or emission?

Hi Glenn, thank you very much for your reply. Maybe I'm still not understanding your approach correctly.

Radiation is absorbed by the fluid (with artificially increased absorption coefficient) in the porous domain and subsequently heats up the solid (depends on defined fluid-solid heat transfer coefficient). If the fluid-solid heat transfer coefficient is artificially increased both the fluid and solid have the same (almost) temperature. Otherwise, the fluid would be considerably hotter than the solid which is physical nonsense. Since participating media has to be selected for the fluid in the porous domain, the fluid will also emitt radiation dependent on its temperature and consequently no radiation source for the solid is needed.

The fluid is argon. Thus, it has very small absorptance, scattering and emission but so small that it can be neglected.

I would check the effect of using a fluid-solid HTC to account for the radiation emmission of the solid. I do not think it will model the real situation too well. At least with a emmission source term you can put factors in there to make it representative of the solid temperature and get the emmission closer to reality.