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Old   April 15, 2014, 17:10
Post Lack of knowledge simulating radiation in solids
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Alex
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Hello everybody!

I'm trying to solve a problem using chtMultiRegionSimpleFoam involving radiation between some solids surrounded by air as a non-participating media. The case is explained in this post: Problems in my first attempt with chtMultiRegionSimpleFoam. There you can see a picture of my geometry.

I am using fvDOM for the calculation of the radiation, but I am a bit confused because there is no multi-region tutorial using fvDOM for the radiation calculation. Thus, I am trying to set it up by following the multiRegionHeaterRadiation and the hotRoomRadiationFvDOM tutorials. Now I need some help and advices to know If I am doing the radiation set up right.

1) Since air is a non-participating media I used this radiationProperties file (taken from the hotRoomRadiationFvDOM tutorial and adapted to my case):

Code:
radiationModel  fvDOM;

fvDOMCoeffs
{
    nPhi    3;          // azimuthal angles in PI/2 on X-Y.(from Y to X)
    nTheta  5;          // polar angles in PI (from Z to X-Y plane)
    convergence 1e-3;   // convergence criteria for radiation iteration
    maxIter 5;         // maximum number of iterations
}

// Number of flow iterations per radiation iteration
solverFreq 10;

absorptionEmissionModel constantAbsorptionEmission;

constantAbsorptionEmissionCoeffs
{
   absorptivity    absorptivity    [ 0 -1 0 0 0 0 0 ] 0.0;
   emissivity      emissivity      [ 0 -1 0 0 0 0 0 ] 0.0;
   E               E   [ 1 -1 -3 0 0 0 0 ] 0;
}

scatterModel    none;
My question is wether is correct or not to set up absorptivity and emissivity to 0 in the air, because I want it to be a non-participating media. It should be the same that setting absorptionEmissionModel to none, shouldn't it?

2) On the other hand, the solid regions set up is what is confusing me more. This is the radiationProperties file I used for one of the solid regions (Also taken from the tutorial and adapted):

Code:
radiationModel  opaqueSolid;

absorptionEmissionModel constantAbsorptionEmission;

constantAbsorptionEmissionCoeffs
{
    absorptivity    absorptivity [ 0 -1 0 0 0 0 0 ] 0.0;  //opaque
    emissivity      emissivity [ 0 -1 0 0 0 0 0 ] 0.5;
    E               E [ 1 -1 -3 0 0 0 0 ] 0;
}

scatterModel    none;
What lead me to a big confusion is the explanation that the solid is opaque because it has an absorptivity of 0. However, it makes no sense according to my knowledge in the field of thermal radiation (which is not much wide, I must say). According to what I know, the main coefficients that define the solid's behavior agains radiation are absorptivity (alpha), reflectivity (rho) and transmissivity (thau), and they satisfy that:


Then, according to Kirchhoff's law we can say that (only valid for black body, in other cases they are equal but different to 1)


(so I maybe should define the same value for both coefficients). But what I don't really understand is that opacity is defined by absorptivity (alpha) in the tutorial, when, as per my knowledge in matters of radiation, opacity is defined by the transmissivity (thau), being 0 when the solid is opaque. Once I found out this little inconsistency (at least to my eyes, I guess I must have missed something or I am mistaken in something) I sought all along the english and spanish literature to see if it was a matter of a bad translation from spanish (the language I studied it from originally) to english, but I couldn't find anything clear.

3) Finally, the last question I have is about the units of both coefficients, that is, m⁻đ. Shouldn't it be dimensionless?


As you can see, I'm a little lost with this simulation and I really need a little help to see what I am doing wrong. Any hint or advice will be welvcome and much appreciated.

Many thanks in advance!!


Alex
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Last edited by zfaraday; April 16, 2014 at 07:27. Reason: Edited a mistake, clarified in green within brackets
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Old   April 20, 2014, 14:48
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I don't know if my explanation was correct enough or not, but i really need a little help to understand the radiation set up process in order to solve my problem. Any hint will be much appreciated!

Alex
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Old   May 9, 2014, 06:03
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I'm currently also looking at radiation modelling with fvDOM, using a participating plasma with a multi-group approach (wideBandAbsorptionEmissionModel). I can't help you too much yet I'm afraid, but absorptivity and emissivity (the properties of the medium), are in m⁻1 because it's the factor in exponential decay of intensity absorped in a unit length.
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Old   May 10, 2014, 14:39
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Thank you so much chriss85 for your replay, that clarifies a little. Then, according to what you said I understant that if I want to work in a non participating media I have to turn these coefficients to 0, haven't I? Or, otherwise, switch absorptionEmissionModel to none.

Thanks again.

Alex
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Old   May 12, 2014, 03:15
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Yes, that's correct I think. If your radiation comes from surfaces only and the medium between doesn't absorb or emit, you can turn these values to 0.
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Old   May 12, 2014, 13:34
Default radiation model in solids
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Thank you for your help chriss85, now I understand a little bit more the matter of radiation. But I still keep having a doubt about it, specifically this is about the radiation in solids as I asked in the second question on the first post of this thread. Here comes the question again just in case you can help me understanding it...

Quote:

2) On the other hand, the solid regions set up is what is confusing me more. This is the radiationProperties file I used for one of the solid regions (Also taken from the tutorial and adapted):

Code:
radiationModel  opaqueSolid;

absorptionEmissionModel constantAbsorptionEmission;

constantAbsorptionEmissionCoeffs
{
    absorptivity    absorptivity [ 0 -1 0 0 0 0 0 ] 0.0;  //opaque
    emissivity      emissivity [ 0 -1 0 0 0 0 0 ] 0.5;
    E               E [ 1 -1 -3 0 0 0 0 ] 0;
}

scatterModel    none;
What lead me to a big confusion is the explanation that the solid is opaque because it has an absorptivity of 0. However, it makes no sense according to my knowledge in the field of thermal radiation (which is not much wide, I must say). According to what I know, the main coefficients that define the solid's behavior agains radiation are absorptivity (alpha), reflectivity (rho) and transmissivity (thau), and they satisfy that:


Then, according to Kirchhoff's law we can say that (only valid for black body, in other cases they are equal but different to 1)


(so I maybe should define the same value for both coefficients). But what I don't really understand is that opacity is defined by absorptivity (alpha) in the tutorial, when, as per my knowledge in matters of radiation, opacity is defined by the transmissivity (thau), being 0 when the solid is opaque. Once I found out this little inconsistency (at least to my eyes, I guess I must have missed something or I am mistaken in something) I sought all along the english and spanish literature to see if it was a matter of a bad translation from spanish (the language I studied it from originally) to english, but I couldn't find anything clear.
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Old   May 13, 2014, 03:00
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I haven't worked with the opaqueSolid model yet, so I can't really tell you anything about it. I suggest that you also take a look into the code of it, to see what equations are being solved. Some comments may also help you.

Regarding the absorptivity, I agree that it should not be 0 in an opaque solid, but rather a very high value instead, because the absorption and the exponential decay of intensity will happen on a very short length scale.

I think transmittivity can only be defined per length, while transmittance is the absolute value related to a specific length. Don't quote me on that though, it's been a while for me.
Reflectivity is only useful on surfaces, not in solids. If you look at a solid of a fixed size, then your equation saying alpha + rho + tau = 1 is correct, but it refers to the absolute ratios of intensity (i.e. reflectance, transmittance, and absorption), not on absorptivity/emissivity, which are per length.
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Old   May 19, 2014, 11:47
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Thank you criss85 for your advice. Now I have taken a look into the code (my knowledge in C++ is more than weak, though) another doubt came out to my mind. This is what the solver solves for the solid region (solveSolid.H):

Code:
 fvScalarMatrix hEqn
        (
          - fvm::laplacian(betav*alpha, h, "laplacian(alpha,h)")
         ==
            fvOptions(rho, h)
        );

        hEqn.relax();

        fvOptions.constrain(hEqn);

        hEqn.solve();

        fvOptions.correct(h);
It seems it is not doing anything about the radiation inside the solid, doesn't it? At least compared to the EEqn.H file (which solves the energy eqution in the fluid region) which does take into acount the radiation model

Code:
    fvScalarMatrix EEqn
    (
        fvm::div(phi, he)
      + (
            he.name() == "e"
          ? fvc::div(phi, volScalarField("Ekp", 0.5*magSqr(U) + p/rho))
          : fvc::div(phi, volScalarField("K", 0.5*magSqr(U)))
        )
      - fvm::laplacian(turb.alphaEff(), he)
     ==
        rad.Sh(thermo)
      + fvOptions(rho, he)
    );
After that I checked the file opaqueSolid.H to see what it was doing and I found the following that lead me to a little confussion...

Code:
Description
    Radiation for solid opaque solids - does nothing to energy equation source
    terms (returns zeros) but creates absorptionEmissionModel and
    scatterModel.
Can anyone explain me what is exactly doing the opaqueSolid radiation model? How important is to define this radiation model in a solid region? Which is the difference between defining opaqueSolid or none in a solid region in chtMultiRegionSimpleFoam?

Thanks in advance!


Alex
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Old   January 20, 2015, 07:01
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Hi Alex,

Where you able to discover exactly how to model radiation between the two solids?

The tutorial seems to be only applicable in the case where the solid is not absorbing any of the radiation, is this correct?

My question more in a modelling sense is: Letīs say that you have two bodies if you model them both as opaque and you take a radiation model for air. Does this mean that air will absorb all the radiation?
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Old   January 20, 2015, 08:48
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Hello Pedro,

Quote:
Originally Posted by pedrojrebelo View Post
Hi Alex,

Where you able to discover exactly how to model radiation between the two solids?
Yes and no. Explanation: I tried to model radiation using two out of the three methods provided with OpenFOAM (viewFactors and fvDOM) and, although I thought I set up everything ok, the results with both methods were way too different one from another. For more information you can check the following thread: trying to validate fvdom and view factors methods.

Quote:
Originally Posted by pedrojrebelo View Post
The tutorial seems to be only applicable in the case where the solid is not absorbing any of the radiation, is this correct?
Well, more or less, the solids don't absorb radiation directly, but they can absorb radiative heat flux (called Qr in the solvers and BC's) in the surface. To make use of it you have to set up correctly the BC's between the solid and the fluid regions.

Quote:
Originally Posted by pedrojrebelo View Post
My question more in a modelling sense is: Letīs say that you have two bodies if you model them both as opaque and you take a radiation model for air. Does this mean that air will absorb all the radiation?
Not exactly, it means that the radiation travels across the air, wether the air absorbs or not radiation, it depends on how you set it up in the constant/fluidRegion/radiationProperties file.

Hope it helps.

Alex
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