[MauricioAguilar]

Hello Foamers,

I have a couple of questions to those that have experience with radiation modeling. I have set up a simple case to validate my simulation, based on the multiregionheaterRadiation tutorial.

I have a couple of parallel solid plates with a non participating fluid (air) the middle.

Plate 1 has a fixed T of 294K.
Plate 2 has a fixed T of 273.
Both measure .1 by .1 m. And the fluid thickness is of .01m

The radiation model in the Air is viewFactors and in the plates is opaqueSolid. My interpretation of the tutorial setup is that the Qr solved by the viewFactors radiation model is taken from the solid radiation inherited from each plate.

Question 1:
in the /0/Air/viewFactorsField i can see values greater than 1. Why is this happening?
Analytically calculating the view factor for the entire plate I get a value of 0.82 using the equation in Incropera's Fundamentals of Mass and Heat Transfer.
Shouldn't the greatest value of a middle cell whose radiation is completely intercepted be limited to 1.

Question 2:

When I set the emissivity of both solids to 1 and their absorptivity to 0 (of an opaque body) I get a net radiative flux , Qr or q'', that corresponds to the analytical solution. Simulations Qr = 106Wm^-2; Analytical Qr = 108 Wm^-2.

However if I set the emissivity on the cold plate to 0.5 the Qr is halved. Taking the net radiative flux (Qr) to be equal to the radiosity (J) minus the Irradiation (G) , Qr = J -G , the results should be different as a change in emissivity in the cold plate should only reduce the Irradiation on the hot side and thus increase the magnitude of heat flux on that plate.

How should I set up these boundary conditions so that I can have solids with different emissivities?

I'll keep trying to figure things out in the mean time but I hope someone will know how to approach this.

kind regards,

Mauricio

[MauricioAguilar]

Question 2:

Total brain fart and I apologize for it.

I forgot that I was dealing with opaque solids and non absorbed energy bounces back(increasing the returning G value ) and satisfies the conservation of energy.

Question 1:

Still uncertain about the view factor matrix and will increase the number of coarse faces to evaluate differences.

[Zeppo]

Originally Posted by MauricioAguilar

Question 1:
in the /0/Air/viewFactorsField i can see values greater than 1. Why is this happening?
Analytically calculating the view factor for the entire plate I get a value of 0.82 using the equation in Incropera's Fundamentals of Mass and Heat Transfer.
Shouldn't the greatest value of a middle cell whose radiation is completely intercepted be limited to 1.

It must be a bug in viewFactorsGen utility which calculates view factors for patches taking part in radiation exchange. I faced with the same problem here: http://www.cfd-online.com/Forums/ope...-thin-gap.html and the solution hasn't been found yet. I am quite motivated to find it though but as for now I had to put it aside till I get familiar with the OpenFoam internals (source code) closely. If you find any solution please let me know.

[MauricioAguilar]

Sergei,

I just read your thread and the error % you are getting is huge!
My error is limited to a 10% discrepancy by comparison to my expected results. If I cannot solve this by increasing the number of coarse faces I may just parse the viewfactor matrix and replace any value>1 with 1.

[Bloerb]

viewFactorCoeffs
{
    smoothing true; //Smooth view factor matrix (use when in a close surface
                    //to force Sum(Fij = 1)
...
}

Did you use this option?

[Zeppo]

Originally Posted by MauricioAguilar

Sergei,

I just read your thread and the error % you are getting is huge!
My error is limited to a 10% discrepancy by comparison to my expected results. If I cannot solve this by increasing the number of coarse faces I may just parse the viewfactor matrix and replace any value>1 with 1.

I seem to have tried all the available options including the maximum number of coarce faces (one coarce face for one cell face) and the result was more or less the same. It is the source code that should be inspected and altered.

Originally Posted by Bloerb

viewFactorCoeffs
{
    smoothing true; //Smooth view factor matrix (use when in a close surface
                    //to force Sum(Fij = 1)
...
}

Did you use this option?

Yes. And, in fact, it didn't make any difference.

[MauricioAguilar]

I've been messing around with radiation lately and I found that values greater than 1 in the ViewFactorField dictionary must get parsed later on, because I wrote a simple program to replace values greater than 1 into 1 and it didn't make much difference.

In the setup I've been working with involving parallel plates at 373 and 273 K with 0.07 emissivity, when spaced at 0.01m the viewFactors for the hot and cold plates revolved around 8, changed them to 1 and got like a 0.02% difference in the resulting heat flux.

However, when the viewFactorGen fails so does the conservation of energy. With very small gaps, as in the previous case I get an unbalanced energy transfer between all surfaces.

As the gap distance increases and the values in the viewFactorField approach 1 or less the net radiative transfer approaches 0. Although my residuals show convergence this post-processing on the heat flux clearly shows otherwise.