Multiband in Radiation Modeling
 

Dear friends

My case:
I am simulating a simple rectangular channel that contains several rods as heat sources. I am interested to investigate the effect of the absorption coefficient. I have provided the CFX my desired absorption coefficient as a function of wavelength and the temperature (is attached).

Now, I am working with multi-band spectral model and I have 2 problems:
1. In CFX, I can only define the bands and not the value of my desired quantities in every band. According to the CFX user's guide and theory guide, the value at every band is the midpoint value. I like to see the chosen exact value (of the absorption coefficient) at each band in the simulation.

2. If I define the bands in a discrete method (e.g. first band:10 micron-20micron and second band:30micron-100micron) the solution will not converge but with continuous bands, it will converge. I would like to define the bands such that they cover only the bumps or the peaks of the absorption coefficient plot(see figure).

I would appreciate it if you share your experiences with me.

In ANSYS CFX, you are discretizing the spectrum range; therefore, it must be continuous.

The software needs to be certain the entire spectrum range is integrated since emission occurs at all frequencies, even the ones where your absorption coefficient is 0.

Where will the emission in your transparent go? How will you account for the energy contained in the missing bands?

I am surprised the software did not write a warning about missing energy in the spectrum range selected, or something related to that effect.

Thank you very much for your fast response. I think CFX calculates the non-defined ranges of the spectrum by an estimation just as it does in the Grey model. Unfortunately, CFX guide did not explain the details.

Do you have any experience that how I can know the absorption coefficient in the defined bands? Even if I define band to cover all the spectrum. I already checked with the CFD post and also the .out file but I found nothing about it.

You seem to be guessing the behavior of the software. If it is not documented, it does nothing.

You have not shown how you have specified the absorption coefficient as a function of frequency, i.e

Ka = f (frequency, or else)

Have you searched this forum for examples of setting up frequency-dependent properties in ANSYS-CFX?

Keep in mind that information computed by the radiation model must produce the "Total Emission" and "Total Absorption" for each control volume, i.e. it must compute

Integral over the WHOLE spectrum of ( emissivity_nu * Eb_nu * du)

Integral over the WHOLE spectrum of ( Ka_nu * I_nu * dnu)

That integral is a piecewise integral where the interval width is the spectral band range.

Hope the above helps you

Dear Opaque

Your answer helped me a lot and now my problem is solved and I thank you very much. I have simulated more cases and as you said the parts of the spectrum which are not included in the bands are totally neglected. I would like to mention a few points for the future viewer:

In ANSYS CFX 2019, in radiation modeling with multiband:
1. If you use discrete bands which they do not cover the whole spectrum, the solver will write an error message in the output file but the solution does not stop.
2. the uncovered part of the spectrum (by your defined bands) is not interfering in the further calculations.
3. The amount of the desired quantity in every band is chosen based on the value of the quantity in the band MIDPOINT which is not the best method possible! So if you have a spectrum, it would be better to define a function (maybe a stepwise function) regarding your desired bands.

Warm regards,
Erfan

You are most welcome, and I hope you got the results you expected.


One note though on
how would you do it? As far as I know, that is what a line-by-line spectral solution does. The accuracy of your solution is a function of the width of the band, and controlled by the user.

That is no different than using a cell-centered finite volume for one-dimensional problems. The cell-centered value represents the mean value of the solution in that volume.

As you said the more band we define the more accurate the results would be. But defining N spectral bands means N-times more computation load (with respect to the gray model). So in the end, it would be a matter of optimization.

I was interested in the spectrum of the absorption coefficient and I had the data provided in a table (Fig. 1) as a function of wavenumber. As you see in Fig.1, I have a fluctuating behavior over the spectrum. Let's call each of these fluctuations a bump. I would like to define my spectral bands covering only these bumps. Leaving CFX alone to choose a value in the midpoint of these defined bands was not considered a wise decision. There are several methods to compensate for this flaw such as averaging the absorption coefficient in every band. But I chose to estimate the AbsCoeff in every band by creating another function that has the same integral as the spectrum does (Fig.2). Using MATLAB and integrating every bump, I have the integral value of f(x) for all my bands by which I can define my new function g(x). The new function g(x) is a step-wise function that has a constant value in each band and a zero value in the other parts of the spectrum. CFX will use the midpoint value which is equal to every value of each band.

I hope I have explained what you were looking for.
Warm regards,

You got it right, but keep in mind it is still a crude approximation.

True multiband radiation calculations MUST be line-by-line of the spectrum due to the highly varying nature of the properties.

That approach has worked wonders for one-dimensional studies in a variety of fields (not just CFD), but for 2D/3D models that approach is not practical as you pointed out earlier.

However, there is no definitive consensus on what is the best reduced spectral model for CFD applications: narrow band, wide band approximation, weighted sum of gray gases, spectral line weighted sum, full-spectrum k distribution, etc.

What is clear is that all the above are nothing else that a weigthed sum of solutions at effective points in the spectrum

How the real properties are weigthed is beyond the scope of any CFD package and it is left to the radiation expert to define.

Hope the above helps