Hi all!

I am currently looking at radiation issues (within CFD) and have looked at various options. I have read the background theory and am now considering the methods that are available and I would like to know more about them.

The methods I am particularly interested in are the "ordinate method", "spherical harmonics" (P1, Pn),"discrete transfer", and "Monte Carlo". I have read briefly about them but I have yet fully understood what they were doing (how they are implemented; the book I have is more based on radiation theory than on its numerical application)and was wondering whether anyone could recommend a good reference on the above. I haven't many references on the web on the subject so far.

Thanks.

Hi friend

I'm working on radiation heat transfer, I'm using the Finite Volume Method. would you like to use it?

Hi,

I have implemented discrete transfer radiation method (DTRM). The best reference is the original paper about the method:

F.C. Lockwood and N.G. Shah. A NEW RADIATION METHOD FOR INCORPORATION IN GENERAL COMBUSTION PREDICTION PROCEDURES. Eighteenth Symposium (International) on Combustion, The Combustion Institute, London, 1981.

However, it is on You to decide which method is best appropriate for You and your problem.

Regards, Mario

Hi Holidays,

I recommend you the book "Radiative Heat Transfer" by Michael F. Modest, McGraw Hill, 1993. It discusses (in addition to the radiation theory) most - if not all - the numerical methods you are interested in. Presentation is very clear.

I have experience with the finite-volume variant of the discrete ordinates (Fiterman, A., Ben-Zvi, R., and Kribus, A., DOTS: Pseudo-Time-Stepping solution of the Discrete-Ordinate Equations. Numerical Heat Transfer B 25, 163-183, 1999) and the Monte-Carlo method. Recently we had integrated them within the framework of a general-purposed CFD code.

Thank you. Would you by any chance have the isbn number for this book by Modest?

Hi Ahmed,

The code I'am using is indeed a FV one. But I need to understand the radiation methods better before embarking on my test case.

Hi,

Depending on what you want to do, if your interest focuses on the participating medium, then discrete ordinate method (DOM) and monte carlo method are some of your choices. However, for DOM, or actually any continual approach on participating medium, the scattering behavior (phase function)of the system should be evaulated beforehand. There are numbers of approximations that you may considered, isotropic or anisotropic scattering could be used. I think both Modest's book and Segiel's book should have very detail description on this. As far as I know (but very limited), you can do very fancy thing in monte carlo. The point is that the more fancy you applied the monte carlo, the more computational power it required. Therefore, you need consider your available computer resource as well.

On the other hand, if your problem is just radiation exhange between boundaries, then typical "Net radiation" method coupled with flow equation and energy equation of the flow would be sufficient. Well, DOM is actually not appliable in such calculation. You can still use monte carlo method to calculate the view factors between boundaries if the geometry is very complex.

Best Regards, Adam

I only have it at work, and I am on vacation now. However, I'm pretty sure you may find it on Amazon.

I agree with Adam that many approaches are possible, each with its cons and pros.

If participating medium is considered, the scattering behaviour should be known, irrespective of the numerical method used (specifically, even if the Monte-Carlo method is applied, the scattering phase function should be specified).

It is true that the Monte-Carlo method is very flexible. It is also very easy for implementation. I also agree it tends to be very CPU-demanding. It has however another benefit, that it is always converging to the exact solution if enough numerical rays are used, and the statistical error may be estimated.

I do not agree the DOM is inapplicable to problems in which only surface radiation prevails. Rather, it is quite inefficient in this case (treated as a transparent medium).

For non-participating medium problems, the use of view factors is indeed recommended when applicable. It is however limited in several respects, e.g., that all surfaces should be diffuse. If at least one of the surfaces is specular reflector, the more general exchange factors approach should be used.

Hi Adam,

Immediatelly I am interested in luminosity on a plane emitted by a lamp and in the accompanying heat transfert in the fluid and on the plane. I was thinking MC was the most adequate in my case but I have little experience in radiation per se (I have used simple models in commercial codes in combustion cases)...

Hi, The main concern of DOM is to deal with the integration term in RTE. Therefore, in case of only radiation exchange between solid surfaces, the whole idea of RTE is not suitable and therefore that is why I believe DOM is not appliable to radiative exchange between surface.

In monte carlo method, there has already paper showing that it can not only handle diffuse surfaces, but also directional surfaces. The idea on directional surfaces is to the total acceptance of irradation from certain directions and total rejection the rest of other. If I remember correctly, paper writtern by M.Kaviany has already done it. Another approach, which is done in my master study can also be achieved in Jounral of numerical heat transfer. If you are interested in it, please take a look. I think it is published around year 2000.

Again, depending on what your problem is, if the fluid is participating, for example, CO2 or dust particles in the air, then the radiation exchange between source and the fluid, source and the plane and fluid and the plane should be considered.

Problem is that scope, even in simple geometry, is very challenging. I think the first thing is to see whether any appropiate approximation can be applied to the problem, such as optically thick medium or optically thin medium. The other thing you may consider is the usage of MC method in the commerical codes you used. In short, MC method can apply to entire RTE. It can calculates the view factor between the source and the plane, the absorption coefficient, the scattering coefficient and even the phase function of the medium. But the computation would be enormous and I doubt whether this will implement into the software.

So please look at the code specification, whether the implemented monte carlo is to calculate the view fator only.

My suggestion is that, if the fluid in the model is a common one, you can take look on the Segiel's book for absorbing and scattering coefficients. From this point on you will have a brief idea whether your medium is optical think, thin or not.

Thanks for you explanations Adam.

I have already looked at the optically thick medium approach but rapidly found out it was not applicable to my case. This is why I looked further, and understood that I needed something more along the lines of MC.

Adam,

Could you give the ref of the book you mention by Segiel?

Thank you again.

Thermal Radiation Heat Transfer, 3rd ed., Robert Siegel and John R. Howell (ISBN 0-89116-271-2)

hi Adam, what do you think about the FVM for resolving the RTE ?

First of all, regardless which discretization method you use, the main issue is still on how you obtain the radiative properties accurately.

But assuming the radiatve property values you got is reasonably accurate to describe your system, I think FVM would be a bit easier to handle complex geometry. FVM for RTE, as I remember correctly, has been developed about 10 to 15 years, which is rather new, compared to other numerical method such as zonal method. The trick in FVM for solving RTE is really on how to describe the in-scattering term. However, the exact detail I really cannot remember, I believe you must come across some papers written by a Professor in Canada published in early 90s. They have very detailed description on it.

Accroding to literature, the predictions made by DOM, FVM(RTE) and Monte carlo differ significantly. The main cause is not on which method more accurate, but because we do not have accurate description on the radiative property on the system, especially on the phase function. This was also part of my master study's goal, to seek a methodolgy to reasonably descibe the radiative property for a given participating medium.

hello, again Adam for the discretization method I'm using the finite volume method. For FVM for radiation, it's true that it is developped in 1990 by Raithby. I think that he's the Professor in Canada that you are refering. I agree with you that is the main problem is to difine the accurate radiative properties. For me I'm using constants values of absorption and diffusion coefficients. I've validate the code in the axisymmetric and noscattering medium. but I found difficulties to validate it in when scattering is considered.

Hi Adam,

I disagree with you that "DOM is not appliable to radiative exchange between surface". As a matter of fact, part of the validation cases we solved in the paper we published (Fiterman, A., Ben-Zvi, R., and Kribus, A., DOTS: Pseudo-Time-Stepping solution of the Discrete-Ordinate Equations, Numerical Heat Transfer B 25, 163-183, 1999) solved such problems and compared them to reference cases by Jeff Moder et al (who used both the finite-volume and exact solutions - either analytical or MC, I assume). I admit it is not very efficient compared to a surface-to-surface method (such as the Monte-Carlo).

As to the limitations I mentioned: they are not limitations of the Monte-Carlo method, but rather of the view factor approach (see my former posting). I know it is possible to use Monte-Carlo in a much broader context - actually, our Monte-Carlo code allows for specular and diffuse surfaces (among few other possibilities which are beyond the scope of the view factor approach, e.g., spectral effects).

P.S. The "professor from Canada" you mentioned in another posting is probably Raithby (and his co-author is Chui).

What I did in my master study, roughly speaking, was first to simulate the radnom behavior of a representative region (unit cell) of the medium. Then based on this unit cell and medium's radiative property (such as scattering behavior of individual particle, in simplest term), I applied monte carlo method to back-calculate the absorption coefficient scattering coefficient and phase function of the medium. Finally, I solve the RTE by using DOM.