RADIATIVE HEAT TRANSFER IN PHOENICS

Overview, by Brian Spalding

1. The magnitude of the problem

Turbulence, chemical reaction, multi-phase flow and radiation are the four main phenomena for which CFD practitioners need to make use of "models", i.e. of mathematical idealisations which, although known to fall far short of complete representations, may still, in favourable circumstances, permit useful predictions to be made.

Of these,

the first receives great attention from CFD specialists, and enjoys high prestige as a scientific challenge;
the second is the active concern of perhaps an even greater number; and
the third, though presenting fewer mysteries, is the subject of continued and large-scale research.

Radiation, however, although presenting even greater practical difficulties, has been a less popular subject for research. As a consequence, inability to model radiation properly is often the main cause of inaccuracy in CFD predictions.

This is understandably true of high-temperature processes, such as those in the combustion chambers of engines and furnaces; but it is no less true of lower-temperature ones, such as:

in electronic equipment; or
in the living accommodation of human beings, where convective, conductive and radiative modes of heat transfer may have similar orders of magnitude.

2. A common misconception

Radiative heat transfer can be described mathematically with exactness. Perhaps for this reason, it is commonly supposed that enabling a CFD code to add radiation to its predictive capabilities is simply a matter of selecting and attaching to it one or other of the available equation-solving methods such as those which go under the names of:-

Monte-Carlo,
discrete transfer,
discrete ordinates,
zone,
etc.

This is a misconception; for, unfortunately, consideration of how these methods will perform when applied to problems of more than modest size, makes plain that they must all require very much more computer time and elapsed time than anyone can afford; and this is so even with neglect of the influences of:

wave-length on absorption and emission,
angle on the reflectivity of surfaces,
temperature on the radiative properties of materials,
the chemical composition and "surface finish" of those materials, and
the complicating presence of turbulent fluctuations of temperature and of multi-phase flow.

It is true that, such are the desires of CFD-code vendors to sell their products, and of purchasers to believe that they have spent their money wisely, that many publications can be found which purport to "validate" the radiation-simulating capabilities of the codes.

Rarely however do these publications contain the results of systematically-conducted parametric studies which alone, in view of the very large number of choices which have perforce been made, truly justify the claims.

3. The "PHOENICS Philosophy"

In view of these considerations, the philosophy adopted in PHOENICS is that represented by the following quotation:

The wise engineer therefore recognises that, if his simulations are to be usefully realistic, within his economic and hardware constraints, it is crucial that his approach must be well-balanced.

Thus, it is pointless to expend large resources on elaborate low-Reynolds-number turbulence models if the grid fineness is hopelessly inadequate; or on complex geometrical radiation-view-factor calculations, if medium participation and wave-length dependences are totally ignored.

It is for this reason that special attention is focussed, in the current Encyclopaedia entry, on the IMMERSOL model.

Click here for an electronics-cooling example, which would be very expensive to solve with accuracy by any of the other methods.

IMMERSOL, by contrast, is so inexpensive that introduction of wave-length-dependent properties can at least be contemplated.