• ### What is the Discrete Transfer method?

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## 1. What is the Discrete Transfer method?

The Discrete Transfer method, developed by Lockwood and Shah [1], exhibits features of the Flux (CF272), Zone (CF271) and Monte Carlo (CF273) methods. It is like the Flux models in that only certain predetermined directions are considered. It resembles the Zone method in that the enclosure is divided into zones of uniform properties, and it resembles the Monte Carlo method in that particular rays of intensity are tracked, Fig.1.

Fig. 1  The geometry for the Discrete Transfer method.  Beams are travelling from points Q to point P on Aj and intersect the volume element boundaries at n-1, n etc.

An enclosure is divided into volume and surface elements. The hemisphere about each surface is also divided into solid angle elements, in each of which, a beam direction is defined, in which the directional incident flux is calculated. Each beam is assumed to contain the radiative flux of the entire solid angle that it represents. The beams impinge on the centre point of the surface element. It is possible to determine the origin of the beam where it intersects with a surface element on the enclosure boundary. The energy of the beam at this point depends on the boundary condition at this surface element. An important advantage of the DTM over the Zone method is that it can more accurately model variation of gas absorption coefficient with position.

It has the advantage of being easy to apply to complex geometries and is conceptually simple. It can be applied to non-homogeneous combustion products [2]. Unlike the Zone method however, the geometric configuration factors are being implicitly determined during every simulation as each beam is tracked.

The DTM method is now being commonly applied with flow models, in which case the volume and surface elements conform to the control volumes in the [GLOSS]CFD[/GLOSS] model. Solution of the flow and radiation equations is not carried out simultaneously, however. The post processing approach described for Monte Carlo solutions is applied.

## Sources

1.        Lockwood F.C., Shah N.G., Eighteenth Symposium (International) on Combustion, The Combustion Institute, 1981, pp 1405-1414

2.       Docherty P.,  Fairweather M., ‘Predictions of Radiative Transfer from Non- homogeneous Combustion Products Using Discrete Transfer Method’, Combustion and Flame 71,  79-87 (1988).

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