Encyclopaedia IndexBack to start of article

### (a) The nature of the eddy-break-up model

Presumed-pdf models, when applied to combustion processes, usually seek to account for fluctuations of the fuel-air ratio.

Another model, having a presumed-pdf character but a different name, seeks to account for variations of reactedness, in gases of uniform fuel-air ratio.

This is the "eddy-break-up" (EBU) model (Spalding 1971), which postulates a two-spike pdf of a special kind, namely:

1. where TM the time-mean temperature of the Mixture lies between TU and TB, those of the fully-Unburned mixture and fully-Burned mixtures, TB, it is because the mixture is made up colder fragments inter-mingled with hotter.
2. the cold fragments are as cold as they can be, namely at TU; and the hot fragments are as hot as they c be, at temperature TB.

### (b) Calculating the mass fractions of the two fluids

Since the temperatures of the two components of the population are fixed, a single differential transport equation, namely that for the time-mean temperature, TM , suffices for the population distribution to be computed.

Specifically, the mass fractions of cold and hot gas, MU and MB, are given by:

MU = 1 - MB

= (TM - TU) / (TB - TU).

### (c) Calculating the reaction rate

• Of course, combustion can not take place (at an appreciable rate) in the cold fragments, because they are too cold:
• nor in the hot fragments, because they are alreaady fully burned.
• Since combustion undoubtedly does take place, it is supposed that:

(1) it does so at inter-faces between the two types of fragments;

(2) these occupy only a small proportion of the mixture volume;

(3) the rate of combustion per unit volume of mixture

is proportional to

the rate of intermingling of the two types of fragments; ..... and finally ......

### Calculating the reaction rate (continued)

(4) this rate of intermingling is proportional to:

MB * MU * MIXRATE

where MIXRATE is proportional to either:

in the first model (Spalding, 1971b) or to:

TURBULENCE_ENERGY_DISSIPATION_RATE / TURBULENCE_ENERGY

in a later version (Mason and Spalding,1973).

### (d) Successes and failures of EBU

The model has been successful in explaining certain otherwise inexplicable experimental findings, for example the fact that the angle subtended by the flame anchored in a plane-walled channel is nearly independent of approach-gas velocity.

However, it has no means for expressing the INFLUENCE OF CHEMICAL KINETICS.

Yet such an influence does exist, as witness the fact that, when the approach-gas velocity becomes very large, flame propagation abruptly ceases.

Therefore, although the EBU is still much used, its main importance appears to be that act acted as a forerunner to:-

• the eddy-dissipation concept of Magnusson and Hjertager (1976);
• the two-fluid model of combustion;
• the multi-fluid model of combustion.

### (e) The eddy-break-up model in PHOENICS

The eddy-break-up model is embodied in the core of PHOENICS.

The relevant user-accessible GROUND coding is fo be found in the user-accessible Fortran sub-routine GXCHSO, in file GXSOR.

This coding is activated by the provision through the Q1 file of a PATCH baned CHSO, and through the appropriate settings of IEBU.

Core library case 492 provides an example.

wbs