6.3 The "eddy-break-up" model

(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:

VELOCITY_GRADIENT * MIXING_LENGTH

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