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:
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).
(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 ......
(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).
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-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.