We present a model for predicting a representative width for the
three-dimensional cells observed on detonation fronts in reactive gases. Its
physical premise is that the dynamics of the transverse waves of irregular
cells obeys a stochastic process both stationary and ergodic and produces the
same burnt mass per unit of time as the average planar steady ZND process.
Graph theory then defines an ideal cell whose grouping is equivalent to the
actual 3D cellular front, geometric probabilities determine the mean burned
fraction that parameterizes the model, and ZND calculations close the problem
with the time-position relationship of a fluid element in the ZND reaction
zone. The model is limited to detonation reaction zones whose sole ignition
mechanism is adiabatic shock compression, such as those of the mixtures with
H2, C3H8 or C2H4 as fuels considered in this work. Indeed, the comparison of
their measured and calculated widths shows an agreement better than or within
the accepted experimental uncertainties, depending on the quality of the
chemical kinetic scheme used for the ZND calculations. However, the comparison
for CH4:O2 mixtures shows high overestimates, indirectly confirming that the
detonation reaction zones in these mixtures certainly include other ignition
mechanisms contributing to the combustion process, such as turbulent diffusion.
In these situations, the cell mean width derived from longitudinal soot
recordings shows a very large scatter and may thus not be a relevant detonation
characteristic length. The model is easily implementable as a post-process of
ZND profiles and provides fast estimates of the cell width, length and reaction
time.Comment: Extended versio