  We present a model for predicting a representative width for the
three-dimensional irregular patterns observed on the front views of cellular
detonation fronts in reactive gases. Its physical premise is that the cellular
combustion process produces the same burnt mass per unit of time as the average
planar steady Zel'dovich-von Neuman-D\"oring (ZND) process. The transverse
waves of irregular cells are described as a stochastic system subject to a
stationary ergodic process, considering that the distributions of the patterns
should have identical temporal and statistical average properties. 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 only ignition mechanism is
adiabatic shock compression, such as those of the mixtures with H2, C3H8 or
C2H4 as fuels considered in this work. 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 widths on longitudinal soot recordings have a very large
dispersion, so a mean width may thus not be a relevant detonation
characteristic length. The model is easily implementable as a post-process of
ZND profiles and provides rapid estimates of the cell width, length and
reaction time.

Fluid Dynamics