We study the transient dynamics of three-dimensional detonation cells when the detonation front is subjected to weak expansion due to the diffraction from a straight channel to a diverging channel. We focus on the effect of the cross-sectional shape, namely square or round, using diverging channels with the same initial cross-sectional area of 16 cm \(^{2}\) as the straight channels and the same expansion rate. The reactive mixture is \(2\,\hbox {H}_{2} + \hbox {O}_{2} + 2\,\hbox {Ar}\) at the initial pressure of 20 kPa and temperature of 294 K, and we use the sooted-foil technique to record the cellular dynamics. The mean cell widths first increase from different initial values, which depend on the cross-sectional shape and then decrease to stabilize at the same value independent of the shape but larger than the initial values. We use a relation of detonation dynamics between the velocity, total curvature and acceleration of the average detonation front to interpret successfully, albeit qualitatively, all the experimental trends. This sensitivity thus makes these experimental data a reliable basis for high-resolution numerical simulations capable of handling three-dimensionality and detailed chemical kinetics mechanisms. Defining a significative mean width of detonation cells requires constant cross-sectional tubes of size and length sufficiently large. Inductively, representing three-dimensional cells requires more statistical descriptors than a single mean width.
