  Two-dimensional simulations are conducted to investigate the direct
initiation of cylindrical detonation in hydrogen/air mixtures with detailed
chemistry. The effects of hotspot condition and mixture composition gradient on
detonation initiation are studied. Different hotspot pressure and composition
are first considered in the uniform mixture. It is found that detonation
initiation fails for low hotspot pressures and supercritical regime dominates
with high hotspot pressures. Detonation is directly initiated from the reactive
hotspot, whilst it is ignited somewhere beyond the nonreactive hotspots. Two
cell diverging patterns (i.e., abrupt and gradual) are identified and the
detailed mechanisms are analyzed. Moreover, cell coalescence occurs if many
irregular cells are generated initially, which promotes the local cell growing.
We also consider nonuniform detonable mixtures. The results show that the
initiated detonation experiences self-sustaining propagation, highly unstable
propagation, and extinction in mixtures with a linearly decreasing equivalence
ratio along the radial direction respectively, i.e., 1 to 0.9, 1 to 0.5 and 1
to 0. Moreover, the hydrodynamic structure analysis shows that, for the
self-sustaining detonations, the hydrodynamic thickness increases at the
overdriven stage, decreases as the cells are generated, and eventually become
almost constant at the cell diverging stage, within which the sonic plane shows
a sawtooth pattern. However, in the detonation extinction cases, the
hydrodynamic thickness continuously increases, and no sawtooth sonic plane can
be observed.
