Abstract :
Ignition and combustion of an initially spherical pocket of fuel in motion relative to a hot oxidizing atmosphere
is studied. The model considers finite rate chemistry represented by an irreversible one-step reaction. Attention
is focused on the development of the ignition process, which, in the end, typically leads to the establishment of
a diffusion flame. For moderate value, of a suitably defined Damk6hler number, three stages are identified in
the burning process. Stage I corresponds to an induction period during which a mixing layer is formed around
the fuel kernel. This stage ends up with a thermal runaway close to the back of the kernel. Stage [] involves the
propagation of a chemical front in the mixing layer: initiated at the point where the thermal runaway occurs,
a first flame travels around the fuel kcrnel towards the nose, triggering during its travel a premixed radial
inwardly propagating flame. The second stage ends when ignition reaches the nose. Stage III corresponds to an
established diffusive burning, which is most active at the front surface.
As the Oamk6hler number, Oa, is increased, stage I and II shrink leading to a practically spherical ignition.
In this limit of large Oa, the ignition time becomes independent of the Reynolds number. Conversely, for
sufficiently low Da, stage III (i.e .. diffusive burning) is absent. In this case, the fuel is practically consumed by
reaction at the back of the kernel, after premixing at the front mixing layer with the oxidizer. The flame
responsible for the burning occupies a quasi-steady stable position close to the maximum cross section position.
Furthermore, the results provide a good appreciation of the dynamics of the combustion process. For
example, it is found for moderate Da that a significant acceleration-deceleration of the fuel pocket takes place
during ignition due to the pressure increase caused by gas expansion. Finally, with the aid of an order-ofmagnitude
analysis, a synthesis of most of the physical results described above is achieved by delimiting different
domains in the Da-Re plane.
