  In the present work, the discrete flame model [1] is augmented by introducing
the thermal inertia of particles in the preheating zone. The effect of particle
thermal inertia on flame speed, propagation limits, and near-limits dynamics of
one-dimensional discrete combustion waves is studied using the new model. It is
found that, with the increase of particle thermal inertia, the propagation
velocity of the discrete flame decreases due to a smaller heating rate of the
particles. Besides, particle thermal inertia extends the propagation limits
compared to the prediction of the old model. Furthermore, it is mathematically
proven that the nonphysical branch of the solutions for the discrete flame
speeds, found using the old discrete model, is a set of solutions for the
propagation limits of steady-state discrete flames with particle thermal
inertia included. The flame speed predicted using the new model is also
compared with that determined analytically using a continuum model considering
the thermal inertia of the condensed phase [2]. We find that the discrete flame
speeds predicted by the both models become closer to each other with increasing
particle thermal inertia. Finally, the two models converge regardless of the
discrete nature of the heat sources when particle thermal inertia is large
enough so that can limit the flame propagation. The particle thermal inertia
controlled flames could be regarded as a new kind of combustion regime.

Fluid Dynamics