Regime of validity of a spatially homogenised reaction model for multilayered particles

Numerical investigation of self-propagating reaction fronts in a network of Ni/Al nanolayered particles is conducted using the generalised reduced continuum model developed by Alawieh, Weihs and Knio [Combustion and Flame, Vol. 160, No. 9 (2013), pp. 1857–1869]. However, due to the high dimensionality and the high computational costs associated with simulating such systems, a further reduction of the model is sought through identifying regimes under which spatial homogenisation at the particle level would be valid. The limiting case of a single chain of particles with no porosity is considered, and comparisons between the computational results of the heterogeneous and the homogeneous reduced model descriptions are carried out. These enable us to determine a narrow region where the homogeneous particle approximation is valid, based on a criterion composed of the non-dimensional ratio of the particle's internal thermal resistance to its thermal contact resistance. We demonstrate that the validity of the homogeneous approximation may hold even for layered particles whose size is almost an order of magnitude larger than the thermal width of a reaction front steadily propagating in a uniform foil. The computations also show that the velocity of the front in the particle compact exhibits large variations as the thermal contact resistance is varied, which would offer the possibility of controlling reaction speed and ignition properties.