Effect of disorderness in two-dimensional discrete adiabatic combustion waves in a heterogeneous solid medium under stable regime.

The effect of disorderness for the propagation of stable combustion waves in a two-dimensional discrete adiabatic system are studied by considering two systems, namely, (i) periodic and (ii) disorder. The discrete periodic system is modeled by regular arrangement of burnt and unburnt point heat sources. In contrast, the discrete disordered system is modeled by the concatenation of regular burnt and randomly distributed unburnt heat sources. Four different kinds of discrete disordered systems (S1, S2, S3, and S4) are modeled by varying the joint frequency count of unburnt heat sources without changing the domain size of the system. Results show that the disordered structure of the discrete system plays a crucial role in the combustion dynamics, shape of the combustion wave, and it affects the propagation of stable combustion waves with the manifestation of sparse and chaotic finger patterns. Quantitative analysis performed for the width and roughness of combustion front show that the disordered structure and ignition temperature (ε) of the discrete system plays a crucial role. The burn rates of discrete system are sensitive to change in structure of the system and ε. It is observed that the burn rates obtained for the discrete disordered system is always less than that of burn rates of the discrete periodic system. The burn rates calculated for the present model are compared with the available experimental data on combustion of thermite systems.