A numerical study of unsteady self-propagating reactions in multilayer foils

Self-propagating reactions in multilayer foils are analyzed using an unsteady computational model. The reactions are described in terms of the energy conservation equation and the evolution equation for a conserved scalar. The model is applied to analyze combustion waves in reacting foils that consist of alternating layers of Ni and Al. The individual layers have thicknesses, 2δ, in the range 20 to 200 nm, and the foils are 1 to 100 μm thick. The interfaces between the layers are assumed to be diffuse, with a characteristic mixed-zone thickness of 4w. The propagation of the flame is analyzed in terms of δ and w. Consistent with experimental observations and steady-state calculations, computed results show that the flame speed increases with decreasing δ, until a critical value, δ_c, is reached. Below δ_c, the trend is reversed-that is, the flame speed decreases with δ. Meanwhile, the flame speed increases monotonically with decreasing w. However, the calculations show that propagation of the reaction occurs in an unsteady fashion. Periodic and quasi-periodic, large-amplitude oscillations in the burning rate and the flame width are observed. As the flame speed increases, the amplitude of the oscillations increases and their characteristic period decreases. The occurrence of superadiabatic temperatures within the flame suggests that the oscillations result in an average propagation speed that is larger than the steady-state prediction.