| Self-propagating, exothermic reactions in multi-layer foils are of growing interest due to their potential utility as controlled heat sources for joining applications, as igniters for explosives and as a technique to form intermetallics into complex shapes. In all of these applications a detailed understanding of how the reactions propagate is necessary in order to optimize the performance of the reactive foils. Numerical and analytical models are developed to investigate the propagation of the reactions. All of the models take account of the pre-mixing which occurs at the interfaces between individual layers during deposition.; In general, the modeling shows that reducing the multilayer period increases the velocity of the reactions, however, below a critical multilayer period the velocity is found to drop dramatically. This is due to the effects of pre-mixing. Both the numerical and analytical models show this sudden drop in velocity, however, the analytical models make the fundamental assumption that the flame propagates in a steady manner, the numerical models do not make this assumption. In fact, the numerical modeling shows that the reactions frequently propagate in an unsteady or oscillatory manner; depending on the specific parameter regime. The oscillatory combustion is characterized by superadiabatic temperature excursions and large variations in the reaction zone width, the flame thermal width, and the instantaneous flame velocity. As a final stage in understanding the propagation of the reactions, the numerical models have been used to investigate the effect of radiative and conductive heat losses on the propagation of the reaction front. Heat losses are shown to decrease the flame speed and the magnitude of the oscillations, and to increase the period of the oscillations. In the parameter range considered, radiative heat losses have a much smaller effect on reaction propagation than conductive heat losses. |
