Effects of Layer Thickness on the Burning Velocity and the Range of Flammability in the SHS Process with Multi-Layer foils

Abstract

Relevant to Self-propagating High-temperature Synthesis (SHS) process, burning velocity and range of flammability are examined theoretically. Use has been made of the heterogeneous theory for the SHS flame propagation in multi-layer foils, consisting of alternating layers of constituents, has been extended to multicomponent systems, by describing a premixed mode of bulk flame propagation supported by a non-premixed reaction that proceeds at the layer surface of a constituent with higher melting-point. The formulation allows for finite rate Arrhenius reaction at the layer surface, temperature-sensitive Arrhenius mass diffusion in the liquid phase, and existence of intermixed region between constituent layers. It is confirmed that thickness ratio of the constituent layers is related to mixture ratio and that thickness ratio of the intermixed region and the constituent layer is related to degree of dilution. Results show that the burning velocity first increases, reaches the maximum, and then decreases rapidly, with decreasing alloy layer thickness, and that the decrease in the burning velocity can be attributed to the increase in the substance in the intermixed region between constituent layers, playing a role of diluent. The range of flammability is also obtained by the general restriction that the combustion temperature should be higher than the melting point of a constituent with lower melting-point. In experimental comparisons, it has been demonstrated that the analytical results agree with available experimental data in the literature, indicating that the present formulation has captured the essential features of the adiabatic, heterogeneous SHS process.