Numerical simulation of superfast shock-induced chemical reaction in titanium-silicon mixture

A phenomenological zeroth-order kinetic model for computations of shock-induced solid-state chemical reactions in porous mixtures is proposed. In the model a porous mixture is considered as a continuous medium whose thermomechanical properties are determined at each time step depending on mass fractions of the components. The kinetic relationships are characterized by a constant rate of chemical transformation under shock wave loading. The heat release due to chemical transformation is introduced in the energy equation. The effect of the dispersity of the mixture components on the reaction rate is taken into account by varying the constants that enter the kinetic model. The results of the numerical computations for porous Ti-Si mixture reflect the fact that the process can be divided into several stages (dynamic; compaction, shock-wave propagation, reaction of synthesis). It is shown that an increase in the chemical-reaction rate can give rise to flow regimes in which the unloading wave almost stops.