Melting effects in condensed phase combustion with applications to combustion synthesis of materials.

摘要

Self Propagating High Temperature Synthesis is a method for using combustion waves to produce a wide variety of advanced materials. While there are a number of variants of this process depending on the nature of the reactants and the intermediate or final products, we concentrate on mathematical modeling for the situation of initially solid reactants. Typically the powdered reactants are mixed and pressed into a sample which is ignited at one point, after which a combustion wave passes through the sample, converting reactants to products. In applications, a one dimensional, uniformly propagating (1dUP) wave structure is usually desired this it leads to the most uniform products, but there are many other more complicated propagation modes depending on the system. We examine the effects of melting on the structure and stability of combustion waves in a number of situations. We show that high temperature melting of an inert diluent can lead to a change in the thermal structure of the combustion wave to include a plateau at the melting temperature and can stabilize the 1dUP structure, in contrast to the case of reactant melting, which is generally destabilizing and does not lead to thermal plateaus. We numerically study combustion waves with reactant melting and investigate the influence of the melting temperature on the propagation of combustion waves and the transition to chaos as a bifurcation parameter is varied. We demonstrate that inert melting can be used to counteract the destabilization of 1dUP waves due to reactant melting. We analyze in detail the effects of flow of a melted reactant on the structure and linear stability of 1dUP waves. We consider the effect of realistic chemical kinetics on liquid flames, in which extensive melting destroys the mechanical integrity of the medium and gravity driven separation can lead to nonuniqueness in the structure of the 1dUP combustion wave. Analytical techniques used in determining combustion wave structure and linear stability include matched asymptotic expansions for large activation energy and numerical techniques include adaptive Chebychev pseudo-spectral methods.