Ignition mechanisms in condensed systems using an incandescent surface for a parabolic interaction law

Using the ignition wave theory, the dependence of the ignition process stage periods for a condensed material and an incandescent surface, when a parabolic interaction law applies to the initial reagents, on the basic problem parameters – the dimensionless temperature gradient and the transformation depth in the intermediate combustion wave – has been determined for the first time. It is shown that the equation for a stage period can be represented in the form of a product of two functions: one being dependent on the temperature gradient, and the other – on the transformation depth. The dependence of the characteristic times on the transformation depth for a constant temperature gradient is found to be linear in nature. It is established that for a parabolic interaction law, there exists no limiting transition to the ignition mechanism that is characteristic of zero order reactions. The following critical conditions are formulated: an ignition does occur if a reaction zone is formed which is capable of spreading through the material in the combustion regime. Specialized numerical computations have confirmed the correctness of the assumptions of the stagelike character of the ignition process and of the wavelike nature of the heating of the material, on which the theory was based, and also validated the basic conclusions drawn from the approximate analysis.