High-Speed Reaction Zone Structure for Variable Mole Chemistry

Abstract

The structure of a high-speed deflagration downstream of a specific origin is investigated theoretically for the exothermic irreversible Arrhenius-type reaction $F + Ox \to \nu P$. Perturbation methods, and, in particular, a nonlinear transformation used in thermal explosion theory, are used to find fully analytical solutions for the spatial structure of the high-speed reaction zone when the activation energy is large. In the rapid reaction region beyond the induction zone, there is a strong interaction between large chemical heat release and flow compressibility. When the chemical reaction causes a mole reduction $( \nu < 2 )$ and there is sufficiently large heat release, the flow velocity reaches a maximum and then declines while the temperature increases monotonically throughout the process. Significantly, it is shown that the flow cannot evolve to the Chapman-Jouguet (C.J.) state where the final local Mach number is unity and the reactant concentration is zero. When the mole number of the evolving flo...