Flame structure in initially unmixed reactants under one-step kinetics

Abstract

The burning of initially unmixed reactants at Lewis—Semenov number unity for a direct one-step reversible reaction of arbitrary order is examined under Arrhenius kinetics. The study concentrates on the stagnation region formed by the blowing of a hot stream of oxidant at an adiabatically vaporising planar wall of pure nongaseous fuel. Asymptotic expansion are developed to describe the chemical behavior for limiting values of the first Damkohler number. i.e. for nearly frozen and nearly equilibrium flow. Because of the nonlinearities owing to the law of mass action, numerical integration is required for intermediate values of the Damkohler number (moderate rates of reaction). Two specific results are sought. First, the relative thickness of the flame zone and departure of maximum temperature from adiabatic flame temperature in the near-equilibrium limit are furnished, with emphasis on variance with the order of the reaction. Further, the asymptotic methods are continued to higher order to indicate the first effects owing to convection in the reaction region. Second the additional insight asymptotic methods give into previously noted possibilities of nonuniqueness of solution to the steady-state combustion problem is developed.