Planar, cylindrical, and spherical flame propagation in closed vessels with nonuniform composition and temperature

The hydrodynamic theory of flame propagation in closed vessels is extended here to configurations involving nonuniform initial distributions of temperature and composition, admitting arbitrary steady-planar-deflagration chemical kinetics not considered in previous publications. The analysis addresses planar, cylindrical, and spherical configurations in the high-Péclet-number limit in which a thin premixed flame separates fresh-mixture and burnt-gas regions that are free from diffusive transport in the first asymptotic approximation. The simplified approach reduces the problem to solving a system of ordinary differential equations in time for the Euler-equation descriptions of the hydrodynamics in the fresh and burnt gases, along with the motion of the deflagration separating them. Planar hydrogen-air flames with a detailed chemical-kinetic description are selected to illustrate the simplified computational procedure and to expose the influences of the nonuniform initial distributions admitted by the new general formulation. The good accuracy of the simplified approach is supported by favorable agreement with a full numerical integration of the problem as originally formulated, prior to imposition of the asymptotic simplifications. The new method may facilitate future investigations of stratified-charge and unexpected-accident scenarios. Novelty and significance statement This work presents a reduced-order formulation of the evolution of flames in closed vessels, taking into account nonuniform initial distributions of temperature and reactant concentrations for the first time. It is significant in that it facilitates investigations of flame propagation under conditions that may arise in many real-world situations.