A residence time-based concept for modeling and analyzing the impact of diffusion on auto-ignition processes with thermal stratification

A meticulous definition of the residence time (also referred to as the fluid age) in the context of auto-ignition in a thermally stratified gas has demonstrated that the age can be considered as a level-set function, which allows the tracking of a self-ignition front propagating. In order to avoid the difficulty of defining the boundary and initial conditions for this age, which can be seen as fluid birth, a normalized age is introduced. Meticulous derivation of the equation revealed additional terms related to the scalar dissipation rates and the gradient in the composition space of the auto-ignition delay. To validate this model equation, two canonical configurations were proposed: one representing a hot spot self-igniting with significant thermal diffusion and the other where a self-ignition front propagates at an almost constant speed. The analysis, based on the normalized age of the particles, reveals the impact of thermal diffusion on the acceleration or deceleration of particle aging. In certain instances, a particle rejuvenation mechanism through thermal diffusion has been identified. Furthermore, this work demonstrates the capacity of the normalized residence time field to map transitions between auto-ignition and laminar flame. Finally, the different cases studied were classified in an auto-ignition/diffusion diagram based on three non-dimensional characteristic numbers, which highlighted five combustion regimes.