A Mathematical Analysis for Spark Ignition for Premixed Flame Based on Extended Perfectly Stirred Reactor (PSR) Model

This study improves the traditional Perfectly Stirred Reactor (PSR) model by incorporating an additional energy source to more accurately represent the spark ignition process in a laminar premixed flame within a counterflow configuration. A non-dimensional system of governing ordinary differential equations (ODEs) is formulated to describe the behavior of temperature and fuel concentration under these conditions. A mathematical analysis is conducted to assess the stability of steady-state solutions in the dynamic system, utilizing the large activation energy asymptotic limit as a primary analytical tool. Analytical solutions for stable regimes, characterized by negative eigenvalues, are derived and it is found that the equilibrium steady states exhibit two stable regimes: one corresponding to failed ignition and the other to successful ignition.