A mathematical approach to spark ignition process in premixed flame systems: modeling and analysis.

Abstract

This study enhances the classic perfectly stirred reactor model by introducing an additional energy source to effectively model the spark ignition process within a laminar premixed flame in a counterflow configuration. A non-dimensional governing ordinary differential equation (ODE) system is developed to describe the behavior of both temperature and fuel concentration under these conditions. An in-depth mathematical analysis is performed to find out the stability of steady-state solutions within the dynamic system, using the large activation energy asymptotic limit as a key analytical approach. Solutions corresponding to stable regimes are derived analytically, which is characterized by negative eigenvalues. This analytical framework is further extended through the direct integration of the non-dimensional ODE system, allowing an investigation on how critical parameters – including the Damköhler number, spark duration time, and the heat released during chemical reactions – affect the ignition process. Particular attention is given to the calculation of the minimum ignition energy , providing valuable insights into optimizing ignition strategies in practical applications.

Felipe C. Minuzzi

Assistant Professor of Mathematics

My research interests include computational fluid dynamics, ocean waves and neural networks, both theoretically and applied to real world problems.