Effects of Weak Electric Fields on Laminar Diffusion Flames Using a High-Order Compact Finite-Difference Scheme

Accurately capturing the interaction between fluid motion, chemical reactions, and electric fields is essential for understanding flame behavior in advanced combustion systems relevant to propulsion, energy conversion, and emissions control. In this work, we present a two-dimensional computational framework in cylindrical coordinates for simulating laminar non-premixed flames with electrostatic coupling representative of weakly ionized plasma-assisted combustion environments. The solver employs a high-order compact finite difference scheme for spatial discretization, enabling improved resolution of steep gradients commonly observed in reacting flows, together with a fourth-order temporal integration method to ensure numerical stability and accuracy. Detailed combustion chemistry is incorporated through a steady flamelet formulation, providing an efficient yet robust description of chemical kinetics within the CFD framework. To account for electric field-assisted effects in a simplified and physically consistent manner, the governing equations are extended to include Poisson’s equation for the electric potential and transport equations for one positively and one negatively charged species, assuming a weakly ionized regime in which neutral species dominate the flow dynamics. Electric field effects are modeled by solving species continuity equations for one positively charged and one negatively charged species, coupled with Poisson’s equation for the electric potential to obtain a self-consistent electric field. The resulting electrostatic and plasma-induced effects enter the governing equations through explicit source terms in the momentum and energy equations, accounting for electric body forces and Joule heating for weakly ionized plasma. A systematic parametric study is conducted using a canonical co-flow methane–air diffusion flame to examine the influence of flow conditions and combustor geometry. The results show that plasma forcing leads to a noticeable increase in flame length, as identified by extended OH and CH radical distributions. This behavior is attributed to a combination of electric-field-driven charged species drift, enhanced convective transport, and localized Joule heating, which collectively modify scalar transport and delay radical recombination along the axial direction. Overall, the proposed high-order framework provides a validated and computationally efficient tool for high-resolution simulation of chemically reacting flows with weak plasma coupling, offering new insight into the role of electric fields in laminar non-premixed flame dynamics.