An asymptotic analysis for detailed mathematical modeling of counter-flow non-premixed multi-zone laminar flames fueled by lycopodium particles

This study aims to present a basic mathematical model for investigating the structure of counter-flow non-premixed laminar flames propagating through uniformly-distributed organic fuel particles considering preheat, drying, vaporization, reaction and oxidizer zones. Lycopodium particles and air are taken as biofuel and oxidizer, respectively. Dimensionalized and non-dimensionalized forms of mass and energy conservation equations are derived for each zone taking into account proper boundary and jump conditions. Subsequently, to solve the governing equations, an asymptotic method is used. For validation purpose, results achieved from the present analysis are compared with reliable data reported in the literature under certain conditions. With regard to the comparisons, although different complex non-homogeneous differential equations are solved in this paper, acceptable agreements are observed. Finally, the impacts of significant parameters including fuel and oxidizer Lewis numbers, equivalence ratio, mass particle concentration, fuel and oxidizer mass fractions and lycopodium initial temperature on the flame temperature, flame front position and flow strain rate are elaborately explained. An asymptotic method for mathematical modeling of counter-flow non-premixed multi-zone laminar flames propagating through lycopodium particles.