Mathematical study of threshold of thermal-diffusive instability in counter-flow non-premixed biomass-fueled flames considering effective parameters

Abstract

Identifying the thermal-diffusive instability boundaries of flames is of great significance in the field of combustion. In this paper, a detailed mathematical analysis is performed to detect the threshold of thermal-diffusive instability in planar counter-flow non-premixed flames using an asymptotic concept. Uniformly-scattered micron-sized lycopodium particles and air are applied as organic fuel and oxidizer, respectively. In order to suggest a basic combustion structure, preheat, vaporization, flame and oxidizer zones are considered. In the first phase of this investigation, time-dependent forms of mass and energy conservation equations are derived considering appropriate boundary and jump conditions. In each of the considered zones, governing equations are solved by Matlab and Mathematica software using perturbation method. To predict the onset of instability, critical values of frequency of the wrinkled flame front, Zeldovich and Lewis numbers are calculated. Eventually, the effects of wave number on the critical Zeldovich and Lewis number are explained. For validation purposes, results of this analysis obtained for critical flow strain rate (corresponding to extinction of the counter-flow non-premixed flame) are compared to those reported in prior studies. Based on the comparisons, proper compatibility is observed between the mathematical results of current study and the data reported in the literature.