Mathematical Modeling of a Non-premixed Organic Dust Flame in a Counterflow Configuration

Abstract

In the present article, an analytical approach is employed to study the counterflow non-premixed dust flame structure in air. Lycopodium is assumed to be the organic fuel in this paper. First, it is presumed that the fuel particles vaporize in a thin zone to form a gaseous fuel to react with the oxidizer. The reaction rate is presumed to be of the Arrhenius type in first order, with respect to the oxidizer and fuel. Mass conservation equations of dust particles, oxidizer, gaseous fuel and the energy conservation equation for non-unity Lewis numbers of the oxidizer and fuel are presented as the governing equations. Boundary conditions are applied for each zone for the purpose of solving the governing equations analytically. The flame temperature, in terms of the Lewis numbers for the oxidizer and fuel, is calculated. Furthermore, the variation of flame position based on the Lewis numbers of the fuel and oxidizer is evaluated. Also, mass fraction and temperature profiles of oxidizer and fuel are presented. In addition, the variation in the ratio of critical extinction values of strain rates, as a function of the non-unity Lewis numbers of the oxidizer and fuel to their unity Lewis numbers, is investigated.