Mathematical Modeling of Non-Premixed Laminar Flow Flames Fed with Biofuel in Counter-Flow Arrangement Considering Porosity and Thermophoresis Effects: An Asymptotic Approach

Abstract

Due to the safe operation and stability of non-premixed combustion, it can widely be utilized in different engineering power and medical systems. The current paper suggests a mathematical asymptotic technique to describe non-premixed laminar flow flames formed in organic particles in a counter-flow configuration. In this investigation, fuel and oxidizer enter the combustor from opposite sides separately and multiple zones including preheating, vaporization, flame and post-flame zones were considered. Micro-sized lycopodium particles and air were respectively applied as a biofuel and an oxidizer. Dimensionalized and non-dimensionalized mass and energy conservation equations were determined for the zones and solved by Mathematica and Matlab software by applying proper boundary and jump conditions. Since lycopodium particles have numerous spores, the porosity of the particles was involved in the equations. Further, significant parameters such as lycopodium vaporization rate and thermophoretic force corresponding to the lycopodium particles in the solid phase were examined. The temperature distribution, flame sheet position, fuel and oxidizer mass fractions, equivalence ratio and flow strain rate were evaluated for the counter-flow non-premixed flames. Ultimately, the thermophoretic force caused by the temperature gradient at different positions was computed for several values of porosity, fuel and oxidizer Lewis numbers.