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

Mehdi Bidabadi (Department of Mechanical Engineering, School of Engineering, Iran University of Science and Technology, Narmak, Tehran)
Sadegh Sadeghi (Department of Mechanical Engineering, School of Engineering, Iran University of Science and Technology, Narmak, Tehran)
Pedram Panahifar (Department of Mechanical Engineering, School of Engineering, Iran University of Science and Technology, Narmak, Tehran)
Davood Toghraie (Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran)
Alireza Rahbari (School of Engineering and Computer Sciences, Australian National University, Canberra, Australia)

ISSN: 0961-5539

Article publication date: 25 July 2019

Issue publication date: 16 April 2020

## Abstract

### Purpose

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.

### Design/methodology/approach

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.

### Findings

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.

### Originality/value

An asymptotic method for mathematical modeling of counter-flow non-premixed multi-zone laminar flames propagating through lycopodium particles.

## Citation

Bidabadi, M., Sadeghi, S., Panahifar, P., Toghraie, D. and Rahbari, A. (2020), "An asymptotic analysis for detailed mathematical modeling of counter-flow non-premixed multi-zone laminar flames fueled by lycopodium particles", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 4, pp. 2137-2168. https://doi.org/10.1108/HFF-11-2018-0617

## Publisher

:

Emerald Publishing Limited