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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.

The purpose of this study is to describe the combustion of a magnesium particle falling into a hot oxidizer medium.

The governing equations, including mass, momentum and energy conservation equations, are numerically solved. Afterward, the influences of effective parameters on the temperature distribution and burning time are investigated. Artificial neural network (ANN) is applied to approximate the particle temperature as a function of time, diameter and porosity factor. To obtain the best arrangement of the ANN structure, an optimization process is conducted.

The results show that by considering variations of the particle size, the maximum temperature increases compared to the case in which the particle diameter is constant. Also, the ignition and burning times and the maximum temperature of the moving particle are lower than those of the motionless particle. Optimum network has the best values of regression coefficient and mean relative error whose values are found to be 0.99991 and 1.58 per cent, respectively.

In this study, particle size varies over the combustion process that leads to calculation of particle burning time. In addition, the effects of the motion and porosity of the particle are examined.

The widespread usage of magnetic nanoparticles (MNPs) requires their efficient synthesis during combustion process. This study aims to present a mathematical model for the oxidation of MNPs in a counter-flow non-premixed combustion system to produce MNPs, where the key sub-processes during the oxidation reaction are involved.

To accurately describe structure of flame and determine distributions of temperature and mass fractions of both reactants and products, equations of energy and mass conservations were solved based on the prevailing assumptions that three regions, i.e. preheating, reaction and oxidizer zones exist.

The numerical simulation was first validated against experimental data and characteristics of the combustion process are discussed. Eventually, the influences of crucial parameters such as reactant Lewis numbers, strain rate ratio, particle size, inert gas and thermophoretic force on structure of flame and combustion behavior were examined. The results show that maximum flame temperature can achieve 2,205 K. Replacing nitrogen with argon and helium as carrier gases can increase flame temperature by about 27% and 34%, respectively. Additionally, maximum absolute thermophoretic force was found at approximately 9.6 × 10–8 N.

To the best of authors’ knowledge, this is the first time to numerically model the preparation of MNPs in a counter-flow non-premixed combustion configuration, which can guide large-scale experimental work in a more effective way.