Analytical assessment of hetero-/homogeneous combustion of magnesium particle: Fully explicit formulas for flame characteristics

In this study, by proposing a comprehensive multi-step model, the combustion of magnesium particles in O2-He, O2-Ar, and O2-N2 is scrutinized. In the current model, both the heterogeneous and homogeneous combustions are considered and the process is divided into four stages solid, liquid, and gas combustion and melting. Moreover, the diffusions of oxygen and unreacted magnesium to droplet and infinity together with surface exothermic reaction are considered. The governing equations are analytically solved and then, the formulas are extracted for combustion time and temperature, flame standoff distance, and evaporation rate as the functions of particle diameter, ambient temperature and pressure, oxygen mass fraction, type of inert gas, and Lewis numbers. For 120 µm particle and oxygen content of 0.05, time contributions of homogeneous and heterogeneous combustions are 85.8% and 14.2%, respectively. The burning time has drastic changes at ambient pressures below l atm, so that the burning time variations relative to the pressure in the environments less than 1 atm and greater than it are equal to 1200–1550 and 70–90 ms/atm, respectively. When the oxygen mass fraction is less than 0.29, combustion in helium-oxygen ends earlier than that in O2-Ar and O2-N2, but for the mass fraction greater than 0.35, it has the longest burning time.