Analytical model for the non-premixed combustion of titanium dust cloud in counter-flow geometry

Today,the study of combustion of metal particles is considered due to applications such as particle oxide production, high energy density and thus increasing the temperature resulting from combustion, medical applications,etc.In this study,the analytical model of titanium dust cloud combustion in counter-flow geometry with a multi-zone approach is examined and presented.Fuel flows on the one hand and oxidizing currents on the other flowed as counter-flow,and in order to analytical modeling,three distinct areas were considered.The equations governing,including the mass fractional survival of the components and the survival of the energy, were expressed and,using appropriate boundary and adaptive conditions,the solution of the equations in each zone was presented using Matlab and Mathematica softwares.Then the temperature distribution and mass fraction of fuel, oxidizer and fuel products in the liquid phase were plotted according to location and the effect of some variables such as Lewis number,particle diameter and mass particle concentration on the flame was investigated. It was observed that with increasing Lewis fuel number from 0.6 to 1.4 at 300 g/m3, the flame temperature decreased from 3600 Kelvin to 3050 Kelvin and also the flame location was transferred to the oxidizer nozzle and the reason for this was the reduction of mass penetration. Also with increasing particle diameter of fuel from 2μm to 200μm, temperature of the flame was shifted from 3600 K to 3400 K.