# A Mathematical Model of Industrial Waste-Derived Fuel Droplet Combustion in High-Temperature Air
## 3 Results and Discussion  
In the numerical simulation, some constants from the source data were not known precisely, thus their values were assumed, on the basis of empirical data, to match the numerical simulation results with the experiment. To establish the main process characteristic (ignition-delay time) as a function of a group of source data, the rates of volatile release from the solid part of the fuel mixture, reaction heat fractions absorbed by the solid and the volatile component fraction/combustible fraction ratios were varied in allowable ranges in Ansys Fluent. Moreover, temperature trends at different heating source temperatures were obtained. The results are presented in Figures 6-9. Figure 5: Establishing ignition-delay times by the CLF droplet temperature evolution as illustrated by composition No. 5 (FC 90% + cardboard 10%) at \(T_{g}=973\) K, \(V_{g}=0\). Figure 8: Relative ignition-delay times of CLF vs. volatile component fraction/combustible fraction ratio of the combustible particle at different temperatures of the radiant heating source. Figure 6: Relative ignition-delay times of CLF No. 4 (FC 90% + plastic 10%) vs. devolatilization constant of the combustible particle at different temperatures of the radiant heating source. Figure 7: Relative ignition-delay times of CLF No. 4 (FC 90% + plastic 10%) vs. reaction heat fraction absorbed by the solid of the combustible particle at different temperatures of the radiant heating source. As seen in Figure 6, changing the devolatilization constant of the combusting particle has a significant impact on the ignition-delay time only when it is varied between 0 and 5 s\({}^{-1}\). The ignition-delay time in this condition is an interval from the calculation initiation until the moment the droplet reaches the ignition temperature. Thus, it includes the gas-phase ignition time and the time the solid residue is heated until the ignition temperature (heterogeneous ignition):  
\[t_{d}=t_{gf}(DC)+t_{hg}(T_{g}) \tag{29}\]  
where \(t_{gf}\)--gas-phase ignition-delay time of the CLF (depending on the devolatilization rate), \(s\); and \(t_{hg}\)--heterogeneous ignition-delay time of the CLF (depending on the ambient air temperature), s.  
Thus, the rate of devolatilization affects primarily the fuel gas-phase ignition time (at a constant devolatilization rate, the gas-phase ignition time is constant). Due to the low content of volatiles in the fuel, the time of the gas-phase ignition of the fuel is much shorter compared to the time of heterogeneous ignition. Despite this fact, the influence of this parameter becomes more considerable with an increase in the surrounding oxidizer temperature. The reason for that is that a higher temperature reduces the heterogeneous ignition-delay time, thus increasing the significance of the gas-phase ignition delay which is constant at a constant devolatilization rate. As the CLF droplet interacts with the heated air, exothermic and endothermic chemical reactions evolve on the surface. Some of the heat they release is absorbed by the fuel solid residue. The higher this value, the faster the solid residue is heated and the lower the ignition-delay time. With the growing ambient temperature, the effect of the absorbed energy from the chemical interaction on the ignition considerably weakens, since the bulk of the energy will come from the radiant and convective heat exchange with the ambient air (Figure 7). The curves of the CLF ignition-delay times vs. the volatile component fraction/combustible fraction ratio of the combusting particle (Figure 8) are close to linear. The total ignition-delay time diminishes as the combustible fraction decreases. This is because the lower the combustible fraction in the fuel composition, the lower the heterogeneous ignition time which makes up most of the total ignition time of CLF. Moreover, the effect of this ratio is significantly reduced by an increase in the surrounding oxidizer temperature.