# A Mathematical Model of Industrial Waste-Derived Fuel Droplet Combustion in High-Temperature Air
## 3 Results and Discussion
This pattern is generally confirmed by the experimental research [23]: the higher the temperature, the less influence the heat exchange in the vicinity of the fuel droplet has on the ignition-delay time. Figure 9: Time dependences of maximum temperature of CLF droplets No. 5 (FC 90% + cardboard 10%) under radiant heating (\(V_{g}\approx 0\)): (**a**) simulation results at different heating temperatures; (**b**) simulation results vs. experimental data [41] at \(T_{g}=1273\) K.  
Thus, for better reliability in the prediction of the CLF ignition characteristics with numerical simulation, the data for the volatile component fraction/combustible fraction ratio of the combustible need to be determined precisely as source values, whereas the devolatilization constant and reaction heat fractions absorbed by the solid of the combustible particle do not require high accuracy and can be taken from reference materials. Using the developed mathematical model, the temperature trends of the CLF droplet were obtained during heating, ignition and combustion (Figure 9a) at different temperatures of the heating source (723 K, 973 K and 1273 K). It has been established that the moment at which the maximum temperature is reached shifts to the left with an increase in the temperature of the heating source, which is mainly due to the faster occurrence of a set of physicochemical reactions. The dynamics of the change in the temperature of CLF droplets is of great practical importance, in particular, for the analysis of the energy characteristics of the fuel combustion process. [10, 11]. In Figure 9b theoretical and experimental temperature trends are compared. It should be noted that there is a satisfactory qualitative agreement between theory and experiment. At the same time, the quantitative differences are significant and reach more than 20-25%, which is mainly due to the assumptions made in the basic mathematical model. Firstly, constant values of evaporation and devolatilization rates were used in the numerical study. Obviously, under real conditions, the rates of evaporation and devolatilization are not constant, but depend on temperature and change during heating. Second, the model did not take into account the non-uniformity of the temperature distribution inside the CLF droplet and its vicinity, which is the root cause of the change in the rates of physicochemical transformations. Thirdly, the developed model makes it possible to obtain the temperature values directly inside the droplet. The experimental data curve illustrates the temperature in the vicinity of the CLF drop, where the gas mixture burns out, which is formed during the evaporation of the liquid combustible component of the fuel (if present) and during the thermal decomposition of solid components (FC and MSW) [41]. Figure 10 presents the curves of the ignition-delay times vs. oxidizer temperature for CLF with different component compositions. The curves of the ignition-delay times vs. oxidizer temperature are nonlinear. This is conditioned by the fact that, with an increase in temperature, the rates of the thermolysis of organic fuel components, water vaporization, combustion of ignitable gases, and heterogeneous firing of solid remainder change exponentially. This dependence of the ignition-delay times on the ambient temperature was also recorded in the experimental research [23]. Figure 10: _Cont_. It should be noted that the numerical simulation of the processes under study was carried out for somewhat idealized fuel compositions without impurities, which, obviously, is not carried out in practice. We believe that the main differences in the results are due both to the heat losses not taken into account in the model, which are typical during the experiment, and to the occurrence of additional chemical reactions with impurities contained in the real fuel. Impurities can be caused by the content of flotation reagents in coal processing waste (oil refinery products and petrochemical waste).