# A Mathematical Model of Industrial Waste-Derived Fuel Droplet Combustion in High-Temperature Air
## 5 Conclusions  
Based on results of previous experimental studies, a mathematical model was developed for the ignition and combustion of a single composite liquid fuel droplet (a mixture of coal processing waste in a wet state with combustible municipal solid waste). The model considers the interdependent sequence of the main chemical transformations and physical interactions of the suspended CLF droplet with the surrounding air environment (passive warming, near-surface water vaporization, thermolysis of coal and municipal waste (solid combustible components), blending of ignitable gases with the oxidizing medium, gas blend firing and burnout, and heating of the solid remainder followed by its heterogeneous ignition and combustion with an ash residue formation) as a result of combined radiant and convective heat transfer, the heating source temperature for which was varied within the ranges of 723-1273 K and 723-973 K, respectively. The numerical simulation of combustion characteristics was carried out in the Ansys Fluent commercial software for five different CLF compositions. Comparison of the ignition-delay times for single droplets obtained by numerical simulation with experimental data showed their good  
Figure 12: Ignition-delay times vs. heating source temperature for CLF composition No. 5 (FC 90% + cardboard 10%) at: (**a**) \(V_{g}=0\); (**b**) \(V_{g}=3\) m/s.  
agreement for mathematical model configuration, considering the temperature gradient inside the fuel droplet and in its vicinity. The results of numerical simulation of a CLF droplet in a heated air flow differ from the experimental data by no more than 19%, both under conditions of radiant heating and convective heating, which does not exceed the confidence limit for the obtained experimental data. The developed mathematical model of the ignition and combustion process of a single CLF droplet makes it possible to predict the main characteristics with good reliability. The mathematical model is most sensitive to changes in the ratio of volatile/combustible fractions of the combusting particle, therefore, an urgent task in the improvement of the correspondence of numerical simulation results with experimental data is to compile an information base with reliable experimental values of such constants for different CLF compositions. It can also be noted that the predictive mechanism developed in Ansys Fluent can significantly reduce the time and material costs of subsequent research.  
Conceptualization, D.G.; data curation, A.R.; formal analysis, D.A.; funding acquisition, D.G.; investigation, K.P.; methodology, D.A.; project administration, K.P.; writing--original draft, K.P.; writing--review and editing, D.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Russian Foundation for Basic Research, National Council of Brazil for Scientific and Technological Development and Ministry of Science & Technology (Government of India) grant number [19-53-80019].  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.