# A Mathematical Model of Industrial Waste-Derived Fuel Droplet Combustion in High-Temperature Air
## 2 Materials and Methods  
### Background of the Model Condition  
The ability of CLS to reliably ignite and burn out completely in a preheated gaseous medium has been established by us experimentally [23]. The identified mechanism and recorded characteristics of the process set the stage for the development of the mathematical model and numerical simulation of single fuel droplet combustion in Ansys Fluent. The main component of the CLF was filter cake (FC) of coking coal C from the Severnaya coal plant (Kuzbass, Russian Federation) [23]. FC is a waste from the coal industry, obtained in the process of coal enrichment. FC has an energy potential due to the content of at least 50% fine (about 100 \(\upmu\)m) coal in the composition (the rest is water) [25; 26; 27]. However, so far, FC is not widely used in any industries, so the main method of its disposal is uncontrolled storage on open sites near the washing plant. This method of coal waste disposal is characterized by many negative consequences, primarily environmental. Moisture evaporation increases the fire hazard of coal dust, allows it to be dispersed by the wind over large areas, polluting the air, open water bodies and soils. Moreover, coal dust contains acidifying agents, high-density metals and other hazardous elements. These become a source of integrated pollution for the environment, when exposed to a severe impact of natural factors (such as air, moisture or solar energy). Besides FC, combustible MSW can also be a CLF component [23; 28]. MSW typically consists [5; 29; 30] of 26-35% organic remains (including former foodstuff); 25-30% (of the total waste volume) mixed paper wastage; 7-10% postconsumer plastics; 5-12% scrap metal and cullet; 2-4% textile wastes, 2-4% wood residue, and 2-4% all-rubber scraps. Based on statistical data, MSW consists of about 82% potentially energy-producing materials (paper, wood, textile, polymer waste). Adding the combustible components of MSW to composite fuel is a promising solution to the problem of commercial disposal of accumulated and newly produced waste. However, the relatively low energy content of combustible MSW (10 MJ/kg [31; 32; 33] versus 20-30 MJ/kg [34] of solid fossil fuels) and a fairly high concentration of hazardous compounds (including carcinogens) limit the amount that can be added to a CLF composition to 10-20% [23]. The main properties, characteristics and ultimate analysis of CLF are presented in Tables 1 and 2[28]. To obtain the characteristics and properties of the CLF components, the samples were preliminarily dried at a temperature of about 378 K to evaporate unbound moisture. In the experimental research [23], MSW characteristics from reference materials were used to analyze the effect of CLF component properties on the patterns of physical and chemical processes with different mechanisms of heat supply [31; 35; 36]. MSW composition and characteristics may vary considerably in different regions (by methods of waste collection and treatment, as well as storage conditions) [5]. To predict the characteristics of CLF droplet ignition and combustion reliably, it is necessary to use the real properties of solid particles and liquids included in the fuel mixture (primarily thermophysical and kinetic characteristics of phase transitions and chemical transformations). An undoubted advantage of modeling is that the component composition fuel suspension, droplet sizes, heat transfer mechanisms and characteristics of heat supply from the external source can be varied in wide ranges. Thus, it is possible to efficiently assess the potential of using promising fuel compositions in practice.