Mathematical Modeling of Coal Dust Screening by Means of Sieve Analysis and Coal Dust Combustion Based on New Methods of Piece-Linear Function Approximation

This study focuses on the development of new methodological approaches to dust-preparation and burning of separated particles, including through the use of polyfractional ensembles. Coal dust screening by means of sieve analysis is described in standard methods. However, in order to further use the results obtained during mathematical modeling of particle motion in fuel-air mixture and exothermal reactions of oxidation while burning in a torch, it must be possible to differentiate and integrate continuous functions. The methodology is based on the continuity of particle motion in a mixture with air in the calculation of aerodynamic and heat-mass exchange processes in a torch. The paper employs new scientific approaches to transforming and normalizing a continuously differentiable function described by the Gauss curve. We propose to combine mathematical modeling of such functions with methods of approximation of piece-linear functions developed by Professor S. V. Aliukov. The implementation of such methods helps reduce calculation errors of particle size and deviations thereof from average equivalent diameter and to avoid the Gibbs effect while differentiating. The paper contains analytical calculations based on the proposed method and experimental data. Quantitative and qualitative results of comparing analytical and experimental data are also presented. We provide recommendations on the further use and extension of the range of the results obtained in a computer simulation of fuel production and burning processes in a torch.