Abstract
A one-dimensional mathematical model of the formation of a fluidized bed and the evolution of its thermal state during the heating of an ensemble of particles is proposed based on the mathematical apparatus of the Markov chain theory. When describing the thermal state of the system, the processes of interfacial heat exchange between the gas flow and particles, as well as between the wall of the apparatus and the gas suspension, were taken into account. The results of previous studies and known empirical regularities for the material constants of the process were used to identify the parameters of the model. The parametric identification made it possible to adapt and apply the mathematical model for calculating the process of heat treatment of the suspension of silicate sand particles in an apparatus with a fluidized bed of a periodic principle of operation equipped with a heating jacket. Verification of the predictive capabilities of the physicomathematical model adapted in this way was carried out by comparing the forecasts obtained by calculation with the results of the full-scale experiment conducted during the study. To conduct the full-scale experiment, a sample of sand particles was placed in the apparatus, which was previously output to the established thermal regime of operation. After loading the material, a set of thermocouples equidistant from each other was placed in the apparatus and temperature readings were taken at different heights from the level of the gas distributor. The temperature distributions obtained in this way along the bed height were in good agreement with the calculated forecasts and show a significant heterogeneity of the gas phase temperature fields. The temperature of the particles was estimated only as an integral characteristic by measurements of the heat content of the bulk medium after unloading from the apparatus. The integral temperature of the particles also turned out to be close to the predicted values. In addition, during the computational and experimental study, the kinetic characteristics of the heating of the suspension of the material were clarified. Thus, the proposed mathematical model has sufficient predictive efficiency for engineering tasks and can be considered as a basis for constructing a computer method for calculating heat exchangers with a heating jacket using the fluidization technique of bulk media.
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