BACKGROUND OF A MATHEMATICAL MODEL DEVELOPMENT OF PUMPKIN SEEDS MOTION IN A VIBRATION DRYER

Abstract

Pumpkin seeds have special physical, mechanical and thermophysical characteristics, which significantly complicate the process of their post-harvest processing. It is because of the adhesion of seeds to the working bodies, the formation of conglomerates and other features of pumpkin seeds, it is recommended to use dryers with vibration activation of the material layer. This process is a complex system with a large number of elements (and, accordingly, a large number of connections between them), external influences on the system, etc. For a successful solution to the task of developing a mathematical model, it is necessary to conduct a critical analysis of existing models in order, taking into account the research carried out, to develop their own model describing the process of behavior of material particles (pumpkin seeds) within the vibrating chamber. An analysis of the latest publications on this issue shows that in most cases the issues of processing a certain material in specific technological conditions were solved. In this study, an attempt is made to generalize the previous experience for the development of our own mathematical model of the process of vibration drying of pumpkin seeds. Several types of models of the movement of a granular medium under the action of vibration over the surface of the working bodies were considered. Models of a single particle with added mass were considered, including, taking into account aerodynamic drag, elastic-visco-plastic models of a layer of a granular medium, a model that considers a granular material as a system divided by horizontal planes into an infinite number of elementary layers with the possibility of movement of such layers relative to each other and some others. Of all the considered models of the grain (seed) layer, the most promising in our opinion is the model of the behavior of a granular medium under the influence of vibration, which is represented as a viscous medium, taking into account the initial shear stress. On the basis of this model, it is possible to simulate all states of a granular medium under the influence of vibration: calmness, regular and unstable motions, studied experimentally, as well as to use the equation of dynamics of motion of a continuous medium, the equation of continuity and the equation of the relationship between stresses and deformations for a viscoplastic medium, which means the use of a well-developed mathematical apparatus of fluid dynamics, which is of great importance for obtaining practical results.