Mathematical Modeling of Wastewater Vibrational Filtering Process

Background/Objectives: The article describes the development of the tools to design wastewater vibrational filtering process based on mathematical modeling of the motion of contaminating particles. Methods/Statistical Analysis: A method of reducing contamination of the filtered surface through forced vibration is considered. To build a mathematical model, we consider the mode of motion of particles without contact with each other. In this case, hydrodynamic resistance forces effect on the particle determined by the difference of water flow velocity at the location of the particle and own velocity of the particle. Findings: The proposed mathematical model is based on representation of solid contaminations of the liquid being treated as a set of spherical particles of different diameters, which allows taking into account the basic properties of interaction of particles with the liquid and contact interaction between the particles and between a particle and the filter screen. Dimensionless performance evaluation criteria of vibrational filtering are proposed, as well as dimensionless parameters to evaluate the properties of the filtering surface with respect to the particle diameter. Applications/Improvements: As a result of mathematical modeling, nonlinear dependence of the average frequency of passage of particles through the filter surface on vibration parameters and on dimensionless parameters of the filter is established. The range of parameters of the filtering element is found ensuring maximum efficiency of the filtering process.