Mathematical models in water supply and water discharge problems

Abstract

Purpose. The purpose of the work is to develop numerical models for calculating the hydrodynamics of flow and mass transfer in a sand trap, which has additional structural elements. Methodology. To solve this problem, a hydrodynamic model of the vortex flows of an ideal fluid was used. To model the propagation of an impurity in a sand trap, the two-dimensional equation of convective-diffusion dispersion of an impurity in a treatment plant is used. This equation allows you to take into account the main physical factors that affect the dispersion of an impurity in a sand trap, namely: the field of the flow rate of wastewater, diffusion transport of an impurity, and the settling of an impurity under the influence of gravity. For numerical integration of modeling equations finite difference schemes are used. To calculate the vorticity transfer equation, a two-step difference splitting scheme is used. For the numerical integration of the equation for the stream function, a multi-step splitting scheme is used. The calculation of the current function at each step of the splitting is carried out according to an explicit scheme. To numerically integrate the equation describing the dispersion of an impurity in a sand trap, an implicit difference-splitting scheme is used. The impurity concentration in the sand trap is also calculated on the basis of an explicit formula. The results. A computational experiment based on the developed numerical models is carried out. A computational experiment was conducted to evaluate the effectiveness of wastewater treatment in a sand trap containing a number of additional structural elements. The presented results of numerical modeling show that the developed numerical models make it possible to calculate the flow hydrodynamics and dispersion of impurities in sewage treatment plants having a complex geometric shape. Scientific novelty. Effective numerical models are presented that make it possible to calculate the efficiency of wastewater treatment in sand traps having a complex geometric shape. Practical significance. The constructed numerical models can be used for conducting serial calculations to assess the efficiency of sand traps at the design stage or during the reconstruction of existing treatment facilities.