MATHEMATICAL MODELS APPLICATION TO PREDICT HEAT AND CHEMICAL AIR POLLUTION IN WORKING AREARS

Abstract

Problem statement. The problem of prediction the level of air pollution in working areas is considered on the basis of mathematical models of aerodynamics and heat and mass transfer. The task is to calculate the concentration field of chemically hazardous substances and the temperature field in the working zones. The purpose of the article. Construction of numerical models that allow determine the distribution of temperature and concentration of chemically hazardous substances in work areas with a complex geometric shape. Methodology. For numerical modeling of the process of air pollution in working areas during the spread of chemically hazardous substances, G. Marchuk's equation is used, which takes into account the transfer of a chemically hazardous substance due to convection, as well as due to turbulent diffusion. The energy equation is used to model the thermal contamination of work areas. To simulate the wind speed field in the presence of various kinds of obstacles, the Laplace equation for the speed potential is used. The integration of the modeling equations is carried out on a rectangular grid. For the numerical integration of the equation describing the propagation of a chemically hazardous substance in the air of working areas, a finite-difference splitting scheme is used. For the numerical integration of the Laplace equation for the velocity potential, two splitting schemes are used. The unknown value of the velocity potential at each splitting step is calculated using an explicit formula. Numerical integration of the energy equation is carried out using an explicit difference scheme. Scientific novelty. The constructed numerical models that allow to calculate the zones of chemical and thermal pollution, taking into account a set of important physical factors. A feature of numerical models is the speed of calculation, which is important when serial calculations are carrying out in practice. Practical significance. A complex of applied programs was created on the basis of the developed numerical models. This complex of programs allows to analyze and predict the intensity and size of zones of thermal or chemical pollution. This set of programs can be useful in determining the affected areas in case of extreme situations at chemically hazardous facilities. Conclusions. Numerical models have been developed. On the basis of these models a complex of applied programs has been created that allow to study multiparameter processes of chemical and thermal air pollution of working areas using the method of computer modeling. The complex of programs can be implemented on computers of low and medium power. The results of a computational experiment are presented.