Bulletin of TUIT: Management and Communication Technologies Volume 4 2021-ikkinchi son Article 2 3-12-2021 Numerical Study Process Distribution of Contaminated Substances in the Atmosphere Taking Into Account the Physical and Mechanical Properties of Particles Normahmad Ravshanov prof. Scientific and innovation center of information and communication technologies at the Tashkent university of information technologies named after Muhammad al-Kharizmi, [email protected] Tursun Shafiev Bukhara State University, [email protected] Follow this and additional works at: https://uzjournals.edu.uz/tuitmct Part of the Physical Sciences and Mathematics Commons Recommended Citation Ravshanov, Normahmad prof. and Shafiev, Tursun (2021) "Numerical Study Process Distribution of Contaminated Substances in the Atmosphere Taking Into Account the Physical and Mechanical Properties of Particles," Bulletin of TUIT: Management and Communication Technologies: Vol. 4 , Article 2. Available at: https://uzjournals.edu.uz/tuitmct/vol4/iss2/2 This Article is brought to you for free and open access by 2030 Uzbekistan Research Online. It has been accepted for inclusion in Bulletin of TUIT: Management and Communication Technologies by an authorized editor of 2030 Uzbekistan Research Online. For more information, please contact [email protected]. 10 “Bulletin of TUIT: Management and Communication Technologies” Numerical Study Process Distribution of Contaminated Substances in the Atmosphere Taking Into Account the Physical and Mechanical Properties of Particles Normakhmad Ravshanov1, Tursun Shafiev2, Gulsina Ataeva2, Lola Yadgarova2 1Tashkent University of Information Technology, Uzbekistan, [email protected] 2Bukhara State University, Uzbekistan, [email protected] one of the effective tools for a comprehensive study of the ABSTRACT above problem. The article deals with the numerical modeling of the processes In recent years, scientists have developed mathematical tools of transfer and diffusion of air pollutants in the boundary layer to research, predict and monitor the ecological state in of the atmosphere. A mathematical model of the spread of industrial regions, based on a mathematical model, a industrial emissions in the atmosphere was developed, taking numerical algorithm and software for conducting experiments into account the motion velocity of finely dispersed on a computer; significant theoretical and applied results on substances and a number of other factors affecting the change the above problem were obtained. in the concentration of harmful substances in the atmosphere. The model is described by multidimensional partial In particular, a mathematical model and software for a system differential equations with corresponding initial and boundary of assessing atmospheric air pollution emissions from motor conditions. For the numerical integration of the problem, the vehicles were developed in [1]. The mathematical model method of splitting into physical processes (of transfer, developed takes into account the traffic intensity, which diffusion and absorption) and an implicit finite-difference differs on the streets of the city at a given time of the day, at a scheme of the second order of approximation in spatial given day of the week, at a given month, considering also the variables and in time were used. A software tool was basic characteristics of vehicles, features of traffic lines and developed to conduct a computational experiment on a computer and to perform a comprehensive study of the traffic modulation by traffic lights at street intersections. processes of transfer and diffusion of harmful substances in the atmosphere. A lot of scientific research was done to assess and predict the ecological state of the environment using mathematical Key words : mathematical model, transfer and diffusion of models, computational algorithms, and software systems. For harmful substances, numerical algorithm example, in [2], topical problems related to solving the problems of salt transfer in soil were considered. The article is 1. INTRODUCTION devoted to the numerical modeling of the processes of salt transfer and diffusion in soils. To study and predict the spread The modern economies of countries are increasingly of harmful substances, a mathematical model and a numerical depleting the power and wealth of nature to accelerate algorithm for conducting a computer experiment were scientific and technological progress. Often these processes developed. bring negative results. Plants and factories are being built at a fast pace, being the main factor of the environmental problem The Aral Sea problem is very critical for the population of of anthropogenic origin. The anthropogenic sources cause Uzbekistan and the territories bordering it. In [3], [4], studies irreparable damage to nature, and the polluted atmosphere of this aspect were conducted to analyze the ecological presents a critical threat to it. Therefore, forecasting, situation in the Aral Sea region of Uzbekistan. The main share monitoring, and assessing the ecological state of the of emissions of harmful substances in the Aral Sea region is atmosphere, design and placement of industrial facilities in dust, salts, and toxic chemicals carried away from the compliance with sanitary standards is a priority in the problem dried-up bottom of the Aral Sea. Thus, in mathematical of environmental protection. modeling of the process of atmospheric scattering, it is necessary to take into account physical and mechanical The study of statistic data on ecology shows that the properties of particles and the principal forces acting on them. deterioration of the ecology in the atmosphere of industrial zones occurs due to an increase in the concentration of In [5], a conjugate mathematical model of the optimal harmful substances and atmospheric gas pollution. It follows placement of industrial facilities was investigated. To develop that the relevance of mathematical modeling of the an adequate mathematical model of the processes of transfer propagation of harmful aerosol particles is obvious and it is and diffusion of harmful substances in the atmosphere, the Normakhmad Ravshanov, Tursun Shafiev, Gulsina Ataeva, Lola Yadgarova 2021, 2 (46) 11 “Bulletin of TUIT: Management and Communication Technologies” authors of the article studied the following factors: soil where U= u2 + v 2 + w 2 . erosion, which, under unstable stratification of the air mass, Here t is time; x,, y z are the coordinates; θ is the substantially changes the concentration of harmful substances in the atmosphere; mass flow rate of atmospheric air in three concentration of the spreading substance; is the coefficient directions in time; change in the diffusion coefficient and the of absorption of harmful substances in the atmosphere; µ is vertical turbulent mixing coefficient at stable and unstable the diffusion coefficient; is the turbulence coefficient; is atmospheric stratification; changes in wind direction over 0 the Dirac function; Q is the power of sources; is the time and due to the orography of the area; change in the interaction coefficient, which depends on the characteristics primary concentration of harmful substances in the of the underlying surface. atmosphere; m is the mass of the particle; c f is the coefficient of drag of particles; r is the radius of the particle; is the The analysis of scientific publications related to the problem a of mathematical modeling of the propagation and diffusion air density; p is the particle density; g is the acceleration of processes of aerosol particles in the atmosphere showed that free fall; k f is the body shape coefficient for the drag force; in mathematical modeling and research of the above is the air viscosity; F is the lifting force of the air flow; processes, changes in the velocities of particles in the a п atmosphere, which change with time and depending on is the coefficient of interaction with the underlying surface; physical and mechanical properties of the substance under F is the number of aerosol particles detached from the consideration were not studied. 0 ground roughness; is the coefficient to reduce the boundary 2. PROBLEM STATEMENT condition to the dimensional form; e is the concentration of suspended solids in neighboring areas of the problem being Considering the above, to study the process of transfer and solved. diffusion of aerosol particles in the atmosphere, taking into account essential parameters u ,,vw that are the p pp 3. SOLUTION METHOD components of the particle velocity in x,, y z directions, Since the problem formulated in (1) - (8) is described by a respectively, we address a mathematical model described on multidimensional nonlinear partial differential equation with the basis of the law of hydromechanics using a corresponding initial and boundary conditions, it is difficult to multidimensional partial differential equation [6], [7]: find its exact solution in an analytical form. +up + v p + w p + = t x y z (1) From the statement of the problem and equation (1), it is clear 22 that they describe three physical processes - the transfer of a =22 + + + Q; xyzz substance in the motion direction of the atmospheric air mass, du mp =− c r22(); u U (2) molecular diffusion of a substance in the atmosphere, and dt f a p absorption of harmful substances in the atmosphere. dv mp =− c r22(); v U (3) dt f a p Considering the above, the method of splitting into physical dw 4 processes at each time level was used in