This work considers the process of dust pollution of the air at an industrial site when using a protective perforated screen. The removal of dust from contaminated land surfaces in areas where there are coal storage facilities leads to intensive air pollution in working areas. This poses a threat to the health of workers. Therefore, for practice, an important solution is to reduce the level of dust pollution of the air at industrial sites. A likely engineering solution to such a task is to use protective screens, in particular, protective screens with perforations. These screens reduce the speed of the oncoming wind flow, which, in turn, reduces the intensity of dust formation. The location of the screens at an industrial site is important. A laboratory experiment was conducted to determine the patterns of air flow velocity distribution behind a protective screen with perforations. The experimental data showed that the screen makes it possible to reduce the wind flow velocity by 5–6 times over an extension of the order of 2H from the screen (H is the height of the screen). The air flow velocity increases intensively behind the screen in the area 2H–4H. These results make it possible to determine the rational location of the screen relative to the dust formation area. For theoretical assessment of the effectiveness of these screens, a numerical model was built based on the fundamental equations of continuum mechanics. The modeling equations include the dust mass transfer equation and the potential motion equation. Using the constructed numerical model, a computational experiment was conducted, which confirmed the effectiveness of using perforated protective screens: the area of dust air pollution in height decreased almost 3 times. The cost of computer time for conducting a computational experiment is 2 seconds. This makes it possible, when carrying out design work, to perform a series of calculations in a short period of time

Abstract The paper considers a technological solution for delivering lunar regolith to subsurface infrastructure facilities. Taking into account existing concepts for lunar exploration and analyzing gravitational methods of vertical transportation, the use of a serpentine channel integrated around a vertical shaft is proposed. This scheme allows combining the functions of regolith transportation with the use of mine space for moving people, cargo, or spacecraft. A mathematical description of the movement of a layer of regolith along a spiral trajectory under the action of its own weight is constructed, taking into account the forces of friction against the supporting surface and the side wall of the channel. It has been shown that the movement process includes a transitional and a steady phase of motion. The derived analytical dependencies make it possible to determine the throughput capacity of the channel and select its geometric parameters in accordance with the productivity of screw conveyors.

Abstract In the paper, based on the concept of destruction of a solid material due to the formation of a compaction core, a mathematical model of the ice destruction process by the chipping method is proposed. This model makes it possible to determine the ice consumption and the torque on the drill shaft depending on the dimensionless drill radius and the dimensionless force with which the cutter moves parallel to the face surface. The model takes into account the drill rotational speed, the number of radial rows of cutters and the number of cutters in each row, the drill radius, and the strength characteristics of ice. By supplementing the model of the destruction process with a mathematical model of loose material transportation using a screw conveyor, a mathematical model of a technological complex for ice extraction and transportation under lunar conditions was obtained. For conditions in which an induction electric motor with a squirrel-cage rotor is used, based on the limitation of its power by the thermal conditions in the stator windings, constraints on the values of the dimensionless drill radius and the dimensionless force with which the cutter moves parallel to the face surface were obtained.

This study investigates the sequential and continuous formation of thermal fields in the main fairing of a launch vehicle when using protective screens. While thermostating, it is necessary to predict the risk in overheating the payload body and, if necessary, take measures to reduce the temperature near the payload. An engineering solution to this problem can be found through the use of protective screens of various configurations inside the main fairing. These screens reduce the heat flow from the heated outer wall of the fairing to the payload surface. However, there are no standard methods for solving this problem. To evaluate the effectiveness of this protection, a numerical model based on the fundamental equations of continuum mechanics has been constructed. The modeling equations include the energy equation and the equation of motion of a non-viscous gas. Using the numerical model built, a computational experiment was conducted, which confirmed the effectiveness of using protective screens to shield the payload body from excessive heating. The computer time required to perform the computational experiment is 3 seconds. This makes it possible to perform a significant number of calculations in a working day. The proposed simple technical means for protecting the payload from excessive heating could be used in the design of new models for rocket technology. Applying these screens slightly reduces the need for large volumes of clean air. The numerical model built could be used at specialized organizations at the “for-sketch” design stage. Numerical experiments have shown that the use of protective screens inside the main fairing makes it possible to achieve a temperature 2–4°C lower than the maximum permissible temperature near the payload

Problem statement. The efficiency of biological water purification depends significantly on the concentration of dissolved oxygen in the volume of the bioreactor. But during the operation of bioreactors, the oxygen regime changes, so it is important to predict the oxygen concentration for different modes of operation of treatment plants. Simplified mathematical models are used to calculate the oxygen regime, but these models are designed for typical bioreactors. An important task is the development of effective multivariate numerical models for evaluating the oxygen regime in reactors of different geometric shapes, which differ from “classical” reactors. The purpose of the article. Development of a CFD model for operational evaluation of the oxygen regime in bioreactors. Methodology. For mathematical modeling of the oxygen regime in the bioreactor, a two-dimensional mass transfer equation is used, which takes into account the place of oxygen supply from the aerator located in the building, the hydrodynamics of the flow in the bioreactor, and the diffusion process. The potential motion model was used to solve the hydrodynamic problem. Numerical integration of modeling equations is carried out by using finite-difference splitting schemes. At each splitting step, the difference equations are solved using explicit schemes. This allows a simple computer implementation of the numerical model. Scientific novelty. A multifactor two-dimensional CFD model was developed, which allows for a quick assessment of the oxygen regime in a bioreactor used for wastewater treatment. Practical significance. The developed CFD model and computer code can be used at the stage of designing or re-engineering bioreactors in order to find the optimal location of aerators in the structure. Conclusions. The software implementation of the developed numerical model was carried out. The results of a computational experiment on the study of the wastewater treatment process in a sedimentation tank are presented.

Purpose. The problem of accidental contamination of workspaces attracts special attention, since in the event of such extreme situations, intense chemical contamination of the air in work areas occurs. This poses a threat of toxic exposure to workers. When assessing the consequences of such situations, it is necessary to take into account the time factor, in particular, to quickly determine the creation of concentrations of chemically hazardous substances. In this regard, an urgent task is to develop effective mathematical models for rapid assessment of the consequences of extreme situations in the working areas of chemically hazardous facilities. The paper considers a CFD model for analyzing the process of chemical air pollution in a workspace during an accidental release of a chemically hazardous substance. The solution of the problem is based on the numerical integration of the fundamental equations of continuum mechanics. Methodology. To calculate the air velocity field in the working room during the operation of supply and exhaust ventilation, a mathematical model of the motion of an inviscid fluid was used. The equation of convective diffusion motion was used to calculate the concentration of a chemically hazardous substance in the workspace. The integration of the modeling equations was carried out using finite difference schemes. Findings. A dynamic model has been created to calculate the spread of a chemically hazardous substance in a workspace. On the basis of the built CFD model, a computer program was created to conduct a computational experiment. Originality. A CFD model has been created to predict the level of air pollution in a workspace in the event of toxic gas emissions. The model is based on the fundamental equations of aerodynamic mechanics and mass transfer. The model makes it possible to determine the effect of the ventilation mode, the intensity of emission of a chemically hazardous substance, the location of equipment in the workspace, and the dynamics of the formation of concentration fields. Practical value. The developed CFD model can be used to quickly analyze the consequences of accidental emissions of a chemically hazardous substance in a workplace and assess the risk of toxic exposure of workers.

Purpose. Today, aeration tanks are widely used to treat industrial and municipal wastewater. Assessing the efficiency of water treatment in aeration tanks under different operating conditions is an important task. To solve this problem, it is necessary to have mathematical models that allow to quickly obtain data on the effect of treatment in aeration tanks. The main objective of this work is to develop a numerical box model to determine the efficiency of wastewater treatment in an aeration tank. Methodology. For mathematical modeling of the biological wastewater treatment process in a bioreactor, zero-dimensional material balance equations are used, which are written in relation to the concentration of substrate, activated sludge, and dissolved oxygen in wastewater. The Monod model is used to calculate the substrate oxidation process. The Euler method is used to integrate the modeling equations. A simplified model of biological water treatment in a bioreactor is considered, which makes it possible to obtain an analytical solution to the problem. The obtained analytical expression makes it possible to quickly determine the change in the concentration of dissolved oxygen in wastewater depending on the change in the concentration of activated sludge in the bioreactor. The constructed numerical model makes it possible to determine the dynamics of changes in the concentration of contaminants, activated sludge and oxygen in wastewater during their stay in the bioreactor. Findings. A tool for theoretical evaluation of the efficiency of biological wastewater treatment in an aeration tank is proposed. A numerical model has been built that allows determining the concentration of dissolved oxygen, substrate and activated sludge at the outlet of the aeration tank. Originality. An effective numerical model has been developed that allows to quickly calculate the dynamics of wastewater treatment in a bioreactor and, based on this information, to evaluate the efficiency of the reactor. Practical value. The constructed mathematical model can be useful in the reconstruction of biological wastewater treatment facilities, as well as at the design stage of bioreactors to take into account their operation under different operating conditions. A computer program has been developed that implements the constructed numerical model. The results of a computer experiment are presented.

Problem statement. Industrial sites where coal storages are located are intensive sources of dust pollution of the environment. There is an important problem of assessing the intensity of dust removal into the atmospheric air from polluted areas. Knowledge of the intensity of dust removal into the atmospheric air makes it possible to scientifically assess the impact of contaminated sites on the pollution of the environment and work zones at industrial sites. The solution to this problem can be obtained experimentally. The purpose of the article. An experimental study of the value of the air flow velocity at which the detachment of dust particles from the surface with coal begins and their removal into the air and the determination of the intensity of the emission of coal dust from the contaminated surface. Methodology. The intensity of removal of coal dust from the contaminated area was studied experimentally in laboratory conditions. The research was conducted on coal samples from DTEK “Pavlohradvuhillya”, grade “ДГ. During the research, the velocity of the air flow at which the process of movement of dust particles along the emission source began and the velocity of “detachment” of dust particles and their removal from the emission source were determined. At the second stage of experimental research, the intensity of removal of coal dust from the polluted area was determined. Scientific novelty. The values of the air velocity at which the removal of coal dust particles from the contaminated area begins were determined experimentally. The regularity of the intensity of the removal of coal dust depending on the velocity of the air flow over the contaminated area was obtained. Practical significance. The obtained experimental data make it possible to determine under which weather conditions there is a risk of dust formation and the removal of dust into the atmosphere. The empirical dependence obtained by processing experimental data can be used for a scientifically based assessment of the level of pollution of working areas at industrial sites where there are coal storage facilities. Conclusions. The value of the velocity of the air flow at which the movement of dust particles on the contaminated surface begins, as well as the value of the velocity of the air flow at which the removal of dust particles into the air begins, was determined experimentally. The resulting empirical model can be used to estimate environmental damage due to dust pollution of atmospheric air.

Purpose. The method of mathematical modeling is an important tool for solving complex problems involving the analysis of groundwater dynamics and heat and mass transfer processes in them when studying their contamination from various anthropogenic sources in the event of accidental spills of chemically hazardous substances, etc. The main purpose of the article is to develop a set of mathematical models for calculating the process of filtration of non-pressure groundwater, mass transfer of impurities and the process of heat transfer in groundwater. Methodology. The two-dimensional Boussinesq equation of filtration was used to predict the dynamics of groundwater. The two-dimensional equation of convective-diffusive transport of impurities was used to model the processes of mass transfer in groundwater. The process of freezing of individual sections of the groundwater flow is modeled using the Laplace equation for the velocity potential (calculation of the flow velocity field in a time-varying geometry) and the two-dimensional equation of heat transfer in groundwater. Finite difference schemes were used to solve the modeling equations of groundwater dynamics and heat and mass transfer. Findings. A set of mathematical models has been developed to calculate the process of filtration of non-pressure groundwater and its chemical contamination. The experiment has confirmed the adequacy of the constructed numerical model of filtration of a non-pressure groundwater flow. An effective mathematical model was developed that allows determining the temperature fields in groundwater during the operation of a well used to freeze certain sections of the flow. The results of computer modeling indicate the effectiveness of the developed mathematical models. Originality. Effective mathematical models for predicting the level of chemical contamination of groundwater, its dynamics and thermal regime are proposed. The constructed mathematical models make it possible to determine the dynamics of changes in the temperature regime of groundwater during the operation of wells through which refrigerant is supplied to freeze individual areas. A computer program has been developed that allows for a comprehensive assessment of groundwater conditions. Practical value. A set of computer programs has been developed to conduct a computational experiment to study the processes of filtration, chemical contamination of groundwater and heat transfer processes in them. This set of programs can be used for the scientific substantiation of engineering solutions aimed at protecting groundwater.

Мета. Сьогодні аеротенки широко використовують для очищення стічних вод підприємств та комунальних стоків. Оцінювання ефективності очищення води в аеротенках за різних режимів експлуатації є важливою задачею. Для розв’язання такої задачі потрібно мати математичні моделі, що дозволяють оперативно отримати дані щодо ефекту очищення в аеротенках. Основною метою роботи є розробка чисельної box-моделі для визначення ефективності очищення стічних вод в аеротенку. Методика. Для математичного моделювання процесу біологічного очищення стічних вод у біореакторі використовують нульвимірні рівняння матеріального балансу, що записані відносно концентрації субстрату, активного мулу та розчиненого кисню в стічних водах. Для розрахунку процесу окислення субстрату використано модель Monod. Для інтегрування моделювальних рівнянь використовують метод Ейлера. Розглянуто спрощену модель біологічного очищення води в біореакторі, що дає можливість отримати аналітичне розв’язання задачі. Отриманий аналітичний вираз дає можливість швидко визначити зміну концентрації розчиненого кисню в стічних водах залежно від зміни концентрації активного мулу в біореакторі. Побудована чисельна модель дає можливість визначати динаміку зміни концентрації забруднень, активного мулу та кисню в стічних водах за час перебування їх у біореакторі. Результати. Запропоновано інструмент теоретичної оцінки ефективності біологічного очищення стічних вод в аеротенку. Побудовано чисельну модель, що дає можливість визначити концентрацію розчиненого кисню, субстрату та активного мулу на виході з аеротенка. Наукова новизна. Розроблено ефективну чисельна модель, що дозволяє швидко розраховувати динаміку очищення стічних вод у біореакторі та на базі цієї інформації оцінювати ефективність роботи реактора. Практична значимість. Побудована математична модель може бути корисна під час реконструкції споруд біологічного очищення стічних вод, а також на етапі проєктування біореакторів для врахування їх роботи за різних умов експлуатації. Розроблено комп’ютерну програму, що реалізує побудовану чисельну модель. Наведено результати комп’ютерного експерименту.

A 2D numerical model has been developed to estimate the airflow velocity field when flowing around the dam of an artificial storage facility for mineral processing waste. To solve the aerodynamic problem of determining the air flow velocity field when flowing around such hydraulic structures with a complex geometric shape, a potential motion model was applied. The numerical integration of the equation for the velocity potential is carried out using the Liebman method. The geometric shape of the tailings storage facility is formed in a discrete model using the marking method. A computer program was created to implement the developed numerical aerodynamics model. Based on the processing of the results of computational experiments, coefficients were obtained that allow us to quickly determine the value of the air flow velocity at the beginning and end of the tailing pond beach, i.e. in the area of the most intense dust emission. This allows for a quick prediction of the risk of dust air pollution at different tailing pile heights.

Purpose. It is known that acid rain has a negative impact on the environment. The formation of acid precipitation in the atmosphere occurs as a result of the chemical interaction of fuel combustion products and atmospheric humidity. Acid rain leads to crop losses, deterioration of soil fertility, and acidification of water in reservoirs. The development of scientifically based methods for studying the intensity of such acidic pollution of the air and soil surface in regions with significant emissions from thermal power plants remains an urgent problem. To solve this problem, it is important to use mathematical modeling, since it is impossible to determine the impact of emissions from thermal power plants on the formation of acid rain experimentally. Therefore, the main goal of the work is to create a mathematical model for predicting the formation of acid rain in the event of emissions from thermal power plants. Methodology. To predict the process of acid rain formation, a three-dimensional equation of convective diffusion transport of a pollutant is used, which takes into account the wind speed profile, atmospheric stratification, emission intensity of an impurity, and wind direction. This equation is also used to describe the process of water vapor transport in atmospheric air. To describe the process of acid formation in atmospheric air, a stoichiometric relationship is used. The numerical integration of the modeling equation of transfer was carried out using the splitting method. Findings. A multifactorial numerical model was built that allows determining the zones where acid rain is formed. The problem of predicting the formation of acid rain in the case of emissions from thermal power plants on the basis of the constructed numerical model is considered. Originality. A numerical model is proposed to predict the occurrence of acid rain due to emissions from thermal power plants. The model is multifactorial and takes into account convection, atmospheric diffusion, and an uneven wind profile. A computer code has been created that allows for rapid assessment of acid pollution zones. Practical value. The developed computer code for analyzing the zones of acidic pollution of the environment in the case of industrial emissions makes it possible to predict the intensity of such pollution in various meteorological conditions.

The paper presents data on the current state of waste storage facilities of mining and processing plants in Kryvyi Rih. They are complex, environmentally hazardous hydraulic structures. When assessing the extent of dust pollution from tailing ponds, it is extremely important to know the intensity of dust emissions from the surface of the alluvium beach. This parameter is the basic one in all prognostic models used to predict environmental pollution. The paper presents the results of experimental studies to determine the wind speed at which the removal of dry dust particles from the surface of the beach of a tailing pond begins, as well as the intensity of dust removal from the surface of the beach for dry sand and wet sand. The experimental studies conducted in the laboratory allowed obtaining data on the intensity of dust emission from the surface of the tailing dump beach. The results obtained by the authors make it possible to more accurately assess the degree of environmental dustiness using predictive models..he data on determining the intensity of dust formation for sand of different moisture content will be useful for determining the effectiveness of dust suppression by supplying water to the beach surface.

Problem statement. The development and practical use of a numerical model for the analysis of the process of air pollution in the workplace during an emergency leak of a toxic substance is considered. The purpose of the article. Creation of numerical models of aerodynamics and mass transfer of the non-stationary process of the spread of a toxic substance in the workplace. Methodology. Modeling of the spread of a toxic substance during the operation of emergency ventilation is carried out on the basis of the Laplace equation for the velocity potential and the mass transfer equation, which takes into account the convective and diffusive transport of the toxic substance. Numerical integration of the modeling equations of the mechanics of a solid medium is carried out using finite-difference schemes using the labeling method. Scientific novelty. A numerical model was created for forecasting the level of air pollution in the working room due to the emission of toxic gas. The model is based on the numerical integration of the fundamental equations of solid medium mechanics. A feature of the numerical model is the consideration of the main physical factors that affect the spread of toxic gas in the room (the presence of equipment in the room, the position of the ventilation holes, the cities of emission of the toxic substance, etc.) and the speed of calculation. Practical significance. The developed numerical model can be used for the scientific substantiation of emergency ventilation parameters for workplaces where the emission of toxic substances is possible. Conclusions. A dynamic multifactorial numerical model was developed to analyze and forecast the process of chemical contamination of the workplace. A feature of the numerical model is the possibility to take into account the main physical factors affecting the formation of pollution areas in the workplace. The developed numerical model can be used for scientific substantiation of emergency ventilation parameters for rapid reduction of the concentration of toxic (or explosive) substance in the working room.

The report considers some classes of numerical models that were built to predict the consequences of emergencies at industrial enterprises. The first class of models has been developed to predict chemical air pollution in case of accidental emissions of toxic substances. Modeling is carried out on the basis of the fundamental equations of aerodynamics and mass transfer. Difference splitting schemes are used for the numerical solution of the modeling equations. The second class of CFD models is designed to assess the risk of thermal damage to people in the event of thermal pollution of the air environment. The third class of models was developed to assess the risk of injury to people when a shock wave moves. To solve this problem Euler equations were used. Computer codes were developed on the base of proposed numerical models.

Problem statement. The task of assessing the risk of damage to an oil storage facility by debris in the event of a drone explosion is considered. An analysis of the debris movement velocity and the effectiveness of the use of a protective barrier to stop the debris movement in the direction of the oil storage facility is carried out. The purpose of the article. Assessment of the risk of damage to the oil storage wall and the effectiveness of the use of a protective barrier against the throwing action of debris during a drone explosion. Methodology. A numerical model based on the integration of the equation of a material point motion and an empirical model is used to analyze the risk of damage to an oil storage facility when the debris of a drone flies off. The developed numerical model takes into account the initial velocity and size of the debris, the direction of the debris movement, and the height of the debris ejection. On the basis of this numerical model, a computer code was created for conducting a computational experiment. Scientific novelty. An effective mathematical model is developed for analyzing the risk of damage to an oil storage facility from the throwing action of debris generated by a drone explosion. The model makes it possible to determine the effectiveness of using an obstacle to protect an oil storage facility from the throwing action of debris. Practical value. A computer code is developed for calculating the dynamics of the debris movement in the air, which are formed during the explosion of a drone. The use of this code makes it possible to select the rational dimensions of the protective barrier at the industrial site to protect the oil storage from damage. Conclusions. An effective tool for analyzing the risk of damage to an oil storage facility from the throwing action of debris created by a drone explosion is developed. The results of computational experiments are presented.

Purpose. Infiltration of contaminated water and accidental spills of chemically hazardous substances into groundwater lead to the formation of large zones of man-made pollution in aquifers. Therefore, it is important to develop protection systems against groundwater pollution. To analyze the effectiveness of such protection systems at the design stage, it is necessary to have scientifically based information on the dynamics of changes in groundwater contamination zones. Such information can be obtained using the method of mathematical modeling. The study aims to create a numerical model for calculating the non-stationary process of geomigration when using chemical protection of groundwater from pollution. Methodology. To describe the dynamics of groundwater flows, two filtration equations are considered, which allow mathematical modeling of the filtration process both for solving planned problems and for solving problems of specialized filtration. A two-dimensional geomigration equation was used to analyze changes in groundwater quality. This equation takes into account the convective transfer of impurities in the filtration flow, dispersion, and the intensity of impurity infiltration into the groundwater flow. This equation is also used to calculate the movement of the neutralizer in groundwater. The numerical integration of the filtration equation was performed using finite difference methods. An implicit splitting scheme was used to numerically integrate the geomigration equation. Findings. A fast-applicable numerical model for calculating groundwater dynamics has been built. The model is also a platform for solving another important task – the calculation of geomigration processes. A numerical model for calculating the unsteady-state geomigration process is proposed, which makes it possible to assess not only the process of formation of contamination zones in the groundwater flow, but also to determine the effectiveness of the method of neutralizing the impurities in the groundwater flow. Originality. Effective numerical models for rapid assessment of changes in groundwater dynamics and quality under the influence of anthropogenic sources have been developed. These models take into account a set of important physical factors that affect the process of geomigration and the process of neutralizing the impurity in the groundwater flow. Practical value. A computer program has been developed that allows determining the effectiveness of the process of neutralizing an aggressive impurity in groundwater by a computational experiment to protect it from anthropogenic pollution.

Problem statement. The design of wastewater treatment systems is a complex process and requires the use of special mathematical models. As a rule, empirical models are used at the stage of designing structures of water drainage systems, which allow obtaining only an “integral” characteristic of the efficiency of wastewater treatment. But in a number of cases, it is important to have information about the spatial distribution of the impurity concentration in the structure. To solve this problem, you need to have three-dimensional mathematical models. In the future, there is a shortage of such models, so the creation of three-dimensional multifactorial models for the analysis of the efficiency of drainage system structures is an urgent task. The purpose of the article. Development of a three-dimensional numerical model for the analysis of the mass transfer process to determine the impurity concentration in the clarifier. Methodology. The analysis of impurity concentration fields in the clarifier is carried out by numerical integration of the three-dimensional equation for the velocity potential and the three-dimensional equation of the convective-diffusion transport of the impurity. For the numerical integration of the Laplace equation for the velocity potential, the variable-triangular method and the Liebmann method are used. Finite-difference splitting schemes are used for numerical integration of the three-dimensional equation of convective-diffusion transport of impurities. Scientific novelty. A dynamic multifactorial numerical model was created for the analysis of the process of mass transfer of impurities in a settling tank by conducting a computational experiment. Practical value. The built multifactorial numerical model makes it possible to analyze the efficiency of wastewater treatment in clarifiers that have a complex geometric shape and cannot be calculated on the basis of existing engineering methods. Conclusions. On the basis of the developed three-dimensional numerical model, a computer code was created, which allows you to quickly obtain information about the distribution of the impurity concentration in the settling tank.