Mathematical Model Of Process Research Articles

Analysis of heat exchange processes in the "metal — non-stick coating — frozen mold" system

The article is devoted to the analysis of heat exchange processes in the "metal — non-stick coating — frozen mold" system, which is an important aspect of research in the field of materials science and industrial technology, as it affects the quality and efficiency of the final product. The study also paid special attention to the processes of heat exchange between the metal, the non-stick coating and the frozen mold thanks to the analysis of the obtained indicators, calculated and experimental data. In addition, it is necessary to take into account the interaction between the various elements of the system, such as the thermodynamic properties of the coating and the thermal insulation properties of the frozen mold. One of the key aspects of the analysis was taking into account the heat capacity and thermal conductivity of the materials that make up the system, since heat capacity indicates the ability of a material to absorb heat, and thermal conductivity determines its ability to transfer heat. The properties of the non-stick coating, which protects the metal from high temperatures and provides optimal conditions for freezing the mold, are considered, since they can affect heat exchange by reducing or increasing the contact between the metal and the frozen mold. Based on the obtained data, a nomogram was constructed to determine the minimum thickness of the frozen rod depending on the thickness of the casting wall and the cooling temperature of the mold. The developed mathematical model of the heat transfer process in the system is based on the method of cellular automata. The model adequately describes the real process and can be used for numerical studies. The results of the work provide an opportunity to help improve production technology and improve the quality of the final product thanks to the analysis of heat exchange processes in the "metal — non-stick coating — frozen mold" system.

ТЕОРЕТИЧНИЙ АНАЛІЗ ОПТИМІЗАЦІЇ УПРАВЛІННЯ БІЗНЕС-ПРОЦЕСАМИ ПІДПРИЄМСТВА В ПАРАДИГМІ ПРОЦЕСНОГО ПІДХОДУ

The article explores the vital subject of optimizing business process management, which is essential for enhancing the efficiency and competitiveness of enterprises. The study evaluates various perspectives, including economic, engineering, and managerial aspects, and underscores the importance of mathematical models over descriptive models in achieving precise and effective optimization. Descriptive models, despite their widespread use, do not guarantee optimal outcomes. The article emphasizes the need for mathematical models to accurately optimize business processes, considering various criteria and constraints. This approach aims to address the limitations of current descriptive models and advocates for the development of specific mathematical models to manage business process optimization under uncertainty. Key findings reveal that optimization in business process management has a significant impact on enterprise efficiency, productivity, and competitiveness. The process approach, which concentrates on enhancing individual business processes, is highlighted as a crucial paradigm in modern management. The research calls for further investigations to develop mathematical models that can deliver more reliable and precise optimization results, especially in uncertain conditions. In conclusion, the article supports the transition from descriptive to mathematical models in optimizing business process management to achieve maximum efficiency and competitiveness in enterprises. Future research will focus on developing mathematical optimization models for business processes, particularly those related to new product development under uncertain conditions. This shift is anticipated to offer more accurate and effective solutions for optimizing business processes in a dynamic and unpredictable business environment. Furthermore, the article highlights the need for continuous development and application of mathematical approaches to ensure that business processes are optimized effectively. It stresses the importance of incorporating various optimization criteria and constraints to achieve the best possible outcomes. By transitioning to mathematical models, businesses can better navigate the complexities and uncertainties inherent in today's competitive landscape, leading to improved performance and sustainable growth.

Implementation of a Globally Linearised Controller in Real Time for Two Conical Tanks Interacting Level Process

The aim of this paper focuses on the design and real-time implementation of a Globally Linearized Controller (GLC) for Two Conical Tanks Interacting Level Process (TCTILP) that exhibits severe non-linear characteristics. Because of its adequate mixing and drainage properties, conical tanks are favoured in the industrial sector, yet control issues arising from their non-linear dynamics are considerable. This method's underlying premise is that a system with non-linear original variables can be transformed in some way to make it linear. The globally linearized controller is designed based on a linear model that accurately represents the entire operating range of a non-linear system, allowing for the practical application of linear control methods to achieve desired system performance. The fundamental dynamics and interactions between the two tanks are captured in a mathematical model of the TCTILP process. For various set points of levels h1 and h2, the performance of the GLC is contrasted with that of the traditional PI controller. According to real-time findings, GLC works better with shorter settling times and smaller error indices than conventional controllers. This work enhances process control by offering a workable and effective method for handling intricate non-linear systems. The robustness and versatility of the globally linearized controller make it an invaluable tool for a wide range of industrial applications requiring conical tank processes.

Selection of controlled parameters of the technological process of obtaining CLT panels with increased sound insulation

The problem of creating high-quality sound insulation materials is an important area of development of the construction industry today. Therefore, at the manufacturing stage, it is necessary to observe many different indicators that affect the quality characteristics of building materials. One of the ways to improve the sound insulation characteristics in the construction of capital walls of buildings is the use of multilayer wooden panels consisting of modernized wooden lamella structures. There are various technologies for the production of multilayer wooden panels, most of which have proven themselves well in the construction industry and allow the use of wood of various breeds and varieties, combine them to achieve optimal characteristics, such as high heat capacity, fire resistance, noise insulation, environmental friendliness, biological resistance, almost complete absence of shrinkage. Mathematical modeling of such multifactorial processes makes it possible to determine the optimal strategy for conducting the technological process. By controlling the technological process in this way, taking into account the specified quantitative and qualitative characteristics, it is possible to obtain a CLT panel with the specified sound insulation properties.

Mathematical modeling of the extraction process of oil-containing raw materials

Mathematical modeling of the extraction process of oil-containing raw materials

Mathematical modeling of heliothermal chemical processes during hardening of multicomponent cement materials

The article considers mathematical modeling of solar-thermal-chemical productions during hardening of multicomponent cement materials and products based on them during solar-thermal-moisture processing. The main assumption of the action of exotherm in a solid (structure-forming) building product of a polystructural structure and the share, which can be estimated at significant costs, is shown to assess the degree of efficiency of the heliothermal chemical treatment of multicomponent cement materials and their base.

Patterns of air temperature changes in air ducts of non-contact air heating or cooling systems

The article is devoted to the study of the patterns of changes in air temperature during its movement in a sheet steel air duct during the operation of non-contact air heating systems, when the temperature of the moving air through the duct is higher than the room air temperature, as well as in the process of non-contact air cooling, when the temperature of the moving air in the duct below the room temperature. Based on the mathematical model of the ongoing physical processes developed in the article, an analytical formula is derived that allows, taking into account the presence of a heat-insulating layer or without it, to determine the patterns of changes in the temperature of moving air through the air duct at a given distance, depending on the thickness of the wall of the air duct and the speed of its movement. A dependence is given that determines the value of the heat transfer coefficient of air moving inside the duct to the inner surface of the duct on the speed, which at a constant flow rate is presented as a dependence of heat transfer on the open cross-sectional area of the duct. An analysis was carried out of the change in temperature of the moving volume of air inside the duct as a result of heat exchange with the surrounding air. A comparative calculation of the change in temperature of air moving in a thermally insulated air duct and in an air duct without thermal insulation was performed. The necessity of carrying out a calculation to determine the patterns of changes in the temperature of moving air inside the air duct when designing air heating systems or air conditioning systems is substantiated. It is concluded that it is necessary to conduct a technical and economic analysis on the feasibility of installing thermal insulation of air ducts made of thin sheet steel.

Повышение эффективности глушения скважин на истощенных газоконденсатных месторождениях с сверх аномально низкими пластовыми давлениями

The problem is studied by the example of gas condensate fields at the final stage of development, where production wells have abnormally low reservoir pressures and their killing for repair work is a serious challenge requiring a search for new solutions. The work is motivated by the need to create a method for controlling hydrodynamic processes in a pre-blocked bottom-hole zone of the formation, for carrying out repair work in wells, preventing destruction of the reservoir formation and ensuring the preservation of its fluid-capacitance properties. The possibilities of an integrated approach to killing wells under conditions of extremely low formation pressures are considered, which includes controlling hydrodynamic processes in the “well-reservoir” system, previously blocked in the near-wellbore zone by special process fluids. It has been specified that the use of blocking fluids (with filler) helps to level the injectivity profile and form an insulating screen in the bottomhole zone of the formation, creating the necessary conditions for killing wells in order to carry out repair work in them. To control hydrodynamic processes, a mathematical model of the blocking process in the near-wellbore formation zone is proposed. It has a three-stage scheme that ensures equalization of the injectivity profile under conditions of extremely low formation pressures. The possibilities of using gel-forming blocking fluids with filler to create a temporary screen that prevents the penetration of killing fluid into highly permeable formations from abnormally low formation pressures have been explored. Based on the results of the study, we can conclude that the control of hydrodynamic processes in the near-wellbore zone of the formation at abnormally low formation pressures creates the necessary condition for effective blocking of the productive horizon in gas and gas-condensate wells, and due to the sequential treatment of the formation with a special liquid to level the injectivity profile and gel-forming blocking composition, allows one to kill the well and prevents the working fluid from penetrating into the depths of the formation during work.

Mathematical modeling of food production technological processes in a computer training complex for operator education

A computer training complex (CTC) structure has been designed for training food production operators, comprising interconnected subsystems generating output parameters. This CTC structure enables the configuration and storage of knowledge on specific technological processes, facilitating the customization of exercises by instructors. Individualized exercises are generated for students to perform in a virtual production environment, utilizing computer programs, tablets, smartphones, or simulated production equipment, including VR/AR technologies. During exercises, student actions are automatically recorded, and a quantitative assessment is provided based on standards, forming a comprehensive evaluation. A mathematical model, represented by a Markov transition graph, captures various states of the virtual production environment during simulated processes at the CTC. This model serves as the basis for constructing specific technological process models in the food industry, tailored to CTC hardware, software, and training methodologies. The methodology presented streamlines the development of training courses for CTC exercises, enhancing personnel knowledge and skills in food production. By utilizing these models, methods, and algorithms, CTCs can be tailored for training operators in diverse food production sectors. The approach outlined simplifies course creation, ensuring personnel development at the desired proficiency level through exercise quality assessment algorithms.

MATHEMATICAL MODEL OF OSHTEС MODERNIZATION WHEN SELECTING SWITCH GEAR EQUIPMENT

In this work, engineering calculations and selection of equipment were performed based on the calculation of short circuits during the modernization of the Osh Thermal Power Plant. Two feasible options for the structural diagram of a thermal power plant are considered. To solve the problem, the following was completed: drawing up technically possible options for a structural diagram and reasoned selection of the best suitable one, taking into account reliability; assessment of new structural schemes of thermal power plants using calculations and comparisons based on technical and economic indicators; the values ​​of the supertransient current in places of short circuit, the shock current and its effective values ​​are determined; selection of new equipment based on short circuit current values. As a result, the circuit breaker was tested for thermal and dynamic resistance to short circuit currents; checking the circuit breaker for breaking and closing capacity. Work was carried out to study methods of practical calculation and develop a mathematical model of the electromechanical transient process using the example of calculating short circuits during the modernization of thermal power plants.

Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. II

Modeling of the impurity diffusion process in a layer under the action of a system of random point sources is carried out. Mass sources of different power are uniformly distributed in a certain internal interval, that may also coincide with the entire region of the layer. The statistics of random sources is given. The solution of the initial-boundary value problem is found as the sum of the homogeneous problem solution and the convolution of the Green's function with the system of the random point sources. Averaging of the solution is performed on the internal subinterval and in the entire body region. The formulas for the variance, correlation function of the concentration field and coefficient of correlation are expressed in terms of the second moment of random mass sources. Software modules are developed for simulating the behavior of the averaged concentration, variance and correlation function. Their numerical analysis also is performed. General properties of the considered function are determined depending on the problem parameters.

Analysis of thermal characteristics of building envelope structure for night storage heating

In order to understand the thermal characteristics analysis of nighttime thermal storage heating, the author proposes a study on the thermal characteristics analysis of nighttime thermal storage heating of building envelope structures. In some places, the writer will use an office room as a research object. The main purpose of the experiment is to measure, compare and analyze the surface temperature and heat flow rate of the room sample volume under two conditions: constant power 24 hour heating and night constant thermal power (12 hours) heating. In order to verify the accuracy of the dynamic thermal process of the heating room, the indoor air time variation will be performed along with the simulation results. Thermal performance parameters and characteristics of building thermal envelope heating effect of storage room were studied. The mathematical model of the thermal dynamic process of the heating room was established using the heat balance method and verified by experiments. According to the experiment, when the heating time increases from 5-12 hours, the additional heating consumption of the building heating system decreases by 500 Wh, and the additional heating consumption decreases to 19.4. In addition, it is important to change the heating time of the night-time packing model and the total heat accumulation. In addition, external wall insulation is useful in reducing additional heating consumption and building heating costs, but all heat transfer between model blocks is low. As the weather changes and the heat transfer coefficient of the external window increases, the additional amount of heat consumption and the additional value of heat consumption for heat storage of the building will increase. In the process of continuous heating operation, the additional heat consumption of the building heating system, the additional heat consumption gradually decreases, the heating equipment changes per hour, and the total heat accumulation of the night packing structure is important.

Особенности нестационарных тепломеханических процессов в выпускном коллекторе автомобильного поршневого двигателя размерности 8,2/7,1

The purpose of this work was to obtain experimental data on unsteady gas dynamics and the intensity of heat transfer of the flow in the exhaust system of an automobile piston engine for different initial conditions. The research was carried out on an experimental stand simulating the exhaust process in a piston engine in dynamics. The pressure at the outlet (in the cylinder) varied from 0.05 to 0.2 MPa, the speed of rotation of the crankshaft - from 600 to 3000 min-1. The method of thermal anemometry was used to determine the gas dynamic, flow and heat exchange characteristics of the flow in the exhaust system. Data on the instantaneous values of the velocity and local heat transfer of the flow in the exhaust system for different boundary conditions are presented in the article. The effect of the outlet pressure on the gas flow through the exhaust system and the level of heat transfer was analyzed. The spectral analysis of changes in the local flow velocity in the exhaust system is additionally presented in the article. The obtained patterns are useful in the applied aspect for clarifying engineering methods for calculating the exhaust system and for verifying mathematical models of gas exchange processes in automotive piston engines.

Mathematical modeling of physical processes in composition media

Mathematical modeling of physical processes in composition media

О генерации электрического разряда в диэлектрике потоком фотонов

The development of an electric discharge during photon scattering in a dielectric material is considered. A preliminary mathematical model of the discharge process is presented. The model is based on a quantum kinetic equation for quasi-free charge carriers produced by bulk radiation effects and impact ionization. Equations are obtained for the concentration, drift current density, and gas temperature of quasi-free electrons. A test example is considered, confirming that the model does not contradict the known conditions for the formation of an electric discharge.

Mathematical modeling of nonequilibrium processes on chair of physical mechanics of St. Petersburg State University. Part 1. Modeling of processes in gas, fluid and solid

The article gives the review of works of employees of chair and laboratory of physical mechanics of St.Petersburg State University from the moment of its establishment in 1986 and till 2023 inclusive, that are devoted to modeling of the non-equilibrium processes in gas, fluid and solid. The basic attention is given several major results: 1) creation of model of adsorption layer for the description of locomotion of flying vehicles in near space and an upper atmosphere; 2) a theoretical and experimental substantiation of the general approach to modeling high-speed and short-duration processes in various mediums; 3) application of the specified general approach to studying of shock-induced processes in solid. The detailed substantiation of necessity of the integro-differential form of the transport equations for nonequilibrium processes is given. That is shown that time’s evolution of system, to which interaction of structural elements of medium on the mesoscale leads, is described by the cybernetic methods developed by A. L. Fradkov within the limits of the Control Theory of adaptive systems with feedback. Other results are given short enough.

Development of technology and methodology for monitoring the technical condition of metalcutting machines

This work was carried out with the aim of developing the basic provisions of an automated vibration monitoring system for metal-cutting equipment. The paper presents the theoretical foundations of vibration monitoring technology, which uses regular measurements of vibration parameters, their frequency analysis, and mathematical modeling of degradation processes in machines. Vibration monitoring technology allows to determine the time points necessary for repair and maintenance of equipment based on its actual condition. Applications of vibration monitoring are reducing losses associated with equipment failures and reducing maintenance and repair costs, as well as increasing the safety of work. The most relevant is the implementation of a vibration monitoring system when diagnosing the technical condition of bearings and gears (metal-cutting machines, hydraulic systems). As a result of the research, diagnostic models of changes in the technical condition of metal-cutting machines and vibration characteristics of typical defects were obtained. A method has been developed for assessing the dynamic quality of metalcutting machines using a complex quality indicator determined by measuring and analyzing the spectral characteristics of vibration signals.

Analysis of the application of optical illusion in the field of art and design

Abstract This study ventures into the captivating realm of visual illusion art, where the enigmatic principles of visual perception are harnessed to enhance artistic creativity. Through mathematical modeling of the visual perception process, we uncover the essence of visual illusions and their profound impact on art and design. Leveraging cellular neural networks, this research merges dynamic processes with the WC visual illusion and color space models to craft a novel visual illusion neural network model adept at reproducing the nuances of visual illusion art. Our investigation into the application of visual illusions in art design reveals a notable affinity for the “transparent” quality, achieving a 57% certainty level and embodying the art’s ethereal nature. Furthermore, we identify significant correlations between interactive effects, color coordination, design structure, visual impact, and the overarching quality of art designs, with correlation indices of 0.508, 0.487, 0.535, and 0.602, respectively. This work highlights visual illusion’s pivotal role in propelling the field of art and design forward, thereby enriching the tapestry of human experience.

Mathematical Modeling of Absorption-adsorption Processes for Waste Free Decontamination of Gases from SO2 in a Bubble Tray Column

Mathematical Modeling of Absorption-adsorption Processes for Waste Free Decontamination of Gases from SO₂ in a Bubble Tray Column

Синтез системы управления температурным полем углеграфитового теплового узла при выращивании кристаллов лейкосапфиров

This article is devoted to the development of a control system of the temperature field in the carbon graphite thermal unit during the growth of leucosapphire crystals by the horizontal directional crystallization (HDC) method. The paper presents the results of developing a model of automated control system for maintaining the specified temperature conditions at the crystallization front. The work solves the following tasks: the mathematical model of the crystal growth process was developed, analysis and identification of the control object based on the numerical solution, calculation of distributed high-precision controller parameters using frequency synthesis method, computer modeling of a closed-loop control system. Based on the obtained transient characteristics, direct quality indicators of the synthesized control system were calculated, which confirmed that the calculated settings of the corrective device allow to achieve the control objective – maintaining the specified temperature conditions at the crystallization front.