Mathematical Model Of Process Research Articles

Large Debris Removal: Using Features of Attitude Motion for Load Factor Regulation during Re-Entry

This paper focuses on the active removal of spent upper stages from LEO using de-orbiting devices. It proposes a method of regulating aerodynamic loads on the target during its re-entry by utilizing the features of spatial attitude motion. A mathematical model of the re-entry process is developed, and numerical simulations are conducted, demonstrating that the nature of the attitude motion during the descent influences the load factors and, thus, the breakup altitude. It is shown that the respective de-orbiting devices should control both the initial tumbling and spin of the target to achieve different mission outcomes, such as minimizing the debris footprint size or maximizing the breakup altitude.

Mathematical modeling of nonequilibrium combustion processes in a liquid rocket engine

The key problems of safety for Space missions begin with safety, reliability and effectiveness of rocket engines of different types used at different launch stages and orbit corrections. Today, the possibilities for improving chemical rocket engines of traditional types are almost completely exhausted and are limited to minor improvements in energy-mass characteristics. A qualitative leap in the development of engine building can only be achieved through the development and implementation of new types of engines. As unburned fuel in the combustion chamber is a loss of thrust for the engine, the study of droplet combustion and evaporation, in particular, the droplet lifetime, is of fundamental importance in the creation of combustion chambers using atomized liquid fuel in their operation.In this paper a quasi-stationary model, which describes the evaporation of a single droplet in a gaseous atmosphere, is presented. Since in the numerical implementation the mass flow from the liquid phase to the gas and the heat flux from the droplet to the gas are calculated based on the Peclet number and the droplet surface temperature obtained from the quasi-stationary problem, approximation formulas for these parameters are developed in this paper. As an example, the problems of evaporation of a liquid oxygen droplet in an atmosphere of gaseous hydrogen and a droplet of liquid n-decane in an atmosphere of gaseous oxygen are considered. Formulas for calculation of mass flow and heat flux from liquid phase to gas based on the solution of the droplet evaporation problem are presented. Estimates of droplets lifetime in engine are provided based on developed droplet evaporation models.

A front-fixing numerical method for a fluvio-deltaic sedimentation process with thespace fractional derivative and variable sediment flux

This paper centers around a space-fractional mathematical model for a fluvio-deltaic sedimentation process which involves a space-fractional derivative (Caputo derivative) and time dependent variable sediment flux to investigates the movement of shoreline in a sedimentary ocean basin. This model is a specific case of a basic shoreline model and analogous to a Stefan problem. The numerical solution to the problem is acquired by employing a front-fixing explicit finite difference method. The consistency, stability and convergence of the numerical scheme are theoretically analyzed. The effects of variable sediment flux on the movement of shoreline position and the height of sediments are also assessed for different cases.

Mathematical modeling of osmotic membrane bioreactor process for oily wastewater treatment

ABSTRACT To evaluate the disposal effluent from the Aldura refinery in Iraq, which comprises oily wastewater, a mathematical model has been developed for both forward osmosis (FO) and osmotic membrane bioreactor (OsMBR). The procedure is explained mathematically, accounting for both the concentration and polarization aspects. As a result of mathematical modeling, the water flux was determined by the osmotic pressure, the concentration, and the polarization of the feed and draw solutions. Based on traditional methods of predicting water flux using external and internal concentration polarizations, it is determined that water flux will occur in the first model (Model-1). To increase the accuracy of Model-1, the resistivity (K) of the solute has been modified to be independent of the diffusivity of the solute. The old model (Model-1) and the updated model (Model-2) overestimated water flux by 17 and 25%, respectively. It was possible to make a valid comparison between the experiment and theory based on the results of both experiments.

Performance improvement of a U-tube heat exchanger based hydrogen storage reactor by phase change materials

Solid-state hydrogen storage technology using metal hydrides as carriers has great application prospects. This study aims to optimize the heat transfer resistance and absorption kinetics issues encountered in practical applications of LaNi5-H2 storage materials in storage reactors. A mathematical model for the hydrogen absorption process in the reactors based on U-tube and straight-tube heat exchangers was built, and the advantages of U-tube structure and the flow characteristics of the heat transfer fluid on its heat transfer and absorption performance were analyzed. To further enhance the U-tube based reactor's performance, phase change materials (PCM) were subsequently introduced as an auxiliary heat transfer medium, while the amount of PCM and the thermal conductivity of the reaction bed were optimized. The results showed that the appropriate PCM dosage could overcome the inherent defects of the U-tube heat exchanger and significantly improve heat dissipation and reaction rates of the reactor, and the H2 absorption completion time was shortened by 1.4 times. In addition, the increased thermal conductivity of reaction beds is equally important for the enhancement of heat transfer and absorption rate. Nevertheless, further increase of PCM's thermal conductivity has a limited effect on the improvement of the performance.

SEAIS: Secure and Efficient Agricultural Image Storage Combining Blockchain and Satellite Networks

The image integrity of real-time monitoring is crucial for monitoring crop growth, helping farmers and researchers improve production efficiency and crop yields. Unfortunately, existing schemes just focus on ground equipment and drone imaging, neglecting satellite networks in remote or extreme environments. Given that satellite internet features wide area coverage, we propose SEAIS, a secure and efficient agricultural image storage scheme combining blockchain and satellite networks. SEAIS presents the mathematical model of image processing and transmission based on satellite networks. Moreover, to ensure the integrity and authenticity of image data during pre-processing such as denoising and enhancement, SEAIS includes a secure agricultural image storage and verification method based on blockchain, homomorphic encryption, and zero-knowledge proof. Specifically, images are stored via IPFS, with hash values and metadata recorded on the blockchain, ensuring immutability and transparency. The simulation results show that SEAIS exhibits more stable and efficient processing times in extreme environments. Also, it maintains low on-chain storage overhead, enhancing scalability.

RESEARCH OF THE DESTRUCTION CONDITIONS OF GLAZING OF ENCLOSING STRUCTURES UNDER THE CONDITIONS OF THERMAL INFLUENCE OF FIRE

The article presents the main results of mathematical modelling of the destruction of glazing of enclosing building structures with translucent elements under fire conditions. The authors analyse literature data on calculating the fire resistance of enclosing building structures with glazing. The results show that improving methods for predicting the fire resistance of glazing is relevant. Mathematical models for the numerical study of the behaviour of glazing under the thermal influence of the standard fire temperature regime are substantiated. Mathematical models of the heat transfer process involve using a non-stationary differential equation of heat conduction with boundary conditions of the third kind, accounting for the convective and radiant heat exchange between the air in the room with the fire and the glazing. As a criterion for the destruction of glazing under the influence of fire, the authors establish the temperature resistance parameter, which is determined based on the mechanical characteristics of the glass. The article highlights the relevant data on the study of temperature indicators and the mechanism of glazing failure, using mathematical modelling with well-founded mathematical models. It obtains the results of the thermal calculation by applying the finite difference method for solving the non-stationary differential equation of thermal conductivity. The methodology for determining the time of glazing failure under the influence of the standard temperature regime of a fire using the calculation parameters obtained based on well-founded mathematical models is substantiated. An analysis of the adequacy of the obtained calculation data was carried out by comparing them with the results of experimental studies using statistical criteria. As a result of the analysis, the authors confirmed the validity of the calculation data. A complete factorial experiment was conducted based on well-founded mathematical models, which revealed the regularities of the dependence of the parameters of thermomechanical processes in single-layer glass on its structural characteristics. The revealed regularities have the form of linear regression dependences of the destruction time on the thickness of the glazing and the maximum length of the glass panel without bars. Using the regularities of the dependence of the parameters of thermomechanical processes in single-layer glazing on its structural characteristics, the authors constructed reference tables for evaluating the fire resistance of enclosing structures with glazing. The research obtained new scientific data on the study of the behaviour of glazing of enclosing building structures under the thermal influence of fire through mathematical modelling, which is the basis for improving the methods of calculating the fire resistance of enclosing structures with translucent elements. Keywords: enclosing building structures, glazing, fire resistance limit, calculation method, glass heat resistance.

Experimental Analysis and Optimization of Clearance between Punch and Die in Sheet Metal Blanking Process for Soft Steel

Blanking process is commonly used process in production of sheet metal industries to fabricate components. The Global market of sheet metal production is facing highly competition. Due to unavailability of skilled operators and shortage of affordable CAD/CAM systems, it is difficult to predict optimum clearance between punch and die to obtain high quality in small scale industries. Blanking is metal fabricating process and it is characterized by complete material separation. The simulation of the shearing process is complicated as the shear band formed is narrow and fracture criterion is inappropriate. The effect of potential parameters like thickness of sheet, punch-die clearance, tool wear, and punch geometry are studied to investigate their interactions on blanking process. It is important to select process leading parameters which can lead the process such that two similar products from two separate materials can be manufactured on same mold with high quality. This study will help to investigate the effect of thickness of sheet, clearance between punch and die and type of material on blanking process and will help to predict optimal set of parameters to obtain reasonable quality. A mathematical model of blanking process is developed and design of experiments method is used to predict optimum punch-die clearance for soft steel which will result into high quality of component.

Визуальная интерпретация парадигмы управления организационной системой c разнородными производственными ресурсами

The object of the study is developing a formalized mechanism for managing an organizational system that implements complex production activities, including different types of industrial production, and applies the corresponding heterogeneous resources. The subject of the article is an important intermediate stage of this development, which is an abstract interpretation of the optimal management paradigm of limited resources of such an organizational system, proposed earlier by the authors. The interpretation will allow reasonably forming a strict mathematical model of objects and control processes. The management mechanism in any subject area, providing for adopting management decisions by people authorized to do so, must have an ergonomic development and appropriate information support for these decisions. The so-called result information plays the role of such support, that is the information on the characteristics of the current and planned states of the management object in the problem being solved which is the productivity of the organizational system resources. It seems advisable to carry out such ergonomic and information development of the designed problem-oriented management mechanism in the form of a visual interpretation of its substantive concept. The prototype of such interpretation tools is graphic images used in modelling and designing technical systems, developed in this work in the field of management in organizational systems with heterogeneous resources. The article provides examples of their application, demonstrating the possibility of visual representation of the current state of the organizational system and the set of its possible controlled states.

Pulsed vacuum drying of fruits, vegetables, and herbs: Principles, applications and future trends.

Pulsed vacuum drying (PVD) is a novel vacuum drying method that has demonstrated significant potential in improving energy efficiency and product quality in the drying of foods and agricultural products. The current work provides a comprehensive analysis of the latest advancements in PVD technology, including its historical development, fundamental principles, and mechanistic aspects. The impact of periodic pulsed pressure changes between vacuum and atmospheric pressure on heat and moisture transfer, as well as structural changes in foods at micro- and macro-scales, is thoroughly discussed. The article also highlights the influential drying parameters, the integration of novel auxiliary heaters, and the applications of PVD across various fruits, vegetables, and herbs. Furthermore, the review examines the current status and needs for mathematical modeling of PVD processes, identifying key challenges, research opportunities, and future trends for industrial application. The findings suggest that PVD not only enhances drying efficiency and reduces energy consumption but also preserves the nutritional value, color, and texture of dried products better than traditional methods. Future research should focus on optimizing process parameters and integrating advanced control systems to further improve the scalability and applicability of PVD technology in the food industry.

Mathematical Modeling of Reverse Processes with Consideration of the Water–Ice Phase Transition

Mathematical Modeling of Reverse Processes with Consideration of the Water–Ice Phase Transition

Использование компьютерной программы «ПРОЕКТ ВПУ» для проведения технологического расчета и анализа технологий обессоливания воды на ТЭС и АЭС

There are many viable options of desalination schemes that allow us to obtain purified water of the required quality. To conduct process design of a water treatment plant, thermal power plants and nuclear power plants use special software provided by manufacturers of ion exchangers and membrane elements. However, these software programs consider individual water treatment technologies and are attached to filter and membrane materials of a specific manufacturer. They do not provide the ability to calculate complete water desalination schemes, as well as determine the performance indicators of the water treatment plant. It is relevant to develop a software program that allows us to conduct process design of complete water treatment schemes, which include various water treatment technologies, and to determine technological, environmental, and technical-economic indicators. Multivariate calculations with different initial data will allow us to identify the advantages and disadvantages of scheme solutions and determine areas of their rational use. The method of mathematical modeling of chemical and technological processes of water treatment at thermal power plants and nuclear power plants has been used. An application software program “PROJECT WTP” has been developed. It is designed for process design of various water treatment schemes, which are visually assembled from individual elements, and allows one to determine the technological, environmental, and performance indicators of the operation of water treatment plant. Computation data on the auxiliary need coefficient has been obtained for the main water desalination schemes and under condition of different mineralization of the source water. The developed software program can be used for process design of various water treatment schemes and assessment of the degree of improvement of water desalination technology.

Optimizing the uncertainty of measurements on a coordinate measuring machine when controlling complex geometric surfaces

The object of this study is the process of optimizing measurement uncertainty on a coordinate measuring machine (CMM) when inspecting complex geometric surfaces. The problem addressed was insufficient accuracy and efficiency of measurements of complex parts on CMMs under production conditions. A method for optimizing measurement uncertainty has been devised, which includes a mathematical model of the measurement process and an adaptive algorithm for optimizing the control strategy, based on the Monte Carlo method. The model takes into account the geometry of surfaces and CMM characteristics, while the algorithm dynamically adjusts measurement parameters. The results demonstrate a reduction in measurement uncertainty by 15–20 % and a reduction in inspection time by 10–12 % compared to conventional methods. This is achieved by taking into account the specificity of complex surface geometry and an adaptive approach. The uniqueness of the developed method is the ability to automatically adapt to different types of CMMs and measured objects, optimizing the number and location of measurement points, the speed of probe movement, and its contact force with the surface. The method takes into account not only the geometric parameters of objects but also the characteristics of the CMM itself, which allows for high accuracy. The method is particularly effective for parts with complex geometry, in which conventional methods often lead to significant errors. Practical application is possible at machine-building enterprises for quality control of complex parts, especially in serial production. The implementation of the developed method allows for improving product quality and reducing production costs by 8–10 % due to optimization of the control process and reduction of defects

Mathematical modeling of the thermal process of arc erosion with current carrying heating effect in a temperature gradient

This paper presents a mathematical model aimed at comprehensively understanding the thermal processes associated with arc erosion of closed electrical contacts triggered by the instantaneous explosion of micro-asperities including Thomson effect and Joule heat source. The phenomenon involves vaporization and liquid zones, and the temperature distribution is governed by a generalized heat equation, accounting for the heating effect due to current flow in temperature gradients and effect of heat source. The proposed model allows for a nuanced analysis of the thermal dynamics, shedding light on the complex phenomena involved in arc erosion. The proposed method in this paper employs similarity transformation techniques to effectively reduce the complexity of the problem, transforming it into a set of manageable ordinary differential equations. The study establishes the existence and uniqueness of the solution through rigorous analysis. The behavior of the solution of the problem is successfully considered for special cases of Thomson and thermal coefficients. By leveraging similarity transformations, the paper offers a powerful approach for unraveling the intricacies of the thermal processes in arc erosion of closed electrical contacts, providing valuable insights into the phenomena associated with current-carrying heating in the presence of temperature gradients.

Development of Methodologies and Software for Design, Simulation and Optimization of Oil Hydraulic Cylinders of Large Dimensions and Power

As part of the research carried out in the field of processing systems and the production process of oil-hydraulic cylinders of large dimensions and power, the specifics of fluid power transmission, in the functioning of hydropower facilities, were analyzed. The research also includes the optimization of the physical–mathematical model of non-stationary processes, which take place inside the chamber of a large hydrocylinder. In parallel with the definition of the optimization model, the work parameters that affect the process of fluid flow and piston movement were determined. The operating and technological construction parameters of the hydraulic cylinder, which most significantly affect the operation of the hydraulic cylinder, were defined, and the observed parameters were optimized, based on which a prototype with improved characteristics compared to existing solutions was realized.

Разработка программно-математической модели движений земной коры для территории Российской Федерации

The author considers the principles of construction, the structure of a software and mathematical model of the Earth`s crust’s movements. It is designed to ensure the maintenance of the state reference frame relevance, the establishment and maintenance of the national reference systems’ relationship with international ones for the Russian Federation’s territory. The software implementation should include mathematical models of geodynamic processes for the state’s territory and algorithms for taking them into account for determining coordinates in a given frame of reference. The author presents a general scheme of the above-mentioned model, which consists of several layers. The first base layer containing a model of the tectonic blocks movement and complemented by those of local solutions. Four stages of the model are described. The mathematical basis and software tools are considered. Employing of the first solution of the crust movements software-mathematical model for the Russian Federation’s territory is presented. It is based on that of lithospheric plates motion NNR-MORVEL56. The results of determining the Earth`s crust’s points velocities are compared with those of the Plate Motion Calculator. The coincidence of the calculated values up to hundredths of a millimeter is noted

Simulation of UV curing of photosensitive resins with phase change materials

Based on the mechanism of the resin polymerization reaction and free radical diffusion under UV irradiation, here, a mathematical model of the curing process was established for the mixture of photosensitive resin (PAA) and polyethylene glycol (PEG, as the phase change material), and the factor influencing the mechanical performance of the cured samples was analyzed. The yield stress (σs) of the pure resin sample can reach 50 MPa when the monolayer curing depth is 5 mm. σs decreases with the increase in the PEG content and monolayer curing depth. With increasing the monolayer exposure time, the yield stress increases and then decreases, and there is an optimum value. The material has the maximum stress at the monolayer exposure time of 13.5 s when the resin content is 50 %.

Determining the coordinates of unmanned aerial vehicles

The purpose of the work was to develop a method for determining unmanned aerial vehicles’ (UAVs) coordinates, trajectory and parameters of their spatial movements by means of kinematic projection. The paper analyses the use of technologies for determining coordinates and spatial movements of aircraft trajectories. The principle of the kinematic scheme of fixing moving objects by means of orthogonal and kinematic design has been developed. The principle scheme of determining UAV coordinates by kinematic projection was studied. The theoretical mathematical dependencies of the determination and calculations of the coordinates of spatial movements of unmanned aerial vehicles have been practically verified. The main object of research in this work was the theory of kinematic design as a means of graphically displaying the patterns of spatial movements of objects. The subject of the study was the specific features of searching and recording the trajectories of spatial movements of unmanned aerial vehicles in order to determine the coordinates of their instantaneous location in space. In the process of conducting theoretical and experimental research, methods and techniques of physical and mathematical modelling of fast-moving processes and mathematical statistics of analysis and classification of their results were used. The basis of the experimental study was the theory of mapping coordinates and trajectories of spatial movements of moving objects by means of graphic geometry when combining classical orthogonal design with dynamic features of kinematic design. For an objective assessment of the results of the theoretical and experimental study of the dynamics of objects moving in space, the classical theory of research planning with a mathematical apparatus for processing their results was used. Graphical models of UAV coordinate fixation were made with the use of computer technology and the AutoCAD graphic editor software.

Mathematical modeling of the onion drying process: Kinetic and Thermodynamic Parameters

Mathematical modeling of the onion drying process: Kinetic and Thermodynamic Parameters

Optimization and Kinetic Study of Manganese Leaching from Pyrolusite Ore in Hydrochloric Acid Solutions with Oxalic Acid

The leaching behavior of pyrolusite minerals was examined in hydrochloric acid solutions, including oxalic acid, to evaluate the influence of various experimental conditions. The optimum parameters for the leaching process were found in the first stage, and the process's kinetics were assessed in the second. The concentrations of oxalic acid, hydrochloric acid, and temperature were chosen as independent variables in the optimization experiments, with the central composite design used to analyze the experimental data. The optimum concentrations for oxalic acid, hydrochloric acid, and temperature were determined to be 0.75 mol/L, 1.2 mol/L, and 60 °C, respectively. The leaching rate was determined to be 97.4% for 120 min of response time in optimum situations. The kinetic assessment experiments studied the effects of solid/liquid ratio, particle size, stirring speed, and temperature on the manganese leaching rate from pyrolusite. In the studies, the leaching rate was shown to rise with increasing temperature and stirring speed, as well as with decreasing particle size and solid/liquid ratio. The kinetic analysis revealed that the leaching kinetics matched the mixed kinetic model, and a mathematical model for the leaching process was developed. This process's activation energy was determined to be 29.05 kJ/mol.Graphical