Mathematical Modeling
Vol. 8 (2024), Issue 1

Table of Contents

  • THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

    • Development of a small hydropower plant model verified on real parameters

      pg(s) 3-6

      Research, optimization and practical implementation of small hydroelectric power plants as a source of clean electricity presents one of the topical tasks in current energetics, which is virtually impossible to solve without powerful computer support due to the strongly nonlinear nature of such systems. The article presents a complete model of a small hydropower plant, modelling its individual subsystems and verifying its dynamic properties in basic operating modes. Also an influence of a major external fault, caused by a drop in the power grid frequency, was investigated. Full Small-Hydropower Plant (SHPP) model properties were verified using MATLAB software package using real parameters of a micro hydro power plant in Dobšina (Slovakia). The obtained results confirmed correctness of the proposed SHPP model, which can be used for design of its control.

  • MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

    • Generalized mathematical model of the transfer processes in the enclosing structures of buildings, constructions, thermal and engineering networks

      pg(s) 7-9

      The problems of heat and moisture transfer, air permeability in single and enclosure constructions (EC) of buildings, facilities and heat, engineering and electrical networks under the influence of environmental factors and the work of heating, ventilation and air conditioning has been analyzed. A general definition of the problem taking into account the transfer processes of internal voluminous or local heat source (drainage) has been considered. A generalized mathematical model (MM) of unsteady heat and mass transfer process for bodies of different canonical form (half-plate, hollow cylinder and sphere) and their analogues has been developed. In particular cases of the mathematical model, the dependence of the physical characteristics of the (solid isotropic) medium, the boundary conditions parameters, the capacity of the mass substance transfer sources (drains) from the transfer potentials (temperature, moisture content) or the space-time continuum has been taken into consideration. The analytical solution of the generalized non-stationary and stationary heat and mass transfer problem under the general boundary conditions of different (first, second, third and mixed) kind on the outline of the researched area has been scrutinized. For constant system parameters of non-stationary transfer processes an algorithm for solving differential transfer equations using Fourier transformation with variable parameters of different kind of boundary conditions has been shown. For large-scale transitions, practical applications, parametric analysis of the solutions obtained, setting optimization and automation tasks for process control systems, the obtained MM, analytical and approximate solutions of direct transfer short circuits are given a criterion form convenient for these purposes.

    • Modelling of combined thermomechanical processing of stainless steel wire

      pg(s) 10-13

      In this article, a number of theoretical studies have been conducted on a new combined process of multicycle thermomechanical processing, including wire drawing and subsequent cooling in liquid nitrogen. When analyzing the deformation, it was found that the presence of intermediate heating to ambient temperature allows calculating the force according to the Krasilshchikov formula and the wellknown nomogram of the tensile strength of AISI-316 steel at 20°C with minimal errors. The lack of heating leads to the fact that the second and third drawing cycles take place at partially negative temperatures in the workpiece section. This leads to an increase in the difference in the force values obtained by calculation and during modeling. To be able to use the Krasilshchikov formula and the nomogram of the tensile strength of AISI-316 steel at 20°C, it is necessary to adjust the resulting force values by increasing by about 30% for a diameter of 6 mm and 20% for a diameter of 9 mm in the absence of heating of the workpiece and by 35% for a diameter of 6 mm and 25% for a diameter of 9 mm in in case of preheating the workpiece.

    • Robust Control Optimized with Particle Swarm Optimization for Robot Manipulators

      pg(s) 14-17

      The integration of robotic systems is widespread across diverse industries, notably in defence, automotive, and industrial sectors. These systems are endowed with the capability to execute precise movements via software programming, facilitating object manipulation and trajectory adjustments. Nonetheless, careful oversight is imperative during operations to avert undesirable outcomes stemming from mishandling. Consequently, the management of robotic systems has emerged as a pivotal concern in contemporary industrial practices. The parameters governing robotic systems are subject to fluctuations contingent upon the loads they bear. Robust control, a methodology geared towards adapting the control system to accommodate such parameter variations, stands as a cornerstone for ensuring stability and optimal performance. This approach enables the maintenance of desired control levels even amidst shifting system parameters. To refine controller parameters, an objective function derived from error functions of the first and second robot arms was minimized. In this endeavour, the particle swarm optimization (PSO) method, renowned for its efficacy, was employed. The efficacy of this proposed control methodology is substantiated through graphical representations, underscoring its utility and effectiveness in real-world applications.

    • Adoption of a digital approach for ship-shape simulation trials with CFD

      pg(s) 18-23

      The prediction of maneuverability is a classic problem in ship hydrodynamics. Likewise, ship motions in restricted waters have been studied for a long time. It is an indisputable fact that full-scale or model tests of the respective ship meet IMO requirements and provide the necessary information for the maneuverability of the ship in deep unconfined waters. However, they are unable to provide practical insight into understanding of ship maneuverability in shallow water, as the maneuvering behavior of a ship in such areas differs significantly. Ship maneuvering in coastal areas and harbor approaches, where space is limited, movement speeds are low, and traffic heavier requires deeper researching. The aim of the present work is to predict the hydrodynamic derivatives in the mathematical model of the maneuvering of ship in shallow waters based on CFD programs with free access like FreeCAD, OpenFOAM and ParaView.
      The sequence of solving the task is described with details in this work:
      1. Generating the shape of the studied body 2. Creating the domains around the experimental body, sizes and boundaries
      3. Defining the continuum, areas and subareas of study, and boundary conditions 4. Generation of the computational grid
      5. Defining the continuum – physical models 6. Selection of the calculation algorithm 7. Substances modeling 8. Motion modeling.
      9. Modeling of currents and energy 10. Flow turbulence modeling.
      Results have been obtained for the linear hydrodynamic derivatives in the mathematical model for the maneuvering motion of a ship.
      They are compared with available experimental and theoretical data in the literature.

    • Isentropic analysis of nuclear power plant steam turbine and turbine cylinders

      pg(s) 24-27

      This paper presents isentropic analysis results of the whole steam turbine (as well as turbine cylinders) from nuclear power plant. In the analyzed steam turbine, LPC (Low Pressure Cylinder) is the dominant mechanical power producer – mechanical power produced in the LPC is more than two times higher in comparison to mechanical power produced in the HPC (High Pressure Cylinder). Whole analyzed steam turbine produces real mechanical power equal to 1372.47 MW, while the highest possible mechanical power which can be produced in the whole turbine when all the losses are neglected (ideal mechanical power) equals 1686.96 MW. LPC has a notably higher isentropic efficiency than HPC, regardless of higher isentropic loss (isentropic efficiencies of the LPC and HPC are 84.41% and 74.84%, respectively). HPC has notably higher specific steam consumption and specific heat consumption in comparison to LPC. Whole turbine has an isentropic efficiency equal to 81.36%, isentropic loss equal to 314.48 MW, specific steam consumption of 9.15 kg/kWh and specific heat consumption of 3799.06 kJ/kWh, what is in the range of similar comparable steam turbines from nuclear power plants.

    • Analysis of thermal mode of transistors in welding inverter

      pg(s) 28-31

      A methodology for thermal analysis of the operation of transistors in a welding inverter is proposed. The results for heating of the transistors obtained by numerical modelling using the finite element method (FEM) are presented. A thermal problem has been solved taking into account the forced movement of air. Based on the obtained solutions, the maximum temperatures on the surface of the heat sink and in the crystal of the field-effect transistor are presented, depending on the speed of air movement and the temperature of the environment in continuous mode of operation of the power source. The presented analysis is applicable to select appropriate heat sink and fan. Results are useable during design of the power source oriented to wire arc additive manufacturing.

    • Advancing Machining Manufacturing: A Comprehensive Evaluation of Finite Element Method Simulation for Cutting Processes

      pg(s) 32-36

      Modeling and simulating cutting processes play a pivotal role in the advancement of machining manufacturing. This enables machining design technologists to scrutinize and optimize intricate machining processes before their implementation in manufacturing. The Finite Element Method (FEM) emerges as a robust numerical technique widely employed for simulating cutting processes in manufacturing. While FEM proves particularly well-suited for cutting simulation, it is imperative to make judicious choices regarding the FEM method and software for effective implementation in cutting simulations.
      The realm of FEM software is diverse, encompassing various analysis options such as mechanical, thermodynamic, and contact analyses. However, the selection of appropriate FEM software is not only contingent upon these analysis options but also influenced by factors like the user interface and the requisite understanding of the physical nature inherent in the modeled cutting process.
      In the scope of this study, a simplistic orthogonal cutting model is formulated utilizing the FEM software DEFORM and the FEM software MARC MENTAT. The attained results are meticulously evaluated by comparing them not only in relation to practical applicability but also considering the challenges and intuitiveness associated with the creation of a machining model.

    • Exploring the Impact of Component Materials on the Energy Efficiency of Solar Panels for Water Heating: A Numerical and Experimental Investigation using labview Software

      pg(s) 37-41

      This study examines the impact of component materials on the energy performance of solar panels designed for water heating. For this purpose, we have integrated numerical simulations and experimental analyzes enabled by algorithms developed with LabVIEW software. The primary objective of this investigation is to assess how the selection of materials in the construction of solar panels affects their overall efficiency in harnessing and converting solar energy into heat for water heating purposes. The research methodology involves the development and implementation of advanced algorithms using LabVIEW, a versatile software platform known for its proficiency in data acquisition, analysis, and control. Numerical simulations focus on modeling the behavior of solar panels under different conditions, taking into account factors such as radiation, temperature and the specific characteristics of different component materials. These simulations provide valuable assessments of theoretical aspects of solar panel performance and enable the identification of optimal material combinations. Through the physical model, experimental studies are conducted to validate the simulated results. Physical prototypes of solar panel components are built using various materials and their performance is rigorously evaluated under real-world conditions. Experimental measurements allow data collection, and enable comparative analysis with numerical simulations. The results of this study aim to contribute to the advancement of solar panel technology by providing a deeper understanding of how material choices affect energy efficiency. Moreover, the use of LabVIEW software in the development of algorithms ensures a systematic and accurate analysis of numerical and experimental data.