Mathematical Model Of Thermal Processes Research Articles

Modeling of thermal processes in anti-icing gratings for arctic purposes

The problem of modeling thermal processes in anti-icing gratings, which are used in arctic conditions, is considered. The task is of practical importance, including for the design of air intake grilles for ship systems operating in arctic conditions. A mathematical model of thermal processes is presented, which takes into account the processes of heat transfer in the lattice due to the thermal conductivity of its internal elements, due to convective heat exchange with the external air, due to heat release during electric heating, and also due to phase transformations during icing and melting of ice. The problem is solved in a three-dimensional formulation, using a software package developed at Bauman Moscow State Technical University. Some results of numerical simulation are presented.

Modeling of Thermal Processes in a Technological System during Electromechanical Processing

The article presents mathematical models of thermal processes of combined methods of electromechanical processing, which are based on the heat conduction equations, which take into account thermophysical properties (thermal diffusivity, heat capacity, thermal conductivity and heat transfer), initial and boundary conditions, technological and other features of the studied processing methods. In view of the fact that electromechanical processing (EMT) is characterized by a process with a volumetric heat release zone, with sufficiently small dimensions and high intensity, it is assumed that the determination of temperature fields can be carried out using the superposition principle. In this case, the main factors affecting the amount of heat propagating into the contacting bodies are the intensity of heat removal, the thermophysical properties of the contacting bodies, and the speed of their relative movement. Dependences are proposed that allow one to describe the temperature fields in the volumes of parts subjected to thermal deformation during electromechanical processing, which have significant geometric parameters that ensure sufficient heat removal from the treated surfaces into the part. It has been established that in the case of processing parts of small dimensions, with insignificant heat removal, it becomes necessary to take into account the accumulation of heat, which will lead to a general increase in temperature in the technological system during processing, and a decrease in the efficiency of the hardening process. The derived mathematical dependencies in the form of heat conduction equations with the established restrictions make it possible to determine the parameters of thermal fields during electromechanical processing in the system “working tool” - “local microvolume of the surface layer”, while these presented mathematical relationships are presented in a linear formulation with thermophysical coefficients. It has been theoretically established and experimentally confirmed that in the process of processing the main factors affecting the amount of heat propagating into the contacting bodies are the intensity of heat removal, the thermophysical properties of the contacting bodies, and the speed of their relative movement. The performed experimental studies have confirmed the adequacy of the mathematical dependencies used to calculate the temperatures in the local microvolumes of the treated surface layer.

Support vector machine applied to the problem of thermal diagnostics of design defects in radio electronic devices

The paper describes a new approach to diagnostics of the technical condition of printed circuit board (PCB) assemblies of electronic devices based on mathematical modelling of thermal processes and on the support vector machine as a tool for classifying design defects of electronic equipment. This work continues the previous study of thermal diagnostics of malfunctions in PCB assemblies. The developed method combines mathematical modelling and physical tests of PCB assemblies under study with subsequent analysis of the obtained characteristics. The tools for method implementation include special-purpose software suites for PCB and hardware design such as Altium Designer, SolidWorks, NI Multisim as well as mathematical modelling software packages and the Python programming language.

Mathematical Model of the Rapeseed Drying Process with the Use of Electromagnetic Microwave Radiation Based on Heat Calculations

Few studies have been devoted to mathematical modelling of the drying process of various crops using microwave drying units. The paper presents a mathematical model of the rapeseed drying process using electromagnetic microwave radiation based on heat calculations. The research aims at mathematical modelling of thermal processes of rapeseed heating when treated by electromagnetic microwave radiation. The computational and technological scheme of drying has been developed. According to the scheme, the drying process includes several cycles, which, in turn, consist of two stages. In the first stage, rapeseeds are heated to the desired temperature by applying electromagnetic microwave radiation. At this stage, there is an intensive release of moisture from rapeseeds, accumulating in the interseminal space. In the second stage, rapeseeds are blown off with atmospheric air to create a fluidized bed. The developed mathematical model allows predicting such parameters as the power of the microwave generator and fan depending on the drying unit capacity.

Математическое моделирование тепловых процессов в системе «Бетон-грунт»

The calculation of concrete curing modes and the development of mathematical models are greatly influenced by the temperature field in the concrete of channel linings. The problem is reduced to solving a nonlinear heat equation that takes into account the exothermic heat release of concrete and the phase transformation of moisture, and time-varying boundary conditions that allow taking into account the impact on concrete of the external environment during laying and maintenance. Variable thermophysical coefficients make it possible to take into account the inhomogeneity of the medium (in the case of laying concrete on the ground) and the change in the aggregate state of the substance when the phase transformation temperature is reached. Since it is impossible to obtain an analytical solution in a general form, a numerical solution method is used, based on a combination of a finite-difference solution with a method for calculating heat release and concrete strength from the corresponding fields of isothermal curves obtained experimentally. When constructing a difference scheme, an integro-interpolation method (balance method) is used, based on the law of conservation of heat. For an extended body of sufficiently large dimensions, the process of heat transfer in it is assumed to be linear, and the coordinate system with the center is taken to be on the axis of the body. The presented mathematical model of thermal processes in the “concrete-soil” system makes it possible to predict the modes of holding monolithic concrete to achieve the necessary technological requirements, as well as to apply the most economical modes.

Оцінювання вогнестійкості вогнезахищених сталевих балок

Purpose. Development of a computer model for the study of fire resistance of steel structures protected by fire-resistant coatings, using the example of a fire-resistant steel beam created in the LIRA-SAPR software complex (Ukraine). Methods. Finite element method, application of computational methods of numerical modelling of the LIRA-SAPR software complex, mathematical modelling of thermal processes of non-stationary thermal conductivity. Results. A computer model was developed in the LIRA- SAPR software complex, with the help of which thermal engineering calculation of the beam was carried out. The model makes it possible to evaluate the fire resistance of both unprotected and fire-protected steel beams, to take into account the properties of the beam material and the material of the fire-resistant coating. The peculiarity of modelling the non-stationary heating of a fire-resistant steel beam is to specify the thermophysical characteristics of the fire-resistant coating when solving the problem of non-stationary thermal conductivity. The results of the calculated determination of the fire resistance of the fire-resistant steel beam were compared with experimental data. As a result, a satisfactory convergence of the results of the calculation and experimental study of fire resistance was established (the error is no more than 12%). The results of the experimental determination of the fire resistance of unloaded beams under fire conditions of the standard fire temperature regime were analysed. The accuracy of the developed computer model was evaluated with the results of the experiment. Scientific novelty. A finite-element model of a fire-resistant steel beam has been developed in the LIRA- SAPR software complex, which allows calculating the fire resistance limits of beams protected by fire-resistant coatings with scientifically justified parameters with sufficient accuracy for engineering calculations. Practical significance. It consists in creating the basis for the calculated assessment of fire resistance of building structures protected by fire-resistant coatings by creating computer models capable of performing fire resistance calculations. Due to this, there should be a significant reduction in the cost of work on fire resistance assessment and, as a result, an increase in the effectiveness of measures to increase the fire resistance of building structures.

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ НАГРЕВА АСИНХРОННОГО ДВИГАТЕЛЯ С КОРОТКОЗАМКНУТЫМ РОТОРОМ НА ОСНОВЕ ЭКВИВАЛЕНТНОЙ ТЕПЛОВОЙ СХЕМЫ

The largest share of failures of asynchronous motors in industry is associated with overheating of the stator winding insulation as a result of improper operation of the equipment. In this paper, methods of mathematical modeling of thermal processes of an asynchronous motor with a squirrel-cage rotor are applied to assess the thermal state of the elements of the electric motor design. The simulation is based on the method of equivalent thermal circuits for stationary heating. The mathematical model consisting of 10 main units of the electric machine is taken as a basis. The aim of the paper is to experimentally test the adequacy of the proposed mathematical model and evaluate the possibi­lity of its application for diagnosing the state of the electric motor by measuring the stator current without using built-in sensors. The simulation results were verified experimentally using thermal imaging equipment. Based on the results of comparing the mathematical model and experimental data, it was concluded that the proposed model can be used to study the thermal regimes of an asynchronous motor with a squirrel-cage rotor.

Modeling of thermal processes in the contact zones of fuel elements

In this work, using two specific examples, a general approach to the mathematical modeling of thermal processes in the contact zones of fuel elements in the development and optimization of 
 various technological processes, systems and devices is considered. In the first example, a mathematical model of heat transfer in the contact zone (metal-hybrid thermal interface) between the heat-generating element and the heat-dissipating radiator is considered. In the second case, the thermal process in the processing of materials with a bonded diamond tool in the contact zone "diamond grain – binder – processed material" is considered and analyzed. The general approach to modeling thermal processes in the contact zones of various fuel elements makes it possible to optimize the parameters of technological processing modes and the correct operating conditions for products and systems

EFFICIENT CONTROL OF FUNCTIONING OF ELECTRICAL GAS PREPARATION COMPLEX TO TRANSPORTATION BY MAIN PIPELINE

The article discusses the problem of increasing the effi ciency of the linear section of the main gas pipeline system by developing eff ective control algorithms for the operating modes of the gas cooling unit. To develop control algorithms for a gas cooling unit, adapted mathematical models of thermal processes in air-cooled gas devices and in a gas pipeline are used. It is shown that when considering the dynamic modes, the gas pipeline system can be represented as consisting of two dynamic links. The link “gas cooling unit”, which includes up to 24 electric drives with heat exchangers, is characterized by relatively short time constants. In the main gas pipeline, heat exchange processes proceed much more slowly. This circumstance allows the main att ention to be focused on the development of an eff ective control system for the cooling plant. The control is carried out by discrete or continuous change in the fl ow rate of the cooling air through the heat exchanger by adjusting the number of switched on air coolers and changing the fan speed. The search for control algorithms for air coolers is carried out by formulating and solving the problem of minimizing the root-mean-square deviation of the gas temperature at the outlet from the heat exchanger from the required value. To implement the obtained control algorithms, a functional diagram of the automatic control system for the operating modes of the gas cooling unit has been developed.

MATHEMATICAL SIMULATION OF THE HEATING SYSTEM RADIATOR OF AS A CONTROL OBJECT

The problem of mathematical modeling of a heating system radiator as a control object is considered. The purpose of its development is to create a generalized mathematical model of thermal processes in a room heated by means of water radiators. A calculation scheme of heat transfer processes between the heat carrier of the radiator and the air of the room has been developed, on the basis of which the heat balance equations are writt en. This takes into account both steady and unsteady heat transfer processes between the coolant, radiator and room air. A block diagram of the mathematical model of a heating radiator has been developed. After the introduction of assumptions and transformation of the structural diagram of the nonlinear model, the structural diagram of the linear mathematical model of the heating radiator was obtained. On its basis, the transfer function of the heating radiator is derived, the output coordinate of which is the thermal power. The resulting transfer function can be used in a generalized mathematical model of a heated room. The analysis of the transfer function of the heating radiator is carried out and it is shown that its dynamics is determined not only by geometric parameters, but also by the fl ow rate of the heat carrier.

Mathematical efficiency model of the block-module cooling system of automotive vehicles and tractors

As related to other heat exchange systems, the operation of a heat exchanger should be based on the quality analysis of the heat carrier flows. One of these quality characteristics is the uneven distribution of temperature and air flow velocity ahead of the heat exchanger. To obtain more accurate performance indicators, it is necessary to build mathematical models of thermal processes in the radiator taking into account the unevenness of the air flow. The improvement of cooling systems is one of the priorities for the development of motor vehicles, as the temperature and dynamic loads in the engines are increasing due to the requirements that are becoming more stringent every year. First of all, this relates to environmental friendliness and fuel efficiency parameters, and secondly, it is service maintenance and labor safety, etc. Given this trend, it is necessary to pay attention to such important issues as improving the design of cooling systems, influencing the efficiency of heat balance distribution in the internal combustion engine. When developing new heat exchangers, a thermal engineering design should be analyzed to determine the heat exchange surface area that ensures the transfer of a given amount of heat from one heat carrier to another.

SIMULATION OF THERMAL PROCESSES OF A NPP STEAM GENERETOR FOR INFORMATION TECHNOLOGY OPTIMIZED CONTROL

Mathematical models of thermal processes in the form of Cauchy in the state space with relative variables of the steam generator PGV-1000 of the power unit of a nuclear power plant with a nuclear reactor VVER-1000 have been developed for the using of models in information technology for optimizing the control of a steam generator. The working thermal processes in the PGV-1000 steam generator associated with the supply of feed water to it from the water treatment system and the coolant from the nuclear reactor and the removal of vapors to the main steam header are considered. The design diagram of the steam generator is presented, which reflects the working processes in it under the evaporation mirror and above it. On the basis of differential equations of the heat balance of the heat carrier in the steam generator and in the metal heat exchange tubes, the simulation of heat transfer from the heat carrier to the feed water in the steam generator is carried out. The heat transfer model in the form of a linear system of differential equations in relative state variables is developed. The processes of vaporization during heating of feed water by the heat transfer surface are considered. Differential equations of material and heat balances of dynamic processes of vaporization in a steam generator are compiled, which are not equations in the Cauchy form. Transformations of the differential equations of material and heat balances in the steam generator to the Cauchy form are carried out. A nonlinear system of differential equations for the balance of vaporization in relative state variables is obtained. The values of the constant parameters of the models for the steam generator PGV-1000 are calculated. The mathematical model of thermal processes in the PGV-1000 steam generator, which is presented in the form of a system of differential equations and includes the processes of heat transfer and steam generation, will make it possible to identify and optimize the steam generator control system with the help of information optimization technology.
 Keywords: nuclear power plant, steam generator, thermal processes, mathematical model, differential equations, optimization, control, information technology.

Mathematical model of thermal processes in metals during pulse processing with concentrated energy fluxes

The paper considers mathematical modeling of thermal processes in metals during pulsed processing by concentrated energy flows. Calculations of thermal processes in steels under pulsed heating are given, considering the phase transformations and the temperature dependences of the thermophysical properties, as well as the space-time characteristics of the thermal energy source. It is shown that the created mathematical model is universal for various sources of thermal energy and adequately describes the space-time distribution of temperature fields during pulsed heating of the surface layers of metals and alloys.

Совершенствование охлаждающих систем автотракторных двигателей и методов контроля их состояния

It has been established that the cooling system of modern tractors and trucks can include 5 to 7 independent cooling circuits. A structural diagram of a modular cooling system for automotive engines and a mathematical model of thermal processes in a heat exchanger of the modular cooling system during machine operation are proposed. It is shown that the development of an algorithm for predicting and monitoring the state of the modular cooling system is possible based on a quantitative relationship between the rate of decrease in heat dissipation capacity and the duration of machine operation.

Development of Siloxane Coating with Oxide Fillers for Kesteritic (CZTS) Photovoltaic Systems

Photovoltaic systems (PV) based on Cu2ZnSn(S, Se)4 (CZTS) solar cells have demonstrated efficiency and high performance. According to the results of comparative studies, the kesterite structure has proven to be ecologically safe and less expensive than other photovoltaic systems. The goal of the present study was to design a disposable high-temperature transparent electrical insulating coating to cover metal plates for photovoltaic devices based on CZTS. The solution was to replace electrically conductive metallics dispersed in a high-temperature siloxane coating with phonon thermal conductivity ceramic particles. Properties of the obtained coating were investigated using different methods. A mathematical model of thermal processes in the film during heating was also developed. For the control sample and the sample with a heat-conducting filler, a quantitative ratio of thermal conductivity was obtained. The research results confirmed the necessary properties of the coating, including resistance to short-term exposure to high temperatures during the synthesis of kesterite.

Mathematical modeling of thermal processes in building enclosures

In the development of automatic control systems (ACS) for heat supply of buildings, mathematical models of their control objects play a significant role, one of the most important elements of which being the enclosing structures. The existing models of thermal processes indoors either do not take into account the dynamic effect of the enclosing structures, or are complex analytical expressions, the use of which in the engineering practice of the synthesis of ACS for the indoor thermal regime is difficult. The purpose of the study was to create a linear mathematical model of the thermal interaction of the external and internal air environment through the enclosing structures. To achieve this goal, a functional diagram of a heated room as a control object was developed, which describes the mechanism of thermal interaction of its elements. On its basis, design schemes of thermal processes for external and internal enclosing structures were developed. They were used to create systems of equations linking temperatures on the surfaces of layers of external enclosing structures and air temperatures outside and inside the premises. At the same time, the assumption was introduced that the dynamic temperature distribution over the thickness of the enclosing structure is linear. To find the temperatures at the boundaries of the layers, the average temperature value over the thickness of the structure was used. As a result of the study, equations for the dynamics of heat transfer processes were obtained, and a generalized structure of a model of multilayer external enclosing structures of a room as an element of a control object was developed. The resulting model can be used to develop a generalized mathematical model of the thermal regime of both individual rooms and the building as a whole.

Mathematical model of heat transfer in the reactor of a biogas plant

The use of technical means for the production of biomethane, as a source of alternative energy, is mainly characterized by design and technological parameters, as well as operating modes of biogas plants. This study was carried out in order to obtain data on the main parameters of a biogas plant and the effect of a heat exchanger-mixer on performance indicators. The convenience of performing mathematical modeling is that it is expensive to carry out experiments on real objects, just as conducting experiments on a real installation is associated with high material costs, as well as high time costs, due to the high inertia of heat exchange processes, and the significant overall dimensions of the biogas plant. The results of mathematical modeling of thermal processes occurring in a biogas plant are presented. The data on the influence of the main parameters of the biogas plant and the heat exchanger-mixer on the quality indicators of its operation were obtained. It is shown that the theoretical temperature homogeneity of the mixed medium is achieved by combining the heat exchanger and the mixing device into one unit, the design and technological parameters characterizing the intensity of the forced movement of the fermented mass, with a change in thermal conductivity.

A Study of the Temperature Modes of the Automatic Switch Contacts in Cutoff of Short-Circuit Currents

This paper considers processes of electric arc damping by automatic switches in the short-circuit mode. Certain conditions for facilitating a successful short-circuit arc damping are shown, such as the limitation of the short-circuit current amplitude by its active resistance, the reduction of the phase shift between current and voltage, and the amplitude loss in returning and restoring voltages. The article features oscillograms of currents and voltages in the short-circuit mode. Anode heating processes are also described within the framework of the process of arc burning (heat saturation mode) and after the change of polarity current transition through zero processes at the cathode in the temperature equalization mode. Mathematical models of processes at the cathode took into account the thermal flows of the ionic component and evaporation. The calculations were carried out with the average values of thermal coefficients for copper, as the arc base moves from contacts to contact holders, which are made of copper and its alloys. The results of the calculations proved the validity of the considered mathematical models of thermal processes at both the cathode and the anode.

Mathematical modelling of thermal and electrical processes during electrosurgical resection of colorectal polyps

This paper is devoted to mathematical modelling of thermal processes in the polyp-colon system during electrosurgical polypectomy. This medical surgery (colonoscopy) is used to remove abnormal growths from the colon (the large intestine) in order to reduce the risk of the colon cancer development.In the electrosurgical polypectomy procedure, a polypectomy snare is passed over the polyp and tightened around the stalk of the polyp. Electric current is then passed for a few seconds through the snare loop to cut off the polyp stalk from the colon wall. The differential equations describing the processes occurring during polypectomy have been proposed. Also, examples of numerical calculations have been presented. Simulation results depending on the geometry (size) of the polyp can be useful for the endoscopist to choice the optimal time and parametrics of the electric current flow by tissues during the endoscopy procedure.

Heat exchanger for neutron thermalization device in beam research vessel reactor

The paper presents a neutron thermalization unit, “a source of ultracold neutrons”, designed for basic research in a beam research hull reactor. For new-generation experiments in the fields of weak-interaction physics and astrophysics, statistical accuracy associated with high density of ultracold neutrons is necessary. To achieve high density for helium-4 in the source chamber, which is used as a converter of cold neutrons into the ultracold ones, it should be at the temperature of about 1 K. In case of applying vacuum pumping of helium-4 vapors in ultracold neutron sources, it has not yet succeeded to obtain a temperature below 1.4 K. To achieve lower temperatures, the required saturated vapor pressure should be less than 50 Pa, which is impossible due to hydraulic losses. It is proposed to use a heat exchanger where helium-4 will be cooled by helium-3. The reason is that the temperature of helium-3 is more efficiently maintained by vacuum pumping since its saturated vapor pressure is an order of magnitude higher than that of helium-4. However, between two heliums the temperature drop occurs due to Kapitsa jump and thermal bridge between the helium capsule and heat exchanger. To solve this problem, we proposed optimization using numerical simulation on the basis of a mathematical model of thermal processes in a chamber with superfluid helium. The model takes into account the contact thermal resistance of Khalatnikov acoustic mismatch model with a correction coefficient. An example of such optimization is presented for the ultracold neutron source located in Gatchina. The mathematical model was implemented in the general solver based on the finite element method. A heat exchanger design geometry was proposed with the temperature drop equal to 0.2 K; the temperature of helium-4 was achieved by vacuum pumping of helium-3 vapors at the pressure of 850 Pa. The temperature fall from 1.4 K to 1 K will increase the density of ultracold neutrons by almost an order of magnitude, and increase statistical accuracy of experiments with ultracold neutrons carried out in a non-beam research reactor.