Nonstationary Thermal Processes Research Articles

Model of the non-stationary thermal processes in the ground heat pump system

One of the main directions for improving heat supply systems is the tendency to switch to low-temperature heating systems by using heat pump units is the tendency of implementation the low-temperature heating systems based on the use of heat pump units. In the work, the main attention is focused on the improvement of thermal parameters and circuit design features of elements of the heat pump system of heat supply using soil energy. For this purpose, the toolkit of mathematical modelling of processes in ground heat pumps is applied, taking into account the climatic conditions of Ukraine. The paper proves the technical possibility of creating an autonomous system of alternative heat supply for energy-saving technologies with the possibility of using ground energy, taking into account environmental requirements. It is substantiated that the use of the proposed systems is a promising direction for Ukraine, which is experiencing a shortage of its own energy resources, because it provides an opportunity to increase the share of organic fuel substitution and reduce the volume of heat emissions into the environment. A mathematical model of heat processes in the elements of the heat exchange equipment of the heat pump system based on renewable energy (soil energy) and secondary energy (wastewater) was developed, taking into account environmental requirements (preventing hypothermia of the soil during the operation of soil pipes and damage to vegetation, respectively), which allows choosing a rational mode of operation of the system under seasonal climatic changes and technological conditions. Numerical modelling of heat processes in elements of the heat exchange equipment of the heat pump system using groundwater and waste water was performed, and the energy and environmental efficiency of the system under variable climatic and technological factors was determined. Analysis and generalization of the calculation results of the heat pump heat supply systems using alternative energy based on the proposed mathematical model, taking into account environmental requirements (preventing thermal relaxation of the soil) allows to take into account the change in the temperature gradient around the soil heat exchanger and more accurately determine the heat flow from each section of the heat exchanger. It has been established that for heat pumps with soil heat exchangers, the maximum substitution ratio of the traditional fuel is 75 %, and the economically feasible quantity of soil heat exchangers is 9 units. Heat pumps using waste water can completely replace traditional heat supply systems. For individual consumers, it is possible to recommend heat pump units with soil heat exchangers, at the same time, it is necessary to provide a backup source of energy to increase the reliability of heat supply.

Improvement of pinch technology for the possibility of integration of non-stationary thermal processes, taken into account of their localization

RELEVANCE. Designing a network of heat exchangers for heat recovery and integration of thermal processes in general is a very urgent task of energy saving. Such a powerful and widely used tool for the synthesis and design of a network of heat exchangers as pinch technology has a number of limitations, and this study is aimed at expanding its capabilities. Pinch technology can only work effectively with stationary heat flows. In practice, cyclic and periodic processes are encountered, which limits the possibilities of using pinch technology. This was the reason for this study with the aim of expanding the boundaries of application of pinch technology. THE PURPOSE. Improving the pinch technology method to expand the possibilities for integrating cyclic and periodic thermal processes, as well as taking into account their localization. METHODS. When solving the problem, the principle of determining heat exchange connections was analyzed, other algorithms for their selection were proposed, and new optimization criteria were synthesized. RESULTS. A criterion for the structural perfection of a system is proposed, which is the ratio of the heat regenerated in the system to its theoretically possible value. The theoretical results are the proposed criterion of structural perfection and a generalized indicator of the structural-parametric perfection of the system. The practical result of the study was the proposed technical device for converting an unsteady flow into a series of stationary flows. Also, the practical result of this scientific research is a program for the synthesis of heat exchange networks. The proposed conversion device expands the capabilities of pinch technology, and the introduced criteria will make it possible to synthesize or design a system based on new target indicators. The program created during the work allows for the synthesis of a heat exchange network in automatic and semi-automatic modes. CONCLUSION. Thanks to the research carried out, it was possible to improve such a powerful tool as pinch technology and significantly expand its capabilities. An improvement of pinch technology has been proposed to enable the integration of non-stationary thermal processes and take into account their localization. To enable the integration of non-stationary thermal processes, a technical device has been proposed that allows converting a non-stationary flow into several stationary ones, and to take into account the localization of heat flows, a software product has been proposed that allows for the synthesis of a heat exchange network in automatic and semi-automatic modes. In addition, two indicators have been introduced that characterize the structural and structural-parametric perfection of the system.

MATHEMATICAL MODELING OF NON-STATIONARY HEAT PROCESSES IN THE GROUND HEAT PUMP SYSTEM

In the work, an analytical study of the efficiency of heat pumps using soil energy for heating, taking into account the climatic conditions of theregion of operation, is performed, which meets the tasks of energy saving and allows reducing emissions of harmful substances into the environment. The main attention is paid to increasing the efficiency of utilization of the technical potential of the soil energy source by the heat pump system using vertical soil heat exchangers. A methodology based on use of the mathematical modeling apparatus as a scientifically based toolkit for calculating non-stationary thermal processes, capable of ensuring the stability and reliability of the ground heat pump system in the short and long term, is proposed. The developed toolkit for calculation and analysis of heat exchange processes allows determining the power of the heat flow, which is removed from the soil, taking into account changes in climatic factors, temperature distribution in the soil around the soil tube and along its length over time, schematic and structural features of the soil tubes for further optimization of the parameters of the heat pump system . It was established that the power of the heat flow, which enters the evaporator of the heat pump from vertical soil pipes, depends on a number of influencing factors: the flow regime of the working fluid circulating in the soil circuit; physical properties of the working body; number of soil heat exchangers; temperature distribution in the soil around the soil tube along its entire length, which changes significantly during long-term operation of the system, affecting the course of heat exchange processes in the system elements. The proposed method makes it possible to perform numerical modeling of thermal processes in the elements of the heat pump, to determine the energy efficiency of the ground heat pump system, which is able to reliably provide consumers with heat during a long period of operation, which can be considered an innovative approach to the analysis of prospects for the development of heat pump heat supply.

Influence of temperature and time modes of polymer pipes welding at low temperatures on the structure and properties of materials of compounds. Part I. Calculation of the heat process

Subject of research: thermal process of welding PE100 saddle branches to polyethylene pipes of existing gas pipelines at low temperatures.
 Purpose of research: development of an effective method for welding saddle branches to polyethylene pipes of gas pipelines at ambient temperatures up to minus 50 C based on thermal process control by introducing preheating into the technological process with subsequent cooling to equalize the temperature and cool the joint under a layer of thermal insulation material of calculated thickness.
 Methods and objects of research: in the first part of the work, the object of study is the non-stationary thermal process of welding. The mathematical model of the thermal process takes into account the heat of the phase transformation of polyethylene in the temperature range, the dependence of thermophysical characteristics on temperature and the degree of crystallinity of the material.
 Main results of research: calculations have determined the welding parameters of the saddle branch, which ensure the flow of the thermal process according to the regularity inherent in welding under conditions of permissible ambient temperature. It is expected that the control of the thermal process will make it possible to obtain a structure of the welded joint material that ensures the strength of the seam corresponding to the strength of the seam obtained by welding under conditions of acceptable temperatures.

ON SOLVABILITY OF THE BOUNDARY INVERSE PROBLEM FOR THE HEAT CONDUCTIVITY EQUATION

In applied problems related to the study of non-stationary thermal processes, quite often a situation arises when it is impossible to carry out direct measurements of the required physical quantity and its characteristics are restored from the results of indirect measurements. In this case, the only way to find the required values is related to the solution of the inverse problem of heat conduction with the initial data known only on a part of the boundary. Problems of this kind arise not only in the study of thermal processes, but also in the study of diffusion processes, the study of the properties of materials associated with thermal characteristics. The article is devoted to solving the boundary inverse problem for solving the heat equation.

Дослідження теплообміну в об’ємі двофазної рідини за умов вимушеної її конвекції

The expediency of using the methods of regular thermal regime under non-stationary thermal processes in the system "environment — solid (set of solids)" to determine the thermophysical parameters of solids and heat transfer intensity is known. The purpose of this study is to establish the possibility of the existence of a regular thermal regime during cooling (heating) of a two-phase liquid — supernatant in a thin-walled cylindrical vessel with forced convection. The heat exchange in the conditions of cooling (heating) of two - phase liquids at the forced convection for a possibility of realization of a regular thermal mode is investigated. It was determined that for the period of time under study, the ratio for excess temperature, which is characteristic of the regular thermal regime in solids, is maintained. The obtained experimental data establish the expediency of applying the theory of regular heat regime to determine the intensity of heat exchange to two-phase liquids during cooling (heating) under conditions of forced convection. The results of calculation of cooling rate (heating), heat transfer coefficients are presented. The existence of a regular thermal regime in a two-phase liquid has been established. Experimental and theoretical studies are conducted for the further development of the experimental calculation method, which is required in the study of heat transfer of media with unknown or partially known information on thermophysical properties and rheological behavior. The results of solving heat exchange problems in a limited volume are planned to be used in solving real technological problems.

Cluster mathematical model for conjugate thermal processes of the isothermal bodies system in the fluid flow

There has been developed a cluster mathematical modelling method for non-stationary thermal processes, occurring in complex technical system structures, which thermal models represent a system of clusters. Each cluster has a core, combining the heat-emitting elements that fall into the said cluster, a shell of the cluster, and a fluid, flowing through the cluster. The state of the thermal process in each cluster at any specific time is characterized by three state variables, namely, by the temperatures of the core, the temperatures of the shell and the ambient temperature. At that, the elements of each cluster (core, shell, fluid flow) exchange heat with each other and the elements of the adjacent clusters. As opposed to existing methods, the cluster method allows modelling thermal processes that occur in complex technical systems, taking into account non-uniform temperature distribution in the fluid flow, conjugate nature of heat transfer between the fluid flow, the cores and the shells of the clusters. The mathematical model, describing state variables of thermal processes in the cluster thermal model, represents a system of block matrix differential equations with matrix and vector blocks, corresponding to the respective clusters of the thermal model. The solution of equations of the mathematical model is the values of the state variables of the thermal processes in the clusters. The methodology of the application of the cluster method is shown on the example of a real technical system.

Influence of thermal insulation of the wall area of the floor on the ground on the heat loss amount

The relevance of the study is explained by the fact that in the Russian Federation, the “by zone” method of heat loss calculations of the floor on the ground does not allow considering various factors that affect heat losses. As the heat loss studying method, this work adopts the calculation of the non-stationary annual thermal regime of floors together with the soil mass. There is no such thermal protection indicator as the heat transfer resistance in a non-stationary thermal process, therefore the paper uses a characteristic, in other words, a conditionally reduced one for heat loss calculations through the floor on the ground in stationary thermal conditions. The purpose of this article is to calculate the average characteristic heat transfer resistances for each design zone for thermal protection of the wall area of the floor on the ground with different width of the insulation stripe and heat transfer insulation resistance. The considerable result of the work is detection of significant impact of the soil type, the width of the floor insulation stripe, and the actual resistance to heat transfer of this insulation on the characteristic heat transfer resistance in the first design zone. It follows from the study that the floor thermal insulation stripe in the wall area is the most effective structure of the floor thermal protection, both in terms of reducing heat losses, and in terms of compliance with the temperature standards for the floor.

Development of a Method for Monitoring the Process of Heating the Lining of High-Temperature Units

This article proposes a new method for monitoring the thermal state of the lining of hightemperature units. Firstly, it is shown that the main methods for monitoring the thermal state of the lining are limited to obtaining data to prevent an emergency situation – leakage of the working medium through the lining and does not allow to obtain data on the temperature distribution over the cross section of the lining, for monitoring nonstationary thermal processes. Secondly, a method for determining the thermal state of the lining of a thermal unit is proposed, which allows one to obtain data on the temperature fields of the lining in the process of nonstationary heat conduction and use these values to control the process. Thirdly, to test the developed method, a physical model of the process of heating the lining of a high-temperature unit was created. Fourth, testing the physical model of the heating process showed that the developed method can be applied in practice, since its error does not exceed 10%

Thermotechnical properties of the fire-extinguishing powder for extinguishing materials based on magnesium alloy chips

The article addresses the relevant issue of determining the thermotechnical characteristics of the fire-extinguishing powder for thermal insulation of the fire center of materials based on magnesium alloy chips to prevent fire development and propagation and its effective extinguishing. To solve this problem, laboratory and field experimental studies of the heat-insulating ability of the fire-extinguishing powder of combined effect were conducted. As a result, we obtained the data on the temperature in the center of the fire of materials based on magnesium alloy chips and outside during their suppressing by the fire-extinguishing powder with a combined effect. In this case, the temperature of the non-heated side of the fire-extinguishing powder layer does not exceed 170 °C at the average temperature of the fire center of 740 °C, which indicates high insulation capacity of the powder and, consequently, its high fire-fighting efficiency in extinguishing the fires of materials based on magnesium alloy chips. The obtained temperature data were used to determine the thermophysical parameters of the layer of the fire-fighting powder using the created mathematical model of the heat transfer process in the powder layer at the heat insulation of the fire center. To create a mathematical model of the heat transfer process, the main provisions during consecutive consideration of several experimental situations were stated. The first experimental situation meets the conditions of the stationary thermal process, and other experimental situations meet the conditions of the non-stationary thermal process. These experimental situations were created with the help of changing the thickness of the fire-fighting powder layer at different parameters of its feeding to the fire center. The mathematical model of the process is based on the use of the differential equation of heat transfer at its approximation by the method of finite differences. At the same time, it is believed that the heat transfer conditions at the boundary between the non-heated side of the insulating layer of the fire-extinguishing powder and the environment in each experimental situation are the same. Using the created model, the coefficient of heat transfer between the non-heated side of the insulating layer of the fire-extinguishing powder and the environment was determined. It amounted to 395.7 W(m 2 ×°С). The dependence of the effective thermal conductivity coefficient on the thickness of the insulating layer was explored. It was shown that this dependence can be approximated by linear dependence l(d)=–0.016+93.907×d (d is the thickness of the layer of the fire-extinguishing powder in meters). After conducting the necessary calculations, we obtained the value of the required thickness of the layer of fire-extinguishing powder d=45.2 mm

Методика идентификации нестационарных тепловых процессов в многослойных конструкциях

Методика идентификации нестационарных тепловых процессов в многослойных конструкциях

INVESTIGATION OF THE HEATING PROCESSES AND TEMPERATURE FIELD OF THE FREQUENCY-CONTROLLED ASYNCHRONOUS ENGINE BASED ON MATHEMATICAL MODELS

The study of the temperature field of the engine for non-stationary modes is done. A numerical simulation of a non-stationary thermal process using dynamic EHD, the characteristic of the rate of rise of temperatures is done. An increase in the temperature of individual parts in the idle interval, when the power of heat release is significantly reduced, is established, and the reverse of the heat flow through the air gap is established. It is shown that the EHD method, in contrast to the FEM, is self-sufficient, which determines its practical value. In various parts of the speed control range in the implementation of various laws of regulation. At the same time, the main electrical, magnetic and additional losses associated with the fundamental voltage harmonics (FVH), and mechanical losses, as well as additional electrical and magnetic losses associated with the higher voltage harmonics, change. When using serial asynchronous engines as frequency-controlled. Permissible under the conditions of heating power is significantly reduced by the power of serial engines. Depending on the synchronous speed, the reduction is from 10 % to 20 %. Given the additional overheating due to higher voltage harmonics, as well as the deterioration of the cooling conditions when adjusting the rotational speed "down" from the nominal, it seems very relevant.

HEAT FLUX IN A PASSIVE MULTI-LAYERED SOLAR PANEL

The paper deals with the question concerning the increase in buildings and structures energy efficiency and environmental safety at the construction and installation of engineering systems with financial constraints. We suggest solving this problem with low-cost method of solar radiation utilization which implies the passive thermal energy transformation into external fencing structures. In spite of the economic expedience of such heating systems, there is an opinion that they are suitable only for climatic conditions characterized by a mild heating period due to low efficiency indicators in comparison with the active solar power plant. As regards this, the paper analyzes the well-known and new building translucent, absorbing, accumulating and insulating materials along with the possibilities to create the multifunctional external fences that can expand the geography of the use of passive systems. We have studied the nonstationary thermal processes arising in multilayer external fences of buildings in order to solve the problems of effective solar radiation utilization by facade integrated panels. The analysis of mathematical methods has shown that theory of thermal waves should be used to describe the diurnal temperature changes inside building structures. The principle of temperature frequency superposition principle has made it possible to calculate the heat transfer in multilayer external panes. In Voronezh region climatic conditions (52º), we have evaluated the solar radiation effect on a two-layer and a four-layer structure consisting of a glass unit, an air layer, reinforced concrete and heater, protected from the outside by double-glass unit. In January at temperature -24 °C of the coldest fiveday period, the average daily heat losses through the surface area of 1 m2 of the two-layer outer wall are 6 W / m2 , and under the same weather conditions an average heat flux through the surface area of 1 m2 of the four-layer solar panel is of 36.3 W / m2 ; the maximum values of the heat flux are achieved in 18 hours. The presented data confirm the expedience of passive solar panels use in case of low temperatures during the cold period of a year. Moreover, considering the facade glazing trends and low cost of the passive solar panels in contrast with the active solar systems, we concluded that they should be used for increase in energy efficient of buildings.

Estimation of heat field and temperature models of errors in fiber-optic gyroscopes used in aerospace systems

Numerical-analytical models of the nonstationary thermal process and the associated with it measurement errors were designed and investigated for fiber-optic gyroscopes (FOG). The models were used for simulating output data of the measuring gyroscopic module (MGM) consisting of a FOG of the studied type at arbitrarily assigned operation temperature conditions. Numerical simulation of nonstationary thermal fields in the instruments at an arbitrarily varying ambient temperature was carried out. Taking into account the temperature values, magnitude of the instrumental measurement errors characteristic of the studied FOG type is predicted. Further, these errors are taken into account when simulating output of the MGM having characteristics similar to the characteristics of the real instrument. To confirm the thermal model veracity, comparison of the numerical modeling results with experimental data was made. Adequacy of the models of instrumental errors for the studied FOG type is ensured by the instrument pre-calibration. A procedure for calibrating models of MGM errors notable for the possibility of joint identification of all IEs using one redundant volume of measurements has been developed. Further evolvement of this procedure will enable refinement of configuration and layout of temperature sensors in the MGM in order to improve quality of the measurement error compensation in the subsequent operation of the instrument and improve the layout of the MGM electronic and structural components in terms of reducing influence of the perturbing thermal factors.

Optimal Control of Nonstationary Thermal Process with Axial Symmetry

Optimal Control of Nonstationary Thermal Process with Axial Symmetry

Analysis of Thermal Conditions within the Flow Conduits of MHD-Devices

The paper presents an experimental and theoretical approach to the modeling of non-stationary thermal processes in the elements of MHD-devices. The theoretical part of the approach is based on a mathematical formulation of the non-stationary heat conduction problem and its numerical implementation by the finite-element method. The experimental part involves a series of preliminary and verification tests. A comparison of the results obtained in these experiments with the calculated data allowed us to specify heat conduction coefficients and to pick up space-time parameters of the algorithm to ensure a high degree of adequacy of mathematical description of thermal fields. The approach made it possible to set the process conditions under which the necessary level of preliminary heating of a conduit of the MHD-pump can be achieved without loss of its mechanical strength.

Mathematical simulation of nonstationary thermal processes, the thermoelastic mode of deformation, and durability of a temperature probe under temperature shock

Interrelated mathematical models of nonstationary thermal processes, the thermoelastic mode of deformation, and durability of a temperature probe are constructed. The probe is used in space technologies and operates under temperature shock conditions. Algorithms and appropriate software are developed. They allow problems of computation and analysis of nonstationary temperature fields of the probe and its thermoelastic mode of deformation to be solved automatically during the design phase. Also, the durability of the probe in the case of sudden temperature differences can be estimated. Computer experiments are carried out; they confirm the efficiency of the mathematical, algorithmic, and software support. Quantitative estimations are obtained, and recommendations for ensuring the efficient functioning of the probe are developed.

Comparisons between molecular dynamics and hydrodynamics treatment of nonstationary thermal processes in a liquid

Molecular dynamics (MD) and Navier-Stokes hydrodynamics have been performed to model thermal relaxation processes arising from an initially established nonequilibrium stationary state. A nanoscale two-layer Lennard-Jones (LJ) liquid system was constructed in which the two parts were initially at a different temperature, with a narrow transitional zone between the two layers that was spatially linear in temperature. The highest-temperature layer had widths of five or 20 LJ particle diameters. The hydrodynamics model used parametrized MD-derived transport coefficients and the LJ equation of state as input functions. The temporal and spatial temperature and density profiles produced by the two methods show good agreement, indicating that a hydrodynamics description is reliable even for nonstationary phenomena down to the scale of a few molecular diameters. We found that at certain locations the Navier-Stokes solution predicted that the pressure and temperature profiles relaxed in a damped oscillatory manner, which we could discern despite the fluctuations in the MD data.

Thermal stability of high-temperature materials. Part 1

Theories of thermal stability for high-temperature materials based on the application of static thermoelasticity equations to nonstationary thermal processes are reviewed. A new criterion for thermal stability, R = ΔTd, is proposed. Anew model, based on the maximum stress theory and the quantum theory of thermal field, is proposed; in terms of this model, the stress-strain state of a solid subjected to thermal shock can be determined by solving equations of thermal strength and heat conduction with allowance made for inertial terms in thermal stability equations. Thermostability is considered as a physical parameter characterizing the resistance of materials to failure in a nonstationary temperature field.

The heat capacity of water ice in interstellar or interplanetary conditions

Three empirical equations are proposed to describe the existing experimental data on the heat capacity of water ice for . This may be important for the rate of non-stationary thermal processes at very low temperatures in cometary nuclei or cosmogonical scenarios.