Вісники та науково-технічні збірники, журнали
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Item A brief overview of stationary two-dimensional thermoelastic state models in homogeneous and piecewise-homogeneous bodies with cracks(Видавництво Львівської політехніки, 2023-02-28) Zelenyak, Volodymyr; Kolyasa, Liubov; Klapchuk, Myroslava; Lviv Polytechnic National UniversityPurpose. A two-dimensional mathematical model of the problem of thermo-elasticity for piecewise-homogeneous component plate containing a crack has been built. The stress intensity coefficients in the vertices of the crack increase affecting strength of the body significantly. This leads to the growth of a crack and, as a result, to further local destruction of a material. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of engineering structures with cracks. Methodology. Based on the method of the function of a complex variable we have studied the two-dimensional thermoelastic state for the body with crack as stress concentrators. As result, the problem of thermoelasticity was reduced to a system of two singular integral equations (SIE) of the first and second kind, a numerical solution of which was found by the method of mechanical quadratures. Findings. The two-dimensional mathematical model of the thermoelastic state has been built in order to determine the stress intensity factors at the top of the crack and inclusion. The systems of singular integral equations of the first and second kinds of the specified problem on closed (contour of inclusion) and open (crack) contours are constructed. The influence of thermophysical and mechanical properties of inclusion on the SIF sat the crack types was investigated. The dependences of the stress intensity factor which characterizes the distribution of the intensity of stresses at the vertices of a crack have been built, as well as its elastic and thermoelastic characteristics of inclusion. This would make it possible to analyze the intensity of stresses in the neighborhoods of crack vertices depending on the geometrical and mechanical factors. As a result, this allows to determine the critical values of temperature in the three-component plate containing a crack in order to prevent the growth of the crack, as well as to prevent the local destruction of the body. It was found that the appropriate selection of mechanical and thermophysical characteristics of the components of a three-component plate containing a crack can be useful to achieve an improvement in body strength in terms of the mechanics of destruction by reducing stress intensity factors at the crack’s vertices. Originality. The solutions of the new two-dimensional problem of thermoelasticity for a specified region due to the action of constant temperature as well as due to local heating by a heat flux were obtained. The studied model is the generalization of the previous models to determine the two-dimensional thermoelastic state in a piecewise homogeneous plate weakened by internal cracks. Practical value. The practical application of this model is a more complete description of the stress-strain state in piecewise homogeneous structural elements with cracks operating under temperature loads. The results of numerical calculations obtained from the solution of systems of equations and presented in the form of graphs can be used in the design of rational modes of operation of structural elements. This takes into account the possibility of preventing the growth of cracks by the appropriate selection of composite components with appropriate mechanical characteristics.Item Modeling the influence of the shape of the local heat flow intensity distribution on the surface of a semi-infinite body on the stress state in the vicinity of a subsurface crack(Видавництво Львівської політехніки, 2023-02-28) Zelenyak, Volodymyr; Kolyasa, Liubov; Klapchuk, Myroslava; Lviv Polytechnic National UniversityA mathematical model to determine the two-dimensional thermoelastic state in a semi-infinite solid weakened by an internal crack under conditions of local heating is examined. Heat flux due to frictional heating on the local area of the body causes changes in temperature and stresses in the body, which significantly affects its strength, as it can lead to crack growth and local destruction. Therefore, the study of the problem of frictional heat is of practical interest. This paper proposes to investigate the stress-deformed state in the vicinity of the crack tip, depending on the crack placement. The methods for studying the two-dimensional thermoelastic state of a body with cracks as stress concentrators are based on the method of complex variable function. Reducing the problem of stationary heat conduction and thermoelasticity to singular integral equations (SIE) of the first kind, the numerical solution by the method of mechanical quadrature was obtained. In this paper, we present graphical dependencies of stress intensity factors (SIF) at the crack tip on the angle orientation of the crack as well as forms of the intensity distribution of the local heat flux. The obtained results will be used later to determine the critical value of the intensity of the local heat flux from equations of limit equilibrium at which crack growth and the local destruction of the body occur. The scientific novelty lies in the fact that the solutions to two-dimensional problems of heat conduction and thermoelasticity for a half-plane containing a crack due to local heating by a heat flux were obtained. This would make it possible to obtain a comparative analysis of the intensity of thermal stresses around the top of the crack, depending on the form of distribution of the intensity of the heat flow on the surface of the body. The practical value is the ability to extend our knowledge of the real situation in the thermoelastic elements of engineering structures with the crack that operate under conditions of heat stress (frictional heat) in various industries, particularly in mechanical engineering. The results of specific values of SIF at the crack tip in graphs may be useful in the development of sustainable modes of structural elements in terms of preventing the growth of cracks.Item Mathematical modeling of stationary thermoelastic state in a half plane containing an inclusion and a crack due to local heating by a heat flux(Видавництво Львівської політехніки, 2020-01-01) М, Зеленяк В.; Zelenyak, V. M.; Нацiональний унiверситет “Львiвська полiтехнiка”; Lviv Polytechnic National UniversityРозглянуто двовимiрнi стацiонарнi задачi теплопровiдностi та термопружностi для напiвнескiнченного пружного тiла, що мiстить включення та трiщину. Для цього побудовано математичнi моделi цих двовимiрних задач у виглядi системи сингулярних iнтегральних рiвнянь (СIР) першого та другого роду. Числовий розв’язок системи iнтегральних рiвнянь одержано методом механiчних квадратур у разi пружної пiвплощини, що локально нагрiвається тепловим потоком i мiстить кругове виключення та теплоiзольовану прямолiнiйну трiщину. Отримано графiчнi залежностi коефiцiєнтiв iнтенсивностi напружень (КIН), якi характеризують розподiл iнтенсивностi напруженнь у вершинах трiщини, залежно вiд пружних та термопружних характеристик включення та матрицi, вiд вiдносного положення трiщини та включення. Отриманi результати використанi для визначення критичних значень теплового потоку, за якого трiщина починає рости. Ця модель є розвитком вiдомих моделей двовимiрних стацiонарних задач теплопровiдностi та термопружностi для кусково-однорiдних тiл з трiщинами.Item Comparison of efficient of the combined solar collector for energy-efficient buldings for different modes of operation(Видавництво Львівської політехніки, 2016) Ulewicz, M.; Zhelykh, V.; Shapoval, S.; Spodyniuk, N.; Vengryn, I.On the whole, alternative energy should contribute to taking the two pressing problems of environmental safety and energy efficiency. Solar energy, as energy resources of the future, has a lot of benefits. It is mainly harmless to people and the environment. It does not distort the landscape. There is no point in exporting or importing it. As for the energy itself, it is both free and renewable, the latter benefit being the most important one. In work paid considerable attention to solar heating systems and proposed to use this solar heating system in energyefficient homes in Ukraine. This the primary solution may be used for decrease energy consumption of buildings. The overall effectiveness of solar installations is largely dependent on the level of solar energy, which in its turn is strongly dependent on the geographical position. Therefore, special attention is paid to the analysis of the heat flux, came onto the plane solar collector during the experiment, in consequence of changes in the intensity of solar radiation. In the work analysis the efficiency combined heating system in the conditions of southern orientation of the territory and the different modes. According to the study, the findings and recommendations of the use of combined solar heating at increasing the share of solar energy industry and efficiency of such systems in the overall energy balance of the country. Альтернативна енергетика покликана сприяти вирішенню передусім двох важливих проблем: екологічної безпеки та енергоефективності. Сонячна енергія як енергоресурс майбутнього має безліч переваг: вона не шкодить здоров’ю людей та довкіллю, не спотворює ландшафт, її не потрібно експортувати та імпортувати, сама енергія є безкоштовним ресурсом, а головною перевагою є те, що вона відновлювана. В праці приділено значну увагу системам сонячного теплопостачання та запропоновано застосовувати геліоустановки в енергоефективних будинках на території України, що може бути основним рішенням для зменшення енергоспоживання. На ефективність геліоустановок насамперед впливає рівень сонячної енергії, який, своєю чергою, залежить від географічного положення території. Тому особливу увагу звернено на аналіз кількості теплового потоку, що надходив на площину сонячного колектора протягом експерименту внаслідок зміни інтенсивності сонячного випромінювання. В праці проаналізовано ефективність використання комбінованої системи теплопостачання за умов південної орієнтації на території та за різних режимів роботи. За результатами дослідження сформульовано висновки та рекомендації застосування комбінованих систем сонячного теплопостачання, спрямовані на збільшення частки сонячної енергетики та ефективності таких систем у загальному енергобалансі країни.Item Моделювання процесів теплообміну в топках водотрубних котлів ДКВР(ДЕ)-10/14(Видавництво Львівської політехніки, 2016) Редько, А. О.; Давіденко, А. В.; Павловський, С. В.; Кулікова, Н. В.; Костюк, В. Є.; Кирилаш, О. І.Надано результати числового дослідження теплообміну в топці водотрубного котла ДКВР(ДЕ)-10/14. На основі креслень котла та пальника ГМГ-7 побудовано геометричну модель внутрішньої порожнини топки і пальника. Математичну модель радіаційно-конвективного теплообміну в газовому тракті котла сформовано на основі осереднених за Рейнольдсом рівнянь Нав’є – Стокса з урахуванням гравітації та з нехтуванням стисливістю. Модель складають рівняння нерозривності, перенесення імпульсу, енергії та хімічних компонентів газової суміші, записані у стаціонарній формі. Рівняння замкнено законом Ньютона для тензора тиску, законом Фур’є для теплового потоку, законом Фіка для потоку маси, законом Клайперона – Менделєєва для термодинамічного стану суміші газів, рівняннями моделі турбулентності k-ε Лаундера – Сполдінга та моделі турбулентного горіння Магнусена – Хертагера. Наведено результати числового моделювання у вигляді розподілу температури газового потоку в характерних перерізах проточної частини котла та розподілу питомих потоків теплоти на поверхнях екранів. Визначено структуру факелу та зону з максимальною температурою та тепловиділенням. Розрахунки також виконано для топки з тупиковим трубчастим вторинним випромінювачем. Показано, що густина радіаційного теплового потоку збільшується на 15–20 %, температура топкових газів на виході з топки знижується та становить 970 °С. Тhe results of a numerical study of heat transfer in water-tube boiler DKVR(DE)-10/14 furnace are provided. The geometric model of the inner cavity of furnaces and burners is constructed with help of boiler and burner GMG-7 drawings. The mathematical model of radiate and convective heat transfer with gravity in the gas path of the boiler on the basis of the Reynolds averaged incompressible Navier – Stokes equations is formed. The model incorporate continuity, momentum, energy and chemical components transfer equations of the gas mixture stored in a stationary manner. Model equations are locked by Newton’s law for a tensor pressure, Fourier law for heat flow, Fick law for mass flow, the Clapeyron law for the thermodynamic state of a gas mixture, k-ε Launder and Spalding turbulence model and Magnussen and Hjertager turbulent combustion model. Such results of numerical simulations as the gas flow temperature distribution in the boiler specific sections and the surface specific heat fluxe distribution on the furnace walls are presented. Determined the structure of the torch and the zone with the maximum temperature and heat. The calculations are also performed for the furnace to a dead-end tubular secondary emitter. It is shown that radiation heat flux density is increased by 15–20%, the flue gas temperature is reduced to 970°C.Item Методика визначення тепловтрат будинку за результатами тепловізійного дослідження(Видавництво Львівської політехніки, 2015) Дзіковська, Юлія; Гоц, НаталіяПроаналізовано методики розрахунку тепловтрат будинку, виявлено їх особливості та недоліки. Розроблено методику проведення розрахунку теплових втрат поверхні огороджувальних конструкцій будинку за результатами тепловізійного дослідження залежно від опору теплопередачі та градієнта температури базової й дефектної ділянок. Проанализированы действующие методики расчета теплопотерь здания, выявлены их особенности и недостатки. Разработана методика проведения расчета тепловых потерь поверхности ограждающих конструкций здания по результатам тепловизионного исследования в зависимости от сопротивления теплопередаче и градиента температуры базового и дефектного участков. The application of infrared thermography as a method of estimation of heat losses of building structures is becoming more popular within the resolve the issues of power resources economy, determination of energy efficiency and increasing of buildings thermal protection. It should be remembered that the output result of buildings thermal imaging research is thermal temperature distribution of the investigated surface on the thermogram. Other information, including the value of the heat losses from the surface of the building envelopes, is gotten by analytical method, which involves the construction of certain algorithm. As the results of the review of recent researches and publications we can conclude that the usage of thermal imaging research is mainly limited by finding places with thermal field deviations from basic values and recognition that they are defective. Quantitative processing of heat losses that are related with it is missing out. Therefore, in the article the brief overview of current methods of heat losses calculation is provided, their features and weaknesses are identified and the method of calculating of heat losses of the building envelopes surface, that is based on the results of thermal imaging research depending on resistance of the thermal transmittance and temperature gradient of the basic and defect areas, is developed. Methods, that are provided by acting normative documents of Ukraine, optimally satisfy the conditions of complex heat exchange because they take into account within the usage of the resulted and subjunctive thermal transmittance coefficients all three types of heat exchange, namely conductivity (through heat conductivity of material), convection (through heat transmission) and radiation (through heat emission). Thus, if we can find all unknown values in the methods formulas such algorithms give us possibility to determine the basic value of building envelope heat losses for a specific rooms and building in general. The negative aspect of the usage of these algorithms is proximity of calculation (for example, as a result of surface heterogeneity of the building envelopes) and the reference to table values of most variables, which can significantly vary from the actual values as a result of the building exploitation, the influence of climatic conditions, the repairs etc. In addition, the awkwardness of the calculations and the need of the simultaneous availability of a large number of normative documents increase the time that is required to their realization, respectively the cost of such work, as well as the growth of subjective component of calculations error. Therefore we propose to add to the normative methods method of heat losses calculation of building that is based on the results of thermal imaging research. The first algorithm involves the determining of the value of resulted resistance of thermal transmittance of defective area using its basic value from formula of the surface temperature distribution of the building envelopes. The second algorithm allows to determining the growth of heat losses compared to its value of the basic area using the identified quantity of the relative resistance of thermal transmittance. The disadvantage of these two algorithms is that to calculate the heat losses we must have information about the structure of the building envelope (its basic area) to determine the resulted resistance of the thermal transmittance of the construction. The effectiveness of these two algorithms is justified in the case of simulation of potential thermal characteristics of the building on the results of the implementation of the recommendations for building thermomodernization, when the resulted resistance of building thermal transmittance is predetermined. The third algorithm allows to consider that in practice in real conditions operators have to work with the buildings of long time exploitation, for which its thermal characteristics are changed due to influence of various factors or data of these characteristics are absent. In this case, in calculating of heat losses we have to be limited only by the data of thermogram and the results of accounting of the research conditions to determine the resulted resistances of basic and defective areas. For this we provide the creation of the system of two equations based on the formula of surface temperature distribution of the building envelopes. Creation of such system is possible in three variants. Selection of each of them depends on the thermograms information of building and the possibility of second thermal imaging research, because each of the options makes its own budget of uncertainty in the resulting value of the resulted resistance of thermal transmittance. The following algorithm for determination of the heat losses suggests their definition only in the radiative component of heat flux. It allows to limit the minimum number of input variables, whose values are provided exclusively by thermal imager and technical documentation on it. It should be remembered that such losses are always smaller than losses that are determined by the total heat flux. On the basis of the calculation of building heat losses increase their monetary evaluation is conducted. It helps to estimate the recoupment of work to eliminate the sources of such heat losses.