Stationary Temperature Field Research Articles

Research of thermal performance properties of the wall construction products made of materials using heat power engineering waste

A technology for the utilization of technogenic waste from the oil and gas industrial complex (sulfur) and ash and slag waste from the combined heat and power plant for the manufacture of thermal insulation material with high strength and performance properties has been developed. A technological scheme is proposed. The optimal parameters and composition of the obtained thermal insulation materials have been determined. A numerical method for determining the thermal conductivity coefficient of a building product based on the calculation of a stationary temperature field is considered. The dependence of the thermal conductivity coefficient of a block on the value of the thermal conductivity coefficients of the base material and filler is obtained. The efficiency of block insulation has been determined. This method can be used at the design stage of wall products, varying their overall dimensions, the geometry of the slots and also using various thermal insulating materials as a void filler.

Numerical simulation on velocity and temperature of a slotted swirl combustor

Cyclone combustion chamber has the advantages of compact structure, short flame length, good combustion stability, high combustion efficiency and low emissions of pollutants, etc. As one of the key components of the cyclone combustion chamber, the cyclone has a direct impact on the working performance of the combustion chamber. In this paper, we propose a slotted swirler and describe its structure in detail. We simulate the cold state flow field and the hot state temperature field in the combustion chamber of a cyclone with open seam using the CFD method, taking into account the effect of open seam on the air flow field and temperature distribution after the cyclone at different angles. The simulation shows that the temperature distribution in the slotted swirl combustor exhibited a center-focused flame of higher temperature, compared with the non-slotted swirler, the slotted swirler exhibits certain advantages in terms of drag reduction, combustion stability and combustion efficiency, which has a certain guiding effect on the improvement of the working performance of the combustion chamber.

MODELING THE PROCESS OF OPERATION OF HIGH-SPEED EQUIPMENT AND THE INFLUENCE OF THERMAL PARAMETERS ON WORKING BODIES

Introduction. The article is devoted to the study of heat transfer processes occurring in space and time. Therefore, the study of thermal conductivity is reduced to the study of space-time temperature changes. Distinguish between stationary and non-stationary temperature fields. A non-stationary temperature field is a field whose temperature changes not only in space, but also over time. A stationary temperature field is a field whose temperature at any point does not change over time. Materials and methods. To solve problems associated with finding the temperature field, it is necessary to have a differential equation of thermal conductivity, which gives the relationship between temperature, time and coordinates of the elementary volume. The differential heat conduction equation describes the transfer of heat inside the body. In order to find the temperature field inside the body at any moment of time, that is, to solve the differential equation, it is necessary to know the geometric shape of the body and the boundary conditions. Boundary conditions consist of initial and boundary conditions. Research results. As a result of modeling the process of upsetting during stage-by-stage deformation, including 30 steps at each impact (total of 3 impacts) using the QForm-2D software package, maps of stress and strain distribution over the volume of the workpiece were obtained. Discussion and conclusions. The main process parameters influencing the nature of the technological force are the accumulated deformation and the resistance of the material to plastic deformation. From the analysis of the obtained pictures of the distribution of deformation over the cross section of the sample after upsetting, that under the accepted conditions it is uneven. The greatest accumulated deformation is observed in the center and in the peripheral layers on the contact surface, and in other areas its value is less than 0.1. The same unevenness is shown by the stress distribution pattern. This is explained by the fact that with an increase in the degree of deformation, the rate of heat release decreases in the same zones where the maximum accumulated deformation is concentrated.

HEAT TRANSFER INVESTIGATION FOR A MULTILAYER INSULATION SYSTEM VIA RADIATIVE-CONDUCTIVE APPROACH UNDER LOW TEMPERATURE CONDITIONS IN SPACE

Thermal insulation is an important area, not restricted to mechanical engineering, but widely studied in environmentalissues, such as global warming and, above all, energy-saving, since controlling the heat flux on microprocessorsthrough temperature control on components in space applications. This work focuses on controlling the temperature incomponents that could not lose or gain so much heat in space, especiallywhen the overall safety of sending satellites onspecific missions is required. To ensure that, Multilayer Insulation (MLI) is used. With fluid mechanics and radiation-conductionheat transfer theory, it was possible to calculate the transient and stationary temperature field and heat flux inMLI. The boundary temperatures are specified at 300K and 4K. The results, from solving the resulting discretized ODE,simulated with fsolve and odeintScipy subroutines in Python, able to solve the equations numerically, were shown. Thedata given by the simulation was able to indicate the impacts of varying the layer density, emissivity of screen, the distancebetween screens and the perforation coefficient in stationary and transient approaches. A way to simulate the performanceof MLI numerically was presented. Modifying emissivity (e) showed variations higher than in the perforation coefficient(ξ). Layer density controls the distance between layers (d ), changing the conduction heat transfer. In the transient casesimulation, it was possible to notice that varying parameters impact in time to reach steady-state and final temperature.

Steady-state temperature distribution under near-field radiative heat transfer inside a linear chain of polaritonic nanoparticles

Thermal transport mediated by near-field interactions is superdiffusive in an ordered network of nanoparticles, such as linear chains. Based on such nanostructures, here we study a classical thermal-nonequilibrium problem, that is, the steady-state temperature distribution inside the chain of equally spaced polaritonic nanoparticles. The existence of the linear temperature profile and anomalous temperature variations in the inner region and near the boundary of a dense chain embedded in vacuum, respectively, is demonstrated by analyzing the effective radiative thermal conductivity within the system. Such temperature distributions are closely relevant to the strength of propagating surface modes sensitive to the chain density and dielectric material. We also demonstrate that, the presence of a homogeneous nonabsorbing background medium renders the steady-state temperature profile of the dense chain nonlinear, as well as enhancing drastically the long-distance heat exchange by two orders of magnitude relative to the vacuum case. This enhancement is a result of the high density of propagating waves in the medium, and is further confirmed by analyzing the energy density distribution over the chain. Furthermore, in a complex system consisting of many parallel chains, we show that, in steady state, temperatures of the thermal drive chain are allowed to tailor by its neighboring chains due to many-body interactions. This work opens ways to qualitatively assess and manipulate the stationary temperature field in advanced nanostructures, such as topological plasmonic chains and nanoparticle arrays.

Rheological Aspects of Multilayered Thick-Wall Polymeric Pipes under the Influence of Internal Pressure

Rheologic of a polymer pipe from cyclic temperature and internal pressure in one-dimensional and two-dimensional formulations is considered. The resulting equations of the finite element method allow one to calculate both single-layer and multilayer thick-walled pipes taking into account creep. In the calculation, the temperature dependences of the elastic and rheological parameters of polymer pipes were used. The effect of variable thermal conditions on the VAT of a PVC pipe is investigated. It has been established that under unsteady thermal conditions, stresses can occur significantly higher than in a stationary temperature field. This is explained by the fact that polymers have a component of deformation that is lagging in phase from stresses (highly elastic deformation).

Chaotic dynamics of size‐dependent curvilinear Euler–Bernoulli beam resonators (MEMS) in a stationary thermal field

AbstractIn this work the chaotic dynamics of flexible curvilinear Euler–Bernoulli micro‐beams embedded into a stationary temperature field is investigated. The temperature field is modelled based on a the Duhamel–Neumann theory and is free from the restrictions on the temperature field distribution along beam thickness. The von Kármán geometric strain–stress relations are employed. The governing nonlinear PDEs are yielded by the Hamilton principle with an account of the modified couple stress theory. The finite dimension problem is truncated to a finite system of nonlinear ODEs using the finite difference method (FDM) and then the Cauchy problem is solved with a help of the Runge–Kutta method. Action of the 2D thermal field is defined by solution to the heat transfer PDE which is also solved by FDM of the second order of accuracy. The so‐called charts of vibration regimes (amplitude‐frequency planes) are constructed. In particular, novel features of nonlinear (chaotic) dynamics versus the change of the magnitude of the size (length) dependent parameter are reported.The carried out numerical analysis is supported by the monitoring of frequency power spectra based on the fast Fourier transform (FFT), phase space projections, Poincaré maps and LLEs (largest Lyapunov exponents). We have also analyzed system chaotic dynamics of the classical and size‐dependent beam models versus series of values of the two control parameters, i.e. beam curvature and its size‐dependent length. Moreover, we have detected and illustrated the novel scenarios of transition form regular to chaotic vibrations of the studied beams, governed by non‐linear PDEs.

CONCEPTION QUASIDERIVATIVES IN THE PROBLEMS OF MATHEMATICAL MODELING OF HEAT TRANSFER

In this paper, in closed form, the problems of determining stationary temperature fields in multilayer (flat, cylindrical and spherical) structures in the presence of discrete-continuous internal and point heat sources are solved. The one-dimensional differential equation of thermal conductivity in different coordinate systems is given through one parametric family of quasi-differential equations. It is assumed that the coefficients of the differential equation of thermal conductivity are piecewise constant functions. A system of two linearly independent boundary conditions is added to the equation, which in the general case are nonlocal. The solutions of such problems are constructive and are expressed exclusively through their initial data. The basic provisions of the concept of quasi-derivatives, the provisions of the theory of heat transfer, the theory of generalized systems of linear differential equations, elements of the theory of generalized functions are used. For the mathematical model of stationary thermal conductivity, the practical use of the concept of quasi-derivatives is illustrated, for the efficient construction, in a closed form, of solutions of boundary value problems with the most general boundary conditions. As an example, the problem of finding the critical radii of thermal insulation of multilayer hollow cylinders and spheres, taking into account the internal heat sources in the layers. Boundary conditions of the first and third kind. It is established that the value of the critical radius does not depend on the number of layers and the intensity of internal heat sources, but only on the thermal conductivity of the outer layer of the structure and the heat transfer coefficient between the structure and the environment. The formula for determining the critical radius of thermal insulation for a multilayer cylindrical and spherical structure is derived. The methods developed in this work have the prospect of further development and can be used in engineering calculations.

Nanobeam Theory Taking Into Account Physical Nonlinearity

In this paper, we construct a new theory of nanobeams taking into account the dependence of the material properties on the stress state. The theory is based on the Euler–Bernoulli kinematic model in the first approximation. The beam material is isotropic but heterogeneous. For the first time, the physical nonlinearity and the dependence of the material properties on the temperature are taken into account in the study of nanobeams, and the theory is developed for arbitrary materials. It is based on the theory of small elasticplastic strains and on the the modified torque theory of elasticity. The stationary temperature field is determined by solving the three-dimensional Poisson equation with boundary conditions of orders 1–3. The initial equations are derived from the Hamilton–Ostrogradskii principle. The desired system of partial differential equations is reduced to the Cauchy problem by the finite difference method of the second order of accuracy, and the Cauchy problem is solved by the Runge–Kutta or Newmark method. At each time step, an iterative procedure is developed by the Birger method of variable elasticity parameters. The stationary solution follows from the dynamic solution of the problem obtained by the method of determination (the method of the parameter position). The convergence of the solution is investigated depending on the number of points of partition along the length and thickness of the beam in the finite difference method as well as on the method of solving the Cauchy problem and the size-dependent parameter, i.e., the solution of the problem is considered to have almost infinite number of degrees of freedom. Numerical examples are given for a beam rigidly clamped at the ends with the stress-strain diagram for aluminum. Accounting for the size-dependent parameter in the nanobeam theory significantly affects the load-carrying capacity of nanobeams.

Heat transfer analysis of an air-cooled turbine generator Stator under ground-wall insulation multi-direction shelling

Insulation aging in large generators is one of critical fault sources for machines. About 1/3 of generator faults are caused by critical temperature under stator winding insulation faults, especially stator ground-wall insulation shelling fault. To determine stator ground-wall insulation aging mechanism under influences of electric-thermal-mechanical stresses, the 3-D temperature field mathematic models considering different stator ground-wall insulation shellings are established. Based on calculated additional copper losses, turbulent movement in the ventilation ducts and boundary conditions of the model, stator temperature field in the generator normal operating is calculated via finite volume method (FVM). The obtained results are compared with the measurements to verify the accuracy of the calculation method. Then, the stator temperature field considering ground-wall insulation non-transfixion shelling, 1/4 lamination stacking in axial direction and 0.5 mm in circular direction, is calculated. Next, stator temperature fields under multiple ground-wall insulation shelling faults are also investigated. Moreover, the heat transfer laws within the stator components such as strands, ground-wall insulation both in shelling side and non-shelling side, row insulation, and air in the shelling gap, etc., are analyzed. The comparative analysis on the heat transfer laws under different shellings are addressed to provide practical reference in insulation failure diagnosis.

Analysis of Dynamical Heat Conductivity of the Reservoir and Fluid Evacuation Zone on the Gas Condensate Well Flow Rate

This study shows that the thermal conductivity of the rock borehole adjacent to the wells varies depending on the operation of the well. This is due to the fact that the actual temperature and temperature difference affect the humidity and other thermal properties of the rocks, which in turn affect the heat transfer coefficient across the section between the moving gas and the rocks. The static temperature field of primitive geothermal gradients acquires changes in a dynamic form. Theoretical consideration of changes in the thermal conductivity of rocks near the face and the wells is proposed to improve the prediction of gas condensate wells production. The result is achieved by introducing the specified equations of the thermal energy balance in the radial filtration and lifting of well products, which contain the coefficients of heat exchange and throttling. The refinement bias estimation of the 10%–15% level of gas condensate well extraction is shown using proposed methodological approach to relatively well-known (traditional in the field development practice) methods for estimating the extraction of a “medium well” from a particular oil and gas field evaluation. The results of this work demonstrate important scientific, applied, educational and methodological significance of using the methodology presented by the authors.

On the Application of Endoscopic Background-Oriented Schlieren Technique for Near-Field Investigation of Density Field

Background-Oriented Schlieren (BOS) is a non-intrusive and non-destructive technique for measuring density gradient in transparent media. Given the dependency of the refractive index and density of a medium, its static density field can be determined as a secondary measurand from BOS measurements. For an ideal gas, if the pressure variation is negligible, the static temperature field can be determined as a tertiary measurand. While the BOS technique for far-field measurements has been extensively researched, the implementation of this technique for near-field measurements still needs to be investigated. Near-field BOS is especially important for the measurement and visualization of internal flows, such as turbomachine flows, in which access to flow passage is limited and might be feasible using endoscopes (borescopes). This paper presents the features and challenges of the endoscopic BOS technique and presents methods and solutions for the application of this method in near-field measurements. The features of endoscopic BOS records as well as the comparison of endoscopic BOS and BOS measurements with camera are presented.

Modeling the influence of variable temperature fields on the stressed state of offshore facilities

The article considers the influence of temperature fields on the stress state of offshore facilities using the example of fixed offshore platforms for oil and gas production. It is noted that there is no theory for offshore oil and gas facilities that would allow a numerical description of the nature and mechanism of action of both conventionally stationary and variable temperature fields. An analysis of various literature sources showed that currently there are solutions for the dynamics of propagation and stress state for an axisymmetric temperature field, for a non-axisymmetric case, characteristic of the operating conditions of the support blocks of offshore platforms, there is no such solution. The author notes that a change in the thermal state of the elements of offshore facilities as a result of various factors leads to a change in their stress state. In some cases, in the presence of significant defects, these defects act as stress concentrators, thereby increasing the nominal strain. A numerical-analytical modeling of the effects of both variable and conditionally stationary fields was carried out, which made it possible to identify a number of patterns.

ЗАДАЧА ТЕРМОПРУЖНОСТІ ДЛЯ КОМПОЗИТНОГО БРУСА ІЗ ПЛОСКОЮ ВІССЮ ДОВІЛЬНОЇ ФОРМИ У ПРИРОДНІЙ СИСТЕМІ КООРДИНАТ

У роботі отримано скалярну форму рівняння теплопровідності, граничних умов різного типу та умов спряження фаз для зв’язаної динамічної задачі термопружного деформування композитного дискретно-неоднорідного бруса із криволінійною плоскою віссю та постійною по довжині структурною будовою. Рівняння та умови виведені у природній, для будови бруса, криволінійній циліндричній системі координат, що робить отримані залежності інваріантними до форми осі бруса. Отримані залежності можуть бути використані для розв’язання широкого кола прикладних задач термопружного деформування композитних стержньових елементів.

Experience in modeling a comfortable environment in the transport compartment

The theoretical base was developed and the mathematical model of dynamic thermal processes in a compartment of public transport was constructed. The software which is realized the constructed mathematical model was developed. The mathematical model provides for the possibility of taking into account the most possible environmental conditions which can have place in the actual operating conditions of a transport even the angle of illumination - the current temperature of the external environment, the presence of solar radiation taking into account the angle of sun’s illumination, and the temperature of the roadway. The software allows calculation and visualization non –stationary temperature fields in the public transport’s compartments using the example of a trolley bus. For a specific trolley bus design, a series of experiments to calculate the comfortable temperature for passengers were conducted, These experiments are showed the performance of the constructed model and allowed to formulate a specific proposal for improving the thermoregulation system of the trolleybus’ passenger compartment.

Определение профиля температурного поля материала, нагреваемого непрерывным лазерным излучением

Spectral pyrometry was used to determine the surface temperature distribution of Si, Nb, Cu, and graphite samples when they were locally heated by continuous radiation of an Nd:YAG laser (λ = 1.064 μm). With prolonged exposure to radiation, a stationary temperature field was established in the samples. The thermal spectra were recorded with a small spectrometer in the visible range in the temperature range above 850 K. The optical fiber used to transmit the radiation spectrum to the spectrometer had an additional diaphragm with a diameter of 1 mm located at a certain distance from the fiber end, which ensured the locality of the recorded spectra. The optical fiber moved continuously along the sample, and the spectrometer recorded up to 100 spectra with a frequency of 5-10 Hz. The temperature profile of the samples was calculated based on the results of processing the spectra using the Spectral Pyrometry program.

Effects of contact pressure and interface temperature on thermal contact resistance between 2Cr12NiMoWV/BH137 and γ-TiAl/2Cr12NiMoWV interfaces

Thermal contact resistance between interfaces is an important parameter in the analysis of temperature distribution for structural components. Thermal contact resistance between heat resistant steel 2Cr12NiMoWV/aluminum alloy BH137 interfaces and 2Cr12NiMoWV/titanium alloy ?-TiAl interfaces were experimentally investigated in the present paper. The effects of contact pressure and interface tem-perature were detailed. The temperature of contacting surfaces was from 80- 250?, and the contact pressure ranged from 2-17 MPa. All experiments were conducted in ambient atmosphere. Results showed that thermal contact resistance decreases with an increment of interface temperature or contact pressure. Under the same conditions of contact pressure and interface temperature, thermal contact resistance between 2Cr12NiMoWV and BH137 interfaces is lower than that between 2Cr12NiMoWV and ?-TiAl interfaces. The temperature dependence of thermal conductivity and mechanical properties was analyzed to explain the results. Furthermore, with the piston and piston pin as the research object, steady state temperature fields were simulated in cases of considering thermal contact resistance and without considering thermal contact resistance, respectively. The results showed that the maximum temperature of the piston pin will be lower when thermal contact resistance is considered.

SOLUTION OF THE PROBLEM OF THERMOELASTICITY FOR NONLINEAR ELASTIC INHOMOGENEOUS THICK-WALL CYLINDRICAL SHELL

The distinctive paper presents the calculation of a thick-walled cylindrical shell with hinged and free ends on the temperature effect. The shell consists of three layers: two layers of heat-resistant concrete and steel out­er layer. The calculation takes into account the piecewise linear inhomogeneity of the shell due to its three-layer construction and the continuous inhomogeneity caused by the action of a stationary temperature field. To take into account the nonlinear nature of concrete deformation, the problem was solved using the method of successive ap­proximations described in [1]. A comparative analysis of the results of the calculation of the shell with and without taking into account the continuous inhomogeneity and the nonlinear nature of the deformation of concrete is given. Comparison of the results showed a significant decrease in circumferential stresses in the most loaded concrete lay­ers when calculating the shell with regard to physical nonlinearity and heterogeneity of materials.

Solution of the axisymmetric problem of thermoelasticity of a radially inhomogeneous cylindrical shell by numerical-analytical method and the finite element method

The aim of research is to compare two calculation methods using the example of solving the axisymmetric thermoelasticity problem. Methods. The calculation of a thick-walled cylindrical shell on the temperature effect was carried out by the numerical-analytical method and the finite element method, implemented in the LIRA-CAD software package. The shell consists of three layers: two layers of heat-resistant concrete and an outer steel layer. In the calculation, a piecewise linear inhomogeneity of the shell due to its three-layer structure and continuous inhomogeneity caused by the influence of a stationary temperature field is taken into account. The numerical-analytical method of calculation involves the derivation of a resolving differential equation, which is solved by the sweep method, it is possible to take into account the nonlinear nature of the deformation of the material using the method of successive approximations. To solve this problem by the finite element method, a similar computational model of the shell was constructed in the LIRA-CAD software package. The solution of the problem of thermoelasticity for an infinite cylinder (under conditions of a plane deformed state) and for a cylinder of finite length with free ends is given. Results . Comparison of the calculation results is carried out according to the obtained values of ring stresses σθ.

The Effect of a Uniform Stationary Temperature Field on the Stress-Strain State of Elastomers under Static Large Deformations

The formulation of the problems of thermoelasticity is demonstrated, taking into account the nonlinear temperature dependence of thermal expansion at finite strains. In the framework of this formulation, a significant effect of the thermal expansion of elastomers on the stress-strain state is shown. As an example, the isothermal deformation of a round elastomeric cylindrical sleeve with the potential energy of the Mooney—Rivlin strain subjected to longitudinal shear forces on the inner and outer side surfaces is considered. Further, the deformed sleeve is placed in a uniform temperature field in which it expands freely.