Nonstationary Temperature Field Research Articles

Experimental observation of the maximum bubble diameter in non-stationary temperature field of subcooled boiling water flow

This paper presents results of the experimental study of the subcooled boiling flow on the surface of the vertical cylindrical steel heater. The initial stages of formation of the fully developed nucleate boiling were investigated over the unsteady stepwise heat flux range from 0.56 to 1.76 MW/m2. The field temperature of heated liquid layers at the moment of the bubble departure was described by numerical modeling under nonstationary conditions. A high-speed digital video camera was used to capture the bubble dynamics. The effects of heat release conditions and inlet water temperature on the bubble maximum diameter and nucleation frequency were studied. We found that the increased heat flux results in reduction of the maximum diameter at non-stationary heat release. Calculations on the basis of prediction models showed that the non-stationary nucleate boiling data cannot be generalized using the models developed by Prodanovic et al. (2002) and Song (2016) with the coefficients obtained for the stationary boiling. However, the heat balance approach to calculation of the bubble maximum diameter proved to be promising, and the correlation between the bubble diameter and the overheated layer thickness was verified.

Influence of the Friction Power on Temperature Stresses in the Course of One-Time Braking

We determine the space and time distributions of quasistatic temperature stresses in friction elements (pads and disks) in the course of one-time braking on the basis of known nonstationary temperature fields. The influence of three rational time profiles of the specific friction power on the stressed states of a pad (FM-16L retinax) and a cast-iron disk is analyzed. It is shown that tensile normal stresses are formed on the working surface of the disk at the end of the process of braking and may lead to the appearance of radial cracks on this surface.

Study of the influence of a fast­changing temperature on metrological characteristics of the tensoresistive pressure sensor

Based on dependences that describe the nonstationary temperature fields in the membrane and casing of the tensoresistive pressure sensor, we derived equations for thermomechanical processes in these elements, specifically equations of thermal deformation and thermal stresses. These equations make it possible to explore the effect of a thermal deflection in the membrane, as well as thermal stresses and thermal deformations in it, on the static and dynamic characteristics of the sensor. It is shown that the combination of thermal elastic processes in the membrane under a fast-changing effect of temperature on it significantly distorts the static and dynamic characteristics. It was established that during thermal deflection relative deformations on the surface of the membrane can be commensurate with the working deformations during pressure measurement, while a transitional characteristic of the sensor may differ from normal by up to 60 %. Our research shows that it is possible, when enabling radial thermal deformation, synchronized with the membrane of the sensor's casing, in the region of coupling with the membrane, to minimize thermal stresses in it. In addition, by minimizing the heat transfer along the perimeter of the sensor's membrane it is possible to eliminate the gradient of a temperature field along the radius. This is the way to minimize a thermal deflection of the membrane and decrease a temperature error of the sensor. Employing such measures may substantially reduce the influence of a fast-changing temperature on metrological characteristics of the sensor.

Mathematical modeling of temperature fields and concrete strength during winter concreting of building structures

In this paper we present a mathematical model of a three-dimensional non-stationary temperature field for concrete that hardens in winter conditions. The developed mathematical model describes heat transfer processes basing on the differential heat equation. We also consider the classical boundary conditions of the I, II, III and IV kinds. We compiled a computer interpolation of the family of nomograms in the second order regression equation in order to calculate the relative theoretical strength of concrete after heat treatment.

Research into non-stationary temperature field in the protected metallic structure under conditions of fire

We tackled a problem of research into temperature field that makes it possible to determine effectiveness of the fire-retardant coating applied onto wall. When stating the problem, we took into account a nonstandard temperature regime and conditions for a non-ideal thermal contact on the conjugating surfaces metallic wall ‒ flame-retardant coating. To solve a nonstationary heat conduction problem, the integral Laplace transform by time was employed. By using the devised mathematical model, we determined a non-stationary temperature field in the examined structure under condition of a non-ideal thermal contact. In the process of research, the time needed to reach a critical temperature was calculated, which is 45 minutes under condition that the value of the critical temperature on the unheated surface is 480 °C. Comparison of experimental data with the obtained numerical results showed that the difference is 9.7 %. The devised adequate and experimentally confirmed mathematical model makes it possible to determine effectiveness of a fire-retardant coating without conducting expensive experimental studies. In future, based on the results obtained, it is necessary to find new formulations for the fire-retardant coating that would enable increasing the time needed to reach the critical temperature for the structure metallic wall ‒ flame-retardant coating.

Simulating the Processes of Nonstationary Heat Conductivity in the Heat-Insulated Cylindrical Wall of a Boiler Drum

This scientific paper is devoted to the investigation of nonstationary axisymmetric heat conductivity in the cylindrical heat-insulated wall of a boiler drum. Consideration was given to the cases of an abrupt change in the temperature of internal surface of the boiler, temperature fluctuations on the internal drum surface near the prescribed average value and also an abrupt change in the temperature of internal drum surface with subsequent fluctuations near a new average value embracing typical states peculiar for the stationary and nostationary boiler operating modes. The investigations carried out showed that abrupt changes in the temperature of internal drum surface during some seconds may result in temperature fields, in which the temperature difference of internal and external surfaces is equal to a change in the temperature of internal surface. It takes the drum wall of 16 mm thick 30 seconds to align the temperature field after an abrupt increase in the temperature of internal surface. Harmonic temperature fluctuations on the internal surface create the temperature field in the drum wall with the temperature difference between the internal surface and the external surface a little bit higher then the half amplitude of vibrations in temperature. In the future, we plan to study mechanical stresses in the boiler drum wall caused by the internal pressure and nonstationary temperature fields considered in this scientific paper. In addition, we will study the influence produced by the temperature relationship for heat conductivity properties of the structural material on the nonuniform distribution of temperature field in the drum wall thickness.

Approximate Analytical Method for the Computation of Asymmetric Heating of the Infinite Plate

The fuel of a variable composition can change heat exchange conditions in the structure elements of heat power equipment. This can be manifested by energy accumulation effects and affect the equipment operation. Computational skills that enable the calculation of nonstationary temperature fields in structure elements are of great importance for the operation controllability. First of all, it concerns analytical computation methods. The purpose of this research was to develop the approximate analytical method for the computation of nonstationary temperature fields inside the infinite plate exposed to the asymmetrical heating, in particular at different heat emission coefficients on its sides, but the same ambient temperature. The solution is based on the use of the method of integral coefficients. It provides for the use of a priori information in the form of a selected profile of a change in temperature. The solution is done with the integral coefficient accuracy. Its value is defined by the comparison of obtained data and already available analytical, numerical and experimental data. As a result, we derived a simple analytical expression that enables the computation of a change in the temperature at different points on the plate. The accuracy of obtained data is comparable with the permissible accuracy of engineering computations. The obtained expression allows for the generalization of computation data due to a decrease in the number of independent variables. In the dimensionless form a modified number of homochronicity is used instead of generally used criteria Bi (Bio) and Fo (Fourier) number. Due to this fact just one curve (one independent variable) is used instead of the set of curves (two independent variables) to determine a relative temperature at some points.

Analysis of the Conditions for Determining the Thermal Diffusivity of Organic Liquids by the Laser Pulse Method

The conditions for conducting experiments to determine the thermal diffusivity of organic liquids by the laser pulse method are analyzed. Under the surface action of a thermal pulse of high power and short duration, the problem of a nonstationary temperature field of a three-layer sample is solved numerically. We establish limits on the range of possible changes in the flux density of the laser beam, which correspond to the conditions for the reliable calculation of the thermal diffusivity of a typical organic liquid, ethanol. The influence of the thickness of the liquid layer on the error of finding the thermal diffusivity is shown.

Application of the planar laser-induced fluorescence method to determine the temperature field ofwater droplets under intensive heating

Presented are results of experimental investigations concerned with formation of a nonstationary and essentially nonuniform temperature field of a water droplet (initial radius of 1 mm to 2 mm) under intensive heating in a flow of heated air (from 50◦C to 1000◦C). The method used for this purpose was a noncontact optical planar laser-induced fluorescence (PLIF) method. It is shown that temperature distribution in a water droplet is essentially inhomogeneous even under prolonged heating (to several tens of seconds). Reliability of the results of measurements by the noncontact PLIF method was analyzed by applying a group of fast miniature thermocouples. Restrictions of using the PLIF method for studying temperatures fields of evaporating droplets under high-temperature heating (over 800◦C) were marked out. Characteristic times of droplet existence (complete evaporation) were determined. It was analyzed how the temperature difference in a water droplet affects this parameter during heating and intensive phase transitions. It was substantiated that it is expedient to consider essentially inhomogeneous and nonstationary temperature field of a water droplet inmathematical modeling of the heat andmass transfer processes in high-temperature gas–vapor-droplet systems (corresponding, e.g., to burning or heat cleaning of liquids, firefighting, production of composite and gaseous fuels, their combustion, etc.).

Numerical modeling of physical fields in the process of drying of paper for corrugating by the infrared radiation

By using a numerical model, developed based on the proposed physical and mathematical models, we performed a numerical study of non-stationary temperature fields and moisture content of the process of infrared radiation drying of fluting. A distinctive feature of present study is a combined consideration of the kinetics of drying process, translucency to the IR radiation of the material using the approximations of the Burgers' models, gray medium and diffuse reflection of boundaries. Verification of the numerical model demonstrated a convergence of results of numerical modeling of the fluting surface temperature, duration and speed of its drying with the data of physical experiment within the range of 5 % on the interval of change in the square meter mass of dry fluting from 0.112 kg/m 2 to 0.2 kg/m 2 . It is substantiated that the developed numerical model makes it possible to define kinetic patterns and basic parameters required to intensify the process of drying and to design the appropriate equipment.

Laser effect on paralimbal and trabecular zones of the eye enchases hydraulic conductivity of the sclera toward normalization of the intraocular pressure

This paper presents the concepts and theoretical basics of the laser activation in drainage system function of eye sclera through laser effect on both paralimbal and trabecular zones including both known tracts of the intraocular fluid outflow from the eye. To address the problem of laser procedure security and consistency of obtained result, the development processes of stationary and non-stationary temperature fields and thermal stresses were studied and leading to increase in eye tissue hydraulic conductivity and providing normalization of intraocular pressure at wavelength of 1.56 µm and 534 nm.

Operator Method of Nonstationary Temperature Field Calculation in Environment With an Isolated Cylindrical Pipe

The following research is important for the understanding of thermal conductivity processes in the setting typical for thermal pumps and for bringing calculations nearer to the real situation. Considering a non-stationary process, the temperature field is described in the polar coordinate system by using Laplace’s equation and corresponding mixed-type boundary data. The solution was obtained by the Laplace transform method, applying an integral function of complex variables. The inverse Laplace transform and the original temperature are expressed as an integral. For the integration, a closed contour, which rules out branching and provides an integral of an analytic function, is employed. Cauchy’s theorem is applied to the calculations. As a result, indefinite integrals have been derived for temperature estimation in the heat pipe coating and the surrounding environment, depending on the fluid temperature within the heat pipe.

Use of the PLIF and LIP methods for definition of non-stationary temperature fields of water droplets

This study illustrates the results of experiments to determine the unsteady and non-uniform temperature fields of evaporating water droplets. It is shown that during the warming up of the droplet inside it an inhomogeneous temperature field is formed. In the droplet trace, formation of a region with lower (relative to the gas flow) temperatures of the vapor-gas mixture is observed. The experiments were carried out for droplets with initial radii of 1-2 mm. The speed of the air flow was 0.5-5 m/s. The temperatures of the gaseous medium varied in the range of 20-600 °C. During the research, modern panoramic methods of non-contact flow diagnostics such as “Planar Laser Induced Fluorescence” and “Laser Induced Phosphorescence” (LIP) were used.

Calculation of Concrete Strength in Winter Conditions Based on Heat Exchange Processes Modeling

The article deals with the problem of using a mathematical model of the three-dimensional non-stationary temperature field to calculate the strength of concrete, the hardening in winter conditions. There is data on the developed mathematical model describing the processes of heat exchange based on the differential equation of heat conduction. The boundary conditions of the III - kind: the heat exchange of a solid with the ambient air, and the IV - kind: the condition of the thermal junction of two solids have been modeled. The realization of the model with the numerical method of heat balances has been proposed. The analysis of advantages and disadvantages of the classical method based on the regular cooling has been conducted. The comparison of the data produced as a result of the calculation through the classical method and the data obtained by the calculation based on the mathematical modeling has been carried out. The conclusion on the effectiveness of using the mathematical modeling to predict the strength of concrete incubating in winter conditions has been made.

A thermal model of resistance spot welding

An analytical model of spot welding of flat components is proposed. An equation is derived for calculating the non-stationary temperature field in the three-dimensional expression. The main geometrical and thermal physical parameters of the welded components are taken into account. It is shown that when developing the welding conditions, it is necessary to take into account not only the type of welded material and the thickness of sheets components, but also the overall dimensions of the component and the spacing of the spot welds.

Nonstationary heat transfer in anisotropic half-space under the conditions of heat exchange with the environment having a specified temperature

An analytical solution to the problem of heating anisotropic half-space by the environment with a spatially and temporally variable temperature (boundary conditions of the third kind at an anisotropic body) has been obtained for the first time based on the construction of the boundary influence function (the Green’s function), which is determined using the Fourier and Laplace integral transforms. Nonstationary temperature fields in anisotropic blunt bodies have been found under the conditions of aero-gas-dynamic heating of hypersonic aircrafts with different heat-transfer coefficients and incoming-flow temperatures. The solution obtained is recommended for determining the state of thermal protection fabricated from composites which are generally anisotropic.

Semitheoretical three-zone model of circulation of liquid in agitated apparatuses

The structure of flows and velocity profiles of a liquid in the mechanically agitated apparatuses in developed turbulence modes have been analyzed. The procedure for calculating nonstationary temperature fields has been developed. The adequacy of the model has been validated on the prototype of the apparatus equipped with a standard three-wing stirrer. The application of the developed model to optimizing stirring has been illustrated.

A Simplified Method for Analytic Calculations of Nonstationary Temperature Fields in Problems Related to Heat Curing of Elastomer Coatings on Fabric Substrates

A Simplified Method for Analytic Calculations of Nonstationary Temperature Fields in Problems Related to Heat Curing of Elastomer Coatings on Fabric Substrates

Open-loop implementation of feedbacks in parametric optimization problems for incompletely determined systems with distributed parameters

A constructive method for the design and real-time implementation of parameterized open-loop controls in the optimal feedback control of ensembles of trajectories of incompletely determined parabolic systems with distributed parameters is proposed. This method uses reduction to semiinfinite optimization problems, alternance properties of their solutions, and additional information about fundamental laws of the application domain. The practical application of the results is illustrated by the example of controlling nonstationary temperature fields under multiple disturbances, which is a problem of independent interest.

Testing of bus bar contact under non stationary current impacts

This research paper is devoted to the analysis of non-stationary temperature field near plane bus bar contact. The possibilities of temperature and contact quality estimation by dynamic sensor on the accessible bus bar surface are showed. There is discussed the algorithm of temperature recognising directly on the contact surface. Numerical methods and analytical approaches are used.