Inhomogeneous Temperature Field Research Articles

Nonlinear flutter response of cylindrical shell in thermal field and supersonic gas flow

The work is devoted to the investigation of flutter oscillations and stability of closed cylindrical shell in supersonic gas flow and placed in an inhomogeneous temperature field. It is assumed that supersonic gas flows on the outside of the shell with an unperturbed velocity U, directed parallel to the cylinder generatrix. Under the action of an inhomogeneous temperature field, the shell bulges out; this deformed state is accepted as unperturbed, and the stability of this state is studied. The main nonlinear equations and relations describing the behavior of the examined system are derived. The formulated boundary value problem is solved using Galerkin method. The joint influence of the flow and the temperature field on the relation between the amplitude and frequency of nonlinear oscillations of a cylindrical shell is studied. The critical velocity values are calculated from the corresponding linear system and are given in tables. The numerical results show that: a) the surrounding flow significantly affects the nature of the investigated relation; b) it is impossible to excite steady-state flutter oscillations (the silence zone) up to a certain value of the oscillations frequency; c) the dependence of the amplitude on the oscillations frequency can be either multi-valued or single-valued.

Thermal Regulation of Space Platform Panels by Using Electric Heaters

In orbital flight, the temperature state of spacecraft and their constituent space platforms complexly changes in time and space. The inhomogeneous temperature field of the space platform can cause shape distortion, which negatively affects the performance of targets. To equalize the temperature field of the space platform, it is proposed to use electric heaters with differentiated power distributions. The formulation of the boundary inverse heat conduction problem is presented and the specific power of the heaters necessary for uniform distribution of the temperature field of a panel of composite material is determined.

Thermoelastic Response of Closed Cylindrical Shells in a Supersonic Gas Flow

The work is devoted to the investigation of flutter oscillations and the stability of the closed cylindrical shell in supersonic gas flow in an inhomogeneous temperature field. It is assumed that supersonic gas flows on the outside of the shell with an unperturbed velocity U, directed parallel to the cylinder generatrix. Under the action of an inhomogeneous temperature field the shell bulges out, this deformed state is accepted as unperturbed, and the stability of this state is studied. The main nonlinear equations and relationships describing the behavior of the examined system are derived. The formulated boundary value problem is solved using the Galerkin method. The joint influence of the flow and the temperature field on the relationship between the amplitude of nonlinear oscillations of a cylindrical shell and the speed of the flowing stream is studied. The critical velocity values are calculated from the corresponding linear system and are given in tables. The numerical results show that: (a) the surrounding flow significantly affects the nature of the investigated relationship; (b) a certain interval of supersonic velocity exists where it is impossible to excite steady-state flutter oscillations (the silence zone); (c) the dependence of amplitude on the supersonic velocity can be either multivalued or single-valued.

CFD MODELING OF HEAT TRANSFER AND HYDRODYNAMICS PROCESSES IN A HEAT STORAGE TANK

Background. Today, heat storage tanks are an integral part of heating systems. However, modern designs of capacitive storage tanks are characterized by the phenomenon of thermocline and high thermal inertia. To minimize the aforementioned disadvantages, it is proposed to use a “thermal core”, for the formation of which it is necessary to select a substance with a high value of heat capacity.Objective. The purpose of the presented study is to simulate the process of heat and mass transfer in a storage tank with a “thermal core”, in the form of the binary tube located on the central axis, the inter tube space of which is filled with paraffin (a mixture of saturated hydrocarbons with melting point – from 45 °C to 65 °C; dense – 0.880–0.915 g/cm3 at 15 °C).Methods. Fluent software determines the temperature distribution in the heat storage tank under free convection conditions. The resulting data were then converted into a calculation module of the Transient Thermal software complex ANSYS, where further calculations of the non-stationary temperature distribution of the “thermal core” were carried out.Results. It is determined that the heat storage tank with a capacity of 1400 liters, heated for one hour by a heat transfer agent with a temperature of 115 °C, is cooled to 50 °C in 4 hours. The analysis of the hydrodynamic structure of the flow based on the distribution of the trajectories of movement of free-convective flows in the water column of the storage tank indicates the need to improve the design of the tank. It is determined that the use of the “thermal core”, regardless of the type of paraffin used for its formation, helps to reduce the stratification of temperature by tank height. The type of paraffin used to form the “heat core” has no significant effect on the cooling time of the heat storage tank as a whole. However, when using “ceresin” as a filler for the “heat core”, the average tank temperature is generally about 0.5 °C higher than for other paraffin types studied. Thus, it is “ceresin” that should be used as a “thermal core”.Conclusions. The result of the calculation of the inhomogeneous temperature field of all elements of the heat storage tank was used to determine the time of its complete cooling. The conducted research allows automating the process of calculation of the storage tanks as well as carrying out their modernization to increase the efficiency of use.

An Unreasonable Universality of the Thermophoretic Velocity.

Thermophoresis is the migration of dispersed molecules or particles in an inhomogeneous temperature field. It has been associated with various nonequilibrium phenomena ranging from stratified oil reservoirs to prebiotic evolution and the origin of life. The thermophoretic velocity is difficult to predict and appears almost random. We show that, in the case of strongly asymmetric mixtures with high molecular mass ratios of the solute to the solvent, it unexpectedly assumes a universal value once the trivial influence of the viscosity has been factored out. This asymptotic behavior is surprisingly universal and a general property of many highly asymmetric molecular mixtures ranging from organic molecules in n-alkanes to dilute solutions of high polymers. A quantitative explanation is provided on the basis of the asymmetric limit of the pseudoisotopic Soret effect.

Development of a Continuous Pulsed Electric Field (PEF) Vortex-Flow Chamber for Improved Treatment Homogeneity Based on Hydrodynamic Optimization.

Pulsed electric fields (PEF) treatment is an effective process for preservation of liquid products in food and biotechnology at reduced temperatures, by causing electroporation. It may contribute to increase retention of heat-labile constituents with similar or enhanced levels of microbial inactivation, compared to thermal processes. However, especially continuous PEF treatments suffer from inhomogeneous treatment conditions. Typically, electric field intensities are highest at the inner wall of the chamber, where the flow velocity of the treated product is lowest. Therefore, inhomogeneities of the electric field within the treatment chamber and associated inhomogeneous temperature fields emerge. For this reason, a specific treatment chamber was designed to obtain more homogeneous flow properties inside the treatment chamber and to reduce local temperature peaks, therefore increasing treatment homogeneity. This was accomplished by a divided inlet into the chamber, consequently generating a swirling flow (vortex). The influence of inlet angles on treatment homogeneity was studied (final values: radial angle α = 61°; axial angle β = 98°), using computational fluid dynamics (CFD). For the final design, the vorticity, i.e., the intensity of the fluid rotation, was the lowest of the investigated values in the first treatment zone (1002.55 1/s), but could be maintained for the longest distance, therefore providing an increased mixing and most homogeneous treatment conditions. The new design was experimentally compared to a conventional co-linear setup, taking into account inactivation efficacy of Microbacterium lacticum as well as retention of heat-sensitive alkaline phosphatase (ALP). Results showed an increase in M. lacticum inactivation (maximum Δlog of 1.8 at pH 7 and 1.1 at pH 4) by the vortex configuration and more homogeneous treatment conditions, as visible by the simulated temperature fields. Therefore, the new setup can contribute to optimize PEF treatment conditions and to further extend PEF applications to currently challenging products.

Temperature Fields of the Droplets and Gases Mixture

In this research, we obtain gas–vapor mixture temperature fields generated by blending droplets and high-temperature combustion products. Similar experiments are conducted for droplet injection into heated air flow. This kind of measurement is essential for high-temperature and high-speed processes in contact heat exchangers or in liquid treatment chambers, as well as in firefighting systems. Experiments are conducted using an optical system based on Laser-Induced Phosphorescence as well as two types of thermocouples with a similar measurement range but different response times (0.1–3 s) and accuracy (1–5 °C). In our experiments, we inject droplets into the heated air flow (first scheme) and into the flow of high-temperature combustion products (second scheme). We concentrate on the unsteady inhomogeneous temperature fields of the gas–vapor mixture produced by blending the above-mentioned flows and monitoring the lifetime of the relatively low gas temperature after droplets passes through the observation area. The scientific novelty of this research comes from the first ever comparison of the temperature measurements of a gas–vapor–droplet mixture obtained by contact and non-contact systems. The advantages and limitations of the contact and non-contact techniques are defined for the measurement of gas–vapor mixture temperature.

Influence of boundary conditions on the aero-thermo-elastic stability of a closed cylindrical shell

In this paper, in a linear formulation, the stability problem of a closed cylindrical shell under the influence of an inhomogeneous temperature field and a supersonic gas stream flowing around the shell is considered. The stability conditions for the unperturbed state of the aero-thermo-elastic system under consideration are obtained. It was shown for different boundary conditions that by the combined action of the temperature field and the flowing stream, the stability process can be controlled and the critical flutter velocity can be substantially changed using the temperature field. The following most significant results were obtained: 1) in the case of a homogeneous temperature field, if the edges of the shell freely move in the longitudinal direction: a) a constant temperature field practically does not affect the value of the critical velocity νcr ; b) the critical velocity function νcr , depending on the number of circumferential waves n, has a minimum point; 2) in the case of a homogeneous temperature field, if the edges of the shell are fixed: a) for negative values of T 0, the lower the temperature, the wider the stability region; b) for positive values of T 0 up to a certain temperature value the stability region narrows, after which, with increasing temperature it expands; c) starting from a certain temperature value for all the system is unstable for any 0 < ν < ν *, and with increasing speed (ν > ν *) the system becomes stable, and the larger the radius of the shell, the smaller this value ; 3) in the case of a temperature field inhomogeneous over the thickness of the shell, if the edges of the shell move freely in the longitudinal direction: a) when Θ > 0 the critical velocity increases significantly and the minimum point of the function νcr (n) moves towards the lower values of n; b) when Θ < 0 the opposite is observed; 4) in the case of a temperature field inhomogeneous over thickness of the shell, if the edges of the shell are fixed: a) the stability region expands with increasing |Θ|; b) for a fixed value of the gradient Θ, an increase in the radius of the shell R leads to an expansion of the stability region; 5) fixing the edges of the shell leads to a significant increase in the value of the critical velocity of the flowing stream.

Влияние размеров области поверхностного упрочнения на напряженно-деформированное состояние балки с надрезом полукруглого профиля

Исследуется влияние размеров области поверхностного пластического упрочнения на напряженно-деформированное состояние балки с надрезом полукруглого профиля. Задача сведена к краевой задаче фиктивной термоупругости, при этом начальные (пластические) деформации моделируются температурными анизотропными деформациями в неоднородном температурном поле. Решение реализовано на основе метода конечных элементов. Для модельных расчетов в качестве исходной информации использовались экспериментальные данные о распределении остаточных напряжений в гладкой балке из сплава ЭП742 после ультразвукового механического упрочнения. Выполнен вариативный численный анализ влияния радиуса надреза и величины зоны упрочнения грани балки на распределение компонент тензора остаточных напряжений в наименьшем сечении от дна концентратора. Показано, что при величине зоны упрочнения более 16-20 % от площади всей грани напряженно-деформированное состояние в наименьшем сечении практически стабилизируется. Установлено, что если радиус полукруглого надреза меньше толщины упрочненного слоя (области сжатия материала), то происходит увеличение (по модулю) нормальной продольной компоненты тензора остаточных напряжений, а если радиус надреза больше толщины упрочненного слоя, то наблюдается уменьшение (по модулю) этой величины по сравнению с аналогичной компонентой для гладкой упрочненной балки для всех величин зоны упрочнения более 16-20 % от площади всей грани балки. Выполнена экспериментальная проверка разработанного численного метода на основе метода конечных элементов для балки с полностью упрочненной гранью.

Thermocapillary migration of droplets and bubbles in a viscous liquid (review)

Investigation of the process of accumulation of gas bubbles in the aria of a heat source is, from a physical point of view, quite interesting problem that leads to important conclusions for practical applications. The peculiarity of the process under consideration is that the surface tension of the bubble changes in an alternating temperature field, which, in turn, leads to the appearance of a flow in the boundary layer of the liquid. In the world scientific literature, the discovery and description of the effect of gas bubble migration in the direction of the temperature gradient is usually associated with the experimental work of Yang, Goldstein and Block (1959). Without diminishing its significance, we note that the effect was first predicted in the theoretical work of Fedosov (1956) as a result of solving the problem of the onset of a microflow of a liquid near plane and spherical interphase boundaries in the presence of a temperature gradient. In both works, a significant factor in explaining the described phenomenon was the dependence of surface tension on temperature. After some time, after which it was realized the need to take into account the migration of not only bubbles, but also droplets, in inhomogeneous temperature fields in space technologies, biomedical and other applications, there was a significant number of publications on this subject, and this phenomenon was called thermocapillary migration. This review is devoted to the analysis of the main, in the opinion of the authors of the article, results of experimental, theoretical and applied research to establish the mechanism of migration bubbles and drops in temperature gradient fields. In most works, it is assumed that there is no dependence of the physical properties of a liquid, except for surface tension, on temperature. There are only a few studies where the influence of the temperature dependence of the viscosity coefficient was considered, which gives a new impetus to the continuation of research and the development of the theory of the effect, taking into account the thermorheological properties of working media.

Метод реконструкции остаточных напряжений в призматическом образце с надрезом полукруглого профиля после опережающего поверхностного пластического деформирования

The stress-strain state in a surface-hardened bar (beam) with a stress concentrator of the semicircular notch type is investigated. A numerical method for calculating the residual stresses in the notch region after an advanced surface plastic deformation is proposed. The problem is reduced to the boundary-value problem of fictitious thermoelasticity, where the initial (plastic) deformations of the model are simulated by temperature deformations in an inhomogeneous temperature field. The solution is constructed using the finite element method. For model calculations, experimental data on the distribution of residual stresses in a smooth beam made of EP742 alloy after ultrasonic mechanical hardening were used. The effect of the notch radius and beam thickness on the nature and magnitude of the distribution of the residual stress tensor components in the region of the stress concentrator is studied. For the normal longitudinal component of the residual stress tensor, which plays an important role in the theory of high-cycle fatigue, it was found that if the radius of a semicircular notch is less than the thickness of the hardened layer (area of material compression), an increase (in modulus) of this component of residual stresses occurs in the smallest section of the part (in the volume immediately adjacent to the bottom of the concentrator). If the depth of the notch is greater than the thickness of the hardened layer, then a decrease (in magnitude) of this value is observed in comparison with a smooth hardened sample. It is shown that in a reinforced notched beam, the deflection value due to induced self-balanced residual stresses is less than in a smooth beam. Experimental verification of the developed numerical method is done for a surface-hardened smooth beam made of EP742 alloy.

Experimental study of macroscopic localization of plastic flow in al-mg alloy under complicated stress-strain state

The main objective of this work is to investigate the spatial-time inhomogeneity due to the jerky flow during plastic deformation of Al-Mg alloy under complex stress conditions. The use of specimens in the form of plates with a rigid circular rim and a reverse curvature rim was considered. Experimental data on the evolution of inhomogeneous strain and temperature fields have been obtained, illustrating the processes of initiation and propagation of deformation bands of the localized plastic flow by using the digital image correlation and infrared thermography.

A Combined Numerical and Experimental Investigation on Deterministic Deviations in Hot Forging Processes

In hot forging processes, geometry of the formed workpieces deviate from the desired target geometry, due to complex interactions between tools and billets which result in inhomogeneous temperature and stress fields. The resulting deviation can only be mapped insufficiently by using numerical simulation which makes it difficult to be considered when designing the tool. Therefore, the development of forging tools requires an iterative adaptation process through a large number of revisions in the tool geometry, which escalates the resulting costs. To compensate the deviations and reduce the number of tool revisions, a holistic view of the influencing factors on the geometrical deviation is necessary. In order to address this issue, a hot forging process was developed, whose geometry is prone to high deviations, and a stress-based compensation model was applied. For this, forging experiments were carried out and a comparison was made between the actual geometry and the desired one by means of 3D coordinate measurements. The compensation methodology, which directly takes into account the complex 3D stress states during forming, allows to determine a compensating tool geometry. This opened up the possibility of validating the simulation results and testing a compensation model while eliminating deterministic deviations in hot forging processes.

A Mechanism for the Formation of the Surface Relief of Falling Meteor Bodies

Based on a number of simplifying assumptions, the constructed physical and mathematical model makes it possible to describe the processes of the formation of the surface relief of meteoroids that penetrate the Earth’s atmosphere and then fall onto it in the form of meteorites. It is explained that, when the influence of an inhomogeneous temperature field initiated on the surface layer of falling meteoroids by various physical factors is taken into account, the resulting deformations and stresses form their external sculptural relief. It is either smooth, as if sanded during fast rotation of the meteoroid, or is represented by a structural formation covered with a network of caverns of different sizes and depths (regmaglypts) in the absence of rotation.

Practical modeling of non-stationary temperature fields of fiber-optic gyroscopes in space flight conditions

Based on the mathematical model presented in the first part of this paper, specialized software was created and computer modeling of nonstationary inhomogeneous temperature fields in a fiber-optic gyroscope was performed. The simulation aimed to analyze the temperature distribution in the gyroscope structural elements, especially in the fiber-optic coil and the electronics unit, since temperature fluctuations in them are one of the main sources of device errors. To achieve this goal, a three-dimensional unsteady field was calculated in a fiber-optic gyroscope. Based on the results of computer modeling, comparative data on the temperature distribution in the gyroscope structural elements on earth and orbital flight conditions, and the degree of influence of space and zero-gravity conditions are obtained.

Problem statement for practical modeling of temperature fields of gyroscopes in space navigation systems

The paper describes a method of studying temperature fields in fiber-optic gyroscopes that are part of complex navigation systems, using the example fiber-optic gyroscope as part of the angular velocity measurement system BIUS-M-1, developed by “Antares” (Saratov). The work relevance is due to the fact that currently existing methods for studying external and internal thermal effects on precision devices, and the resulting three-dimensional non-stationary temperature fields may be too complicated for practical application, or require significant computation and time resource. Also, not all contemporary models take into account such parameters, as low pressure and vacuum, the importance of which for devices operating in space orbital conditions cannot be underestimated. Therefore, modeling of the thermal process in various devices should be carried out at the design stage. At the same time, such modeling should not be labor-intensive, do not require large financial investment and computing resources. In this paper, the authors formulate a research problem, develop a thermal model, and present the main relations that are the components of the mathematical model of nonstationary three-dimensional inhomogeneous temperature fields in the fiber-optic gyroscope. The resulting model can be implemented quite simply in computational algorithms and software.

Ударные волны в термоупругой среде с точечными дефектами

The propagation of plane longitudinal waves in an infinite medium with point defects located in a non-stationary inhomogeneous temperature field is studied. A self-consistent problem is considered, taking into account both the influence of an acoustic wave on the formation and movement of defects, and the influence of defects on the propagation features of an acoustic wave. It is shown that in the absence of heat diffusion, the system of equations reduces to a nonlinear evolution equation with respect to the displacements of the particles of the medium. The equation can be considered a formal generalization of the Korteweg-de Vries-Burgers equation. By the method of truncated decompositions, an exact solution of the evolution equation in the form of a stationary shock wave with a monotonic decrease has been found. It is noted that dissipative effects due to the presence of defects prevail over the dispersion associated with the migration of defects in the medium.

Modeling of corrosion-mechanical behavior of composition rotation shells in a temperature field

In the process of exploitation, vessels and apparatuses of chemical productions can be subjected to the joint action of long-acting loads, temperatures, and corrosive working media. Real vessels and apparatuses are a combination of shells of rotation of various configurations: cone, torus, sphere, cylinder, etc. When calculating, one should take into account the edge effect at the points of inflection of the guide. Many vessels and apparatuses of chemical engineering work in uneven thermal and power fields, which cause local corrosion. The article considers the problem of calculating geometrically and physically nonlinear composite shells of revolution subjected to corrosion wear in an inhomogeneous temperature field, and the corrosion rate depends on both the stress state and temperature. Equations are obtained that describe the corrosion-mechanical behavior of shells of revolution, taking into account corrosion wear in force and thermal fields. The stress-strain state of the shell of rotation is studied by the method of successive perturbations of the parameters (in this case, time), and the time step value is selected from the condition of satisfying the required accuracy of solving the problem. At each time step, the method of initial parameters with orthogonalization of S. K. Godunov solves the boundary-value problem for a system of resolving equations with the corresponding boundary conditions. The results of calculating an autoclave, which is a combined shell of revolution: a sphere - a spherical torus - a cylinder, are presented.

Influence of conjugate convective heat transfer on temperature fields in thin walls that organize liquid layers of various orientations

Numerical studies of unsteady conjugate natural convective heat transfer in the model of a thin-walled fuel tank are carried out in the conjugate formulation. The fields of temperature in liquid and in solid walls of the tank are calculated. The evolution of convective flows and temperature fields after a sudden supply of heat to the base of the tank is investigated. Flat layers of liquid enclosed between flat walls of different orientations with inclination angles of 0, 30, 45, 60 and 90 degrees are considered. With the angle of inclination of 0 degrees the outer surface of the side walls is insulated. The outer surface of the lower wall heats up suddenly, the outer surface of the upper wall is isothermally cold. The system of equations of thermogravitation convection in the Boussinesq approximation in dimensionless form, written in terms of temperature, vector potential of the velocity field and velocity vortex, is solved. It is shown that an inhomogeneous temperature field is formed inside the solid walls of the finite thermal conductivity. The thermal conductivity of walls and conditions at the upper boundary of the liquid layer affect significantly the spatial form of convective fuel flows in fuel tanks and laws of conjugated natural convective heat exchange.

Laminar flow and heat transfer in the entrance region of elliptical minichannels

Three-dimensional laminar flow and convective heat transfer for T, H1 and H2 thermal boundary conditions at the entrance region in elliptical minichannels have been investigated numerically. The effects of Reynolds number (25 ≤ Re ≤ 2000) and aspect ratio (0.2 ≤ ε ≤ 1) on the friction coefficient, Nusselt number and the entrance length are examined in detail. The results demonstrate that the apparent friction factor and Reynolds number product and the local Nusselt number are both weak function of the cross-sectional geometry but quite sensitive to Reynolds number at the entrance region. The entrance lengths, including the hydrodynamic and the thermal entrance lengths, are both decreasing functions of Reynolds number and aspect ratio. In the entrance region, the velocity overshoots near the wall results in strong pressure gradient and the temperature distribution is almost the same for H1 and H2 conditions. The local maximum of the pressure first arises at the end of major semi-axis and thereafter moves towards the channels core as the fluid flows in the axial direction. When close to the fully developed region, the inhomogeneous cross-sectional temperature field in H2 boundary condition deteriorates the heat transfer performance especially for the elliptical minichannel with small aspect ratios. General correlations are proposed for the first time for the apparent friction coefficients, as well as the entrance lengths for elliptical channels.