Two-dimensional Temperature Field Research Articles

Comprehensive experimental thermal analysis of single bubble nucleation in vertical flow boiling: Whole field temperature and microlayer dynamics

Nucleate boiling, an important heat transfer phenomenon, holds significance in the thermal management of numerous engineering applications. Understanding and predicting its heat transfer characteristics are vital for system optimization. The formation of a microlayer, resulting from rapid bubble growth on a heater substrate, subsequently facilitates further bubble growth through evaporation playing a critical role in overall bubble dynamics. This study examines the intricate relationship between bubble and microlayer dynamics and their impact on heat transfer rates. Experimental work is conducted for varying heat fluxes using rainbow schlieren deflectometry (RSD) and thin-film interferometry (TFI) in tandem for simultaneous mapping of key parameters: bubble dynamics, microlayer dynamics, and two-dimensional temperature field in vertical flow boiling. The analysis of these parameters has provided significant insights into some fundamental aspects of boiling. Firstly, this study emphasizes that the bubble growth rate models need to take into initial microlayer thickness in accurately predicting bubble growth dynamics. The iteratively obtained constant Ceff (describing the initial microlayer thickness) for bubble growth models matches well the value of Ceff obtained experimentally from thin film interferograms. Additionally, this study also validates the applicability of the kinetic theory-based model in predicting the evaporative heat transfer coefficient during the initial stage of flow boiling, while demonstrating that the accommodation coefficient is ∼0.04 for the investigated range of heat fluxes. Subsequently, using the experimentally obtained evaporative heat transfer coefficient, further insights are provided into the dry patch dynamics. Experimental dry patch dynamics were in good agreement with theoretical predictions up to the rewetting phase. The results also indicate a substantial contribution of microlayer evaporation, constituting approximately 34 % of the total heat flux.

The Discrete, Fractional Order Model of a Two-Dimensional Temperature Field using Grünwald-Letnikov Definition

In the paper a new, fractional order, discrete model of a two-dimensional temperature field is addressed. The proposed model uses Grünwald-Letnikov definition of the fractional operator. Such a model has not been proposed yet. Elementary properties of the model: practical stability, accuracy and convergence are analysed. Analytical conditions of stability and convergence are proposed and they allow to estimate the orders of the model. Theoretical considerations are validated using exprimental data obtained with the use of a thermal imaging camera. Results of analysis supported by experiments point that the proposed model assures good accuracy and convergence for low order and relatively short memory length.

Temperature field reconstruction based on femtosecond laser prepared of multiwavelength fibre bragg grating array

Temperature field measurements are of great significance in industrial production, scientific research, and other fields. Contact temperature measurements usually achieve high spatial resolution by increasing the layout density of the sensors. However, in practical applications, achieving high-density sensor placement is often difficult. Therefore, when the number of sensors is limited, it is necessary to perform function fitting or interpolation of the temperature of the sampling points to reconstruct the temperature field distribution. This study proposed a temperature field reconstruction method based on femtosecond laser prepared multiwavelength fibre Bragg grating (FBG) array. A multiwavelength FBG array was prepared using the femtosecond laser phase mask method combined with stress stretching, and applied for measuring the temperature field distribution in a tubular high-temperature furnace. Cubic spline interpolation and backpropagation (BP) neural networks were used to construct two-dimensional temperature field models for the temperature field distribution data measured by the FBGs, and the prediction accuracies of the two models were compared. The test results show that the root mean square error of the temperature field distribution constructed using the BP neural network is 0.7333 °C, which is approximately 23.18% of the predicted results of the cubic spline interpolation model, indicating that it is a high-precision temperature field reconstruction method.

Study on Sunlight Temperature Field of Steel Box Arch Ribs in Irregular Arch Bridges

Due to their excellent thermal conductivity and sensitivity to temperature changes, special attention should be paid to the influence of temperature on steel-structure bridges. The temperature effect is complex, especially for unstable steel arch bridges with complex structural forms. This paper proposes an approximate method that measures the three-dimensional temperature field of the symmetrical arch rib with the two-dimensional temperature field of multiple sections. In addition, it converts the complex radiant intensity calculation of the special-shaped steel box arch rib into the calculation of numerous planar radiant intensities. It uses the ANSYS Workbench to establish the three-dimensional transient thermal analysis finite element model of the No. 2 steel box arch rib. The influence of seasons and arch rib direction on the temperature field of steel box arch ribs and the stress and deformation of steel box arch ribs under non-linear temperature effects were analyzed. The results show that the temperature changes in different seasons significantly impact the temperature changes in the arch ribs. The change in the azimuth angle of the arch rib has a significant impact on the temperature difference between the web plates on both sides of the arch rib; under the influence of the temperature field at the most unfavorable time in summer and winter, symmetrical stress concentration occurs in the arch foot area. Furthermore, the maximum vertical displacement is 13.9 mm and 10.8 mm, respectively. Finally, when the angle is 40°, the maximum temperature difference between the web plates on both sides is 6.9 °C.

Analytical Confirmation of the Calculated Dependencies for Heat Exchange in a Plate Recuperator when Humidifying the Auxiliary Flow

The relevance of the study is related to the need to ensure maximum reduction of energy consumption while ensuring the calculated parameters of the indoor climate in buildings under the Law of the Russian Federation “On Energy Saving...” and the updated version of SP 131. The purpose of the study is to obtain an approximate analytical expression of this dependence, which makes it possible to additionally confirm the results of field and numerical experiments previously performed by the authors for this flow treatment scheme. The objective of the study is to build a simplified mathematical model of the processes of changing the heat and humidity state of the air in the recuperator, identify the main factors affecting the increasing multiplier to the coefficient of temperature efficiency of the device and obtain the necessary numerical coefficients in formulas linking the desired and initial parameters. The general equation of thermal balance and heat transfer for the heat exchanger as a whole is used, including the integral characteristics of the apparatus in a dimensionless form, as well as standard techniques of algebraic transformations. An approximate analytical expression is obtained for an increasing multiplier to the coefficient of thermal efficiency of the recuperator taking into account the additional cooling of the inflow due to the heat consumption for evaporation. It is shown that the general structure of this ratio coincides with the one found by the authors earlier by processing the results of numerical modeling of a two-dimensional temperature field in a heat exchanger, taking into account experimental data on the amount of moisture carried away, which confirms their correctness and reliability.

ANALYTICAL SOLUTION OF THE DIFFERENTIAL EQUATION OF HEAT CONDUCTIVITY FOR DAMAGED THERMAL INSULATION OF PIPELINES

For heat supply systems of Ukraine, the determination and forecasting of thermal energy losses during the transportation of heat carrier is an urgent problem. The thermal lines of the heating networks are long and its insulation is damaged. Installation of heat energy metering devices at all sources and all consumers (i.e. buildings) without exception allows determining and forecasting real heat losses in the heat network, but this is a difficult task, not all consumers and sources are actually covered by heat consumption accounting. The task of determining heat losses is also relevant for energy management systems of heat supply systems, energy companies and industry. The solution to the problem is proposed by a separate mathematical modeling of the temperature state of the section of the damaged insulating layer with the determination of the heat flow through it. It is proposed to solve the problem by the method of analytical solution of the differential equation of heat conduction with boundary conditions of the third kind. With the uniform distribution of characteristic damages along the total length of the pipeline, knowing the limits of damage influence, the share of insulation damage and the number of damages on the pipeline, it is possible to determine the real heat flow from the outer surface of the pipelines, including coefficient of increase of heat losses on the section of the heat pipe in relation to those determined by regulatory documents. Traditionally, one-dimensional models or determinations of the two-dimensional temperature field and actual heat fluxes in a cross-section to the axis of a characteristic damaged section of insulation are considered. But this does not take into account the two-dimensionality of the temperature field of the damaged layer of insulation along the length (that is, along the axis) of the pipeline. Therefore, the purpose of this work is to develop a methodology for determining heat losses through pipelines, taking into account the damage to their insulation and the distribution of characteristic damages along the length. The following simulation was carried out for one of the areas. Also, experimental and numerical studies using the finite difference method in combination with the method of running variable directions for similar models confirmed the coincidence of the analytical solution of the proposed model and the finite difference model within the permissible error.

КОМПЬЮТЕРНОЕ МОДЕЛИРОВАНИЕ ЭНЕРГОЭФФЕКТИВНЫХ СТЫКОВ ДЕРЕВОКОМПОЗИТНЫХ ПАНЕЛЕЙ

High air permeability and the presence of thermal bridges at the junctions of wooden frame wall panels have a significant impact on the thermal balance of the building and its operational characteristics. The importance of improving the energy efficiency of nodal interfaces of panels with a wooden frame is undeniable.
 To date, there is no single generally accepted method for calculating heat losses through nodal interfaces of panels with a wooden frame. Based on the analysis carried out, it is necessary to carry out calculations and measurements that allow creating this calculation methodology. To carry out numerical studies, a list of characteristics and parameters affecting their conduct is formulated: the influence of the thickness of a li-ear-discrete inclusion on the heat-protective properties of the panel docking unit; the thermal conductivity characteristics of the material used to fill linear-discrete inclusions affecting the heat flux density of the node interface; consideration of the influence of the outdoor temperature of air depending on different climatic zones on the density of heat flow. The dependences of the heat flux density on the "inner" surface of the experimental samples on the thermal conductivity coefficient of the material of the insulating insert, the width of the insulating insert and the outside air temperature were revealed and the nature of the temperature distribution on the "inner" surface of the prototypes was established. By calculating two-dimensional temperature fields in the cross section of the node, isofields of temperature distribution inside the structure, isofields of heat flux density and its direction, lines of temperature distribution and heat flux density along the inner and outer surfaces are obtained. It was found that the heat flux density in the ribs with heat-insulating inclusions is lower in comparison with solid wood parts by an amount from 13% to 52%.

SIMULATION OF THE COOLING PROCESS OF RAILWAYS UNDER NATURAL CONDITIONS

SIMULATION OF THE COOLING PROCESS OF RAILWAYS UNDER NATURAL CONDITIONS

Two-dimensional temperature field inversion of turbine blade based on physics-informed neural networks

Two-dimensional temperature field inversion of turbine blade based on physics-informed neural networks

CntTSP visualization technique for rotating blade surface flow at low Reynolds number

Research and development of aircraft with rotating wings at low Reynolds numbers have received much attention. This study proposes using a carbon nanotube temperature-sensitive paint (cntTSP) measurement technique to visualize the surface flow of rotor blades at low Reynolds numbers. Temperature-sensitive paint (TSP) can optically measure a two-dimensional temperature field using the thermal quenching of luminophores. A carbon nanotube thin layer is used to heat the TSP layer in cntTSP measurements. For the experimental condition, the low Reynolds number at 75% of the rotor radius was 1.1 × 104, and a blade tip speed of 7.2 m/s. Temperature distributions showing a leading edge vortex (LEV) were observed in the visualization results. Furthermore, the LEV region expanded from the wing-tip side to the wing-root side at high-pitch angles. These visualization results show the applicability of the cntTSP measurement technique for investigating the surface flow field of rotor blades at low Reynolds numbers.Graphical abstract

СОВЕРШЕНСТВОВАНИЕ РАСЧЕТА ПРОСТРАНСТВЕННЫХ СТЕРЖНЕВЫХ КОНСТРУКЦИЙ ИЗ ПОЛИМЕРНЫХ МАТЕРИАЛОВ С УЧЕТОМ ТЕМПЕРАТУРНОГО ВОЗДЕЙСТВИЯ.

The influence of temperature effects on the technical condition of cross-bar spatial structures (CSRS) made of polymer building materials (PSM) is considered using the example of tubular elements made of polyvinyl chloride (PVC). From numerous scientific studies by various authors, it is known that low and high temperatures significantly affect the mechanical safety of engineering plastics: tensile-compressive strength, bending, loss of stability, torsion, which ultimately reduces the operational reliability and durability of CSRS. The current regulatory and technical construction documentation on loads and impacts provides only climatic temperature impacts. In the documentation for building structures, technological temperature effects do not take into account the time factor. The general solution to the problem of unsteady heat transfer of a cylindrical element is considered in a nonlinear formulation to calculate the two-dimensional temperature field separately for the rod cylindrical element and the node connection in the “cylinder-cylinder” system. Graphic illustrations of the calculations are provided.

Research on the nonuniform contact characteristics and thermal behavior of friction pairs involving the radial conical buckling deformation in hydro-viscous drive

An equivalent model and a finite element method was established and used for simulating the change of contact state and pressure distribution of friction pairs under the axial pressure to obtain the radial nonuniform contact characteristics and temperature field of conical friction pairs during the soft-start condition. A two-dimensional temperature field calculation model was established based on the results of contact characteristics and convective heat transfer conditions, and the transient temperature field of friction pairs during soft-start was calculated by the finite difference method. Finally, the effects of the soft-start time, deformation degree, and thickness of the steel disk were studied. The results show that the temperature and contact pressure distribution of conical deformation friction pairs exhibit local high-temperature and high-pressure areas during the soft-start process. In the early stage of soft-start, the conical friction element locally contacts in its radial central area. The contact area spreads from the center to both sides as the soft start time increases, and two contact pressure peak areas are formed near the inner and outer diameters with the increase in axial pressure. The degree of axial deformation of conical steel disk has a significant impact on contact pressure. The larger the axial deformation, the pressure distribution would be more uneven. The distribution of temperature field is significantly affected by the contact pressure. It spreads from the middle to both sides, forming high-temperature regions in the pressure peak areas. Meanwhile, the temperature on the outer side of the friction element is higher than that of the inner side due to the influence of convective heat transfer. The duration of soft start also has a significant impact on the maximum temperature and maximum temperature difference. The results could provide a theoretical basis for exploring the correlation between the thermal buckling deformation and torque instability.

Flame Imaging Technology Based on 64-Pixel Area Array Sensor.

High-resolution flame temperature images are essential indicators for evaluating combustion conditions. Tunable diode laser absorption spectroscopy (TDLAS) is an effective combustion diagnostic method. In actual engineering, due to the limitation of line-of-sight (LOS) measurement, TDLAS technology has the problems of small data volume and low dimensionality in measuring combustion fields, which seriously limits the development of TDLAS in combustion diagnosis. This article demonstrates a TDLAS imaging method based on a 64-pixel area array sensor to reconstruct the two-dimensional temperature field of the flame. This paper verifies the robustness of the Algebraic Reconstruction Technique (ART) algorithm through numerical simulation and studies the effects of temperature, concentration, and pressure on the second harmonic intensity based on the HITRAN database. The two-dimensional temperature field of the flame was reconstructed, and reconstruction accuracy was verified using thermocouples. The maximum relative error was 3.71%. The TDLAS detection system based on a 64-pixel area array sensor provides a way to develop high-precision, high-complexity flame temperature measurement technology.

Constructing a physical-mathematical model of grain mass self-heating by a rod site of rectangular cross-section

This paper considers the issue related to improving the energy and resource efficiency of the process of storing raw materials of plant origin, namely, preventing self-heating of grain masses in elevator silos. It was noted that the effectiveness of the analysis of self-heating of grain mass increases with the use of mathematical models of temperature fields of grain mass during storage together with data obtained experimentally. A physical-mathematical model has been built that describes a two-dimensional localized non-stationary temperature field of seed material generated by a homogeneous rod cell with a rectangular cross-section. A technique for accelerating the convergence of the series is proposed for the constructed analytical solution, which is based on the selection and analytical calculation of the sum of the component of slow convergence. The adequacy of the physical-mathematical model has been proven by calculations and by comparing the temperature of the self-heating site, obtained theoretically, and the temperature obtained under industrial setting. The established temperature kinetics of grain mass volumes during storage, obtained experimentally and theoretically, correlate with each other in the duration range from 0 to 30 days with a correlation coefficient of at least 0.98. This proves the possibility of applying forecasts of the temperature of self-heating sites in the volume of grain mass, obtained by using the physical-mathematical model built, under industrial setting. A limitation of the study is that the model is not universal. It is another stage on the way to a universal model. A limitation of the study is that for storage periods of more than 30 days, a new excess temperature forecast must be made

Enhancing remote sensing of water temperature using acoustic tomography and 3-D-RPS algorithm

Remote sensing of water temperature and flow dynamics is of paramount importance for water environment management. Coastal acoustic tomography (CAT), an innovative method for remote sensing in underwater environments, utilizes the dual-way travel time of multiple sound paths to reconstruct the underwater temperature field. However, the transmission experiments are susceptible to data noise caused by station drift and inaccuracies in travel time extraction. In this study, a three-dimensional Rousseeuw Phase-Space (3-D-RPS) thresholding algorithm is proposed to remove outliers in the travel time data obtained from Huangcai Reservoir using three CAT systems on September 16, 2020. Additionally, this work includes grid partitioning based on sound path propagation, calculation of sound path lengths, and reference transmission time within each grid, construction of a sparse matrix, and inversion of the two-dimensional temperature field and its associated inversion error. The accuracy and applicability of the proposed method are confirmed through a comparison with data obtained from temperature–depth (TD) sensors. The results demonstrate the precision and suitability of this approach. By effectively mitigating the impact of station drift and extraction accuracy issues, this method provides a reliable temperature field estimation.

A method to reduce open optical path noise interference in two-dimensional gas detection of farmland

The two-dimensional distribution method based on the laser spectrum is widely used in the reconstruction of two-dimensional temperature fields or concentration fields. However, the existing methods are all based on small-scale measurements. In large-scale spatial detection of farmland, the detection accuracy cannot reach the expected result due to the long optical path and the noise of various frequencies brought by environmental factors such as vibration, temperature, and other interfering gases. Aiming at the above-mentioned problems, this paper proposes a method to reduce open optical path noise interference in two-dimensional gas detection of farmland to improve detection accuracy. The signal denoising approach combines variational modal decomposition with the SG filtering algorithm to decompose, smooth out, and rebuild the detection signal. In addition, we built a two-dimensional detection system based on an open optical path. Throughout experimental validation, the proposed method outperformed the traditional method by 24% and 19%, respectively, in terms of the fitting degree and fitting effect of the gas absorption curve.

Optimization of elastic wave propagation in a reconfigurable medium by genetic algorithms with adaptive mutation probability

We introduce a reconfigurable medium for the manipulation of elastic propagation properties of Lamb waves. It is based on a shape memory polymer (SMP) with temperature-dependent Young’s modulus. Waves are excited by a laser pulse and detected by a laser vibrometer. A two-dimensional temperature field is controlled by a scanning heating laser. We use genetic algorithms to determine optimal distributions of mechanical properties for the following criteria: the wave amplitude has to be maximized at a given location and at the same time minimized at one or two other locations. Due to the reconfigurability of the medium, the optimization process is performed directly on the object of optimization, and not on a numerical or analytical representative, based on a direct measurement of the fitness. The optimized configuration makes the waves propagate away from (or around) the point of minimization towards the point of maximization. We improve the genetic algorithm by adapting the mutation probability of individual genes according to specific criteria, which depend on the surrounding genes (distributed in two dimensions). This provides the advantages: concentrating the mutations in the areas of genetic inconsistencies and counterbalancing the error of the fitness measurement. The method is applicable for the intelligent design of wave energy harvesters, ultrasonic transducers, and analogue wave computing devices.

3D printing of high-temperature thick film platinum resistance temperature detector array

Dynamic high-temperature field measurements have garnered substantial interest for various promising applications, such as the health monitoring of aviation components. 3D printing offers unprecedented opportunities for the development of curved structure-function integrated sensors. However, most current resistance temperature detector (RTD) arrays based on 3D printing technology work well only within a narrow temperature range. Their application at high temperatures remains a significant challenge because of the lack of efficient manufacturing processes. Herein, a high-temperature thick film platinum (Pt) RTD array is presented based on 3D printing technology, suitable for high-temperature field measurement sensing applications at 50−800 °C. Three stages of Pt film sintering were revealed through the analysis of the microstructure, phase composition, and electrical properties during the sintering process. Compared to sputtered films, printed Pt films, which are confirmed to contain glass powder, exhibit excellent anti-aggregation and high-temperature properties. The resulting Pt RTD array shows outstanding stability (drift rate of 0.07%/h at 800 °C), high accuracy (0.75% full-scale), and can realize temperature gradient monitoring of a two-dimensional temperature field. The potential applications of the Pt RTD array, including bolt and rocket engine tester exhaust flame temperature monitoring, were demonstrated. This study paves the way for printing RTD arrays directly on curved parts.

ВЫБОР ОПТИМАЛЬНЫХ ПАРАМЕТРОВ ПРОСТРАНСТВЕННО-ВРЕМЕННОЙ СЕТКИ ПРИ МАТЕМАТИЧЕСКОМ МОДЕЛИРОВАНИИ НАГРЕВА ЗАГОТОВОК В ПРОМЫШЛЕННЫХ ПЕЧАХ

The efficiency of two numerical methods for solving multidimensional problems of the theory of thermal conductivity ‒ the fractional steps method and the Liebman method - is evaluated. The efficiency of these methods is compared for the operating conditions of industrial furnaces by the example of calculating the symmetrical heating of a two-dimensional cylinder and a three-dimensional plate made of materials with different thermophysical properties (corundum, ceramic brick and carbon steel). A two-dimensional axisymmetric temperature field for a cylinder and a three-dimensional temperature field for a workpiece in the form of a parallelepiped were found by the grid method under boundary conditions of the II and III genera. The difference approximation of differential equations and boundary conditions is performed by the control volume method according to an implicit finite difference scheme. The developed algorithms for solving multidimensional problems of internal heat transfer by fractional steps and the Liebman method are implemented in the form of computer programs in the Object Pascal programming environment. When comparing the effectiveness of solving multidimensional problems with these methods, the criterion of the effectiveness of difference schemes (CERS) proposed by V.V. Bukhmirov and T.E. Sozinova was used as an optimization criterion. Nomograms are constructed to select the optimal parameters of the space-time grid and the best numerical method for solving multidimensional problems for a specific process of heating (cooling) a solid body

Development of two-dimensional temperature field solution method based on the stress–strain response of 316LN stainless steel at cryogenic temperatures

To better understand the tensile fracture behavior and temperature variation during the tension testing of the 316LN at cryogenic temperatures, a two-dimensional temperature field solution method is developed based on two-dimensional strain field measured by the digital image correlation technology combined with the Taylor Quinney coefficient model and the intrinsic model of strain-induced martensitic phase transformation. The method allows for visualization of the strain field and temperature variation of the 316LN austenitic stainless steel at cryogenic temperature. By numerical simulation, the localized temperature elevation of the 316LN is determined to be 13.3 K during the tensile test at 77 K, which is in good agreement with the experimental result of 10.2 K. This model reconstructed the two-dimensional temperature field variation throughout the entire tensile test, which is beneficial for facilitating the analysis of the mutual relation between the mechanical properties and microstructural evolution of the 316LN and other metastable austenitic stainless steels in cryogenic temperatures.