Non-uniform Temperature Field Research Articles

Real-time reconstruction of 3D transient non-uniform temperature field for thermal protection system based on machine learning

Reconstructed temperature field will provide critical input for monitoring the aerodynamic heating on the thermal protection system (TPS). In this paper, a novel data-driven method is proposed that allows real-time reconstruction of the 3D transient non-uniform temperature field in a TPS ceramic tile. The measured temperature is obtained by embedding sparse sensors at different layers of the tile. The spatial feature bases and time projection coefficients of the non-uniform temperature fields are extracted using the multi-parameter proper orthogonal decomposition (POD) method. The Fully-connected Long Short-Term Memory (FC-LSTM) networks are used to establish the prediction relationship between the measurements and the full-field temperatures. The problem to estimate the projection coefficients of the spatial feature bases is solved by optimizing the loss function using Adam algorithm. The numerical examples show an approximation error less than 5% and the reconstruction time-consuming less than 1 s in 3D temperature field reconstruction (TFR). The proposed reconstruction method is robust at different measurement noise levels and tested point arrangements.

The metamaterial with high thermal-mechanical stability and the practical application as the microwave antenna: Mechanical designs, theoretical predictions, and experimental demonstrations

To address the demand of maintaining the structural configuration upon extreme temperature changes, metamaterials with high thermal-mechanical stability have attracted wide attention recently. However, there are still some challenges for previous studies regarding mechanical design and practical application exploration. This manuscript proposes the design strategy for the lattice sandwich metamaterial with excellent zero thermal-induced warping, along with the metamaterial-based antenna with a high stability of electromagnetic signal transmission. Through the design strategy of discrete lattice units of the metamaterial, the ultra-low thermal warping of the metamaterial is realized upon the non-uniform temperature field. Here, the theoretical model is established to predict both heat transfer and thermal-induced deformation behavior upon complex mechanical-thermal loading conditions. The combination of theoretical predictions, finite element analysis, and experiments verifies the thermal dimensional stability of the metamaterial proposed here. Compared with the heterogeneous bilayer plate, experimental thermal warping of the metamaterial specimen is reduced by 99.7%. Additionally, compared with the bilayer-based specimen, gain attenuation, the main lobe's offset angle, and the voltage standing wave ratio offset of the metamaterial-based antenna specimen are experimentally reduced by 99.5%, 99.9% and 74.2%, revealing the huge application potential of this metamaterial in the field of spacecraft communication.

Thermal fatigue behaviors of thin-walled structures with holes: Experiments and phase field fracture modeling

The assessment of thermal fatigue behaviors of thin-walled structures with holes is a challenging task. A novel experimental approach was designed to test the thermal fatigue behaviors of thin-walled structures with holes. The experiments were conducted under three test conditions (300–850/950/1000 ℃) to investigate the behaviors of crack initiation and early propagation. The cyclic temperature loading exhibits high-transient and wide-ranging characteristics, enabling the construction of a non-uniform transient temperature field in the heating step. A thermal fatigue phase field model was developed for elastoplastic solids, and thermal fatigue fracture modeling and life prediction were performed. The phase field effectively reproduces crack morphology, and the experimental results closely match the simulation results when fatigue parameters are properly selected. Raising the upper limit of temperature will significantly diminish thermal fatigue life, accelerate crack growth, and induce a broader range of material damage. The temperature gradient in the heating step enhances the cyclic plastic behavior at the edge of the hole, significantly amplifying the detrimental impact of thermal fatigue.

A refined cylinder fire model for thermal radiation calculation from localized fire to exposed horizontal surface

Fire is the most frequent hazard to buildings. The current design methods for predicting the temperatures of structures in fire are originally developed for the standard fire that assumes a uniform gas temperature field and are invalid for natural fires with high non-uniform gas temperature fields. Localized fire is a typical natural fire with high non-uniform gas temperature field, which is often considered in fire safety design. There are currently no validated simple general models for calculating the heat transfer from localized fire to exposed structures. To address the need of design method, this paper develops a refined cylinder fire model for calculating the incident radiant heat fluxes on horizontal structural members inside and outside the flame region of a localized fire. The model uses a cylinder, centered at the fire plume axis, to represent the localized fire. The height of the cylinder is not fixed, different to any other fire models. The temperatures in the cylinder are highly non-uniform in three dimensions and are determined based on the classic fire plume theory. For radiation calculation, the cylinder is evenly divided into several elements along the radius and height. Each element is assumed to be a homogenous, isotropic, and absorbing-emitting (participating) graybody. By careful consideration of the spatial gas temperature distribution, the radiation properties (emissivity and transmissivity) of the elementary graybody, and the configuration factor between the elementary graybody and the horizontal target surface, the model can get relatively accurate and conservative incident radiant heat flux. The relative deviations against both the experiment data and numerical results are within ± 30 %. The model introduces a new concept of calculating the heat fluxes from fire to structures, is a relatively simple general model (compared with the sophisticated computational fluid dynamics models), and is more precise and accurate than other simple ones. The model is recommended for use in performance-based fire safety design.

Modeling via peridynamics for crack propagation in laminated glass under fire

Despite laminated glass is widely used in building construction, its susceptibility to cracking and collapsing during an accidental fire can intensify fire propagation, leading to substantial casualties and economic losses. In this work, we developed a meshfree framework for modeling thermomechanical cracking of laminated glass via peridynamic (PD) theory. First, to overcome the incomplete input experimental data for implementing thermal boundary conditions, we proposed both the uniform and non-uniform temperature field strategies. Second, PD interface model and the stochastic distribution of defects were implemented within this framework. Third, the challenging problem of crack path selection in thermally loaded borosilicate/steel bi-material beams was studied to validate the feasibility of the proposed model. It is demonstrated that the proposed framework can capture the temperature history and crack features of laminated glass under fire, showing great consistency with experimental results. Our findings show that with the decrease of the glass strength or the increase of the defect content, more islands form in the central region of the glazing, implying higher risks of glass fall-out in fire conditions. This model constitutes a promising tool for predicting the fire performance of laminated glass and contributes to designing safer engineering structures.

Non-uniform temperature fields in steel tubes with different inclinations under solar radiation

The temperature distribution within steel tubes is subject to non-uniformity due to the influence of surrounding environmental factors, which could pose safety concerns for steel structures. In response, this study undertook a comprehensive long-term experimental investigation, aimed at elucidating the temperature distribution characteristics of inclined steel tubes. The results underscored the non-uniform distribution of temperature fields in steel tubes under the influence of solar radiation, with notable sensitivity to their inclinations and orientations. In addition, a numerical simulation model specifically tailored to represent the thermal behavior of inclined steel tubes was developed and subsequently validated using empirical data gathered from the aforementioned experiments. Based on the developed simulation model, the thermal behaviors of a steel-arch-tower were numerically analyzed. It was shown that distinct vertical temperature variations exist across different sections of the tower, while the horizontal temperature differentials exhibit consistent trend. The outcomes of this combined experimental and numerical study provide useful references to understand the thermal effects in steel structures.

An Oxide Growth-Coupled Viscoplasticity Model and Its Application to Interfacial Stress Analysis near an Air Hole within a Thermal Barrier Coating

Strength assessment for thermal barrier coatings (TBCs) is vital in the safety design of hot-section components in engines. However, several crucial factors, including thermally grown oxide (TGO) growth and creep–plasticity interaction, have been less considered in thermo-mechanical analyses for TBCs near air holes. In this study, a unified viscoplastic constitutive model incorporating TGO growth is developed and integrated into a finite element framework. The model considers multiple factors, including TGO growth, creep–plasticity interaction, interface undulation, and temperature gradient. Additionally, an analytical solution for the non-uniform temperature field of a TBC is derived. The model is then applied to calculate interfacial stresses and accumulated strain energies in the TBC near an air hole, which promote interface debonding. The obtained results can be utilized to investigate the mechanisms of hole edge delamination in TBCs, considering the combined effects of multiple complex factors. A competition for the potential failure initiation location is revealed between the first oxide layer and the evolving TGO/bond coat interface. The developed viscoplasticity model demonstrates effective capability in modelling a range of dynamic behaviors that collectively contribute to hole edge delamination failure.

Sound radiation characteristics of a beam under supersonic airflow and non-uniform temperature field

This paper investigates vibro-acoustic behaviour of an isotropic beam subjected to in-plane varying temperature field and supersonic flow. For a given elevated temperature and non-uniform temperature (NUFT) field, the aerodynamic pressure (ADP) is varied in fraction of its critical value, and the consequent effect on sound radiation characteristics is investigated. Shear and normal deformable beam theory (SNDBT) based kinematics is used, and equations of motion are obtained using Hamilton's principle. Following that, the Ritz method is used to solve the equations. To start with, aeroelastic flutter and vibro-acoustic response characteristics (as a function of critical aerodynamic pressure (λcr)) are analyzed without considering any thermal stress effect. Following that, for a given temperature field, the critical buckling temperature (ΔTcr) of the beam is obtained. Then, the impact of thermal stress caused by the NUFT field on the flutter and sound radiation characteristics is studied. The study observed that the combined effects of the NUFT field and variable ADP significantly impacted the beam's flutter and vibro-acoustic responses.

Variational mode decomposition framework for modal shape visualization of honeycomb sandwich structures for full-field vibration measurements in non-uniform temperature fields

Thermal effects in hypersonic vehicles, such as severe aerodynamic heating, can greatly influence their thermodynamic behavior. These effects can cause uneven temperature distributions and drastic vibrations, which in turn impact the vibration characteristics of the vehicle structure. To address this issue, a comprehensive approach was developed to study the behavior of honeycomb sandwich structures in high-temperature environments. Firstly, a full-field thermal vibration testing system was established, which allowed for free-boundary multi-temperature region heating at 900 °C while applying unconnected excitation. Through this setup, we were able to obtain modal frequencies and modal shapes of the honeycomb sandwich structures under high-temperature conditions. To accurately simulate the heat transfer distribution of the honeycomb sandwich structure, the Q-learning algorithm was employed, which proved effective in achieving accurate and detailed predictions of the full-field heat transfer distribution. Furthermore, for the purpose of further enhancing the accuracy of the finite element model, a multi-state non-uniform temperature field model updating method was utilized. This updated model accounted for the influence of the multi-temperature region heating, resulting in a more reliable representation of the structure's behavior. Additionally, a variational mode decomposition (VMD) framework was applied to visualize and analyze the modal shapes of the honeycomb sandwich structures. By decomposing the time-domain signals with VMD, it is possible to efficiently obtain the modal shapes of the output-only response signals. Experimental results demonstrated that the identification method used in this study produced modal frequencies and modal shapes that closely matched those obtained using the PolyMAX method at room temperature. Therefore, the proposed approach offers an effective means of identifying the modal characteristics of structures subjected to non-uniform temperature fields, particularly in output-only scenarios.

Magnetic nanofluid [formula omitted] in passive cooling system based on thermo-osmotic effect

Due to the dependence of the magnetic susceptibility of nanofluid on temperature, magnetic nanofluid is able to move in a nonuniform temperature field and an external magnetic field. In a passive cooling system based on the thermomagnetic effect, the coolant can move without the use of a pump. Here we demonstrate the principle of operation of a brand-new passive cooling system, where the convective flow of a magnetic nanofluid is driven by the combined action of thermo-osmosis and magnetic force. Therein lies the fundamental difference between the passive cooling system proposed here and the previously known systems, where the movement of ferrofluid is due to the action of the thermomagnetic effect. Based on nonequilibrium thermodynamics, a phenomenological model is proposed to describe the motion of a magnetic nanofluid in a channel in nonuniform temperature and magnetic fields. In the experimental study, the motion of ferrofluid Fe3O4 in the micro-channel is analyzed with variations in temperature, temperature gradient, channel thickness, and nanoparticle concentration. It is shown that in a non-uniform temperature field water-based ferrofluid moves in the direction of increasing temperature, while tridecane-based ferrofluid moves in the direction of decreasing it. If the thickness of the micro-channel exceeds a certain critical value, then the movement of ferrofluid under the influence of thermo-osmosis degenerates. It has been established that with an increase in concentration of nanoparticles the velocity of ferrofluid motion decreases due to the opposite direction of nanoparticle motion under the action of thermophoresis and the motion of liquid under the action of thermo-osmosis.

Integrated novel modeling approaches for non-uniform heat source and temperature field in gear profile grinding

Integrated novel modeling approaches for non-uniform heat source and temperature field in gear profile grinding

Thermal error compensation in length inspection of large-scale aircraft spars in nonuniform temperature environments

As the primary load-bearing structures, large-scale aircraft spars are subject to the influence of nonuniform temperatures in field conditions, resulting in thermal errors during on-site length inspections. These errors require accurate compensation. Conventional linear scaling methods, based on the assumption of uniform temperatures and a retrieved coefficient of thermal expansion (CTE), suffer from low accuracy in nonuniform temperature environments. To address this issue, this paper proposed a thermal error compensation method that incorporates CTE recalibration. First, we established a predictive model for thermal errors in nonuniform temperature fields through differential thermoelastic analysis. Secondly, a recalibration technique for the sensitive parameter, CTE, was introduced to enhance the prediction accuracy. Finally, leveraging the equivalent form of the model, an uncertainty assessment approach tailored for nonuniform temperature conditions was formulated for the compensated lengths. Numerical and case studies of a nearly 1 m long simplified wing spar were implemented to validate the performance of the thermal error compensation method. The results indicate that the presented method improved accuracy by over 57.6% in terms of RMSE compared to the linear scaling method using average temperatures, which would provide a viable approach to achieve a more accurate on-site length inspection of aircraft components.

Plastic flow and interfacial bonding behaviors of embedded linear friction welding process: Numerical simulation combined with thermo-physical experiment

In this study, a new linear friction welding (LFW) process, embedded LFW process, was put forward, which was mainly applied to combination manufacturing of long or overlong load-carrying titanium alloy structural components in aircraft. The interfacial plastic flow behavior and bonding mechanism of this process were investigated by a developed coupling Eulerian-Lagrangian numerical model using software ABAQUS and a novel thermo-physical simulation method with designed embedded hot compression specimen. In addition, the formation mechanism and control method of welding defects caused by uneven plastic flow were discussed. The results reveal that the plastic flow along oscillating direction of this process is even and sufficient. In the direction perpendicular to oscillation, thermo-plastic metals mainly flow downward along welding interface under coupling of shear stress and interfacial pressure, resulting in the interfacial plastic zone shown as an inverted “V” shape. The upward plastic flow in this direction is relatively weak, and only a small amount of flash is extruded from top of joint. Moreover, the wedge block and welding components at top of joint are always in un-steady friction stage, leading to non-uniform temperature field distribution and un-welded defects. According to the results of numerical simulation, high oscillating frequency combined with low pressure and small amplitude is considered as appropriate parameter selection scheme to improve the upward interfacial plastic flow at top of joint and suppress the un-welded defects. The results of thermo-physical simulation illustrate that continuous dynamic recrystallization (CDRX) induces the bonding of interface, accompanying by intense dislocation movement and creation of many low-angle grain boundaries. In the interfacial bonding area, grain orientation is random with relatively low texture density (5.0 mud) owing to CDRX.

Transfer-Learning-Based Temperature Uncertainty Reduction Algorithm for Large Scale Oil Tank Ground Settlement Monitoring.

Sensors operating in open-air environments can be affected by various environmental factors. Specifically, ground settlement (GS) monitoring sensors installed in oil tanks are susceptible to non-uniform temperature fields caused by uneven sunshine exposure. This disparity in environmental conditions can lead to errors in sensor readings. To address this issue, this study aimed to analyze the impact of temperature on GS monitoring sensors and establish a mapping relationship between temperature uncertainty (fluctuations of measurement caused by temperature variation) and temperature variation. By collecting the temperature information and inferring the temperature uncertainty being introduced, this interference can be removed. However, it is crucial to note that in real-world complex scenarios, the relationship between temperature uncertainty and temperature variation is not always a constant positive correlation, which limits the data available for certain periods. Moreover, the limited availability of data presents a challenge when analyzing the complex mapping relationship. To overcome these challenges, a transfer-learning-based algorithm was introduced to develop a more accurate model for predicting temperature uncertainty based on temperature variation, even with limited data. Subsequently, a practical test was conducted to validate the proposed algorithm's performance. The results demonstrated that the algorithm outperformed a simple linear fitting model using the least squares method (LSM), achieving an improvement of up to 21.9%. This outcome highlights the algorithm's potential for enhancing the performance of GS sensors in daytime monitoring and contributing to the safe operation of oil tank facilities and infrastructure health monitoring.

Self-regulation of bed temperature field of the fixed-bed reactor unit by composite-filled oxygen carriers for chemical looping combustion of methane

Fixed-bed reactors (FBRs) are suitable for chemical looping combustion (CLC) of gaseous fuels. However, the non-uniform temperature field such as the formation of hotpots can easily lead to the deactivation of oxygen carriers (OCs), ultimately leading to the degradation of the CLC performance and the durability of the OCs. This work systematically investigates the effect of individual CuO/SiO2 and Fe2O3/Al2O3 OC-filled FBR units on the bed temperature field using a self-built experimental setup to monitor the real-time bed temperature evolution. In addition, a strategy for self-regulating the bed temperature field by composite OCs-filled FBR units is proposed based on the differences in the thermodynamic properties of different OCs, including CuO/SiO2, Fe2O3/Al2O3, Mn2O3/ZrO2 and NiO/ZrO2. It has been found that the radial bed temperature of a single CuO/SiO2 OC-filled FBR unit is significantly higher than that at the central axis, and the bed temperature fluctuates within a range of ± 50 °C throughout the CLC process. The bed temperature of a single Fe2O3/Al2O3 OC-filled FBR unit fluctuated within a range of ± 25 °C during the reduction stage, but the bed temperature increased by nearly 100 °C due to the strong exothermic reaction of the oxidative regeneration of the reduced Fe2O3/Al2O3 OCs. The use of composite OCs-filled FBR units not only improves the CH4 conversion and CO2 selectivity, but also maintains a stable bed temperature fluctuates within a range of ± 15 ℃ during the different reaction stages of the CLC process. The synergistic effect between the OCs contributes to the bed temperature field remaining in a relatively stable state. The results indicate that the rational distribution of composite-filled OCs in FBRs can achieve self-regulation of the bed temperature field to some extent by exploiting the OCs’ endothermic and exothermic properties.

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.

Theoretical Analysis on Thermo-Mechanical Bending Behavior of Timber–Concrete Composite Beams

In this study, an analytical approach is introduced for predicting the bending behavior of a timber–concrete composite (TCC) beam subjected to a mechanical load and a non-uniform temperature field, in which the orthotropy of timber as well as interfacial slip are taken into consideration. The analytical model addresses the non-uniform temperature field using Fourier series expansion based on the heat transport theory. The stresses and displacements of the TCC beam under the thermo-mechanical condition are governed by the thermo-elasticity theory, and the corresponding solution is derived analytically by solving a group of non-homogeneous partial differential equations. The proposed solution is in good agreement with the finite element solution and exhibits higher accuracy compared to the Euler–Bernoulli beam solution that relies on the assumption of transverse shear deformation and isotropy. An extensive investigation is carried out to analyze how the bending behavior of TCC beams is influenced by variations in interfacial shear stiffness and temperature field.

Numerical investigation of non-uniform temperature fields for proppant and fluid phases in supercritical CO2 fracturing

The non-uniform temperature distribution in supercritical CO2 (Sc-CO2) fracturing influences the density, viscosity, and volume expansion or shrinkage rate of Sc-CO2, impacting proppant migration. This study presents a coupled computational fluid dynamics-discrete element method and heat transfer model to examine the effects of proppant bed shape and the heat transfers of proppant-wall, proppant-fluid, and fluid-wall on the fluid and proppant temperature fields. The Sc-CO2 volume expansion is assessed under various temperature conditions by evaluating the volume-averaged Sc-CO2 density. Several factors, including proppant size, shape, thermal conductivity, concentration, temperature difference, and injection velocity, are carefully analyzed to elucidate their impacts. The findings elucidate the existence of four distinct zones in the fluid temperature field. Each zone exhibits different magnitudes of temperature change under diverse conditions and undergoes dynamic transformations with the development of the proppant bed. The fluid-wall heat transfer and the fluid temperatures in Zones C and D are significantly subject to the fluid injection velocity (governing the heating duration), the temperature difference between fluid and formation (impacting the magnitude of heat flux), and the proppant bed shape (controlling the effective heating area). Additionally, the proppant-wall and proppant-fluid heat transfers determine the temperatures of both the proppant bed and the fluid within Zone B, showing a strong correlation with proppant thermal conductivity, proppant size, injection velocity, and temperature difference. The proposed coupled model provides valuable insights into the temperature distributions and flow behaviors of temperature-dependent fracturing fluids and proppants.

Free vibrations of axially loaded thin-walled shaft-disk rotors subjected to non-uniform temperature field

Research on vibrations of shaft-disk rotors in non-uniform thermal field is essential for the design of rotating machinery. In this paper, the dynamic model of axially loaded thin-walled shaft-disk rotors in axial non-uniform temperature field is developed, considering three-dimensional displacement fields of the shaft and disk. This model introduces the temperature-dependent properties of materials, and gyroscopic and centrifugal effects. Based on the Euler-Bernoulli beam theory and the Kirchhoff plate theory, Lagrange's equation is used to derive the differential equations of motion. By comparing with the results of the existing reference and finite element results, the accuracy of the present model is verified. The effects of the axial displacement of shaft, temperature-dependent material property, temperature difference, temperature distribution, disk position and axial preload on the free vibration of shaft-disk rotors are discussed. Results show that the present model can effectively predict free vibrations of shaft-disk rotors in axial non-uniform temperature field. The effect of thermal field on vibrations of shaft-disk rotors is affected by the rotational speed and disk location as well.

Flexural–torsional buckling of steel circular arches with I-section under central concentrated load in elevated-temperature environment

This article reports the fire resistance experiments conducted on I-section circular steel arches, as well as the observed out-of-plane flexural–torsional buckling (FTB) behavior and in-depth finite element numerical simulation results. The test was carried out using a large fire test furnace to provide a real fire environment with a nonuniform temperature field. A specially designed loading device allowed for unconstrained out-of-plane deformation of the specimens inside the furnace, thereby achieving effective load conditions and noncoupled response of the components. Numerical analyses were performed using a combination of the general codes Fluent and Abaqus, with the former used for heat transfer analyses, and a structural FE model including the loading device and complex geometric imperfections was established based on the measured data. Thus, accurate simulation of the out-of-plane behavior of the steel arches at elevated temperature was achieved. On this basis, an in-depth parametric study was carried out to investigate the effects of temperature field variations, load ratio (LR), and geometric imperfection. The analysis results show that FTB occurs at nonuniform temperatures for the arches under concentrated load, and the difference in temperature distribution in fire has a minimal effect on the FTB behavior. LR is negatively correlated with critical temperature; the smaller the LR, the more significant the weakening of critical loads by fire. The effect of initial geometrical imperfections on FTB at elevated temperatures is similar to that at ambient temperatures, and the effect on the critical temperature of FTB can almost be ignored when the imperfection amplitude is less than S/400.