Time-varying Temperature Distribution Research Articles

Investigation of temperature effects on wide steel box girder of suspension bridge based on long-term monitoring data

The time-varying temperature distributions on bridge structures may remarkably change structural performance, which may result in differential strain/stress responses on structural members compared with the design conditions. Therefore, it is crucial to have a comprehensive understanding of temperature distributions and its effects on bridges. In this study, taking advantage of structural health monitoring technology, 1-year field monitoring data collected from a long-span suspension bridge were used to investigate the temperature distributions and their effects on the steel box girder. Specifically, the distributions and probability statistics of temperatures on the top and bottom plates were firstly analyzed. Based on which, the transverse and vertical temperature differences on the box girder were further examined, moreover, the representative values of temperature differences for various return periods were calculated by exceedance probability method. At end, a temperature prediction method was proposed to simulated the temperature field distributions during bridge life cycle, to provide substantial temperature data for estimating future operation condition. The results of this study were beneficial to structural evaluation of in-service bridges to ensure their serviceability and integrity in the life cycle.

Effect of Temperature Distribution on Interfacial Bonding Process between CFRTP Composite and Aluminum Alloy during Laser Direct Joining

Laser direct joining enables non-destructive and lightweight joining of carbon fiber reinforced thermoplastic (CFRTP) composites and aluminum alloys. The interfacial bonding process determines the joint performance and is influenced by the time-varying temperature distribution. However, the interfacial bonding process occurs inside the joint, making it difficult to study the effect of temperature distribution. To resolve this issue, a novel online observation device for the interfacial bonding process between CFRTP composites and aluminum alloys is design, and the polymer melting, flowing, and bonding with metal during laser direct joining are observed. Further, temperature field simulation models for laser direct joining are established, and temperature distribution and gradient are calculated. The results show that the temperature distribution determines the melting of CFRTP composites, and bubbles generated by the thermal decomposition of the polymer hinder the melting. The temperature gradient is related to the movement of the molten matrix and fibers, and the movement towards the aluminum alloy induces cracking and delamination. Once the interface is filled with polymer, the motion changes to along the laser scanning direction and the joining defects are reduced. The study can provide a foundation for promoting interfacial bonding and reducing the defects of laser direct joining.

Accelerating Thermal Simulations in Additive Manufacturing by Training Physics-Informed Neural Networks With Randomly Synthesized Data

Abstract The temperature history of an additively manufactured part plays a critical role in determining process–structure–property relationships in fusion-based additive manufacturing (AM) processes. Therefore, fast thermal simulation methods are needed for a variety of AM tasks, from temperature history prediction for part design and process planning to in situ temperature monitoring and control during manufacturing. However, conventional numerical simulation methods fall short in satisfying the strict requirements of time efficiency in these applications due to the large space and time scales of the required multiscale simulation. While data-driven surrogate models are of interest for their rapid computation capabilities, the performance of these models relies on the size and quality of the training data, which is often prohibitively expensive to create. Physics-informed neural networks (PINNs) mitigate the need for large datasets by imposing physical principles during the training process. This work investigates the use of a PINN to predict the time-varying temperature distribution in a part during manufacturing with laser powder bed fusion (L-PBF). Notably, the use of the PINN in this study enables the model to be trained solely on randomly synthesized data. These training data are both inexpensive to obtain, and the presence of stochasticity in the dataset improves the generalizability of the trained model. Results show that the PINN model achieves higher accuracy than a comparable artificial neural network trained on labeled data. Further, the PINN model trained in this work maintains high accuracy in predicting temperature for laser path scanning strategies unseen in the training data.

Comparison of the corrugated steel web composite box-girder and traditional girders regarding temperature field under solar radiation

The corrugated web composite box-girder (CWCB) is a novel structural form and has been widely adopted in bridge engineering due to its excellent mechanical properties and construction convenience. However, researches on the temperature field in CWCB is very limited, which may augment the risk of concrete cracking and steel web bucking and deteriorate the durability of bridge structures. This paper thereby experimentally investigates the time-varying and spatial temperature distribution features of CWCB based on a long-term temperature monitoring system. The experimental results indicate that the temperature field in CWCB is non-uniformly distributed and the vertical and horizontal temperature differences can reach up to 13.4 ℃ and 19.1 ℃, respectively. Meanwhile, the observed temperature distribution profile of the experimental CWCB is varying with seasons owing to the different exposure to solar radiation. Then, a refined numerical thermal simulation approach is developed and its reliability and accuracy have been validated by the experimental temperature data of three types of box-girders, i.e., CWCB, ordinary composite box-girder (OCB), and conventional concrete box-girder (CCB). Based on the validated numerical approach, the temperature fields of three full-sized box-girders are therewith compared and the results demonstrate that the temperature field in CWCB is much more complicated than the traditional box-girders. Besides, the obtained cross-sectional temperature differences of CWCB are significantly larger than that of the traditional box-girders. Finally, two temperature profiles have been proposed to characterize the thermal actions in CWCB, which are composed of parabolas and polylines. The outcome of this study can provide a useful tool for analyzing the temperature field and calculating the design thermal load of CWCB.

Time-varying solar radiation-induced non-uniform temperature distribution of steel-concrete composite box girder-ballastless track system

Aiming to investigate the non-uniform temperature distribution of the steel-concrete composite box girder-ballastless track system induced by the time-varying solar radiation, the ray-tracing algorithm was used to calculate the environmental parameters. The segment finite element model (SFEM) for spatial interaction between the bridge and the ballastless track was used to perform several numerical simulations. The temperature variation induced by solar radiation was evaluated based on the numerical simulations. The results showed that the peak temperature of the system (on the western side of the steel web) was 49.59 Co (at 16:00). Regarding time-varying solar temperature distribution of the steel-concrete composite box girder-ballastless track system, a difference was found between the western and eastern sides of the steel webs. Finally, the vertical temperature gradient model of the steel-concrete composite box girder-ballastless track system was established according to the most unfavorable temperature. The results provided a reference for constructing and maintaining a steel-concrete composite box girder equipped with the ballastless track.

Overall deformation of steel-concrete-steel immersed structures during construction stage considering temperature effect

Temperature effect is one of the most significant factors to be considered in large-scale structures. For steel–concrete-steel composite immersed structures, the overall deformation is a closely watched indicator in the construction process. The main aim of this study is to investigate the overall deformation of steel–concrete-steel composite immersed structures during the construction stage, and thus a new numerical method comprehensively considering the temperature effect and material properties of early-age concrete is proposed. In the proposed method, a new finite element program for composite immersed structures, including thermal and structural modules, is developed in ANSYS. Firstly, the time-varying temperature distribution of the structure during the construction stage is accurately simulated by a transient thermal analysis, allowing for concrete hydration, solar radiation, air temperature, and changes of thermal properties comprehensively. Secondly, based on the ANSYS User-Programmable Features (UPFs), the stress–strain constitutive law of the concrete is redefined by modifying the material subroutine to consider the hardening and shrinkage of early-age concrete, then the overall structural deformation during the construction stage is estimated in the case that accurate temperature distribution and material properties are fully considered. Finally, a full-scale model of the composite immersed tunnel in Shenzhong Link is taken as an application case. The accuracy of simulation results is verified with the data of on-site monitoring. The results show that the temperature field of the composite immersed structure is obviously non-uniform and time-varying, and the overall contraction in lateral and longitudinal directions happens after the construction due to the variation of temperature and behaviors of early-age concrete.

Development of a Methodology for Calculating the Stress State and Resource of a Hydrogen Generator Using the Finite Element Method

An experimental stand was created to study the thermobaric and chemical influence of hydrogen on the identification of hydrocarbon production. The said stand allows to reproduce chemical-technological processes as close as possible to real formation ones. This stand makes it possible to study the kinetics of not only hydrogen, thermobaric and chemical effects, but also other thermal gas chemical processes, including hydrogen generation. The main element of the experimental stand is a hydrogen generator, the components of which work at high pressures and temperatures under conditions of hydrogen embrittlement of mechanical properties and an aggressive environment that causes corrosion of its inner surface. Based on this, the development of a methodology for calculating the thermal stress state of the generator, its strength under hydrogen embrittlement conditions, and its resource becomes relevant. Based on the finite element method, a methodology for calculating non-stationary temperature fields and the thermal stress state that occur in the hydrogen generator during thermobaric and chemical processes of varying intensity is proposed. The methodology allows to take into account the features of the geometry of the structure, the time-varying temperature and pressure distributions of the reaction products, the temperature dependence of the thermophysical and mechanical properties of the hydrogen generator material. Thanks to the application of the developed software, a study of the hydrogen generator thermal stress state during two real thermobaric and chemical processes of different intensity was carried out. Graphs of temperature and pressure changes of the reaction products of hydroreactive substances in the generator over time, which were registered during the experiment conduction, were used. The distribution of non-stationary temperature fields and stresses in the hydrogen generator elements was obtained. Areas of maximum load of generator elements are defined. It was established that during the flow of the studied thermobaric and chemical processes, pressure makes a greater contribution to the thermal stress state. The obtained results and the developed theory and software can be used in the study of generators of other designs with other thermobaric and chemical processes occurring in them.

Variable duty cycle heating strategy based online two-dimensional model for self-heating lithium-ion battery

It is a challenge to online obtain the time-varying temperature distribution of self-heating lithium-ion battery (SHLB), which results in a lack of theoretical basis for heating strategies to optimize heating time and temperature distribution uniformity. To reveal the evolution of temperature distribution and improve the temperature distribution uniformity of SHLB during heating, a variable duty cycle heating strategy with online two-dimensional model is proposed. Distributed thermal equivalent circuit model coupled with electrical model can obtain the two-dimensional temperature distribution of battery in real-time. The results show that the maximum temperature gap between the proposed model and the finite element model (FEM) is only 1.2 °C, while 90 % of the calculation time is saved. The proposed model can calculate the temperature distribution almost as accurately as FEM under different conditions. Based on the proposed model, heating currents of different values and duty cycles are applied to investigate their effects on the temperature distribution evolution of SHLB. Finally, we propose a variable duty cycle heating strategy that can automatically switch the duty cycle of the heating current according to the heating uniformity requirements in order to consider both heating time and the temperature distribution uniformity. The results show that compared with constant duty cycle heating, the variable duty cycle heating strategy can reduce the temperature difference by 35 % and limit the temperature difference to the pre-set boundary. The proposed strategy and method have considerable potential for use as improved temperature uniformity in battery management system.

Time-varying non-uniform temperature distributions in concrete box girders caused by solar radiation in various regions in China

Non-uniform temperature distributions of concrete box girders are induced by solar radiation depending on the structural shapes and shadows cast on them. Using a real-time shadow-selection algorithm and finite element method, the thermodynamic analysis of concrete box girders is carried out to simulate their time-varying temperature distributions. The theoretical results of the finite element model (FEM) are verified by measured data. Based on this, a series of FEMs of concrete box girders are established considering regional influences, and the temperature gradients of concrete box girders in different climatic zones in China are studied. The most unfavorable temperature gradient of concrete box girders in China is obtained, and it is important for design and not only for health monitoring. Moreover, comparing the temperature gradient modes in the specifications of various countries, the temperature gradient of concrete box girders in the China Highway Bridges Design Code is conservative for structural design. Furthermore, the influences on structural temperature distributions of varying environmental factors induced by regional influences are explored, including atmospheric transparency coefficient (ATC) and solar radiation absorptivity (SRA).

Theoretical analysis of unsteady convective heat transfer from a flat plate with time-varying and spatially-varying temperature distribution

Convective heat transfer due to laminar, incompressible flow past a flat plate has been extensively researched due to applications in a variety of engineering systems. In several cases, such as thermal management of Li-ion cells and phase change based energy storage, the flat plate temperature may vary as a function of both time and space, and the resulting plate heat flux is of interest. This paper presents an integral method based analytical model for predicting the heat flux distribution from a flat plate with a time-varying and spatially-varying temperature. Third-order Karman-Pohlhausen polynomial forms of velocity and temperature distributions are used in the integral energy equation to derive an ordinary differential equation that predicts the plate heat flux distribution in response to an arbitrary time- and space-dependent plate temperature distribution. The generalized results derived here are shown to reduce to previously reported results for special cases of only time-dependent or only spatially varying or constant plate temperature. Results are also shown to be in good agreement with finite-element simulations. The analytical model developed here is used to predict the plate heat flux in response to realistic plate temperature distributions that may be encountered in practical applications. These results improve the fundamental understanding of an important convective heat transfer process, and may help in the design and optimization of a broad variety of engineering systems involving convective heat transfer.

Thermal Distortion of Signal Propagation Modes Due to Dynamic Loading in Medium-Voltage Cables

Temperature variation from dynamic cable loading affects the propagation characteristics of transient signals. The distortion of modal signal components as a function of temperature in a three-phase medium-voltage cable is investigated. The temperature influence arises mainly through the complex insulation permittivity, which has a non-linear relationship with temperature. Near the maximum operating temperature of the cross-linked polyethylene insulation, the propagation velocity increases by 0.56% per degree centigrade but is an order of magnitude less sensitive at ambient temperature. The paper presents modeling results based on cable impedance and admittance matrices obtained from electromagnetic field simulation, taking into account the time-varying temperature distribution in the cable cross-section. The results are verified by applying Rayleigh–Schrödinger perturbation analysis. In the time domain, signal patterns shift when the modal propagation velocities change upon cable loading. Moreover, separation of degenerate modes is observed when the cable phase conductors carry an unbalanced current. The perspectives for exploiting the temperature dependency of signal propagation for pinpointing cable defects and for dynamic rating of underground power cables are discussed.

Precise thickness profile measurement insensitive to spatial and temporal temperature gradients on a large glass substrate.

When manufacturing glass substrates for display devices, especially for large-sized ones, the time-varying spatial temperature gradient or distribution on the samples is remarkably observed. It causes serious degradation of thickness measurement accuracy due to the combination of thermally expanded thickness and temperature-dependent refractive index. To prevent or minimize the degradation in thickness measurement accuracy, the temperature distribution over an entire glass substrate has to be known in real time in synchronization with the thickness measurement to specify the refractive index of the sample based on an exact mathematical model of the temperature-dependent refractive index. In this paper, a measurement method for determining the thickness profile of a large glass substrate regardless of precise measurement of temperature distribution and the mathematical model of the refractive index was demonstrated. The widely used glass substrates with nominal thicknesses of 0.6 mm and 1.3 mm were measured at room and high temperatures. Through comparison of thickness profiles of hot glass substrates having large temperature gradients and those estimated through thermal expansion of thickness profiles measured at room temperature, it was confirmed that the proposed method can provide highly reliable thickness measurement results under such challenging conditions, unlike simple calculation from the optical thickness using the well-known refractive index.

Finite Element Modeling of Geothermal Source of Heat Pump in Long-Term Operation

Model simulation allows to present the time-varying temperature distribution of the ground source for heat pumps. A system of 25 double U-shape borehole heat exchangers (BHEs) in long-term operation and three scenarios were created. In these scenarios, the difference between balanced and non-balanced energy load was considered as well as the influence of the hydrogeological factors on the temperature of the ground source. The aim of the study was to compare different thermal regimes of BHEs operation and examine the influence of small-scale and short-time thermal energy storage on ground source thermal balance. To present the performance of the system according to geological and hydrogeological factors, a Feflow® software (MIKE Powered by DHI Software) was used. The temperature for the scenarios was visualized after 10 and 30 years of the system’s operation. In this paper, a case is presented in which waste thermal energy from space cooling applications during summer months was used to upgrade thermal performance of the ground (geothermal) source of a heat pump. The study shows differences in the temperature in the ground around different Borehole Heat Exchangers. The cold plume from the not-balanced energy scenario is the most developed and might influence the future installations in the vicinity. Moreover, seasonal storage can partially overcome the negative influence of the travel of a cold plume. The most exposed to freezing were BHEs located in the core of the cold plumes. Moreover, the influence of the groundwater flow on the thermal recovery of the several BHEs is visible. The proper energy load of the geothermal source heat pump installation is crucial and it can benefit from small-scale storage. After 30 years of operation, the minimum average temperature at 50 m depth in the system with waste heat from space cooling was 2.1 °C higher than in the system without storage and 1.6 °C higher than in the layered model in which storage was not applied.

Experimental Analysis on Skid Damage of Roller Bearing with the Time-Varying Slip and Temperature Distribution

Skid damage affects the performance of aviation bearing, which covers different disciplines in tribology, thermology, materials science, dynamics, et al. In this manuscript, a novel horizontal skid damage test rig of a rolling bearing with higher rotation accuracy and better linear contact was built, which can simulate the rolling/sliding contact between the roller and inner ring. Combining with temperature, load, speed, slip, and surface microscopy, the skid damage mechanism of roller bearings was analyzed from a multi-information perspective. Meanwhile, the dynamic lubrication failure process of the contact pair in rolling bearings with the time-varying slip and temperature distribution was revealed. The effect of different radial loads, inner ring speeds, lubricating oil quantities, and states of cleanliness on the time-varying characteristics of the temperature and the slip of the rolling bearing were obtained. Among them, the radial load has the greatest influence on the slip rate of rolling bearing. In addition, the test results show that the skid damage under extremely light load is the comprehensive effect of adhesive wear and thermal failure.

Experimental study of mode shifting in an asymmetrically heated rectangular plate

Modal shifting and jumping in thermally buckled plates has been investigated previously using computational models; however, relatively few experimental explorations have been reported. In this study, the modal shifts and jumps in a simple rectangular plate or panel were investigated using digital image correlation to obtain detailed mode shapes. One face of the planar panel, which was 219 × 146 mm, was speckled and viewed with a stereoscopic digital image correlation system using pulsed-laser illumination and with a laser vibrometer at a single point. The other face was heated using a set of 1 kW quartz lamps to produce a non-uniform temperature distribution which progressively increased from room temperature to around 760 K. An infra-red camera recorded the time-varying temperature distribution on the panel while it was excited with an electrodynamic shaker. A waterfall plot, or time-frequency spectrogram, showing natural frequencies as a function of time was generated, which highlighted the shifting response of the panel with temperature. The heating sequence was repeated and the panel excited at the natural frequencies identified in the waterfall plot, which permitted the corresponding mode shapes to be measured. These data showed that mode shifting and jumping was present with asymmetric heating, but not with spatially uniform heating, and was associated with thermally-induced buckling.

Transient Temperature Effects on the Aerothermoelastic Response of a Simple Wing

Aerothermoelasticity plays a vital role in the design and optimisation of hypersonic aircraft. Furthermore, the transient and nonlinear effects of the harsh thermal and aerodynamic environment a lifting surface is in cannot be ignored. This article investigates the effects of transient temperatures on the flutter behavior of a three-dimensional wing with a control surface and compares results for transient and steady-state temperature distributions. The time-varying temperature distribution is applied through the unsteady heat conduction equation coupled to nonlinear aerodynamics calculated using 3rd order piston theory. The effect of a transient temperature distribution on the flutter velocity is investigated and the results are compared with a steady-state heat distribution. The steady-state condition proves to over-compensate the effects of heat on the flutter response, whereas the transient case displays the effects of a constantly changing heat load by varying the response as time progresses.

Effect of fluid-thermal–structural interactions on the topology optimization of a hypersonic transport aircraft wing

Aerothermoelasticity plays a vital role in the design of hypersonic aircraft as the coupling between the thermodynamics, aerodynamics and structural dynamics cannot be ignored. While topology optimization has been used in the design of aircraft components, thus far, existing optimization algorithms lack the capability to include aerothermodynamic coupling effects. This article presents an original evolutionary structural topology optimization algorithm that includes hypersonic aerothermoelastic effects. The time-varying temperature distribution is applied through a conjugate heat transfer analysis integrated in time by an unsteady conduction solver, and is coupled to the aerodynamics, which is calculated by a supersonic vortex lattice method. This article analyses the effect of fluid-thermal–structural interactions on the optimization of a hypersonic transport aircraft wing, by optimizing the wing structure with various degrees of coupling. The coupling of the aerothermodynamics drives the optimization of the structural design and therefore must be considered for hypersonic applications. This new optimization algorithm allows the coupling of the aerothermodynamics to be considered in the early stages of the design, potentially avoiding a costly re-design.

A Hypersonic Aircraft Optimization Tool with Strong Aerothermoelastic Coupling

The design and optimization of hypersonic aircraft is severely impacted by the high temperatures encountered during flight as they can lead to high thermal stresses and a significant reduction in material strength and stiffness. This reduction in rigidity of the structure requires innovative structural concepts and a stronger focus on aerothermoelastic deformations in the early design and optimization phase of the design cycle. This imposes the need for a closer coupling of the aerodynamic, thermal and structural design tools than is currently in practice. The paper presents a multi-disciplinary, closely coupled optimization suite that is suitable for preliminary design in the hypersonic regime. The time varying temperature distribution is applied through an equilibrium analysis, and is coupled to the aerodynamics through the Tranair® solver. An analysis of the effect that the aerothermodynamic coupling has on the sizing of the aircraft is given, along with the effect of skin buckling. It is shown that the coupling of the aerothermodynamics drives the sizing of the structure and therefore must be considered for hypersonic applications.

Natural convection effects in the heat transfer from a buried pipeline

In the present paper, the effect of the buoyancy on the heat transfer from a buried pipeline is investigated. The soil surrounding the pipe is modelled as a porous medium saturated by water, and the Darcy’s law is assumed. Reference is made to a time-varying temperature distribution on the soil surface, and uniform and constant temperature on the pipe wall. The steady state regime is investigated as particular case. The heat power per unit length is evaluated for different values assumed by the Darcy–Rayleigh number, thus revealing that, for high values of Ra, the natural convection effects are non trivial. A comparison with the case of pure conduction is made for the limiting case of a vanishing value of Ra, revealing an excellent agreement.

Reconstruction of the deep temperature by the acoustothermometric method and with consideration for the heat conduction equation

An acoustothermometric algorithm for reconstruction of the time-varying spatial temperature distribution is proposed and studied. The algorithm is based on the following a priory information: temperature variations is described by the heat conduction equation. Two distribution parameters are determined: the source and the temperature conductivity coefficient. Reconstruction is carried out on the basis of experimental data obtained when the model object (beef liver) is heated up. Obtaining these data requires 10 seconds (for a measurement error of about 0.1 K). In the reconstruction process, an error of about 0.5 K, which completely meets the medical requirements, is attained.