3D Thermal Field Research Articles

Thermal structure of the southern Caribbean and northwestern South America: implications for seismogenesis

Abstract. The seismogenesis of rocks is mainly affected by their mineral composition and in situ conditions (temperature and state of stress). Diverse laboratory experiments have explored the frictional behaviour of the rocks and rock-forming minerals most common in the crust and uppermost mantle. However, it is debated how to “upscale” these results to the lithosphere. In particular, most earthquakes in the crust nucleate down to the crustal seismogenic depth (CSD), which is a proxy for the maximum depth of crustal earthquake ruptures in seismic hazard assessments. In this study we propose a workflow to upscale and validate those laboratory experiments to natural geological conditions relevant for crustal and upper-mantle rocks. We used the southern Caribbean and northwestern South America as a case study to explore the three-dimensional spatial variation of the CSD (mapped as D90, the 90 % percentile of hypocentral depths) and the temperatures at which crustal earthquakes likely occur. A 3D steady-state thermal field was computed for the region with a finite-element scheme using the software GOLEM, considering the uppermost 75 km of a previously published 3D data-integrative lithospheric configuration, lithology-constrained thermal parameters, and appropriate upper and lower boundary conditions. The model was validated using additional, independent measurements of downhole temperatures and heat flow. We found that the majority of crustal earthquakes nucleate at temperatures less than 350 ∘C, in agreement with frictional experiments of typical crustal rocks. A few outliers with larger hypocentral temperatures evidence nucleation conditions consistent with the seismogenic window of olivine-rich rocks, and can be due to either uncertainties in the Moho depths and/or in the earthquake hypocentres or the presence of ultramafic rocks within different crustal blocks and allochthonous terranes accreted to this complex margin. Moreover, the spatial distribution of crustal seismicity in the region correlates with the geothermal gradient, with no crustal earthquakes occurring in domains with low thermal gradient. Finally, we find that the largest earthquake recorded in the region (Mw=7.1, Murindó sequence, in 1992) nucleated close to the CSD, highlighting the importance of considering this lower-stability transition for seismogenesis when characterizing the depth of seismogenic sources in hazard assessments. The approach presented in this study goes beyond a statistical approach in that the local heterogeneity of physical properties is considered in our simulations and additionally validated by the observed depth distribution of earthquakes. The coherence of the calculated hypocentral temperatures with those expected from laboratory measurements provides additional support to our modelling workflow. This approach can be applied to other tectonic settings worldwide, and it could be further refined as new, high-quality hypocentral locations and heat flow and temperature observations become available.

Entropy generation and natural convection on a cubic cavity with a pair of heat source at different configurations

Entropy generation and natural convection in a discretely heated cubic air-filled cavity has been numerically investigated in this study. A pair of discrete heat sources located at the bottom wall is at first considered for three different configurations. Both side walls are fixed at ambient condition, while the remaining walls are kept insulated. The three-dimensional, time-dependent continuity, momentum and thermal energy equations are selected as the governing equations of the present analysis. Galerkin finite element method is employed to solve those equations in non-dimensional forms. Parametric investigation is carried out by varying Rayleigh number within the range of 103–106 at fixed Prandtl number of 0.71. Results are presented in terms of qualitative plots of 3D velocity and thermal fields, and the quantitative evaluation of average Nusselt number and total entropy generation. A functional dependence of Nusselt number on the Rayleigh number and the distance between the symmetrically positioned heaters has also been presented in terms of empirical correlation. This comparative study shows that the configuration of the heaters has a great impact on the thermal characteristics, and thus provides one the opportunity to obtain an optimum arrangement for the system.

Three-dimensional exact analytical solutions of transversely isotropic plate under heat sources

An accurate and efficient calculation method for the transversely isotropic thermoelastic plates plays an important role in exact design and quality control of the engineering structures. In this study, the three-dimensional (3D) thermal stress field of transversely isotropic plates under arbitrary heat source is obtained using Green’s function method. To achieve the purpose, the 3D Green’s function solutions of transversely isotropic plate under a point heat source are firstly derived based on the general solutions which are presented in potential functions. The concise harmonic potential functions are constructed in simple functions with undetermined constants by mirror image principle. Then, the Green’s functions are achieved by substituting the harmonic functions into the general solution. All temperature and stress components can be analytically expressed using simple functions which are convenient to use. The present method without simplifying assumption of dimensions has the applicability and reliability to analysis plate structures with arbitrarily thickness. Numerical calculations show the good convergence and high efficiency of the method. This study presents a high precision and efficiency predesign method for the thermos elastic plate structures. The numerical results provide theoretical guideline for the accurate design and quality control of plate structures.

Three-Dimensional Electromagnetic and Thermal Field Coupled Analysis of Different Types of REBCO Coils Under Overcurrent Conditions

The RE (rare earth) Ba <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> (REBCO)-coated conductor has shown its high potential in various applications. However, the quench problem under overcurrent conditions, as well as some other problems, is still hindering its practical use. In this research, we have developed a versatile 3D electromagnetic and thermal field coupled FEM analysis tool for REBCO coils, and verified its capability in studying the transient electromagnetic and thermal behaviors, such as current density, Joule heating, temperature distribution, etc., with two case studies. In the first case study, the transient electromagnetic and thermal behaviors of SFCL REBCO coils under overcurrent are studied in the cases of uniform J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> distribution and local J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> degradation. The influence of current leads and local J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> degradation on the quench is investigated. In the second case study, the influence of external energy input, input area, and different time constants of current decrease on the quench of magnet REBCO coils is studied. Moreover, the limitation and improvement of the quench detection scheme based on voltage detection are discussed. The influence of external energy input on the current density distribution is also investigated.

A 3D Thermal Field Restructuring Method for Concrete Dams Based on Real-Time Temperature Monitoring

Temperature monitoring and control is of great significance to ensure concrete quality during the construction of dam concrete. In this study, a 3D thermal field restructuring method is developed for the complex evolution process of thermal field in dam concrete during construction, based on real-time temperature monitoring. The proposed method is related to the ordinary Kriging interpolation and the distributed optical fiber temperature sensing (DTS) technology. Based on the temperature monitoring of the Wudongde (WDD) super-high arch dam, the 3D thermal field can be acquired effectively and fast by the proposed restructuring method. The results indicate the temperature difference between the temperature measured by thermometers and the restructured temperature is within 1 °C. The evolution process of the restructured 3D thermal field for the WDD arch dam is in good agreement with the site situation. In addition, the uncertainty, cons and pros of the proposed method and the optimal layout of temperature sensors are further discussed. Although the proposed thermal field restructuring method has some limitations, it is believed to be a valuable tool for acquiring the 3D thermal field and thermal gradient of dam concrete.

The 3D thermal field across the Alpine orogen and its forelands and the relation to seismicity

Abstract Temperature exerts a first order control on rock strength, principally via thermally activated creep deformation and on the distribution at depth of the brittle-ductile transition zone. The latter can be regarded as the lower bound to the seismogenic zone, thereby controlling the spatial distribution of seismicity within a lithospheric plate. As such, models of the crustal thermal field are important to understand the localisation of seismicity. Here we relate results from 3D simulations of the steady state thermal field of the Alpine orogen and its forelands to the distribution of seismicity in this seismically active area of Central Europe. The model takes into account how the crustal heterogeneity of the region effects thermal properties and is validated with a dataset of wellbore temperatures. We find that the Adriatic crust appears more mafic, through its radiogenic heat values (1.30E-06 W/m3) and maximum temperature of seismicity (600 °C), than the European crust (1.3–2.6E-06 W/m3 and 450 °C). We also show that at depths of

A novel local temperature change detection approach in a 3D thermal field

ABSTRACT Local thermal field monitoring is of great importance in industrial engineering practice. In view of the complex thermodynamics of a 3D thermal field, the local temperature change beneath the global thermal field is relatively challenging to detect using existing approaches. To fill this gap, we propose a thermal field monitoring method that decomposes the dynamic thermal field into global trend and local variability parts. Specifically, a universal kriging model that characterises the spatial correlation at each time epoch is developed to model the local variability using sensing data. To efficiently monitor the thermal field changes, a multivariate cumulative sum chart that uses the estimated parameters is designed. An actual case study of the thermal field of a granary is used to validate the performance of the proposed method.

Artificial Neural Network (ANN) Based Fast and Accurate Inductor Modeling and Design

This paper analyzes the potential of Artificial Neural Networks (ANNs) for the modeling and optimization of magnetic components and, specifically, inductors. After reviewing the basic properties of ANNs, several potential modeling and design workflows are presented. A hybrid method, which combines the accuracy of 3D Finite Element Method (FEM) and the low computational cost of ANNs, is selected and implemented. All relevant effects are considered (3D magnetic and thermal field patterns, detailed core loss data, winding proximity losses, coupled loss-thermal model, etc.) and the implemented model is extremely versatile (30 input and 40 output variables). The proposed ANN-based model can compute 50'000 designs per second with less than 3% deviation with respect to 3D FEM simulations. Finally, the inductor of a 2 kW DC-DC buck converter is optimized with the ANN-based workflow. From the Pareto fronts, a design is selected, measured, and successfully compared with the results obtained with the ANNs. The implementation (source code and data) of the proposed workflow is available under an open-source license.

The Assessment of Construction Details in Terms of 3D Thermal Fields and the Impact on Building Design

Thermal bridge is a very common and undesirable phenomenon in a building. Thermal joint (bridge) is usually based on material or geometry reasons or their combinations. Many types (connection of window – wall, pillar – wall), can be calculated and evaluated sufficiently in 2D section, but in some types it is necessary to take into account 3D heat conduction. For example: a corner with ceiling (roof) and two walls where is strong deformation of isotherms and the internal surface temperature is definitely lower than in 2D section. According to the Czech Technical Standard it is necessary to fulfil law requirement – Temperature Factor at internal surface lowest temperature „at each location“. Recommendation is solving of “differential equation multi-dimensional of thermal field”. In this case of “building corner” project engineer has to decide for 3D modelling. In the contribution there is presented a mistake in 2D model, the situation when it is necessary to use 3D model. Additionally, there are recommendations to eliminate the risk of condensation and mould.

Modeling and simulation of thermal field and solidification in laser powder bed fusion of nickel alloy IN625

Finite element modeling and simulation of laser powder bed fusion process (L-PBF) provides physical insight about the laser processing that is often not possible or highly difficult by in-situ monitoring or in-process measurements. A three-dimensional (3D) thermal field especially into depth direction that is not visible by a thermal camera can be obtained by solving the 3D heat transfer problem. Furthermore, microstructure growth can be modelled to predict the direction of solidification in the fabricated part. This paper presents 3D Finite Element Method (FEM) based simulation models developed for laser processing of single- and multi-tracks with different energy density levels dependent upon process parameters such as laser power and scan velocity. This 3D L-PBF process model is validated with in-situ thermal measurements and further improved by utilizing predicted spattering of powder material which is in turn included as a stochastic heat loss in the 3D FEM model. Thermal gradients extracted from these simulations utilized to compute the directions in the resulting solidification which are found to be in reasonable agreements with experimental observations. Finally, a phase field method based post processing is applied on the thermal solution to simulate the nucleation phenomenon and columnar dendrite formation during solidification.

Refining the thermal structure of the European lithosphere by inversion of subsurface temperature data

Abstract We present an updated thermal model of the European lithosphere based on a new stochastic modeling work flow. We developed this work flow to estimate subsurface temperatures from site- to regional-scale, up to the depth of the lithosphere-asthenosphere boundary (LAB). Our model is composed of four layers, consisting of sediments, upper crust, lower crust and lithospheric mantle. We asigned thermal properties, including radiogenic heat production and temperature- and pressure-dependent bulk thermal conductivity on the base of broad-scale lithological variation within the European crust. We corrected thermal properties with a 1D steady-state temperature approximation, assuming only vertical heat flow. Using these corrected thermal properties, we calculated the 3D thermal field with a conjugate-gradient method, assuming fixed temperatures at the surface and at the base of the lithosphere. To obtain more robust results for our thermal model, we applied data assimilation, aiming at consistency between temperature and heat flow observations and tectonic model predictions. We used an Ensemble Smoother Multiple with Data Assimilation (ES-MDA) method to update prior estimates of thermal properties and the thermal field with temperature data. We calibrated our European thermal model with available regional thermal models due to the present lack of a unified dataset with public borehole temperature measurements. A large dichotomy is observed in the model along the Trans-European Suture Zone (TESZ). Northeast of the TESZ, geothermal gradients up to 10 km depth are mainly below 20 °C km−1. Southwest of the TESZ, gradients range from 20 °C km−1 near the Adriatic coast to more than 50 °C km−1 in volcanically and tectonically active regions. We show that the large scale thermal structure is locally and regionally perturbed by non-conductive heat transfer and affected by transient effects.

3D magnetic and thermal fields for in the transformer with homogenised amorphous C-core under high frequency

3D magnetic and thermal fields for in the transformer with homogenised amorphous C-core under high frequency

A 3D gravity and thermal model for the Barents Sea and Kara Sea

In the frame of this study, we investigate the lithosphere-scale 3D physical state of the Barents Sea and Kara Sea region. Therefore, we test an existing 3D structural model against the gravitational field by considering the heterogeneous upper mantle to further assess the structural and density configuration of the continental crystalline crust. The resulting 3D density configuration of the crust is discussed in terms of its relationships with the spatial distribution of tectonically different domains. In addition, it provides the base for a lithology-controlled parameterisation of the crust with thermal properties to calculate the 3D conductive thermal field. The deeper thermal field is controlled by the depth configuration of the lithosphere–asthenosphere boundary. Accordingly, deeper isotherms such as the 450°C isotherm deepen from below the rifted SW Barents Sea towards the intracratonic basins of the eastern Barents Sea and Kara Sea, indicating an increase of the lithospheric strength in the same direction. Temperature measurements of the upper 800m below the SW Barents Sea reveal an increased thermal gradient which cannot be reproduced by a steady-state 3D conductive model alone. Beside fault-induced fluid flow to be active there, an alternative scenario could involve a phase of subsidence long enough to increase the temperature of the upper 800m, followed by an uplift and erosion phase that prevented the positive thermal anomaly to propagate towards larger depths. The final lithosphere-scale 3D model is the first to integrate the geological, density and thermal configuration of the entire Barents Sea and Kara Sea region and hence provides an ideal base for future thermomechanical studies addressing, for instance, questions on the present-day, past and future relationships between lithospheric strength and deformation.

Computational Simulation of Thermal and Spattering Phenomena and Microstructure in Selective Laser Melting of Inconel 625

Computational modelling of Laser Powder Bed Fusion (L-PBF) processes such as Selective laser Melting (SLM) can reveal information that is hard to obtain or unobtainable by in-situ experimental measurements. A 3D thermal field that is not visible by the thermal camera can be obtained by solving the 3D heat transfer problem. Furthermore, microstructural modelling can be used to predict the quality and mechanical properties of the product. In this paper, a nonlinear 3D Finite Element Method based computational code is developed to simulate the SLM process with different process parameters such as laser power and scan velocity. The code is further improved by utilizing an in-situ thermal camera recording to predict spattering which is in turn included as a stochastic heat loss. Then, thermal gradients extracted from the simulations applied to predict growth directions in the resulting microstructure.

The 3D conductive thermal field of the North Alpine Foreland Basin: influence of the deep structure and the adjacent European Alps

We use a databased lithospheric-scale 3D structural model of the Molasse Basin area and the adjacent part of the Alpine orogen to calculate the present-day 3D thermal field of this continental collision zone. With our work we contribute to the understanding of the temperature distribution and the existence of pronounced positive and negative thermal anomalies in the Molasse Basin. We assume conductive heat transport and compare calculated temperatures to measured values and to other published 3D models. Areas where predicted and observed temperatures match closely are interpreted to be dominated by conductive heat transport. For areas, where a poor fit between modelled and observed temperatures has been obtained, we discuss possible reasons of this misfit. In particular, an additional contribution by fluid flow to the heat transport is likely. We conclude that the thermal field is controlled by conduction in the lithospheric mantle and the crystalline crust. Furthermore, we show that the positive and negative thermal anomalies in the Molasse Basin are partly triggered by the structural configuration of the crystalline crust. In particular, the domains of the Tauern Body and the upper part of the Alpine crust on the one hand and the insulating Molasse Basin sediments on the other hand control the shallow thermal field of the Molasse Basin area in response to their contrasting thermal properties. Our results demonstrate that the foreland basin and the adjoining Alps have to be regarded as an interdependent system that needs to be considered adequately if the present-day 3D thermal field of that area is assessed.

Design of permanent magnet synchronous motors including thermal aspects

Purpose – The purpose of this paper is to include thermal analysis in the design process of permanent magnet synchronous motor (PMSM). The additional objective is a comparison of PMSM with induction motor (IM) in terms of thermal phenomena. Design/methodology/approach – Numerical investigation using commercial software MotorSolve was performed. Parameterized models of PMSM and IM were used. Calculations of motor parameters and temperature distribution were made using Finite Element Method. Findings – The results of the calculations show that thermal calculations should be included in the design process because the maximum permissible operating temperature of permanent magnets should not be exceeded. A comparative analysis of PMSM and IM shows that the PMSM has better parameters than the IM which was used as a base of the PMSM construction. Research limitations/implications – Computational models should be verified experimentally on a physical model or by using more complex numerical models. In the case of IM thermal calculations, a method of air speed calculation should be proposed. Air speed is a parameter that is necessary in thermal analysis of IM, but during the design process it is unknown. Originality/value – This paper presents modelling methodology of 3D transient thermal field coupled with electromagnetic field applied in a three-phase IM at rated load conditions. This paper presents a design strategy which includes thermal analysis of the designed PMSM. Moreover, the paper shows a comparison between PMSM and IM indicating advantages of PMSM over IM.

Calculation of 3D Fluid Flow Field and Thermal Field of Air-Cooled Medium Motor

For a medium air-cooled asynchronous motor, the physical model of cooling air inside the motor was established to research the air flow distribution and characteristics of the internal flow of the medium motor. By the finite volume method according to the computational fluid mechanics (CFD) principle, the three-dimensional turbulent flow field in computational domain was simulated numerically using boundary conditions of the pressure inlet and outlet obtained from engineering calculations. From the result, the thermal field of stator and rotor was calculation. The results show that the wind speed of cooling air duct which near the both ends was higher than the middle. It causes the temperature of the motor which near the both ends was lower than the middle part. The maximum temperature rise of the motor appear in the middle of the upper windings, and the specific value was 74K.

A Comprehensive Model for Laser Hardening of Carbon Steels

This article illustrates the development of a complete and exhaustive mathematical model for the simulation of laser transformation hardening of hypo-eutectoid carbon steels. The authors propose an integrated approach aimed at taking into consideration all the phenomena involved in this manufacturing process, with particular attention to implementing easy mathematical models in order to optimize the trade-off between the accuracy of the predicted results and the computational times. The proposed models involve the calculation of the 3D thermal field occurring into the workpiece and predict the microstructural evolution of the target material exploiting an original approach based on the definition of thermodynamic thresholds, which can be considered as a physical constant of the material itself. Several parameters and phenomena are taken into consideration in order to accurately simulate the process: laser beam characteristics, fast austenization of the steel, and tempering effect due to mutually interacting beam trajectories. The accuracy of the model is presented by means of hardness comparisons between hardness predictions and measurements in single and double paths surface treating of AISI 1040.

Analysis of Water Cooled Permanent Magnet Traction Motors Using 3D Fluent and Thermal Field

This paper gives a method to calculate the temperature rise of the water cooled PM railway traction motor using 3D fluent and thermal field. Building a 3D Finite Element Method (FEM) model of 20kW PM synchronous traction motor, the heat transfer coefficient of each tunnel wall is calculated by fluent field, and then the temperature distribution is got from thermal field. Compared with the experimentation, the precision of this method is verified and some conclusions are obtained.

Thermal analysis of high speed permanent magnetic generator

High-speed permanent magnetic generators (HSPMG) are common and important power generation equipments used in distributed generation systems. A 100 kW level HSPMG is investigated in this paper, and it is fluid-thermal coupling analyzed. The transient 2D electromagnetic field while machine is under rated operating is analyzed by using the time-stepping FEM, from which the electromagnetic performances and the loss distributions are obtained. Then, an analysis model for fluid-solid temperature field analysis is established. Taking losses as the distributed heat sources, the 3D thermal field is coupling calculated. The variations of heat transfer coefficient and temperature of fluid in stator grooves along the axial direction, as well as the whole region 3D temperature distribution in HSPMG are obtained. Then, considering the variations of heat sources distributions and heat transfer conditions, 3D temperature fields of HSPMG operating under different speeds are calculated, and the influences of machine operating speed on the HSPMG thermal performance are studied, based on which, the functions of machine temperature with operating speed and stator windings resistance are proposed. The obtained conclusions may provide a useful reference for the design and research of HSPMG.