Three-dimensional Heat Conduction Model Research Articles

Coupled Monte Carlo and Thermal-Hydraulics Modeling for the Three-Dimensional Steady-State Analysis of the Xi’an Pulsed Reactor

The Xi’an Pulsed Reactor (XAPR) is characterized by its small core size and integrated fuel moderator structure, which results in a non-uniform core power and temperature distribution. Consequently, a complex coupling relationship exists between its core neutronics and thermal hydraulics, necessitating the assurance for the operational safety of the XAPR. To optimize the experimental scheme in the reactor, a refined three-dimensional steady-state nuclear-thermal coupling analysis is imperative. This study focuses on investigating the coupling calculation of a three-dimensional steady-state neutronics and thermal-hydraulics model for the XAPR by utilizing an open-source multi-physical coupling framework known as Cardinal. The neutron transport equation is effectively solved using OpenMC, while a three-dimensional heat conduction model is employed to compute the heat conduction of the fuel elements. Furthermore, a parallel multi-channel model is utilized to determine the fluid heat transfer. The research is centered on the XAPR, whereby Monte Carlo and thermal-hydraulics coupling calculations of the core under steady-state full-power conditions are conducted, specifically at an operational capacity of 2 MW. The results demonstrate a strong agreement between the simulation and experimental outcomes. The maximum temperature recorded for the thermometric fuel element in the XAPR is 795.1 K, with a deviation of approximately −5.7% from the measured value. Moreover, the outlet fluid temperature of the thermal channel is observed to be 360 K, exhibiting a deviation of around −2.7% from the measured value.

Experimental investigation and modeling of falling film heat transfer on partial dry-out condition

Falling film heat transfer has been applied for decay heat removal in more and more nuclear reactors, in which the coolant feed rate is set small to prolong the effective cooling time during accident conditions. Previous works have shown that the cooling surface is under partial dry-out condition for most of the time during the accident, while the existing falling film experiments are mainly focused on fully-wetted condition. In this paper, falling film experiments were conducted on a horizontal plain copper tube within 0.019–0.099 kg/m·s coolant flow rate, 0–164.1 kW/m2 heat flux, and dry-out condition is emphasized. In the experiments, it is found that the overall liquid coverage rate measured by infrared equipment was between 45.2 % and 100 %, and the dry-out process is recorded and analyzed as well. Moreover, HTC (Heat Transfer Coefficient) at wetting area is defined to characterize the heat transfer on the surface covered by liquid and is obtained based on a three-dimensional heat conduction model of test tube. Boiling HTCs on falling film are found 10 % approximately higher than that in pool boiling condition. The difference is attribute to the different mechanism of bubble departure and bubble growth environment, with which the falling film condition is found to result in a 1–3 times bubble departure diameter and a 0.85 times bubble growth rate compared with pool boiling condition. Finally, a general falling film heat transfer model is developed based on the conservation equations with consideration of liquid coverage, gas–liquid interface evaporation and liquid sub-cooling. The model shows effective for falling film heat transfer prediction on both fully-wetted and dry-out, convection and boiling conditions with different working fluids through the validation with a number of experimental data. The findings in this work could be helpful for the design and analysis of nuclear cooling system, as well as the falling film evaporation system.

Experimental study on dressing concave trapezoidal diamond grinding wheel by electrical discharge grinding method

Electrical discharge grinding (EDG) method is proposed for dressing bronze bonded diamond grinding wheel for the first time. The advantage of this dressing method is that it can realize the discharge removal of non-conductive diamond abrasive particles and greatly improve the dressing efficiency. It is suitable for dressing coarse-grained complex forming grinding wheel. The material removal mechanism in EDG dressing is deeply analyzed, and a three-dimensional heat conduction model in the discharge process is established. The temperature field distribution in bronze and diamond under corresponding discharge parameters is obtained by numerical simulation, and the grinding depth is optimized based on the softening depth of diamond. The dressing scheme of quickly removing the rectangular block area first and then approaching layer by layer according to the design profile is formulated. The high-precision concave isosceles trapezoidal grinding wheel is dressed by using the optimized machining parameters. Finally, the dressing accuracy is evaluated by grinding the graphite plate. The detection results show that the dimensional errors of the upper and lower lines are all within 5 μm, the dimensional error of the height is 9 μm. The maximum error of the angle between the two waist is 0.33°. The minimum transition arc radius between waist and lower line is 202 μm. The straightness errors of the lower line and the two waist oblique lines are less than 7 μm. The profile error at the transition between waist and lower line is less than 62 μm.

Numerical Simulation of the Temperature Distribution and Evolution Law of Underground Lignite Gasification.

To study the temperature distribution characteristics and evolution law of underground lignite gasifiers, a three-dimensional heat conduction model of underground lignite gasification was constructed. Moreover, the effects of different coal thicknesses, advance speeds of the flame working face, and surrounding rock types on the gasifier were analyzed. The results show that with the increase in the coal thickness, the transfer range and distance of temperature in the roof, floor, and coal seam gradually increase, as does the coal quantity in the three zones. The heat loss rate of the gasifier decreased gradually with the coal seam thickness. When the advance speed of the flame working face is 0.5 m/d, the ideal gasification coal thickness range of lignite is 2.5–17.5 m. With the increase in the gasification rate, the maximum transfer distance of temperature to the roof and floor, the average temperature of the gasifier, and the coal quantity of the three zones gradually increase. Conversely, the coal thickness corresponding to the intersection of the coal quantity of the oxidation and reduction zones and the heat loss rate of the gasifier gradually decrease. When the coal seam below 2.5 m is gasified, the gasification rate can be increased appropriately. When the coal seam is above 13 m, increasing the gasification rate will make the coal quantity in the oxidation zone close to or even higher than that in the reduction zone. Regarding the surrounding rock types comprising a combination of siltstone, mudstone, sandy mudstone, and fine sandstone, the most favorable roof and floor type for underground coal gasification is the combination of fine sandstone and sandy mudstone (without considering the sealing and mechanical properties). These results provide important theoretical support for the industrialization of underground coal gasification.

Optimization of the processing parameters in laser sharpening of bronze-bonded diamond grinding wheels

In this paper a new contribution to the optimization of processing parameters in the process of laser sharpening grinding wheels is presented. In the establishment of the three-dimensional heat conduction model, the laser heat source model is improved and the temperature field of the pulsed laser ablation material is obtained. The effects of laser power, laser line spot overlap ratio and laser scanning track overlap ratio on the sharpening efficiency and accuracy have been studied through the established numerical model. Like what happened in the actual machining process, the morphology of the bond material surface after laser sharpening was obtained by the simulation. The results show that the optimal values of laser power, laser line spot overlap ratio and laser scanning track overlap ratio are 20 W, 70%, and 70%, respectively. The simulation results have been verified and compared with the experimental results, revealing a good correlation between the simulation and experimental data. In a word, the numerical model established in this paper can be conveniently used in the optimization of the process parameters in the laser sharpening grinding wheel.

Investigation into the effect of transverse condudction on the thermal performance of a flat-plate pulsating heat pipe

The effect of transverse wall conduction on the thermal performance of a flat-plate pulsating heat pipe (FP-PHP), whose channels are engraved on a flat-plate, is numerically investigated. For this, a numerical model for the FP-PHP that combines a one-dimensional slug/plug flow model for two-phase flow in rectangular channels with a three-dimensional heat conduction model for the solid wall is developed and experimentally validated. Using the proposed model, the effect of thermal interaction between adjacent channels on the thermal performance is numerically investigated. For quantitative examination, the difference in the thermal performance of the FP-PHP without thermal interaction and that of the FP-PHP with thermal interaction is compared for various wall materials, working fluids, and distances between adjacent channels. Finally, a criterion for assessing the importance of thermal interaction between adjacent channels in determining the thermal performance of the FP-PHP is provided: It is confirmed that thermal interaction has a significant influence on the thermal performance and should be taken into account when the Fourier number (Fo) is higher than 5 × 105.

Particle–Substrate Transient Thermal Evolution During Cold Spray Deposition Process: A Hybrid Heat Conduction Analysis

A hybrid analytical heat conduction model was developed to predict the transient thermal evolution at the particle–substrate interface during the deposition of cold spray process. First, three-dimensional heat conduction model based on classical diffusion approach was developed to predict the transient surface temperature of the substrate. To that end, the traveling wave solution technique was utilized in order to take into account the effect of the movement of the cold spray nozzle. The results of the analytical model were validated with the experimentally measured surface temperature which was obtained by employing a low-pressure cold spray unit to generate the impingement of a compressed air jet on a flat substrate. The analytical model was further utilized to investigate the effect of the non-dimensional characteristic velocity of the traveling heat source on the surface temperature profile of the substrate. It was found that both the maximum surface temperature and the spatial variation of surface temperature profile of the substrate decreased as the non-dimensional characteristic velocity increased. The mathematical model was further extended by developing a one-dimensional hyperbolic (non-Fourier) heat conduction model to predict the temperature rise at the particle–substrate interface during the cold spray deposition process. In order to validate the results of the hybrid model, a three-dimensional finite element model was developed in ABAQUS to simulate the thermal and dynamic behavior of a single particle upon impact. The results of the hybrid analytical model for the temperature at the particle–substrate interface were compared to the results of the numerical model, and good agreement was found. It was concluded that by coupling the classical diffusion theory and hyperbolic heat conduction approach, the proposed hybrid analytical model can be utilized to predict the transient temperature of the particle–substrate interface during the cold spray deposition process a priori before experimentation.

The heat conduction model and leakage characterization of the sealing interface

In this paper, a new leakage characterization method for the sealing interface is proposed to detect the leakage location and measure the leakage rate based on the temperature field and the temperature gradient field. First, the formulas of the leakage rate are theoretically established based on the two-dimensional and the three-dimensional heat conduction model, respectively. Second, the finite element models of the general leakage area and the concentrated leakage area are built, in which the leakage rate calculated by means of heat conduction model fits the simulated leakage rate well. Finally, the interface leakage experiment is conducted using a sealed box with a rubber-aluminum alloy sealing interface, which validates the effectiveness of this new characterization principle for determining the leakage rate and the leakage location. The results indicate that the feasibility of the leakage characterization method for the sealing interface based on the temperature field and the temperature gradient field obtained from the infrared thermography technique.

Improvement of thermal properties of micro head engine electroplated by graphene: experimental and thermal simulation

ABSTRACTThe present work deals with to improve knowledge of the mechanism of deposition of graphene on a complex geometry. The component of this study is an aluminum micro head engine that represents an interesting study case for its application in the field of heat dissipation. It has been coated with copper and graphene nanoplatelets by an electrodeposition process. The tests are conducted by realizing a system heat source similar to engine thermal behavior. The analysis has been developed on a micro head engine with a comparison between thermography results and finite element method (FEM) thermal analysis by commercial software Ansys. A three-dimensional heat conduction model in the coating structure was built, based on which FEM simulation was done. The influence of convection conditions has been evaluated by a comparison with FEM analysis without computational fluid dynamics simulations. The increase of thermal conductivity of coated specimen has been evaluated with the original one. Data analysis was performed by a comparison with 2-norm of fitting curves between the laboratory tests and simulations.

Development of a dynamics model for graphite-moderated channel-type molten salt reactor

A molten salt reactor (MSR) is one of the six advanced reactor concepts selected by the generation IV international forum because of its advantages of inherent safety, and the promising capabilities of Th-U breeding and transuranics transmutation. A dynamics model for the channel-type MSR is developed in this work based on a three-dimensional thermal–hydraulic model (3DTH) and a point reactor model. The 3DTH couples a three-dimensional heat conduction model and a one-dimensional single-phase flow model that can accurately consider the heat conduction between different assemblies. The 3DTH is validated by the RELAP5 code in terms of the temperature and mass flow distribution calculation. A point reactor model considering the drift of delayed neutron precursors is adopted in the dynamics model. To verify the dynamics model, three experiments from the molten salt reactor experiment are simulated. The agreement of the experimental data and simulation results was excellent. With the aid of this model, the unprotected step reactivity addition and unprotected loss of flow of the 2 MWt experimental MSR are modeled, and the reactor power and temperature evolution are analyzed.

Ground thermal and geomechanical conditions in a permafrost-affected high-latitude rock avalanche site (Polvartinden, northern Norway)

Abstract. On 26 June 2008, a rock avalanche detached in the northeast facing slope of Polvartinden, a high-alpine mountain in Signaldalen, northern Norway. Here, we report on the observed and modelled past and present near-surface temperature regime close to the failure zone, as well as on a subsequent simulation of the subsurface temperature regime, and on initial geomechanical mapping based on laser scanning. The volume of the rock avalanche was estimated to be approximately 500 000 m3. The depth to the actual failure surface was found to range from 40 m at the back of the failure zone to 0 m at its toe. Visible in situ ice was observed in the failure zone just after the rock avalanche. Between September 2009 and August 2013, ground surface temperatures were measured with miniature temperature data loggers at 14 different localities, close to the original failure zone along the northern ridge of Polvartinden and on the valley floor. The results from these measurements and from a basic three-dimensional heat conduction model suggest that the lower altitudinal limit of permafrost at present is at 600–650 m a.s.l., which corresponds to the upper limit of the failure zone. A coupling of our in situ data with regional climate data since 1958 suggests a general gradual warming and that the period with highest mean near surface temperatures on record ended four months before the Signaldalen rock avalanche detached. A comparison with a transient permafrost model run at 10 m depth, representative for areas where snow accumulates, strengthen these findings, which are also in congruence with measurements in nearby permafrost boreholes. It is likely that permafrost in and near the failure zone is presently subject to degradation. This degradation, in combination with the extreme warm year antecedent to the rock failure, is seen to have played an important role in the detaching of the Signaldalen rock avalanche.

Thermal-Hydraulic Model and Program Development for Helium-Cooled Accelerator-Driven System

The accelerator-driven subcritical reactor system (ADS) is a kind of nuclear reactor which can burn minor actinide waste products produced from conventional reactors with inherent safety features. In this paper, the thermal-hydraulic model and a corresponding program for a 10 MW helium-cooled experimental ADS are presented. Through the analysis of the heat transfer mechanism in ADS, the thermal-hydraulic model of ADS was built, in which the solid domain is simulated with three-dimensional heat conduction model and the fluid domain is simulated with the one-dimensional quasi-static model. In order to analyze the transient characteristics of ADS with cooling system, a RELAP5–TRCAP coupling model for the cooling system was established, in which the decay heat of the target and core is considered. The results of steady condition and transients demonstrate the effectiveness of the transient model.

Heat dissipation analysis of bendable AlGaInP micro-LED arrays

A strategy for fabricating bendable AlGaInP light emitting diode (LED) arrays is presented in this paper. Sample LED arrays with 8 × 8 pixels were fabricated and subjected to bending. Bending only weakly affected the light output power and the current–voltage characteristics of the arrays. LED arrays suffer from a thermal problem owing to the energy loss during the electrical-to-optical energy conversion. We have designed a three-dimensional heat conduction model for analyzing the effect of the polymer substrate, the configuration of pixels, and the micro-structure on heat dissipation in bendable LED arrays. Thermal conductivity of the polymer substrate critically affected the heat dissipation, suggesting that the substrate thickness should be in the 500–1000 μm range. A larger pixel distance yielded more distributed heat sources and more uniform temperature distribution. Micro-structured polymer substrates yielded lower temperature, especially for the fins array micro-structure. Based on enhancing the polymer’s thermal conductivity and distributing LED pixels, optimizing the substrate’s micro-structure is an effective method to improve heat dissipation in bendable LED arrays. Optimized heat dissipation could effectively reduce heat accumulation in LED arrays and alleviate an increase in the junction temperature, allowing to increase the output power of the device.

Theoretical and experimental study on thermal barrier coating (TBC) uneven thickness detection using pulsed infrared thermography technology

TBC uneven thickness detection has been carried out using pulsed infrared thermography technology. A three-dimensional heat conduction model of pulsed heat in the coating structure was built, based on which FEM simulation was done, and the influence of coating thickness, sampling frequency and sampling time was analyzed. Pulsed infrared thermography experiments were carried out to SiC coated superalloy specimens with uneven coating thickness prepared by plasma spraying method, and the relationship between parameters including impulse energy, sampling frequency, sampling time and the characterization parameter contrast ratio was analyzed.

Accident analysis of tungsten target coupled with ADS core

The Accelerator Driven Subcritical Reactor System (ADS) is a kind of nuclear reactor which can burn minor actinide waste produced from conventional reactors with inherent safety features. Because of the characteristics of a sub-critical reaction process, the fission chain reaction is maintained by additional neutrons generated by protons in spallation target. This paper presents a concept design and the accident analysis of helium gas-cooled tungsten target for 10 MW helium-cooled experimental ADS.The thermal-hydraulic model of the target coupling with core was built, in which the solid domain was simulated with three-dimensional heat conduction model and the fluid domain was simulated with one-dimensional quasi-static model. In order to analyze the transient characteristics of the target with cooling system, a RELAP5-TRCAP coupling model for cooling system was established, in which the decay heat of the target and core was considered. The simulated results indicate that the peak temperature in the target is lower than the limiting value under the rated operation state and during four typical transient with actuation of the safety system.

Thermal–hydraulic modeling and transient analysis of helium-cooled tungsten target coupled with ADS core

The Accelerator Driven Subcritical Reactor System (ADS) is a kind of nuclear reactor which can burn minor actinide waste produced from conventional reactors with inherent safety features. This paper presents a concept design of helium gas-cooled tungsten target for 10MW helium-cooled experimental ADS.In the design scheme, the tungsten spallation target was modeled into the honeycomb structure. The thermal–hydraulic model of the target coupling with core was built, in which the solid domain was simulated with three-dimensional heat conduction model and the fluid domain was simulated with one-dimensional quasi-static model. The target was modeled with fine meshes. The core was modeled roughly as the boundary condition of the target. In order to analyze the transient characteristics of the target with cooling system, a RELAP5–TRCAP coupling model for cooling system was established, in which the decay heat of the target and core was considered. The simulated results indicate that the peak temperature in the target is lower than the limiting value under the rated operation state and during the Loss of Flow Accident (LOFA) transient with actuation of the safety system.

Channel Temperature Measurement of AlGaN/GaN HEMTs by Forward Schottky Characteristics

Channel temperature measurements of multi-finger AlGaN/GaN HEMTs by forward Schottky characteristics are presented. The temperature dependence of the forward gate-source Schottky junction voltage is investigated and it is used as the temperature sensitive parameter (TSP) by pulsed switching technique. The channel-to-mounting thermal resistance of the tested AlGaN/GaN HEMT sample is 19.6°C/W. Compared with both the measured results by micro-Raman method and simulated results of a three-dimensional heat conduction model, the physical meaning of the channel temperature for AlGaN/GaN HEMT tested by pulsed switching electrical TSP method is investigated quantitatively for the first time.

Thermal footprint of an eroded thrust sheet in the southern Appalachian thrust belt, Alabama, USA

Erosion of the leading hanging-wall cutoffs of thrust sheets commonly obscures the magnitude of thrusting. The Jones Valley thrust fault in the southern Appalachian thrust belt in Alabama, USA, is exposed along a northwest-directed, large-scale frontal ramp, and the leading part of the thrust sheet has been eroded. Previously published and newly collected vitrinite reflectance data from Pennsylvanian coal beds document a distinct, northeast-trending, elongate, oval-shaped thermal anomaly northwest of the trace of the Jones Valley fault. The northwest edge of the thermal anomaly is ~18 km northwest of the fault trace, suggesting the original extent of the eroded thrust sheet. The anomaly ends both northeastward and southwestward along strike at lateral ramps. The southeast edge of the anomaly corresponds to the location of a footwall frontal ramp. A three-dimensional heat conduction model for simultaneous horizontal (two-dimensional) and vertical heat flow in a rectangular thrust sheet is designed to test whether the documented thermal anomaly (%Ro = 1.0–1.6) may reflect the former extent of thrust-sheet cover. The model uses a 3-km-thick thrust sheet with horizontal dimensions of 10 x 30 km, as well as a three-dimensional analytical solution to the heat conduction equation, whereby the thrust sheet cools both laterally and vertically. The model reproduces the magnitude and oval shape of the vitrinite reflectance anomaly at 100–500 k.y. after thrust emplacement. The geothermal gradient reaches a steady state at ~2 m.y., and is never fully reestablished even for long times because of lateral cooling in the hanging wall. Thickness and extent of the thrust sheet from the thermal model are consistent with balanced and restored cross sections of the Jones Valley thrust sheet based on geologic data; a thrust sheet ~3 km thick was emplaced ~18 km onto the foreland over the site of the thermal anomaly. The three-dimensional thermal evolution of both the hanging wall and the footwall is distinct from that predicted from one-dimensional models; a three-dimensional model predicts less heating of the footwall because of horizontal heat loss across bounding ramps.

Numerical analysis of the design parameters on the performance of thin film temperature sensors

An embedded thin film temperature sensor onto the surface of lubricated mechanical components is promising for real-time machine condition monitoring. The present study has been concerned with the performance of thin film temperature sensors due to the design parameters such as sensor film thickness, width, length, sensing materials, insulating and protecting layer. An improved three-dimensional heat conduction model has been developed to study the influence of those design parameters on the performance of thin film sensors designed for monitoring temperature distribution in elastohydrodynamic lubrication (EHL) contacts. The finite-volume method was utilized to solve the transient, three-dimensional heat conduction equation with time-dependent heat generation due to friction over the sensor. The time response to temperature change in a lubricated contact was predicted. This research work provided more deep insights for selection of the design parameters to ensure sufficient sensitivity, fast response time and the appropriate temperature range of the EHL temperature sensor to be used.

Heat transfer analysis of ground heat exchangers with inclined boreholes

Consisting of closed-loop of pipes buried in boreholes, ground heat exchangers (GHEs) are devised for extraction or injection of thermal energy from/into the ground. Evolved from the vertical borehole systems, the configuration of inclined boreholes is considered in order to reduce the land plots required to install the GHEs in densely populated areas. A transient three-dimensional heat conduction model has been established and solved analytically to describe the temperature response in the ground caused by a single inclined line source. Heat transfer in the GHEs with multiple boreholes is then studied by superimposition of the temperature excesses resulted from individual boreholes. On this basis, two kinds of representative temperature responses on the borehole wall are defined and discussed. The thermal interference between inclined boreholes is compared with that between vertical ones. The analyses can provide a basic and useful tool for the design and thermal simulation of the GHEs with inclined boreholes.