Two-dimensional Heat Conduction Model Research Articles

A three-dimensional criticality safety analysis code for spent fuel solution system

The nuclear criticality safety analysis is crucial for the nuclear safety of spent fuel reprocessing plants. Thus, a set of numerical tools with high accuracy and efficiency to predict the criticality and simulate the hypothetical accidents in the reprocessing procedure is of great importance. Among them, this paper focus on the analysis of the storage tank which is used for dissolution and storage of the spent fuel. According to the characteristics of spent fuel solution system, a parallel 3D critical safety analysis tool for fissile solution system, Hydra-TD, is developed. Generally, it contains the cross-section generation model, the three-dimensional space-time neutron kinetics model, and the R-Z two-dimensional heat conduction and radiolysis gas simulation model. The verifications based on the experiments of the SILENE and TRACY facility are conducted. The results show good accuracy of the prediction of the first fission power peak, multiplication time and total fission energy, indicating the reliability of these numerical models.

Numerical Analysis of Thermal Runaway in Copper-Plated Multifilament Coated Conductor

We have developed a numerical analysis model to simulate the thermal runaway in copper-plated multifilament coated conductors. We combined a circuit model to calculate current distribution in filaments and copper and a two-dimensional heat conduction model to calculate temperature distribution. The thermal runaway simulations of multifilament coated conductor with local defects were performed, and compared with the experimental results to validate the developed model. According to the simulation results, the effect of current sharing on the initiation of thermal runaway was determined.

Research on Unsteady Inverse Heat Conduction Based on Dynamic Matrix Control

For the unsteady multi-boundary inverse heat conduction problem, a real-time solution method for boundary heat flux based on dynamic matrix control is proposed in the paper. The method solves the heat flux at the boundary in real-time by measuring the temperature information at the measurement points of the heat transfer system. A two-dimensional direct heat conduction model of the heat transfer system is established in the paper, and is solved by the finite difference method to obtain the temperature information of the measurement points under any heat flux boundary. Then, the correspondence between the heat flux of boundary and the temperature information is presented by means of a step-response model. The regularization parameters are introduced into the method to improve the stability of the inversion process, and the effect of real-time inversion on the heat flux of the boundary is achieved through rolling optimization. The experimental results show that the proposed method can achieve real-time inversion of the heat fluxes of the two-dimensional boundary with good accuracy.

A self-scaling sequential quasi-Newton method for estimating the heat transfer coefficient distribution in the air jet impingement

Accurate knowledge of the heat transfer coefficient (HTC) distribution is of great significance to the control and optimization of the heat transfer system in the air jet impingement. For this purpose, the estimation of the temporally-spatially varying HTC in the air jet impingement is studied based on the inverse heat conduction problem. The transient two-dimensional heat conduction model of the target disc under a single cooling air jet is established and utilized as the direct problem. A self-scaling sequential quasi-Newton method (SS-SQNM) is developed for accurately and efficiently solving the inverse problem. As a modification of the sequential quasi-Newton method (SQNM), the SS-SQNM adopts the self-scaling updating equation to accelerate the single-step convergence rate during iteration, and thus attains higher inversion efficiency than the SQNM. A series of numerical tests are carried out to investigate the performance of the SS-SQNM and the effects of the regularization parameters on inverse results. The results reveal that the SS-SQNM can give stable and accurate estimates of the HTC when regularization parameters are appropriately selected through the discrepancy principle. The mean absolute percentage error of the estimated HTC distribution is generally less than 10.2% in the presence of measurement noises. Additionally, the iteration number required by the SS-SQNM for inversion is only about 7.81%∼27.78% of that of the SQNM under the same conditions, which saves lots of computational time for the SS-SQNM. Therefore, the SS-SQNM developed in this study is a promising inverse algorithm, which can be employed to estimate the HTC distribution in the air jet impingement with reasonable accuracy and efficiency.

Incorporating two-dimensional conduction modeling techniques into an energy simulation program: The EnergyPlus radiant system example

Due to the inherent complexity of multi-dimensional solutions for transient conduction in a multilayered building element, most heat balance-based algorithms assume that conduction occurs only in one dimension—through the building element between the inside and outside environments. Usually, since the length and width of the elements are much greater than the thickness of the element, this is a valid assumption. However, there are some cases such as hydronic radiant slabs where this assumption may not lead to an accurate estimate of the energy consumption of the system. In a hydronic radiant slab, water tubes are embedded in a slab, and hot or chilled water is circulated to meet any heating or cooling loads. The energy consumption of such a system will depend highly on the temperature of the water being sent to the slab (i.e., produced by the boiler or chiller). The temperature of the water that must be sent to the slab will depend on the spacing of the tubes, the multilayer construction of the building element, and the boundary conditions to which the construction is exposed. Thus, to accurately predict the energy consumption of such a system, a transient two-dimensional heat conduction model must be integrated with a heat balance-based simulation. This paper demonstrates the potential loss of accuracy associated with the one-dimensional radiant system models by providing a comparison of one- and two-dimensional solutions using EnergyPlus.

Evaluation of defect depth in CFRP composites by long pulse thermography

Long pulse thermography (LPT) is an emerging non-destructive technique that has been used for rapid, cost-effective and accurate damage assessment of composite materials. This paper proposes three analytical models for the in-depth evaluation of defects in a carbon fibre-reinforced plastic (CFRP) specimen by long pulse thermography. The first two models rely on the estimate of the peak temperature-contrast and the peak temperature-contrast slope from the thermal data recorded by an infrared (IR) camera. Both the analytical and experimental results showed that the arriving time of the peak temperature-contrast depends on both the depth and the diameter of defects, whilst the contrast time slope is mainly proportional to the square of the damage depth. The third model here proposed consists of a two-dimensional (2D) axisymmetric heat conduction model based on virtual heat sources. Compared to previously reported analytical models, the proposed 2D one showed higher accuracy on the depth estimation.

A novel 2-D equivalent numerical model of helix energy pile based on heat transfer characteristics of internal heat convection

Numerical modeling has been widely used to simulate the heat transfer of ground heat exchanger (GHE), However, there is a lack of analysis and comparison of different models and methods, for helix energy pile, there is a lack of an efficient and accurate numerical model to study the complex heat transfer problems. In this paper, taking a novel truncated cone helix energy pile (CoHEP) as the object, a two-dimensional(2-D) equivalent heat conduction model considering the heat transfer characteristics of the heat convection in the buried pipe was established, at the same time, a three-dimensional(3-D) full scale model and a 2-D ring coils model were established. By comparing the simulation results of three numerical models with the experimental results under the same conditions, the effects and suggestions of meshing on different models, the model characteristics and main error sources of different models were analyzed. The long-term and short-term simulation results and temperature distribution characteristics of different models were further analyzed. The study shows that the 3-D model has the highest accuracy in the simulation process, but the simulation efficiency is low, and it is easy to be affected by meshing. The 2-D ring coils model has high simulation efficiency, but the long-term simulation error is large, and the thermal influence radius of the pipe is smaller than the actual situation. For the 2-D equivalent model, the simulation error is small, and the thermal influence radius is close to those of the 3-D full scale model, and the effect of long-term simulation is obviously better than that of the 2-D ring coils model. The results indicate that the 2-D equivalent model effectively improves the simulation accuracy of the 2-D heat conduction numerical model, it can obtain the temperature distribution inside and outside the buried pipe which is closer to the actual situation with less calculation and higher simulation accuracy.

Code development and analysis on the operation of liquid metal high temperature heat pipes under full condition

Heat pipe cooled reactor (HPR) is an innovative solid-core reactor which utilizes heat pipes to extract heat from the core to the energy conversion system. In this paper, a mathematical model for high-temperature heat pipes from a frozen state to a steady state is developed based on experimental data. The model is simplified and solved numerically. The two-dimensional transient heat conduction model of the wall and wick and the one-dimensional quasi-steady compressible vapor flow model are coupled to simulate the operation of a heat pipe when vaporization and condensation occur at the liquid–vapor interface. And the equivalent heat capacity model and the rarefied vapor model are introduced to simulate the process of heat pipe startup from a frozen state. Numerical results indicate that the model of heat pipe can predict the operation of high-temperature heat pipe with an error of less than 1.04% at steady state and 23.4% during the startup. Based on the simulation results, the velocity of vapor decreases with the heat transfer power in the steady state and the velocity of potassium vapor is 58.4% of sodium vapor velocity under the same operation condition. During the startup, when the rarefied-continuum interface located in the end of the evaporator section, the maximum vapor velocity occurs which is 1.3 times of steady velocity. This work makes it possible to predict the operation of a high-temperature heat pipe and provides a reference for the design and application of HPR.

Transient, Two-Dimensional Heat Conduction Model for Rewetting a Hot Vertical Plate Surface by a Falling Liquid Film.(Dept.M)

A transient, two-dimensional heat conduction model for rewetting a hot plate surface by a falling liquid film is developed. It is assumed that the plate thermal properties are Independent on temperature, and the heat transfer coefficient is a constant value in the wet region and zero in the dry region. The mathematical model equations are transformed to a dimensionless form solved numerically . The results indicate that the heat conduction problem in the rewetting process is substantially two-dimensional one, not only for thick plates, I.e., a large Bolt number, but also for a low initial wall temperature. An explicit simple formula for predicting the rewetting velocity is obtained by correlating the numerical results, Comparisons with other studies are made.

A local character based method for solving linear systems of radiation diffusion problems

The radiation diffusion problem is a kind of time-dependent nonlinear equations. For solving the radiation diffusion equations, many linear systems are obtained in the nonlinear iterations at each time step. The cost of linear equations dominates the numerical simulation of radiation diffusion applications, such as inertial confinement fusion, etc. Usually, iterative methods are used to solve the linear systems in a real application. Moreover, the solution of the previous nonlinear iteration or the solution of the previous time step is typically used as the initial guess for solving the current linear equations. Because of the strong local character in ICF, with the advancing of nonlinear iteration and time step, the solution of the linear system changes dramatically in some local domain, and changes mildly or even has no change in the rest domain.In this paper, a local character-based method is proposed to solve the linear systems of radiation diffusion problems. The proposed method consists of three steps: firstly, a local domain (algebraic domain) is constructed; secondly, the subsystem on the local domain is solved; and lastly, the whole system will be solved. Two methods are given to construct the local domain. One is based on the spatial gradient, and the other is based on the residual. Numerical tests for a two-dimensional heat conduction model problem, and two real application models, the multi-group radiation diffusion equations and the three temperature energy equations, are conducted. The test results show that the solution time for solving the linear system can be reduced dramatically by using the local character-based method.

Scale-up of Q‑carbon and nanodiamonds by pulsed laser annealing

Q‑carbon is a densely-packed metastable phase of carbon, which is harder than diamond. It is formed by nanosecond laser melting and ultrafast quenching of amorphous carbon films. The formation of Q‑carbon is a strictly undercooling driven phenomenon and requires uniform sp3/sp2 composition of as-deposited diamond-like carbon (DLC) films. This study illustrates the growth of wafer-scale DLC and its conversion into Q‑carbon and diamond by nanosecond pulsed laser annealing (PLA). A two-dimensional transient heat conduction model was created to analyze the melt front and regrowth conditions of PLA processing, utilizing a temporal and spatial Gaussian heat source at a laser fluence of 800 mJ/cm2. The transient temperature and melt-depth profiles obtained revealed successful melting of carbon with regrowth of Q‑carbon phase. By optimizing laser plume energetics, uniformity in sp3 content (~40%) of DLC films was achieved, which led to the formation of Q‑carbon over a large area. Here, the challenges associated with the scale-up of Q‑carbon are discussed along with analysis of the interfacial bonding between the undercooled layers using atomic-force and electron microscopy techniques. The wafer scale-up of DLC films with controlled sp3/sp2 content will be useful for making scalable Q‑carbon based longer-lasting protective coatings and Q‑carbon based electronic devices. These findings should help to further the development of Q‑carbon and diamond-related materials technology for commercialization of high-performance systems.

Inverse Identification of Temperature-Dependent Thermal Properties Using Improved Krill Herd Algorithm

A novel intelligent algorithm, krill herd (KH), is firstly introduced to solve the inverse identification of temperature-dependent thermal properties of materials. To promote the searching ability and accelerate the convergence velocity, three improved KH (IKH) algorithms are proposed and developed for solving the optimization tasks. The temperature-dependent thermal conductivity and specific heat of a building material are estimated by using the KH algorithms, and the IKHs achieve better performance than the original KHs. Moreover, the functional forms of thermal conductivity of insulating and refractory materials are also reconstructed. The IKH algorithm is proved to be more accurate than other algorithms. Finally, a two-dimensional nonhomogeneous heat conduction model is investigated and the thermal conductivities of materials at specified temperatures are reconstructed, in which no prior information is needed for the expressions of the thermal conductivity to be identified. All the retrieval results show that IKH algorithm is robust and effective for solving the inverse heat conduction problems.

Investigation on plume expansion and ionization in a laser ablation plasma thruster

The laser ablation plasma thruster is a novel electric propulsion thruster, which combined the laser ablation and electromagnetic acceleration. In order to investigate the plume expansion and ionization in the laser ablation plasma thruster which was difficult to obtain from experiments, the two-dimensional heat conduction model and fluid dynamics model were established. The heat conduction model was established to calculate the target ablation, taking into account temperature dependent material properties, phase transition, dielectric transition and phase explosion. The fluid dynamics model was used to calculate the plume properties, taking into account ionization, plume absorption and shielding. The good agreement between calculated and experimental data validated our model, while the plume velocity, temperature and electron number density were predicted by using the numerical method. The calculated results showed that the plume uniformly expanded into the ambience with a mushroom shape, and the peak values of plume velocity, temperature and electron number density fraction were distributed at the front of the plume. The ceramic tube limited the radial expansion of the plume, and enhanced the velocity, temperature and ionization degree nearby the wall, due to the interaction between the plume and the wall. Otherwise, the effects of laser fluence on plume properties and thrust performance of the thruster were investigated utilizing the numerical model.

A generalized model for thermoelastic damping in beams with mid-plane stretching nonlinearity

This work presents a general model to accurately capture thermoelastic damping in beams with mid-plane stretching nonlinearity. The model consists of a nonlinear Timoshenko beam model coupled with a two-dimensional heat conduction model. The heat conduction model accounts for heat transfer in both the transverse and the axial directions of the beam. Numerical solutions are obtained by discretizing the beam using spectral element method (SEM). Using the proposed model, the thermoelastic damping (QTED) quality factor is obtained for beams actuated by electrostatic force using the eigenfrequency analysis and the energy approach. The eigenfrequency analysis conducted on the beams under the electrostatic actuation showed significant difference from the results published in literature. A detailed numerical analysis is performed in order to understand the discrepancy. It is shown that the discrepancy primarily occurs due to the differences in the methods to couple the displacement and thermal fields, with the model presented in the paper being the more general one.

Simulation analysis of zinc ablation process and mass by intense pulsed ion beam irradiation

AbstractAs the strong thermal effect in the surface, intense pulsed ion beam (IPIB) has been extensively used in material surface modification. The ablation is an important part in the interaction process between IPIB and material. In order to investigate the ablation mechanism, combined with IPIB dynamic energy spectrum and infrared imaging diagnostic results, a two-dimensional axisymmetric heat conduction model considering the effect of ablated material was constructed to describe the ablation process and calculate the lost mass of the targets. The influences of beam parameters and ablated matter on the ablation rate were discussed. The experimental and simulative results of ablation threshold and mass were compared.

Two-dimensional numerical study of ELMs-induced erosion of tungsten divertor target tiles with different edge shapes

Thermal performance of the divertor tile with different edge shapes was assessed numerically along the poloidal direction by a two-dimensional heat conduction model with considering the geometrical effects of castellated divertor tiles on the properties of its adjacent plasma. The energy flux density distribution arriving at the castellated divertor tile surface was evaluated by a two-dimension-in-space and three-dimension-in-velocity particle-in-cell plus Monte Carlo Collisions code and then the obtained energy flux distribution was used as input for the heat conduction model. The simulation results showed that the divertor tiles with any edge shape of interest (rectangular edge, slanted edge, and rounded edge) would melt, especially, in the edge surface region of facing plasma poloidally under typical heat flux density of a transient event of type-I ELMs for ITER, deposition energy of 1MJ/m2 in a duration of 600μs. In comparison with uniform energy deposition, the vaporizing erosion was reduced greatly but the melting erosion was aggravated noticeably in the edge area of plasma facing diveror tile. Of three studied edge shapes, the simulation results indicated that the divertor plate with rounded edge was the most resistant to the thermal erosion.

Reducing surface cracking in hot charged HSLA cast slabs by surface quenching prior to hot charging – experimental study on heat transfer behaviour

Surface quenching of cast slabs between casting and hot charging to prevent the occurrence of surface cracks in high strength low-alloy steel slabs has been investigated. In order to accurately control the quenching process and obtain the desired cooling rate, an experimental study on the heat transfer behaviour of a high temperature slab cooled by a water nozzle was performed. The surface temperature and heat transfer flux were calculated using a two-dimensional transient inverse heat conduction model, based on the finite element method. The effect of the water flowrate and inclination of the spray on the heat transfer is discussed. Based on a regression analysis of the experimental data, the heat transfer coefficient is provided as a function of slab temperature and water flow density. A surface quenching trial with a water flowrate of 46 m3 h−1 was conducted in a steel mill. Good correlation was found between the temperature predicted using the proposed heat transfer coefficient and the temperature measured during the surface quenching process.

Formation heating by steam circulation in a horizontal wellbore

Abstract A two-dimensional transient heat conduction model is developed that predicts heat transfer from a horizontal wellbore to the formation during a steam circulation process. The model takes into account the partial penetration of the wellbore, which is not included in previously developed analytical models applicable for reservoir heating. This inclusion makes the problem mathematically challenging as the inner boundary condition of the problem becomes non-homogenous. The governing heat conduction equation is solved for an infinite acting reservoir and semi-analytical solutions for the heat flux from the wellbore and temperature distribution in the formation are obtained using a combination of Laplace and finite Fourier cosine transforms. The average formation temperature and the heat flow across the wellbore are calculated and the results are presented. This analysis has applications in thermal stimulation of oil wells with low injectivity, where it is required to preheat the formation prior to steam injection.

0.53 μm毫秒脉冲激光对GaAs热分解损伤特性

In order to study the surface thermal decomposition damage of millisecond pulse lasers irradiating GaAs at 0.53 m wavelength, a two-dimensional axisymmetric heat conduction model was established. Considering the temperature dependences of the thermophysical parameters, the transient temperature fields in the material were simulated by using the finite element method. The distributions of transient temperature fields and variation law with time have been obtained, and the curve of the thermal decomposition damage thresholds on the material surface was also given. Numerical results show that, heat conduction affects the whole process of millisecond pulsed laser interaction and its damage mechanism is mainly thermal effects. The temperature of the center is the highest on the irradiated surface, where it could be damaged by thermal decomposition first. With the increasing of laser energy density, the time of thermal decomposition damages occurrence would be advancing.

H111 準定常一方向熱流比較法による熱伝導率測定法の研究(OS-2: 機器冷却における熱物性)

In order to establish measurement method of effective thermal conductivity of specimens such as isotropic electrically conductive adhesives for use electronic equipment, steady state comparative-longitudinal heat flow method using cartridge type specimens have been developed. This method needs long time to get some temperature dependent thermal conductivities by waiting several times to get some steady state conditions. We have studied an improved method nnamed quasi-steady state comparative longitudinal heat flow method in which temperature dependency of the thermal conductivity can be obtained by only one time heating. We demonstrated the possibility to obtain the temperature dependency of the thermal conductivity of the specimen by numerical simulation using two-dimensional transient heat conduction model. The error of the thermal conductivity obtained by this quasi-steady method using quasi-steady condition was less than 2%.