Partly three-dimensional global modeling of a silicon Czochralski furnace. II. Model application: Analysis of a silicon Czochralski furnace in a transverse magnetic field

A three-dimensional (3D) global analysis was carried out numerically for a small silicon Czochralski (CZ) furnace in a transverse magnetic field by a proposed 3D global model. The modeling was conducted with moderate requirements of computer resources and computation time. Most 3D features of the melt flow and thermal field in the furnace could be reproduced in the modeling. The results showed that the melt–crystal interface shape is three-dimensional and temperature difference over the circumference on the crystal and crucible sidewalls is prominent. The non-uniformity of temperature in the azimuthal direction decreases with increase in distance from the melt region. The influence of a transverse magnetic field on the flow pattern of melt and global thermal field in the furnace was analyzed.     

Computer modeling of crystal growth of silicon for solar cells

A computer simulator with a global model of heat transfer during crystal growth of Si for solar cells is developed. The convective, conductive, and radiative heat transfers in the furnace are solved together in a coupled manner using the finite volume method. A three-dimensional (3D) global heat transfer model with 3D features is especially made suitable for any crystal growth, while the requirement for computer resources is kept permissible for engineering applications. A structured/unstructured combined mesh scheme is proposed to improve the efficiency and accuracy of the simulation. A dynamic model for the melt-crystal (mc) interface is developed to predict the phase interface behavior in a crystal growth process. Dynamic models for impurities and precipitates are also incorporated into the simulator. Applications of the computer simulator to Czochralski (CZ) growth processes and directional solidification processes of Si crystals for solar cells are introduced. Some typical results, including the turbulent melt flow in a large-scale crucible of a CZ-Si process, the dynamic behaviors of the mc interface, and the transport and distributions of impurities and precipitates, such as oxygen, carbon, and SiC particles, are presented and discussed. The findings show the importance of computer modeling as an effective tool in the analysis and improvement of crystal growth processes and furnace designs for solar Si material.     

Online simulation model of the slab-reheating process in a pusher-type furnace

This paper presents an online simulation model of the slab-reheating process in a pusher-type furnace in Acroni d.o.o. in Slovenia. The simulation model is connected to the information system of a hot-processing plant that provides online measuring and charging data of the furnace. The simulation model considers the exact geometry of the furnace enclosure, including the geometry of the slabs inside the furnace. A view-factor matrix of the furnace enclosure was determined using the Monte Carlo method. The heat exchange between the furnace gas, the furnace wall and the slab’s surface is calculated using a three-temperature model. The heat conduction in the slabs is calculated using the 3D finite-difference method. The model was validated using measurements from trailing thermocouples positioned in the test slabs during the reheating process in the furnace.A graphical user interface (GUI) was developed to ensure a user-friendly presentation of the simulation-model results.     

Numerical simulation of the Czochralski growth process of oxide crystals with a relatively thin optical thickness

For the single crystal growth of an oxide, the global analysis of heat transfer in the inductively heated Czochralski (CZ) furnace was carried out to investigate the effect of optical properties of crystal on the CZ crystal growth process. Here, the finite volume method (FVM) was used as the radiative transfer model to solve the radiative transfer equation, and consequently the crystal with a relatively thin optical thickness (∼0.01) could be accounted for. As a result, it was found that the melt/crystal interface becomes more convex toward the melt for a small crystal rotational Reynolds number as the optical thickness of the crystal, κ_s, decreases, although its dependence is slight for κ_s < 0.1. In addition, the critical Reynolds number, at which the interface inversion occurs, decreases with the optical thickness of the crystal.     

Simulation of flow and heat transfer with evaporation in a porous wick of a CPL evaporator on pore scale by lattice Boltzmann method

A three-dimensional transient double-population thermal lattice Boltzmann BGK scheme for the global evaporator of a CPL is proposed to describe the heat and mass transfer in the porous wick, the cover plate and the vapor groove. The lattice BGK D3Q6 model, developed on passive-scalar approach, is proposed to represent the energy distribution function. The D3G15 incompressible lattice BGK model is chosen to represent the pressure distribution function to calculate the pressure and velocity fields. The random porous structure is reconstructed by the quartet structure generation set (QSGS) and is coupled to the lattice Boltzmann method (LBM) by some special boundary schemes for pore scale simulation. The numerical results of different working conditions and different working fluids are presented, which can improve the understandings of heat and mass transport mechanisms in a CPL evaporator and provide guidance for the evaporator design in a CPL system.     

A mixed isogeometric analysis and control volume approach for heat transfer analysis of nonuniformly heated plates

Abstract

A framework for conducting heat transfer analysis of nonuniformly heated plates using isogeometric analysis (IGA) is proposed. The modeling approach represents a method that is capable of capturing the full 3D thermal states of plate structures subjected to nonuniform heating. The formulation can be deemed a mixed IGA and control-volume scheme that describes the governing equations using a set of 2D lumped temperature layers. The non-matching grids between the fire domain and the solid domain are weakly coupled. Numerical results demonstrate that the approach is a suitable first step towards coupled CFD-IGA-based fire-structure simulation.     

空气预热温度对燃烧状况的影响

空气预热是有效的节能技术,但预热温度的提高同时带来NOx排放浓度增加的问题。为了了解其规律,本文针对某烯烃厂芳烃加热炉的空气预热改造项目,对不同空气预热温度情况下的燃烧状况和NOx排放规律做了研究。首先利用数值模拟方法,构建了加热炉三维几何模型,将燃烧模型和NOx生成模型结合,对不同空气温度下的燃烧温度和NOx排放进行模拟,对炉膛内部温度分布及NOx排放规律做了研究,最后找出空气预热最佳温度。     

Numerical analysis of heat transfer under a radiant warmer

The main objective of this paper is to present numerical modeling and assessment of heat transfer in neonatology. In the present study, numerical simulation is performed over a simplified infant model with specific boundary conditions in a closed chamber. The proposed approach is based on three‐dimensional (3D) computational fluid dynamics (CFD) simulation to capture the combined effect of air flow and heat transfer phenomena: natural convection and radiation heat transfer taking place around an infant and radiant lamp. A 3D model is numerically investigated using the commercial CFD package StarCCM+. The results presented are compared and found to be in qualitative agreement with the results available in the literature and published measurement data.     

Application of the time discontinuous Galerkin finite element method to heat wave simulation

This paper deals with the numerical simulation of heat wave propagation in the medium subjected to different kinds of heat source, particularly heat impulse. The discontinuous Galerkin finite element method (DGFEM) proposed for the stress wave propagation in solids [X.K. Li, D.M. Yao, R.W. Lewis, A discontinuous Galerkin finite element method for dynamic and wave propagation problems in non-linear solids and saturated porous media. Int. J. Numer. Meth. Eng. 57 (2003) 1775–1800] is extended to numerically solve for the non-Fourier heat transport equation constructed according to the CV model [C. Cattaneo, A form of heat-conduction equation which eliminates the paradox of instantaneous propagation, Compute Rendus 247 (1958) 431–433; P. Vernotte, Les paradoxes de la theorie continue de l’equation de la chaleur, Compute Rendus 246 (1958) 3154–3155]. Temperature and its time-derivative are chosen as primitive variables defined at each FE node. The main distinct characteristic of the proposed DGFEM is that the specific P3–P1 interpolation approximation, which uses piecewise cubic (Hermite’s polynomial) and linear interpolations for both temperature and its time-derivative, respectively, in the time domain is particularly proposed. As a consequence the continuity of temperature at each discrete time instant is exactly ensured, whereas discontinuity of the time-derivative of temperature at discrete time levels remains. Numerical results illustrate good performance of the present method in the numerical simulation of heat wave propagation in eliminating spurious numerical oscillations and in providing more accurate solutions in the time domain.     

Transient 3D analysis of borehole heat exchanger modeling

This paper presents the development and application of a three-dimensional (3D) numerical simulation model for U-tube borehole heat exchangers (BHEs). The proposed model includes the thermal capacities of the borehole components, viz., the fluid inside the tubes, as well as the grouting material, making it possible to consider the transient effects of heat and mass transports inside the borehole. In this approach, the use of simplified thermal resistance and capacity models (TRCMs) provides accurate results while substantially reducing the number of nodes and the computation time compared with fully discretized computations such as finite element (FE) models. The model is compared with a fully discretized FE model which serves as a reference. Furthermore, the model is used to evaluate thermal response test (TRT) data by the parameter estimation technique. Comparison of the model results with the results of an analytical model based on the line-source theory further establishes the advantage of the developed 3D transient model, as the test duration can be shortened and results are more accurate.     

A semi-analytical boundary collocation solver for the inverse Cauchy problems in heat conduction under 3D FGMs with heat source

Abstract

In this article, the inverse Cauchy problems in heat conduction under 3D functionally graded materials (FGMs) with heat source are solved by using a semi-analytical boundary collocation solver. In the present semi-analytical solver, the combined boundary particle method and regularization technique is employed to deal with ill-pose inverse Cauchy problems. The domain mapping method and variable transformation are introduced to derive the high-order general solutions satisfying the heat conduction equation of 3D FGMs. Thanks to these derived high-order general solutions, the proposed scheme can only require the boundary discretization to recover the solutions of the heat conduction equations with a heat source. The regularization technique is used to eliminate the effect of the noisy measurement data on the accessible boundary surface of 3D FGMs. The efficiency of the proposed solver for inverse Cauchy problems is verified under several typical benchmark examples related to 3D FGM with specific spatial variations (quadratic, exponential and trigonometric functions).     

Heat pump system utilizing produced water in oil fields

As the alternative to the heating furnace for crude oil heating, a heat pump system utilizing produced water, a main byproduct, in oil fields was proposed and the thermodynamic model of the system was established. A particular compression process with inner evaporative spray water cooling was applied in the screw compressor and an analysis method for the variable-mass compression process was introduced. The simulation results showed that the efficiency of the screw compressor, the temperature of produced water and the temperature difference in flash process are key parameters affecting the system performance. The energy cost of the heat pump system was compared to that of the heating furnace, revealing that the heat pump system with EER, 4.67, would save over 20% energy cost as compared with the heating furnace. Thus, the heat pump system was energy saving, money saving and environmentally benign.     

Dual-phase-lag heat conduction in a furnace wall made of functionally graded materials

In this article, the transient heat transfer in a furnace wall, which is made of functionally graded materials (FGMs), is investigated based on the hyperbolic-type dual-phase-lag (DPL) heat conduction model to consider the microstructural interactions in the fast transient process of heat conduction. All material properties of the furnace wall are assumed to vary following a power-law form along the radial direction with arbitrary non-homogeneity indices. For simplicity, the values of the phase lags are taken constant. A semi-analytical solution for the temperature field is obtained in the Laplace domain. The transformed temperature solution is inverted to the physical quantity by using numerical inversion of the Laplace transform. A comparison between the hyperbolic-type DPL model and thermal wave model in the temperature responses of the furnace wall is made. Effects of different phase-lag values on the behavior of heat transfer are also investigated.     

能够反映炉膛上下温度偏差的循环流化床动态仿真模型的研究

分析了以往循环流化床动态仿真模型不能反映流化床炉膛温度分布特性的深层次原因，提出了由底部集中参数的流化床燃烧室和顶部出口假想换热器构成的新的物理模型结构，利用它可以根据可获得的流化床整体性能数据计算出炉膛上下温度差异，而且不会过多地增加计算时间消耗，对某250t/h循环流化床的仿真计算表明了所建模型的正确性。     

Investigation of the slab heating characteristics in a reheating furnace with the formation and growth of scale on the slab surface

In this work, the development of a mathematical heat transfer model for a walking-beam type reheating furnace is described and preliminary model predictions are presented. The model can predict the heat flux distribution within the furnace and the temperature distribution in the slab throughout the reheating furnace process by considering the heat exchange between the slab and its surroundings, including the radiant heat transfer among the slabs, the skids, the hot combustion gases and the furnace wall as well as the gas convection heat transfer in the furnace. In addition, present model is designed to be able to predict the formation and growth of the scale layer on the slab in order to investigate its effect on the slab heating. A comparison is made between the predictions of the present model and the data from an in situ measurement in the furnace, and a reasonable agreement is found. The results of the present simulation show that the effect of the scale layer on the slab heating is considerable.     

Numerical simulation and experimental investigation of temperature distribution in the circumferentially butt GTAW of Incoloy 800H pipes

The multi-pass circumferential butt GTAW process of Incoloy 800H pipes was modelled with the FEM in 3D. The element birth and death technique was used for the addition of filler material. Goldak model was used to simulate the distribution of arc heat source. The validation of the simulation model was carried out based on the precise temperature measurements within the HAZ of the welds by thermocouples as well as metallographic characterisation of the cross section of the welds. A good agreement was found between the simulation and experimental results for both thermal field and weld zone shape. The present model showed that increasing the heat input resulted in a wider weld zone as well as a higher HAZ peak temperature. These effects were related to the net heat input and not to either welding current or welding speed, individually. The developed simulation model is a useful tool to investigate the welding thermal regime and the weld pool profile.     

Application of the Conservative Discrete Transfer Radiation Method to a Furnace with Complex Geometry

ABSTRACT

A conservative form of the discrete transfer radiation method (DTRM) has been applied in a computational fluid dynamics (CFD) simulation of the radiative heat transfer in an experimental furnace with complex geometry. The furnace was operated under nonpremixed conditions, burning preheated heavy fuel oil. For combustion simulation a semiempiric oil combustion model has been applied, while for the flow field resolution an unstructured CFD code has been used. The simulation results are compared with available experimental data, showing acceptable level of prediction accuracy. The conservative DTRM formulation is shown to be superior to the original formulation in this particular case.     

Evaluation of bioenergy resources with a global land use and energy model formulated with SD technique

Bioenergy is expected to become one of the key energy resources for global sustainable development. However, bioenergy cannot be infinite, because the land area available for biomass production is limited and a certain amount of biomass must be reserved for food and materials. The purpose of this study is to evaluate global bioenergy potential: for this purpose, the authors developed a global land-use and energy model (GLUE) formulated using a SD (System Dynamics) technique. Through a simulation, the following results were obtained. (1) There will be a certain potential for energy crops harvested from surplus arable land in the developed regions of the world. However, care must be taken because the potential is sensitive to the global food supply and demand. (2) There will be a large bioenergy potential for biomass residues, such as cereal-harvesting residues, animal dung, roundwood felling residues, and timber scrap. The ultimate bioenergy potential, from all the biomass residues, will be 277 EJ/yr in A.D. 2100 in the world. (3) The mature-forest area in the developing regions decreases from 2.1 billion ha in 1990 to 0.8 billion ha in 2100, although it is assumed that the felling area is reforested completely after A.D. 2025. Thus, there will not be much room to obtain more fuelwood from forests in the developing regions.     

Heating and Flow Analysis in Hot‐Rolled Stainless Strip Continuous Annealing Furnace Based on CFD Modeling

A three‐dimensional mathematical model was found for a continuous annealing furnace, the temperature field, and flow field of the furnace and the temperature of the stainless strip could be calculated by using this model. The simulation results were compared with measured data and the accuracy of the model was proved by the predicted temperature distribution. By using this model, the convective heat transfer coefficient and equivalent radiation heat transfer coefficient of the strip surface were also analyzed.     

圆形铝熔炼炉内非稳态热工过程数值模拟

针对铝熔铸过程中常用的圆形铝熔炼炉,利用FLUENT软件,根据能量守恒方程、动量方程建立铝熔炼炉内热工过程数学模型,采用标准k-ε湍流模型、P-1辐射模型对铝熔炼炉内非稳态传热及流动过程进行数值模拟研究。考虑到铝料熔化过程会消耗一部分能量,采用等效比热法将铝料的熔化潜热转换为相应的比热值进行计算。通过数值模拟得到了炉内流场、炉膛及铝料温度场分布情况。模拟结果与实际情况相符,为铝熔炼炉的设计与优化研究提供了理论依据。