Performance Evaluation of Two Heat Transfer Models of a Walking Beam Type Reheat Furnace

Two different heat transfer models for predicting the transient heat transfer characteristics of the slabs in a walking beam type reheat furnace are compared in this work. The prediction of heat flux on the slab surface and the temperature distribution inside the slab have been determined by considering thermal radiation in the furnace chamber and transient heat conduction in the slab. Both models have been compared for their accuracy and computational time. The furnace is modeled as an enclosure with a radiatively participating medium. In the first model, the three-dimensional (3D) transient heat conduction equation with a radiative heat flux boundary condition is solved using an in-house code. The radiative heat flux incident on the slab surface required in the boundary condition of the conduction code is calculated using the commercial software FLUENT. The second model uses entirely FLUENT along with a user-defined function, which has been developed to account for the movement of slabs. The results obtained from both models have a maximum temperature difference of 2.25%, whereas the computational time for the first model is 3 h and that for the second model is approximately 100 h.     

采用辐射管加热的辊底式热处理炉数值仿真及其分析

以某公司拟建的采用辐射管加热的辊底式热处理炉为研究对象,在详细分析其传热机理的基础上,建立了炉内钢坯加热过程的二维传热数学模型.采用交替隐式格式的TDMA数值计算方法,开发出了采用辐射管加热的辊底式热处理炉钢坯加热过程二维传热模型计算机数值仿真系统,并进行了大量的数值仿真计算.所得结论为该公司即将开展的辊底式热处理炉模型优化控制奠定了坚实的理论基础.     

Novel Approach to Estimate the Optimum Zone Fuel Mass Flow Rates for a Walking Beam Type Reheating Furnace

Three-dimensional numerical simulation is performed to predict the heat transfer performance in a walking-beam reheating furnace. The furnace uses a mixture of coke oven gas as a heat source to reheat the slabs. The fuel is injected into the furnace at four zones: preheating zone, first heating zone, second heating zone, and soaking zone. This numerical model considers turbulent reactive flow coupled with radiative heat transfer in the furnace; meanwhile, the conductive heat transfer dominates the energy balance inside the slabs. An initial iterative method is proposed to estimate the fuel mass flow rate at each zone of the reheating furnace, while the required heating curve of the slabs is specified. In addition, a simplified two-dimensional numerical model is performed to estimate the fuel mass flow rate for the consideration of computational time consummation. The results of the two-dimensional numerical simulations are compared with those of three-dimensional numerical simulation and the in situ data. Furthermore, velocity and temperature distributions are examined for two cases under different heating curves of the slabs.     

Estimation for inner surface geometry of furnace wall using inverse process combined with grey prediction model

In this work the inner surface geometry of a cylindrical furnace wall is estimated using inverse process method combined with grey prediction model. In estimating process a virtual area extended from the inner surface of furnace wall is used for analysis. The heat conduction equation and the boundary condition are first discretized by finite difference method to form a linear matrix equation; the inverse model is then optimized by linear least-squares error method and the temperatures of virtual boundary are obtained from a few of measured temperatures in furnace wall using the linear inverse model; and finally the temperature distribution of system is got by direct process and the inner surface geometry of furnace wall can be estimated accordingly. The result shows that using inverse process combined with grey prediction model the geometry can be exactly estimated from relatively small number of measured temperatures. Moreover, the effects of measurement error, location, and number of measured points on the estimation for inner surface geometry of furnace wall are discussed in detail.     

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.     

Modeling and Experiments for Heat Transfer Process in Pulverized Coal-Firing Furnace With Two-Dimensional Radiation Characteristics

A dimension-reducing method for calculating the radiant heat transfer with two-dimensional characteristics is introduced in this article. Using this dimension-reducing method, the two-dimensional discrete transfer method (DTM) was applied to a cylindrical enclosure where the medium was absorptive and emissive. The two-dimensional DTM was proved to produce equivalent prediction results as the three-dimensional radiation computation. Then the two-dimensional DTM was incorporated into a general pulverized coal combustion model to estimate radiant heat transfer. The temperature distribution and the net heat flux distribution of an axisymmetric pilot furnace, in which three kinds of lignite were burned, respectively, were calculated using the comprehensive model. The prediction using this model has been found to have a high agreement with the measured data, that the temperature errors was at ± 5% and the net heat flux error was at about ± 15%. The results have demonstrated the feasibility and potential of using the two-dimensional DTM for radiation modeling in pulverized coal flame, and confirmed that the dimension-reducing method and the overall model will be simple and convenient for engineers to use.     

Transient radiative heating characteristics of slabs in a walking beam type reheating furnace

Transient radiative heating characteristics of slabs in a walking beam type reheating furnace is predicted by the finite-volume method (FVM) for radiation. The FVM can calculate the radiative intensity absorbed and emitted by hot gas as well as emitted by the wall with curvilinear geometry. The non-gray weighted sum of gray gas model (WSGGM) which is more realistic than the gray gas model is used for better accurate prediction of gas radiation. The block-off procedure is applied to the treatment of the slabs inside which intensity has no meaning. Entire domain is divided into eight sub-zones to specify temperature distribution, and each sub-zone has different temperatures and the same species composition. Temperature field of a slab is acquired by solving the transient 3D heat conduction equation. Incident radiation flux into a slab is used for the boundary condition of the heat conduction equation governing the slab temperature. The movement of the slabs is taken into account and calculation is performed during the residence time of a slab in the furnace. The slab heating characteristics is also investigated for the various slab residence times. Main interest of this study is the transient variation of the average temperature and temperature non-uniformity of the slabs.     

A numerical analysis of slab heating characteristics in a walking beam type reheating furnace

Numerical analysis of slab heating characteristics in a reheating furnace has been accomplished using FLUENT, a commercial software. The phenomena in the furnace are periodically transient because the slabs are transported toward a rolling mill with every time interval controlled. Unsteady calculation has been performed to obtain a periodically transient solution. A User-Defined Function (UDF) program has been developed to process the movement of slabs because FLUENT cannot handle the movement using its default functions. When the mean temperature of a slab emitted to the rolling mill does not change, calculation is considered to have converged and is stopped. This convergence criterion is appropriate for achieving an analytical solution. With the boundary and initial conditions given, over 55 new slabs are inserted to get a converged solution. Skid posts and beams are included in the calculation because they disturb radiation heat transfer from hot combustion gas to the slabs. This article examines what the slabs experience in the furnace before they are emitted to the rolling mill and whether a slab emitted to the rolling mill satisfies the required slab conditions, such as target temperature and skid severity.     

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.     

Numerical Solution of Melting in a Discretely Heated Enclosure using an Interfacial Tracking Method

Melting in a discretely heated rectangular enclosure is solved using an interfacial tracking method. The interfacial tracking method combines advantages of both deforming and fixed grid approaches. The location of the melting front was obtained by calculating the energy balance at the solid-liquid interface. Through validating the numerical method with experimental results, it was demonstrated that the interfacial tracking method can be used to solve melting in a discretely heated enclosure at high Rayleigh numbers. Effect of Stefan number and geometry of the heaters on the melting process are also investigated.     

Inverse Geometry Design of Radiating Enclosure Filled with Participating Media Using Meshless Method

A new inverse geometry design methodology is presented in this work for designing a two-dimensional radiating enclosure filled with participating media to meet the pre-specified radiative heat flux distribution on a designed boundary wall. Akima cubic interpolation is employed to approximate the shape of the unknown design surface and transform the continuous geometry shape design to the discrete points' position design. To avoid the tedious remeshing of the variable computational domain in the inverse geometry design processes, the direct collocation meshless method is adopted to solve the radiative transfer problem in the enclosure. The geometry shape of the design surface is optimized using the conjugate gradient method, and the zeroth order regularization method is chosen to stabilize the inverse solutions. A test example is taken to verify the new method presented in this work. The inverse design results show that pre-specified design requirement on the boundary wall can be successfully obtained using the new methodology.     

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。     

A heat transfer model for the analysis of transient heating of the slab in a direct-fired walking beam type reheating furnace

A mathematical heat transfer model for the prediction of heat flux on the slab surface and temperature distribution in the slab has been developed by considering the thermal radiation in the furnace chamber and transient heat conduction governing equations in the slab, respectively. The furnace is modeled as radiating medium with spatially varying temperature and constant absorption coefficient. The steel slabs are moved on the next fixed beam by the walking beam after being heated up through the non-firing, charging, preheating, heating, and soaking zones in the furnace. Radiative heat flux calculated from the radiative heat exchange within the furnace modeled using the FVM by considering the effect of furnace wall, slab, and combustion gases is introduced as the boundary condition of the transient conduction equation of the slab. Heat transfer characteristics and temperature behavior of the slab is investigated by changing such parameters as absorption coefficient and emissivity of the slab. Comparison with the experimental work show that the present heat transfer model works well for the prediction of thermal behavior of the slab in the reheating furnace.     

Efficiency analysis of radiative slab heating in a walking-beam-type reheating furnace

The thermal efficiency of a reheating furnace was predicted by considering radiative heat transfer to the slabs and the furnace wall. The entire furnace was divided into fourteen sub-zones, and each sub-zone was assumed to be homogeneous in temperature distribution with one medium temperature and wall temperature, which were computed on the basis of the overall heat balance for all of the sub-zones. The thermal energy inflow, thermal energy outflow, heat generation by fuel combustion, heat loss by the skid system, and heat loss by radiation through the boundary of each sub-zone were considered to give the two temperatures of each sub-zone. The radiative heat transfer was solved by the FVM radiation method, and a blocked-off procedure was applied to the treatment of the slabs. The temperature field of a slab was calculated by solving the transient heat conduction equation with the boundary condition of impinging radiation heat flux from the hot combustion gas and furnace wall. Additionally, the slab heating characteristics and thermal behavior of the furnace were analyzed for various fuel feed conditions.     

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。     

Comparisons of different heat transfer models of a walking beam type reheat furnace

Four different heat transfer models (Model-1 to -4) for the prediction of temperature of the slabs of a walking beam type reheat furnace have been compared. The models are classified based on the solution methodology and simplifications. In the first three models (Model-1 to -3), the furnace is modelled as radiating medium with spatially varying known temperature. Model-1 solves the 3D transient conduction in the slab and radiation in the furnace separately and is coupled via the boundary condition. In the second model, both radiation in the furnace and conduction in the slab are solved simultaneously. A user defined function (UDF) programme has been developed to process the movement of the slabs. Model-3 is similar to Model-2 but it includes additionally the skid support systems for the slabs. In the Model-4, convection in the furnace has been included in addition to all the features considered in Model-3. The convection has been modelled with the consideration of flow of hot gas through the inlet of the burners. All the models have been compared for their performance and computational time. Model-1 has been found to be quite economical and accurate. The inclusion of skid supporting system has little effect in the temperature distribution in the slab.     

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.     

Electromagnetic‐Thermal Modeling of Induction Heating of Moving Wire

The strength in a high carbon wire is attributed to the pearlitic microstructure, which is required for ease of wire drawing. During cold drawing of high carbon steel wires, residual stress develops which has to be relieved in order to obtain the desired mechanical properties. To achieve this, the wire is passed through a closed loop online an induction furnace at a particular speed in order to heat it to a uniform temperature range. This research work presents the electromagnetic‐thermal modeling of the induction heating of a moving wire based on the finite element method using the software package, COMSOL MultiphysicsTM. The furnace had a complicated geometry for the coils and this is, perhaps, for the first time an exhaustive study which is being reported. A unique grid generation technique was developed considering the skin effect. This work is aimed at enabling modeling of the process and will in turn be useful when defining individual parameters affecting the temperature distribution in a component, subjected to induction heating. The temperature distribution in the work piece depends primarily on parameters like coil position, line speed, frequency of the current, thermal and magnetic properties of the work piece, and so on. The impact of power supply frequency and line speed were studied during the heating of the moving wire (workpiece). An in‐situ customized furnace of lower capacity was developed to carry out the validation experiments. The present modeling results are validated with online plant trial data and found to be in good agreement. Finally, the desired mechanical property achieved during trials was confirmed through tensile testing.     

220t_h锅炉再燃改造的数值模拟

为了对锅炉进行再燃改造,借助Fluent 6.3软件平台,采用数值模拟的方法,对某电厂一台220 t/h四角切圆燃烧锅炉再燃改造前后炉内的气流场、温度场和污染物排放特性进行了分析,并对再燃区过量空气系数对再燃改造效果的影响进行了探讨。湍流模型分别采用了realizable k-εmod-el和大涡模型(LES),并对模拟结果进行了比较;LES模拟和结果与现场的实验数据进行了对比验证,包括温度场、组分场和NOx,LES数值模拟结果与实验结果吻合比较好。计算结果表明:使用再燃改造后炉膛温度分布更加均匀;再燃喷口附近形成了还原性气氛,降低了NOx浓度;当再燃区过量空气系数为0.90时,再燃效果最佳,此时炉膛出口处NOx浓度下降33.87%;LES模拟结果较realizable k-εmodel准确。     

基于有限元分析的火化炉热能传递仿真研究

利用有限元分析手段,对遗体火化过程中炉膛的温度、速度分布进行模拟.通过将实际检测结果与模拟结果进行对比,验证数值模拟所用模型的可靠性和数值模拟方法与结果的可信性,然后通过分析几种不同炉膛结构的温度、速度分布,对炉体主要设计参数进行了优化.研究结果为设计更加合理、高效节能的火化设备提供了理论依据,对优化遗体火化燃烧过程具有重要意义.