Radiative slab heating analysis for various fuel gas compositions in an axial-fired reheating furnace

A transient radiative slab heating analysis was performed to investigate the effect of various fuel mixtures on the performance of an axial-fired reheating furnace. The various fuel mixtures tested were assumed to be attained by mixing COG (coke oven gas) and BFG (blast furnace gas), which are the two main byproduct gases found in the integrated steel mill industry. The numerical prediction of radiative heat transfer was calculated using an FVM radiation solving method, which is a well-known and efficient method for curvilinear coordinates. The WSGGM (weighted sum of gray gas model) was also adopted to calculate the radiative heat transfer in composition dependent media. The entire furnace was divided into fourteen sub-zones to calculate the radiative thermal characteristics of the furnace without flow field calculations. Each sub-zone was assumed to have homogeneous media and wall temperatures. All of the medium and wall temperatures were computed by calculating the overall heat balance using some relevant assumptions. The overall heat balance was satisfied when the net heat input equaled the three sources of heat loss in each sub-zone, wall loss, skid loss, and slab heating loss.     

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 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.     

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.     

Numerical investigation of combustion with non-gray thermal radiation and soot formation effect in a liquid rocket engine

A numerical analysis was carried out in order to investigate the combustion and heat transfer characteristics in a liquid rocket engine in terms of non-gray thermal radiation and soot formation. Governing gas and droplet phase equations with PSIC model, turbulent combustion model with liquid kerosene fuel, soot formation, and non-gray thermal radiative equations are introduced. A radiation model was implemented in a compressible flow solver in order to investigate the effects of thermal radiation. The finite-volume method (FVM) was employed to solve the radiative transfer equation, and the weighted-sum-of-gray-gases model (WSGGM) was applied to model the radiation effect by a mixture of non-gray gases and gray soot particulates. After confirming the two-phase combustion behavior with soot distribution, the effects of the O/F ratio, wall temperature, and wall emissivity on the wall heat flux were investigated. It was found that the effects of soot formation and radiation are significant; as the O/F ratio increases, the wall temperature decreases. In addition, as the wall emissivity increases, the radiative heat flux on the wall increases.     

THREE-DIMENSIONAL ANALYSIS OF THE WALKING-BEAM-TYPE SLAB REHEATING FURNACE IN HOT STRIP MILLS

Three-dimensional analysis is performed for the turbulent reactive flow and radiative heat transfer in the walking-beam-type slab reheating furnace by FLUENT. A simplified burner is validated against the results of the actual burner with the detailed grid resolution to avoid an excessive number of grids. The predicted temperature distribution in the furnace and global energy flow fractions are in reasonable agreement with available data. Distribution of the heat flux to the slabs, velocity vectors, and all major scalar variables in the furnace also are predicted. This study shows that three-dimensional analysis may be a useful tool to understand quantitatively the complicated combustion and heat transfer characteristics in the furnace.     

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.     

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.     

环形加热炉热工过程CFD数值模拟及其应用

借助CFD商业软件CFX，考虑流动、辐射、燃烧等，对宝钢环形加热炉的热工过程进行了数值模拟，得到了炉膛内的温度、速度矢量等热工参数的分布图。通过简化处理，对环形加热炉各控制段内的加热过程进行了模拟分析，并根据所得到的管坯表面辐射热流、热电偶温度及管坯表面温度研究了各个段总括热吸收率的分布情况，主要分析了总括热吸收率在管坯圆周方向、长度方向以及各个段之间的变化规律。     

Modeling of trickle flow liquid fuel combustion in inert porous medium

Present work is a numerical analysis of fuel oil combustion inside an inert porous medium where fuel oil flows through the porous medium under gravity wetting its solid wall with concurrent movement of liquid fuel and air under steady state conditions. A one-dimensional heat transfer model has been developed under steady state conditions using a single step global reaction mechanism. The effects of optical thickness, emissivity of medium, flame position and reaction enthalpy flux on radiation energy output efficiency as well as the temperature, position and thickness of vaporization zone have been presented using kerosene as fuel. Low values of optical thickness and emissivity of porous medium will ensure efficient combustion, maximize downstream radiative output with minimum upstream radiative loss.     

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.     

Measurements of Some Characteristics of Thermal Radiation in a 400-kW Grate-Fired Furnace Combusting Biomass

A comprehensive experimental investigation relevant to thermal radiation has been performed in a grate-fired test furnace. Thermal radiation is the dominating mode of heat transfer in the grate-fired furnace and yet only a few studies have focused on thermal radiation. No previous works, to the authors' knowledge, have been carried out concerning measurements on radiative heat transfer in grate-fired furnaces. In this work measurements of temperature have been carried out for all boundaries and the flue gases at a large number of locations. The gas species volume fraction, particle mass–size distributions, and wall irradiation have also been measured at a number of spatial locations. These data are useful in a computational framework to describe the radiative heat transfer reaching the boundaries. Comparing modeled wall irradiation to the measured one makes it possible to obtain a deeper insight into the thermal radiative transport inside the grate-fired furnace.     

Experimental investigation on simultaneous measurement of temperature distributions and radiative properties in an oil-fired tunnel furnace by radiation analysis

The paper reports experimental investigations on simultaneous measurement of temperature distribution and radiative properties in an oil-fired tunnel furnace by radiation analysis. Two color CCD cameras were used to obtain visible thermal radiation in the furnace. A radiation imaging model was established by the calculation of radiative transfer equation in the furnace. The temperature distribution and radiative properties can be obtained from the inversion of the radiative imaging model. The validity of radiative imaging model was verified by the numerical analysis of cavity radiation and isothermal system radiation, and the accuracy of reconstruction method was validated by simulation reconstruction. The experimental analysis was divided into two parts. Firstly, the temperatures of wall surface were calculated from the radiative image of refractory wall and compared with the measured temperature of a thermocouple. The difference between the two methods was only about 20 K. Secondly, the temperature distributions in the furnace, absorption coefficients of combustion medium, and emissivities of refractory wall were reconstructed. Because of a single burner in the tunnel furnace, the temperature distributions in the XY vertical sections in the furnace were with temperature higher in the center and lower near the refractory wall surface, and the temperatures decreased along the length of the tunnel furnace. The measured emissivity of refractory wall showed that the refractory material of RPA-MC30 is with high reflectivity in visible spectrum.     

Estimation of slab surface radiative emissivities by solving an inverse coupled conduction,convection, and radiation problem

Slab surface radiative emissivities severely affect the radiative heat transfer in a reheating furnace, as well as the slabs’ coupled conduction, convection, and radiation. Accurate evaluation of these parameters is of significance to ensure the high accuracy of the mathematical model for a reheating furnace, which is beneficial to the energy saving. However, it is difficult to directly and accurately measure these parameters. In this article, slab surface radiative emissivities in a reheating furnace are estimated by solving a nonlinear inverse problem, which is an inverse coupled conduction, convection, and radiation problem. An efficient and accurate gradient method, i.e., Levenberg–Marquardt algorithm, is applied to obtain the solution of the inverse problem. First, a finite difference method and the complex-variable-differentiation method are used for sensitivity analysis, and the inversion accuracy coupled with the efficiency is demonstrated. Then, effects of initial guesses, measurement errors, and measurement locations on estimated slab surface radiative emissivities are investigated in detail. Finally, conclusions are drawn based on the results and analysis.     

Simultaneous radiation and conduction heat transfer in a graded index semitransparent slab with gray boundaries

The simultaneous radiation and conduction heat transfer in a semitransparent slab of absorbing-emitting gray medium is solved in this paper. The refractive index of the medium spatially varies in a linear relationship, and the two boundary walls are diffuse and gray. A curved ray tracing technique in combination with a pseudo-source adding method is employed to deduce the radiative intensities on gray walls. Resorting to some of the results presented by Ben Abdallah and Le Dez, an exact expression of the radiative flux in medium is deduced. The influences on the temperature and radiative flux fields are examined, which are caused by the refractive index distribution, absorbing coefficient, thermal conductivity and the boundary wall emissivities. The results display the significant influences of the refractive index distribution and boundary wall emissivities on the radiative flux and temperature in medium.     

Characteristics of Oxyfuel and Air–Fuel Combustion in an Industrial Water Tube Boiler

The characteristics of oxyfuel combustion and air–fuel combustion in the furnace of a typical industrial water tube boiler using methane as the operating fuel are investigated. Two oxyfuel cases are considered. The analysis is conducted for two oxyfuel cases that correspond to 21% O₂ and 29% O₂ in the oxidizer mixture (O₂ + CO₂). A renormalized group (RNG) turbulence model and the eddy dissipation model are utilized in the present work to provide the turbulence characteristics and the production rate of species. The solution of the radiative transfer equation was obtained using the discrete ordinates radiation model. The set of governing equations and the boundary conditions are solved numerically using Fluent computational fluid dynamics code considering a single-step reaction kinetics model for methane–oxyfuel combustion. Comparison of both oxyfuel combustion and air–fuel combustion indicates that the temperature levels are reduced in oxyfuel combustion. The results show that the temperature levels are greatly reduced as the percentage of recirculated CO₂ is increased. It is concluded that the flame propagation speed in the CO₂ environment is lower than that in N₂. It is found that the natural gas and oxygen consumption rates are slower in oxyfuel combustion relative to air–fuel combustion. Heat transfer from the burnt gases to the water jacket along the different surfaces of the furnace is calculated. It is shown that the energy absorbed is much lower in the case of oxyfuel combustion along all surfaces except for the end part of the furnace close to the furnace rear wall. However, the same performance of the methane-oxy-flames is expected by increasing the oxygen concentration slightly above 29%.     

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.     

SIMULATION OF GASEOUS COMBUSTION AND HEAT TRANSFER IN A VORTEX COMBUSTOR

This article presents the numerical simulation of gaseous combustion and heat transfer in a novel vortex combustor (VC) recently developed for commercial heating applications. A new algebraic Reynolds stress model for strongly swirling turbulence, the eddy break up model for turbulent combustion, and the four-heat-flux model for thermal radiation were employed in the present calculations. Different thermal boundary conditions were specified on the combustor walls. The calculations were conducted on a 22-cm ID VC firing gaseous fuel at 58-, 41-, and 38-kW thermal inputs. Detailed effects of firing rate on the gas axial and tangential velocities, streamlines, temperature, species mass concentrations and wall heat removal are presented, from which the distinct features of the VC flow, combustion, and heat transfer are delineated.     

基于燃烧与水动力耦合模型的锅炉蒸汽管超温特性研究

提出一种基于燃烧与水动力耦合模型的锅炉蒸汽管壁温度数值模拟方法,对某660 MW超临界切圆燃烧锅炉壁温进行了计算分析。以均匀外壁温为边界条件,利用Fluent软件模拟了煤粉气固流动、燃烧和辐射等过程,获得了炉内不同位置受热管的传热热流。再以热流分布为边界,采用MATLAB软件建立了工质流动及气-壁-汽换热方程组,Fluent软件重新计算的壁温边界。通过编写模型间的网格映射函数,实现壁温的耦合计算。研究表明:壁温计算值与实测值的最大相对误差在2%以内;炉膛出口残余旋转使水平烟道左侧和右上方热流较大,高温再热器和末级过热器的外壁温沿炉宽方向呈双峰分布;高温再热器整级受热管出口壁温的峰谷差值远高于末级过热器,实际运行中应特别注意高温再热器靠烟道左侧管屏外圈管子向火侧弯头处的超温。     

步进式加热炉内热工过程的数值模拟

建立步进式加热炉内流动、燃烧和传热的数学模型.炉内流场的模拟采用κ-ε双方程模型,辐射换热计算采用P-1辐射模型,气相燃烧采用Species Transport模型,流场计算采用Simpler算法.采用上述模型与算法得到了炉内详细合理的温度、速度和浓度分布,并对其中影响板坯加热的温度场进行了试验验证.