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.     

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.     

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.     

A Coupled Numerical Study of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab Reheating Furnace

In the present study, a three-dimensional simulation is performed for the turbulent reactive flow and radiactive heat transfer in the walking-beam-type slab reheating furnace using STAR-CD software. The geometric model takes care of all components of the furnace. To obtain a steady solution, the walking beams are assumed fixed in the furnace and the slab is modeled as a laminar flow having a very high viscosity and thus moving at a nearly constant speed. The temperature distributions of the slab and the gas mixture are obtained through a coupled calculation. The simulation results successfully predict the temperature distribution inside the slab and the heat flux on the slab surfaces, providing an opportunity for a full exploration of the influence of the walking beam system on the skid marks. The simulation results show that the radiative shielding by the static beams is the main cause of the skid marks. The heat loss through the skid button to the cooling system worsens the skid marks.     

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.     

混合煤气成分变化对加热炉内温度场影响的数值模拟研究

以燃用高炉、焦炉混合煤气的实验加热炉为研究对象,建立炉内二维稳态传热、流动及燃烧的数学模型,研究混合煤气成分变化对加热炉内温度场的影响,计算结果显示高炉煤气含量在一定范围内增加时,炉内温度水平和钢坯加热区温度均匀性逐渐降低.这些与华凌涟钢集团轧钢加热炉的实际情况基本一致.     

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.     

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.     

A simple solution for transient heat transfer during heating of a slab product

A theoretical and experimental study of transient heat transfer in the heating of an individual slab product, subjected to an air flow at a temperature of 50°C and a velocity of 1 m/s, is presented. Experimental temperature measurements at the centre of the slab product were made, and the experimental heat-transfer rates were derived from the temperature data. A simplified analytical technique, using the boundary condition of the third kind in transient heat transfer, was used to predict the theoretical heat transfer rates for two cases, the first considering that the heat transfer coefficient is a convective heat transfer coefficient, and the second considering that heat transfer coefficient is the sum of the convective and radiative heat transfer coefficients. The experimental heat-transfer rates were compared with the predictions for two cases, and a very good agreement was obtained.     

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.     

普碳钢与某型不锈钢混合加热的可行性初探

以某厂板坯步进梁式加热炉为背景,建立了数学模型,计算出了在相同炉温制度下,普碳钢与某型不锈钢的升温过程,对不同钢种、不同规格的钢坯在炉内混装加热的可行性进行了初步探索。     

Research on a 3D Temperature Field Model of a Slab with Oxide Layer Growth

Slab heating plays an important role in the production of iron and steel materials. However, it is a very complex process involving physical and chemical change. In this study, we built a numerical heat transfer model to predict the three‐dimensional transient temperature field of a slab based on the implicit finite difference method. The model takes the growth of the oxide layer into account, as well as the impact on heat transfer. Slab temperature and oxide layer thickness were calculated in each step. The model considers three kinds of boundary conditions. It displays the temperature variation of each part of the slab in the furnace at all time, the heating curve, and the growth in the thickness curve of the oxide layer. This model can be used to control heating time, optimize the heating curve, and improve production efficiency, thereby reducing cost. The model is also useful for calculation of rolling force, as well as the control of carbon isolation and product microstructure.     

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.     

板坯加热炉内加热特性的数值分析

以某公司热轧厂常规与双蓄热烧嘴组合供热的板坯加热炉为研究对象,建立该加热炉炉内流动、传热、燃烧和板坯运动吸热过程的三维物理数学模型,运用CFD仿真技术对其进行详细的数值计算,得到炉内稳态的速度场和温度场分布规律、板坯的升温曲线以及板坯温度分布均匀性,计算结果与"黑匣子"实验测量数据吻合良好。本文给出的板坯加热特性计算方法为研究加热炉新工艺、优化板坯加热温度制度提供了科学依据。     

板坯加热炉内常规燃烧与富氧燃烧数值计算对比分析

以某公司热轧厂板坯加热炉为研究对象,建立该加热炉内流动、传热、燃烧和板坯运动吸热过程的三维物理数学模型,运用CFD仿真技术对其进行详细的数值计算,重点对比分析了常规燃烧和富氧燃烧特性,得到了各自的炉内速度场和温度场分布规律、板坯的升温曲线以及板坯温度分布均匀性,计算结果与“黑匣子”实验测量数据吻合良好.总结出的富氧燃烧...     

连铸板坯热装工艺节能效果分析

利用二维板坯加热数模对板坯加热过程热行为的模拟，探讨了热装温度对加热炉单位热耗、炉子产量及氧化烧损的影响。在热装条件下，加热炉在最优生产率条件下运行时，既能大幅度降低能耗又能明显减少板坯的氧化烧损。     

蓄热式连续加热炉内流动与换热特性的数值模拟

以某公司大方坯蓄热式连续加热炉为研究对象,对该炉建立了三维物理数学模型,分别采用可实现双方程湍流模型,PDF非预混燃烧模型、离散坐标法辐射模型(DO模型),应用Fluent数值仿真软件进行了模拟研究,得到了蓄热式连续加热炉内的流场和温度场的分布规律,并对炉内对流换热系数的分布进行了详细的分析研究.结果表明:钢坯表面局部对流换热系数在各加热段内分布不均匀,这主要是由于烧嘴进口射流所引起的局部流速的差异性,从整体上来看,预热段和加热1段的对流换热系数要高于其它各段.     

连铸连轧辊底式加热炉薄板坯的温度场计算

分析了CSP工艺中辊底式加热炉及炉中板坯的换热特性,建立了板坯换热的二维非稳态数学模型,用差分法计算出了加热炉中不同时刻板坯断面的温度场,给出了板坯在加热炉中的温度变化曲线,为优化加热炉的加热制度提供了理论依据。     

连续推钢式轧钢加热炉的数值模拟

运用流体动力学计算软件（CFD）FLUENT,对湘潭钢铁公司第二高速线材厂轧钢加热炉的三维流场进行了数值模拟,获得该轧钢加热炉内的气体流动、流速和压力的分布规律.通过与加热炉内的结构特点和实际操作状况对照分析,表明该加热炉的局部结构与操作不相适应,尤其是压力分布不适应加热炉的操作要求,造成炉内供热调节的灵活性降低,从而影响到加热质量.分析结果与加热炉的实际运行状况相符,为加热炉的进一步结构改造提供依据.     

连续式轧钢加热炉在线控制数学模型与应用

以理论计算和实测数据为依据,开发了连续式加热炉最佳炉温设定和在线控制数学模型,并应用于安钢中型厂5点供热推钢式加热炉。结果表明：在轧机产量波动时,不但加热炉供热合理,而且钢温波动小、加热质量好、节能效果显著。