中间包连浇过程非稳态流场与温度场的数值模拟研究

通过计算得出在浇注过程中连铸中间包包壁瞬态热量损失作为边界条件的基础上,建立了连铸中间包内钢液流动与传热耦合数学模型,对连浇过程中中间包内非稳态的温度场和流场进行了数值模拟,考察了中间包连浇5个包次过程中钢液热量损失、温度分布以及流场情况,为现场操作和工艺优化提供依据和指导。     

Determination of interfacial heat transfer coefficients in casting and quenching using a solution technique for inverse problems based on the boundary element method

Both casting and quenching are processes during which several physical phenomena like heat transfer, fluid flow, phase transformation,etc. interact in a complex manner. To obtain a nu-merical model which is capable of accurately simulating the actual process, one has to be able to quantify all the parameters affecting the process. One parameter which substantially influ-ences heat transfer in these processes is the heat transfer coefficient at the interface between the mold and the metal in casting and that between the metal and the quenchant in quenching. The heat transfer coefficient could vary on the surface of a casting or a quench metal both spatially and with time. Its accurate determination is imperative for a realistic simulation of these processes. In this work, an algorithm based on the boundary element technique is proposed to solve for the interface heat transfer coefficient. The problem is cast as one of inverse heat conduction in two dimensions where some of the boundary conditions, namely, the previously mentioned heat transfer coefficients, are unknowns. Since it is the boundary properties that are being determined, the boundary element method (BEM) is the most suitable technique to use. The algorithm uses experimentally measured temperature data inside the domain to determine the interface heat transfer coefficient. The technique is outlined in detail and some casting and quenching examples are presented to demonstrate its capability.     

A mathematical model of the heat and fluid flows in direct-chill casting of aluminum sheet ingots and billets

A finite-element method model for the time-dependent heat and fluid flows that develop during direct-chill (DC) semicontinuous casting of aluminium ingots is presented. Thermal convection and turbulence are included in the model formulation and, in the mushy zone, the momentum equations are modified with a Darcy-type source term dependent on the liquid fraction. The boundary conditions involve calculations of the air gap along the mold wall as well as the heat transfer to the falling water film with forced convection, nucleate boiling, and film boiling. The mold wall and the starting block are included in the computational domain. In the start-up period of the casting, the ingot domain expands over the starting-block level. The numerical method applies a fractional-step method for the dynamic Navier-Stokes equations and the “streamline upwind Petrov-Galerkin” (SUPG) method for mixed diffusion and convection in the momentum and energy equations. The modeling of the start-up period of the casting is demonstrated and compared to temperature measurements in an AA1050 200×600 mm sheet ingot.     

Model for temperature profile estimation in the refractory of a metallurgical ladle

Modeling of the transient thermal state of metallurgical ladels is motivated by the need for estimating the drop in temperature of the liquid metal in the ladle. On-line estimation of the state is required, since the same ladle is used in a number of casting cycles with rapid changes in boundary conditions for the temperature field, and the conditions in the current as well as previous cycles affect the thermal state. Although a large number of methods for the numerical solution of conduction-diffusion partial differential equations have been developed, there are still advantages to keeping thermal field computations at a relatively simple level, in contrast to the situation in the design process of ladles, where two-dimensional modeling may be required. Extensive computations under nonverifiable boundary and initial parameter values are not especially suited for real-time simulation of industrial processes. This article presents a novel approach to the solution of the one-dimensional transient heat conduction problem applied to ladle linings, relying on classical analytical techniques in combination with numerical methods. The performance of the model was validated by a comparison of predictions to thermocouple measurements from the refractory of a steelmaking ladle during a campaign of 26 casting cycles. Reasonable agreement between the measured and simulated variables could be established, which demonstrates the feasibility of the approach.     

Hydrostatic, Temperature, Time-Displacement Model for Concrete Dams

This paper presents frequency domain solution algorithms of the one-dimensional transient heat transfer equation that describes temperature variations in arch dam cross sections. Algorithms are developed to compute the temperature T(x,t), spatial distribution, and time evolution for the “direct” problem, where the temperature variations are specified at the upstream and downstream faces, and for the “inverse” problem, where temperatures have been measured at thermometers located inside instrumented dam sections. The resulting nonlinear temperature field is decomposed in an effective average temperature, Tm(t), and a linear temperature difference, Tg(x,t), from which the dam thermal displacement response can be deducted. The proposed frequency domain solution procedures are able to reproduce an arbitrary transient heat response by appending trailing temperatures at the end of thermal signals, thus transforming a periodic heat transfer problem in a transient one. The frequency domain solution procedures are used to develop the HTT (hydrostatic, temperature, time) statistical model to interpret concrete dam-recorded pendulum displacements. In the HTT model, the thermal loads are arbitrary and can contain temperature drift or unusual temperature conditions. The explicit use of Tm(t) and Tg(x,t) in the HTT dam displacement model allows extrapolation for temperature conditions that have never been experienced by the dam before (within the assumption of elastic behavior). The HTT model is applied to the 131-m-high Schlegeis arch dam, and the results are compared with the HST (hydrostatic, seasonal, time) displacement model that is widely used in practice.     

Finding boundary conditions: A coupling strategy for the modeling of metal casting processes: Part I. Experimental study and correlation development

A generalized temperature boundary condition coupling strategy for the modeling of conventional casting processes was implemented via experiments and numerical simulations with commercial purity aluminum, aluminum alloy, and tin specimens in copper, graphite, and sand molds. This novel strategy related the heat transfer coefficient at the metal-mold interface to the following process variables: the size of the air gap that forms at the metal-mold interface, the roughness of the mold surface, the conductivity of the gas in the gap, and the thermophysical properties of both the metal and mold. The objective of this study was to obtain, apply, and evaluate the effect of incorporating an experimentally derived relationship for specifying transient heat transfer coefficients in a general conventional casting process. The results are presented in two parts. Part I details the implementation of a systematic experimental approach not limited to a specific process to determine the heat transfer coefficient and characterize the formation of the air gap at the metal-mold interface. The heat transfer mechanisms at the interface were identified, and seen to vary in magnitude during four distinct stages, as the air gap formed and grew. A semiempirical inverse equation was used to characterize the heat transfer coefficient-air gap relationship, across the various stages, for experimental data from the literature and this study.     

Heat transfer and microstructure during the early stages of metal solidification

Transient heat transfer in the early stages of solidification of an alloy on a water-cooled chill and the consequent evolution of microstructure, quantified in terms of secondary dendrite arm spacing (SDAS), have been studied. Based on dip tests of the chill, instrumented with thermocouples, into Al-Si alloys, the influence of process variables such as mold surface roughness, mold material, metal superheat, alloy composition, and lubricant on heat transfer and cast structure has been determined. The heat flux between the solidifying metal and substrate, computed from measurements of transient temperature in the chill by the inverse heat-transfer technique, ranged from low values of 0.3 to 0.4 MW/m² to peak values of 0.95 to 2.0 MW/m². A onedimensional, implicit, finite-difference model was applied to compute heat-transfer coefficients, which ranged from 0.45 to 4.0 kW/m² °C, and local cooling rates of 10 °C/s to 100 °C/s near the chill surface, as well as growth of the solidifying shell. Near the chill surface, the SDAS varied from 12 to 22 (μm while at 20 mm from the chill, values of up to 80/smm were measured. Although the SDAS depended on the cooling rate and local solidification time, it was also found to be a direct function of the heat-transfer coefficient at distances very near to the casting/chill interface. A three-stage empirical heat-flux model based on the thermophysical properties of the mold and casting has been proposed for the simulation of the mold/casting boundary condition during solidification. The applicability of the various models proposed in the literature relating the SDAS to heat-transfer parameters has been evaluated and the extension of these models to continuous casting processes pursued.     

Experimental Determination of Heat Transfer Within the Metal/Mold Gap in a DC Casting Mold: Part II. Effect of Casting Metal, Mold Material, and Other Casting Parameters

Extensive experimental studies were conducted to quantify the effect of different parameters that can affect the heat transfer from the metal to the mold during the steady-state phase of DC casting. In the first part previously published, the experimental technique was established and results were reported for the effect of gas type (atmosphere within the mold) and the gap between the metal and the mold. The results showed the significant effect of gas thermal conductivity and the metal-mold gap on the mold wall heat transfer coefficient. In this second publication on heat transfer in the mold wall region of a DC casting mold, the results from the effect of casting temperature, gas flow rate, casting alloy, mold material, and the mold insert material on the mold wall heat transfer coefficient are described. The experiments reported in the current paper show that these additional factors tested do not affect the heat flux through the mold wall to the same extent as the gap size or the gas type. The heat transfer coefficient changes by less than 5 pct when casting temperature is changed by ±25 K, less than 15 pct when the gas flow rate within the metal-mold gap flows at up to 3 LPM, and approximately 30 pct when the mold material is changed from stainless steel to AA601 to copper. Similar results were obtained when different insert materials were used. These results are explained with the help of an electrical analogy of heat transfer and are consistent with the heat transfer theory.     

板坯连铸结晶器中三维凝固壳厚度分布的数值模拟及实验验证

建立了连铸结晶器中三维凝固壳厚度分布的计算模型和计算方法，提出了非耦合计算时流动计算域与凝固传热计算域的衔接问题，以及铸坯表面换热系数确定的方法。针对２５０ｍｍ×１３００ｍｍ板坯连铸实际工况，用所建立的模型放处理方法数值模拟了其结晶器中的三维温度场和三维凝固壳厚度分布。同时用实测的凝固壳厚度分布数据验证了本计算听模型、边界条件和计算方法。本采用的方法可满足工程精度、并较简便实用。     

Heat-flow-based analysis of surface crack formation during the start-up of the direct chill casting process: Part I. development of the inverse heat-transfer model

A method for determining the temperature dependence of heat transfer in the direct chill (DC) water regime of the DC casting process has been developed. The technique uses as input the data acquired from one embedded thermocouple and involves the application of one-dimensional (1-D) and two-dimensional (2-D) finite element based heat conduction models in succession. The technique has been verified using hypothetical temperature data obtained from a transient casting simulation conducted with a known, idealized, heat flux profile. The results of the comparison indicate that the technique converges to the applied heat flux profile in approximately 12 seconds process simulation time; thus, it is suitable for investigation of the flow of heat during the start-up phase of the process. The accuracy of the technique was found to be satisfactory with thermocouples placed up to a depth of approximately 10 mm below the face of the ingot. The analysis of industrial thermocouple data, the suggested mechanism for crack formation during the start-up, and the remedial action are presented in part II.     

Metal-Mold interfacial heat transfer

During the solidification of metal castings, an interfacial heat transfer resistance exists at the boundary between the metal and the mold. This heat transfer resistance usually varies with time even if the cast metal remains in contact with the mold, due to the time dependence of plasticity of the freezing metal and oxide growth on the surface. The present work has studied interfacial heat transfer on two related types of castings. In the first type, a copper chill was placed on the top of a cylindrical, bottom gated casting. Using the techniques of transducer displacements and electrical continuity, a clearance gap was detected between the solidified metal and the chill. The second type of casting had a similar design except that the chill was placed at the bottom. Owing to the effect of gravity, solid to solid contact was maintained at the metal-chill interface, but the high degree of interface nonconformity resulted in a relatively low thermal conductance as indicated by solution of the inverse heat conduction problem. Finally, the influence of interfacial heat transfer on solidification time with three mold ma-terials is compared by a numerical example, and criteria for utilizing Chvorinov's rule are discussed. Formerly Graduate Student.     

基于无网格伽辽金法的连铸坯凝固计算方法

为考察无网格方法求解铸坯凝固过程的可行性,本文依据移动最小二乘和变分原理,推导并建立了基于无网格伽辽金法的结晶器内铸坯凝固过程二维非稳态传热/凝固数学模型。以小方坯凝固过程为对象,分别采用节点均匀布置、加密布置、随机布置方式,模拟分析了小方坯凝固过程的温度场变化,并将计算结果与参考解、有限元法数值解进行了对比,结果证实无网格伽辽金法在计算精度、自适应性、网格依赖性等方面均优于有限元法。研究结果为无网格方法应用于连铸过程的传热、凝固以及应力/应变行为的数值计算提供参考。      

Transient Thermo-fluid Model of Meniscus Behavior and Slag Consumption in Steel Continuous Casting

The behavior of the slag layer between the oscillating mold wall, the slag rim, the slag/liquid steel interface, and the solidifying steel shell, is of immense importance for the surface quality of continuous-cast steel. A computational model of the meniscus region has been developed, that includes transient heat transfer, multi-phase fluid flow, solidification of the slag, and movement of the mold during an oscillation cycle. First, the model is applied to a lab experiment done with a “mold simulator” to verify the transient temperature-field predictions. Next, the model is verified by matching with available literature and plant measurements of slag consumption. A reasonable agreement has been observed for both temperature and flow-field. The predictions show that transient temperature behavior depends on the location of the thermocouple during the oscillation relative to the meniscus. During an oscillation cycle, heat transfer variations in a laboratory frame of reference are more severe than experienced by the moving mold thermocouples, and the local heat transfer rate is increased greatly when steel overflows the meniscus. Finally, the model is applied to conduct a parametric study on the effect of casting speed, stroke, frequency, and modification ratio on slag consumption. Slag consumption per unit area increases with increase of stroke and modification ratio, and decreases with increase of casting speed while the relation with frequency is not straightforward. The match between model predictions and literature trends suggests that this methodology can be used for further investigations.     

On the development of a three-dimensional transient thermal model to predict ingot cooling behavior during the start-up phase of the direct chill-casting process for an AA5182 aluminum alloy ingot

The control of the heat transfer during the start-up phase of the direct-chill (DC) casting process for aluminum sheet ingots is critical from the standpoint of defect formation. Process control is difficult because of the various inter-related phenomena occurring during the cast start-up. First, the transport of heat to the mold is altered as the ingot base deforms and the sides are pulled inward during the start-up phase. Second, the range of temperatures and water flow conditions occurring on the ingot surface as it emerges from the mold results in the full range of boiling-water heat-transfer conditions—e.g., film boiling, transition boiling, nucleate boiling, and convection—making the rate of transport highly variable. For example, points on the ingot surface below the point of water impingement can experience film boiling, resulting in the water being ejected from the surface, causing a dramatic decrease in heat transfer below the point of ejection. Finally, the water flowing down the ingot sides may enter the gap formed between the ingot base and the bottom block due to butt curl. This process alters the heat transfer from the base of the ingot and, in turn, affects the surface temperature on the ingot faces, due to the transport of heat within the ingot in the vertical direction. A comprehensive mathematical model has been developed to describe heat transfer during the start-up phase of the DC casting process. The model, based on the commercial finite-element package ABAQUS, includes primary cooling via the mold, secondary cooling via the chill water, and ingot-base cooling. The algorithm used to account for secondary cooling to the water includes boiling curves that are a function of ingot-surface temperature, water flow rate, impingement-point temperature, and position relative to the point of water impingement. In addition, a secondary cooling algorithm accounts for water ejection, which can occur at low water flow rates (low heat-extraction rates). The algorithm used to describe ingot-base cooling includes both the drop in contact heat transfer due to gap formation between the ingot base and bottom block (arising from butt curl) as well as the increase in heat transfer due to water incursion within the gap. The model has been validated against temperature measurements obtained from two 711×1680 mm AA5182 ingots, cast under different start-up conditions (nontypical “cold” practice and nontypical “hot” practice). Temperature measurements were taken at various locations on the ingot rolling and narrow faces, ingot base, and top surface of the bottom block. Ingot-based deflection data were also obtained for the two test conditions. Comparison of the model predictions with the data collected from the cast/embedded thermocouples indicates that the model accounts for the processes of water ejection and water incursion and is capable of describing the flow of heat in the early stages of the casting process satisfactorily.     

Transient thermal model of the continuous single-wheel thin-strip casting process

A transient heat-transfer model (STRIP1D) has been developed to simulate the single-roll continuous strip-casting process. The model predicts temperature in the solidifying strip coupled with heat transfer in the rotating wheel, using an explicit finite difference procedure. The model has been calibrated using strip thickness data from a test caster at ARMCO Inc. (Middletown, OH) and verified with a range of other available measurements. The strip/wheel interface contact resistance and heat transfer were investigated in particular, and an empirical formula to calculate this heat-transfer coefficient as a function of contact time was obtained. Wheel temperature and final strip thickness are investigated as a function of casting speed, liquid steel pool depth, superheat, coatings on the wheel hot surface, strip detachment point, wheel wall thickness, and wheel material.     

Numerical Simulation of Filling Process During Twin-Roll Strip Casting

The modeling and controlling of flow and solidification of melt metal in the filling process is important for obtaining the optimal pool level and the formation of the solidified metal layer on the surface of twin-rolls during the twin-roll strip casting. The proper delivery system and processing parameters plays a key role to control flow characteristics in the initial filling stage of the twin-roll strip casting process. In this paper, a commercial CFD software was employed to simulate the transient fluid flow, heat transfer, and solidifications behaviors during the pouring stage of twin-roll strip casting process using different delivery systems. A 3D model was set up to solve the coupled set of governing differential equations for mass, momentum, and energy balance. The transient free-surface problem was treated with the volume of fluid approach, a k–? turbulence model was employed to handle the turbulence effect and an enthalpy method was used to predict phase change during solidification. The predicted results showed that a wedge-shaped delivery system might have a beneficial impact on the distribution of molten steel and solidification. The predicted surface profile agreed well with the measured values in water model.     

Approximate Analytical Solution for the Temperature Field in Welding

To determine the temperature fields associated with welding, significant efforts have been made to establish the relative merits of numerical approaches with variable material properties and the analytical approaches with constant material properties. Currently, analytical solutions are either based on the temperature field generated by a point source of heat or are developed for a finite domain derived approximately by using an infinite or semi-infinite heat kernel. Furthermore, the heat kernel applied in these solutions is derived from the Image method (for example, Nguyen’s book (Thermal Analysis of Welds, 2004)). The main problem with the heat kernels obtained from Image method is that they face the problem of singularity at and around the point where the heat source is located, and they do not satisfy the boundary condition accurately. That is why the Laplace transform method has been applied here instead of using the Image method to formulate a heat kernel that (1) converges rapidly, (2) avoids the problem of singularity, and (3) gives a good and robust approximation of the real analytic solution for the temperature field. The results obtained from the analytical solutions were compared with the results obtained from finite element method. The current work is believed to make a considerable contribution to the avoidance of previously mentioned problems by deriving a new approximate analytical solution for the temperature field on a three-dimensional finite body.     

待定系数法确定双辊薄带铸轧中的边界热流

熔池与铸轧辊接触的边界热流是进行双辊薄带铸轧数值模拟研究的重点,通过铸轧过程中金属凝固机制和传热过程的研究,提出结晶辊和熔池接触的边界热流分布函数形式,利用凝固初始位置、薄带坯出坯厚度,再结合能量守恒原理进行求解,确定函数中的待定参数,避开传统方法需要求解坯壳和铸轧辊间气隙热阻的难题;通过施加所提出的边界热流函数对某试验铸轧辊温度场进行求解,结果与实测结果相吻合,这表明文中提出的边界热流分布函数形式与实际相符合。     

The effect of in-situ dynamic mold flux melting and crystallization on heat transfer in continuous casting

A mold flux is widely used to modify heat transfer rates in continuous casting,and crystallization of the mold flux has been identified as a primary factor that influences heat flux from the strand to the mold.As the harsh environment and the very high transient nature of the mold caster,the study of dynamic mold flux melting and crystallization as well as their effects on heat transfer has not been conducted widely.By using an infrared radiation emitter,a high level heat flux was applied to a copper mold covered with solid mold flux disk to simulate the heat transfer phenomena in continuous casting.By this technique it is possible to have a liquid layer,a crystalline layer and a glassy layer in contact with one another and,by varying the energy input,it is possible to study the dynamic nature of the film and its effect on the heat transfer rate.A general heat transfer model was also developed to allow the prediction of the effect of varying the thickness of the three potential layers in the flux film.     

A Framework for Soft Sensing of Liquid Pool Length of Continuous Casting Round Blooms

Liquid pool length is a vital parameter for solidification control of continuous casting round bloom but it is difficult to be measured by direct hardware measurement. So in this paper, a framework based on heat transfer model for soft sensing of the liquid pool length has been presented. In the framework, the heat transfer model is the kernel and it has been calibrated for its machine-dependent parameters by solving the inverse heat transfer problem with the surface temperature measurements using a color pyrometer. The inverse heat transfer problem has been solved by the optimizer using chaos particle swarm optimization algorithm. After the calibration, the liquid pool lengths were predicted under different casting conditions. Finally, the predictions were validated by shell-thickness measurements using nail-shooting, as the measurements and calculations showed good agreement with the relative errors less than 1.5 pct. And the application of the framework for final electromagnetic stirring has also been presented.