Numerical Analysis of Secondary Cooling in Continuous Slab Casting

In the present study, a numerical optimization program has been developed for predicting the optimal secondary cooling patterns in a continuous slab caster. Optimization strategy using Broydon-Fletcher-Goldfarb-Shanno （13FGS） method is carried out by determining the constant heat transfer coefficients in each spray zone, which could satisfy the casting conditions and metallurgical criteria specified by the engineer. From the present results, it is found that even a slight variation in the pouring temperature, allowable surface temperature, and casting speed could give rise to the changes in the cooling pattern throughout the spray zones.     

Numerical Simulation of Solidification Process on Single Crystal Ni-Based Superalloy Investment Castings

Bridgman directional solidification of investment castings is a key technology for the production of reliable and highly efficient gas turbine blades. In this paper, a mathematical model for three-dimensional （3D） simulation of solidification process of single crystal investment castings was developed based on basic heat transfer equations. Complex heat radiation among the multiple blade castings and the furnace wall was considered in the model. Temperature distribution and temperature gradient in superalloy investment castings of single blade and multiple ones were investigated, respectively. The calculated cooling curves were compared with the experimental results and agreed well with the latter. It is indicated that the unsymmetrical temperature distribution and curved liquid-solid interface caused by the circle distribution of multiple turbine blades are probably main reasons why the stray grain and other casting defects occur in the turbine blade.     

Grain Size Distribution and Interfacial Heat Transfer Coefficient during Solidification of Magnesium Alloys Using High Pressure Die Casting Process

The objective of this study is to predict grain size and heat transfer coefficient at the metal–die interface during high pressure die casting process and solidification of the magnesium alloy AM60. Multiple runs of the commercial casting simulation package, ProCAST~(TM), were used to model the mold filling and solidification events employing a range of interfacial heat transfer coefficient values. The simulation results were used to estimate the centerline cooling curve at various locations through the casting. The centerline cooling curves, together with the die temperature and the thermodynamic properties of the alloy, were then used as inputs to compute the solution to the Stefan problem of a moving phase boundary,thereby providing the through-thickness cooling curves at each chosen location of the casting. Finally, the local cooling rate was used to calculate the resulting grain size via previously established relationships.The effects of die temperature, filling time and heat transfer coefficient on the grain structure in skin region and core region were quantitatively characterized. It was observed that the grain size of skin region strongly depends on above three factors whereas the grain size of core region shows dependence on the interfacial heat transfer coefficient and thickness of the samples. The grain size distribution from surface to center was estimated from the relationship between grain size and the predicted cooling rate.The prediction of grain size matches well with experimental results. A comparison of the predicted and experimentally determined grain size profiles enables the determination of the apparent interfacial heat transfer coefficient for different locations.     

Numerical Simulation of Morphology and Microsegregation Evolution during Solidification of Al-Si Alloy

A stochastic model coupled with transient calculations for the distributions of temperature, solute and velocity during the solidification of binary alloy is presented. The model can directly describe the evolution of both morphology and segregation during dendritic crystal growth. The model takes into account the curvature and growth anisotropy of dendritic crystals. Finite difference method is used to explicitly track the sharp solid liquid (S/L) interface on a fixed Cartesian grid. Two-dimensional mesoscopic calculations are performed to simulate the evolution of columnar and equiaxed dendritic morphologies of an AI-7 wt pct Si alloy. The effects of heat transfer coefficient on the evolution of both the dendrite morphology and segregation patterns during the solidification of binary alloys are analyzed. This model is applied to the solidification of small casting. Columnar-to-equiaxed transition is analyzed in detail. The effects of heat transfer coefficient on final casting structures are also studi     

Modeling and Simulation of the Microstructure Evolution of the Gas-atomized Alloy Droplets during Spray Forming

In order to understand the solidification process of an atomized droplet and predict the fraction solidification of droplets with flight distance during spray forming, a numerical model based on thepopulation dynamics approach is developed to describe the microstructure evolution under the common action of the nucleation and growth of grains.The model is coupled with droplets heat transfer controlling equations and solved for Al-4.5 wt pct Cu alloy. It is demonstrated that the numerical results describe the solidification process well.     

Prediction of spatial distribution of the composition of inclusions on the entire cross section of a linepipe steel continuous casting slab

In the current study, the transformation in the composition of non-metallic inclusions from the molten steel to the solidified steel was studied and the composition distribution of inclusions on the cross section of a linepine continuous casting slab was predicted. During cooling and solidification of the continuous casting strand, Al₂O₃-CaO inclusions reacted with the bulk steel and transformed to CaS-Al₂O₃-MgO-(CaO) ones in the continuous casting slab. The composition of inclusions on the cross section of the slab varied with locations due to the varied cooling rate. A model was established to predict the distribution of the composition of inclusions on the cross section of the continuous casting slab, coupling solidification and heat transfer of the continuous casting slab, the kinetic mass transfer of the dissolved elements in the solid steel, and thermodynamic calculation of inclusion transformation at different temperatures. The composition transformation of inclusions mainly occurred at the temperature between the liquidus and solidus of the linepipe steel. Inclusions were mainly CaS-Al₂O₃-MgO-(CaO) in slab center and were MgO-Al₂O₃-CaO-CaS within the subsurface of the slab. In the slab, the transformation fraction of inclusions was less than 10 % at corners while it reached 70 % at 50 mm below the surface of the slab.     

Free Boundary Problems in the Steel Industry

This paper considers two novel free boundary problems that emerge from modelling processes basic to steel manufacture. The first process concerns the spray cooling of hot steel sheet during the process of continuous casting. Here, an important practical consideration is the non-monotonicity of the measured heat transfer from the steel as a function of the steel temperature. In order to understand this phenomenon, a two-phase flow model is written down for the heating and vapourisation of the water spray. This model relies on a microscale analysis of droplet vapourisation and, in a steady state, it reduces to a coupled system of nonlinear ordinary differential equations for the spray temperature and water content. This system predicts the conditions for the existence or otherwise of a free boundary separating the two-phase region from a dry vapour layer close to the steel plate.The thickness of this vapour layer is determined by the solution of a generalised Stefan problem. The second process concerns the macroscopic modelling of pig .iron production in blast furnaces. In the simplest scenario, the blast furnace may be roughly divided into a porous solid region overlaying a hot high pressure gaseous zone. The gas reacts with the solid in a thin “intermediate region“ at the base of the solid region and it is in this intermediate region that the pig iron is produced. A free boundary model is proposed for the location of the intermediate region and its stability is investigated.     

Research on Flow and Heat Transfer Characteristics Inside Spiral Pile-honeycomb Structures with Different Shapes

Spiral plate heat exchanger is a traditional compact heat exchanger,and widely used in the occasion of the high heat transfer capacity requirements,such as waste heat recovery. In the situation of energy shortage and rapid development of heat transfer technology~(1-3),cylindrical,elliptical and rhombic spiral pile-honeycomb heat transfer models are established~(4-5). The internal flow and heat transfer are simulated by using CFD software FLUENT15. 0 and RNG k-ε turbulent model,and then the three models are analyzed. The results show that the secondary flow and vortex are induced again in the secondary honeycomb,which further increases the turbulence intensity of the fluid. The thickness of the boundary layer is reduced twice,and the heat transfer effect is better than that of the honeycomb spiral structure. The spiral pile-honeycomb model for the rhombus is better than the models of cylinder and ellipse in heat transfer performance.     

Experimental Study and Numerical Simulation of Directionally Solidified Turbine Blade Casting

The directional solidification process of turbine blade sample castings was investigated in the work. Variable withdrawal rates were used in one withdrawal process and compared with the other using uniform rate. A mathematical model for heat radiation transfer and microstructure simulation of directional solidification process was developed based on CA-FD method. The temperature distribution and microstructure w.ere simulated and compared with the experimental results. The stray grains were predicted and compared with the experimental results. The uneven temperature distribution of platform was the main reason of the formation of stray grains.     

Study on Numerical Simulation of Mold Filling and Solidification Processes under Pressure Conditions

The mold filling and solidification simulation for the high pressure die casting (HPDC) and low pressure die casting (LPDC) processes were studied.A mathematical model considering the turbulent flow and heat transfer phenomenon during the HPDC process has been established and paralled computation technique was used for the mold filling simulation of the process.The laminar flow characteristics of the LPDC process were studied and a simplified model for the mold filling process of wheel castings has been developed.For the solidification simulation under pressure conditions,the cyclic characteristics and the complicated boundary conditions were considered and techniques to improve the computational efficiency are discussed.A new criterion for predicting shrinkage porosity of Al alloy under low pressure condition has been developed in the solidification simulation process.     

连铸板坯凝固过程的数值模拟

为得到连铸坯凝固末端的液相穴分布,以便选取轻压下参数,依据实际生产中二冷边界换热条件,采用有限元法对连铸厚板坯冷却传热过程进行数值模拟,并用远红外测温仪测试并校准Q235B300 mm×1650 mm铸坯表面温度,得到了连铸坯在任意段截面的温度场分布、凝固末端液相穴形状及铸坯中心纵截面固相率分布.结果表明,可以根据铸机...     

On numerical simulation of the continuous casting process

In this paper a steady-state nonlinear parabolic-type model, which simulates the multiphase heat transfer during solidification in continuous casting, is presented. An enthalpy formulation is used and we apply a FE-method in space and an implicit Euler method in time. A detailed solution algorithm is presented. We compute the temperature distributions in the strand when the boundary conditions (mold/spray cooling) on the strand surface are known. The numerical model gives thereby a good basis for the testing of new designs of continuous-casting machines. An application of the model to continuous casting of billets is presented.     

相变材料蓄冷板凝固过程的传热研究

采用精确解法与积分近似相结合的方法,对一种自制相变材蓄冷材料充冷凝固过程的相变导热问题进行了求解.获得了该蓄冷介质在板式蓄冷器中凝固时的相界面移动速度,边界面热流密度随时间变化的规律,及不同工况下蓄冷板厚度与预测蓄冷时间的关系.计算结果与实验结果吻合较好.结果表明,边界面的热流密度随固相区厚度的增加而减小;预测蓄冷时间随冷媒流体温度的降低而减小,随平板厚度的增加而增加.     

雾化特性及系统参数对闭式喷雾冷却系统性能的影响

搭建了以R22为冷却介质的闭式喷雾冷却实验台,通过更换3种不同的喷嘴,分析对比了不同喷嘴类型和喷雾高度下传热性能的变化规律。实验结果表明:选择喷嘴时必须同时考虑喷雾流量和雾化角度的影响;雾化角较小的喷嘴在低高度下适用性较好。同时,研究了系统参数如过冷度和充注压力对喷雾冷却传热性能的影响,得出过冷度对喷雾冷却性能有一定促进作用,但过冷度越大,促进效果越弱;表面传热系数和表面温度均随充注压力的升高而升高,因此高充注压力不适用于需严格控制温度的表面冷却。     

Surface heat transfer characteristics of R404A pulsed spray cooling with an expansion-chambered nozzle for laser dermatology

Cryogen spray cooling is applied to protect epidermis from thermal damage in laser dermatology. However, R134a shows insufficient cooling capacity for minimizing the laser energy absorption by melanin in darkly pigmented human skin. By contrast, the cooling capacity of R404A can be improved with a low boiling point. This study examined the temporal and spatial variations in surface heat transfer during R404A spray cooling using a straight-tube nozzle with an expansion chamber. Substitution of R134a with R404A increases the maximum heat flux by 19%, whereas introducing an expansion chamber enhances the maximum heat flux by 18%. Results indicate that surface heat transfer during R404A spraying exhibits intense temporal and spatial non-uniformity. A sub-region of uniform cooling with a radius of 2 mm appears around the spray center with a high transient heat flux above 300 kW/m². This finding can help physicians precisely control the therapy area with enhanced laser energy.     

热金属表面多喷嘴风冷过程气-固耦合传热模拟

目的 获得多喷嘴风冷过程的界面换热系数,并研究风冷工艺参数对界面换热的影响规律.方法 基于Fluent软件对三喷嘴强制风冷传热过程进行"气-固"耦合分析,获得高压气流的流速场和钢板表面温度场.基于"气-固"耦合分析得到钢板表面平均温度曲线,利用自开发的反传热软件计算得到"气-固"耦合界面换热系数,并将界面换热系数以第三...     

Computer model of unidirectional solidification of single crystals of high temperature alloys

Abstract

I t has been common practice to use mould withdrawal unidirectional solidification to produce single crystal castings. To grow single crystals successfully, it is important to control several solidification parameters, such as the morphology of the solidification front (solid/liquid interface), thermal gradient, and growth rate during solidification. It is the aim of this study to develop a solidification model that can predict such solidification parameters for various design and operating conditions. The solidification phenomena in the process modelled are basically controlled by two heat transfer mechanisms: conduction and radiation. A set of heat transfer equations and boundary conditions were employed to describe mathematically the heat transfer phenomena. Then the finite difference method was used numerically to solve these equations for specified boundary conditions to obtain the temperature distribution and temperature variation in the casting. The solidification parameters can subsequently be deduced from these temperature data. Several thin plate castings were tested using the model developed. The following design and operating conditions were evaluated: susceptor temperature (power input), withdrawal speed, changes of cross-sectional area in the casting, and geometrical arrangement of the casting tree.

MST/1422     

Non-equilibrium solidification of undercooled droplets during atomization process

Thermal history of droplets associated with gas atomization of melt has been investigated. A mathematical model, based on classical theory of heterogeneous nucleation and volume separation of nucleants among droplets size distribution, is described to predict undercooling of droplets. Newtonian heat flow condition coupled with velocity dependent heat transfer coefficient is used to obtain cooling rate before and after nucleation of droplets. The results indicate that temperature profile of droplets in the spray during recalescence, segregated and eutectic solidification regimes is dependent on their size and related undercooling. The interface temperature during solidification of undercooled droplets rapidly approaches the liquidus temperature of the alloy with a subsequent decrease in solid-liquid interface velocity. A comparison in cooling rates of atomized powder particles estimated from secondary dendrite arm spacing measurements are observed to be closer to those predicted from the model during segregated solidification regime of large size droplets.