Effect of thermosolutal convection on directional solidification

Absract The impact of thermosolutal convection during directional solidification is explored via results of numerical investigations. Results from fully transient numerical simulations of directional solidification in a differentially heated cavity under terrestrial conditions and Bridgman cytstal growth in space are discussed. The pivowl role ofboth thermaland solutal convection in the solidifaction process is illustrated by examining these two cases. In particular, radical and longitudinal macrosegregation resulting from this thermosolutal convection is discussed.     

Modelling convection in solidification processes using stabilized finite element techniques

Solidification of dendritic alloys is modelled using stabilized finite element techniques to study convection and macrosegregation driven by buoyancy and shrinkage. The adopted governing macroscopic conservation equations of momentum, energy and species transport are derived from their microscopic counterparts using the volume‐averaging method. A single domain model is considered with a fixed numerical grid and without boundary conditions applied explicitly on the freezing front. The mushy zone is modelled here as a porous medium with either an isotropic or an anisotropic permeability. The stabilized finite‐element scheme, previously developed by authors for modelling flows with phase change, is extended here to include effects of shrinkage, density changes and anisotropic permeability during solidification. The fluid flow scheme developed includes streamline‐upwind/Petrov–Galerkin (SUPG), pressure stabilizing/Petrov–Galerkin, Darcy stabilizing/Petrov–Galerkin and other stabilizing terms arising from changes in density in the mushy zone. For the energy and species equations a classical SUPG‐based finite element method is employed with minor modifications. The developed algorithms are first tested for a reference problem involving solidification of lead–tin alloy where the mushy zone is characterized by an isotropic permeability. Convergence studies are performed to validate the simulation results. Solidification of the same alloy in the absence of shrinkage is studied to observe differences in macrosegregation. Vertical solidification of a lead–tin alloy, where the mushy zone is characterized by an anisotropic permeability, is then simulated. The main aim here is to study convection and demonstrate formation of freckles and channels due to macrosegregation. The ability of stabilized finite element methods to model a wide variety of solidification problems with varying underlying phenomena in two and three dimensions is demonstrated through these examples. Copyright © 2005 John Wiley & Sons, Ltd.     

轴向磁场下分离结晶熔体内热毛细对流的数值模拟

为研究轴向磁场对分离结晶Bridgman法生长CdZnTe晶体熔体热毛细对流的影响,采用有限差分法进行了三维数值模拟。结果表明轴向磁场能有效抑制熔体内的热毛细对流;轴向磁场对熔体内部温度分布也有较大的影响,能使等温线分布变得平缓;当磁场强度不变时,随着狭缝宽度的增大熔体内部的流动减弱。     

Influence of liquid metal feeding on the flow and macrosegregation in DC casting

ABSTRACT

The influence of liquid metal feeding on the flow and macrosegregation during direct chill (DC) casting of Al-4.5wt-%Cu billets is investigated. An analytical study for constricted inlets predicts that the inflow only reaches the bottom of the sump for narrow inlets, a result confirmed by steady-state axisymmetric simulations of equiaxed solidification. For wide inlets, and inlets using a combo bag, the inflow is swiftly entrained towards the chill and the final macrosegregation predictions are all similar. For narrow inlets without a combo bag, penetration of the thermal jet to the bottom of the sump locally delays solidification producing an inclination in the packed solid interface and the possible growth of columnar dendrites in this region.     

Studies on macrosegregation and double diffusive convection during directional solidification of binary mixture

Abstract

Experimental and numerical studies on macrosegregation during directional solidification of an aqueous ammonium chloride solution in a rectangular cavity are presented. Depending on the initial concentration and boundary temperature conditions, three distinct situations in the liquid during the solidification process are studied: mass diffusion only, solutal convection and double diffusive convection. The time dependent concentration of the solution inside the cavity is measured online for the above three situations using a laser based technique. This technique measures refractive index of the solution, which indirectly gives the concentration variation at a point in the solution during solidification. The interface growth is photographed using a shadowgraph technique, and the flow is visualised using a sheet of laser light scattered by neutrally buoyant, hollow glass spheres seeded in the fluid. Corresponding numerical studies are performed using a macroscopic model based on a fixed grid, enthalpy based, control volume approach. A good agreement between the experimental and computational results is observed.     

Transport Properties and Transport Phenomena in Casting Nickel Superalloys

Nickel superalloys that are used in the high-temperature regions of gas-turbine engines are cast by directional solidification (DS). In the DS processes, the castings are cooled from below, and three zones exist during solidification: (1) an all-solid zone at the bottom, (2) a “mushy zone” that is comprised of solid and liquid material, and (3) an overlying all-liquid zone. Computer simulations can be useful in predicting the complex transport phenomena that occur during solidification, but realistic simulations require accurate values of the transport properties. In addition to transport properties, the thermodynamic equilibria between the solid and liquid during solidification must also be known with reasonable accuracy. The importance of using reasonably accurate estimations of the transport properties is illustrated by two-dimensional simulations of the convection during solidification and the coincidental macrosegregation in the DS castings of multicomponent Ni-base alloys. In these simulations, we examine the sensitivity of the calculated results to measured partition ratios, thermal expansion coefficients, and viscosities that are estimated by regression analyses and correlations of existing property data.     

不同冷却条件下Al-Si/SiC颗粒系统二维凝固过程数值模拟

本文采用多相流模型对不同冷却条件下Al-Si/SiC系统二维凝固过程进行了数值模拟,对顶面冷却、底面冷却、侧面冷却和四面冷却条件下,无颗粒、小颗粒和大颗粒的情况进行了研究。溶质分布表明:对于分凝系数小于1的合金,先凝固的地方出现负偏析,后凝固的地方出现正偏析。顶面冷却和底面冷却时会出现A型偏析,侧面冷却和四面冷却时出现V型偏析。共晶分布验证了Scheil方程,共晶的产生会受到宏观偏析的影响,而且大颗粒的堆积会抑止共晶的产生。     

对流影响枝晶生长的相场法模拟研究进展

液态金属的对流和枝晶生长的相互作用在凝固模型中是非常重要的,因为铸造和焊接过程常伴随有自然或强迫对流。综述了耦合对流时相场的数学模型、数值计算方法以及在凝固微观组织模拟中的应用和进展,指出了该领域目前面临的问题和未来发展趋势。     

动态布流平面凝固铸造AA1070/AA7050合金

提出了一种新的用于大尺寸复层铸锭平面凝固铸造的布流系统,并使用软件FLUENT对铸造过程中分流方式对温度场的影响进行了模拟分析,模拟结果表明,使用动态布流时熔体温度的均匀性显著优于定口布流,因而可实现凝固时固/液界面在上升过程中保持平坦。使用动态布流平面凝固铸造方法实现了1070/7050大尺寸双层铝合金的铸造复合,铸造结果表明,复合铸锭中两种铝合金的界面清晰平直,无气孔夹杂等缺陷,实现了冶金结合并存在元素扩散层;7050侧金相组织均匀,厚度方向上无明显宏观偏析。     

Freckle formation in a solidifying binary alloy

The effect of solutal solidification on the unidirectional solidification of a binary alloy cooled from below is considered. Soon after the onset of convection a mushy region often forms, and is accompanied by vigorous convection in the molten alloy above. In contrast, the fluid in the mush appears unaffected by the neighbouring flow and remains essentially quiescent. This work considers the nonlinear convective stability of the mush and determines a criterion for channelling in the mush to occur. The basic state is a similarity solution, so that a quasi-static approximation must be applied in order to apply conventional stability theory. Moreover, although the model for solidification is relatively simple, an analytical expression for linear stability is not available. Thus the series of equations arising from the nonlinear stability analysis lead to a complicated set of symbolic and numerical calculations. Stable finite-amplitude solutions are found for Rayleigh numbers larger than critical for all values of the chosen superheat. The nonlinear solutions demonstrate the possibility of channelling within the mush dependent upon the strength of convection. These finite-amplitude solutions are extended further by the calculation of a numerical solution of the model equations. The evolution of the stream function and the mass fraction is followed, the onset of convection and freckling can then be deduced from the numerical simulation. The onset of convection in the mush is found in terms of the mush Rayleigh number, and compares favourably with linear stability theory and experimental data. The onset of freckling is also given in terms of a Rayleigh number, but is sensitive to the initial conditions. This appears to explain the large disagreement found in experiments aimed at finding a criterion for freckling.     

Modelling mixed columnar-equiaxed solidification with melt convection and grain sedimentation – Part II: Illustrative modelling results and parameter studies

A volume-averaging multiphase solidification model was introduced in Part I. In Part II, illustrative simulations are made for two benchmarks, a unidirectional solidification benchmark and a cylindrical ingot casting, using a binary Al–Cu alloy. For the case of unidirectional solidification the competing growth of columnar and equiaxed structures, evolution of different phase regions, solute redistribution, and the influence of grain sedimentation and melt convection are analyzed in detail. The columnar-to-equiaxed transition (CET) is investigated, with important insights derived from the CET prediction. The new features of the model and its applicability to industrial-type castings are demonstrated with simulations of a cylindrical ingot casting. This is done in both a 2D axisymmetric and a full 3D geometric domain to demonstrate the ability of the model to produce consistent results. The main features of the model that are verified include tracking of the columnar primary dendrite tip, nucleation of equiaxed grains ahead of the columnar tip front, hydrodynamic and solutal interactions between the equiaxed and columnar structures, the columnar-to-equiaxed transition (CET), melt convection and grain sedimentation, and macrosegregation and the final macrostructure. With appropriate modelling parameters the typical columnar-equiaxed macrostructure observed in experiments can be reproduced. Uncertainties due to model parameters and assumptions are addressed and discussed.     

Continuum model for predicting macrosegregation in dendritic alloys

“Macrosegregation” represents a class of defects in cast products of serious concern to both alloy producers and users. Many types of macrosegregation result from thermosolutal convection in the solid plus liquid and all-liquid regions of a solidifying alloy, and this has spurred modeling and simulations, which treat the solid plus liquid region (i.e., the mushy zone) as a porous medium of variable porosity and permeability. Simulations include scenarios in which the convection is strong enough to make channels in the mushy zone region, and these channels lead to localized segregates known as “freckles”. Using Pb-10 wt.% Sn as a model alloy, we simulated vertical solidification with various solidification rates. By sufficiently increasing the cooling rate at the bottom surface, convection can be suppressed enough to prevent the formation of freckles. The simulation is an example of relating microstructural metrics to a macroscopic property of the porous medium used in continuum theory. In this case, the property is the permeability, which is governed by two microstructural metrics: the volume fraction of liquid and a characteristic length in the dendritic microstructure. Permeability data, relevant to columnar dendritic solidification, are reviewed, and recommendations for future work on determining the permeability in terms of microstructural metrics are given.     

Macrosegregation in direct-chill casting of aluminium alloys

Semi-continuous direct-chill (DC) casting holds a prominent position in commercial aluminium alloy processing, especially in production of large sized ingots. Macrosegregation, which is the non-uniform chemical composition over the length scale of a casting, is one of the major defects that occur during this process. The fact that macrosegregation is essentially unaffected by subsequent heat treatment (hence constitutes an irreversible defect) leaves us with little choice but to control it during the casting stage. Despite over a century of research in the phenomenon of macrosegregation in castings and good understanding of underlying mechanisms, the contributions of these mechanisms in the overall macrosegregation picture; and interplay between these mechanisms and the structure formation during solidification are still unclear. This review attempts to fill this gap based on the published data and own results. The following features make this review unique: results of computer simulations are used in order to separate the effects of different macrosegregation mechanisms. The issue of grain refining is specifically discussed in relation to macrosegregation. This report is structured as follows. Macrosegregation as a phenomenon is defined in the Introduction. In “Direct-chill casting – process parameters, solidification and structure patterns” section, direct-chill casting, the role of process parameters and the evolution of structural features in the as-cast billets are described. In “Macrosegregation in direct-chill casting of aluminium alloys” section, macrosegregation mechanisms are elucidated in a historical perspective and the correlation with DC casting process parameters and structural features are made. The issue of how to control macrosegregation in direct-chill casting is also dealt with in the same section. In “Role of grain refining” section, the effect of grain refining on macrosegregation is introduced, the current understanding is described and the contentious issues are outlined. The review is finished with conclusion remarks and outline for the future research.     

Macrosegregation and thermosolutal convection-induced freckle formation in dendritic mushy zone of directionally solidified Sn-Ni peritectic alloy

Compared with the growing applications of peritectic alloy,none research on the freckle formation during peritectic solidification has been reported before.Observation on the dendritic mushy zone of Sn-36 at.％Ni peritectic alloy during directional solidification at different growth velocities shows that the freckles are formed in two different regions:region Ⅰ before peritectic reaction and region Ⅱ after peritectic reaction.In addition,more freckles can be observed at lower growth velocities.Examination on the experimental results demonstrates that both the temperature gradient zone melting(TGZM)and Gibbs-Thomson(G-T)effects have obvious influences on the morphology of dendritic network during directional solidification.The current theories onKI Rayleigh number Ra characterizing the thermoso-lutal convection of dendritic mushy zone to predict freckle formation through the maximum of Ra can only explain the existence of region Ⅰ while the appearance of region Ⅱ after peritectic reaction cannot be predicted.Thus,a new Rayleigh number RaP is proposed in consideration of evolution of dendritic mushy zone by both effects and peritectic reaction.Theoretical prediction of RaP also shows a maximum after peritectic reaction in addition to that before peritectic reaction,thus,agreeing well with the freckle formation in region Ⅱ.In addition,more severe thermosolutal convection can be predicted by the new Rayleigh number RaP at lower growth velocities,which further demonstrates the reliability of RaP in describing the dependence of freckle formation on growth velocity.     

二元复合结构聚合物涂层的制备及其机理研究

采用高压空气喷涂工艺,基于界面流与界面变形理论,制备出一种聚合物涂层。利用白光干涉三维形貌仪对涂层表面形貌进行表征。结果表明涂层表面具有亚毫米级和微米级二元复合的形貌特征。利用光学显微镜和红外热像仪对涂料成膜过程进行实验观察,并通过计算流体力学方法对其进行数值模拟,在此基础上讨论了涂层表面形貌的形成机理。利用小型高速水洞对聚合物涂层减阻性能进行初步测试,结果表明聚合物涂层可有效降低摩擦阻力。     

Effects of dendritic arm coarsening on macroscopic modelling of solidification of binary alloys

Abstract

A pure macroscopic two-dimensional numerical model has been developed, capable of capturing the effects of dendritic arm coarsening on the transport phenomena occurring during a binary alloy solidification process. The general continuum conservation equations are aptly modified to take into account shrinkage induced fluid flow. Simultaneously, the effective permeability of the mushy zone is numerically modelled according to the microscopic coarsening kinetics. Moreover, a new nodal latent heat updating algorithm is proposed that takes into account dendritic arm coarsening considerations. The numerical results are first tested against experimental results reported in the literature, corresponding to the solidification of an Al-Cu alloy in a bottom cooled cavity. It is concluded that dendritic arm coarsening leads to an increased effective permeability of the mushy region as well as an enhanced eutectic fraction of the solidified ingot. Consequently, an enhanced macrosegregation is predicted, compared with that dictated by shrinkage induced fluid flow alone. Physical insights are also developed regarding the effects of various parameters on the overall macrosegregation.     

Microstructure Evolution of Cu-Pb Monotectic Alloys Processed in Drop Tube

Rapid solidification of Cu-Pb monotectic alloys has been accomplished during free fall in a 3m drop tube.Both macrosegregated and uniformly dispersed structures are observed in Cu-40wt pct Pb alloy droplets,whereas droplets of composition Cu-64wt pct Pb exhibit only macrosegregation morphologies.The microstructures are strongly dependent on droplet size.The higher undercooling tends to facilitate liquid phase separation and results in more extensive macrosegregation in smaller droplets.There exists a pronounced tendency for the Pb-rich liquid to occupy the surface of the droplets of both compositions,resulting from the quite lower surface tension of the Pb-rich phase and cauing a Pb-rich layer at the surface of the solidified droplet.The nucleation of monotectic cells in the Cu-40 wt pct Pb droplets with dispersed structures preferentially occurs at the droplet surface.A single nucleation event takes place more frequently as droplet size is reduced.     

Effect of transverse static magnetic field on radial microstructure of hypereutectic aluminum alloy during directional solidification

The effect of different scales thermoelectric magnetic convection(TEMC)on the radial solidification microstructure of hypereutectic Al alloy has been investigated under transverse static magnetic field during directional solidification,focusing on the formation of freckle.Our experimental and numerical simulation results indicate that the TEMC circulation at sample scale under transverse static magnetic field leads to the enrichment of solute Al on one side of the sample.The TEMC and the solute enrichment degree increase with the increase of magnetic field when the magnetic field increases to 0.5 T.The enrichment degree of solute elements under magnetic field is affected by temperature gradient and growth rate.The non-uniform distribution of solute Al in the radial direction of the sample results in the non-uniform distribution of primary dendrite arm spacing(PDAS).Moreover,the applied magnetic field can lead to freckle formation and its number increases with the increase of magnetic field.The change of freckle is consistent with the anisotropy TEMC caused by the anisotropy of primary dendrite or primary dendrite network under magnetic field.Finally,the mechanism of synergism effect of the anisotropy TEMC,the distribution of solute Al and the PDAS on freckle formation and evolution is studied during directional solidification under magnetic field.     

对流扩散-多相相变体系内柱状晶/等轴晶形成过程的数值模拟

采用扩散支配相变动力学方法对Fe-Bi-Mn系易切削合金侧向快速凝固过程进行数值研究。建立对流扩散-多相相变体系三维凝固模型,考虑固、液、气三相扩散流动相变对合金凝固的影响,模拟研究合金中MnS和Bi(易切削相)的柱状晶/等轴晶形成过程。结果表明:合金凝固过程中MnS和Bi的柱状晶/等轴晶形成模式强烈受对流扩散和多相相变影响;对流扩散为正值处,溶质的多相质量相变速率较大且富集程度较低,流动稳定易形成柱状晶;对流扩散为负值处,溶质的多相质量相变速率较小且富集程度较高,当晶尖处溶质富集到一定程度,对流扩散与多相相变产生的紊流使柱状晶尖端断裂,成为等轴晶形核中心,此处为等轴晶稳定形成区域。     

等轴晶移动条件下金属凝固温度场、流场及溶质分布数值模拟

本文利用作者提出的固相移动条件下金属凝固传热、传质及动量传输数学模型对砂型铸造 Al-4.5%Cu 合金铸锭凝固过程进行了数值模拟研究与试验验证。模拟冷却曲线及宏观偏析与试验结果基本相符。