Numerical simulation of filling and solidification of permanent mold castings

Filling of a mold is an essential part of the permanent mold casting process and affects significantly the heat transfer and solidification of the melt. For this reason, accurate prediction of the temperature field in permanent mold castings can be achieved only by including simulation of filling in the analysis. In this work we model filling and solidification of a casting of an automotive piston produced from an aluminum alloy. Filling of the three-dimensional mold is modeled by using the volume-of-fluid method. Fluid mechanics and heat transfer equations are solved by a finite element method. Comparisons of numerical results to available experimental data show that the formulated model provides a solution of acceptable accuracy despite some uncertainty in material properties and boundary and initial conditions. This implies that the model can be a viable tool to design permanent molds.     

A Numerical Study of 3D Turbulent Melt Flow and Solidification in a Direct Chill Slab Caster with a Porous Combo Bag Melt Distributor

A 3D turbulent melt flow and solidification of an aluminum alloy (AA-1050) for an industrial-sized direct chill slab casting process is modeled. The melt is delivered through a rectangular submerged nozzle and a non-deformable combo bag fitted with a bottom porous filter. The non-Darcian model, incorporating the Brinkman and Forchheimer extensions, is used to characterize the turbulent melt flow behavior passing through the porous filter. The casting speed and the effective heat transfer coefficient at the metal–mold contact region within the mold are varied. The above two parameters are found to have significant influence on the solidification process.     

枝晶尺度溶质再分配对连续铸造凝固过程的影响

阐述了凝固微细尺度结构上的溶质再分配与宏现尺度传热传质现泉之问的关联，总结比较了多种徽现健析模型，并针对反向凝固工艺和传统的薄板坯连铸连轧(CSP)工艺的传热传质现泉进行了数值模拟，与实验数据进行对比分析。结果表明，微细尺度固—液相界面上的溶质再分配对凝固宏观传输过程的影响不可忽略。     

Numerical Method for Calculation of Complete Casting Processes—Part I: Theory

This article presents a method for calculation of the complete casting process, including the pouring of the liquid metal into the mold, its solidification, the deformation of the solidified cast, the formation of airgaps between the cast and the mold and their influence on the heat transfer, and the residual stresses. An original phase-change procedure is developed, valid for an arbitrary number of pure metals and/or alloys. A collocated version of a segregated finite-volume method is used to calculate both the liquid metal flow and the deformations and stresses in solids.     

Interfacial heat transfer coefficients and solidification of an aluminum alloy in a rotary continuous caster

The present study describes the development of an experimental set-up representing the metal/mold system of a rotary continuous caster as part of a methodology, which connected to a numerical heat transfer model permits to determine transient metal/mold heat transfer coefficients, h, during solidification. By using this approach the variation of h along the different mold walls and the metal surface has been investigated by a method based on numerically calculated/experimental fit of thermal profiles (IHCP). The results have shown that the used methodology permits the characterization of h and may be used in the simulation of solidification in industrial processes.     

Role of the Mold Properties on Gap Nucleation in Solidification

The role of the mold properties on gap nucleation in pure metal solidification is investigated. The mold is assumed to be finite and deformable, and has a sinusoidal surface micro-geometry. Unlike previous models, the model developed herein assumes that the mold material has a non-negligible thermal capacitance. Of particular interest are the roles played by the mold thickness and mold thermal capacitance on the existence of critical mold surface wavelength that corresponds to the situation where both contact pressure and its time derivative simultaneously fall to zero. The present work also assumes that the thermal and mechanical problems in the mold-shell interface are uncoupled. It is shown that the inclusion of the thermal capacitance of the mold material, together with thermal capacitance of the shell and the mold distortion, may be sufficient to predict a critical wavelength beyond which no gap nucleation occurs at the troughs. The role of the mold properties is examined through qualitative comparisons of the present and previous models. Gap nucleation times, associated mean shell thicknesses, and critical wavelengths are calculated for pure copper and pure iron molds under identical process conditions. It is found that a copper mold leads to faster gap nucleation compared to an iron mold. The associated critical wavelengths of iron molds are shown to be larger than those of copper. An optimum mean mold thickness corresponding to the longest gap nucleation time for a given set of process parameters is determined. The effect of the mean pressure on the optimum mold thickness is also investigated.     

Numerical Simulation of Segregation Phenomena Coupled with Phase Change and Fluid Flow: Application to Metal Matrix Composites Processing

The injection of a liquid metal through a fibrous preform, located in an initially preheated mold, is one of the techniques used to manufacture metal matrix composites (MMCs). In order to reduce the chemical reactions between the fibers and the metal matrix, the fibrous reinforcement and the mold are commonly preheated up to initial temperatures much lower than the metal solidification temperature. Therefore, local metal solidification instantaneously occurs on fiber during liquid metal infiltration. When infiltrating metal alloy, unlike what happens when infiltrating a pure metal, both temperature and composition may vary within the matrix; this heterogeneity induces segregation within composites. A fiber scale numerical simulation was developed taking into account coupled physical phenomena which occur during the processing: flow of the liquid metal around the fibers, phase change phenomena, solute redistribution at the liquid/solid interface during alloy solidification, and species diffusion. This model predicts the segregation phenomena associated with fibrous preform infiltration by a binary alloy.     

Spatial variation of heat flux at the metal–mold interface due to mold filling effects in gravity die-casting

Most of the research work pertaining to metal–mold heat transfer in casting solidification either assumes no spatial variation in the air gap formation or limits the study to only those experimental systems in which air gap formation is uniform. However, in gravity die-casting, filling effects induce variation in thermal field in the mold and casting regions. In this paper, we show that this thermal field variation greatly influences the time of air gap initiation along a vertical mold wall, which subsequently leads to the spatial variation of air gap and in turn, the heat flux at the metal–mold interface.In order to study the spatial variation of heat flux at the metal–mold interface, an experimental setup that involved mold filling was devised. A Serial-IHCP (inverse heat conduction problem) algorithm was used to estimate the multiple heat flux transients along the metal–mold interface. The analysis indicates that the fluxes at different mold segments (bottom, middle, and top) of the metal–mold interface reaches the peak value at different time steps, which shows that the initiation of air gap differs along the mold wall. The experimental and numerical results show that the heat transfer in the mold is two-dimensional during the entire period of phase change, which is initially caused by the filling effects and further enhanced by the spatial variation of the air gap at the metal–mold interface.     

Mathematical Model for Predicting Solidification and Cooling of Steel Inside Molds and in Air

A two-dimensional mathematical model is presented to describe the solidification and cooling of liquid steel. The liquid steel is poured into a mold to obtain a solid mass of desired shape, called an ingot. After cooling of the steel in the mold for some time, the mold is removed. Then the leftover ingot mass is cooled in air. This article is concerned with the above process. Nevertheless, the technique can be very applicable to other processes such as continuous casting.

Partial differential equations describing the process have been discretized using control-volume (or finite-volume) technique. The discretization equations obtained are of tridiagonal matrix form, which have been solved using the well-known tridiagonal matrix algorithm (TDMA) and the alternate direction implicit (ADI) solver. The model has been validated by measuring surface temperatures of molds and ingots using an infrared thermo-Vision scanner. This is then used to compute temperature distribution and solidification status of the ingot as a function of time and type of ingot.     

大圆坯连铸凝固传热过程的数值模拟

以Φ600 mm大圆坯连铸为研究对象,建立了描述连铸大圆坯凝固传热的柱坐标一维瞬态传热数学模型,计算了连铸坯的温度场,并分析了拉速、过热度和钢种对铸坯表面温度和凝固进程的影响.分析结果表明拉速对凝固终点位置影响明显,拉速每提高0.05 m/mm,凝固终点后移约3.87m.其计算结果与实际生产的实测数据吻合良好.     

Effect of pressure on heat transfer coefficient at the metal/mold interface of A356 aluminum alloy

The aim of this paper is to correlate interfacial heat transfer coefficient (IHTC) to applied external pressure, in which IHTC at the interface between A356 aluminum alloy and metallic mold during the solidification of casting under different pressures were obtained using the inverse heat conduction problem (IHCP) method. The method covers the expedient of comparing theoretical and experimental thermal histories. Temperature profiles obtained from thermocouples were used in a finite difference heat flow program to estimate the transient heat transfer coefficients. The new simple formula was presented for correlation between external pressure and heat transfer coefficient. Acceptable agreement with data in literature shows the accuracy of the proposed formula.     

A foam ablation model for lost foam casting of aluminum

A model is developed for heat transfer, polymer vaporization, and gas diffusion at the interface between the advancing liquid metal and the receding foam pattern during mold filling in lost foam casting of aluminum. Most of the pattern interior decomposes by ablation, but the boundary cells decompose by a collapse mechanism, which creates an undercut in the pattern next to the coating. By regulating how much of the pattern coating is exposed to gas diffusion, the undercut controls the overall filling speed of the metal through the mold. Computed values for the foam decomposition energy from this model compare very well with experimental data on foam pyrolysis, and predicted filling speeds are consistent with observations in published experiments. In addition, the model explains several unusual observations about mold filling that until now have not been understood.     

Perturbation solution for solidification of pure metals on a sinusoidal mold surface

A linear perturbation method is used to solve two-dimensional heat conduction problem in which a liquid, becomes solidified by heat transfer to a sinusoidal mold of finite thickness. The finite difference method is used to discretize the governing equations. The molten metal perfectly wets the mold surface prior to the beginning of solidification, and this leads to a corresponding undulation of the metal shell thickness. The influence of physical parameters such as the thermal capacities of shell and mold materials, and mold surface wavelength on the growth of solidified shell thickness is investigated. Analytical results are obtained for the limiting case in which diffusivities of the solidified shell and the mold materials are infinitely large, and compared with the numerical predictions to establish the validity of the model and the numerical approach.     

Numerical simulation of the casting process of a wind turbine rotor hub

An integrated numerical model was applied to simulate the mold filling and solidification process as well as predict the occurrence of relative casting defects for a rotor hub casting. The goal was to conduct a numerical experimentation to obtain an optimal alloy design of ductile cast iron for the rotor hub casting. A computer‐aided engineering software based on the finite element method was employed in this study. Numerical simulations were conducted for the rotor hub casting with two different types of alloy composition for ductile cast iron. The mold filling and solidification process were examined to predict the occurrence and extent of casting defects and a better alloy design was then proposed based on the simulated results to alleviate casting defects of the rotor hub casting. Copyright © 2010 John Wiley & Sons, Ltd.     

Developing a new 2D model for heat transfer and foam degradation in EPS lost foam casting (LFC) process

In this study, a 2D model is developed for heat transfer, foam degradation and gas diffusion at the interfaces of the liquid metal, foam pattern and gaseous gap in between, for EPS lost foam casting process. In this model based on mass and energy balance between gas and molten metal, radiation and conduction between foam and molten metal and convection between gas and molten metal are considered, both metal and foam surfaces are tracked and gap volume and pressure are calculated. A combination of energy balance and geometric correlations is used to define receding foam surface during mold filling. Gas flow in the gap is considered as wedge flow and Nusselt number for a laminar incompressible wedge flow is used for it. To apply our model to an example case, SOLA-VOF algorithm was used to simulate the flow of molten metal with free boundaries. Model results are compared with some data reported in the literature which show acceptable agreement. It is found that besides radiation in the gaseous area between foam and molten metal, conduction also plays an important role in foam degradation and control of molten metal velocity. This model can acceptably predict the effect of some parameters like foam density, coating permeability and foam degradation temperature.     

Analysis of molten metal spreading and solidification behaviors utilizing moving particle full-implicit method

To retrieve the fuel debris in Fukushima Daiichi Nuclear Power Plants (1F), it is essential to infer the fuel debris distribution. In particular, the molten metal spreading behavior is one of the vital phenomena in nuclear severe accidents because it determines the initial condition for further accident scenarios such as molten core concrete interaction (MCCI). In this study, the fundamental molten metal spreading experiments were performed with different outlet diameters and sample amounts to investigate the effect of the outlet for spreading-solidification behavior. In the numerical analysis, the moving particle full-implicit method (MPFI), which is one of the particle methods, was applied to simulate the spreading experiments. In the MPFI framework, the melting-solidification model including heat transfer, radiation heat loss, phase change, and solid fraction-dependent viscosity was developed and implemented. In addition, the difference in the spreading and solidification behavior due to the outlet diameters was reproduced in the calculation. The simulation results reveal the detailed solidification procedure during the molten metal spreading. It is found that the viscosity change and the solid fraction change during the spreading are key factors for the free surface condition and solidified materials. Overall, it is suggested that the MPFI method has the potential to simulate the actual nuclear melt-down phenomena in the future.     

Physical modeling and numerical investigation of fluid flow and solidification behavior in a slab caster mold using hexa-furcated nozzle

Slag entrapment from metal–slag interface during continuous casting operations has been a major area of concern for steelmakers globally. The presence of inactive regions in the upper region of the mold poses another challenge. Proper flow behavior of the molten metal coming out of the nozzle in the mold is required to overcome these challenges. Nozzle design greatly affects the flow pattern of the molten steel inside the mold. The present investigation is an attempt to study the flow and solidification behavior in a slab caster mold with the use of a novel-designed hexa-furcated nozzle using numerical investigation results. The casting speed and submerged entry nozzle (SEN) depth are varied to study the effect of these parameters on minimizing the inactive zones in the mold and the steel/slag interface fluctuations. The results show that the interface fluctuation increases at higher casting speed and lower SEN depth. The residence time distribution (RTD) analysis was also performed for different cases to investigate the flow behavior. The validation of the fluid flow and RTD curve inside the computational domain is carried out with the use of physical modeling.     

A Reduced Numerical Model for the Thermit Rail Welding Process

In this article, a reduced numerical model for the heat transfer in a commonly used Thermit rail welding procedure is presented. A geometrically reduced calculation domain was deduced from the welding system consisting of rails, weld material and mold. The geometrical domain is restricted to heat transfer in the rail web. Unsteady heat conduction in base rail and weld regions undergoing melting and solidification are modeled using the finite difference method. Therefor the consecutive periods of the process are described by specified initial and boundary conditions: preheating, tapping time, pouring and the final cooling. The solid-liquid phase change occurring during pouring and cooling is described using the enthalpy method. Thermal radiation between rail and mold surfaces is considered. Validation is carried out against results of models using computational fluid dynamics and solidus temperature isothermal positions in micrographs of longitudinal weld cuts from experiments. A sensitivity analysis was performed for the reduced model. The temperature of the liquid steel melt and the specific heat of the rail steel have the largest impact on the fusion zone width whereas mold material properties show negligible influences. The calculated width of the final fusion zone agrees within a deviation of 16% to experimental results.     

Computational Modeling of GMAW Process for Joining Dissimilar Aluminum Alloys

A three-dimensional transient model is developed to solve for heat transfer, fluid flow, and species distribution during a continuous gas metal arc welding (GMAW) process for joining dissimilar aluminum alloys. The phase-change process during melting and solidification is modeled using a fixed-grid enthalpy-porositytechnique, and Scheil's model is used to determine coupling among composition, temperature, and the liquid fraction. The effect of molten droplet addition to the weld pool is simulated using a “cavity” model, in which the droplet heat and species addition to the molten pool are considered as volumetric heat and species sources, respectively, distributed in an imaginary cylindrical cavity within the molten pool. To establish the model for joining dissimilar alloys, results for joining two pieces of a similar alloy are also presented. The dissimilar welding model is demonstrated using a case study in which a plate of wrought aluminum alloy (with approximately 0.5 wt% Si) is butt-welded to an aluminum cast alloy plate (with approximately 10 wt% Si) of equal thickness using a GMAW process. Macrosegregation, along with the associated heat transfer and fluid flow phenomena and their role in the weld pool development, are discussed. The model is able to capture some of the key features of the process, such as differential heating of the two alloys, asymmetric weld pool development, mixing of the molten alloys, and the final composition after solidification.     

A Fast Numerical Simulation for Modeling Simultaneous Metal Flow and Solidification in Thin Cavities Using the Lubrication Approximation

A numerical algorithm for modelling steady flow of liquid metal accompanied by solidification in a thin cavity is presented. The problem is closely related to a die cast process and in particular to the metal flow phenomenon observed in thin ventilation channels. Using the fact that the rate of metal flow in the channel is much higher than the rate of solidification, a numerical algorithm is developed by treating the metal flow as steady in a given time-step while treating the heat transfer in the thickness direction as transient. The flow in the thin cavity is treated as two dimensional after integrating the momentum and continuity equations over the thickness of the channel, while the heat transfer is modelled as a one-dimensional phenomenon in the thickness direction. The presence of a moving solid-liquid interface introduces non-linearity in the resulting set of equations, and which are solved iteratively. The location and shape of the solid-liquid interface are found as a part of the solution. The staggered grid arrangement is used to discretize the flow governing equations and the resulting set of partial differential equations is solved using the SIMPLE algorithm. The thickness direction heat-transfer problem accompanied by phase change is solved using a control volume formulation. The results are compared with the predictions of the commercial software FLOW3D® which solves the full three-dimensional set of flow and heat transfer equations accompanied with solidification. The Reynolds's lubrication equations accompanied by the through-the-thickness heat loss and solidification model can be successfully implemented to analyze flow and solidification of liquid metals in thin channel during the die cast process. The results were obtained with significant savings in CPU time.