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.     

Modeling and simulation of heat transfer phenomena during investment casting

Determining the heat transfer phenomena during casting processes is an important parameter for measuring the overall performance of process. It gives information about the properties of the metal being casted and its possible behavior in the mold during casting process. Improper determination of heat transfer phenomena and use of improper molding materials and casting conditions leads to defects such as misruns, cold shuts, shrinkage, pin holes, air holes and porosity in final product. A mathematical model was developed using standard transport equations incorporating all heat transfer coefficients to calculate the time for solidification of metal in casting and computer simulation of the model was carried out in C++ to validate the model. The metal used was pure iron casted in investment molds of silica sand with zircon coating. It was shown that airflow near the mold surfaces was partially restricted due to geometry of the molds and arrangement of the pieces around a tree. So, the changes in heat transfer coefficient also contribute towards time of solidification. The time calculated was found to be in good agreement with experimental values.     

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.     

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.     

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.     

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.     

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.     

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.     

Determination of the interfacial heat transfer coefficient h in unidirectional heat flow by Beck's non linear estimation procedure

In the numerical simulation of casting solidification, the thermal behavior of the casting/mold interface is characterized by the interfacial heat transfer coefficient, ‘h’. The determination of h is difficult as it involves the solution of the Inverse Heat Conduction Problem (IHCP). One of the satisfactory solution procedures for solving the IHCP is the Beck's non linear estimation procedure. In this work, this procedure has been used successfully by the authors for the determination of h in steady state unidirectional heat flow.     

A FINITE ELEMENT METHOD FOR CASTING SIMULATIONS

This paper presents a finite element model for the three-dimensional simulation of industrial mold filling and solidification problems. The finite element solutions of mold filling problems involve highly convective fluid flow coupled with free surface, heat transfer, nonconstant material properties, and complex three-dimensional geometries. They present unusual challenges for both the finite element modeling and numerical solution algorithms. In this work a segregated algorithm is proposed to solve Navier-Stokes, energy, and front tracking equations. The streamline upwind Petrov-Galerkin formulation is used to obtain stable solutions. The position of the free surface is modeled using a level-set approach. The whole procedure is shown to present the accuracy, robustness, and cost-effectiveness needed for complex three-dimensional industrial applications.     

Optimal control of accelerator concentration for resin transfer molding process

Resin cure following mold filling is an essential element in resin transfer molding. To fabricate a composite part with high dimensional stability and minimize residual stress, uniform resin cure should be achieved. This study considers a three-part resin system composed of epoxy, hardener and accelerator. The cure kinetics can be controlled by the accelerator concentration at the injection gate. A numerical method that can predict degree of cure distribution based on accelerator concentration at the gate was proposed. The degree of cure distribution is obtained by solving the resin flow, heat transfer, accelerator concentration and cure problems sequentially. Utilizing this numerical method, an optimal variation of accelerator concentration during mold filling was sought by solving a constrained optimization problem. The effect of accelerator control on degree of cure distribution was investigated and its validity was examined for two different geometries.     

The mathematical model of solidification latent heat under high cooling rate

Treatment of solidification latent heat is a key point in solidification simulation by the finite difference method. When latent heat is dealt with in a traditional method of equivalent latent heat, it was found that heat was increased when casting with a high cooling rate, and then the simulation result was distorted. In this paper, a new method is proposed to deal with solidification latent heat. Moreover, a mathematical model was suggested, in which the latent heat can be dealt with accurately under high or normal cooling rates. By contrasting the simulation results from this new method with the traditional one, it was indicated that this new model can obtain more accurate simulation results than the traditional model under high or normal cooling rates. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(2): 115–121, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20104     

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.     

A numerical study of solidification in powder injection molding process

Thermal analysis of mold filling and post-filing solidification has been carried out for the powder injection molding process. The filling material comprised alumina powder and polymeric binder was used to fill a rectangular cavity. The interphase momentum transfer was accounted for using a momentum exchange model due to Wang et al. [Y. Wang, S. Ahuja, C.Beckerman, H.C. de GROH III, Multiparticle interfacial drag in equiaxed solidification, Metall. Mater. Trans. B 26B (1995) 111–119]. Though both the alumina powder and polymeric binder are treated as fluids, as the alumina powder does not undergo a phase change, only the solidification of the binder has to be considered. The liquid fraction of the binder was assumed to follow a linear rule between the liquidus and solidus temperature. An iterative latent heat recovery formulation has been developed to obtain the liquid fraction during solidification. It was found that the predictions for pressure rise at the inlet compares favorably with the results from the single-phase mixture model. However, the multi-phase model could predict the powder segregation unlike the mixture model. The multi-phase model predicts higher temperature compared to mixture model due to powder particle migration.     

Investigation on the effect of filling ratio on the steady-state heat transfer performance of a vertical two-phase closed thermosyphon

Filling ratio of the working fluid has a predominant effect on the heat transfer characteristics of a two-phase closed thermosyphon (TPCT). A comprehensive model is developed to investigate the effect of filling ratio on the steady-state heat transfer performance of a vertical TPCT. Three types of flow pattern and two types of transition, according to the distribution of liquid film and liquid pool, are considered in this model, while other models generally focus on only one or two types of them. The total heat transfer rate of liquid pool, including those of natural convection and nucleate boiling, is calculated by combination of their effective areas and heat transfer coefficients. New correlations of the effective area are proposed based on the experimental results from other study. Two different geometries of the TPCT with nitrogen as working fluid are performed experimentally, and the evaporator temperatures accord well with the theoretical calculation. And the calculated results are compared with those by other empirical heat transfer correlations for liquid pool. The range of filling ratio, which can keep a TPCT steady and effective, is proposed based on analysis and comparison. The effects of heat input, operating pressure and geometries of the TPCT on the range are also discussed.     

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.     

Fluid flow and heat transfer behavior of liquid steel in slab mold with different corner structures. Part 1: Mathematical model and verification

A three-dimensional model considering the fluid and temperature field of the liquid steel and cooling water, along with the copper plate temperature was established to study the fluid flow and heat transfer behavior of liquid steel in slab mold with different corner structures. Then, a two-dimensional stress–strain model was established to calculate the strand shrinkage. The two-dimensional stress and three-dimensional temperature were connected through the thermal resistance. The model was validated by the measured solidification shell, copper plate temperature, and cooling water temperature rise. Results show that this model is suitable to study the complex transmission behavior in slab mold.     

Numerical and Experimental Investigation of Solidification Shrinkage

The solidification heat transfer, melt convection, and volume shrinkage in the casting of an energetic material are analyzed through numerical modeling and experimental investigation. The shrinkage resulting from phase change is considered through the volume-of-fluid method. The model is validated against an analytical solution and then applied to study the volume contraction during the casting of trinitrotoluene (TNT). Good agreement is obtained between experimental results and predictions of temperatures at selected locations as well as shrinkage shape. New casting conditions are suggested based on the analysis, and improved results are observed both numerically and experimentally.     

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.     

A FIXED GRID FRONT-TRACKING MODEL OF THE GROWTH OF A COLUMNAR FRONT AND AN EQUIAXED GRAIN DURING SOLIDIFICATION OF AN ALLOY

In a new model of alloy solidification in a square mold, the interface being followed by a front-tracking technique is representative of a curve joining the tips of growing solid dendrites. The coupled heat equation is solved via an Eulerian control-volume formulation. In the absence of convection, the nucleation and nonequilibrium growth of both a front of columnar grains and a single equiaxed grain have been modeled and animated. This is a major step toward the computationally efficient complete direct numerical simulation of the developing grain structure in a casting process.