Determination of heat transfer coefficients at metal/chill interface in the casting solidification process

The present work focuses on the determination of interfacial heat transfer coefficients (IHTCs) between the casting and metal chill during casting solidification. The proposed method is established based on the least-squares technique and sequential function specification method and can be applied to calculate heat fluxes and IHTCs for other alloys. The accuracy and stability of the method has been investigated by using a typical profile of heat fluxes simulating the practical conditions of casting solidification. In the test process, the effects of various calculation parameters in the inverse algorithm are also analyzed. Moreover, numerically calculated and experimental results are compared by applying the determined IHTCs into the forward heat conduction model with the same boundary conditions. The results show that the numerically calculated temperatures are in good agreement with those measured experimentally. This confirms that the proposed method is a feasible and effective tool for determination of the casting-mold IHTCs.     

Non Newtonian annular alloy solidification in mould

The annular solidification of an aluminium–silicon alloy in a graphite mould with a geometry consisting of horizontal concentric cylinders is studied numerically. The analysis incorporates the behavior of non-Newtonian, pseudoplastic (n?=?0.2), Newtonian (n?=?1), and dilatant (n?=?1.5) fluids. The fluid mechanics and heat transfer coupled with a transient model of convection diffusion are solved using the finite volume method and the SIMPLE algorithm. Solidification is described in terms of a liquid fraction of a phase change that varies linearly with temperature. The final results make it possible to infer that the fluid dynamics and heat transfer of solidification in an annular geometry are affected by the non-Newtonian nature of the fluid, speeding up the process when the fluid is pseudoplastic.     

The effects of casting speed on steel continuous casting process

A three dimensional simulation of molten steel flow, heat transfer and solidification in mold and “secondary cooling zone” of Continuous Casting machine was performed with consideration of standard k−ε model. For this purpose, computational fluid dynamics software, FLUENT was utilized. From the simulation standpoint, the main distinction between this work and preceding ones is that, the phase change process (solidification) and flow (turbulent in mold section and laminar in secondary cooling zone) have been coupled and solved jointly instead of dividing it into “transient heat conduction” and “steady fluid flow” that can lead to more realistic simulation. Determining the appropriate boundary conditions in secondary cooling zone is very complicated because of various forms of heat transfer involved, including natural and forced convection and simultaneous radiation heat transfer. The main objective of this work is to have better understanding of heat transfer and solidification in the continuous casting process. Also, effects of casting speed on heat flux and shell thickness and role of radiation in total heat transfer is discussed.     

Planar solidification of a warm flowing-liquid under different boundary conditions

Planar solidification of a warm flowing liquid with the convective heat transfer to the growing solid layer, has been analysed for the boundary conditions of constant temperature, constant heat flux and convective heat flux at the surface respectively. The mathematical formulation of the problem resulted in a coupled set of two differential equations in temperature and solid thickness as function of position, time and the problem parameters. Analytical expressions for the temperature distribution within the growing solid layer, the rate of solidification and the solidification time are obtained. The perturbation techniques employed here is simple and straight forward in contrast with the earlier techniques. Good agreement between the experimental results and the present solutions is obtained for the convective heat flux boundary condition. The results of this analysis are useful in the design and analysis of experiments dealing with freezing/melting in one dimension. The role of the parameter Stefan number which is small for phase change materials, is discussed in context with the storage of thermal energy.     

Using nucleators to control freckles in unidirectional solidification

Buoyancy-induced fluid flow, which is responsible for most forms of macro-segregation and channel-type segregates in castings, is not directly controllable. If left uncontrolled, natural convection will contribute to non-uniform distribution of alloy constituents and grain structure during solidification of a casting. Non-uniform distribution of chemical composition and physical structure in an alloy casting can significantly affect the reliability of mechanical components. Therefore, materials with acceptable defects can be produced only by trial-and-error and their acceptability is determined by costly inspections. We present a novel technique to control the formation of chimneys and resulting freckles in the mushy zone during the solidification of ammonium chloride that is cooled from below. This is done by placing metallic nucleators in particular arrangements on the bottom cooling plate. With this technique, freckles in a casting might be avoided and/or be forced to form where stresses are expected to be lower during use of the part.The objective of this study is to investigate the effects of the arrangement, spacing, and size of the nucleators on finger formation, plume structure, and the solidification process. Results showed that it is possible to obtain a relatively large area free of channel-segregates in a metal analog directionally solidified upward by placing nucleators in certain arrangements at the bottom of the casting. The outcomes of this study will serve as a baseline for subsequent investigations that will examine the solidification of binary alloys, and could be used to test and develop mathematical and numerical models.     

The effect of carbon nanotubes in enhancing the thermal transport properties of PCM during solidification

This study is aimed to prepare a novel class of nanofluid phase change material (NFPCM) by dispersing a small amount of multi-walled carbon nanotubes (MWCNT) in liquid paraffin, to enhance the heat transfer properties and examine the characteristics of the NFPCM during the solidification process. The stable NFPCMs are prepared by dispersing the MWCNT in liquid paraffin at 30°C with volume fractions of 0.15, 0.3, 0.45 and 0.6% without any dispersing agents. The rheology measurement illustrates the Newtonian fluid behavior in the shear stress range of 1–10?Pa. The differential scanning calorimetric results showed that there is no observable variation in the freezing/melting temperature of the NFPCM, and only a small observable change in the latent heat values. The thermal conductivity of various NFPCM is measured. The enhancement in thermal conductivity increases with the increased volume fraction of the MWCNT, and shows a weak dependence on the temperature. Further, for the NFPCM with a volume fraction of 0.6%, there is an appreciable increase in heat transfer with a reduction in the solidification time of 33.64%. The enhancement in the heat transfer performance would alleviate the major problems that have been encountered in the conventional phase change materials since several years.     

An Enthalpy Control Volume Method for Transient Mass and Heat Transport with Solidification

A single domain enthalpy control volume method is developed for solving the coupled fluid flow and heat transfer with solidification problem arising from the continuous casting process. The governing equations consist of the continuity equation, the Navier–Stokes equations and the convection–diffusion equation. The formulation of the method is cast into the framework of the Petrov–Galerkin finite element method with a step test function across the control volume and locally constant approximation to the fluxes of heat and fluid. The use of the step test function and the constant flux approximation leads to the derivation of the exponential interpolating functions for the velocity and temperature fields within each control volume. The exponential fitting makes it possible to capture the sharp boundary layers around the solidification front. The method is then applied to investigate the effect of various casting parameters on the solidification profile and flow pattern of fluids in the casting process.     

铸件凝固温度场有限元分析中界面热阻的处理

提出一种处理铸件与铸型界面热阻问题的虚拟界面单元法，并给出了有限元计算公式。由于该公式不显含单元厚度(△l)，故该单元厚度△l可取任意值。当△l取为零时，使问题处理变得极为方便。针对某一具体金属型铝合金活塞的铸造凝固过程，按考虑和不考虑铸件与铸型间热阻影响两种方法作了有限元计算，通过与实测值相比较，本文提出的算法其计算精度远高于不考虑铸件与铸型间热阻影响的计算结果。另外．该方法使有限元建模方便、通用性强。     

Numerical simulation of heat transfer in pressurized solidification of Magnesium alloy AM50

Based on finite difference and control-volume scheme, a model was developed to simulate fluid flow in forced convection and heat transfer in pressurized solidification of a cylindrical squeeze casting of magnesium alloy AM50. Pressure-dependent heat transfer coefficients (HTC) and non-equilibrium solidification temperatures were determined by experimental measurements. With the measured HTC and temperatures under the different pressures, the temperature distributions and the cooling behaviors of squeeze cast were simulated.     

Numerical simulation of solidification processes in enclosures

The present work deals with the development and application of numerical models for the simulation of solidification problems liquid/solid taking diffusion and convection into account. For the calculation of the thermal coupled flow process the finite element method is applied. In order to improve the numerical stability of the free convection problems, the streamline-upwind/Petrov–Galerkin method is used. Solidification processes are moving boundary problems. Three different models are set up which consider latent heat at the solidification front respectively in the mixed zone during the phase transition. Moreover, numerical methods are investigated in order to describe the behaviour of the flow at the boundary of the moving phase. Three examples serve illustrations; the technical example – casting of a transport and storage container – was provided by the company Siempelkamp Gießerei GmbH.     

Effect of variable ambient temperature on fin efficiency in a two-dimensional flow passage

The fin efficiency in a heat exchanger element that is a simplification of one row in a tube-and-fin heat exchanger was theoretically examined within wide ranges of the affecting variables: the conventional fin efficiency and the isothermal effectiveness of the heat exchanger. These variables are suggested for use also in the further studies. An analytical solution can be found for the case of a constant heat transfer coefficient. The ambient temperature variation alone decreases the fin efficiency less than 4%. The local heat transfer coefficient obtained from the numerical fluid flow simulations is strongly affected by the fin properties because the thermal boundary conditions for the fluid flow changes. On a poorly conducting fin surface the heat transfer coefficient in front of the fin base is much larger than on an isothermal fin because the heat flux is increasing in the flow direction. At low fin efficiencies this compensates for the decrease in fin efficiency due to ambient temperature variation.     

Development of an inverse heat conduction model and its application to determination of heat transfer coefficient during casting solidification

The interfacial heat transfer coefficient (IHTC) is required for the accurate simulation of heat transfer in castings especially for near net-shape processes. The large number of factors influencing heat transfer renders quantification by theoretical means a challenge. Likewise experimental methods applied directly to temperature data collected from castings are also a challenge to interpret because of the transient nature of many casting processes. Inverse methods offer a solution and have been applied successfully to predict the IHTC in many cases. However, most inverse approaches thus far focus on use of in-mold temperature data, which may be a challenge to obtain in cases where the molds are water-cooled. Methods based on temperature data from the casting have the potential to be used however; the latent heat released during the solidification of the molten metal complicates the associated IHTC calculations. Furthermore, there are limits on the maximum distance the thermocouples can be placed from the interface under analysis. An inverse conduction based method have been developed, verified and applied successfully to temperature data collected from within an aluminum casting in proximity to the mold. A modified specific heat method was used to account for latent heat evolution in which the rate of change of fraction solid with temperature was held constant. An analysis conducted with the inverse model suggests that the thermocouples must be placed no more than 2 mm from the interface. The IHTC values calculated for an aluminum alloy casting were shown to vary from 1,200 to 6,200 Wm^?2 K^?1. Additionally, the characteristics of the time-varying IHTC have also been discussed.     

Exact analytical solution to three-dimensional phase change heat transfer problems in biological tissues subject to freezing

Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.     

Deterministic physical influence control of interfacial motion in thermal processing of solidified materials

In this paper, a new experimental method of phase interface motion control with time dependent boundary cooling is presented for ice–water solidification problems. A numerical method for inverse heat transfer problems was developed to predict the transient boundary conditions, which produce a prescribed phase interface motion. In the experimental study, the predicted boundary temperatures from the numerical simulation were used to control the ice–water interface movement for various specified interface motions. Two cases of different phase interface velocities were considered. Water supercooling was observed during each experiment. A time delay in the thermal control was calculated based on an analytical solution. Close agreement between measured data and specified interface motion was achieved for the ice–water solidification problems.     

Fluidization behavior of graphitized glassy particles in a fluidized carbon bed cooling process for investment casting

Fluidized Carbon Bed Cooling (FCBC) is an innovative investment casting process for directional solidification of superalloy components. It takes advantage of a fluidized bed with a base of small glassy carbon beads for cooling and other low-density particles that form an insulating layer by floating to the bed surface. This so-called “Dynamic Baffle” protects the fluidized bed from the direct heat input from the high-temperature heating zone and provides the basis for an improved bed microstructure. The prerequisites for a stable casting process are stable fluidization conditions where neither collapse of the bed nor particle blow out at excessive bubble formation occur.This work aimed to investigate the fluidization behavior of spherical carbon bed material in argon and air at temperatures between 20 to 350 °C. Systematic studies at reduced pressures using the FCBC prototype device were performed to understand the stable fluidization conditions at all stages of the investment casting process. The particle shape factor and size distribution characterization and the measurement of the powder’s minimum fluidization velocity and bed voidage show that this material can be fully utilized as a cooling and buoyancy medium during the FCBC process.     

A mathematical model for an alloy solidification problem in the presence of an electric field

A one-dimensional mathematical model for a process of solidification of a binary alloy in the presence of an electric field is studied. A situation in which the thermal properties of each phase are different and the latent heat is non-zero is considered. A quasi-static approximation for the thermal and electric fields is used. Local existence and uniqueness of a classical solution to the resulting free boundary problem are proved for two kinds of boundary conditions. Moreover, under particular hypotheses, the monotonicity of the free boundary and the global existence of the solution is proved.

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Sommario Si studia un modello matematico unidimensionale per un processo di solidificazione di una lega binaria in presenza di un campo elettrico. Si considera una situazione in cui le proprietà termiche di ogni fase sono differenti e il calore latente è non nullo. Si usa una approssimazione quasi-statica per i campi elettrico e termico. Si dimostra l'esistenza locale e l'unicità di una soluzione classica per il problema di frontiera libera risultante con due tipi di condizioni di bordo. Inoltre si dimostra, sotto particolari ipotesi, la monotonia della frontiera libera e l'esistenza di soluzione globale.

     

Heat transfer during heat sterilization and cooling processes of canned products

In this paper, an analysis of transient heat transfer during heat sterilization and cooling processes of a cylindrical canned product is presented. In the analysis, most practical case including the boundary condition of third kind (i.e., convection boundary condition, leading to 0.1 ≤ Bi ≤ 100) was employed. A simple analytical model for determining effective heat transfer coefficients for such products is developed. For the heat sterilization process, heating coefficient is incorporated into heat transfer coefficient model. An experimental study was performed to measure the thermal center temperatures of the short-cylindrical canned products (i.e., Tuna fish) during heat sterilization at the retort medium temperatures of 115^∘C and 121^∘C, and during cooling process at 16^∘C. The effective heat transfer coefficient model used the experimental temperature data. Using these effective heat transfer coefficients the center temperature distributions were calculated and compared with the experimental temperature distributions. Agreement was found considerably high. The results of the present study indicate that the heat-transfer analysis technique and heat-transfer coefficient model are reliable, and can provide accurate results for such problems. Received on 12 November 1997     

Simulation of heat transfer and stress analysis of continuous casting

Summary Due to high productivity and the ability to cast to a form which could be rolled directly to a final product, continuous casting was selected for analysis and simulation. Three-dimensional finite element was used because of its capability to analyze any type of ingot with arbitrary section. Various types of boundary conditions which occur during the solidification process, as well as temperature dependent material properties were discussed. Two generalized models for heat transfer and stress analysis were developed. The first model, based on variation of heat transfer boundary conditions, was used to predict temperature distribution and solid shell formation. The second model, by considering applied thermal and mechanical loads and enforced displacements on the ingot, was used to calculate the stress distribution within the solid shell.These models provided design engineers with a reliable method of optimizing the casting processes and parameters. The computer results of the temperature distribution compared favorably with the other literature. Application of the temperature history along with other boundary loads and displacements into analysis, determined that the maximum stress occurs at the mold exit, the pinch and bending rolls, and the complete solidification areas. To predict the places with higher chance of crack formation a ratio of calculated stress to von Mises stress was used. The maximum stress ratio was detected at the location of the bending rolls.

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Simulation von Wärmeübergang und Spannungszustand beim Stranggießen

Übersicht Das Stranggießen wird mit dreidimensionalen finiten Elementen, die beliebige Barrenformen zulassen, simuliert. Berücksichtigt werden die sich bei der Erstarrung ändernden Randbedingungen und die Temperaturabhängigkeit der Materialeigenschaften. Mit Hilfe eines ersten Simulationsmodells wird unter Berücksichtigung des ortsabhängigen Wärmeübergangs die Temperaturverteilung und die Bildung der festen Schale berechnet. Mit einem zweiten Modell wird dann die Spannungsverteilung in der Schale unter der gegebenen thermischen und mechanischen Belastung sowie der erzwungenen Barrenbewegung berechnet.Die Simulationsmodelle stellen eine zuverlässige Methode zur Optimierung des Stranggießens und seiner Parameter dar. Die Rechenergebnisse für die Temperature stimmen gut mit Referenzresultaten überein. Einsetzen des Temperaturverlaufs und der Randbedingungen in die weitere Berechnung ergeben, daß Maximalspannungen am Austritt der Gußform, bei den Antriebs- und Umlenkrollen sowie den Erstarrungsfronten auftreten. Als Vorhersagekriterium stärker rißgefährdeter Stellen wird das Verhältnis der von Misesschen Vergleichsspannung zur Fließspannung herangezogen. Das maximale Spannungsverhältnis tritt an den Biegerollen auf.

     

铁基大块非晶合金的摩擦磨损性能研究

采用电弧熔炼、铜模吸铸法制备Fe基大块非晶合金,利用球-盘式摩擦磨损试验机进行干摩擦磨损试验,研究了铸态Fe基大块非晶合金的摩擦磨损行为及热处理对其耐磨性的影响,利用扫描电子显微镜观察合金磨损表面形貌,分析了Fe基大块非晶合金以及相同成分晶态合金的磨损机理.结果表明:在本试验条件下,铸态Fe基大块非晶合金的耐磨性高于相同成分的晶态合金,热处理可以有效提高铸态Fe基大块非晶合金的耐磨性,在保持完全非晶状态的前提下,退火态非晶合金的磨损率较铸态非晶合金减小约40%;材料的结构和性能对合金的摩擦系数影响不大,当进入稳定阶段后Fe基大块非晶合金的摩擦系数稳定在0.58左右;不同处理状态的Fe基大块非晶合金和相同成分晶态合金的磨损机制不同,非晶合金的磨损机制以疲劳磨损为主兼有磨粒磨损,相同成分晶态合金的磨损机制为粘着磨损和磨粒磨损共同作用的结果.     

Dependence of interfacial heat transfer coefficient on casting surface temperature during solidification of Al–Si alloy castings cast in CO2 sand mold

Interfacial heat transfer coefficient at the metal–mold interface (IHTC) was estimated by an iterative algorithm based on the function specification method. An Al–9 wt% Si alloy plate casting was made in a sand mold prepared by CO₂ process. Thermal history obtained from the experiment was used to solve an inverse heat conduction problem. Acquired transient IHTC values are then given in function of the casting surface temperature at the interface. By comparing the obtained results with previous findings, the influence of grain fineness number and consequently of mold roughness on maximum IHTC values is revealed.