Mould Heat Transfer Research Articles

Analysis of metal mould heat transfer coefficients during continuous casting of steel

Heat transfer coefficients in the mould were determined by the inverse method and they are related to both process conditions and carbon equivalents of steels. Experimental data were obtained from an industrial plant by temperatures measured in moulds of the continuous casting machine by thermocouples placed in the mould wall in known positions. The temperatures are compared to profiles of simulations by the numerical model of both solidification and heat transfer processes previously examined. As a result, the numerical model calculates the heat transfer coefficients in the metal/mould interface for heats cast with different process parameters. The results make possible the determination of expressions for the calculation of the interfacial metal/mould heat transfer coefficients that include the effects of steels grades, mould faces, casting speed, mould taper, mould section and pouring temperatures for a range of process parameters.

Numerical Analysis of Coupled Fluid Flow, Heat Transfer and Macroscopic Solidification in the Thin Slab Funnel Shape Mold with a New Type EMBr

As an expansion of our former work, a series of numerical simulations of fluid flow, heat transfer, and macrosolidification under the control of both the conventional and the new type electromagnetic brake (EMBr) were carried out. In the present work, the physical models and parameters remain the same as those measures in our former research, and the solution processes of the flow field and electromagnetic field are similar. The specific heat method is used to treat the latent heat of solidification, and the Darcy’s Law-type porous media treatment is used to account for the effect of phase change on convection. User-defined functions (UDFs) are compiled for the following two aspects: One is the Darcy source term, and the other is the thermal conductivity, which varies in mushy zones. From the comparisons of two kinds of EMBr produced by two type magnets separately, the new type EMBr gives its superiorities of the effects on the flow field, heat transfer, and solidification with lower cost of electrical energy.

Mould cooling simulation for injection moulding using a fast boundary element method approach

The existing cooling simulations for injection moulding are mostly based on the boundary element method (BEM). In this paper, a fast BEM approach for mould cooling analysis is developed. The actual problem is decoupled into a one-dimensional transient heat conduction problem within the thin part and a cycle-averaged steady state three-dimensional heat conduction problem of the mould. The BEM is formulated for the solution of the mould heat transfer problem. A dynamic allocation strategy of integral points is proposed when using the Gaussian integral formula to generate the BEM matrix. Considering that the full and unsymmetrical influence matrix of the BEM may lead to great storage space and solution time, this matrix is transformed into a sparse matrix by two methods: the direct rounding method or the combination method. This approximated sparsification approach can reduce the storage memory and solution time significantly. For validation, six typical cases with different element numbers are presented. The results show that the error of the direct rounding method is too large while that of the combination method is acceptable.

Combination of inverse problem and neural network for thermal behaviour calculation of mould process based on temperature measurements in plant trial

Heat transfer between mould and strand has a critical influence on billet quality, caster productivity and operating safety. It is very important to obtain the correct distributions of temperature and heat flux, and many studies are made on the calculation methods of heat transfer between strand and mould, aiming to reduce the computation time and improve the calculation accuracy. In the present paper, based on measured data of temperature and heat flux during round billet continuous casting, the calculation method which combines the online measurement data and numerical simulation was investigated. Through identifying the local thermal resistance and its distribution between the mould and the strand by an inverse heat transfer model, the heat flux and shell thickness profiles were calculated. To avoid the iterative solution by inverse model, a faster alternative model using an artificial neural network was developed to predict the thermal resistance from the measured temperature. After training, there is an exact correspondence between the observed temperature values and the thermal resistance. The calculation results obtained by the combination of neural network and numerical simulation can correctly reflect the characteristics of non-uniform heat transfer around the mould circumference, which provides a worthwhile and applicable method for online calculation and visual technology of heat transfer and solidification in continuous casting mould.

Influence of Aspect Ratio on Fluid Flow and Heat Transfer in Mould when Using Swirl Flow during Casting

Mathematical modelling was used to study the effect of a changed aspect ratio of a continuous casting mould on the resulting flow field in the upper part of the mould when using a swirl flow in the nozzle. Model predictions were initially compared to physical modelling data. More specifically, the predicted axial velocities were found to differ only at the most ~3 mm/s from the measured data. Thus, the model was concluded to be sound. By changing the aspect ratio of a billet mould from 1 to 3 systematically, a numerical analysis of the mould region of a billet continuous caster was performed with a novel injection concept using swirling flow in the immersion nozzle in order to control the heat and mass transfer in the continuous casting mould. The predictions showed that the aspect ratio of the mould has a large influence on the flow field in the upper part of the mould. The meniscus temperature was found to increase with an increasing aspect ratio from 1 to 2, but the maximum temperature was found to decrease when the aspect ratio was increased above 2.

An integrated simulation for the whole forming process of the picture tube panel

An integrated model for the whole forming operation of the picture tube panel is developed in this paper, which couples the behaviors of glass and mold. The molten glass is modeled by an incompressible Newtonian liquid undergoing flow. And a three-dimensional finite element method is used to perform the simulation of the fluid and heat flow. A local one-dimensional transient analysis in the thickness direction is adopted for the part cooling stage after pressing, which employs the finite-difference method. The mold heat transfer is established by boundary conditions analysis and its numerical implementation is a three-dimensional boundary element method. The glass and mold simulations are coupled by matching the temperature and heat flux on the glass-mold interface. For residual stresses analysis, a thermo-rheologically simple viscoelastic material model is introduced to consider the stresses relaxation effect and to describe the mechanical behavior according to the temperature change. The shrinkage of formed parts induced by the residual stresses is calculated based on the theory of shells, represented as an assembly of flat elements formed by combining the constant strain and the discrete Kirchhoff triangular elements. A thermoelastic model is presented to predict the deformation of the mold blocks during pressing, which is based on the steady mold temperature field and thermoelastic boundary element method.

Heat Transfer in Funnel-mould Casting: Effect of Plate Thickness

Plant measurements and three-dimensional models are used to develop an accurate and efficient model of heat transfer in a thin-slab continuous casting mould, interface, and solidifying shell. A finite-element model of the complex-shaped mould, developed using ABAQUS, is applied to find offset correction factors that enable the efficient CON1D model to accurately predict temperature at thermocouple locations. Model interface parameters are calibrated using an extensive database of plant data obtained from the Corus Direct Sheet Plant in IJmuiden, The Netherlands, including measurements of mould heat removal, mould temperature, oscillation mark shape, mould-powder consumption, and mould thickness. The validated CON1D model is applied to quantify the combined effects of casting speed and mould plate thickness on mould heat transfer. Increasing casting speed causes a thinner solidified steel shell, higher heat flux, higher mould hot face temperature, a thinner slag layer and lower solid slag layer velocity. Increasing mould plate thickness increases hot face temperature, lowers solid slag layer velocity, increases slag layer thickness, and lowers mould heat flux.

Effect of Nozzle Angle on Flow Field and Temperature Distribution in a Billet Mould when using Swirl Flow

Recently, interesting effects have been noted in studies of swirl flow, particularly regarding billet moulds when considering a specific divergent angle of the immersion nozzle. Therefore, in the present work a numerical analysis and water model study of the mould region of a continuous casting apparatus are performed with changing the outlet divergent angles of the immersion nozzle using swirling flow in the pouring tube, to control the heat and mass transfer in the continuous casting mould. To make our studies consistent with the previous research, which was done based on a square billet, this time we investigate round billets. The results show that the distance from the meniscus of the centres of both the lower and upper circulation loops decreases systematically with increasing the divergent angle. This, in turn, leads to: (i) a more active heat and mass transport near the meniscus (particularly over 100°); (ii) a gradual change from a concentric circulation to a more clearly logarithmic spiral from the mould wall to the nozzle on the meniscus, which leads to more active heat and mass transfer; (iii) a decreased penetration depth of nozzle outlet flow (even at a comparatively small divergent angle such as 20°) and a superheat dissipation in the melt.

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.

Analysis of flow field and temperature distribution in compact strip production casting process

A three-dimensional finite difference model has been formulated, using the commercial code CFX4, to describe the fluid flow and heat transfer in the funnel mould and secondary cooling segment of the compact strip production (CSP) casting process. Through simulation and computation with the established simulation model, influences of the factors such as casting speed, casting superheat, immersion depth of submerged entrance nozzle, amount of cooling water in the secondary cooling segment on flow field and temperature field in the funnel mould and secondary cooling segment of CSP technology were analysed.

Analysis and Control of Heat Transfer in an Industrial Composite Mold in RTM Polyester Automotive Process

A composite mold was developed to manufacture pieces by the resin transfer molding process. This mold can be instrumented with different sensors which allows us to obtain great amounts of information during realistic conditions of production. The main features of the mold, as well as the used metrology, are detailed. The results of different experiments and the influence of temperature on the molding are presented. The experimental heat fluxes are compared to the predictions of a kinetic model. A thermal optimization of the curing cycle is proposed.

Effect of Mold Coating Materials and Thickness on Heat Transfer in Permanent Mold Casting of Aluminum Alloys

In permanent mold casting or gravity die casting (GDC) of aluminum alloys, die coating at the casting-mold interface is the most important single factor controlling heat transfer and, hence, it has the greatest influence on the solidification rate and development of microstructure. This investigation studies the influence of coating thickness, coating composition, and alloy composition on the heat transfer at the casting-mold interface. Both graphite and TiO2-based coatings have been investigated. Two aluminum alloys have been investigated: Al-7Si-0.3Mg and Al-9Si-3Cu. Thermal histories throughout the die wall have been recorded by fine type-K thermocouples. From these measurements, die surface temperatures and heat flux density have been evaluated using an inverse method. Casting surface temperature was measured by infrared pyrometry, and the interfacial heat-transfer coefficient (HTC) has been determined using these combined pieces of information. While the alloy is liquid, the coating material has only a weak influence over heat flow and the thermal contact resistance seems to be governed more by coating porosity and thickness. The HTC decreases as the coating thickness increases. However, as solidification takes place and the HTC decreases, the HTC of graphite coating remains higher than that of ceramic coatings of similar thickness. After the formation of an air gap at the interface, the effect of coating material vanishes. The peak values of HTC and the heat flux density are larger for Al-7Si-0.3Mg than for Al-9Si-3Cu. Consequently, the apparent solidification time of Al-9Si-3Cu is larger than that of Al-7Si-0.3Mg and it increases with coating thickness.

Evaluating the use of functionally graded materials inserts produced by selective laser melting on the injection moulding of plastics parts

The demand for productivity and shape complexity on the injection moulding industry necessitates new research to improve tool design, material, and manufacturing. A research field is the development of functionally graded materials (FGMs) to build injection moulds. For example, moulds built with the FGMs technique can have distinctive regions with higher heat conduction. Higher rates of heat transfers from thicker regions of the injected part can be useful to produce better and cheaper injection moulded polymer parts. It is possible to obtain moulds with differential conductivity by adding locally, during the fabrication of the mould, copper to the mould base material such as tool steel. In this work, an investigation into the effect of FGM copper (Cu)-tool steel mould insert over polymer injected parts is presented. The work is divided in two parts: a numerical thermal analysis comparison between Cu-tool steel graded and tool steel inserts and an injection moulding experiment with comparisons between mould surface temperature and degree of crystallinity of polypropylene parts. The numerical model was used to compare different behaviour of the mould heat transfer according to the mould insert material. Thereafter, a bolster was built to hold FGMs and tool steel inserts obtained by a selective laser fusion process. Polypropylene was injected over the inserts to compare with the numeric results. To observe the effect of the cooling rate in the polypropylene parts using the graded inserts, the degree of crystallinity of the parts was measured by differential scanning calorimetry (DSC) test. The temperature of the mould was also evaluated during the injection cycles. The results showed that the graded Cu-tool steel inserts tested had lower capacity to store heat energy. As Cu was added to the tool steel, the mixture proved to transfer heat more efficiently but it had less capacity to absorb heat.

Mould Heat Transfer in the Continuous Casting of Round Billet

Mould heat transfer behaviors during the continuous casting of round billets are elucidated in this paper. Round copper moulds were instrumented with 72 thermocouples and mould temperature together with heat flux were monitored simultaneously with mould powder lubrication during continuous casting of a diameter 178 mm round billets. The profiles of the temperature and heat flux were analyzed based on the longitudinal and circumferential monitoring data under different installation status of moulds. The influences of steel carbon content, casting speed, and mould oscillation frequency on heat transfer have been discussed especially at position 70–110 mm below the meniscus where the heat transfer was the highest and most sensitive to operational parameters. Eventually, the correlation coefficient, defined as the correlation of local heat flux and temperature (CCHT) in the hot face of mould around the mould circumference at the same mould height, has proved to be a good characteristic parameter for analyzing the influence of scale on abnormal heat transfer in quantity.

Integrated simulation of the glass and mould in the TV panel pressing process

An integrated model of the behaviour of molten glass and mould during the pressing operation of TV panel is developed in this paper. The molten glass is modelled by an incompressible Newtonian liquid undergoing flow. And a 3D finite element method is used to perform the simulation of the fluid and heat flow, which employs an equal-order velocity-pressure interpolation method. Mould cooling system design is important and significantly affects productivity and the quality of the final part. The mould heat transfer during the TV panel pressing process is established by boundary conditions analysis. Numerical implementation is a 3D boundary element method. These two simulations are coupled by matching the temperature and heat flux at the glass-mould interface. As compared with the experimental data, the presented model and developed system are sufficiently accurate.

Heat Withdrawal in the Mold in Continuous Casting of Steel. Review and Analysis

Two principal methods are used to investigate the heat transfer in the continuous casting mold. The direct way is to measure cooling water temperatures, mold wall temperatures, strand temperatures and shell thickness in actual operation, and then deduce from these data the correlations for heat flux densities. The other way is to investigate the “unit operations” of heat transfer theoretically or experimentally in the laboratory, viz. heat transfer through a layer of casting flux or of gas, and heat transfer in a copper wall cooled on one side by water. The results obtained in this approach can then be used to explain the data determined with the direct method and to optimize the heat transfer behaviour of the mold in the machine. In the first part of this paper some unit operations are discussed and engineering formulae are given for computation of the heat resistances of the gap and the copper/water system. In the second part of the paper the available operational data on heat flux density are analysed. Algorithms are presented for computation of local and average heat flux density as functions of casting speed, carbon content of the steel and composition of the casting flux. Finally, values of shell thickness are computed with the correlation for heat flux density and are compared with the measured data.

Analysis of variability and non-uniformity of mould heat extraction for round billet continuous casting in plant trials

Maintaining a stable and uniform heat transfer from steel shell to mould is important to produce high quality casting billet. In the present paper, a large amount of measured data of heat flux and temperature for round billet continuous casting mould from a plant trial has been analysed to shed light on the variability and non-uniformity of mould heat transfer around the perimeter. The results show that the variability and non-uniformity of heat extraction from the steel through the mould is affected slightly by operational parameters, such as pouring temperature, casting speed, meniscus, electromagnetic stirring current, but strongly by the steel carbon content and mould powder type. The installation of the mould in caster machine determines the magnitude of non-uniformity of heat transfer to a great extent. The relative root mean square (rRMS) of mould heat flux, presenting the variability and non-uniformity of mould heat transfer around the perimeter in transverse section, has wider range of variation and higher mean value compared with that of temperature. When the abnormality of heat transfer happens, such as deposit, the non-uniformity of mould heat transfer is also studied.

EXPERIMENTAL RESEARCH AND NUMERICAL SIMULATION OF MOLD TEMPERATURE FIELD IN CONTINUOUS CASTING OF STEEL

Mold is the heart of the continuous casting machine. Heat transfer and solidification in a watercooled mold are the most important factors during the continuous casting of steel. For studying the temperature distribution of a mold wall, a simulated apparatus of mold was designed and experiments were performed by it. The measured results indicated that the mold wall temperature approaches the temperature of cooling-water. An equivalent thermal-conductivity coefficient was proposed and deduced on the basis of the conclusion of the experiments. This coefficient was applied to solve the heat transfer between the melt and cooling water, and to characterize the heat transfer capacity of the mold. By this equivalent thermal-conductivity coefficient, it is very easy and convenient to numerically simulate the solidification process of continuous casting. And the calculation results are in agreement with the experiments. The effects of casting speed and water flow rate on the mold temperature field were also discussed.

3-D Inverse Problem Continuous Model for Thermal Behavior of Mould Process Based on the Temperature Measurements in Plant Trial

A three-dimensional mathematical model for round billet continuous casting of steel in the mould, adopting the surface revolution theory, together with an appropriate inverse problem method from the measured temperatures by the thermocouples buried in various locations in the mould, has been developed to elucidate the real thermal behavior of mould process in plant production, including the mould heat transfer, steel solidification, and slag film distribution, with the objective of understanding the relationship among them. The results show that the vertical component of heat condition and the slag rim at meniscus decreases mould temperatures and the former also lower the level of the peak temperature, and the minimum thickness of solid slag film about 80 mm below meniscus results in the peak mould heat flux and temperature. The magnitude and profile of mould heat transfer around the perimeter between the shell and mould, having corresponding relationship with solid slag, determines that of shell thickness. And the channel the liquid slag entering at meniscus determines the mould heat transfer to some extent.

The Inverse Problem‐Based Interfacial Heat Transfer between the Billet and Mould, and the Crack Sensitiveness Area of Strand

AbstractA coupled thermo‐mechanical model has been established including the finite difference method (FDM) simulating the mould heat transfer based on the inverse problem algorithm from measured temperatures, and the finite element method (FEM) predicting the strand stress. Calculation results show that the distribution of mould heat flux, which determines the shell thickness, corresponds to that of thermal resistance between the mould and shell. The safety index of billet quality illustrates that the surface cracks are likely to originate near the meniscus and propagate from beneath the surface at the lower part of mould. In this study, the thickness distributions of liquid and solid slag films are also calculated, showing that the heat transfer is determined mainly by the solid slag film in the upper mould.