Thermal analysis of the roll in the strip casting process

Coiled strip can be directly produced through the twin-roll strip casting process from the melt by incorporating casting and hot rolling together into a single step. In this unique process, the strip formation from the molten metal critically relies upon the casting rolls. Thus, the design of the rolls is extremely essential. The coupled heat transfer and deformation analysis of the casting roll is carried out in a two-dimensional numerical model, using a finite element program (MARC) to examine the thermal stress and displacement. The effects of several factors such as the nickel overlay thickness on the roll surface, the casting speed, and the roll diameter on thermal characteristics are investigated.     

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.     

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.     

Modeling the film casting process using a continuum model for crystallization in polymers

In this paper, the film casting process has been simulated using a new model developed recently using the framework of multiple natural configurations to study crystallization in polymers (see Rao and Rajagopal Z. Angew. Math. Phys. 53 (2002) 265; Polym. Eng. Sci. 44(1) (2004) 123; Simulation of the film blowing process for semicrystalline polymers, in press, 2004). In the film casting process, the material starts out as a viscoelastic melt and undergoes deformation and cooling, resulting in a semi-crystalline solid. In order to model the complex changes taking place in the material and predict the behavior of the final solid it is important to use models that are capable of describing these changes. The model used here has been formulated within a general thermodynamic framework that is capable of describing dissipative processes. In addition it handles in a direct manner the change of symmetry in the material; it thus provides a good basis for studying the crystallization process in polymers. The polymer melt is modeled as a rate type viscoelastic fluid and the crystalline solid polymer is modeled as an anisotropic elastic solid. The initiation criterion, marking the onset of crystallization and equations governing the crystallization kinetics arise naturally in this setting in terms of the appropriate thermodynamic functions. The mixture region, wherein the material transitions from a melt to a semi-crystalline solid, is modeled as a mixture of a viscoelastic fluid and an elastic solid. This is in marked contrast to earlier approaches where in the simulation has been done assuming that the material was a viscous fluid and the transition to a solid like behavior is achieved by increasing the viscosity to a large value resulting in a highly viscous fluid and not an elastic solid. The results of our simulations compare well against experimental data available in literature. In addition to these quantitative comparisons have carried out parametric study to study the influence of the different parameters on the film casting process.     

Hydraulic analysis of free-surface flows with solidification

Summary The paper is concerned with a one-dimensional analysis of plane open-channel flow with continuous solidification. The process is of relevance for recent developments in the casting of steel and other metals. The bottom of the channel consists of a rotating casting roll and a horizontal cooling table, where the solidified material is withdrawn with given velocity. The study is restricted to the region downstream of the top of the casting roll. Surface tension is neglected. In the main part of the analysis inviscid fluid flow is considered since the Reynolds number is very large in the applications. It is found that the steady-state solutions are nonunique in a certain parameter range. In addition to a continuous solution, there are two solutions including hydraulic jumps, with one hydraulic jump being located on the casting roll, the other one on the cooling table. Regarding the stability of the non unique solutions, the evolution of disturbances is investigated numerically as an initial-value problem. It is concluded that the hydraulic jump on the cooling table is unstable, while the other discontinuous solution as well as the continuous solution are stable for sufficiently small disturbances. Which stable solution is attained in the steady state, depends on the history of the process. Friction at the liquid/solid interface is taken into account in the last part of the analysis. A constant friction coefficient is assumed. It is found that the history of the process determines the steady-state solution if, and only if, the friction coefficient is sufficiently small. For larger values of the friction coefficient, the steady-state solution is unique and independent of the history of the transient process. Furthermore, for sufficiently large friction coefficients, stable hydraulic jumps are found, in contrast to the inviscid case, also on the cooling table. Received 19 March 1999; accepted for publication 3 May 1999     

A finite element model for the simulation of lost foam casting

In this paper, we present a numerical model to simulate the lost foam casting process. We introduce this particular casting first in order to capture the different physical processes in play during a casting. We briefly comment on the possible physical and numerical models used to envisage the numerical simulation. Next we present a model which aims to solve ‘part of’ the complexities of the casting, together with a simple energy budget that enables us to obtain an equation for the velocity of the metal front advance. Once the physical model is established we develop a finite element method to solve the governing equations. The numerical and physical methodologies are then validated through the solution of a two‐ and a three‐dimensional example. Finally, we discuss briefly some possible improvements of the numerical model in order to capture more physical phenomena. Copyright © 2004 John Wiley & Sons, Ltd.     

Comparison of interfacial heat transfer coefficient estimated by two different techniques during solidification of cylindrical aluminum alloy casting

The interfacial heat transfer coefficient (IHTC) is necessary for accurate simulation of the casting process. In this study, a cylindrical geometry is selected for the determination of the IHTC between aluminum alloy casting and the surrounding sand mold. The mold surface heat flux and temperature are estimated by two inverse heat conduction techniques, namely Beck’s algorithm and control volume technique. The instantaneous cast and mold temperatures are measured experimentally and these values are used in the theoretical investigations. In the control volume technique, partial differential heat conduction equation is reduced to ordinary differential equations in time, which are then solved sequentially. In Beck’s method, solution algorithm is developed under the function specification method to solve the inverse heat conduction equations. The IHTC was determined from the surface heat flux and the mold surface temperature by both the techniques and the results are compared.     

Non-isothermal analysis of extrusion film casting using multi-mode Phan-Thien Tanner constitutive equation and comparison with experiments

Extrusion film casting (EFC) is an industrially important process which produces thousands of tons of polymer films, sheets, and coating used for various industrial as well as household applications. In this paper, we focus on an instability which occurs during certain polymer processing operations operating under predominantly elongational flow, such as extrusion film casting and fiber spinning. This instability, called the draw resonance, occurs in the form of sustained periodic fluctuations in the film dimensions. It appears when the process goes beyond the critical line speed of the EFC process. In this work, a conventional linear stability analysis is carried out for nonisothermal EFC process to determine the onset of the draw resonance. The polymer rheology is modeled by the Phan-Thien Tanner (PTT) multi-mode constitutive equation. For the implementation, a conventional shooting method approach is used. Extrusion film casting experiments were also carried out using a conventional linear low-density polyethylene (LLDPE) by varying process parameters such as draw ratio and aspect ratio, to observe the effect on the stability of the process. Linear stability analysis results under non-isothermal conditions are compared and validated with existing results from literature and with our own experimental data. This work displays the effect of multiple relaxation modes as well as the temperature influence on the stability of EFC process. Finally, results also indicate that the temperature highly affects the stability of the EFC process and cannot be ignored from modeling of EFC process.     

Spray and jet cooling in steel rolling

Prediction and control of roll and strip cooling are necessary in modern steel mills because they not only affect the process efficiency but also strongly influence the quality of rolled products. In this article, relationships among metallurgy, heat transfer, and control of the cooling system in steel rolling are first discussed. Heat transfer characteristics associated with the water spray and jet cooling used in rolling processes are then studied. The effects of important convective heat transfer parameters on cooling perormance for both stationary and moving surfaces are examined. Results indicate that local heat fluxes up to 20 × 10⁶ W/m² are observed in the nucleate boiling regime. The present results are compared with typical boiling heat transfer studies in terms of heat fluxes, heat transfer coefficients, spray rate, and cooling efficiency. The effect of surface motion is found to increase the cooling efficiency of roll and strip cooling. Finally, implementation of the present finding in roll and strip cooling to thermomechanical processing in steel rolling is proposed.     

Free-surface magnetohydrodynamic flow with solidification

The paper considers an analysis of a liquid metal flow, occurring in the horizontal belt strip casting process. The liquid metal flows over a moving copper belt with a growing solidifying phase beneath the melt. The effect of applying a transverse magnetic field is investigated. A set of three-dimensional shallow water equations is derived. Supercritical flow is assumed and the shallow water equations are solved numerically using a shock-capturing method, which automatically takes care of the possibility of oblique hydraulic jumps.It is shown that non-uniform conditions introduced in the feeding region give a pattern of steady hydraulic jumps, which propagate downstream and are reflected at the sidewalls. The effect of the magnetic field is to brake the flow and damp the standing hydraulic jump pattern. Different feeding methods are compared and it is shown that the magnetic field erases the initial differences in liquid distribution using different feeding techniques.     

Heat transfer associated to a hot surface quenched by a jet of oil-in-water emulsion

In hot rolling, the mechanical properties of steel alloys are conditioned by the rolling process but a great part is ensured by the cooling of the hot strip mill. Well controlling this cooling rate and its homogeneity is thus of primary importance for obtaining steels with desired mechanical properties. As the water used in the cooling stage of the rolling process can be polluted by oil (in hot mill strip, some oil is used to lubricate the rolls and a part of it can pollute the water), it is important to know how much varies the cooling rates when water is polluted. In this study, transient cooling has been investigated during quenching of a hot metal disk with various subcooled oil-in-water emulsion jets. The aim of this work is to compare the cooling efficiency of oil-in-water emulsion jet with a pure water jet. Experimental investigations of axisymmetric jet impingements on a preheated hot metal disk (500-600 °C) have been performed with various oil-in-water emulsions. The transient cooling heat fluxes on the quenched side are estimated by coupling the measurement of the temperature field of the other side (rear face) with a semi-analytical inverse heat conduction model.     

PIV measurements of flow in drying polymer solutions during solvent casting

An experimental method based on confocal microscopy and particle image velocimetry (PIV) is used to characterize the flow in a polymer solution during solvent casting. The flow inside a 200-μm-thick film of a poly(vinyl alcohol) (PVA) solution is visualized near a vertical wall of a mold using confocal microscopy of seed particles during solvent evaporation at 25, 35, and 45°C, and the corresponding velocity vector fields are determined from projections of the confocal images. Flow toward the vertical wall is observed inside the film as well as a slower Marangoni-type counter flow at the film surface during the initial phase of solvent evaporation, resulting from a polymer concentration gradient along the film due to a local variation in evaporation rate. Total volume of the polymer solution in the observation volume as well as solvent evaporation rate are determined as a function of time, both revealing close correlation to average horizontal velocity data from PIV. The PIV measurements show significant differences in the flow velocity fields at different temperatures. The PIV measurements correlate with the solvent evaporation rates as well as the final polymer thicknesses on the vertical wall of the mold. Surface tension and viscosity measurements are taken for different concentrations of PVA solution.     

The conjugate heat transfer from an internal heated small strip in a forced laminar flow

 An asymptotic and numerical investigation was conducted for the cooling process, by a forced laminar flow, of a small strip with a non-uniform heat source. The nondimensional temperature distribution in the strip has been obtained as a function of the following parameters: (a) the intensity and distribution of the internal heat sources, (b) the aspect ratio of the strip, (c) the longitudinal heat conductance of the strip and (d) the Prandtl number of the fluid. Both the thermally thin as the thick wall approximations were considered in this paper. The total thermal energy or averaged temperature of the strip is found to decrease as the influence of the longitudinal heat conduction effects in the strip decreases in the thermally thin wall regime. After reaching a minimum, it increases again in the thermally thick wall regime. Received on 19 May 2000     

Three-dimensional finite element model for metal displacement and heat transfer in squeeze casting processes

A three-dimensional finite element model for the numerical simulation of metal displacement and heat transfer in the squeeze casting process has been developed. In the model, a numerical approach, termed as ‘Quasi-static Eulerian’, is proposed, in which the dynamic metal displacement process is divided into a certain number of sub-cycles. In each of the sub-cycles, the dieset configuration is assumed to be static and a fixed finite element mesh is created, thus making the Eulerian approach applicable to the solution of metal flow and heat transfer. Mesh-to-mesh data mapping is carried out for any two adjacent sub-cycles to ensure that the physical continuity of the real metal displacement process is represented. A numerical example is presented, which shows the application of the present model to geometrically complex three-dimensional squeeze casting problems. To cite this article: R.W. Lewis et al., C. R. Mecanique 335 (2007).     

Analysis of high-speed continuous casting with inverse finite elements

A recently proposed inverse isotherm finite element method is further extended in order to account for processes with distorted isotherms. With this method a variety of problems can be solved which require the explicit calculation of characteristic material lines along with the common field of unknowns in transport phenomena. The method is applied to high-speed metal casting, where the location and shape of the extensive solidification front is calculated simultaneously with the primary unknowns, the velocity and the pressure, whereas the temperature is fixed at the moving nodes of the finite element tessellation. This is achieved by solving the energy equation inversely along with the rest of the conservation equations, i.e. the temperature field is fixed and its location is calculated. Empirical correlations may be derived which give the shape of the solidification front as a function of the process parameters. This may be used to improve the control means of metal casting, which is currently based on one-dimensional approximate analyses.     

Non-isothermal film casting: Determination of draw resonance

The important industrial process of casting polymeric films suffers from the “draw resonance” instability that appears as sudden oscillations in the product dimensions. This instability influences the quality of the end-product and negatively limits productivity and efficiency of the process. The draw resonance originates when a material is being processed beyond the limits of its intrinsic properties. Research is conducted with the intention to find those process and material properties that allow to optimize the production process while keeping it stable.This paper concentrates on a non-isothermal analysis of the stability of the film casting. The mathematical model of the process is given by a quasi-linear system of first order PDEs with two point boundary conditions. The constitutive polymer behavior is approximated by the modified Giesekus model. Linear stability analysis combined with the Laplace transformation of the resulting linear system is applied to find parameters that determine mathematical and thus process instability. It all comes down to determining the spectrum of a compact operator; corresponding eigenfunctions can be regarded as the characteristic modes of the system. For implementation, the modification of Galerkin approach is used. The major advantage of the mathematical and numerical method is that the full spectrum is calculated in a matter of seconds. Our results agree perfectly with the ones from literature for isothermal case, and with the experimental data for the non-isothermal case. The results also indicate that non-isothermality is highly important and cannot be excluded from modeling.     

Use of experiment and an inverse method to study interface heat transfer during solidification in the investment casting process

A technique to determine the thermal boundary conditions existing during the solidification of metallic alloys in the investment casting process is presented. Quantitative information about these conditions is needed so that numerical models of heat transfer in this process produce accurate results. In particular, the variation of the boundary conditions both spatially and temporally must be known. The method used involves the application of a new inverse heat conduction method to thermal data recorded during laboratory experiments of aluminium alloy solidification in investment casting shell moulds. The resultant heat transfer coefficient for the alloy/mould interface is calculated. An experimental programme to determine requisite mould thermal properties was also undertaken. It was observed that there is significant variation of the alloy/mould heat transfer coefficient during solidification. It is found to be highly dependent on the alloy type and on the vertical position below the initial free surface of the liquid metal. The aluminium casting alloys used in this study were 413, A356, 319 (Aluminum Association designations), and commercially pure aluminium. These alloys have significantly different freezing ranges. In particular, it was found that alloys with a high freezing range solidify with rates of heat transfer to the mould which are very sensitive to metallostatic head.     

Experimental investigation of the start-up phase during direct chill and low frequency electromagnetic casting of 6063 aluminum alloy processes

On the basis of conventional hot-top casting and Casting, Refining and Electromagnetic process, a lower frequency electromagnetic field was applied during the conventional hot-top casting process. Nine thermocouples (type K) were introduced into the metal to study the temperature profile in the ingot during the start-up phase of casting process. The experimental results show that under the effect of the low frequency electromagnetic filed, the heat transfer is changed greatly and the film boiling disappears, which could restrain the formation of fine subsurface cracks; the sump is shallow, and the macrostructure of the ingot butt is fine during the start-up phase of direct chill casting process.     

Optimal control of film casting processes

We present an optimal control approach for the isothermal film casting process with free surfaces described by averaged Navier–Stokes equations. We control the thickness of the film at the take‐up point using the shape of the nozzle and the initial thickness. The control goal consists in finding an even thickness profile. To achieve this goal, we minimize an appropriate cost functional. The resulting minimization problem is solved numerically by a steepest descent method. The gradient of the cost functional is approximated using the adjoint variables of the problem with fixed film width. Numerical simulations show the applicability of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

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。