Unsteady Flow Predictions of Initial Surface Formation in Aluminum Strip Casting

A comprehensive multidomain computational fluid dynamics model is described for examining the unsteady thermal-fluid dynamic conditions at the early onset of surface formation in aluminum strip casting. By employing zones for the solidifying melt, substrate, high-speed water jets, and active film for thermal buffering between the melt and the substrate, a fully implicit in time solution is obtained. Furthermore, the melt domain transport equations are cast in an Eulerian–Lagrangian form to include the motion of a backward-facing compliant step and its associated contact line, both affecting the initial melt–substrate contact cooling conditions. The influence of the compliant step motion on the thermal-fluid history at the earliest stages of surface formation is examined. Results show a well-defined characteristic response between the contact line motion and the solid fraction/temperature history. Associated recirculation cells are affected profoundly by contact line motion and exhibit cyclical removal and reappearance. Coupled with large relative velocity between phases at the contact line, overall flow patterns suggest conditions for alloy segregation.     

Numerical Simulation of Filling Process During Twin-Roll Strip Casting

The modeling and controlling of flow and solidification of melt metal in the filling process is important for obtaining the optimal pool level and the formation of the solidified metal layer on the surface of twin-rolls during the twin-roll strip casting. The proper delivery system and processing parameters plays a key role to control flow characteristics in the initial filling stage of the twin-roll strip casting process. In this paper, a commercial CFD software was employed to simulate the transient fluid flow, heat transfer, and solidifications behaviors during the pouring stage of twin-roll strip casting process using different delivery systems. A 3D model was set up to solve the coupled set of governing differential equations for mass, momentum, and energy balance. The transient free-surface problem was treated with the volume of fluid approach, a k–? turbulence model was employed to handle the turbulence effect and an enthalpy method was used to predict phase change during solidification. The predicted results showed that a wedge-shaped delivery system might have a beneficial impact on the distribution of molten steel and solidification. The predicted surface profile agreed well with the measured values in water model.     

A two-dimensional heat and fluid-flow model of single-roll continuous-sheet casting process

Single-roll continuous-sheet casting process has been simulated using a mathematical model based on considerations of fluid flow, heat transfer, and solidification. The principal model equations include momentum and energy balances which are written for various zones comprising the process. The flow of liquid metal in the pool is taken to be a two-dimensional recirculatory flow. The concepts of vorticity and stream function are used to reduce the number of equations and number of unknowns, respectively. Model equations and boundary conditions are written in terms of dimensionless variables and are solved, using an implicit finite difference technique, to give stream functions and velocity fields in the metal pool, temperature fields in the metal pool, sheet, and caster drum, and the final sheet thickness for various operating parameters. The parameters examined are: (1) rotational speed of the caster drum, (2) liquid metal head in the tundish, (3) superheat of the melt, (4) caster drum material, and (5) cooling conditions prevailing at the inner surface of the caster drum. The final sheet thickness decreases with increasing rotational speed of the caster drum and melt superheat, but it increases with increasing standoff distance and metal head in the tundish.     

Ab‐initio Predictions of Interfacial Heat Flows during the High Speed Casting of Liquid Metals in Near Net Shape Casting Operations

When metals are cast into solid shapes, the quality of the solid casting depends on many things, but heat flow management is a critical factor. It is relatively easy to predict heat flows through the liquid metal, and the solid mould, but heat flows through the interconnecting interface have been much more difficult to quantify. In the present work, following a review of our progress up to date on near net shape casting, the approach is to model this interfacial resistance from first principles. By conducting experiments in which liquid aluminum is cast at high speed (～0.5 m/s), onto a copper substrate, fitted with extremely sensitive embedded thermocouples, heat fluxes from the first moments of metal contact, to final freezing of the strip, have been measured. Similarly, by using a 3D profilometer that is able to rapidly characterize and quantify the surface topography of a substrate, to ±1 µm, one can have the necessary data to mathematically model the transfer of heat from the overlaying metal, through the interfacial layer, into the copper substrate. The thermal model briefly described, makes the assumption of point contact between pyramidal peaks of the metal substrate and molten metal, with gas pockets trapped in the “valleys” of the substrate, through which heat must be transferred by conduction. Ab‐initio instantaneous heat fluxes predicted in this way proved to be in good agreement with those measured, provided adjustments were made for expansion of the “air gap”.     

Heat Flow Model for Surface Melting and Solidification of an Alloy

The heat flow model previously developed for a pure metal is extended to the solidification of an alloy over a range of temperatures. The equations are then applied to rapid surface melting and solidification of an alloy substrate. The substrate is subjected to a pulse of stationary high intensity heat flux over a circular region on its bounding surface. The finite difference form of the heat transfer equation is written in terms of dimensionless nodal temperature and enthalpy in an oblate spheroidal coordinate system. A numerical solution technique is developed for an alloy which precipitates a eutectic at the end of solidification. Generalized solutions are presented for an Al-4.5 wt pct Cu alloy subjected to a uniform heat flux distribution over the circular region. Dimensionless temperature distributions, size and location of the “mushy” zone, and average cooling rate during solidification are calculated as a function of the product of absorbed heat flux,q, the radius of the circular region, a, and time. General trends established show that for a given product ofqa all isotherms are located at the same dimensionless distance for identical Fourier numbers. The results show that loss of superheat and shallower temperature gradients during solidification result in significantly larger “mushy” zone sizes than during melting. Furthermore, for a given set of process parameters, the average cooling rate increases with distance solidified from the bottom to the top of the melt pool.     

Two-dimensional heat transfer model for secondary cooling of continuously cast beam blanks

Abstract

A two-dimensional heat transfer model was developed for the secondary cooling system during beam blank continuous casting. The finite element method was used to calculate the heat transfer. Accurate cooling boundary conditions in the secondary cooling zone are involved, including spray water cooling, water evaporation cooling, radiation cooling and roll contact cooling in the casting direction and non-uniform distribution of spray water flow density in the cross-section. The causes of longitudinal crack at the fillet during Q235 steel continuous casting were analysed on the basis of the simulation of the developed model, and then the spray water flow and the transverse nozzle layout were optimised. Practical results show that the surface quality of the beam blank improved after optimisations. Numerical results from the present model were validated using previous experimental measurements, which show good agreement.     

Mathematical modeling of a melt pool driven by an electron beam

Physical vapor deposition (PVD) assisted by an electron beam is one of several methods currently used to apply thermal barrier coatings (TBCs) to aircraft components subjected to high-temperature environments. The molten pool of source material inherent in this process shall be the subject of analysis in this investigation. A model of the melt pool and the ingot below shall be generated in an effort to study the fluid flow and heat transfer within the pool. This model shall incorporate all of the following mechanisms for heat transfer into and out of the melt pool/ingot system: electron-beam impingement upon the melt pool surface, absorption of latent heat of evaporation at the melt pool surface, radiation from the melt pool surface, loss of sensible heat carried off with the vapor, and cooling by the crucible containing the melt pool/ingot. Fluid flow within the melt pool model shall be driven by both natural convection and by surface tension gradients on the melt pool surface. Due to the complexity of the differential equations and boundary equations governing the model, this detailed study shall be performed through a finite element analysis. Reduced order models of the system will be generated from this investigation. An analysis will also be performed to ascertain the error introduced into these models by uncertainty in the thermophysical property data used to generate them.     

On the development of a three-dimensional transient thermal model to predict ingot cooling behavior during the start-up phase of the direct chill-casting process for an AA5182 aluminum alloy ingot

The control of the heat transfer during the start-up phase of the direct-chill (DC) casting process for aluminum sheet ingots is critical from the standpoint of defect formation. Process control is difficult because of the various inter-related phenomena occurring during the cast start-up. First, the transport of heat to the mold is altered as the ingot base deforms and the sides are pulled inward during the start-up phase. Second, the range of temperatures and water flow conditions occurring on the ingot surface as it emerges from the mold results in the full range of boiling-water heat-transfer conditions—e.g., film boiling, transition boiling, nucleate boiling, and convection—making the rate of transport highly variable. For example, points on the ingot surface below the point of water impingement can experience film boiling, resulting in the water being ejected from the surface, causing a dramatic decrease in heat transfer below the point of ejection. Finally, the water flowing down the ingot sides may enter the gap formed between the ingot base and the bottom block due to butt curl. This process alters the heat transfer from the base of the ingot and, in turn, affects the surface temperature on the ingot faces, due to the transport of heat within the ingot in the vertical direction. A comprehensive mathematical model has been developed to describe heat transfer during the start-up phase of the DC casting process. The model, based on the commercial finite-element package ABAQUS, includes primary cooling via the mold, secondary cooling via the chill water, and ingot-base cooling. The algorithm used to account for secondary cooling to the water includes boiling curves that are a function of ingot-surface temperature, water flow rate, impingement-point temperature, and position relative to the point of water impingement. In addition, a secondary cooling algorithm accounts for water ejection, which can occur at low water flow rates (low heat-extraction rates). The algorithm used to describe ingot-base cooling includes both the drop in contact heat transfer due to gap formation between the ingot base and bottom block (arising from butt curl) as well as the increase in heat transfer due to water incursion within the gap. The model has been validated against temperature measurements obtained from two 711×1680 mm AA5182 ingots, cast under different start-up conditions (nontypical “cold” practice and nontypical “hot” practice). Temperature measurements were taken at various locations on the ingot rolling and narrow faces, ingot base, and top surface of the bottom block. Ingot-based deflection data were also obtained for the two test conditions. Comparison of the model predictions with the data collected from the cast/embedded thermocouples indicates that the model accounts for the processes of water ejection and water incursion and is capable of describing the flow of heat in the early stages of the casting process satisfactorily.     

Two-fluid simulation on the mixed convection flow pattern in a nonisothermal water model of continuous casting tundish

A transient two-fluid model is applied to simulate fluid flow and heat transfer in a nonisothermal water model of continuous casting (CC) tundish. The original liquid in the bath is defined as the first fluid, and the inlet stream, with the temperature variation, is defined as the second fluid. The flow patterns and heat transfer are predicted by solving the three-dimensional (3-D) transient transport equations for each fluid. The results predicted by the two-fluid model make the effect of natural convection more clear compared with the generally used single fluid model k-ɛ turbulence model.     

Variables affecting the nature of the chill zone

Structures and substructures in the chill zone have been studied in Al-Cu alloys as a function of the following solidification conditions at the substrate chill: a) heat sink capacity; b) surface microprofile; c) nature of the liquid metal fluid flow as it makes substrate contact. The parameters taken in account both experimentally and analytically are: heat transfer coefficient of the metal/mold interface, surface rugosity of the mold walls, and the Reynolds number of the liquid metal fluid flow. The results obtained show definite correlations between the structural characteristics of the chill zone and the values of the studied parameters.     

Effect of holding time and surface cover in ladles on liquid steel flow in continuous casting tundishes

Mathematical modeling of fluid flow and heat transfer of melt in a typical two-strand slab caster tundish has been done for a complete casting sequence. The complete casting sequence consists of 1 minute of tundish emptying period during the ladle transfer operation followed by 1 minute of tundish filling period by the new ladle and pouring at the normal operating level of the tundish for 46 minutes. The effect of varying ladle stream temperature conditions on the melt flow and heat transfer in the continuous casting tundish has been studied. When the ladle stream temperature decreases appreciably over the casting period, corresponding to heat loss of the melt in the ladle from the top free surface, the incoming melt temperature becomes lower than that of the melt in the bulk of the tundish after about 30 minutes from the start of teeming. This results in melt flow along the bottom of the tundish instead of the normal free surface directed flow. The ladle melt stream temperature shows little variability when the ladle has an insulated top. Corresponding to this situation, the temperature of the incoming melt remains higher than that of the melt in the bulk of the tundish and the normal free surface directed flow is maintained throughout the casting period. The product cast under such condition is expected to have a uniformly low inclusion content. The heat loss condition from the top of the ladle has been shown to be the dominant factor in determining fluid flow and heat-transfer characteristics of the melt in the tundish rather than the holding time of the melt in the ladle. Formerly Graduate Student, Department of Materials Science and Engineering, Ohio State University     

Heat flow model of glass formation and crystallization on rapid quenching

The theoretical model of glass formation and partial crystallization during rapid solidification of a metallic melt describes the homogeneous nucleation within the undercooled melt as well as the heat transfer into the metallic chill substrate. The calculated maximum thicknesses of amorphous foils at quenching onto a copper substrate increase in the order of alloys FeC, FeB, NiSiB and PdSi. Reducing the foil-substrate heat transfer coefficient, increasing the casting temperature and utilizing a steel substrate cause the attainable amorphous foil thickness to decrease. In foils with a large volume fraction crystallized the cooling process is not monotonous. The minimum density of quenched-in nuclei is situated at the substrate-side surface in amorphous foils and at the surface away from the substrate in crystalline foils.     

Heat Transfer and Cooling Rate Model of Flow Melt on Vibration Wall

In this paper, a model of heat transfer of melt flow on a vibration wall has been established. Calculation results show that the temperature boundary layer thickness decreases with the increase of vibration frequency and amplitude. As the vibration frequency and amplitude increase, the heat transfer coefficient between alloy melt and slope and between cooling water and slope increase. Cooling rate of melt can reach 400-600 K/s which belong to the sub-rapid solidification regime. The heat transfer mode doesn’t change during the flow process, so vibration not only strengthens the cooling rate of melt, but also stabilizes heat transfer between melt and slope. The grain size of solidification microstructure decreases with increasing vibration intensity, which indicates that vibration increases cooling rate and accelerates nucleation rate. So, the established model agrees with verification experiment, and can relatively well explain the heat transfer and cooling rate of melt flow on vibration plate.     

Heat flow model for surface melting and solidification of an alloy

The heat flow model previously developed for a pure metal is extended to the solidification of an alloy over a range of temperatures. The eq11Ations are then applied to rapid surface melting and solidification of an alloy substrate. The substrate is subjected to a pulse of stationary high intensity heat flux over a circular region on its bounding surface. The finite difference form of the heat transfer eq11Ation is written in terM_s of dimensionless nodal temperature and enthalpy in an oblate spheroidal coordinate system. A numerical solution technique is developed for an alloy which precipitates a eutectic at the end of solidification. Generalized solutions are presented for an Al-4.5 wt pct Cu alloy subjected to a uniform heat flux distribution over the circular region. Dimensionless temperature distributions, size and location of the “mushy” zone, and average cooling rate during solidification are calculated as a function of the product of absorbed heat flux,q, the radius of the circular region,a, and time. General trends established show that for a given product ofqa all isotherM_s are located at the same dimensionless distance for identical Fourier numbers. The results show that loss of superheat and shallower temperature gradients during solidification result in significantly larger “mushy” zone sizes than during melting. Furthermore, for a given set of process parameters, the average cooling rate increases with distance solidified from the bottom to the top of the melt pool.     

Steel Flow into a Mold from a Submerged Nozzle with Eccentric Outputs

The flow of steel melt into a mold has not been adequately studied. In general, analysis of the melt flow is a complex mathematical problem, and accordingly numerical modeling is employed. The present work employs Odinokov’s numerical method, which is based on a finite-difference form of the initial system of equations. This method has been successfully employed in continuum mechanics; in casting to determine the stress–strain state of shell-type molds; and in solving other technological problems. That suggests its universality. In the present work, it is applied to the hydrodynamic fluxes of liquid metal when steel is cast in a mold of rectangular cross section. The use of a submerged nozzle with eccentric holes for steel supply requires a three-dimensional mathematical model describing the metal fluxes into the mold. Odyssey software is used to simulate the processes in the mold. The calculation is based on the fundamental hydrodynamic equations and the proposed numerical model. The solution is obtained numerically and takes the form of a system of differential equations. The region of interest is divided into finite elements, and the system of equations is written in difference form for each element. The result obtained is the field of metal flow velocities into the mold. A numerical approach and a corresponding algorithm are developed for solution of the system of algebraic equations obtained and are incorporated in a computation program written in Fortran-4. By means of the mathematical model, the geometric dimensions of the mold and the cross section of the exit holes in the submerged nozzle may be varied. The model clarifies the pattern of metal flows, which affects the heat transfer by the mold walls, and permits determination of the optimal parameters of metal exit from the submerged nozzle in different casting conditions. As an example, the model is applied to steel casting in a mold of rectangular cross section (height 100 cm, horizontal dimensions 2000 × 40 cm). Steel flow from the submerged nozzle is eccentric in two directions within the horizontal plane. The results of solution are presented in graphic form. The pattern of metal fluxes into the mold is shown, and the magnitude and intensity of the fluxes is determined.     

Modelling of crystal growth during the ribbon formation in planar flow casting

The crystalline solidification during rapid substrate quenching in planar-flow casting was simulated by using a numerical model based on a rapid solidification algorithm and the infinite viscosity approximation. The calculation shows that the existence of a real melt puddle shape suppresses undercooling and recalescence on the melt surface as well as on the solidifying ribbon. The melt puddle length is mainly determined by the heat-transfer coefficient. With increasing heat transfer across the melt – substrate interface the melt puddle length decreases. If the formation rate of critical nuclei on the substrate surface is low compared to the present cooling rate a large undercooling may occur. The performed calculations reveal that an undercooling of up to 600 K does neither affect the temperature distribution on the surface of the melt nor the melt puddle length, perceptibly. Therefore, investigations on microstructural features of rapidly quenched metals might give detailed information on the amount of undercooling present at the beginning of solidification.     

Influence of surface morphology, water flow rate, and sample thermal history on the boiling-water heat transfer during direct-chill casting of commercial aluminum alloys

An experimental investigation has been conducted on as-cast samples from three commercially significant aluminum alloys (AA1050, AA3004, and AA5182) to quantify the influence of surface morphology, water flow rate, and sample thermal history on the boiling-water heat transfer under conditions similar to those experienced in the direct-chill (DC) casting process. The study involved characterization of the as-cast surface morphology using a laser profilometer and quantification of the sample surface temperature and heat extraction to the cooling water using a DC casting simulator in combination with an inverse heat-conduction (IHC) analysis. The results from the study indicate that alloy’s thermal conductivity, surface morphology, and sample initial temperature all dramatically influence the calculated “boiling curve.” The intensity of the heat extraction was found to be enhanced at high heat fluxes in the nucleate boiling regime as the thermal conductivity was increased and was also found to increase as the surface of the sample became rougher, presumably through promotion of nucleation, growth, and/or detachment of bubbles. The heat transfer was also found to increase with increasing sample starting temperature, resulting in a series of boiling curves dependent on initial sample temperature. Finally, the effect of the water flow rate on heat transfer was found to be comparatively moderate and was limited to the sample with the smooth (machined) surface.     

Mechanisms of initial melt/substrate heat transfer pertinent to strip casting

An experimental study of initial solidification of 304 stainless steel melts in direct contact with copper substrates under conditions approximating the meniscus region of a strip caster has highlighted the importance of interfacial heat transfer during the first 30 ms of contact. The mechanisms governing initial heat transfer are strongly influenced by dynamic wetting phenomena. This has been illustrated experimentally by the effects of the buildup and melting of oxide films such as manganese silicates at the interface during successive immersions, by the role of surface active agents such as tellurium in the melt, and by the use of specially designed substrate textures to control contact areas. This article is based on a presentation made in the “Geoffrey Belton Memorial Symposium,” held in January 2000, in Sydney, Australia, under the joint sponsorship of ISS and TMS.     

Pool boiling cooling for melt spinning quench wheels

The production of rapidly quenched metal ribbons by melt spinning on a cylinder produces very high average heat fluxes through the cylinder. The problem of maintaining a low average casting surface temperature can be solved by boiling on the plain interior of the cylinder. An experimental, boiling cooled, amorphous iron alloy ribbon casting wheel was constructed to verify the concept and expand the available data on boiling heat transfer. Experiments were performed with water, near atmospheric pressure, in pools less than 0.03 m deep and at accelerations between 100 and 200 times earth gravity. Heat fluxes between 0.6 and 3.5 million W/m² were achieved. Heat transfer coefficients up to 0.1 million W/m² • K were measured. A loss of cooling occurred in a number of instances, at heat fluxes well below the predicted critical heat flux, and at heat flux conditions which were duplicated or exceeded in the remaining experiments. These conditions, possibly precipitated by local variations in the boiling heat transfer coefficient, are not considered to represent new boiling phenomena associated with high acceleration.