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.     

Numerical modeling of the flow in the mold of the continuous casting machine

The quality of the half products is conditioned by the conditions of cooling of molten steel during its transfer through the various exchangers and in particular the mold. The latter constitutes the first phase where molten steel starts to be solidified. The instantaneous solidified crust must be sufficiently thick to contain liquid steel and to avoid the phenomena of opening under the effect of the ferrostatic pressure. Among the recurring concerns of the steel industry is the appearance of the mastery of content inclusions in metallic alloys. Despite the dramatic increase in the cleanliness of steel, it still happens now that macro-inclusions (accidental) are found in the metal. The objective of this work is to demonstrate the influence of the nozzle geometrical modification of the flow structure and the behavior of the particles in the mold of the casting machine. The obtained results show the advantage of an inclined nozzle because it makes it possible to widen the recirculation zone what supports the increase in the residence time of the particles on the one hand and the formation of a solidified crust sufficient thick on the other hand. Numerical tests of the particles behavior (Al₂O₃) showed the advantage of using the geometric shapes of well designed nozzles. Due to symmetry, only half of the area is considered.     

THE TEMPERATURE ANALYSIS OF THE BILLET WITH PHASE CHANGE DURING CONTINUOUS CASTING

ＴＨＥＴＥＭＰＥＲＡＴＵＲＥＡＮＡＬＹＳＩＳＯＦＴＨＥＢＩＬＬＥＴＷＩＴＨＰＨＡＳＥＣＨＡＮＧＥＤＵＲＩＮＧＣＯＮＴＩＮＵＯＵＳＣＡＳＴＩＮＧＺｈａｏＸｉｎｇ－ｈｕａ（赵兴华）,ＣｈｅｎｇＸｉａｏ－ｄｉ（陈小弟）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙ...     

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.     

Influence of calcium on cracking of steel during the welding or casting process

The influence of calcium on the brittle–ductile transition temperature is studied for the solidification range. The test bars were cast from carbon steel with and without the addition of calcium. Mechanical properties at different temperatures around the solidus were evaluated. The fractured surfaces were examined using a scanning microscope coupled with a Kevex analyser. For the modified steel, the liquid phase appears (on heating) for higher temperature while the temperature range within which fracture can nucleate, during casting or welding, is markedly narrowed. In medium-carbon steel, calcium changes the manner of fusion of the grains. The inclusions of the liquid phase form at the triple points and the surfaces of grains remain solid above the solidus temperature.     

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.     

The importance of the sigma phenomenon in the study of the flow of blood

Summary During the past three decades, work on blood and on nonbiological systems concerning anomalies in theR ⁴ law of capillary flow has been proceeding along parallel and usually unconnected lines.The present paper attempts to draw together these diverse lines of work and stresses the importance to haemo-pathology of a fuller understanding of the sigmaphenomenon in blood.

---

Zusammenfassung Während der letzten 3 Jahrzehnte wurden Untersuchungen an Blut und an nichtbiologischen Systemen, die die Abweichung vomR ⁴-Gesetz beim kapillaren Fließen betreffen, auf parallelen und im allgemeinen getrennten Wegen vorangetrieben.Die vorgelegte Arbeit versucht, diese verschiedenen Forschungsrichtungen zusammenzubringen und ein volleres Verständnis des Sigma-Phänomens beim Blut in seiner Bedeutung für die Hämopathologie zu schaffen.

     

Axial dispersion of solids in rotary solid flow systems

Summary A simple unidirectional diffusion model is employed to analyze the axial dispersion of solid particles flowing through a rotary solid flow system, namely a rotary dryer. It is shown that the reciprocal of the Peclet number D/uL is uniquely correlated as a function of the dimensionless number F/dSN which characterizes the operating conditions of the rotary dryer.List of Symbols C concentration of tracer, mass/(length)³ - d diameter of rotary dryer, length - d _p diameter of solid particles, length - D longitudinal dispersion coefficient or axial mixing coefficient, (length)²/time - F volumetric flow rate of solid, (length)³/(length)² time - L length of rotary dryer, length - N rate of rotations of dryer, time^–1 - Q volume of tracer injected, based on bulk density of particles, (length)³ - S slope of the rotary dryer - u average flow velocity, based on effective flow volume of dryer, length/time - v volumetric flow rate, based on bulk density of particles, (length)³/time - V effective volume of rotary dryer, (length)³ - x distance from entrance of experimental section of dryer, length Greek letters time, measured from instant of introducing tracer into flowing material - 1– volumetric solid hold-up fraction - standard deviation - ² variance - _r relative standard deviation     

On the relativistic thermodynamics of a continuous system in electromagnetic fields

Summary Whithout adopting a particular interaction between matter and fields, we deduce the relativistic equations of balance -for charged differential materials which move in electromagnetic fields. Successively, restriction for the relativistic constitutive equations are deduced by adopting a relativistic reduced dissipation inequality obtained from the 2nd principle of thermodynamics by P. M. Quan.

---

Sommario Si determinano le equazioni relativistiche del bilancio per materiali differenziali carichi, con distribuzione continua di momento angolare interno, in moto in campi elettromagnetici senza ricorrere ad alcuna interazione particolare tra materia e campi. Successivamente si deducono delle restrizioni per le equazioni costitutive derivanti dall'imporre che esse rendano soddisfatta una diseguaglianza di dissipazione ridotta relativistica ottenuta dal2 ^o principio della termodinamica di P. M. Quan.

     

An analytical solution for the solidus and liquidus position in the solidification of materials with a phase change range applied to the continuous casting of steel

In continuous casting processes it is important to know how the growth of the solidification layer thickness depends on the properties of the material to be casted. With help of a known approximate solution for the one dimensional solidifcation of a body with fixed wall temperature the solidified layer thickness can be calculated. In this paper it has been done for steel. Also a temperature transition range for the solidification process has been taken into account. The results are given in a few dimensionless numbers representing the relation between the solidification front position and time. The data obtained can be used as an estimation for the effects that occur in practice with steel casting processes.     

Viscous incompressible flow over the surface of a rotary disk

Viscous incompressible film flow over the surface of an impermeable rotary disk is studied. An exact self-similar solution of the complete Navier-Stokes system of equations is obtained and the velocity and pressure fields together with the radial profiles of the fluid film are determined. A physical interpretation of the results obtained is given.Volgograd. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 39–43, November–December, 1995.     

Modeling flow induced crystallization in film casting of polypropylene

Data from iPP film casting experiments served as a basis to model the effect of flow on polymer crystallization kinetics. These data describe the temperature, width, velocity and crystallinity distributions along the drawing direction under conditions permitting crystallization along the draw length.In order to model the effect of flow on crystallization kinetics, a modification of a previously defined quiescent kinetic model was adopted. This modification consisted in using a higher melting temperature than in the original quiescent model. The reason for the modification was to account for an increase of crystallization temperature due to entropy decrease of the flowing melt. This entropy decrease was calculated from the molecular orientation on the basis of rubber elasticity theory applied to the entangled and elongated melt. The evolution of molecular orientation (elongation) during the film casting experiments was calculated using a non-linear dumbbell model which considers the relaxation time, obtained from normal stress difference and viscosity functions, to be a function of the deformation rate.The comparison between experimental distributions and model based crystallinity distributions was satisfactory.     

A new transient method for analysis of solidification in the continuous casting of metals

Solidification processes involve complex heat and mass transfer phenomena, the modelling of which requires state-of-the art numerical techniques. An efficient and accurate transient numerical method is proposed for the analysis of phase change problems. This method combines both the enthalpy and the enhanced specific heat approaches in incorporating the effects of latent heat released due to phase change. The sensitivity and accuracy of the proposed method to both temporal and spatial discretization is shown together with closed-form solutions and the results from the enhanced specific heat approach. In order to explore the proposed method fully, a non-linear heat release, as is the case for binary alloys, is also examined. The number of operations required for the new transient approach is less than or equal to the enhanced heat capacity method depending on the averaging method adopted. To demonstrate the potential of this new finite-element technique, measurements obtained on operating machines for the casting of zinc, aluminum and steel are compared with the model predictions. The death/birth technique, together with the proper heat-transfer coefficients, were employed in order to model the casting process with minimal error due to the modelling itself.Nomenclature [A] conductance matrix - [B] matrix containing the derivative of the element shape functions - c, C _p specific heat (J kg^–1°C^–1) - effective specific heat (J kg^–1°C^–1) - f(T) local liquid fraction - f thermal load vector - H enthalpy (J kg^–1) - [H] capacitance matrix - h, h _r,h _c heat transfer coefficient (W m^–2°C^–1) - K thermal conductivity (W m^–1°C^–1) - L latent heat of solidification (J kg^–1) - l overall length (m) - N _i shape functions - Q rate of heat generation per unit volume (J m^–3) - q heat flux (W m^–2) - R residual temperature (°C) - T temperature (°C) - T _s solidus temperature (°C) - T _l liquidus temperature (°C) - T _pouring pouring temperature (°C) - T _top temperature at the top of the mould (°C) - T _w temperature of the water spray (°C) - approximated temperature (°C) - T surrounding temperature (°C) - cooling rate (°C/s) - t time (seconds) - x _i,x, y, z spatial variables (m) - t time step (s) - x element size (m) - diffusivity (m²s^–1) - density (kg m^–3) - time marching parameter - _n direction cosines of the unit outward normal to the boundary     

SOLVING THE FREE BOUNDARY PROBLEM IN CONTINUOUS CASTING BY USING BOUNDARY ELEMENT METHOD

ＳＯＬＶＩＮＧＴＨＥＦＲＥＥＢＯＵＮＤＡＲＹＰＲＯＢＬＥＭＩＮＣＯＮＴＩＮＵＯＵＳＣＡＳＴＩＮＧＢＹＵＳＩＮＧＢＯＵＮＤＡＲＹＥＬＥＭＥＮＴＭＥＴＨＯＤＬｉＹａｏｙｏｎｇ（李耀勇）；ＺｈａｎｇＺｈｉｌｉ（张自立）（ＲｅｃｅｉｖｅｄＪｕｎｅ，１８，１９...     

On the continuous squeezing flow in a wedge

The paper is concerned with the continuous squeezing flow of Oldroyd-type fluids in a two-dimensional wedge. The flow mimics the lubrication action in a squeezing flow and is important in that there exists a similarity solution for any simple fluid. We are only concerned with Oldroyd-type fluids, however. It is shown by using a parameter continuation method that the Oldroyd-B model has a limiting Weissenberg number. The Phan Thien/Tanner model does not have this limiting Weissenberg number.     

The simulation of secondary flow effects in turbulent non-circular passage flows

A finite difference method has been developed to predict the overall features of the local mean flow in fully developed turbulent non-circular passage flows. The main transport effects of secondary flow have been identified and simulated with diffusion transport in a simple way which eliminates solution of the cross-plane momentum and continuity equations and produces a compact calculation method. Predictions are presented for four different passage shapes and are discussed in relation to experimental measurements and predictions from other more complex methods. Although some minor details were not predicted, the main effects of secondary flow on the mean flow were found to have been quite well simulated, yielding predictions that are in reasonable overall agreement with experiment.     

Branching of secondary modes in the flow between rotating cylinders

The steady secondary flows (Taylor vortices) of a viscous incompressible fluid between concentric rotating cylinders are studied. The range of wave numbers a and Reynolds numbers R in which there are several secondary flow modes is determined. The branching of these modes is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp.47–53, January–February, 1977.