A 3-D numerical prediction of turbulent flow,heat transfer and solidification in a continuous slab caster for steel

This study describes the numerical modeling of three-dimensional coupled turbulent flow, heat transfer, and solidification in a continuous slab caster for stainless steel. The model uses generalized transport equations which are applicable to the liquid, mushy and solid regions within the caster. The turbulent characteristics in the melt pool and mushy region are accounted for using the low-Reynolds number k–ε turbulence model by Launder and Sharma. This version of the low-Reynolds number turbulence model is found to be more easily adaptable to the coupled flow and mushy region solidification caster problem compared to the standard high-Reynolds number and other low-Reynolds number turbulence models. The macroscopic solidification process itself is based on the enthalpy-porosity scheme. The governing transport equations are solved employing the primitive variables and using the control volume based finite-difference scheme on a staggered grid. The process variables considered are the casting speed and the inlet superheat of the melt. The effects of these process variables on the velocity and temperature distributions and on the extent of the solidification and mushy regions are reported and discussed. The numerical predictions of solidification profile are compared with the limited experimental data available in the literature, and very good agreement was found.     

A numerical and experimental study of the rate of transformation in three directionally grown peritectic systems

Three systems, Ag-Sn, Cu-Sn, and Cd-Ag, with very different peritectic phase diagrams, have been investigated. Specimens were directionally grown then quenched. The volume fraction of the two solid phases and the quenched liquid were measured using image analysis of cross sections. A numerical model was developed to calculate the quantity of the phases as a function of temperature and the results were compared with experiment. It is concluded that the quantities of the different phases can be predicted reasonably well with a simple diffusion model. The shape of the phase diagram, the size of the primary phase, and the solid-state diffusion coefficients play a crucial role in determining the volume fraction of the final products.     

Rheological behavior of Al-Cu alloys during solidification constitutive modeling,experimental identification,and numerical study

The rheological behavior of a solidifying alloy is modeled by considering the deforming material as a viscoplastic porous medium saturated with liquid. Since the solid grains in the mush do not form a fully cohesive skeleton, an internal variable that represents the partial cohesion of this porous material is introduced. The model parameters are identified using shear and compressive stress states under isothermal conditions on an Al-Cu model alloy. The model is partially validated with non-isothermal conditions and we complete this study with tensile conditions. Such conditions, when applied on the mush, may lead to severe defects in many casting processes. The model has been implemented into a commercial finite-element code to simulate a tensile test. Comparison with experimental data shows that the model is able to reproduce the main features of a solidifying alloy under tension, although fracture is not directly addressed here. We show that two critical solid fractions must be introduced in the model to account for the rheology: the coherency solid fraction at which the mush acquires significant strength and the coalescence solid fraction at which solid grains start to form solid bridges.     

An experimental and analytical study of the solidification of a binary dendritic system

Experimental measurements are reported on the controlled solidification of a 30 pct aqueous solution of ammonium chloride in a two-dimensional slot. The actual measurements taken include the transient temperature profiles, the transient velocity fields (using tracers) and photographic observations. Through the statement of the differential energy balance and the laminar Navier-Stokes equations, written for both the liquid and the two phase regions, a mathematical model has been developed for the system. The theoretically predicted temperature and velocity profiles were found to be in good agreement with the experimentally measured values for both the two phase regions and the liquid region. For the experimental conditions the velocities in the liquid region were of the order of 0.4 to 0.8 cm/s, while the corresponding values for the two phase region were at least an order of magnitude smaller.     

An experimental and analytical study of the solidification of a binary dendritic system

Experimental measurements are reported on the controlled solidification of a 30 pct aqueous solution of ammonium chloride in a two-dimensional slot. The actual measurements taken include the transient temperature profiles, the transient velocity fields (using tracers) and photographic observations. Through the statement of the differential energy balance and the laminar Navier-Stokes equations, written for both the liquid and the two phase regions, a mathematical model has been developed for the system. The theoretically predicted temperature and velocity profiles were found to be in good agreement with the experimentally measured values for both the two phase regions and the liquid region. For the experimental conditions the velocities in the liquid region were of the order of 0.4 to 0.8 cm/s, while the corresponding values for the two phase region were at least an order of magnitude smaller.     

A water-model experimental study of vortex characteristics due to nozzle clogging in slab caster mould

Vortex formation in the continuous slab casting mould is a troublesome phenomenon that can pull mould powder/slag deep down into the liquid core and potentially damage the product quality. Submerged entry nozzle (SEN) clogging is one of the prime causes of vortex formation. This work is designed to investigate and quantify the inter-related effects of nozzle clogging, casting speed (CS) and SEN submergence depth on vortex frequency and penetration depth through water-model experiments. It is observed that the increase in degree of clogging and CS has an inter-related effect on flow asymmetry and impacted the vortex characteristics. At the combination of highest values of degree of clogging and CS, vortices formed are found to have high values of top-diameter, rotational speed, penetration depth, frequency and life. On the contrary, the SEN submergence depth has showed limited effect on these aspects except the penetration depth. With the increase in SEN submergence depth values, it is found that the number of vortices having depth greater than 80?mm is increased.     

Computational and experimental study of turbulent flow in a 0.4-scale water model of a continuous steel caster

Single-phase turbulent flow in a 0.4-scale water model of a continuous steel caster is investigated using large eddy simulations (LES) and particle image velocimetry (PIV). The computational domain includes the entire submerged entry nozzle (SEN) starting from the tundish exit and the complete mold region. The results show a large, elongated recirculation zone in the SEN below the slide gate. The simulation also shows that the flow exiting the nozzle ports has a complex time-evolving pattern with strong cross-stream velocities, which is also seen in the experiments. With a few exceptions, which are probably due to uncertainties in the measurements, the computed flow field agrees with the measurements. The instantaneous jet is seen to have two typical patterns: a wobbling “stair-step” downward jet and a jet that bends upward midway between the SEN and the narrow face. A 51-second time average suppressed the asymmetries between the two halves of the upper mold region. However, the instantaneous velocity fields can be very different in the two halves. Long-term flow asymmetry is observed in the lower region. Interactions between the two halves cause large velocity fluctuations near the top surface. The effects of simplifying the computational domain and approximating the inlet conditions are presented.     

A numerical scheme for solidification of an alloy

In modeling the solidification of an alloy, two central numerical problems are:1. The calculation of thermal and species transport fields which satisfy the conservation equations and are also consistent with the underlying thermodynamics.2. The treatment of local scale solute diffusion.In this paper, in the context of modeling inverse segregation in a uni-directionally solidified casting, a recently proposed implicit⧹explicit time integration scheme for coupling thermal and solutal fields is presented and possible ways of capturing the local scale solute diffusion in a macroscopic model are explored. A key element in this work is the validation of the proposed approach by comparison with a sophisticated similarity solution. © 1998 Canadian Institute of Mining and Metallurgy.     

板坯连铸结晶器钢液行为的水模拟试验

以某钢厂250mm×2 100mm断面板坯连铸结晶器为研究对象,采用水力模拟的方法研究了拉速在0.88m/min条件下不同水口结构参数对钢液行为的影响。研究表明:1号水口(原方案)在浸入深度为57mm时,液面波峰谷差值达到3.67mm,卷渣严重,冲击深度为205mm;优化设计的5号水口在浸入深度为57mm时,液面波峰谷差值减小为2.74mm,卷渣现象基本消失,冲击深度为177mm。确定5号水口为最优水口结构参数,浸入深度以57~67mm为宜。     

Surface solidification with a moving heat source: A study of solidification parameters

The heat flow and solidification parameters, such as the temperature gradient and solid-liquid interface velocity, have been studied for the case of a moving heat source on an aluminium substrate. The problem was developed and solved for both the large initial transient and the final quasi steady state. Results indicate that exceptionally high temperature gradients may exist in the liquid pool. During the initial transient, the temperature gradient at the solid-liquid interface drops from a high value to a low one at a near constant interface velocity. These results are expected to aid in the design of solidification experiments. The predictive capacity of the model was tested by measuring the secondary dendrite arm spacing (SDAS) along the region of the initial transient on the surface of a Al-4.5% Cu alloy laser treated with a 5 kW laser. Results obtained showed the SDAS increasing to a steady state value only after the melt width had achieved a steady state, thus validating the theoretical conclusions of the model.     

An experimental and numerical study of deformation in metal-ceramic composites

The deformation characteristics of ceramic whisker- and particulate-reinforced metal-matrix composites were studied experimentally and numerically with the objective of investigating the dependence of tensile properties on the matrix microstructure and on the size, shape, and distribution of the reinforcement phase. The model systems chosen for comparison with the numerical simulations included SiC whisker-reinforced 2124 aluminum alloys with well-characterized microstructures and 1100-o aluminum reinforced with different amounts of SiC particulates. The overall constitutive response of the composite and the evolution of stress and strain field quantities in the matrix of the composite were computed using finite element models within the context of axisymmetric and plane strain unit cell formulations. The results indicated that the development of significant triaxial stresses within the composite matrix, due to the constraint imposed by the reinforcements, provides an important contribution to strengthening. Systematic calculations of the alterations in matrix field quantities in response to controlled changes in reinforcement distribution give valuable insights into the effects of particle clustering on the tensile properties. The numerical results also deliver a mechanistic rationale for experimentally observed trends on: (i) the effects of reinforcement morphology and volume fraction on yield and strain hardening behavior of the composite, (ii) the pronounced influence of reinforcement clustering on the overall constitutive response, (iii) ductile failure by void growth within the composite matrix, (iv) the insensitivity of the yield strength of the composite to changes in matrix microstructure, and (v) the dependence of ductility on the microstructure of the matrix and on the morphology and distribution of the reinforcement. The predictions of the present analyses are compared and contrasted with current theories of elastic and plastic response in multi-phase materials in an attempt to develop an overall perspective on the mechanisms of composite strengthening and of matrix and interfacial failure.     

Heat transport and solidification in the electromagnetic casting of aluminum alloys: Part I. Experimental measurements on a pilot-scale caster

While many investigators have examined electromagnetic and magnetohydrodynamics phenomena in electromagnetic casting (EMC) of aluminum, there appears to be no published work on heat transport and solidification in such casters. This two-part series is an attempt to remedy this deficiency. The first part describes two experimental campaigns, carried out on a pilot-scale electromagnetic caster at Reynolds Metals Company, in which sacrificial thermocouples were used to obtain many data on temperature distributions within the aluminum of a pilot-scale caster and thereby to obtain the shape of the liquid metal pool (“sump”). The data reveal a strong dependence of temperature distribution and sump depth on casting speed but a relatively weak dependence on the flow rate of the quenching water striking the outside of the ingot.     

仿真计算在板坯连铸机工程设计中的应用

针对板坯连铸机设计,采用数值仿真技术（基于板坯连铸浇铸过程静态仿真软件CCPS OFFLINE）对二次冷却水量进行了优化计算,并对结晶器锥度、扇形段辊缝和铸坯应变分布等相关的重要工艺／结构参数进行了理论预测。部分研究成果已投入到某钢厂板坯连铸机的实际生产运用中,取得了较好的效果,并在其新建板坯连铸机的设计工作中进行了充分应用。     

A numerical and experimental study of deformation characteristics of the plane strain punch stretching test

Recently, a simple new test method called the plane strain stretching (PSS) test has been developed to evaluate the stamping formability of sheet materials. The PSS test has been proven to have good reproducibility and show good correlation with press performance. In order to clarify the deformation characteristics of the PSS test and investigate the effect of material and process variables on the performance of the PSS test, three-dimensional finite element simulations for the PSS test were performed and the results compared with experiments.     

Analytical,numerical, and experimental analysis of inverse macrosegregation during upward unidirectional solidification of Al-Cu alloys

The present work focuses on the influence of alloy solute content, melt superheat, and metal/mold heat transfer on inverse segregation during upward solidification of Al-Cu alloys. The experimental segregation profiles of Al 4.5 wt pct Cu, 6.2 wt pct Cu, and 8.1 wt pct Cu alloys are compared with theoretical predictions furnished by analytical and numerical models, with transient h _i profiles being determined in each experiment. The analytical model is based on an analytical heat-transfer model coupled with the classical local solute redistribution equation proposed by Flemings and Nereo. The numerical model is that proposed by Voller, with some changes introduced to take into account different thermophysical properties for the liquid and solid phases, time variable metal/mold interface heat-transfer coefficient, and a variable space grid to assure the accuracy of results without raising the number of nodes. It was observed that the numerical predictions generally conform with the experimental segregation measurements and that the predicted analytical segregation, despite its simplicity, also compares favorably with the experimental scatter except for high melt superheat.     

Effect of in-mould electromagnetic stirring on the flow,initial solidification and level fluctuation in a slab mould: a numerical simulation study

In-mould electromagnetic stirring (M-EMS) is a widely used technique during slab continuous casting. To investigate the effect of M-EMS on the flow and initial solidification in a slab mould, a three-dimensional model coupling electromagnetic field, flow and solidification was developed. To track the steel/slag interface, the volume of fraction (VOF) model was coupled in the model. The electromagnetic force presents a centrally symmetrical distribution on the cross-section. The influences of stirring current and stirrer position on flow, initial solidification and level fluctuation have been discussed. M-EMS enhances the transversal flow and shrinks the lower recirculation in mould. The results indicate that both a higher stirring current and a lower stirrer position produce a reduction of the temperature in the mould centre. Furthermore, a higher stirrer position and a lower stirring current are favourable to the solidified shell growth. However, M-EMS aggravates the level fluctuation, which may lead to slag entrainment.     

A study of the solidification of argon bubbles in aluminium

A study has been carried out of the solidification of argon in a wide range of argon bubble sizes in aluminium. Using a cryogenic stage samples have been cooled to 78K and the freezing range and lattice parameter of solid argon determined. The results indicate that for very small crystal sizes diffraction from argon will be difficult to detect, at intermediate sizes the argon solidifies epitaxially with the host matrix and for large bubble sizes random crystals may form.     

An experimental and numerical study of cyclic deformation in metal-matrix composites

The cyclic stress-strain characteristics of discontinuously reinforced metal-matrix composites are studied both experimentally and numerically. The model systems used for investigation are aluminum alloys reinforced with SiC particulates and whiskers. Finite element analyses of the fatigue deformation of the composite are performed within the context of axisymmetric unit cell formulations. Two constitutive relations are used to characterize the matrix of the composite: the fully dense Mises model of an isotropically hardening elastic-viscoplastic solid and the Gurson model of a progressively cavitating elastic-viscoplastic solid (to simulate ductile matrix failure by the nucleation and growth of voids). The brittle reinforcement phase is modeled as elastic, and the interface between the ductile matrix and the reinforcement is taken to be perfectly bonded. The analyses provide insights into the effects of reinforcement shape and concentration on (1) constrained matrix deformation under cyclic loading conditions, (2) cyclic hardening and saturation, (3) the onset and progression of plastic flow and cavitation within the matrix, and (4) cyclic ductility. The numerical predictions of flow strength, strain hardening, evolution of matrix field quantities, and ductility under cyclic loading conditions are compared with those predicted for monotonic tensile deformation and with experimental observations. formerly Visiting Scientist, Division of Engineering, Brown University     

A melting and solidification study of alloy 625

The melting and solidification behavior of Alloy 625 has been investigated with differential thermal analysis (DTA) and electron microscopy. A two-level full-factorial set of chemistries involving the elements Nb, C, and Si was studied. DTA results revealed that all alloying additions decreased the liquidus and solidus temperatures and also increased the melting temperature range. Terminal solidification reactions were observed in the Nb-bearing alloys. Solidification microstructures in gastungsten-arc welds were characterized with transmission electron microscopy (TEM) techniques. All alloys solidified to an austenitic (γ) matrix. The Nb-bearing alloys terminated solidification by forming various combinations of γ/MC(NbC), γ/Laves, and γ/M₆C eutectic-like constituents. Carbon additions (0.035 wt pct) promoted the formation of the γ/MC(NbC) constituent at the expense of the γ/Laves constituent. Silicon (0.4 wt pct) increased the formation of the yJLaves constituent and promoted formation of the γ/M₆C carbide constituent at low levels (<0.01 wt pct) of carbon. When both Si (0.4 wt pct) and C (0.035 wt pct) were present, the γ/MC(NbC) and γ/Laves constituents were observed. Regression analysis was used to develop equations for the liquidus and solidus temperatures as functions of alloy composition. Partial derivatives of these equations taken with respect to the alloying variables (Nb, C, Si) yielded the liquidus and solidus slopes t(m _L , m _S ) for these elements in the multicomponent system. Ratios of these liquidus to solidus slopes gave estimates of the distribution coefficients (k) for these same elements in Alloy 625.