Influence of convection and grain movement on globular equiaxed solidification

A two-phase volume averaging model was used to study convection and grain movement, and their influence on the globular equiaxed solidification. Both liquid and solid phases were treated as separate interpenetrating continua. The mass, momentum, species and enthalpy conservation equations for each phase and a grain transport equation were coupled. An ingot casting (Al-4 wt.% Cu) with near globular solidification morphology was simulated. Case studies with different modeling assumptions such as with and without grain movement, and with slip and non-slip boundary conditions for solid phase were presented and compared. Understanding of grain evolution and macrosegregation formation in globular equiaxed solidification was improved.     

Heat, mass and momentum transport behaviors in directionally solidifying blade-like castings in different electromagnetic fields described using a continuum model

A previous continuum model proposed and recently modified by the authors for describing the heat, mass and momentum transport phenomena in dendrite solidification process of alloy castings was further extended to the solidification cases in an arbitrary electromagnetic (EM)-fields. The extended continuum model and a FEM/FDM joint solution technique were successfully applied to the numerical simulations of directional solidification transport processes in blade-like castings of Pseudo-binary In718 base-4.85 wt.%Nb and Al-4.5 wt.%Cu alloys under a static or harmonic EM-field of different strengths/frequencies. The computational results demonstrate the availability of the present continuum modeling to treat an EM-STP problem, and also reveal that the volume-contraction-driven liquid feeding flow is much more difficult to be suppressed than the buoyancy-induced by means of applying a static magnetic field.     

Solidification of electrically conducting liquid flow driven by shear and pressure gradients subject to viscous and Joule heating

Solidification of a liquid in motion driven by shear and pressure gradients occurs in many natural settings and technological applications. When the liquid is electrically conducting, its solidification rates can potentially be modulated by an imposed magnetic field. The shearing motion results in viscous dissipation and the Lorentz force induced by the magnetic field causes Joule heating of the fluid, which can influence the structure of the flow, thermal fields, and thereby the solidification process. In this study, a mathematical model is developed to study the combined effects of shear and pressure gradients in the presence of a magnetic field on the solidification of a liquid between two parallel plates, with one of them being insulated and under constant motion, and the other being cooled convectively and at rest. Under the quasi-steady assumption, closed-form semianalytical solutions are obtained for the instantaneous location of the solid–liquid interface, Nusselt number, and dimensionless power density as a function of various characteristic parameters such as the Hartmann number, pressure gradient parameter, Brinkman number, and Biot number. Furthermore, an interesting remelt or steady-state condition for the interfacial location is derived as arising from the competing effects of the solid side heat flux and viscous dissipation and Joule heating on the liquid side. The newly derived analytical results are shown to reduce to the various classical results in the limiting cases. A detailed systematic study is performed by the numerical solution of the semianalytical formulation, and the effects of different characteristic parameters on the solidification process are discussed.     

Numerical prediction of a two-phase fluid driving system using cavitating flow of magnetic fluid

A new concept of a two-phase fluid driving system using cavitating flow of a magnetic fluid is proposed, and the driving and acceleration performance of the system is numerically predicted. A typical computational model for cavitating flow of a magnetic fluid is proposed and several flow characteristics, taking into account the strong nonuniform magnetic field, are numerically investigated to realize the further development and high performance of the proposed new type of two-phase fluid driving system using magnetic fluids. Based on numerical results, the two-dimensional structure of the cavitating flow as well as the cloud cavity formation of the magnetic fluid through a vertical converging–diverging channel are shown in detail. The numerical results demonstrate that an effective two-phase magnetic driving force and fluid acceleration can be obtained by the practical use of magnetization of the working fluid. Also clarified is the cavitation number in the case of a strong magnetic field with a larger value than that in the case of a nonmagnetic field. Magnetic control for suppression of cavitation bubbles is remarkably enhanced in the condition of high Reynolds number. Further clarified is the precise control of the cavitating flow of magnetic fluid that is possible by effective use of the magnetic body force that acts on cavitation bubbles.     

Analysis of magnetohydrodynamics peristaltic transport of hydrogen bubble in water

This paper established the theoretical and analytical analysis of a unidirectional laminar bubbly two-phase flow in a symmetric channel with flexible wall. The two-phase model uses water as base fluid with hydrogen bubble suspended in it. Rayleigh-Plesset equation in term of volume fraction is used to model void produce due to presence of hydrogen. The flow is driven by symmetric peristaltic movement of the wall. A uniform magnetic field in the transverse direction to peristaltic motion is applied. Homotopy perturbation Method (HPM) is utilized to formulate the series solution, after simplifying the differential governing equations under the influence of long wave length and low Reynolds number. The volume of the void and radius of the bubble is analyzed graphically. The consequence demonstrates that the void fraction bubbles rapidly approaches to unity, which is due to quasi-statically unstable. Due to Lorentz force fluid velocity suppresses by increasing the transverse magnetic field while reverse performance is noted for Weber number and power law index.     

Solidification of a pure metal in the presence of a stationary magnetic field

The role of natural and damped convections during solidification of pure tin in an annular crucible was studied. The damped convection was produced by a stationary magnetic field. Temperature measurements allowed to follow both the evolution of the solidification front and temperature distribution inside the bulk liquid with time. These experiments were performed from various degrees of superheat in the absence and presence of magnetic field. A discussion is presented relating the metallurgical findings (growing of large single crystals) to the thermal measurements.     

埋地原油管道停输期间温降及原油凝固传热模型及数值模拟

假设原油凝固区域为一固相和液相组成的动态多孔介质区域,建立了土壤、管道能量方程与原油质量、动量和能量方程相互耦合的传热模型,并对埋地原油管道停输温降过程进行了数值模拟.数值模拟结果能够合理解释停输期间温度场、凝固界面和自然对流规律.     

Effects of magnetically damped convection during the controlled solidification of metals and alloys

The role of natural and damped convection during the thermally controlled solidification of tin and aluminium alloys in a toroidal mould was studied. The damped convection was caused by a stationary and uniform magnetic field parallel to the gravity field. Temperature measurements made it possible to follow both the evolution of the solidification front and that of the temperature distribution inside the bulk liquid with time. These experiments were performed from various degrees of superheat, in the absence and presence of a magnetic field. A discussion is presented relating the crystallographical findings to the temperature field patterns.     

The study on polymer melt front,gas front and solid layer in filling stage of gas-assisted injection molding

The algorithms are developed to predict the polymer melt front, gas front and solid layer in gas-assisted injection molding. The simulation of two-dimensional, transient, non-isothermal and high viscous flow between two parallel plates with the generalized Newtonian fluid is presented in detail. During solidification while an injection mold fills, a solid-liquid interface moves and a two-phase zone exists; an enthalpy model is used to predict this interface in the two-phase flow problem. The model takes into account the three-phase flow including the effects of the gas front, solid layer and polymer melt front.     

Numerical simulation of air solidification process in liquid hydrogen with LBM-CA coupled method

The solidification process of solid-air is a significant risk in liquid hydrogen system. To predict the solidification of air in liquid hydrogen, the coupled model of Lattice Boltzmann Method (LBM) and Cellular Automation (CA) has been proposed. Results shows that the local oxygen mass ratio can reach up to 30% at 0.1s when the air-proportioned nitrogen and oxygen mixture is solidified. The LBM-CA method is further used to study the effects of forced convection on the solid-air dendrite. It is shown that the upstream latent heat and the rejected solutes accumulate in the downstream with the flow field, leading to higher oxygen concentration in the downstream as the flow velocity increases. In addition, the solid-phase fraction of solid-air increases faster with the increasing flow velocity which indicates an increasing safety risk for the liquid hydrogen with solid-air system.     

Effect of magnetic field on g-jitter induced convection and solute striation during solidification in space

A 2-D finite element model is presented for the melt growth of single crystals in a microgravity environment with a superimposed DC magnetic field. The model is developed using deforming finite element methodology and predicts steady and transient convective flows, heat transfer, solute distribution, and solidification interface morphology associated with the melt growth of single crystals in microgravity with and without an applied magnetic field. Numerical simulations were carried out for a wide range of parameters including idealized microgravity condition, synthesized g-jitter and real g-jitter data taken by on-board accelerometers during space flights. The results reveal that the time varying g-jitter disturbances, although small in magnitude, cause an appreciable convective flow in the liquid pool, which in turn produces detrimental effects during the space processing of single crystal growth. An applied magnetic field of appropriate strength, superimposed on the microgravity, can be very effective in suppressing the deleterious effects resulting from g-jitter disturbances.     

Solutocapillary convection in the float-zone process with a strong magnetic field

This paper treats the steady axisymmetric flow and mass transport in a cylindrical liquid bridge between the melting end of a feed rod and the solidifying end of an alloyed semiconductor crystal. There is a strong, uniform, steady, axial magnetic field. The surface tension depends on the temperature and the concentration of the species, while variations of the concentration occur because one species is rejected into the liquid during solidification. The thermocapillary and solutocapillary convections tend to cancel over part of the liquid bridge. For certain parameter ranges, there are two different stable solutions: one where the concentration gradient along the free surface leads to dominance by the solutocapillary convection and one where the mass transport due to the thermocapillary convection makes the concentration gradient along the free surface small, so that the thermocapillary convection is dominant.     

A numerical study of unidirectional solidification of a binary metal alloy under influence of a rotating magnetic field

In this paper we present a numerical study of the fluid flow during directional solidification of a binary alloy (Pb85wt%Sn) in presence of a forced convection. The latter is driven by a rotating magnetic field (RMF) the strength of which, expressed by the magnetic Taylor number, varies between 10⁴ < Ta < 2 × 10⁶. The focus of this paper is the problem when cooling starts simultaneously with the acceleration of the melt from a state of rest. Thus, we study the interference of the so-called spin-up problem with the solidification of the melt. The numerical simulations are based on a mixture model formulation. We show that three distinct fluid flow phases exist. During the first two phases (initial adjustment and inertial phase) the acceleration of the liquid takes place which occurs in close similarity to the isothermal spin-up [P.A. Nikrityuk, M. Ungarish, K. Eckert, R. Grundmann, Spin-up of a liquid metal flow driven by a rotating magnetic field in a finite cylinder. A numerical and analytical study, Phys. Fluids 17 (2005) 067101]. The third phase is characterized by a braking of the fluid flow due to the progressive solidification increasing the aspect ratio of the liquid (2R₀/H_l) and decreasing the forcing. We show that as soon as the velocity of the secondary flow exceeds the velocity of the solidification front, a convex shape of the mushy zone can be observed. In parallel, Taylor–Görtler vortices advected by the secondary flow towards the mushy zone might impose a wavy substructure on the latter. At the end, predictions with respect to heat flux and macrosegregations are given.     

合金凝固传热传质宏微观耦合数值研究及验证

建立了描述二元合金凝固的平面枝晶一维微观偏析数学模型,考虑溶质在固相中有限扩散,在液相中完全扩散。通过数值模拟,分析比较了A l-Cu和F e-C合金的微观偏析特性。同时,进一步将微观数值模型与宏观凝固实验的传热传质数学模型相耦合,实现了凝固宏微观复合尺度的全数值模拟。研究表明,数值计算结果与实验数据吻合良好,证明微观模型能较准确地反映微观质量传输并能可靠地与宏观相变传热传质模型相耦合。此外,从微观到宏观的计算结果都说明F e-C合金的凝固过程几乎接近平衡凝固。     

Control of macrosegregation during the solidification of alloys using magnetic fields

Numerical modeling of convection damping and macrosegregation suppression during solidification of alloys with prominent mushy zones through the use of tailored magnetic fields is demonstrated here. Macrosegregation leads to commonly observed defects such as freckles, channels and segregates in cast alloys that severely affect the performance and suitability of the alloy for further applications. The current work demonstrates the successful use of magnetic fields in suppressing thermosolutal convection and eliminating some of these defects in solidifying metallic alloys. The computational model presented utilizes volume-averaged governing transport equations and stabilized finite element techniques to discretize these equations. A finite-dimensional optimization problem, based on the continuum sensitivity method is considered to design the time history of the imposed magnetic field required to effectively damp convection. The coefficients that determine this time variation are the main design parameters of this optimization problem. Continuum sensitivity equations are derived by design-differentiating the governing equations of the direct problem. The cost functional here is given by the square of the L₂ norm of an expression representing the deviation of the volume-averaged velocity corresponding to conditions of convection less growth. The cost functional minimization process is realized through a non-linear conjugate gradient algorithm that utilizes finite element solutions of the continuum direct and sensitivity problems. Design of the time history of the imposed magnetic field is highlighted through different examples with the main objective being the suppression of convection and macrosegregation during alloy solidification.     

Heat and mass transport performance of MHD elastico-viscous fluid flow over a vertically oriented magnetized surface with magnetic and thermo diffusions

The key objective in this study is to examine the heat and mass transport behavior of magnetohydrodynamic elastic-viscous fluid flow over a vertically oriented magnetized surface placed in a uniform permeable regime with magnetic and thermo diffusions. The fluid is partially ionized and permeated to flow in the presence of a strong magnetic field domain. Hence the Hall current effect is considered in this investigation. The significance of rotation and induced magnetic field on the flowing nature are also scrutinized in this study. The mathematical model of the problem is converted to a similar model by introducing suitable nondimensional variables. To obtain the closed-form solutions of the flow leading equations, the regular perturbation analysis is utilized. For the exhibition of results, figures and tables are generated with the assistance of scientific computation software MATHEMATICA. Computed results are validated with the existing result in the limiting case. Such an investigation is important in evaluating the flow characteristics of low magnetic diffusive viscoelastic fluid. A noteworthy result seen is that magnetic diffusion significantly controls the fluid flow by altering the magnetic drag force. Mass diffusion factor brings an increase in the fluid velocity. Furthermore, we observed that the surface current density along the principal flow direction is significantly reduced by magnetic diffusion and mass diffusion factor.     

The “tornado” effect induced by magnetohydrodynamic convection in an electrolytic cell with a wire-electrode

High energy consumption is the key problem to be solved in water electrolysis for hydrogen production. Imposing magnetic field during electrolysis is proved to be a research-worthy method to reduce the required electrical energy, since the magnetohydrodynamic convection can be induced without additional energy input. Considering the structure of commercial electrolyzers, the magnetic field perpendicular to the electrode surface is most likely to be applied in practical engineering. But there is still a lack of research on the gas-liquid two-phase flow in the electrolytic cell under this condition. To avoid mutual blocking between a large number of bubbles and obtain clear two-phase flow images of the electrolysis process, a wire electrode is used as cathode to generate hydrogen bubbles in this work. The cell voltage is obviously reduced by external magnetic field, and an interesting “bubble tornado” is formed under the action of induced magnetohydrodynamic convection. The numerical simulation results and theoretical analysis indicate that: (1) the formation of the bubble chain is caused by low-pressure region along the vertical axis; (2) the unstable low-pressure region is the key factor leading to the formation of continuously deformed bubble chain; (3) the bubble dispersion may be related to Kelvin-Helmholtz flow instability. We anticipate our work being a starting point for the application of magnetic field in practical engineering.     

NUMERICAL MODELING OF INTERNAL RADIATION AND SOLIDIFICATION IN SEMITRANSPARENT MELTS IN MAGNETIC FIELDS

This article presents a numerical study on the effects of magnetic fields and internal radiation on the melt flow and solidification morphology during solidification processing of semitransparent oxide melts. The numerical solution of the integral differential equation characterizing the internal radiation and the magnetohydrodynamic equations describing the magnetic and transport phenomena is obtained by applying the combined discontinuous and continuous finite-element method. Deforming finite elements based on an arbitrary Eulerian-Lagrangian formulation are used to track the moving boundaries resulting from solidification. Computed results show that both internal radiation and external magnetic fields can have strong effects on the melt flow, temperature distribution, and solidification behavior during the melt processing of oxide materials.     

A simulation for predicting the refrigerant flow characteristics including metastable region in adiabatic capillary tubes

Assumptions that no metastable flow phenomenon and flow in two-phase region is homogeneous have been used exclusively to study the flow characteristics in capillary tubes used as an expansion and controlling device in refrigerating systems. However, some experimental results show that due to the delay of vapourization, the onset of vapourization may not take place at the end of the sub-cooled liquid region. The two-phase flow in small diameter tubes may be also not entirely homogeneous due to phase interaction. In this paper, a mathematical model based on conservations of mass, energy and momentum is presented to simulate the refrigerant flow in adiabatic capillary tubes. Different from most previous studies, the metastable flow region is accounted in the model and the annular flow is also assumed to take place in the two-phase region. The model is validated by comparing with the experimental data reported in literature. The agreement between experimental and simulation results indicates that the model with appropriate correlations of pressure at vapourization and slip ratio can be used to predict the two-phase flow behaviour of refrigerant in capillary tubes. Copyright © 2002 John Wiley & Sons, Ltd.