Mushy Zone Thickness Research Articles

Importance of Melt Flow in Solidifying Mushy Zone~!2009-09-25~!2010-02-26~!2010-04-16~!

A mixture solidification model is employed to study the interaction between the melt flow and the growing mushy zone. The goal is to address the importance of considering the melt flow and flow pattern (laminar or turbulent) in the growing mushy zone. A simple 2D benchmark with parallel flow passing by/through a vertically growing mushy zone is considered. Parameter studies with different velocities and flow patterns are performed. It is found that the flow velocity and flow pattern in and near the mushy zone plays an extremely important role in the formation of the mushy zone. The mushy zone thickness is dramatically reduced with the increasing melt velocity. Simulations with/without considering turbulence show significantly different results. The turbulence in the mushy zone is currently modeled with a simple assumption that the turbulence kinetic energy is linearly reduced with the mush permeability.

Optimal operation of alloy material in solidification processes with inverse heat transfer

A transient nonlinear inverse heat transfer problem arising from alloy solidification processes is considered. In practice, the solidus and liquidus interface motions and thus the mushy zone thicknesses are pre-given to control the material quality. To achieve the desired front motions, the required time-dependent boundary conditions have to be predicted on both mold sides simultaneously. In this study, the enthalpy method is used for the derivation of governing equations. Hence, the inverse problem will be solved only in a single spatial and temporal domain. The conjugate gradient method with adjoint equation is applied for the resulting minimization problem. The method is applied as comparison for pure material with other previous studies. Then, alloy material with different front velocities is set up to investigate the solidification process. The obtained results show a close agreement between the desired and computed front motions and mushy zone thickness.

On the Stefan problem with volumetric energy generation

This paper presents results of solid–liquid phase change, driven by volumetric energy generation (VEG), in a vertical cylinder. We show excellent agreement between a quasi-static, approximate analytical solution valid for Stefan numbers less than one, and a computational model solved using the computational fluid dynamics code FLUENT®. A computational study also shows the effect that the VEG has on both the mushy zone thickness and convection in the melt during phase change.

Modelling of a thin mushy layer evolution during binary solid-liquid interactions

Further development of the Brody-Flemings approximation in application to a thin mushy zone at the interface between binary liquid and solid phases, typical in the context of corium evolution in the reactor pressure vessel during severe accidents at nuclear power plants, is presented. The main assumption of the Brody-Flemings approximation concerning local equilibrium between the solid and liquid phases in the two-phase zone is confirmed for the considered case of a thin mushy layer and supplemented with the heat and diffusion flux matches at its interfaces. The approach allows a relatively simple description of the mass and heat transfer through the mushy zone along with the zone formation, growth and/or shrinkage (depending on varying external conditions) in the course of solid-liquid material interactions. In order to prove consistency of the developed approach, two important limiting cases, when the solidification rate is controlled either by the diffusion of heat or by solute diffusion, are studied analytically in a steady-state approximation. It is shown that in both limiting cases, explicit expressions for the mushy zone thickness are directly associated with the criterion of the plane front instability. In particular, this implies that the emergence or vanishing of the mushy zone in the course of liquid-solid interactions is described in a self-consistent manner in the developed approach.

Numerical Studies on Channel Formation and Growth During Solidification: Effect of Process Parameters

In the present work, solidification of a hyper-eutectic ammonium chloride solution in a bottom-cooled cavity (i.e. with stable thermal gradient) is numerically studied. A Rayleigh number based criterion is developed, which determines the conditions favorable for freckles formation. This criterion, when expressed in terms of physical properties and process parameters, yields the condition for plume formation as a function of concentration, liquid fraction, permeability, growth rate of a mushy layer, and thermophysical properties. Subsequently, numerical simulations are performed for cases with initial and boundary conditions favoring freckle formation. The effects of parameters, such as cooling rate and initial concentration, on the formation and growth of freckles are investigated. It was found that a high cooling rate produced larger and more defined channels which are retained for a longer durations. Similarly, a lower initial concentration of solute resulted in fewer but more pronounced channels. The number and size of channels are also found to be related to the mushy zone thickness. The trends predicted with regard to the variation of number of channels with time under different process conditions are in accordance with the experimental observations reported in the literature.

One-dimensional solidification of an alloy with a mushy zone: thermodiffusion and temperature-dependent diffusivity

The effect of a temperature-dependent solute diffusion coefficient on a model of unidirectional solidification of a binary melt with a quasi-equilibrium mushy (two-phase) zone is studied. The Soret effect (thermodiffusion) is also included in the analysis. The concentration field in the liquid, solid and mushy phases, as well as the rate of solidification and mushy zone thickness, are found analytically as functions of all thermophysical parameters. The role of the nonlinear solute transport is detailed in the analysis. On the basis of analytical solutions, the regime of solidification with a quasi-equilibrium mushy zone is replaced by an equivalent discontinuity surface (frontal) regime with new boundary conditions

An experimental study on channels formation during solidification of aqueous ammonium chloride

The formation of freckles during the unidirectional solidification of aqueous ammonium chloride inside a test cell cooled from the bottom was investigated experimentally with and without the vibration of the test cell. The effects of base temperature, initial concentration, inclination of the test cell, vibration amplitudes and vibration frequencies on the channel formation inside a test cell were investigated. Experiments were carried out for 15%, 25%, 30% and 32% NH 4Cl concentrations, at base plate temperatures of −21, −26 and −38 °C, and at inclination of 0–30° from the vertical, and vibrated at several amplitudes of 2.54, 4.45 and 6.35 mm under vibration frequencies from 10 to 50 Hz. The experimental results show that channels are formed during the solidification for all concentrations except at the 15% concentration. The channels formed during solidification are observed to be more pronounced and lesser in number with increasing concentration. The channels formed decreases in number with decreasing base plate temperature. Channel suppression is influenced by the vibration amplitude, with the larger-amplitude vibration being more effective. The application of vibration to the test cell shows that the mushy zone thickness and the number of channels are reduced. Vibration at a lower frequency of 10 Hz does not suppress the formation of channels as good as vibration at a higher frequency of 50 Hz. The suppression effect of the inclination angle on the occurrence of channels is observed to be insignificant.

An experimental investigation on freckles formation during solidification of aqueous ammonium chloride

The formation of freckles during the unidirectional solidification of aqueous ammonium chloride from the bottom is investigated experimentally under a constant base temperature of -27 °C. The test rig could be inclined at15° and 30° and vibrated at several amplitudes of 2.54 mm, 4.45 mm and 6.35 mm under a constant frequency of 20 Hz. The effects of inclination angle and vibration on the freckles formation are investigated from the observations of channels and temperature distribution inside the solid and mushy zone. The application of vibration to the test cell shows that the mushy zone thickness and the number of channels are reduced. Channel suppression is influenced by the vibration amplitude, with the larger-amplitude vibration being more effective. The effect of inclination angle on the suppression on the occurrence of channels is negative.

A Parametric Study of Solute Redistribution DuringTransient Liquid Phase Diffusion Bonding Process

A parametric study is performed to investigate the solute redistribution during the transient liquid phase (TLP) diffusion bonding process. The macroscopic solute diffusion in the liquid and the solid phase, as well as the solid transformation to the liquid due to solute macrosegregation, are considered in this study. The effects of the following parameters are considered: ratio of solute diffusivity in liquid and solid state alloy (ξ = Dl/Ds), holding temperatures (θ), a combined parameter related to solidus and liquidus slopes in the phase diagram (ϕ), and the re‐melting and re‐solidification time (τ). The thickness of the pure liquid zone and the mushy zone of the TLP diffusion bonding process are demonstrated with respect to the above‐mentioned parameters. It is shown numerically that the holding time, the holding temperature, and solute diffusivity ratio influence the solute distribution strongly, which in turn influences the liquid zone and mushy zone thickness significantly. It is concluded that for the TLP diffusion bonding process, the optimal technique parameters are high holding temperature, long holding time, and a large liquidus and solidus temperature slope ratio (ml/ms) of the interlayer material.

A Thermal Model for Mushy Zone Formation in Binary Solutions

In this paper, the solidification of a binary solution on a cold isothermal surface will be studied by using an inetgral approximate method. The advantage of solving the solidification of a binary solution using an integral approximate method is that the mushy zone thickness will be able to be expressed as a simple algebraic equation which can be easily solved

Formation and suppression of channels during upward solidification of a binary mixture

Characteristics of the mushy zone were experimentally investigated in the upward solidification of a binary mixture. The formation of channels and techniques for their suppression were ex-plored. The experiments were carried out in a rectangular test section using aqueous ammonium chloride as the phase-change material at hypo- and hypereutectic concentrations ranging from 15 to 33 wt pct of salt. The cold-plate temperature was varied in the range of -60 ‡C to-14 ‡C. Transient temperature profiles as well as the positions of the liquidus and solidus interfaces were obtained. The mushy-zone characteristics, the nature and distribution of chan-nels, and the associated fluid flows were studied as a function of initial solution concentration and cold-plate temperature. The application of low-amplitude vibration to the test cell was found to reduce the mushy-zone thickness and the number of channels for all concentrations; chan-neling was almost completely suppressed at the lower concentrations. Channel suppression was influenced by vibration amplitude rather than frequency, with the larger-amplitude vibration being the more effective. The vibration results suggest that the formation and sustenance of channels is influenced more by developments within the mushy zone than by bulk liquid behavior.