Shape Of Solidification Front Research Articles

Interactions between a cavitation bubble and solidification front under the effects of ultrasound: Experiments and lattice Boltzmann modeling.

The phenomena of melting and dendritic fragmentation are captured by using an in-situ device during the ultrasound-assisted solidification of a succinonitrile-acetone (SCN-ACE) alloy. The experimental results show that the dendrite arms detach from primary trunk due to the melting of the solid phase, which is caused by a moving ultrasound cavitation bubble. To quantify the interactions between the ultrasound cavitation bubble and the solidification front, a coupled lattice Boltzmann (LB) model is developed for describing the fields of temperature, flow, and solid fraction, and their interactions. The multi-relaxation-time (MRT) scheme is applied in the LB model to calculate the liquid-gas flow field, while the Bhatnagar-Gross-Krook (BGK) equation is executed to simulate the evolution of temperature. The kinetics of solidification and melting are calculated according to the lever rule based on the SCN-ACE phase diagram. After the validation of the LB model by an analytical model, the morphologies of the cavitation bubble and solidification front are simulated. It is revealed that the solidification interface melts due to the increase of the temperature nearby the cavitation bubble in ultrasonic field. The simulated morphologies of the cavitation bubble and solidification front are compared well with the experimental micrograph. Quantitative investigations are carried out for analyzing the melting rate of the solidification front under different conditions. The simulated data obtained from LB modeling and theoretical predictions reasonably accord with the experimental results, demonstrating that the larger the ultrasonic intensity, the faster the melting rate. The present study not only reveals the evolution of the solidification front shape caused by the cavitation bubbles, which is invisible in the ultrasound-assisted solidification process of practical alloys, but also reproduces the complex interactions among the temperature field, acoustic streaming, and multi-phase flows.

Solidification front shape control through modulating the traveling magnetic field

This paper is concerned with studying the process of indirect control of the molten metal solidification front by means of modulating power supply of a linear induction machine (LIM). The influence of the LIM power supply mode on the flow in the molten metal is considered. The structure of the flow and the position of the solidification front are determined by a noninvasive method using an ultrasonic Doppler velocimeter. The obtained experimental data are used to determine the shape of solidification front profiles for four LIM power supply modes, and to establish the dependence of the shape of the front profiles on the characteristics of the supply current (magnitude and period of low-frequency modulation). A comparative analysis of the interphase boundary smoothing is carried out for different power supply modes of the LIM.

Parameter study of traveling magnetic field for control of melt convection in directional solidification of crystalline silicon ingots

Melt convection plays a critical role in the quality of crystalline silicon ingots produced by directional solidification (DS), through influencing the solidification front shape and impurities distribution. The utilization of a traveling magnetic field (TMF) is a promising way to control melt convection pattern. Lorentz forces induced by a TMF will present various characteristics under different imposed electric current parameters, such as current amplitude, frequency and phase shift. Understanding the effects of current parameters on melt convection pattern is crucial for the selection of suitable parameters to achieve the enhancement of melt mixing and a preferable solidification front. Based on a coupled model of global heat transfer, this paper explores the effects of these current parameters on the melt convection pattern in a DS furnace of crystalline silicon ingots under the action of a downward TMF. The melt mixing effect and solidification front shape are further elucidated based on different melt convection patterns. The results indicate that the effects of current parameters on the melt mixing effect and solidification front shape is quite complicated, which is not monotonous. By precisely tailoring the combination of current parameters, a flat or slightly convex solidification front and decent melt mixing are simultaneously obtained. This study can facilitate the successful and optimum utilization of a TMF in the DS process of crystalline silicon ingots.

Sessile droplet freezing on polished and micro-micro-hierarchical silicon surfaces

Droplet freezing on a polished silicon wafer and a micro-micro-hierarchically structured silicon surface, the contact angles of water (at 25.7 °C) on which were 78.77° and 143.82° respectively, were experimentally observed. The surface temperature was maintained at −6.3 °C. Combining high-resolution photography and infrared thermometry, the ice nucleation onset of the droplet was captured. It is found that the hierarchical surface remarkably postpones the ice nucleation compared with the hydrophilic polished silicon because of enhanced free energy barrier for nucleation. The unique micro-micro-scale topology determines the dominance of wetting characteristics on ice nucleation. Besides, the formation of ice shell is initiated randomly at the water-surface-air trijunction base and propagated both circumferentially and vertically upwards during the surface recalescence stage. Subsequently, the internal solidification proceeds from bottom up when the ice shell develops. Moreover, the duration of surface recalescence and internal solidification stages, as well as the shape of solidification front (SF) are evaluated based on the local droplet surface temperatures. The surface recalescence begins simultaneously but ends earlier as closer to the droplet bottom. The temperature at SF edge is higher than that in the middle. Compared with the fully frozen solid cooling stage, the heat transfer rate is much higher during internal solidification.

Numerical and experimental study of the traveling magnetic field effect on the horizontal solidification in a rectangular cavity part 2: Acting forces ratio and solidification parameters

In recent decades, many phase change processes in metals have been optimized using traveling magnetic fields due to a better understanding of their electromagnetic impact in such applications. In this paper, numerical and experimental study of the effect of traveling magnetic field on the solidification process was evaluated. A three-dimensional numerical model based on the multi-domain method was used to analyze the process of gallium horizontal solidification under the electromagnetic impact in a laboratory-size rectangular cavity. A linear inductor creating traveling magnetic field was designed and built for appropriate measurements and validation the calculations. The analysis was focused on the influence of the ratio between the applied electromagnetic forces and natural convective forces on the solidification front location and shape and on the velocity field. Since the overall electromagnetic force impact on the melt reduced during the solidification, when the melt area was converting into a solid, a new approach to control the solidification parameters was analyzed. In this approach, the value of electromagnetic force acting on the remaining melt during the process was maintained. The main result is the development and improvement of an effective tool for the analysis of direct solidification parameters.The experimental setup included an ultrasonic Doppler velocimeter (UDV) for noninvasive measurements of the velocities in the liquid part of the metal and the liquid-solid interface position, its profile and displacement. All important characteristics of the process were measured, and the results of computations agreed well enough with experimentally obtained data.

Comparison of Three-Dimensional Multidomain and Single-Domain Models for the Horizontal Solidification Problem

In this paper, horizontal solidification of gallium in a rectangular cavity was studied both experimentally and numerically. Two three-dimensional (3D) numerical models related to different numerical approaches were built. The first is a single-domain (SD) model based on the volume-of-fluid (VOF) method. This model also takes into account the presence of a mushy zone. The second model is a multidomain (MD) one; it includes two different meshes for the two phases and uses Stephan's boundary condition to determine the front velocity. The 3D models were tested under various thermal boundary conditions and compared with experimental results obtained in an appropriate experimental setup. The experimental setup included an ultrasonic Doppler velocimeter (UDV) for noninvasive measurements of the velocities in the liquid part of the metal, liquid–solid interface position and profile, its displacement, and longitudinal mean velocity. For determining the boundary influence, both 3D and 2D models were built. The comparison was carried out for the solidification front location and shape and the velocity and temperature fields. In general, the 3D numerical model gave more accurate results than the 2D model with respect to the experiments results. Although the MD model is more complicated to build and requires more computational efforts than the VOF model, the 3D MD model provides the most accurate results in comparison with current experiments.

Control of liquidus isotherm shape during solidification of Ni-based superalloy of single crystal platforms

The influence of internal thermal baffle between casting and central rod of the ceramic mould on the shape of liquidus isotherm was studied. Convex or nearly flat shape of solidification front was obtained after selection of suitable location of internal thermal baffle relative to the platform, based on measured and predicted temperature distribution. The results were compared with those acquired for castings manufactured with the use of standard mould. Application of internal thermal baffle brought about decrease of solidification front curvature, as well as transverse temperature gradient Gx=0.2°C/mm and maximum undercooling value ΔTm=16.5°C, which succeeded in proper growth of dendrites compared with Gx=2.8°C/mm and ΔTm=36.5°C in the mould without internal baffle. The convex shape of liquidus isotherm induced directional course of solidification process in the area, where casting cross-section changed significantly its dimensions, but it also led to excessive growth of shrinkage porosity on the platform surface. The increase of the distance between the platform and thermal baffle resulted in significant reduction of amount and size of pores along the length of the internal zone of platform.

Controlling solidification front shape and thermal stress in growing quasi-single-crystal silicon ingots: Process design for seeded directional solidification

To control the solidification front shape and thermal stress in the growing silicon ingot and reduce the small-grain region at its periphery, a moving insulation partition block was designed in an industrial seeded directional solidification furnace for quasi-single-crystal silicon ingots. We propose several moving process designs of the partition block. A transient global model of heat transfer in which all types of heat transfer are included was established to investigate the thermal field, solidification front evolution, and thermal stress in the growing ingot. Corresponding experiments were conducted to validate the simulation results through the relationship between solidification front shape and the small-grain region. It was found that the moving process can significantly influence the thermal field, solidification front shape, and thermal stress in the growing ingot during the solidification process. The moving partition block design is feasible to control the solidification front shape and reduce the small-grain region at the periphery of the solidified ingot. A favorable moving process design of the partition block was obtained that can simultaneously achieve a small small-grain region and low thermal stress in the solidified ingot.

EFFECT OF WITHDRAWING RATE ON PORE MORPHOLOGY OF LOTUS-TYPE POROUS COPPER PRODUCED BY SINGLE-MOLD GASAR TECHNIQUE

A single mold Gasar process was developed to fabricate lotus-type porous copper with long and straight pores. The effects of withdrawing rate on the solidification front shape, pore morphology and average solid- ification rate of porous copper ingots were investigated through experimental study and Procast simulation. The re- sults show that the solidification front shape evolves from convex to planar, then to concave with increasing with- drawing rate. In this work, 1.0 mm/s is an appropriate rate for planar solidification front. In this case, all of the gas pores grow along the axial direction (parallel to the withdrawing direction) and the poresstraightness is the best. The average porosities of copper ingots are constant and independent of the withdrawing rate. But the average pore

Effect of Grain Orientation and Cooling Rate on Stress Distribution in a Small-scale Silicon Ingot

Small-scale solidification simulations were carried out in order to study the effect of the grain orientation and cooling rate on the stresses in mono- and bi-crystals. First, a 2D-axisymetric heat-transfer model of the global furnace is established to provide input to the sub-model. The sub-model takes into account only the crucible and silicon ingot. The flux histories are transferred from the global model. A finite element crystal plasticity model solves the mechanical deformation in the ingot. Ingots were grown in the small-scale Bridgman furnace with different pulling rates ranging from 0.2 to 50 mm/min. The results show the asymmetric effect of the crystal orientation and the stress build-up at the grain boundary due to different orientations. The change in pulling rate affects strongly the solidification front shape and the residual stresses. The 3D mechanical model illustrates also the limitations of the 2D-axisymmetric approach when silicon crystal anisotropy is taken into account.

Numerical and Experimental Study of the Influence of Thermal Processes on the Shape of Solidification Front in Czochralski Model for Heptadecane and Gallium

Convective heat transfer and solidification have been studied using a simplified but unified simulation/experimental model of the Czochralsky method for two materials with melting points close to room temperature: heptadecane (low heat conductivity) and gallium (high heat conductivity). Due to the transparency of the heptadecane melt we have been able to visualize the melt flow patterns and the solidified structures in a laboratory experiment to provide the simulation model with source data. Based on calculations we have studied the parameters of melt flow patterns, heat flows on the cooled disc and the dependence of solidification front shape for both materials on convective heat transfer modes: thermogravity and mixed (i.e. with additional crystal rotation) convection.

Solidification front shape of the molten metal in a thermally thin cylinder

Reported data are reviewed briefly. When a molten metal is extruded to produce a wire directly from the melt, a capillary stream 0.2–3 mm in diameter is directed into a cooling medium so that external heat exchange ensures faster solidification of the metal as compared to capillary disintegration of the stream into drops. The following two assumptions regarding the shape of the solidification front exist: a planar solidification front normal to the axis and a curved axisymmetric front surface. Both assumptions are considered. The assumption of a curved axisymmetric solidification front surface of the molten metal in a cylinder is shown to be more realistic.

Microstructural characterization of Co-based coating deposited by low power pulse laser cladding

A detailed microstructural study of Stellite 6 coating deposited on a low carbon ferritic steel substrate using preplaced powder method and low power Nd:YAG pulse laser is performed. The grain structure and solidification texture of the coating are investigated by orientation imaging microscopy (OIM) and scanning electron microscopy. In addition, the effect of consecutive pulses on the microstructure of the coating is examined. The orientation relationship (OR) at coating/substrate interface and the solid state phase transformation in heat-affected zone are studied as well as the Vickers microhardness profile measurement in order to support the microstructural observations. An important conclusion is reached that the shape of solidification front during pulsed laser cladding is similar to the shape of solidification front during continuous cladding with a doubled laser beam scanning speed. Further, OIM reveals the Greninger–Troiano OR between the face centered cubic coating and bcc substrate grains. It is concluded that at the moment of solidification epitaxial growth of the grains in the coating occur on the austenitic grains of the substrate and that an austenite–ferrite transformation occurs in the heat-affected zone upon subsequent cooling.

Experimental and numerical modelling of the flow field in a CuxSny direct chill caster

To investigate the influence of the casting speed on the flow field and the shape of the solidification front in an industrial bronze caster, numerical calculations have been performed and experimental flow field measurements were used to validate the numerical model. Both numerical and experimental model represented 1:1 the real caster geometry of 820 × 250 × 800 mm3. A steady-state calculation, considering solidification and turbulent flow, was performed. Furthermore, a 1:1 water model of the industrial bronze caster has been built and combined with a Particle Image Velocity (PIV) setup to measure the apparent flow fields. Amongst other parameters, the numerical model provided information on the influence of the casting speed on the solidification front shape. The water model gave the experimentalist the facility to adjust the shape of the solidification front to the one predicted by the numerical model and compare the resulting flow field with the numerical prediction. This work presents a comparison of the results of both numerical and experimental models for different casting speeds with the same numerical parameters and boundary conditions.

Growth of Al 2O 3/ZrO 2(Y 2O 3) eutectic rods by the laser floating zone technique: effect of the rotation

The laser floating zone technique has been applied to the growth of Al 2O 3/ZrO 2(Y 2O 3) rods in the eutectic composition to reveal the effect of forced convection induced by rotation on the rod microstructure. A systematic experimental study of this effect has been carried out combining different source rod and/or eutectic rod rotation (0–200 rpm) and travelling speeds (10–1500 mm/h) in an axial thermal gradient close to 6 × 10 5 C/m. The results indicate that the rotation is useful to achieve a more homogeneous temperature distribution, especially in thick rods but it has a limited effect in the change of the solidification front shape. The forced convection in the floating zone caused by rotation slightly flattens the solidification interface enhancing the homogeneity of the phase distribution across the sample. However, it introduces several new microstructural features like banding and phase coarsening that can deteriorate the mechanical behaviour of the rods. On the other hand, rods above 1.6 mm in diameter cannot be grown without cracks, even with fast eutectic rod rotation. Rotation does not change the pulling rate threshold (50 mm/h) at which the transition from coupled to dendritic and cellular growth morphology takes place.

Optimization of Wall Electrodes for Electro-Hydrodynamic Control of Natural Convection during Solidification**

This article presents a numerical procedure to reduce and possibly control the natural convection effects in a cavity filled with a molten material by applying an external electric field whose intensity and spatial distributions are obtained by the use of a hybrid optimizer. This conceptually new approach to manufacturing could be used in creation of layered and functionally graded materials and objects. In the case of steady electro-hydrodynamics (EHD), the flow-field of electrically charged particles in a solidifying melt is influenced by an externally applied electric field while the existence of any magnetic field is neglected. Solidification front shape, distribution of the charged particles in the accrued solid, and the amount of accrued solid phase in such processes can be influenced by an appropriate distribution and orientation of the electric field. The intensities of the electrodes along the boundaries of the cavity were described using B-splines. The inverse problem was then formulated to find the electric boundary conditions (the coefficients of the B-splines) in such a way that the gradients of temperature along the horizontal direction are minimized. For this task we used a hybrid optimization algorithm that incorporates several of the most popular optimization modules; the Davidon-Fletcher-Powell (DFP) gradient method, a genetic algorithm (GA), the Nelder-Mead (NM) simplex method, the quasi-Newton algorithm of Pshenichny-Danilin (LM), differential evolution (DE), and sequential quadratic programming (SQP). The transient Navier-Stokes and Maxwell equations were discretized using the finite volume method in a generalized, curvilinear nonorthogonal coordinate system. For the phase change problems, we used the enthalpy method. **This paper was presented at the International Mechanical Engineering Congress and Exhibition (IMECE'03), Washington, D.C., USA, November 16–21, 2003 as American Society of Mechanical Engineers (ASME) paper IMECE 2003–41703.

Optimization of Wall Electrodes for Electro-Hydrodynamic Control of Natural Convection during Solidification**

Abstract This article presents a numerical procedure to reduce and possibly control the natural convection effects in a cavity filled with a molten material by applying an external electric field whose intensity and spatial distributions are obtained by the use of a hybrid optimizer. This conceptually new approach to manufacturing could be used in creation of layered and functionally graded materials and objects. In the case of steady electro-hydrodynamics (EHD), the flow-field of electrically charged particles in a solidifying melt is influenced by an externally applied electric field while the existence of any magnetic field is neglected. Solidification front shape, distribution of the charged particles in the accrued solid, and the amount of accrued solid phase in such processes can be influenced by an appropriate distribution and orientation of the electric field. The intensities of the electrodes along the boundaries of the cavity were described using B-splines. The inverse problem was then formulated to find the electric boundary conditions (the coefficients of the B-splines) in such a way that the gradients of temperature along the horizontal direction are minimized. For this task we used a hybrid optimization algorithm that incorporates several of the most popular optimization modules; the Davidon-Fletcher-Powell (DFP) gradient method, a genetic algorithm (GA), the Nelder-Mead (NM) simplex method, the quasi-Newton algorithm of Pshenichny-Danilin (LM), differential evolution (DE), and sequential quadratic programming (SQP). The transient Navier-Stokes and Maxwell equations were discretized using the finite volume method in a generalized, curvilinear nonorthogonal coordinate system. For the phase change problems, we used the enthalpy method.

Numerical simulation of gravitational effects during directional solidification

Two kinds of methods are considered for the investigation of crystal growth systems. The homogenization method is used for simulating the shape of solidification front and its motion. The interface during growth is investigated for various values of the growing parameters (Ra, Pe, …). The spectral method is used for the analysis of the complex fluid dynamics in the melt phase (instability, bifurcation, time dependency …). The relevant instability and time-dependent regimes are studied and some effects of a magnetic field are presented for the control of convection.

Process Analysis of Non-contact Continuous Casting of Materials Using Cold Crucible.

An axi-symmetric process model for the cold crucible continuous casting is developed based on analyses of elctromagnetic and temperature fields coupled with force balance around the free boundary of melt. The electromagnetic field around the system is predicted by means of a wire model using the vector potential method. A characterstic temperature field in the charge which is electromagnetically repelled by the crucible is given by a finite difference solution of the heat balance equation taking transitional phase change into consideration. The validity of he proposed theoretical model has been confirmed by experimental measurements of the electromagnetic field around the cold crucible and temperature field in the charge. Numerical predictions show that keeping a molten charge without contact of a surrounding crucible is possible when the position and shape of solidification front is properly controlled by a regulated water cooling of the surface in the lower part of the charge. A laboratory experiment has been conducted to support this predicted fact. Theoretical operational criteria as to casting speed, cooling position and its rate which allow a stable and non-contact melting of the charge are shown.

Electromagnetic field application in the processes of single crystal growth under microgravity

The paper discusses problems of electromagnetic field employment in space technologies for semiconductor single crystal growth as means to stabilize and suppress residual convective flows of a non-gravity character. Here one can find the data on the steady magnetic field effects on hydrodynamics and heat mass transfer in melt as well as simple criteria dependencies to estimate these effects on the thermogravity and thermocapillary convections are proposed. A possibility of generation of specific additional types of melt convective flows in the steady fields is analyzed here. The example of the thermoelectromagnetic convection illustrates the effect of the above fields of the growth process characteristics. The features of effect of alternating magnetic fields on hydrodynamics and heat mass transfer in melt and at the solidification front are also discussed. A rotating magnetic field serves here as an example of the alternating magnetic field employment for flow stabilization, stirring of many-component melts, change of the solidification front shape, etc. A combination of two types of magnetic fields in one electromagnetic device is proposed in order to control growth processes by combined field effect.