Melt Convection Research Articles

Mathematical modeling of conductive–convective melting with a two-phase region by the enthalpy-porosity method

Mathematical modeling of conductive–convective melting with a two-phase region by the enthalpy-porosity method

Solute and phase heterogeneous distribution at different scales and its effect on ageing physical phenomena in a laser powder bed fusion produced maraging steel

The Laser Powder Bed Fusion process involves complex thermodynamic and heat transfer mechanisms which results in a complicated understanding of the material’s microstructure and phase transformation processes. In the case of additive manufacturing maraging steels, these present heterogeneous structures which mainly consist of Body-Centred Tetragonal (BCT) martensite and retained austenite (Face-Centred Cubic (FCC) phase structure), unlike conventionally processed material. Research has already been done on the competitive or collaborative nature of austenite growth/reversion and precipitation in these materials. However, for Laser Powder Bed Fusion maraging steels, studies have focused on either the effect of the heterogeneous structures on austenite reversion kinetics or the formation, evolution and behaviour of precipitation. Still, no comprehensive research exists that covers in detail the relation between solute heterogeneity from the meso- to the nanoscale and its influence on both phase distribution and ageing physical phenomena. To do so, multiscale chemical analyses and microstructural characterisation techniques were used to investigate a maraging steel M300 in different transformed conditions: as-built, aged at 480 and 540 °C. The results showed that competing mechanisms during printing caused segregation at the mesoscale, which remains in aged samples. Vaporisation led to Cr segregation, while melt convections caused Ni and Ti depletion at melt pool boundaries. Retained austenite location was found at melt pool boundaries and away from them on the as-built structure. Its preferential location remains unclear. Dissimilarities from conventional material were identified in nanosized clustering and precipitates on aged samples.

Effect of Crystal Rotation on Melt Convection and Resistivity Distribution in 200 mm Floating Zone Silicon Single Crystal Growth.

Floating silicon is particularly suitable for the production of power devices and detectors due to its high purity and high resistivity. However, when the crystal diameter increases to 200 mm, the inhomogeneous distribution of dopants in the radial direction of the crystal becomes an important factor affecting the quality of the crystal. In this paper, the melt flow and crystal interface dopant distribution of 200 mm floating zone silicon under different crystal rotation modes using 2D axisymmetric models was calculated. In the simulation, the crystal rotates unidirectionally clockwise or alternates between clockwise and counterclockwise rotations and is compared with the corresponding experimental results. The results of alternate rotation show a significant improvement in the distribution of resistivity, which is explained from the perspective of melt flow, providing ideas for the industrial production of high-quality FZ silicon crystals.

Effects of horizontal magnetic field position on oxygen control in 12-inch Czochralski silicon

The application of a horizontal magnetic field is an important method for controlling point defects and impurity distribution in 12-inch Czochralski silicon used in integrated circuits. This work introduces the effects and mechanisms of horizontal magnetic field positioning on oxygen concentration in 12-inch single crystal silicon used for commercial integrated circuits. Effect of melt convection, and temperature distribution on oxygen concentration at the bodying length of 500 mm was presented and analyzed by combining growth experiments and numerical simulations (using CGSim_23_2 from STR) with different horizontal magnetic field positioning. This study found that the mechanism of magnetic field control of oxygen is not directly correlated with the convection suppression effect. It is important to avoid the overlap of strong magnetic regions with high-temperature areas, as this can lead to additional oxygen dissolution.

Achieving efficient hardfacing on stainless steel using single SiC powder in laser directed energy deposition

Generally, in a laser hardfacing process, a mixture of ceramic and metal powder is used to clad a hard surface, resulting in enhanced wear characteristics of metal parts. This study proposes an efficient hardfacing process that uses a single and minimal amount of ceramic powder (0.079 g/min in this work). This process, named as Laser Directed Energy Deposition of Minimal Ceramic Powder (LDED-MCP), features that the melt pool is generated inwardly because only the substrate participates in forming the melt pool. Furthermore, due to the minimal powder flow rate used and sparse particle-melt pool collision events, ripple formations leading to the convective melt pool flow and inhomogeneous microstructures would be suppressed. Consequently, the produced layer is nearly flat and free of incompletely melted metallic particles, thus minimizing post-machining. For a 316 L substrate and SiC powder material combination, a crack-free layer about 560 μm thick with an average hardness of about 417 HV was created through process parameter optimization. This layer showed a eutectic structure composed of γ-austenite and chromium carbides, partially melted SiC particles between dendrites, and in-situ synthesized SiC nanoparticles decorating the cell walls. Through this work, near-net-shape hardfacing of stainless steels is realized through LDED-MCP process minimizing powder pre-processing and post surface machining.

Evaluation of melting front kinetics in cylindrical phase change materials module using infrared thermography and digital imaging

An experimental study examined buoyancy-driven convection in the unconstrained melting of PCM within a cylindrical module. Melting progress and PCM fraction were analyzed using IRT and digital imaging. Initial symmetric melting led to accelerated phase change at the bottom and a rippled PCM surface. Thermal stratification in the lower module was evident, with molten liquid displacing colder fluid. Observations underestimated bottom PCM waviness and melting. As the melt zone expanded, buoyancy-driven convection intensified, speeding up melting at the top while the bottom relied more on conduction. The study details transient front positions, temperature profiles, solid PCM amounts, and melting times. Unstable fluid layers near the bottom caused waviness due to chaotic fluctuations. Nucleation rates critically impacted PCM crystallization kinetics and properties.

Systematic and quantitative testing simulations and theories on phase coarsening by experiments

Microgravity experiments on phase coarsening in solid-liquid mixtures provided an ideal tool to closely and accurately explore the kinetics of phase coarsening because the sedimentation and convective melt flow are eliminated in the International Space Station. In this study, we employed phase-field simulations to systematically investigate the microstructure evolution during phase coarsening at various volume fractions. Simulated microstructure evolution during phase coarsening are compared quantitatively with the microstructure evolution archived from microgravity experiments. Furthermore, kinetics of phase coarsening in Pb-Sn solid-liquid mixtures at various volume fractions is studied theoretically and numerically, which is compared with microgravity experiments. In particular, particle size distribution, relative coarsening rate constants, and scaled maximum particle radii, are predicted from theories, and deduced from microgravity experiments, then calculated from phase-field simulations. This systematic and quantitative study of phase coarsening confirms the consistency to the results from phase-field simulation, microgravity experiments and theories at lower volume fractions, and stimulates more careful microgravity experiments at higher volume fractions (≥0.7).

Structures in grain-refined directionally solidified hypoeutectic Al-Cu alloys: Benchmark experiments under microgravity on-board the International Space Station

Benchmark solidification experiments were successfully performed under microgravity conditions on-board the International Space Station (ISS) within the ESAprogramme CETSOL (Columnar-to-Equiaxed Transition in SOLidification Processing). Cylindrical samples of grain-refined Al-4wt.%Cu, Al-10wt.%Cu and Al-20wt.%Cu alloys were directionally solidified in a gradient furnace to investigate columnar and equiaxed dendritic growth structures as well as the columnar to equiaxed transition under diffusive conditions. The determination of temperature gradients; interface velocities; and cooling rates at liquidus, solidus, and eutectic front positions provides well-defined thermal experimental characterization. The evaluation of the flight samples demonstrates that no significant macrosegregation along the sample axis occurred and no radial effects were observed. Therefore, purely diffusive solidification behaviour without any residual melt convection can be assumed for these microgravity experiments. The analyses of the microstructure in longitudinal cross-sections show dendritic structures without any pore formation and the averaged eutectic fraction is largely constant along the sample. The samples of refined Al-4wt.%Cu alloy show a sharp CET from columnar dendrites to a fine equiaxed steady-state grain structure whereas in the samples of refined Al-10wt.%Cu and Al-20wt.%Cu alloy, only equiaxed dendritic grain growth is observed. A quantitative analysis of the equiaxed grain morphology shows, that the shapes of the equiaxed dendrites depend on the applied temperature gradient, but the grain sizes in radial and longitudinal directions are identical. Therefore, a fully equiaxed dendritic growth structure without dendrite elongation was obtained. Compared to experiments in microgravity with non-refined Al-Cu alloys the average equiaxed grain size is about three times smaller.

Global weak solutions to a phase-field model for seawater solidification with melt convection

Global weak solutions to a phase-field model for seawater solidification with melt convection

Growth and pinch-off of sidearm necks: a model of dendrite fragmentation

Dendrite fragmentation commonly occurs by pinch-off of sidearms at the narrow neck with the parent stem. Comprehensive measurements of the local neck dynamics are performed using in-situ synchrotron radiography experiments in which a flat sample of a Ga–35wt%. In alloy is solidified under both steady and transient growth conditions with minimal effects of melt convection. The measurements reveal two characteristic limits where the neck radius follows universal self-similar t1/3 power laws, with a positive rate constant in the limit of steady growth and a negative rate constant in the isothermal pinch-off limit. The temporal power law for steady growth found here relates the sidearm neck radii to the tip radius of the primary dendrite stem, and the neck radius probability density distribution is shown to be symmetric. For the more general case of decelerated growth, it is observed that the neck initially widens along the steady growth limit, is then increasingly limited by the pinching tendency, and for sufficiently large decelerations converges ultimately to the pinch-off limit. A dynamical model is derived that predicts the behavior of the sidearm neck radius under arbitrary decelerating growth conditions. The highly variable nature of dendrite fragmentation is explained by the stochastic properties of the initial sidebranch development process. The model can be used to estimate the number of dendrite fragments forming during a certain time interval at any location behind the primary tips.

Effect of horizontal magnetic field position on oxygen distribution in CZ silicon crystal growth

The horizontal magnetic field-assisted Czochralski(CZ) method is gaining significant popularity in the semiconductor industry for producing 200 mm semiconductor-grade silicon wafers. In this study, the impact of the horizontal magnetic field position on the oxygen content and radial uniformity of semiconductor-grade silicon crystals produced by the CZ method was investigated. Three-dimensional simulations were conducted using finite element software to calculate the melt convection and oxygen content before and after adjustment of the magnetic field position, respectively. The simulations results predicted a decrease in the oxygen content of the crystals following the adjustment of the magnetic field position from 0 to 75 mm below the free surface, and this was experimentally verified. The velocity distribution of the free melt surface exhibits better uniformity when lowering the magnetic field position. The influence of the magnetic field position on the temperature distribution and Marangoni flow in the melt was investigated, and the result of oxygen concentration difference identified the adjustment of the magnetic field position promoted the greater Marangoni flow below the free melt surface, which promoted the volatilization of SiO gas and thus reduced the oxygen concentration in the silicon ingot. Therefore, adjusting the position of the magnetic field is an effective way to increase the Marangoni flow and to obtain semiconductor-grade silicon crystal with lower oxygen content and better oxygen radial homogeneity.

Long-distance settling simulation of equiaxed dendrite by a moving-frame algorithm: phase-field lattice Boltzmann study with parallel-GPU AMR

In large-ingot castings, the settling of equiaxed dendrites often results in distinct cone-shaped negative segregation in the lower region of the ingot. To accurately predict and control such macrosegregation, it is important to understand the kinetic behavior of equiaxed dendrites in the melt. The phase-field lattice Boltzmann (PF-LB) model is powerful for simulating dendrite growth with melt convection and solid motion. However, it is computationally expensive and represents only the short-distance motion of dendrites in three-dimensional (3D) simulations. For an efficient 3D evaluation of the effect of dendrite motion and rotation on growth behavior, we introduce the moving frame algorithm to PF-LB simulations. Here, the computational domain tracks the settling dendrite to express long-distance settling without restricting the domain size. The PF-LB simulations were accelerated by parallel computing using a combination of multiple GPUs and adaptive mesh refinement (AMR), also referred to as parallel GPU-AMR. The moving-frame algorithm was modified to adapt to AMR. From the simulation results, we demonstrate that the proposed method helps evaluate the effect of dendrite rotation on the settling and growth velocities of equiaxed dendrites in 3D.

Melting of a phase change material in a rectangular cavity in the presence of metallic fins

The melting of the phase change material (PCM) octadecane, confined in a rectangular cavity heated from the bottom, is numerically studied. Simulations are performed through finite element software in order to analyze the impact of metal fins within the enclosure on the melting time. The results are analyzed in terms of the time-dependent position of the melting front, time-dependent average liquid fraction, and time needed for the PCM melting. The obtained outcomes highlight how, with a low number of metallic fins, the initial melting regime dominated by conduction at a certain time gives way to a convective melting regime characterized by Rayleigh–Bénard cells, in full agreement with the results of the theoretical analysis. On the contrary, with a high number of metallic fins, conduction is the only mechanism that governs heat transfer and the rapid melting slows down when the phase change front reaches the top of the fins. More specifically, the addition of the fins within the cavity yields a reduction in the time needed for the complete PCM melting up to 90% in the analyzed cases. The reported results provide new insights regarding the heat transfer mechanisms involved in PCMs melting within bottom-heated enclosures.

NUMERICAL SIMULATION OF ENERGY-EFFICIENT SOLUTIONS OF THE ARC FURNACE STEEL MELTING BATH

Numerical modeling of hydrodynamics and heat and mass transfer in the arc furnace (EAF) steel melting bath under pneumatic stirring conditions demonstrates that the introduction of a «deep» bath with a form factor (ratio of diameter to depth) of 2.5 against the traditional 5.0 provides an energy-efficient bubbling mode of purging at higher inert gas flowrate. An increase in the diameter of the porous plug and the volume of the two-phase region in the "deep" bath allows in 150-ton EAF to increase the mixing power and the coefficient of convective heat transfer in liquid steel by 2-2.2 and 1.4 times on average, respectively. In the context of the «flat bath» process, it is shown the possibility of intensifying the convective melting of scrap in the bath by 24% in average and, thus, increasing productivity and, accordingly, improving the energy efficiency of the EAF.

Study on convective melting heat transfer of a solid-liquid phase change slurry in U-shaped curved tubes

As a phase change material, ice slurry has been successfully applied in HVAC&R systems due to its high energy storage density. The heat exchangers are the key equipment realizing energy conversion of ice slurry. In HVAC&R systems, U-tubes are frequently used in shell and tube heat exchanger. However, there are few studies on thermo-fluidic characteristics of ice slurry in U-tubes. Therefore, the thermo-fluidic characteristics of ice slurry in U-tubes are numerically studied in this paper using Euler-Euler approach. The results indicated that as enlarging the inlet ice content and velocity, the ice concentration distribution becomes more uniform along in vertical profile. Due to the secondary flow in bend section, the ice concentration decreases in the inner wall and increases in the outer wall as the inlet velocity increases; At the high Reynolds number, the inlet ice content and ice particle diameter have a more significant fluence on pressure drop (Δp). The local heat transfer coefficient (hlo) in bend section exhibits a tendency of first increasing and then decreasing, with the maximum value of hlo occurs at θ = 90° of the bend section. Finally, a correlation is suggested between the average resistance coefficient (fave) and local Nusselt number (Nulo).

Natural Convection Melting in a Rectangular Heat Storage Tank of Carbon Nanotube Dispersed Latent Heat Storage Material

Natural Convection Melting in a Rectangular Heat Storage Tank of Carbon Nanotube Dispersed Latent Heat Storage Material

Heat transfer simulation and performance optimization of plate-type phase change energy storage unit

As the core of the phase change energy storage technology, the heat transfer performance of the phase change energy storage unit has an important impact on the operating efficiency of the energy storage system. In this study, a three-dimensional CFD model of the plate-type phase change energy storage unit is established to simulate the melting process of paraffin wax. Three types of plate-type phase change energy storage unit models are established, without fins, single fin, and double fins. The influence of cylindrical fin on natural convection melting process of paraffin is studied, which provides the basis for the design and performance optimization of plate-type phase change energy storage unit, and improve its application value. The results show that the melting time of paraffin in the energy storage unit without fins is 858 s, and the melting time is shortened to 827 ~ 842 s after adding single fin. The melting time of paraffin wax with single fin is lower than that with double fins. For the plate-type phase change energy storage unit, adding fins at the central section can effectively improve the melting rate of phase change material. The single fin A located at the lower part of the central section has the greatest promotion effect on paraffin melting. The key to enhance the phase change heat transfer process in plate-type phase change energy storage unit is the paraffin in the lower half of the symmetry plane.

Petrology of the Skaergaard Layered Series

The Skaergaard intrusion is a layered, ferrobasaltic intrusion emplaced during the Early Eocene into the rifting volcanic margin of East Greenland. The magma chamber crystallised in response to cooling from the roof and margins upwards and inward, forming upper, marginal and bottom series, the latter referred to as the Layered Series. The phase layering in the bottom series suggests an evolved, olivine-normative tholeiitic melt saturated in plagioclase and olivine, followed by augite, and then simultaneously by ilmenite and magnetite forming primocrysts. Pigeonite appears in the lower parts and continues until the centre of the series. Apatite appears in the upper part concurrently with liquid immiscibility. Cryptic variations of the individual primocrysts record a systematic upward increase in iron and decrease in magnesium for the mafic minerals and a systematic increase in sodium and decrease in calcium for plagioclase. The appearance of pigeonite is caused by reactions and crystallisation in the trapped melt and by subsolidus adjustments without this phase reaching liquidus saturation. The high mode of olivine at the base of the upper part with the appearance of apatite is interpreted to mark the onset of liquid immiscibility. This may have led to the separation of conjugate melts with granophyre migrating upward and the basic component largely staying stationary or sinking. Petrologic and geochemical observations indicate differentiation in the lower part of the intrusion, principally controlled by crystal fractionation with the efficiency of fractionation controlled by the evolution and escape of liquid from the solidifying mush. During the final stages of solidification, the onset of liquid immiscibility and termination of melt convection impeded differentiation. Modelling by perfect Rayleigh fractionation shows that major and included trace elements conform reasonably to observations, while excluded elements deviate from model predictions. This decoupling is caused by the mobility of a granophyre component formed in the trapped melt and in the main residual magma chamber. Consequently, the sampled gabbros may not be representative of the final solid-melt mush. By restoring the gabbros to their original mush compositions, it is possible to constrain granophyre migration pathways. We suggest that the granophyre formed in the trapped melt in the lower part of the intrusion mostly migrated laterally through pressure release pathways to form lenses and pockets with only limited upward migration into the main magma reservoir. Near the end stage of differentiation, the residual magma exsolved and formed complex mixtures of ferrobasaltic and granophyric melts. Estimates predict that a substantial amount of the granophyric melt penetrated as sills into the downward crystallising, upper part of the body as well as into the host rocks. The redistribution of granophyric melts within the solidifying crystal mush complicates predictions of trapped-melt content and mass-balance calculations but helps to explain apparent decoupling of included and excluded trace elements, especially towards the end stages of evolution. Final crystallisation was controlled mostly by in situ crystallisation leaving complex mixtures of ferrodiorite and granophyre components.

Bistability in Radiatively Heated Melt Ponds.

Melting and solidification processes, intertwined with convective flows, play a fundamental role in geophysical contexts. One of these processes is the formation of melt ponds on glaciers, ice shelves, and sea ice. It is driven by solar radiation and is of great significance for Earth's heat balance, as it significantly lowers the albedo. Through direct numerical simulations and theoretical analysis, we unveil a bistability phenomenon in the melt pond dynamics. As solar radiation intensity and the melt pond's initial depth vary, an abrupt transition occurs: this tipping point transforms the system from a stable fully frozen state to another stable equilibrium state, characterized by a distinct melt pond depth. The physics of this transition can be understood within a heat flux balance model, which exhibits excellent agreement with our numerical results. Together with the Grossmann-Lohse theory for internally heated convection, the model correctly predicts the bulk temperature and the flow strength within the melt ponds, offering insight into the coupling of phase transitions with adjacent turbulent flows and the interplay between convective melting and radiation-driven processes.

Solute trapping and non-equilibrium microstructure during rapid solidification of additive manufacturing

Solute transport during rapid and repeated thermal cycle in additive manufacturing (AM) leading to non-equilibrium, non-uniform microstructure remains to be studied. Here, a fully-coupled fluid dynamics and microstructure modelling is developed to rationalise the dynamic solute transport process and elemental segregation in AM, and to gain better understanding of non-equilibrium nature of intercellular solute segregation and cellular structures at sub-grain scale during the melting-solidification of the laser powder bed fusion process. It reveals the solute transport induced by melt convection dilutes the partitioned solute at the solidification front and promotes solute trapping, and elucidates the mechanisms of the subsequent microstructural morphology transitions to ultra-fine cells and then to coarse cells. These suggest solute trapping effect could be made used for reducing crack susceptibility by accelerating the solidification process. The rapid solidification characteristics exhibit promising potential of additive manufacturing for hard-to-print superalloys and aid in alloy design for better printability.