Melt Flow Structure Research Articles

ON HEAT SOURCE IN SUBDUCTION ZONE

The subduction of an oceanic plate is studied as the motion of a high-viscosity Newtonian fluid. The subducting plate spreads along the 670-km depth boundary under the influence of oppositely directed horizontal forces. These forces are due to oppositely directed horizontal temperature gradients. We consider the flow structure and heat transfer in the layer that includes both the oceanic lithosphere and the crust and moves underneath a continent. The heat flow is estimated at the contact between the subducting plate and the surrounding mantle in the continental limb of the subduction zone. Our study results show that the crustal layer of the subducting plate can melt and a thermochemical plume can form at the 670-km boundary. Our model of a thermochemical plume in the subduction zone shows the following: (1) formation of a plume conduit in the crustal layer of the subducting plate; (2) formation of a primary magmatic chamber in the area wherein the melting rate equals the rate of subduction; (3) origination of a vertical plume conduit from the primary chamber melting through the continent; (4) plume eruption through the crustal layer to the surface, i.e. formation of a volcano. Our experiments are aimed to model the plume conduit melting in an inclined flat layer above a local heat source. The melt flow structure in the plume conduit is described. Laboratory modeling have revealed that the mechanisms of melt eruption from the plume conduit differ depending on whether a gas cushion is present or absent at the plume roof.

The influence of crucible and crystal rotation on the hydrodynamics of a melt with a Prandtl number 16 and on heat transfer in the Czochralski method

The effect of crucible rotation on the evolution of the melt flow structure at a Prandtl number 16 on the temperature and velocity fields and on convective heat transfer in the Czochralski method is simulated numerically in the mixed convection regimes at a given crystal rotation rate. The ranges of similarity parameters corresponding to stationary and unsteady melt flows and heat transfer regimes, as well as regimes with the most uniform radial distributions of local heat fluxes are determined. In the initial regime Reynolds, Grashof and Marangoni numbers are set to ReK = 95, Gr = 4870 and Ma = 5835.

EXPERIMENTAL AND THEORETICAL MODELING OF DIAMONDIFEROUS PLUMES

We consider thermochemical mantle plumes with thermal power 1.6·1010 W<N<2.7·1010 W (relative thermal power 1.15<Ka<1.9) as plumes with an intermediate thermal power. Such plumes are formed at the core–mantle boundary beneath cratons in the absence of horizontal free‐convection mantle flows beneath them, or in the presence of weak horizontal mantle flows. A proposed scheme of convection flows in the conduit of a plume with an intermediate thermal power is based on laboratory and theoretical modeling data. A plume ascends (melts out) from the coremantle boundary to critical depth xкр from which magma erupts on the Earth’s surface. The magmatic melt erupts from the plume conduit onto the surface through the eruption conduit. The latter forms under the effect of superlithostatic pressure on the plume roof. While the thickness of the block above the plume roof decreases to a critical value xкр, the shear stress on its cylindrical surface reaches a critical value (strength limit) τкр.Rock fails in the vicinity of the cylindrical block and, as a consequence, the eruption conduit is formed. We estimate the height of the eruption conduit and the time for the plume to ascent to the critical depth xкр. The volume of erupted melt is estimated for kinematic viscosity of melt =0.5–2 м2/с. The depth Δx from which the melt is transported to the surface is determined. Using the eruption volume, we obtain a relationship between the depth Δx and the plume conduit diameter for the above‐mentioned kinematic viscosities. In the case that the depth Δx is larger than 150 km, the melt from the plume conduit can transport diamonds to the Earth’s surface. Thus, the plumes with an intermediate thermal power are diamondiferous. The melt flow structure at the plume conduit/eruption conduit interface is determined on the basis of the laboratory modeling data. The photographs of the simulated flow were obtained. The flow line velocities were measured in the main cylindrical conduit (plume conduit) and at the main conduit/eruption conduit interface. A stagnant area is detected in the 'conduit wall/plume roof’ interface zone. The melt flow in the eruption conduit was analyzed as a turbulent flow in the straight cylindrical conduit with diameter dк. According to the experimental modeling and theoretical data, the superlithostatic pressure in the plume conduit is the sum of the frictional pressure drop and the increasing dynamic pressure in the eruption conduit. A relationship between the melt flow velocity in the eruption conduit and superlithostatic pressure has been derived.

FEATURES OF MELTING IN THE THERMOCHEMICAL PLUME CONDUIT AND HEAT AND MASS TRANSFER DURING CRYSTALLIZATION DIFFERENTIATION OF BASALTIC MELT IN A MUSHROOM-SHAPED PLUME HEAD

The number Ka=N/N1is used to evaluate the thermal power of a plume;Nis the thermal power transferred from the plume base to its conduit, andN1is the thermal power transferred from the plume conduit into the surrounding mantle. At the relative thermal power 1.9<Ka<10, after eruption of the melt from the plume conduit to the surface, melting occurs in the crustal block above the plume roof, resulting in the formation of a mushroom-shaped head of the plume. A thermochemical plume originates at the core-mantle boundary and ascends (melts up) to the surface. Based on laboratory and theoretical modeling data, we present the flow structure of melt in the conduit and the head of the thermochemical plume. The features of melting in the plume conduit are elucidated on the basis of the phase diagram of the CaO-MgO-Al2O3-SiO2model system. The two upper convection cells of the plume conduit relate to the region of basic and ultrabasic compositions. Our study shows that melting in these cells proceeds according to monovariant equilibria of eutectic type L=Cpx+Opx+An+Sp and L=Fo+An+Cpx+Opx. In case of the CaO–MgO–Al2O3–SiO2–Na2O system, crystallization differentiation proceeds as separation of plagioclase crystals. Separation of plagioclase crystals enriched in anorthite component leads to enrichment of the residual melt in silica and alkaline components. Assuming the initial basaltic melt, we calculated the compositional changes in the melt, which are powered by the heat and mass transfer processes in the mushroom-shaped plume head. The calculations were performed in two stages: (1) after settling of refractory minerals; (2) after settling of plagioclase in the melt resulting from the first stage. In the second stage, the melt contains 88.5 % of plagioclase component. The calculations were performed for melt temperatureTmelt=1410 °C and pressureP=2.6 kbar and 6.3 kbar. The calculated weight contents of oxides, the normative compositions for solid phase, and the oxide content and normative composition for the residual melt were tabulated. The SiO2content in the residual melt amounts to 59.6–62.3 % and corresponds to the crustal SiO2content.

A study of thermo-fluid characteristics of Czochralski melt using rotation and curvature corrected Partially-Averaged Navier-Stokes (PANS) turbulence models

A Czochralski melt flow encounters the effects of anisotropic body forces owing to the system rotation as well as significant streamline curvature due to inherent vortical structures and flow past curved surfaces. Two-equation eddy-viscosity models lack the ability to capture the flow anisotropy and curvature effects. Here we present the first study on the thermo-fluid characteristics of Czochralski melt using rotation and streamline curvature corrected Partially-Averaged Navier-Stokes (PANS) adaptations of the low-Re k-ε and SST k-ω models. The paper presents physical insights to the new PANS turbulence modelling approach highlighting improvements in the predicting capability of PANS models with the incorporation of rotation and curvature corrections. The PANS models showed good agreement with the results available in the literature (both experimental and computational). In addition for the PANS low-Re k-ε model it was observed that the prediction of the typical Czochralski melt flow structure in terms of shape, relative size and orientation of the characteristic cells improved with rotation and curvature corrections. Further thermal fluctuations and vortex cores also reduced in the melt in the case of the PANS low-Re k-ε model showing stabilization of flow. The corresponding rotation and curvature modification to the PANS SST k-ω model corrected the flow dynamics from a buoyancy dominated to rotationally driven along with an increase in the thermal fluctuations and vortex cores in the Czochralski melt resulting in a destabilization of the melt flow.

Numerical simulation of MHD oscillatory mixed convection in CZ crystal growth by Lattice Boltzmann method

A two-dimensional axisymmetric swirling thermal lattice Boltzmann model is presented to study the magnetohydrodynamics (MHD) oscillatory mixed convection in the melt of Czochralski silicon crystal growth in this paper. The governing equations are all solved by lattice Boltzmann method. The D2Q9 model is applied to solve the radial and axial velocities of the melt. Two D2Q5 models are adopted to solve the azimuthal (swirling) velocity and the temperature. The comparison with experiment and finite volume method proves that the presented model can be used as an alternative for simulating the axisymmetric crystal growth. Furthermore, simulations of the melt flow structure and heat transfer under a vertical magnetic field are conducted. And the critical Reynolds numbers Recr, which lead to the onset of the oscillatory melt convection, are calculated in different Richardson numbers (Ri), Ri=0.1,0.5,1.0,1.5,2.0,3.0, and different Hartmann numbers (Ha), Ha=0,10,20,30,40,50. In addition, the magnetic stability diagram is established according to a series of computations and the relationship between crystal rotation parameter and the state of the melt convection are analyzed. Compared with the traditional three-dimensional computational model, the proposed model in this paper has less computation time in simulating the axisymmetric swirling flow without affecting the accuracy of the results. The obtained critical Reynolds number has certain reference for improving the crystal growth parameter in practice.

Effect of Port Angle of Sen on Melt Flow in a Mold

The molten metal from tundish is directed to continuous casting mold by submerged entry nozzle SEN The SEN is usually bifurcated nozzle which is made of different shape and angle The melt flow structure in mold plays an important role Thus port of SEN is made at different angles to control the melt structure Many authors have reported that longitudinal high magnitude of melt and subsequent production of turbulence causes severe defects in casted products In the present work the melt flow structure has been studied under different port angles It has been seen that melt flow has been modified in the continuous casting mold Moreover it was found that the change in SEN port angle affects vertical downward velocity and turbulence behavior in the molten steel region nbsp

Effects of process parameters on melt-crystal interface in Czochralski silicon crystal growth

A two-dimensional axisymmetric immersed boundary thermal lattice Boltzmann (IB-TLB) model is presented to study the phase transition in Czochralski silicon crystal growth for improving the morphology of the melt-crystal interface and the crystal quality. Specifically, the Euler grid and the Lagrange grid are established, respectively. The melt-crystal interface is considered as an immersed boundary, and it is described by a series of Lagrange nodes. In this paper, the melt-crystal interface is tracked by the immersed boundary method, and the melt flow and heat transfer are simulated by the lattice Boltzmann method. The D2Q9 model is adopted to solve the axial velocity, radial velocity, swirling velocity and temperature of the melt. The finite difference method is used to solve the temperature distribution of the crystal. Then the solid-liquid transition in crystal growth with moving boundary is solved by the proposed IB-TLB model. The proposed model is validated by the solid-liquid phase transition benchmark. In addition, the flatness of the melt-crystal interface is evaluated by the mean value of the absolute value of the interface deviation and the standard deviation of the interface deviation. The effects of the process parameters on the morphology of melt-crystal interface, melt flow structure and temperature distribution are analyzed. The results show that the morphology of the melt-crystal interface is relevant to the interaction of the crystal pulling rate, the crystal rotation parameter, and the crucible rotation parameter. When the crystal and crucible rotate together, the deviation and fluctuation of the melt-crystal interface can be effectively adjusted, whether they rotate in the same direction or rotate in the opposite directions. And a flat melt-crystal interface can be obtained by appropriately configurating the ratio of crystal rotation parameter to crucible rotation parameter. Finally, according to a series of computations, it is found that when the crucible and crystal rotate in the opposite directions, the crystal rotation parameter and the crucible rotation parameter satisfy a functional relation, with a flat interface maintained. The obtained relationship has a certain reference for adjusting and improving the crystal growth parameters in practice.

Opening of a system of cracks—on the mechanism of the cyclic lateral eruption of the St. Helens volcano in 1980

The dynamic behavior of a magma melt filling a slot channel (crack) in a closed explosive hydrodynamic structure is considered. The explosive hydrodynamic structure includes the volcano focal point with a connected vertical channel (conduit) closed by a slug and a system of internal cracks (dikes) near the dome, as well as a crater open into the atmosphere. A two-dimensional model of a slot eruption is constructed with the use of the Iordanskii–Kogarko–van Wijngaarden mathematical model of two-phase media and the kinetics that describes the basic physical processes in a heavy magma saturated by the gas behind the decompression wave front. A numerical scheme is developed for analyzing the influence of the boundary conditions on the conduit walls and scale factors on the melt flow structure, the role of viscosity in static modes, and dynamic formulations with allowance for diffusion processes and increasing (by several orders of magnitude) viscosity. Results of the numerical analysis of the initial stage of cavitation process evolution are discussed.

Effect of Location of Zero Gauss Plane on Oxygen Concentration at Crystal Melt Interface During Growth of Magnetic Silicon Single Crystal Using Czochralski Technique

A numerical simulation approach has been adopted to investigate the effect of location of zero Gauss plane (ZGP) on oxygen concentration at crystal melt interface for growth of Silicon single crystal using Czochralski (CZ) method. ZGP location for the CUSP magnetic field has been moved above and below the melt free surface by 10% of the melt height. Crucible melt of aspect ratio 1, 0.5 and 0.25 have been taken into consideration. Oxygen concentration at crystal melt interface reduces with reduction of melt aspect ratio, irrespective of the ZGP location. Melt flow structure for low aspect ratio breaks down into two toroidal cells as compared to single cell structure for higher melt aspect ratio. Oxygen concentration at crystal melt interface varies along the radius of the crystal for high aspect ratio melt. Effect of change of location of ZGP on oxygen species incorporated into growing crystal depends on the melt aspect ratio.

Analysis and optimization of Czochralski laser oxide crystal growth

Gallium Gadolinium Garnet (Gd3Ga5O12 or GGG) oxide crystal is a promising material for the use in fabrication of various optical components, and is an important substrate for magneto-optical films and high-temperature superconductors. The primary focus of GGG single crystal growth is to produce high quality and large size boules to satisfy such applications. A series of defects often emerge during the growth, such as hollow ingot, cracks, color center, dislocation and inclusions, which significantly degrade the crystal quality and limit the productivity. In this paper, numerical and theoretical analyses have been conducted to discuss the mechanisms of defect formation during the crystal growth. The hollow ingot, color center and inclusion are closely related to the complex reactions in the melt. The reaction products dissolve in the melt to be saturated, and then accumulate where the fluid flow is slow or stagnant. Therefore, the formation of the bubbles and inclusions is governed by the hydrodynamics of the melt. The relationship between the crystal rotation rate and the stagnant position is found to be linear. Crystal cracks and dislocation are related to thermal stress during the growth process. The locations in the crystal ingot with high possibility to crack or with large dislocation density can be evaluated by analyzing von Mises stress aligned in the direction supporting the maximum shear load. The submerged tube/ring designs are proposed for the adjustment of the melt flow structure by suppressing natural convection. The integrated solutions of melt convection and thermal stress are obtained to evaluate the feasibility of the proposed designs for the control of solute inclusions and thermal stress-related defects in the crystal.

Liquid flow in a cubic cavity generated by gas motion along the free surface

Flow and turbulence generation in a cubic cavity filled by the liquid driven by the gas shear stress over a liquid/gas interface are considered. The coupled gas/liquid flow model is formulated to gain basic understanding of gas flow effects on melt convection, heat and mass transfer during crystal growth by the Czochralski and Directional Solidification methods. As in real crystal growth applications, the gas velocity is assumed to be much higher than the liquid velocity. The gas flow is considered to be laminar for both case of laminar and turbulent liquid convection. The flow of liquid is studied to find conditions of liquid turbulent transition at increasing gas shear stress. A novel dimensionless number is proposed and validated to describe the gas shear stress effect on the liquid flow. Engineering applications to control melt flow structure and oxygen transport during silicon crystal growth are discussed.

Possible explanations for different surface quality in laser cutting with 1 and 10 μm beams

In laser cutting of thick steel sheets, quality difference is observed between cut surfaces obtained with 1 and 10 μm laser beams. This paper investigates physical mechanisms for this interesting and important problem of the wavelength dependence. First, striation generation process is described, based on a 3D structure of melt flow on a kerf front, which was revealed for the first time by our recent experimental observations. Two fundamental processes are suggested to explain the difference in the cut surface quality: destabilization of the melt flow in the central part of the kerf front and downward displacement of discrete melt accumulations along the side parts of the front. Then each of the processes is analyzed using a simplified analytical model. The results show that in both processes, different angular dependence of the absorptivity of the laser beam can result in the quality difference. Finally, the authors propose the use of radial polarization to improve the quality with the 1 μm wavelength.

Numerical Study of Melt Convection and Interface Shape in a Pilot Furnace for Unidirectional Solidification of Multicrystalline Silicon

Multicrystalline silicon is widely used in the photovoltaic industry. A key point is to increase the ingot quality during the growth process to increase the solar cells efficiency. Numerical calculations were performed to investigate the melt convection and interface shape in a pilot furnace for unidirectional solidification of multicrystalline silicon. It was found that growth parameters like temperature gradients and growth rate strongly influence the melt flow and interface shape. The results indicate that both interface deflection and melt flow structure are sensitive to the variation of considered growth parameters. The regularity of the melt flow pattern increases with the increase of temperature gradient in the melt and growth rate.

Geology of the Gushan iron oxide deposit associated with dioritic porphyries, eastern Yangtze craton, SE China

The major Gushan iron oxide deposit, typical of the Middle‐Lower Yangtze River Valley, is located in the eastern Yangtze craton. Such deposits are generally considered to be genetically related to Yanshanian subvolcanic‐volcanic rocks and are temporally‐spatially associated with ca. 129.3–137.5 Ma dioritic porphyries. The latter have a very narrow 87Sr/86Sr range of 0.7064 to 0.7066 and low εNd(t) values of −5.8 to −5.7, suggesting that the porphyries were produced by mantle‐derived magmas that were crustally contaminated during magma ascent. The ore bodies occur mainly along the contact zone between dioritic porphyries and the sedimentary country rocks. The most important ore types are massive and brecciated ores which together make up 90 vol.‐% of the deposit. The massive type generally occurs as large veins consisting predominantly of magnetite (hematite) with minor apatite. The brecciated type is characterized by angular fragments of wall‐rocks that are cemented by fine‐grained magnetite. Stockwork iron ores occur as irregular veins and networks, especially with pectinate structure; they are composed of low‐temperature minerals (e.g. calcite), which indicate a hydrothermal process. The similar rare earth element patterns of apatite from the massive ores, brecciated ores and the porphyries, coupled with high‐temperature fluids (1000°C) suggest that they are magmatic in origin. Furthermore, melt flow structure commonly developed in massive ores and the absence of silicate minerals and cumulate textures suggest that the iron ores formed by the separation of an immiscible oxide melt from the silicate melt rather than by crystal fractionation. Combined with theoretical and experimental studies, we propose that the introduction of phosphorus due to crustal contamination during mantle‐derived magma ascent could have been a crucial factor that led to the formation of an immiscible oxide melt from the silicate magma.

Effect of high frequency magnetic field on CZ silicon melt convection

Melt flow structure during the silicon single crystal growth process strongly affects the crystal quality. Therefore, melt convection control technique should be developed to obtain the high quality single crystal. For this purpose, we proposed a high frequency magnetic field applied method, and numerically investigated the effect of high frequency magnetic field on Czochralski (CZ) silicon melt convection. The results revealed that the melt convection was strongly affected by the applied electric current and frequency. The temperature distribution just below the crystal became flat if the applied electric current and frequency were selected as optimized value.

Computational modeling of turbulent melt flow in CdZnTe crystal growth

A computational model of CdZnTe crystal growth including turbulent phenomena in the melt is presented as a continuation of the previous work by Černý, Kalbáč and Přikryl [Comp. Mater. Sci. 17 (2000) 34]. The ternary CdZnTe system is treated as pseudobinary in the temperature range under consideration. The phase interface between the solid and liquid is modeled as a discontinuity surface. The k– ε model for low turbulent Reynolds numbers is used for the description of the turbulent processes. The numerical solution of the model is done using the Galerkin finite element method in two-dimensional approximation with cylindrical symmetry. The problem of moving boundary is solved by a front-fixing method. The results obtained with the turbulent model are compared to those of the previous laminar model and the influence of including the turbulence into the model is discussed. It is shown that the laminar and the turbulent models exhibit significant differences in the structure of melt flow, concentration profiles, and also in the movement of the phase interface for larger time periods.

Effect of beam width on melt characteristics in large-area laser surface alloying

This article presents an investigation of the convection behavior of the melt pool for laser surface alloying with a wide beam. A line beam source with a dimension of 6 mm × 0.7 mm from a 3 kW cw Nd–YAG laser was used. The work concentrated on studies of the influence of various laser operating conditions, especially the melt width of the tracks and the substrate thermal properties, on the convection behavior during the laser surface alloying process. Three different substrates precoated with a Ni layer were selected on the basis of their different thermal properties. An investigation of the relationships between the laser beam dimension, the structure of melt flow, and concentration fields of the alloying elements was carried out. It was found that the beam width had a significant effect on the alloying patterns on solidification. It was also found that a wider beam width (varied with a mask aperture) produced a greater melt depth. A three-dimensional mathematical model was applied to numerically simulate the temperature field and convection flow of the melt pool. Some specific alloying patterns were found favorable for coinage applications.

Effect of internal radiative heat transfer on interface inversion in Czochralski crystal growth of oxides

A global analysis of heat transfer was carried out to investigate the effect of internal radiative heat transfer in the crystal and/or melt on the interface inversion in Czochralski growth of an oxide crystal. As a result, it was found that the critical Reynolds number at which the interface inversion occurs decreases with the optical thickness of the crystal when the melt is opaque. However, when the melt is semitransparent and its optical thickness is the same as the crystal's, the critical Reynolds number has a maximum value for a certain optical thickness of the crystal and melt, depending on the melt flow structure composed of the free convection and the forced convection caused by the crystal rotation.

Effects of system parameters on MHD flows in rotating magnetic fields

A numerical study is presented of the electromagnetic and hydrodynamic field distributions induced by rotating magnetic fields in a conducting fluid contained in a cylindrical vessel with insulated and conducting walls and ends. Simulations are carried out to determine the effect of various rotating electromagnetic field configuration parameters on magnetohydrodynamic melt flow structure and velocity distributions. Results show that the flow motion consists of the primary azimuthal and secondary meridional flows and that the detailed pattern of these flows changes with the system parameters such as the electric conductivities of the container and the liquids, and the relative positions of the inductor and melts. It is found that the basic structure of the melt velocity distribution is not affected noticeably by the distribution of electromagnetic forces in the case of symmetric distribution, but it changes significantly if this symmetry breaks.