H. C. De Groh

A numerical and experimental study of natural convection and interface shape in crystal growth

Abstract A numerical and experimental study has been conducted on the crystal growth of succinonitrile in a horizontal Bridgman apparatus. The shape of the solid—liquid interface was significantly influenced by three-dimensional natural convection in the liquid adjacent to the interface. The interface profile observed during experiments was compared with predictions from a two-dimensional (2D) finite element analysis and a three-dimensional (3D) finite difference approach. Good agreement was achieved between the experimental and predicted results. The computed velocities in the vicinity of the interface were found also to be in good agreement with the measured experimental velocities.

NUMERICAL STUDY OF g-JITTER INDUCED DOUBLE-DIFFUSIVE CONVECTION

A finite element study is presented of double-diffusive convection driven by g-jitter in a microgravity environment. M athematical formulations are presented and extensive simulations are carried out for g-jitter induced fluid flow, temperature distribution, and solutal transport in an alloy system under consideration for space flights. Computations include the use of idealized single-frequency and multifrequency g-jitter as well as the real g-jitter data taken during an actual Space Shuttle flight. Little correlation is seen between these velocity components for the g-jitter components studied. The temperature field is basically undisturbed by convection because of a small Pr number for the fluid. The disturbance of the concentration field, however, is pronounced, and the local variation of the concentration follows the velocity oscillation in time. It is found that although the concentration field varies in both position and time, the local concentration gradient remains approximately constant in time. Numerical study further indicates that with an increase in g-jitter force (or amplitude) , the nonlinear convective effects become much more obvious, which in turn drastically change the concentration fields. The simulated results computed using the g-jitter data taken during space flights show that both the velocity and concentration become random, following approximately the same pattern as the g-jitter perturbations.

Three-dimensional finite element method simulation of Bridgman crystal growth and comparison with experiments

The crystal growth of succinonitrile (SCN) in a horizontal Bridgman apparatus is studied through a three-dimensional numerical simulation. The governing equations considered include the steady state Navier-Stokes and the thermal energy equations. The temperature boundary conditions imposed at the outer surface of the glass ampoule are taken from experimental measurements. To model the phase change in SCN, we use the effective specific heat formulation of the enthalpy method and treat the SCN as a generalized Newtonian fluid. We solve the numerical model using the segregated solution approach provided by a commercial finite element code, FIDAP. The numerical results are compared with data from experiments, and very good agreement has been achieved. The advantages of applying the segregated solution approach in large-scale three-dimensional (3-D) computations are shown through detailed comparisons of efficiency and memory requirements between the segregated and the conventional fully coupled solution approa...

Magnetic field effects on g-jitter induced flow and solute transport

Abstract Numerical modeling and analyses are presented of magnetic damping of g -jitter driven fluid flow and its effect on the solutal striation in a simplified Bridgman–Stockbarger crystal growth system under microgravity. The model development is based on the finite element solution of the momentum, energy and solute transport equations under g -jitter conditions in the presence of an external magnetic field. The numerical model is verified by comparison with analytical solutions obtained for a simple parallel plate channel flow driven by g -jitter in a transverse magnetic field. Simulations are carried out to study the behavior of convective flow and solutal transport induced by the combined g -jitter and magnetohydrodynamic forces. Both the idealized single frequency g -jitter force and the real g -jitter perturbation taken during space flight are considered. Results indicate that an applied magnetic field can effectively damp the velocity caused by g -jitter and help to reduce the time variation of solute redistribution. A stronger applied field is more effective in suppressing the convective flows and hence reducing concentration variation. It is found that g -jitter driven flows have the same oscillation period as the driving force with or without the applied field. However, an applied magnetic field shortens the transient period over which the flow field evolves into a quasi-steady state time harmonic oscillation after g -jitter sets in. The flow intensity increases with an increase in g -jitter magnitude but decreases with an increase in the applied field strength. The reduced convection in the liquid pool by the applied magnetic field results in a reduction of the concentration oscillation. The magnetic field is very useful in suppressing the spiking velocities that are induced by the spikes in the real g -jitter data. The damping effect is more pronounced if the magnetic field is switched on before the onset of g -jitter disturbances.

Three-dimensional gravity-jitter induced melt flow and solidification in magnetic fields

A full three-dimensional transient numerical model is presented for gravity- ( g-) jitter induced melt e ow and solidie cationphenomenawithandwithoutexternallyappliedmagnetice eldsduringthemeltgrowthofSn-dopedBi singlecrystalsin microgravity.Themodel isdeveloped basedonaEulerian‐ Lagrangian e niteelementformulation, coupled with a mesh-deforming algorithm to track the solidie cation front. Extensive numerical simulations are carriedout,andthestudiedparametersincludesoluteconcentration-dependentmeltingtemperature,solidie cation interface morphology, magnetic e eld direction and magnitude, idealized microgravity condition, and synthesized and real g-jitter data conditions. Computed results show that g-jitter induced melt e ow is time dependent and exhibits a complex three-dimensional structure and that the e ow can have detrimental effects on solute concentration distribution. The g-jitter induced melt e ow and its deleterious effects on solidie cation can be suppressed by externally applied magnetic e elds. The three-dimensional numerical simulations suggest that a two-dimensional model is useful in providing some essential features of g-jitter induced e ow and solidie cation behavior with and without externally applied magnetic e elds and that a three-dimensional model is required to resolve fully the complex spatial e ow structure when all g-jitter components are operative during a realistic space e ight.

Directional solidification and convection in small diameter crucibles

Abstract Pb–2.2 wt.% Sb alloy was directionally solidified in 1, 2, 3 and 7 mm diameter crucibles. Pb–Sb alloy presents a solutally unstable case. Under plane–front conditions, the resulting macrosegregation along the solidified length indicates that convection persists even in the 1 mm diameter crucible. Al–2 wt.% Cu alloy was directionally solidified because this alloy was expected to be stable with respect to convection. Nevertheless, the resulting macrosegregation pattern and the microstructure in solidified examples indicated the presence of convection. Simulations performed for both alloys show that convection persists for crucibles as small as 0.6 mm of diameter. For the solutally stable alloy, Al–2 wt.% Cu, the simulations indicate that the convection arises from a lateral temperature gradient.

Numerical Analysis of Double-Diffusive Convection/Solidification Under g-Jitter/Magnetic Fields

A e nite element model is presented for the g-jitter induced double-diffusive convection and solidie cation phenomena with and without the presence of magnetic e elds in an Sn-doped Bi crystal growth system planned for space experiments. The model is developed based on the deforming e nite element formulation with the penalty formulation forpressure approximation. An isothermalfront tracking algorithm is used to predict thesolid‐ liquid interface. Extensive numerical simulations are carried out and parameters studied include the solute concentration dependent melting temperature and magnetic e eld strength under both steady state and g-jitter conditions. Both synthesized g-jitter and real g-jitter data taken from space e ights are used. Computed results show that the concentration effects on interface morphology must be considered for an accurate prediction of solidie cation interface morphology, and g-jitter can induce signie cant convective e ows in the liquid pool, which, in turn, cause solute concentration nonuniformity during the space crystal growth. The use of an applied magnetic e eld can be effective in suppressing the deleterious g-jitter induced convection and solute nonuniformity and their effects on solidie cation.

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

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

NUMERICAL STUDY OF G-JITTER DURING DIRECTIONAL SOLIDIFICATION

A study of directional solidification of a weak binary alloy (specifically, Bi-1% Sn) using a fixed grid single domain approach has been undertaken. The enthalpy method is used to solve for the temperature field over the computational domain, including both the solid and liquid phases. The vorticity-stream function formulation is used to describe thermosolutal convection in the liquid region. Results on the solute field and segregation are presented, showing the effects of the periodic disturbances for a range of amplitudes and frequencies (multicomponent) and for actual acceleration data obtained during a space flight.

Directional Solidification of Bi-Sn on USMP-4

The experiments used MEPHISTO hardware to study the solidification and melting behavior of bismuth alloyed with 1 at% tin. Three samples, each approximately 900 mm long and 6mm in diameter, were used. A portion of each sample also included a 2 mm diameter growth capillary, to assist in the formation of a single grain. One sample provided the Scebeck voltage generated during melting and freezing processes. Another provided temperature data and Peltier pulsed demarcation of the interface shape for post flight analysis. The third sample provided resistance and growth velocity measurements. as well as additional thermal data. The third sample was also quenched at the end of the mission to preserve the composition of the liquid near the interface for post flight determination. A total of 450mm of directionally solidified samples were preserved for post mission structural and compositional characterization. Substantial differences were observed in the Seebeck signal between the ground-based experimeats and the space-based experiments. The temperature gradient in the liquid for the ground-based experiments was significantly lower than the temperature gradient in the liquid for the space-based experiments.