SEARCH · Engineering Papers
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
The topics are presented in viewgraph form and include: (1) a problem statement; (2) the rapid pressure models tested (both linear and nonlinear); (3) the computational problem; and (4) shortcomings and future work.
The onset of laminar axisymmetric Rayleigh-Benard convection is investigated for a low-Prandtl number liquid metal in a cylindrical container. All surfaces are considered to be solid and no-slip. Two separate cases are examined for the thermal boundary conditions at the side wall, one with conducting and the other with insulated surface. The governing Boussinesq system is first perturbed and then simplified by introducing a Stokes stream function. Subsequently, a Chebyshev Galerkin spectral model is employed to reduce the simplified system to a system of first-order nonlinear ordinary differential equations. A local stability analysis determines the two values of the first critical Rayleigh number, Ra(sub cl), for the insulated and conducting side walls. As expected, the conducting Ra(sub cl) value of 2882.5 obtained from the present approach exceeded the corresponding insulated Ra(sub cl) value of 2331.6. For the insulated case, an earlier study using a different numerical approach suggests that Ra(sub cl) = 2261.9, while an experimental study measured Ra(sub cl) = 2700.
Results of two recent crystal growth experiments conducted aboard Skylab are analyzed for thermoconvective aspects. Theoretical temperature and velocity profiles in the crystal melts are predicted via computer modeling. These results are compared with experimental data obtained from Skylab investigators. From theoretical considerations, both indium-antimonide experiments should have exhibited substantial thermocapillary convection, but did not due to probable oxide film interference and/or opposing solutal effects.
The glass transition, crystallization and melting of Au(55)Pb(22.5)Sb(22.5) alloys have been studied by differential scanning calorimetry DSC. Crystallization on heating above the glass transition temperature Tg (45 C) begins at 64 C. Further crystallization events are observed at 172 C and 205 C. These events were found to correspond to the formation of the intermetallic compounds AuSb2, Au2Pb, and possibly AuPb2, respectively. Isothermal DSC scans of the glassy alloy above Tg were used to monitor the kinetics of crystallization. The solidification behavior and heat capacity in the glass-forming composition range were determined with droplet samples. An undercooling level of 0.3T(L) below the liquidus temperature T(L) was achieved, resulting in crystallization of different stable and metastable phases. The heat capacity C(P) of the undercooled liquid was measured over an undercooling range of 145 C.
During solidification of a binary alloy at constant velocity vertically upward, thermosolutal convection can occur if the solute rejected at the crystal-melt interface decreases the density of the melt. We assume that the crystal-melt interface remains planar and that the flow field is periodic in the horizontal direction. The time-dependent nonlinear differential equations for fluid flow, concentration, and temperature are solved numerically in two spatial dimensions for small Prandtl numbers and moderately large Schmidt numbers. For slow solidification velocities, the thermal field has an important stabilizing influence: near the onset of instability the flow is confined to the vicinity of the crystal-melt interface. Further, for slow velocities, as the concentration increases, the horizontal wavelength of the flow decreases rapidly - a phenomenon also indicated by linear stability analysis. The lateral inhomogeneity in solute concentration due to convection is obtained from the calculations. For a narrow range of solutal Rayleigh numbers and wavelengths, the flow is periodic in time.
The melting and crystallization behavior of four quaternary CaO-MgO-Al2O3-SiO2(CMAS) silicates were investigated. The CaO:SiO2 ratios of these systems were based on various terrestrial sources of ingested particles relevant to gas turbine engine operating environments. Melting behavior was characterized using differential scanning calorimetry, and high temperature intrinsic crystallization products were determined by furnace heat treatments of the glasses at 1200°C, 1300°C, and 1400°C. The silicates exhibited a wide range of melting temperatures from ~1240°C up to ~1500°C, with most of the compositions exhibiting incongruent melting behavior. High temperature crystallization products included CaSiO3,CaAl2Si2O8, Ca2MgSi2O7, and Ca(Mg,Al)Si2O6, although SiO2 was the only crystalline phase observed at 1400°C.
Recent experiments have shown that the presence of a vertical buoyancy-driven flow adjacent to an initially cylindrical crystal-melt interface may produce a time-dependent helical deformation of the interface, with a rotation period ranging from several minutes to many hours, depending upon the width of the melt. The temperature distribution is such that the interface is expected to be morphologically stable in the absence of fluid flow. A linear stability analysis reveals that the instability is due to a coupling between a basic hydrodynamic instability in the buoyant flow and the deformable boundary separating the two phases. The crystal-melt interface lowers the critical Grashof number of an analogous rigid-walled system by an order of magnitude for succinonitrile with a Prandtl number P = 22.8; furthermore, the hydrodynamic mode that is actually destabilized by the interface is not the least stable mode in the rigid-walled system for P = 22.8. The results show that the instability may be regarded either as a rather large alteration of a basic hydrodynamic instability by the crystal-melt interface, or as a significant modification of the morphological stability of the interface by the presence of the buoyant flow.
The effects of asymmetry in furnace temperature profile and pulling velocity on the crystal interface shape are demonstrated while neglecting the latent heat of solidification. It is seen that the furnace temperature profile may be varied in order to influence the shape of the melt-crystal interface. An exact thermal analysis is then performed on the Bridgman technique by including the latent heat of solidification as a source term. The exact temperature field required for yielding a flat melt-crystal interface is obtained. The earlier observation regarding the influence of furnace temperature profile on the interface shape is confirmed and a criterion for achieving a flat interface is obtained. Various furnace temperature profiles are selected and their corresponding melt-crystal interface results are presented.
Polysiloxanes morphology crystallized isothermally from melt using electron microscopy, noting fracture ease increment with molecular weight decrease
In detached Bridgman growth, a gap exists between the growing crystal and the crucible wall. According to crystal shape stability theory, only specific gap widths will be dynamically stable. Beginning with a crystal diameter that differs from stable conditions, the transient crystal growth process is analyzed. The transient shapes are calculated assuming that the growth angle is constant. Anisotropy and dynamic contact angle effects are considered. In microgravity, dynamic stability depends only on capillary effects and is decoupled from heat transfer. However, heat transfer will influence the crystal-melt interface shape. The local angles and the crystal-melt-vapor triple junction are analyzed and the applicability of the Herring formula is discussed. A potential microgravity experiment is proposed which would enhance our understanding of the detached growth dynamic stability problem.
The effects of cooling the crystal side surface by blowing a jet of an inert gas are examined in detail for Czochralski crystal growth. A combined model of the crystal + melt, which incorporates the detailed radiation calculations, the shape of the melt-gas meniscus, predicts the growth rate and the crystal-melt interface shape, is used for this study. The convective heat transfer coefficient for the jet is estimated from the correlation available in the literature. The effect of the jet cooling on the interface shape and the pulling rate is significant. The crystal diameter as well as the interface shape tend to be more stable in the environment of the rapid cooling of the crystal by the jet. The crystal diameter or the interface shape can be easily controlled by adjusting the gas flow rate through the jet. This gives the Czochralski pulling an additional degree of freedom facilitating the control of crystal diameter and interface shape.
The formation by melt quenching of such metastable structures as glassy or microcrystalline solids and highly supersaturated solutions is made possible by the extreme resistance of most melts to homophase crystal nucleation at deep undercooling. This nucleation resistance contrasts sharply with the very low kinetic resistance to the movement of crystal-melt interfaces, once formed, in metals and other fluid systems at even minute undercooling. The methods of nucleation study which have proven especially effective in bypassing nucleation by heterophase impurities thereby exposing the high resistance of melts to homophase nucleation may be summarized as follows: observation of the crystallization behavior of dispersed small droplets; drop tube experiments in which liquid drops solidify, under containerless conditions, during their fall in the tube; and observation of the crystallization of bulk specimens immersed in fluxes chosen to dissolve or otherwise deactivate (e.g., by wetting) heterophase nucleants. This method has proven to be remarkably effective in deactivating such nucleants in certain pure metals.
A three-dimensional weakly nonlinear analysis for conditions near the onset of instability at the crystal-melt interface was carried out to second order, taking into account the effects of latent heat generation and surface-tension anisotropy of the crystal-melt interface; particular consideration was given to the growth of a cubic crystal in the 001-, 011-, and 111-line directions. Numerical calculations by McFadden et al. (1987), performed for an aluminum-chromium alloy with the assumption of a linear temperature field and an isotropic surface tension, showed that only hexagonal nodes (and not hexagonal cells) occurred near the onset of instability. The results of the present analysis indicate that the nonlinear temperature field (which occurs when thermal conductivities of the crystal and the melt are different and/or the latent heat effects are not negligible) can modify this result and, for certain alloys and processing conditions, can cause the occurrence of hexagonal cells near the onset of instability.
Experimental data on Al-0.8Au horizontal solidification of a 1 mm thick specimen in a BN crucible shows the effect of growth rate on the solidification interface shape. For translation rates below 0.5 micron/s the interface maintains a plain and flat shape. When the translation rate is 3 to 5 micron/s or more, the interface appearance changes to two planar zones, with the zone closer to the bottom having higher inclination. The interface shapes were measured by first quenching in place during growth. X-ray microscopy shows the interface shape within the quenched sample by viewing through the side of the specimen. In order to provide theoretical explanation of the phenomena, numerical modeling was undertaken using finite element code FIDAP. Double diffusion convection in Al-0.8Au melt and crystal-melt interface curvature during directional solidification was analyzed numerically. Actual thermophysical properties of Al-0.8Au including the binary Al-Au phase diagram were used. Although convection in the sample is weak, for the slower translation rate convection and diffusion is sufficient for the redistribution of initial compositional stratification caused by gravity. When translation rate is raised, neither convection nor diffusion can provide proper mixing so that solidification temperatures differ significantly near the bottom within the bulk of the sample. As a result, the solid-liquid interface appears to have two planar zones with different inclination.
During directional solidification of a binary alloy at constant velocity, buoyancy-driven fluid flow may occur due to the solute gradients generated by the solidification process. Numerical calculations of the solute and fluid flow fields in the melt have been carried out using finite differences in a two-dimensional, time-dependent model that assumes a planar crystal-melt interface and allows time-dependent gravitational accelerations. The container walls are rigid and perfectly insulating for solute. For constant vertical gravitational accelerations, as the solutal Rayleigh number is varied, multiple steady states and time-dependent states may occur. The bifurcation from the quiescent state may be subcritical or transcritical, depending on the aspect ratio of the container. Calculations have also been performed for a gravitational acceleration that is assumed to be uniform in magnitude with its direction rotating uniformly. Numerical results have been obtained for a Schmidt number of 10 and a gravitational acceleration of 0.0001 G. The maximum variation in the solute concentration at the crystal-melt interface is calculated for various values of the rotation rate of the gravitational acceleration.
The previously developed Ginzburg-Landau theory for calculating the crystal-melt interfacial tension of bcc elements to treat the classical one-component plasma (OCP), the charged fermion system, and the Bose crystal. For the OCP, a direct application of the theory of Shih et al. (1987) yields for the surface tension 0.0012(Z-squared e-squared/a-cubed), where Ze is the ionic charge and a is the radius of the ionic sphere. Bose crystal-melt interface is treated by a quantum extension of the classical density-functional theory, using the Feynman formalism to estimate the relevant correlation functions. The theory is applied to the metastable He-4 solid-superfluid interface at T = 0, with a resulting surface tension of 0.085 erg/sq cm, in reasonable agreement with the value extrapolated from the measured surface tension of the bcc solid in the range 1.46-1.76 K. These results suggest that the density-functional approach is a satisfactory mean-field theory for estimating the equilibrium properties of liquid-solid interfaces, given knowledge of the uniform phases.
Kilbourne Hole (NM, USA) and Dish Hill (CA, USA) mantle xenoliths sample continental mantle in two different tectonic settings. Kilbourne Hole (KH) is located in the Rio Grande rift. Dish Hill (DH) is located in the southern Mojave province, an area potentially affected by subduction of the Farallon plate beneath North America. FTIR analyses were obtained on well characterized pyroxenite, dunite and wehrlite xenoliths, thought to represent crystallized melts at mantle depths. PUM normalized REE patterns of the KH bulk-rocks are slightly LREE enriched and consistent with those of liquids generated by < 5% melting of a spinel peridotite source. Clinopyroxenes contain from 272 to 313 ppm weight H2O similar to the lower limit of KH peridotite clinopyroxenes (250-530 ppm H2O). This is unexpected as crystallized melts like pyroxenites should concentrate water more than residual mantle-like peridotites, given that H is incompatible. PUM normalized bulk REE of the DH pyroxenites are characterized by flat to LREE depleted REE profiles consistent with > 6% melting of a spinel peridotite source. Pyroxenite pyroxenes have no detectable water but one DH wehrlite, which bulk-rock is LREE enriched, has 4 ppm H2O in orthopyroxene and <1ppm in clinopyroxene. The DH pyroxenites may thus come from a dry mantle source, potentially unaffected by the subduction of the Farallon plate. These water-poor melts either originated from shallow oceanic lithosphere overlaying the Farallon slab or from continental mantle formed > 2 Ga. The Farallon subduction appears to have enriched in water the southwestern United States lithospheric mantle further east than DH, beneath the Colorado plateau.
The dynamics and structure of the crystal melt interface are of great importance in crystal growth, melting, and other properties of the solid-liquid interface. The Embedded Atom Method (EAM), a semiempirical method developed by Daw and Baskes for determining the energetics of atoms in a bulk environment, is a useful method in the computer simulation. The EAM functions of PB in conjunction with the MD code are employed to study melting and disordering of the Pb(100) surface. The EAM functions are fitted to the bulk experimental data at zero temperature, and it is not clear if it will behave correctly at higher temperatures. In fact, it is shown that use of a similar type of potential at higher temperatures might result in a negative coefficient of thermal expansion. The primary purpose here is to perform MD simulation combined with the EAM functions of PB to study melting of the Pb(100) surface. This provides an accurate test of the EAM functions at higher temperatures. In particular, we calculate the two dimensional structure factor, the two dimensional distribution function, and density profile as a function of temperature up to the melting point of lead.