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  • FLUID MECHANICS AND HEAT TRANSFER  (16)
  • ASTRONAUTICS (GENERAL)  (7)
  • 1
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    Modeling of the float zone process (1981)
    In:  CASI
    Details
    Publication Date: 2006-07-02
    Description: The interaction of heat, mass, and momentum transport in the floating zone method for growing single crystals from the melt is examined. Methods for detailed numerical simulation of the transport phenomena in a floating zone are developed. Results of the calculations are combined with experiments to determine the effects of solidification induced, surface tension driven, and buoyancy driven convection in establishing dopant redistribution in the melt and the roles of heat transfer in crystal and melt and melt/solid interface shape in determining crystal quality. State of the art finite element techniques were developed for calculating the influence of natural convection in the melt on the shape of a melt/crystal interface and dopant segregation in the crystal. These techniques are demonstrated for solidification by the Bridgman technique. Numerical techniques are developed that calculate the shapes of both the melt/solid and melt/gas interfaces simultaneously with the thermal fields in melt and solid. Models for the fluid flows due to the rotation of the feed and crystal rods are completed and the effects of these flows on dopant segregation are studied, especially in the case of zones longer than can be achieved on Earth.
    Keywords: ASTRONAUTICS (GENERAL)
    Type: NASA. Marshall Space Flight Center Float Zone Workshop; p 175-199
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  • 2
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    Quadratic resonance in the three-dimensional oscillations of inviscid drops with surface tension (1986)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The moderate-amplitude, three-dimensional oscillations of an inviscid drop are described in terms of spherical harmonics. Specific oscillation modes are resonantly coupled by quadratic nonlinearities caused by inertia, capillarity, and drop deformation. The equations describing the interactions of these modes are derived from the variational principle for the appropriate Lagrangian by expressing the modal amplitudes to be functions of a slow time scale and by preaveraging the Lagrangian over the time scale of the primary oscillations. Stochastic motions are predicted for nonaxisymmetric deformations starting from most initial conditions, even those arbitrarily close to the axisymmetric shapes. The stochasticity is characterized by a redistribution of the energy contained in the initial deformation over all the degrees of freedom of the interacting modes.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physics of Fluids (ISSN 0031-9171); 29; 2788-279
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  • 3
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    The role of three-dimensional shapes in the break-up of charged drops (1987)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The nonlinear dynamics of nonaxisymmetric inviscid charged conducting drops near the Rayleigh charge limit (R = 4) is investigated analytically. It is shown that only axisymmetric spheroid drops bifurcate from the sphere family when the charge is increased, that oblate spheroids at R greater than 4 are unstable to nonaxisymmetric disturbances governing drop breakup, and that prolate spheroids at R less than 4 are unstable only to axisymmetric disturbances tending to increase the length of the drop along its symmetry axis. The effects of external electric fields and rigid-body rotation are also analyzed, and the solutions for the amplitude equations at R just less than 4 (equivalent to the dynamical equations of the Henon-Heiles Hamiltonian) are explored.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Proceedings, Series A - Mathematical and Physical Sciences (ISSN 0080-4630); 410; 1838,; 209-227
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  • 4
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    Bifurcation structure and the Eckhaus instability (1989)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The bifurcation diagram corresponding to the Eckhaus stability curve has been constructed for the one-dimensional Swift-Hohenberg equation in a finite domain. Finite-amplitude solutions with particular spatial wavelength recover linear stability, as predicted by the Eckhaus curve, after a sequence of secondary bifurcations from the branch of solutions with this wavelength. No connectivity between the primary-solution branches is admissible if the stability predicted by this bifurcation diagram is to correspond to the prediction of the Eckhaus analysis. The Eckhaus curve does not exist if nonlinear couplings destroy this pattern. This is demonstrated by analysis of a coupled pair of Swift-Hohenberg equations.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physical Review Letters (ISSN 0031-9007); 63; 2048-205
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  • 5
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    New class of asymmetric shapes of rotating liquid drops (1980)
    In:  Other Sources
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    Publication Date: 2011-08-17
    Description: Shapes and stability of surface-tension-endowed drops rotating rigidly at fixed angular momentum are calculated by finite-element analysis. A new family of asymmetric two-lobed drop shapes is discovered that branches from, and rejoins, the Pik-Pichak family of symmetric two-lobed shapes. The computations are verified for axisymmetric and symmetric two-lobed drop shape by comparison with previous approximations.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physical Review Letters; 45; July 21
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  • 6
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    Flow in a differentially rotated cylindrical drop at moderate Reynolds number (1984)
    In:  Other Sources
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    Publication Date: 2011-08-18
    Description: Galerkin finite-element approximations are combined with computer-implemented perturbation methods for tracking families of solutions to calculate the steady axisymmetric flows in a differentially rotated cylindrical drop as a function of Reynolds number Re, drop aspect ratio and the rotation ratio between the two end disks. The flows for Reynolds numbers below 100 are primarily viscous and reasonably described by an asymptotic analysis. When the disks are exactly counter-rotated, multiple steady flows are calculated that bifurcate to higher values of Re from the expected solution with two identical secondary cells stacked symmetrically about the axial midplane. The new flows have two cells of different size and are stable beyond the critical value Re sub c. The slope of the locus of Re sub c for drops with aspect ratio up to 3 disagrees with the result for two disks of infinite radius computed assuming the similarity form of the velocity field. Changing the rotation ratio for exact counter-rotation ruptures the junction of the multiple flow fields into two separated flow families.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Fluid Mechanics (ISSN 0022-1120); 144; 403-418
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  • 7
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    Finite element calculation of buoyancy-driven convection near a melt/solid phase boundary (1983)
    In:  Other Sources
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    Publication Date: 2011-08-18
    Description: Two iterative schemes based on the mixed finite element method are developed for analyzing steady natural convection in a melt adjacent to its solid phase. The simplest method decouples the calculation of the field variables and the shape of the melt/solid interface into two interlocked iterations that are performed successively. The second method uses Newton's iteration to solve simultaneously for both types of unknowns and has a quadratic convergence rate. Results for a model problem of melt and solid in a cylindrical ampoule show the Newton algorithm to be a factor of three more efficient.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
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  • 8
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    Natural convection in steady solidification - Finite element analysis of a two-phase Rayleigh-Benard problem (1984)
    In:  Other Sources
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    Publication Date: 2011-08-18
    Description: Galerkin finite-element approximations and Newton's method for solving free boundary problems are combined with computer-implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt. The Newton method gives rapid convergence to steady state velocity, temperature and pressure fields and melt-solid interface shapes, and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability. The power of this combination is demonstrated for a two-phase Rayleigh-Benard problem composed of melt and solid in a veritical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt-solid interface is always a solution. Multiple cellular flows bifurcating from the static state are detected and followed as Rayleigh number is varied. Changing the boundary conditions to approach those appropriate for the vertical Bridgman solidification system causes imperfections that eliminate the static state. The flow structure in the Bridgman system is related to those for the Rayleigh-Benard system by a continuous evolution of the boundary conditions.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Computational Physics (ISSN 0021-9991); 53; 1-27
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  • 9
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    The shape and stability of rotating liquid drops (1980)
    In:  Other Sources
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    Publication Date: 2011-08-17
    Description: Equilibrium shapes and stability of rotating drops held together by surface tension are found by computer-aided analysis that uses expansions in finite-element basis functions. Shapes are calculated as extrema of appropriate energies. Stability and relative stability are determined from curvatures of the energy surface in the neighborhood of the extremum. Families of axisymmetric, two-, three-, and four-lobed drop shapes are traced systematically. Bifurcation and turning points are located and the principle of exchange of stabilities is tested. The axisymmetric shapes are stable at low rotation rates but lose stability at the bifurcation to two-lobed shapes. Two-lobed drops isolated with constant angular momentum are stable. The results bear on experiments designed to further those of Plateau (1863).
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
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  • 10
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    The dependence of the shape and stability of captive rotating drops on multiple parameters (1982)
    In:  Other Sources
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    Publication Date: 2011-08-18
    Description: Asymptotic and numerical techniques in bifurcation theory are applied to the Young-Laplace equation governing meniscus shape in order to analyze the dependence of the shape and stability of rigidly rotating drops held captive between corotating solid faces on multiple parameters. Asymptotic analysis of the evolution of drop shape from the cylindrical as a function of distance between the solid faces, drop volume, rotational Bond number and gravitational Bond number shows that some shape bifurcations from cylinders to wavy, axisymmetric menisci are ruptured by small changes in drop volume or gravity. Computer calculations of axisymmetric drop shapes based on a finite element representation of the interface and numerical algorithms for tracking shape families and singular points are then used to map drop stability for the four-dimensional parameter space. The results of the asymptotic and numerical analyses are shown to agree well within the limited range of parameters where the asymptotic analysis is valid.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Philosophical Transactions, Series A (ISSN 0080-4614); 306; 1493,; Aug. 27
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