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  • 1
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    Coupled convective instabilities at crystal-melt interfaces (1984)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The stability of the parallel flow between a vertical crystal-melt interface and a vertical wall held at a temperature above the melting point of the crystal is analyzed for Prandtl numbers, P, ranging from 0.01 to 100. Three modes of instability occur: (1) a buoyant mode, (2) a shear mode, and (3) a coupled crystal-melt mode. The buoyant and shear modes are similar to those that occur for flow between two vertical rigid walls held at different temperatures. For Prandtl numbers greater than approximately two, the coupled crystal-melt mode occurs at a lower Grashof number than the other two modes. Specific results are given for succinonitrile (P = 22.8) and lead (P = 0.0225). These calculations and similar calculations for a cylindrical geometry were motivated by and are in general agreement with recent experiments on succinonitrile.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Crystal Growth (ISSN 0022-0248); 66; 514-524
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  • 2
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    Thermosolutal convection during directional solidification. II - Flow transitions (1987)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The influence of thermosolutal convection on solute segregation in crystals grown by vertical directional solidification of binary metallic alloys or semiconductors is studied. Finite differences are used in a two-dimensional time-dependent model which assumes a planar crystal-melt interface to obtain numerical results. It is assumed that the configuration is periodic in the horizontal direction. Consideration is given to the possibility of multiple flow states sharing the same period. The results are represented in bifurcation diagrams of the nonlinear states associated with the critical points of linear theory. Variations of the solutal Rayleigh number can lead to the occurrence of multiple steady states, time-periodic states, and quasi-periodic states. This case is compared to that of thermosolutal convection with linear vertical gradients and stress-free boundaries.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physics of Fluids (ISSN 0031-9171); 30; 659-671
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  • 3
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    Elimination of spurious eigenvalues in the Chebyshev tau spectral method (1990)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: A very simple modification is presented for the Chebyshev tau method which can eliminate spurious eigenvalues, proceeding from a consideration of the vorticity-streamfunction reformulation of the Chebyshev tau method and the Chebyshev-Galerkin method, which have no spurious modes. Consideration of a model problem indicates that these two approaches are equivalent, and that they reduce to the present modification of the tau method. This modified tau method also eliminates spurious eigenvalues from the Orr-Sommerfeld equation.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Computational Physics (ISSN 0021-9991); 91; 228-239
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  • 4
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    Stabilization of Taylor-Couette flow due to time-periodic outer cylinder oscillation (1990)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case when the inner cylinder is rotated at a constant angular velocity and the outer cylinder is driven sinusoidally in time with zero mean rotation. This configuration was studied experimentally by Walsh and Donnelly. The critical Reynolds numbers calculated from linear stability theory agree well with the experimental values, except at large modulation amplitudes and small frequencies. The theoretical values are obtained using Floquet theory implemented in two distinct approaches: a truncated Fourier series representation in time, and a fundamental solution matrix based on a Chebyshev pseudospectral representation in space. For large amplitude, low frequency modulation, the linear eigenfunctions are temporally complex, consisting of a quiescent region followed by rapid change in the perturbed flow velocities.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physics of Fluids A (ISSN 0899-8213); 2; 2147-215
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  • 5
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    Effect of a crystal-melt interface on Taylor-vortex flow (1990)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case that the stationary outer cylinder is a crystal-melt interface rather than a rigid surface. A radial temperature difference is maintained across the liquid gap, and equations for heat transport in the crystal and melt phases are included to extend the ordinary formulation of this problem. The stability of this two-phase system depends on the Prandtl number. For small Prandtl number the linear stability of the two-phase system is given by the classical results for a rigid-walled system. For increasing values of the Prandtl number, convective heat transport becomes significant and the system becomes increasingly less stable. Previous results in a narrow-gap approximation are extended to the case of a finite gap, and both axisymmetric and nonaxisymmetric disturbance modes are considered. The two-phase system becomes less stable as the finite gap tends to the narrow-gap limit. The two-phase system is more stable to nonaxisymmetric modes with azimuthal wavenumber n = 1; the stability of these n = 1 modes is sensitive to the latent heat of fusion.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physics of Fluids A (ISSN 0899-8213); 2; 700-705
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  • 6
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    Double-diffusive convection with sidewalls (1985)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: Stommel et al. (1956) have first described an instability, known as thermosolutal convection, thermohaline convection, or double-diffusive convection. This instability may occur in the case of a fluid in a gravitational field with two diffusing components present. The present study is concerned with the effect of sidewalls on flow in the fingering regime in the absence of applied horizontal gradients. The work was motivated by numerical results obtained on the basis of a simulation of thermosolutal convection occurring during the unidirectional solidification of a binary alloy. In this case, the unperturbed solute field in the liquid ahead of the solidifying planar interface has an exponential vertical profile because of the rejection or preferential incorporation of solute by the solid phase.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physics of Fluids (ISSN 0031-9171); 28; 2716-272
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  • 7
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    Asymmetric instabilities in buoyancy-driven flow in a tall vertical annulus (1984)
    In:  Other Sources
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    Publication Date: 2011-08-18
    Description: Linear stability of the one-dimensional flow between infinite vertical coaxial cylinders induced by heating the inner cylinder is considered for various ratios (kappa) of the inner radius to the outer radius, and for Prandtl numbers (P) appropriate to air and water. For air with P = 0.71 the least stable disturbance is nonaxisymmetric for kappa less than 0.44 and is axisymmetric for kappa greater than 0.44, and in either case the instability is due to the action of the shear forces. For P = 3.5, the situation is similar, except that the asymmetric shear mode is superseded by an axisymmetric instability driven by buoyancy forces for kappa = 0.03-0.16. Wave speeds, wavenumbers, and critical Grashof numbers for these cases and for the case of zero Prandtl number are given.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physics of Fluids (ISSN 0031-9171); 27; 1359-136
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  • 8
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    Interaction of flows with the crystal-melt interface (1986)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: The coupling between a crystal-melt interface and fluid flow is investigated. The solidification boundary conditions at the crystal-melt interface are described. The influences of morphological and double-diffusive instabilities during directional solidification on the interface are studied. The experiments by Glicksman and Mickalonis (1982) and Fang et al. (1985) which examine the relationship between the hydrodynamic state of the phase melt and phase-change interface are analyzed. The Rayleigh-Benard problem, and the effect of crystal-melt interaction on the Rayleigh number are examined. Various applications for melt-flow interactions with solid-liquid interface to engineering and welding are discussed.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
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  • 9
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    Convective influence on the stability of a cylindrical solid-liquid interface (1985)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: Experiments in which a long vertical, heated wire is surrounded by concentric annuli of a melt and its crystalline solid show that the convection state changes from a stable unicell surrounded by a stationary cylindrical solid-liquid interface, to a complex time-dependent flow surrounded by a rotating, helical solid-liquid interface. This transition occurs at a Grashof number of approximately 150, which is an order of magnitude less than the critical Grashof number calculated for a liquid annulus surrounded by rigid walls. A linear stability analysis has been carried out for an infinitely tall vertical annulus. When the deformable nature of the crystal-melt interface is taken into account in the boundary conditions, two new modes of instability arise. The most dangerous mode is asymmetrical and corresponds to helical waves travelling vertically upwards. The critical Grashof number and the scaling properties of the eigenstate agree with experiments. The results clearly demonstrate the coupling of convection with crystal-melt interfacial instabilities.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Fluid Mechanics (ISSN 0022-1120); 151; 121-140
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  • 10
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    Elimination of spurious eigenvalues in the Chebyshev tau spectral method (1989)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Spectral methods have been used to great advantage in hydrodynamic stability calculations; the concepts are described in Orszag's seminal application of the Chebyshev tau method to the Orr-Sommerfeld equation for plane Poiseuille flow in 1971. Orszag discusses both the Chebyshev Galerkin and the Chebyshev tau methods, but presents results for the tau method, which is easier to implement than the Galerkin method. The tau method has the disadvantage that two unstable eigenvalues are produced that are artifacts of the discretization. An extremely simple modification to the Chebyshev tau method is presented which eliminates the spurious eigenvalues. First a simplified model of the Orr-Sommerfeld equation discussed by Gottlieb and Orszag was studied. Then the Chebyshev tau method is considered, which has two spurious eigenvalues, and then a modification which eliminates them is described. Finally, results for the Orr-Sommerfeld equation are considered where the modified tau method also eliminates the spurious eigenvalues. The simplicity of the modification makes it a convenient alternative to other approaches to the problem.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: PB89-209282 , NISTIR-89/4090
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