Engineering topics

Boisvert, R. F.

Publications and source records attributed to Boisvert, R. F..

13 records

NASA NTRS1990

Elimination of spurious eigenvalues in the Chebyshev tau spectral method

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.

Mcfadden, G. B.↗

NASA NTRS1989

Elimination of spurious eigenvalues in the Chebyshev tau spectral method

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.

Mcfadden, G. B.↗

NASA NTRS1988

Numerical simulation of morphological development during Ostwald ripening

The morphological evolution of a small number of particles undergoing Ostwald ripening in two dimensions was investigated using a boundary integral technique. The numerical calculations show that, in many cases, interparticle diffusional interactions do not induce large distortions in particle morphology from a circle, due to the strong local interaction between regions of different curvature on the same particle. Particle migration due to interparticle diffusional interactions was observed, with the migration distance larger than the initial radius of a particle, which is linked to the particle spatial arrangement. As diffusion is the mechanism for the migration, it is expected that particle movement is a generic aspect of the coarsening process at high volume fractions of coarsening phase and, possibly, at low volume fractions. The calculations support unambiguously the Ostwald ripening mechanism for flat formation during liquid-phase sintering. As such, the appearance or regions of low interfacial curvature is a dynamic phenomenon dependent on interparticle diffusion.

Voorhees, P. W.↗

NASA NTRS1987

Nonplanar interface morphologies during unidirectional solidification of a binary alloy. II - Three-dimensional computations

A finite difference method is used to obtain three-dimensional steady-state solutions for nonplanar interface morphologies in order to study the situation of equal thermal properties in the crystal and melt with negligible latent heat release. Stable steady-state solutions corresponding to two-dimensional bands and three-dimensional hexagonal nodes, as well as to rectangular interface planiforms, are found using a model of an aluminum-chromium alloy with a distribution coefficient of greater than one. Hexagonal nodes are predicted near the onset of instability, in agreement with weakly nonlinear theory.

Mcfadden, G. B.↗

NASA NTRS1985

Double-diffusive convection with sidewalls

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.

Mcfadden, G. B.↗

NASA NTRS1985

Convective influence on the stability of a cylindrical solid-liquid interface

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.

Fang, Q. T.↗

NASA NTRS1984

Morphological stability in the presence of fluid flow in the melt

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.

Mcfadden, G. B.↗

NASA NTRS1984

Asymmetric instabilities in buoyancy-driven flow in a tall vertical annulus

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.

Mcfadden, G. B.↗

NASA NTRS1984

Effect of a forced Couette flow on coupled convective and morphological instabilities during unidirectional solidification

The effect of a forced Couette flow, parallel to a horizontal crystal-melt interface during directional solidification of an alloy of lead containing tin, on the onset of convective and morphological instabilities, is calculated numerically via a linear stability analysis. Such a flow does not affect perturbations with wave vectors perpendicular to the flow. For perturbations with wave vectors parallel to the flow, the onset of morphological instability is somewhat suppressed and thermosolutal convection is greatly suppressed. When instabilities occur, they are oscillatory and correspond to travelling waves. For values of the crystal growth velocity for which mixed morphological and convective modes occur, the presence of a forced flow produces sufficient decoupling to allow otherwise degenerate branches to be identified.

Coriell, S. R.↗

NASA NTRS1984

Coupled convective instabilities at crystal-melt interfaces

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.

Coriell, S. R.↗

NASA NTRS1983

Convection effects at solid-liquid interfaces: Influence of gravity

The stability of the flow between two vertical, infinite, rigid, coaxial cylinders held at different temperatures is analyzed by linear stability theory. For a Prandtl number of 22.8 and a radius ratio of 0.02, the flow is unstable to an axisymmetric perturbation at a critical Grashof number of 2150; the wave speed of the instability is comparable to the maximum velocity of the unperturbed flow. When the rigid outer cylinder-fluid interface is replaced by a crystal-melt interface which can change shape, two new modes of instability occur at lower Grashof numbers.

Glicksman, M. E.↗

NASA NTRS1983

Morphological and convective instabilities during solidification

Linear stability theory is employed in the present analysis of flow stability between two vertical, infinite, rigid coaxial cylinders at different temperatures. These calculations have been prompted by, and are found to be in general agreement with, experiments on succinonitrile. A long, vertical cylinder sample of this material was heated so that a vertical melt annulus formed between the coaxial heater and the surrounding crystal/melt interface. Above a critical Grashof number of about 200, a helical crystal/melt interface formed which steadily rotated about the cylinder axis and whose wave speed was several orders of magnitude lower than the base flow velocity.

Coriell, S. R.↗

NASA NTRS1975

An interactive graphics package for the automatic node renumbering of finite element matrices

An interactive graphics software package which allows users to display the non-zero structure of large sparse symmetric materials was described and methods used to implement it as a portable FORTRAN callable subroutine were summarized. In particular, the system permits the display of the resulting matrix after reordering the rows and columns, with the reordering scheme either defined by the user or automatically generated by the program with the aim of reducing matrix bandwidth and profile. Although the primary application of the package has been to the finite element analysis of structures, it is equally well suited to the many other areas of engineering and science which use sparse matrices.

Boisvert, R. F.↗