Engineering topics

Merchant, G. J.

Publications and source records attributed to Merchant, G. J..

5 records

NASA NTRS1992

Pulsatile instability in rapid directional solidification - Strongly-nonlinear analysis

In the rapid directional solidification of a dilute binary alloy, analysis reveals that, in addition to the cellular mode of Mullins and Sekerka (1964), there is an oscillatory instability. For the model analyzed by Merchant and Davis (1990), the preferred wavenumber is zero; the mode is one of pulsation. Two strongly nonlinear analyses are performed that describe this pulsatile mode. In the first case, nonequilibrium effects that alter solute rejection at the interface are taken asymptotically small. A nonlinear oscillator equation governs the position of the solid-liquid interface at leading order, and amplitude and phase evolution equations are derived for the uniformly pulsating interface. The analysis provides a uniform description of both subcritical and supercritical bifurcation and the transition between the two. In the second case, nonequilibrium effects that alter solute rejection are taken asymptotically large, and a different nonlinear oscillator equation governs the location of the interface to leading order. A similar analysis allows for the derivation of an amplitude evolution equation for the uniformly pulsating interface. In this case, the bifurcation is always supercritical. The results are used to make predictions about the characteristics of solute bands that would be frozen into the solid.

Merchant, G. J.↗

NASA NTRS1992

Pulsatile instability in rapid directional solidification: Strongly-nonlinear analysis

In models of rapid directional solidification, non-equilibrium interfacial conditions are employed. As a result, there is an oscillatory mode of instability, as well as the steady cellular mode, found in the equilibrium model of Mullins and Sekerka. When the temperature field is decoupled from the problem, the preferred wave number for the oscillatory mode is zero, and the interface pulsates in time while remaining spatially uniform. Results from multiple scale analyses in the two limiting cases of the parameters are reported. In these limits, it is found that the instability is a bifurcation to relaxation oscillations; these nonlinear oscillations may be related to the observed microstructure that results from rapid solidification processes such as laser surface remelting.

Braun, Richard J.↗

NASA NTRS1990

Morphological instability in rapid directional solidification

Mullins and Sekerka (1964) showed for fixed temperature gradient that the planar interface is linearly stable for all pulling speeds V above some critical value, the absolute stability limit. Near this limit, where solidification rates are rapid, the assumption of local equilibrium at the interface may be violated. Here, nonequilibrium effects are incorporated into a linear stability analysis of the planar front by allowing the segregation coefficient and interface temperature to depend on V in a thermodynamically consistent way. The absolute stability limit of the cellular mode is modified. A new oscillatory state is formed which, in the absence of latent heat, has a critical wavenumber of zero; by itself this instability would lead to the formation of solute bands in the solid. This mode has its own absolute-stability limit determined by solute trapping and kinetics. Under certain conditions, there exists a window of stability above the steady absolute-stability boundary and below the oscillatory-stability boundary; here the planar segregation-free state is restabilized.

Merchant, G. J.↗

NASA NTRS1989

Flow-induced morphological instabilities due to temporally-modulated stagnation-point flow

The influence of periodically-modulated planar stagnation-point flow on the morphological stability of a directionally-solidifying interface is presently considered with a view to the effect of unsteady nonparallel flows on single-crystal growth. The modeling of the system assumes that the viscous boundary layer thickness is much greater than that of the solute boundary layer, and that the modulation frequency is much smaller than the strength of plane stagnation-point flow. The solidifying interface is either stabilized or destabilized depending on the ratio of the period of modulation to the solute-diffusion time.

Merchant, G. J.↗

NASA NTRS1989

Shallow cells in directional solidification

The existing theory on two-dimensional transitions (appropriate to thin parallel-plate geometries) is presented in such a way that it is possible to identify easily conditions for the onset of shallow cells. Conditions are given under which succinonitrile-acetone mixtures should undergo supercritical bifurcation in experimentally accessible ranges. These results suggest a means for the quantitative test of the Mullins and Sekerka (1964) model and its weakly nonlinear extensions.

Merchant, G. J.↗