On buoyant convection in binary solidification

We consider the problem of nonlinear steady buoyant convection in horizontal mushy layers during the solidification of binary alloys. We investigate both cases of zero vertical volume flux and constant pressure, referred to as impermeable and permeable conditions, respectively, at the upper mush???liquid interface. We analyze the effects of several parameters of the problem on the stationary modes of convection in the form of either hexagonal cells or non-hexagonal cells, such as rolls, rectangles and squares. [More ...]published or submitted for publicationis not peer reviewe

Analytical and Computational Studies of Convection in Solidifying Binary Media

111 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2005.The behavior of convective instabilities in solidifying media is of interest in applications spanning materials processing and geophysics. Under a broad set of circumstances, constitutional supercooling occurs, resulting in the formation of a layer of dendritic growth called a mushy layer. The mushy layer has both solid and fluid components. We consider the problem of nonlinear steady buoyant convection in horizontal mushy layers during the solidification of binary alloys. Both cases of zero vertical volume flux and constant pressure at the upper mush-liquid interface were investigated. We analyze the effects of several parameters of the problem on the stationary modes of convection in the form of either hexagonal cells or nonhexagonal cells such as rolls, rectangles, and squares. No assumption is made on the thickness of the mushy layer, and a number of simplifying assumptions made in previous nonlinear analyses are relaxed here in order to study a richer set of phenomena. Using both analytical and computational methods, we determine the steady solutions to the weakly nonlinear problem by using a perturbation technique for both constant and variable permeability, referred to as passive and reactive mushy layer cases, respectively. Both the nonlinear basic state and the reactive mushy zone of the present problem favor hexagon-pattern convection. The results of the analyses and computations indicate in particular that, depending on the range of values of the parameters, bifurcation to nonhexagonal convection can be either supercritical or subcritical, while bifurcation to hexagon-pattern convection, corresponding to the smallest value of the Rayleigh number, is subcritical. For reactive mushy layers, subcritical down-hexagons with downflow at the cell centers and upflow at the cell boundaries, which have been observed in related experiments, were predicted. Supercritical nonhexagons were also predicted in particular ranges of values of the parameters.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

Effect of coriolis force on instabilities of liquid and mushy regions during alloy solidification

Linear flow instabilities of the liquid and mushy regions during directional solidification of a binary alloy are studied for a horizontal solidified system rotating about an axis inclined with respect to the gravity vector. Stability analysis and numerical computation are carried out to determine the results for the stationary disturbances at several values of the rotation rates and for given values of the other parameters of the problem. The results provide information about the effects of Corioiis force on various flow features in the liquid and mushy layers including critical modes of convection, neutral stability curves, preferred flow pattern, streamlines and density plots for the solid fraction perturbation in the mushy layer. The preferred structure of the mush-liquid interface is found to be that of longitudinal rolls. The main mode of convection is found to be the so-called mushy layer mode of convection, which can generate double-cell structure in the vertical direction in the presence of the Coriolis force. The Coriolis force appears to strengthen the mushy layer mode of convection, while it can virtually eliminate the so-called boundary layer mode of convection which can be present in the absence of rotation. The rotational effects were found to significantly weaken the convection modes in the liquid layer, while they strengthen the convection modes in the mushy layer. The Coriolis force appears to be generally stabilizing in the sense that the motion in the liquid zone is significantly weakened, tendency for the chimney formation in the mushy zone is reduced and the critical values of the controlling parameters (liquid and mush Rayleigh numbers) and the wave numbers of the critical modes of convective flow mostly increase with increasing the rotation rate