Effects of centrifugal and Coriolis forces on chimney convection during alloy solidification

Abstract

Nonlinear natural convection in cylindrical chimneys within a mushy layer during solidification of a binary alloy is investigated under a high-gravity environment, where the rotation axis is inclined at an angle γ to the high-gravity vector. These chimneys produce freckles in the final form of the solidified materials. Freckles are imperfections that reduce the quality of the solidified materials. Asymptotic and scaling analyses are applied to weakly nonaxisymmetric convection in the chimneys. Three important nondimensional parameters are the solutal Rayleigh number R, the centrifugal acceleration parameter A and the Coriolis parameter T. It is found that, for some moderate values of the rotation rate and sinγ ≠ 0, axial convection in the chimneys decreases rapidly with increasing A above some azimuthally dependent axial level. This level can also depend on the radii of the chimneys and on γ and T. The axial convection also decreases with increasing T in certain range which depends on γ, T and R. The Coriolis effect is destabilizing for T outside this range of values, but it is less destabilizing for γ = γ0 > 180° as compared with those cases with inclined angle (γ0 − 180°).