High gravity convection in mushy layer during alloy solidification

Nonlinear natural convection, driven by compositional buoyancy, in the melt and in cylindrical chimneys within a mushy layer during solidification of binary alloys is investigated under a high gravity environment. In the final form of the solidified material. the chimneys produce freckles, which are imperfections that reduce the quality of the solidified material. Asymptotic and scaling analyses are applied to a non-axisymmetric convection in the melt and in the chimneys. Important parameters in this study are the solutal Rayleigh number R, the centrifugal accelerntion parameter A, the Coriolis parameter T, the Prandtl number Pr, angle ϒ between the rotation axis and the high gravity vector, and ratio H of R in the chimney's liquid zone to that outside in the mushy zone. It is found that there exist Pr, A and T dependent ranges for the radius of the chimney where the wall of chimney may or may not be vertical. For some particular ranges of the rotation rate and sin ≠ 0, convection in the chimneys can increase or decrease with increasing about or below some azimuthally dependent axial level. This level can also depend on Pr, ϒ and T. and on the radii of the chimneys. The chimney convection can also increase or decrease with increasing T in certain P,. y. T and R dependent ranges. Some particular moderate rates of inclined rotation can become so effective. by either centrifugal or Coriolis force. that they lead to vanishingly small radii of the chimneys and suppression of the chimneys' convection. A bound on number density of chimneys is also determined