Non-Axisymmetric Chimney Convection in a Mushy Layer Under a High Gravity Environment

Abstract

Nonlinear buoyancy-driven chimney convection in arbitrary Prandtl number melts within mushy layers during alloy solidification is considered under a high-gravity environment, where the rotation axis is inclined at an angle γ to the high-gravity vector. The chimneys within the mushy layer produce undesirable freckles in the final form of the solidified material. These are imperfections that reduce the quality of the material. Methods of control aiming at eliminating or reducing significantly the convective flows in the chimneys also serve to eliminate or reduce significantly the existence and presence of the chimneys in the mushy layer, resulting in higher quality castings. Asymptotic and scaling examinations of the governing system for a non-axisymmetric and weakly unsteady mode of chimney convection resulted in new analytical expressions for the leading order magnitudes of the basic flow quantities as functions of the basic flow parameters. These results indicate that chimney convection can be reduced significantly in certain ranges of the parameter values under certain high gravity conditions and for prescribed and independent values of the radius of the chimneys.