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Fluid Dynamics Seminar

Monday, Oct. 31, 2011, 4:00 PM
Cullimore, Room 611
New Jersey Institute of Technology

Optimal potential energy fluxes: casting new light on convection and alloy solidification

Andrew Wells

Yale University Applied Mathematics Program

Abstract

Fluid convection during the solidification of binary alloys is significant in diverse settings, ranging from the growth of sea ice in the polar oceans, to the casting of metal turbine blades. The rapid solidification of a binary alloy leads to the formation of a chemically reactive porous medium, or mushy layer, within which convection and dissolution can generate chimneys: drainage channels devoid of solid. We consider a theoretical model of the dynamics and stability of convective flow states that control the evolution of chimneys. Applying a variational principle of optimal potential energy transport predicts scalings of solute fluxes and chimney spacing consistent with previous simulations and laboratory experiments. The theoretical framework is then combined with an experimental study of solidification in a Hele-shaw cell to investigate the influence of a finite sample width on chimney formation, and provide insight into controlling defect formation in industrial casting processes.