Interaction of Interdendritic Convection and Dendritic Primary Spacing: Phase-field Simulation and Analytical Modeling

摘要

Experimental work on directional solidification has shown, that the dendrite primary spacing λ depends on the gravity level. Despite the major theoretical and practial interests present models fail to predict the interdependence between interdendritic flow and spacing selection. We derive a) a scaling relation describing this dependence as λ/(λ_0) ～ Ra_0~(-1/8), where λ_0 is the spacing without flow and the Rayleigh number Ra_0 bases on λ_0. This relation fits in experimental data. We study this interdependence in more detail by b) phase-field modeling of the dendrite evolution coupled to fluid flow. Our model matches the relevant free boundary conditions for flow and microstructure formation. Preliminary numerical results in AlCu4 show, that flow pattern and microstructure crucially depend on the direction of g: buoyancy opposed to growth direction keeps the flow pattern almost interdendritic and λ increases. Buoyancy in growth direction forms plumes instably interacting with solid evolution and λ decreases.