Phase Field Simulation Of Dendritic Growth Of Alloy Under A Forced Flow

Phase field method is one of the most powerful methods in the modeling of solidification. Through phase-field, solute field, flow field and other fields coupling, the solute segregation in solid and liquid phases, the formation of dendritic branch, ripening and remelting and so on in the solidification can be directly simulated, also, the effects of solid/liquid interface curve effect, kinetics, noise intensity and anisotropy on the shape of the microstructure can be investigated quantificatively. Phase field simulation of dendritic growth under a forced flow is reviewed the present development condition in this area at home and abroad.This paper based on the binary phase-field model, the phase-field model coupling with solute field, temperature field and flow field was developed. The mass and momentum conservation equations are solved by using the Simple algorithm, the difficulty in calculation induced by the pressure avoided. The governing equations are discretized on uniform grids using the Finite Difference method, and a double grid method is used for the mesh slice to save the time. The thermal governing equation is numerically solved using an alternating direct implicit (ADI) method, which is unconditionally stable, irrespective of the time step employed. Base on the VC++ language, the phase-field simulation program of the dendrite growth into the supercooled melt under a forced flow are completed. The dendrite growth processes during isothermal and non-isothermal solidification of the Al-Cu binary alloy under convection was simulated. The dependence of simulation results upon the mesh size, the interface anisotropy and noise is investigated, and how to choose the values of these key parameters is determined. The effects of the forced convection velocity and undercooling on the distribution of the solute field, temperature field and the growth of the dendrite are investigated, The result of dendrite growth during isothermal and non-isothermal solidification were compared. The effect of latent heat on the dendrite growth under convection was analyzed.The results indicate that upstream and downstream dendritic crystal present asymmetric pattern under a forced flow, the growth velocity of the dendritic tip gets promoted and inhibited on the upstream and downstream side respectively, while the tip perpendicular to the flow are slightly influenced, but the vertical main become tilted towards the upstream direction. The dendrite morphologies and solute profiles under different supercooling and different convection velocity are consistent on the isothermal and non-isothermal condition. As the velocity of convection increase, the growth velocity of upstream dendritic crystal speeded up, the lateral branching is getting more and the second dendritic arm in upstream direction is getting stronger; and the radius of curvature is getting smaller. The growth velocity of downstream dendritic crystal is getting slow, while the radius of curvature is getting larger. The vertical main stem has become more tilted towards the upstream direction. The larger supercooling , the quicker of the dendrite tip velocity; the smaller of the curvature radius. The dendritic growth of alloy non-isothermal solidification become slower and the second dendritic are less developed than isothermal growth.