Dendritic solidification under natural and forced convection in binary alloys: 2D versus 3D simulation

A model of both equiaxed and columnar dendritic growth was developed that incorporates thermal, solutal and fluid flow effects in either two or three dimensions. The model solves the momentum, mass and energy transport equations, including phase change. An imposed anisotropy algorithm, combined with a modified projection method solution of the Navier-Stokes equations, allows a relative coarse mesh and hence excellent computational efficiency. The model was used to study the effect of dimensionality (2D versus 3D) on dendritic growth with and without convection. The influence of forced convection on unconstrained equiaxed growth was studied first. In 3D, the upstream boundary layer is much thinner with a lower concentration than in 2D. This increases tip undercooling, accelerating upstream tip growth and promoting secondary branching. The influence of natural convection on constrained, columnar dendritic, growth was then studied. The 2D flow is blocked by the primary dendrite arms (which are effectively plates), while the 3D flow can wrap around the primaries. This change in flow strongly alters solute distribution and consequently the developing dendritic microstructure. 3D simulations are required to correctly predict unconstrained solidification microstructures.