Numerical simulation of dendritic solidification with convection: Two-dimensional geometry

A front tracking method is presented for simulations of dendritic growth of pure substances in the presence of flow. The liquid-solid interface is explicitly tracked and the latent heat released during solidification is calculated using the normal temperature gradient near the interface. A projection method is used to solve the Navier-Stokes equations. The no-slip condition on the interface is enforced by setting the velocities in the solid phase to zero. The method is validated through a comparison with an exact solution for a Stefan problem, a grid refinement test, and a comparison with a solution obtained by a boundary integral method. Three sets of two-dimensional simulations are presented: a comparison with the simulations of Beckermann et al. (J. Comput. Phys. 154, 468, 1999); a study of the effect of different flow velocities; and a study of the effect of the Prandtl number on the growth of a group of dendrites growing together. The simulations show that on the upstream side the dendrite tip velocity is increased due to the increase in the temperature gradient and the formation of side branches is promoted. The flow has the opposite effect on the downstream side. The results are in good qualitative agreement with published experimental results, even though only the two-dimensional aspects are examined here.