Fig. 1. Schematic of numerical domain and boundary conditions.

Fig. 2. Velocity field and velocity vectors during free dendritic growth under density change induced flow for shrinkage β = 0.2 (a) and expansion β = -0.2 (b) when ε4 = 0.05. The time interval is 40τ0.

Fig. 3. Predicted liquid velocity vector and dimensionless temperature field for various relative density β at t/τ0 = 180 when ε4 = 0.05. Top left quadrant is for β = 0.2, top right quadrant is for β = 0.1, bottom right quadrant is for β = -0.2 and bottom left quadrant is for β = -0.1.

Fig. 4. Predicted dendritic morphologies of free dendritic growth for various relative density β at t/τ0 = 180 when ε4 = 0.05.

Fig. 5. Predicted dimensionless temperature profile ahead of the dendritic tip along the crystal symmetry axis (the dashed line in the inert) for various relative density β at t/τ0 = 180.

Fig. 6. Variation of predicted steady-state dimensionless tip velocity of the dendritic growth with relative density change for ε4 = 0.05 and ε4 = 0.03.

Fig. 7. Comparison of predicted steady-state dendritic shape with relative density change for ε4 = 0.05 (a) and ε4 = 0.03 (b).

Fig. 8. Comparison between the dendritic tip growth Péclet number as a function of relative density change from analytical solution [20] and numerical simulations for ε4 = 0.05 and ε4 = 0.03.

Fig. 9. Comparison between selection parameter and modified selection parameter from numerical simulations with relative density change for ε4 = 0.05 and ε4 = 0.03.