Phase field method study on the directional solidification microstructure of a Fe–C alloy under forced convection

A specific columnar crystal structure is obtained using the directional solidification technique, which has a substantial effect on the optimization of the axial mechanical properties of the alloy. Additionally, the convection phenomenon in the melt changes the temperature field and concentration field at the front of the solid–liquid interface, affecting the shape of this interface. Thus, the influence on alloy properties cannot be ignored. Although the phase field method has more research on the microdendrite growth morphology, the results of coupling the flow field into the phase field and exploring the microdendrite morphology of directional solidification are still scarce. In this paper, the phase field model of a coupled flow field is used to simulate dendritic growth during directional solidification. The effects of the anisotropy coefficient and interfacial energy on the growth of directionally solidified dendrites and the growth behavior of dendrites under forced convection were studied. For the numerical solution procedure, a uniform grid of the finite difference method was used to discretize the governing equations. A combined solution of the MAC algorithm and a phase field discrete calculation was realized. When addressing the coupling of the microvelocity and pressure fields, the MAC algorithm was used to solve the Navier–Stokes equation and pressure Poisson equation, and the interlocked grid method was applied to handle the complex free interface. The results show that the growth rate of the dendrite tip increases, and the radius of curvature and the solute concentration at the root of the dendrite decrease with an increasing anisotropy coefficient. When the anisotropy coefficient is a maximum of 0.065, the wall of the dendrite tends to develop toward a secondary dendrite because of the influence of the anisotropy coefficient; with increasing interfacial energy, the radius of curvature of the dendrite tip increases. When the interfacial energy is a maximum of 0.6 J·m⁻², the solidification shows a flat interface advancing mode; forced convection has a great influence on the growth direction of directional solidification dendrites. The directional solidification of dendrites in the upstream direction is coarse and grows faster with increasing flow rate. Additionally, the dendrite growth morphology observed using an optical microscope agrees well with the experimental results.