Criteria for revealing the onset and severity of solute inhomogeneity during directional solidification

Understanding and predicting the interplay between non-equilibrium flow dynamics and solidification behavior is pivotal for enhancing solute homogeneity in alloy solidification. This study employs a multiphase solidification model to simulate directional solidification processes under varying forced convection intensities and cooling rates. The model demonstrated robust predictive capabilities for columnar growing direction, channel segregation, and macrosegregation distribution. Building upon the method of the Rayleigh number (Ra), two dimensionless parameters, Ch_Ra and Ch_g, were formulated to characterize the state of interdendritic phase forces at the solidification front, including gravitational, thermosolutal buoyancy, and drag forces. A third parameter, Ch_v, was defined as the ratio of liquid flow velocity to columnar tip growth velocity. Combined with the Womersley number (Wo), which quantifies vortex shedding frequency in cylindrical flows, the correlations between these four dimensionless criteria and solute segregation were analyzed. Results revealed that Ch_v and Wo exhibited strong correlations with segregation severity, while Ch_Ra and Ch_g showed limited predictive utility. All criteria followed a similar evolutionary trajectory, aligning temporally with the formation of segregated channels in the ingot. Channel segregation ceased entirely when the maximum Wo value decreased to the critical range of 0.03–0.13 in this paper. These findings demonstrated that dimensionless criteria quantifying perturbations in interfacial flow and dendritic growth kinetics not only predicted the onset of segregated channels but also assessed the severity of solute inhomogeneity. This work establishes a novel dimensionless framework for predicting solute inhomogeneity, offering insights for optimizing solidification processes in casting applications.