Determination of Spearman's rank correlation for melt spreading-solidification dynamics through the combination of integrated experiments and Monte Carlo method

Abstract

Molten metal spreading and solidification behaviors are crucial phenomena in various fields. This study employs Spearman's rank correlation to identify the key parameters influencing spreading behaviors through a series of experiments and Monte Carlo simulations. The experiments utilized three different low melting point alloys, systematically varying parameters such as water level, subcooling, superheating, and jet velocity, among others. The results revealed that the spreading behaviors can be classified into three distinct modes: (1) clear spreading, (2) irregular spreading, and (3) clear sedimentation. These modes are determined by the energy balance between jet inertia and solidification.

Dimensionless analyses were conducted to investigate the spread areas and thicknesses. The findings demonstrated that thickness increases exponentially with decreasing the dimensionless volume while the spread area decreases due to enhanced cooling efficiency. Additionally, an empirical dimensionless correlations were developed to predict the spread area and thickness based on the interplay between jet-driven inertial forces and solidification. This correlation indicates that the transition between spreading and sedimentation occurs within a threshold range of 0.1 to 0.3. This threshold corresponds to the solid fraction at which the melt immobilizes as the dynamic viscosity sharply increases due to cooling.

Finally, Monte Carlo simulations, utilizing a combination of random sampling and Bayesian modeling, were employed to estimate Spearman's rank correlation. The analysis revealed that the critical parameters for spreading are the latent heat of fusion and the superheat of the melt, as these factors significantly impact the melt's ability to maintain fluidity. In contrast, the melting temperature and subcooling were found to predominantly influence sedimentation by accelerating solidification and enhancing cooling efficiency. These results underscore an empirical correlation that is broadly applicable to general melt spreading phenomena, providing a quantitative framework for identifying the key parameters that govern the process.