Heat Flow during Rapid Solidification of Undercooled Metal Droplets

Abstract

The solidification of undercooled spherical droplets with a discrete melting temperature is analyzed using both a Newtonian and a non-Newtonian (Enthalpy) model. Relationships are established between atomization parameters, the growth kinetics, the interface velocity and undercooling, and other important solidification variables. A new mathematical formulation and solution methodology is developed for simulating the solidification process in an undercooled droplet from a single nucleation event occurring at its surface. The computational mesh used in the enthalpy model is defined on a superimposed bispherical coordinate system. Numerical solutions for the solidification of pure aluminum droplets based on the enthalpy model are developed, and their results are compared to the trends predicted from the Newtonian model. The implications of single vs multiple nucleation events are also discussed. In general, the results indicate that when substantial undercoolings are achieved in a droplet prior to nucleation, the thermal history consists of two distinct solidification regimes. In the first, the interface velocities are high, the droplet absorbs most of the latent heat released, and the external cooling usually plays a minor role. The second regime is one of slower growth, and strongly depends on the heat extraction at the droplet surface. The extent of “rapid solidification”, as determined from the fraction of material solidified at temperatures below a certain critical undercooling, is a function of the nucleation temperature, the particle size, a kinetic parameter, and the heat translow as 10~4.