Heat flow in atomized metal droplets

Abstract

The solidification of spherical droplets with a discrete melting temperature is analyzed using an enthalpy model. Equations describing the cooling of the initially superheated liquid droplet and a numerical heat flow model for its subsequent solidification are presented. Important parameters like times for initiation and completion of solidification, cooling rates and interface velocities in aluminum, iron, and nickel are related to the process variables governing the rate of heat extraction from the droplets. The analysis is performed for the range of Biot numbers of practical interest where Newtonian cooling models are not considered applicable, 0.01 ≤ Bi ≤ 1.o, and the results are presented in the form of normalized or dimensionless quantities. It is shown that the average cooling rate in the liquid prior to solidification can be computed with the Newtonian cooling expressions. However, significant temperature gradients are noted at the droplet surface even for Biot numbers as low as 0.01. Reducing the droplet diameter reduces the time necessary for the initiation and completion of solidification, increases the interface velocities at equivalent fractions solidified and decreases theG L /R ratio. Although smaller droplet diameters promote higher cooling rates in the liquid at the beginning and in the solid at the end of solidification, the effect at the intermediate stages is more complex and depends on the initial superheat, the Biot number and the thermophysical properties of the material.