Solidification of a Liquid Column Between Two Rods of Unequal Sizes and Different Temperatures

Abstract

A liquid column hanging between two surfaces (e.g., rod ends) appears in many engineering applications. This study focuses on its solidification with volume expansion through the use of an axisymmetric front-tracking method. The phase boundaries are handled by connecting points while the momentum and energy equations are solved on a fixed, rectangular grid. The rods holding the column in the vertical direction have different radii and temperatures and initiate solidification from their ends due to their temperatures smaller than the liquid melting point. As the upper rod is hotter than the lower rod, the lower phase-change interface moves faster than the upper one, resulting in an increase in the difference between the lengths of the upper and lower solid phases. The liquid phase changing into the lighter solid phase results in a ring formed near the midplane of the column at the end of solidification. The ring is located above the midplane and shifts more away from it as the upper rod has a higher temperature and a smaller radius than the lower rod. Increasing the upper rod radius or the column length or decreasing the Stefan number causes the solidification of the column to progress longer.