Axisymmetric forced convection solidification of a liquid drop on a cold plate

Abstract

In this paper, we present a fully resolved numerical simulation of the solidification process of a liquid drop on a cold plate under axisymmetric forced convection. The numerical method used is an axisymmetric front-tracking method to represent the interface separating two phases. An interpolation technique is also used to impose the non-slip velocity boundary condition at the solid surface. Because of the forcing flow introduced from the top, the solidifying drop initially experiences an oscillation in the vertical direction, then the oscillation is suppressed as time progresses. In addition, the forcing flow slows down the solidification process. To investigate more in detail this solidification problem, we vary many dimensionless parameters including the Reynolds number (in the range of 25–800), Prandtl number Pr (in the range of 0.01–1.0), Stefan number St (in the range of 0.01–1.0), and Capillary number Ca (in the range of 3.16 × 10−5–0.316) to show their effects on the process. The results show that an increase in Re or Pr, or a decrease in St slows down the solidification process. However, the variation of Re or Pr has a minor effect on the solidified drop height and the conical angle at the solidified drop top. The most affecting parameter is Ca whose variation results in two modes: on-axis and off-axis solidification because of the forcing flow. We also investigate the effects of the growth angle at the triple point and the contact angle at the plate on the solidification process under axisymmetric forced convection.