Numerical simulation of natural convection and phase‐change in a horizontal Bridgman apparatus

The purpose of this paper is to present a 2D numerical simulation of natural convection and phase‐change of succinonitrile in a horizontal Bridgman apparatus. Three different heat transfer mechanisms are specifically studied: no growth, solidification and melting.

The analysis is carried out with a preexisting thermally coupled fixed‐mesh finite element formulation for generalized phase‐change problems.

In the three cases analyzed, the predicted steady‐state liquid‐solid interfaces are found to be highly curved due to the development of a primary shallow cell driven by the imposed furnace temperature gradient. In the no growth case, the heating and cooling jackets remain fixed and, therefore, a stagnant liquid‐solid interface is obtained. On the other hand, the phase transformation in the solidification and melting cases is, respectively, controlled by the forward and backward movement of the jackets. In these last two growth conditions, the permanent regime is characterized by a moving liquid‐solid interface that continuously shifts with the same velocity of the jackets. The numerical results satisfactorily approach the experimental measurements available in the literature.

The numerical simulation of the no growth, solidification and melting cases in a horizontal Bridgman apparatus using a finite element based formulation is the main contribution of this work. This investigation does not only provide consistent results with those previously computed via different numerical techniques for the no growth and solidification conditions but also reports on original numerical predictions for the melting problem. Moreover, all the obtained solid‐liquid interfaces are validated with experimental measurements existing in the literature.