Numerical Study of Freezing of Water Using Taylor-Galerkin based Non-Linear Temperature Recovery Method

Abstract

*† Several numerical algorithms can be found in the literature for analyzing solidification phenomena. However, it is still an active area of research, due to the presence inherent complexities, such as phase change and natural convection. In order to attack this phase change problem, two important methods, namely fixed and deforming mesh methods, have been proposed. The fixed grid method is mostly widely used because of the simplicity in its numerical implementation. However, most of the available fixed grid methods have difficulties in achieving convergence, when the phase change occurs isothermally. Temperature recovery, which is found to easily overcome this problem, can be successfully employed for solving both isothermal and alloy solidification. The major goal of this paper is to extend the temperature recovery method for solving solidification in the presence of natural convection. This paper first validates our FEM code using standard benchmark problems. Then, testing of our implementation based on temperature recovery method for freezing of water is carried out by comparing the numerical results with recent experimental PIV results. Numerical predictions of our FEM code show good agreement with the experimental data, even for a coarse grid. Further, the effect of the complex flow field on the solid/liquid interface created by anomalous expansion of water near its freezing range is discussed in this paper.