Institute of Fundamental Technological Research

A semi-implicit finite element method (FEM) is presented for the two-dimensional computer simulation of solid-liquid phase change controlled by natural convection and conduction. The algorithm is based on a combination of (1) a projection method to uncouple velocity calculations from pressure calculations for incompressible fluid flow, (2) the backward Euler and explicit Adams-Bashforth schemes to effectively integrate diffusion and advection in time, and (3) an enthalpy-porosity approach to account for the latent heat effect on a fixed finite element grid. Credibility of the obtained numerical predictions is investigated through computational model verification and validation procedures. Commonly used benchmark problems are employed to verify the algorithm accuracy and performance. The natural convection of freezing pure water is studied experimentally through the use of sophisticated full-field acquisition experimental techniques. The measured velocity and temperature fields are compared with the pertinent calculations. The range of congruity of the experimental and numerical results is thoroughly studied, and potential reasons of some disparity in a local structure of the natural convection flow and in the interface shape are discussed.

An experimental and numerical study has been made of transient natural convection of water freezing in a cube-shaped cavity. The effect of the heat transfer through the side walls is studied in two configurations: with the cavity surrounded by air and with the cavity immersed in an external water bath of constant temperature. The experimental data for the velocity and temperature fields are obtained using liquid crystal tracers. The transient development of the ice/water interface is measured. The collected data are used as an experimental benchmark and compared with numerical results obtained from a Finite-difference code with boundary fitted grid generation. The computational model has been adopted to simulate as closely as possible the physical experiment. Hence, fully variable fluid properties are implemented in the code, and, to improve modelling of the thermal boundary conditions, the energy equation is also solved inside the bounding walls. Although the general behaviour of the calculated ice front and its volume matches observations, several details of the flow structure do not. Observed discrepancies between experimental and numerical results indicate the necessity of verifying and improving the usual assumptions for modelling ice formation.

Natural convection, freezing, phase change, experimental benchmark, water density anomaly, liquid crystals, particle image velocimetry and thermometry, boundary fitted grid, finite differences vorticity-vector potential method