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Streszczenie:
A numerical and experimental study of unsteady natural convection during freezing of water is presented. The mathematical model for the numerical simulations is based on the enthalpy-porosity method in vorticity-velocity formulation, equations are discretised on a fixed grid by means of a finite volume technique. A fully implicit method has been adopted for the mass and momentum equations. Experiments are performed for water in a differentially heated cube surrounded by air. The experimental data for natural convection with freezing in the cavity are collected to create a reference for comparison with numerical results. The method of simultaneous measurement of the flow and temperature fields using liquid crystal tracers is used. It allows us to collect transient data on the interface position, and the temperature and velocity fields. In order to improve the capability of the numerical method to predict experimental results, a conjugate heat transfer problem was solved, with finite thickness and internal heat conductivity of the non-isothermal walls. These results have been compared with the simulations obtained for the idealised case of perfectly adiabatic side walls, and with our experimental findings. Results obtained for the improved numerical model shown a very good agreement with the experimental data only for pure convection and initial time of freezing process. As time passes the discrepancies between numerical predictions and the experiment became more significant, suggesting a necessity for further improvements of the physical model used for freezing water.

Streszczenie:
The problem of transient natural convection in a cube-shaped cavity is investigated experimentally and numerically. The motion is driven by a sudden temperature difference applied to two opposite side walls of the vessel. The experiments are performed at a Rayleigh number of 1.66 × 105 and a Prandtl number of 1109, inside a 5 × 5 × 5 cm3 cavity made of Plexiglas, with two isothermal copper walls kept at a prescribed temperature. Numerical simulation has been performed using a finite difference vorticity-velocity model of the Navier-Stokes equation with the Boussinseq approximation. The theoretical predictions are found to be in good agreement with the experimental results.